Understanding the E ect of Surface Topography on Stiction and Friction
in MEMS
by
Naveed Mohammed Asgar Ansari
A dissertation submitted to the Graduate Faculty of
Auburn University
in partial ful llment of the
requirements for the Degree of
Doctor of Philosophy
Auburn, Alabama
December 12, 2011
Keywords: MEMS, Tribology, Topography, Stiction, Friction, Roughness, Thin  lms
Copyright 2011 by Naveed Mohammed Asgar Ansari
Approved by
William R. Ashurst, Chair, Associate Professor of Chemical Engineering
Christopher B. Roberts, Uthlaut Professor of Chemical Engineering
Steve R. Duke, Alumni Associate Professor of Chemical Engineering
Robert Dean, Associate Professor of Electrical and Computer Engineering
Abstract
The  eld of micro-electromechanical systems (MEMS) undoubtedly has the po-
tential of producing great technological innovations. However, a precise understand-
ing of the tribological behaviour of MEMS surfaces is needed for the realization of
the full potential of a variety of complex, sophisticated and extremely useful MEMS.
While on one hand, the number of smaller, more complex and more useful new MEMS
prototypes, which are commercially extremely attractive, is continuously increasing,
on the other hand, despite years of research, the Micro-electromechanical Systems
(MEMS) community is yet to  nd a solution that su ciently addresses the reliability
issues (stiction, friction and wear) that limit the commercial success of most MEMS
prototypes. The main bottleneck, which limits the ability of MEMS community
to devise an appropriate solution, is their poor understanding of the factors, espe-
cially surface topography, that govern the tribological behaviour of MEMS surfaces.
Therefore, there is a serious and urgent need to conduct a systematic investigation
for understanding the e ects that the surface topography of a MEMS surface has on
the stiction and friction experienced by it. Accordingly, the main objective of this
study is to understand the e ects that the surface topography of a MEMS surface
has on the stiction and friction experienced by it.
This study reports on the development of a test platform (TP), which not only
overcomes the limitations of the previously reported test platforms but is also a ver-
satile tool that can be used to systematically study the tribology of MEMS surfaces.
The details of the design and fabrication of the Test Platform are discussed in the
study. Further, in order to be able to fabricate the TP using a facile, inexpensive
and less time consuming fabrication process, a single mask scheme is devised in this
ii
study for fabricating the Test Platform. Additionally, in order to ensure that the
sidewall surfaces of the microinstruments included in the Test Platform are relatively
smooth so that a systematic investigation of the e ects that the surface topographies
of MEMS surfaces have on their stiction and friction characteristics can be conducted,
a polishing technique to smoothen the scalloped as-fabricated sidewalls of the Test
Platform is developed in this study.
The designs, actuation procedures and modeling of the various (i.e., seven types
of) microinstruments included in the Test Platform are explained in detail in this
study. The details of the key features of all the (seven types of) microinstruments
are successfully highlighted in this study. Additionally, some of the microinstruments
developed in this study are convincingly shown to overcome some of the limitations
of the previously reported corresponding microinstruments. Further, all the (seven
types of) microinstruments developed in this study are successfully used to investigate
two standard test surfaces, namely, surfaces coated with n-OTS (C18H37SiCl3) SAM
coating (i.e., hydrophobic surfaces) and surfaces having only a layer of native oxide
on them (i.e., hydrophilic surfaces). Additionally, the apparent work of adhesion of
the OTS SAM coated sidewalls, which has never been reported to-date, is obtained
in this study using the Sidewall Beam Array. The apparent work of adhesion of the
OTS SAM coated sidewalls is 37.65  J/m2. Also, the engineering coe cients of static
and kinetic friction of the OTS SAM coated sidewalls, which have also never been
reported to-date, are obtained in this study using both the Sidewall Friction Tester as
well as the Sidewall Friction and Adhesion Tester. The mean engineering coe cients
of static and kinetic friction of the OTS SAM coated sidewalls are 0.15 and 0.11,
respectively.
Further, the investigation conducted to study the e ect of surface topography
reports the successful use of a dodecanethiol-capped gold nanoparticle-based surface
texturing technique for tailoring the topographies of the surfaces (in-plane as well
iii
as sidewall) of  ve Test Platform chips. Additionally, it reports the successful in-
vestigation of six Test Platform chips ( ve textured using the dodecanethiol-capped
gold nanoparticle-based surface texturing technique and one untextured (control))
conducted to understand the e ect that the surface topography of a surface has on
its tribological (i.e., stiction and friction) characteristics. The surface topographies of
the surfaces of each of the six Test Platform chips investigated in this study are char-
acterized qualitatively using SEM and quantitatively using AFM. The quantitative
characterization of the surface topographies of the surfaces of the six Test Platform
chips investigated in this study is used to quantify them in terms of two measurable
parameters, namely, the rms roughness and the surface coverage of the interacting
asperities present on the surface. Further, in order to understand the e ects that
the surface topography of a MEMS surface has on its stiction and friction character-
istics, three important tribological properties of the surfaces of each of the six Test
Platform chips investigated in this study, which are the apparent work of adhesion of
the in-plane surfaces, the apparent work of adhesion of the sidewall surfaces and the
engineering coe cient of static friction of the sidewall surfaces, are determined. The
tribological characterization of the surfaces of the six Test Platform chips investigated
in this study provided an experimental con rmation of the already believed theory
that the friction experienced by contacting MEMS surfaces shows a strong depen-
dence on the stiction experienced by them. Additionally, it indicated that both the
micro-scale as well as the nano-scale topographies of a surface have a strong in uence
on its stiction and friction characteristics.
In order to mathematically correlate the surface topography of a surface with
its stiction and friction characteristics, a dimensionless parameter called Tribotopog-
raphy number (i.e.,  topo) is formulated in this study. Further, the Tribotopography
number is successfully used to develop two mathematical correlations, one between
the surface topography of a surface and its apparent work of adhesion, and the other
iv
between the surface topography of a surface and the friction experienced by it. In
order to use the two mathematical correlations developed in this study for a partic-
ular type of surface, the value of index  , which is the index of the denominator of
the fraction that represents the Tribotopography number, for that type of surface
must be determined  rst. The value of index  for silicon-type surfaces (i.e., surfaces,
whose tribological behaviours are governed by the same type of interfacial forces that
govern the tribological behaviour of silicon surfaces) is determined in this study. This
study also reports an analysis (i.e., experimental validation), which substantiates
the validities of the two mathematical correlations developed to correlate the sur-
face topography of a surface with its stiction and friction characteristics, respectively.
Additionally, it also discusses the constraints, under which, the two mathematical
correlations are valid. Lastly, the study reports the results of the investigation con-
ducted to determine the in uence of the geometry of the contact interface on the
e ect that the surface topographies of the surfaces forming the interface have on its
tribological characteristics.
Owing to the fact that the surface coverage of the coating can serve as an e ective
parameter in the comparison between the e ectivenesses of various nanoparticle-based
(sub-)monolayer coatings, a chapter in this study (i.e., chapter 10) reports a simple
experimental technique based on optically determined resonance that can be used for
determining the surface coverage of the nanoparticle-based monolayer coatings used
to texture MEMS surfaces. The modeling as well as the experimental validation of
the technique are presented in that chapter. The factor that de nes the resolution of
the technique is also discussed in that chapter.
The results obtained during the investigation of the e ect of surface topography
on the stiction and friction characteristics of a surface revealed that the e ectiveness
of AuNP-based surface texturing not only depends on the roughness of the uncoated
test surfaces but also depends strongly on the surface coverage of the coating (refer to
v
results reported in Chapter 9). Accordingly, a chapter in this study (i.e., chapter 11)
reports on a novel gold nanoparticle (AuNP) coating, which is deposited on micro-
electromechanical systems (MEMS) surfaces using the gas-expanded liquid technique,
and has the potential to be used as an alternative of OTS SAM for reducing the
stiction and friction experienced by them. A complete characterization of the AuNP
coating is presented in that chapter.
Lastly, one of chapters of this study (i.e. chapter 7) reports on an experimental
requirement of the phase shifting interferometry, which is a technique widely used in
optical testing, and used in this study for determining the height pro les of actuated
cantilever beams. The chapter reports on a class of  ve frame interferogram-collecting
sequence, which, due to its mathematical equivalence with the one suggested by
Hariharan et al. and ease of execution, is more commonly used, but is much less
e ective in reducing the height pro le errors caused by phase step errors. It presents
a mathematical as well as experimental analysis of two distinct classes of the  ve
frame interferogram-collecting sequence used in PSI.
vi
Acknowledgments
Throughout the entire course of my doctoral studies, I have received support,
advice and help from numerous people, and they deserve my sincere thanks. First and
foremost, I would like to thank my parents and my brother for being patient with,
and extending unconditional support to me, during my years as a graduate student.
Without them, I would not have sailed through the turbulent phases of my doctoral
studies. Next, I would like to extend my sincere thanks to my research advisor Dr.
W. R. (Bob) Ashurst (Associate Professor, Department of Chemical Engineering,
Auburn University). He has been a true mentor in every sense of the word. Not only
was he a constant source of technical and administrative guidance but was also an
honest critic and guide for issues related to my personal life. He has become a friend
for life. The long conversations that I had with him about issues outside the realm of
my doctoral studies as well as life in general are some of the fondest memories I have
collected at Auburn.
I would also like to thank the other members of my doctoral research advisory
committee, especially Dr. C. B. Roberts (Department Chair and Uthlaut Professor,
Department of Chemical Engineering, Auburn University), for their encouragement
as well as their inciteful suggestions and advices. Additionally, special thanks are
due to three more individuals Mr. B. A. Schwieker (Machinist, Department of Chem-
ical Engineering, Auburn University), who expertly built all the custom designed
hardwares that I needed for my experiments, Mr. C. Ellis (Manager, AMSTC?s mi-
crofabrication lab at Auburn University), who not only allowed me to use the tools
of the microfabrication facility but also unconditionally o ered his expertise when I
needed it, and Karen Cochran (Administrative Assistant II - Academic, Department
vii
of Chemical Engineering, Auburn University), whose expert help in administrative
matters saved a lot of my time, and jovial nature made me feel that I belonged to
the Chemical Engineering Department.
In addition to thanking the former members of the Ashurst research group, Dr.
Adam Anderson (graduated with a Ph. D. in 2009) and Dr. Aimee Poda (graduated
with a Ph. D. in 2010), for making my transition into the group smooth and easy,
and the special bond they shared with me, I would like to o er special thanks to Dr.
Kendall Hurst (graduated with a Ph. D. in 2010) of the Roberts research group for
collaborating with me on a research project. Our project was very fruitful and it
yielded some very exciting results. Additionally, working on that project helped me
to signi cantly expand my knowledge base.
Lastly, I would like to thank all the friends in Auburn for making my stay here
very pleasant and enjoyable. A special person, who deserves a mention here is Payal
Agarwal. I am really grateful to her for being there for me like a sister at all times
throughout my doctoral studies. I would also like to acknowledge Nidhi Sehgal, who
was the  rst friend I made in Auburn, and has been my closest friend in Auburn since
then.
viii
Table of Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii
1 MEMS Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Miniaturization: Exploring the Room at the Bottom . . . . . . . . . 1
1.2 MEMS: A Technological Evolution . . . . . . . . . . . . . . . . . . . 2
1.3 Tribology: Role in Hindering the Commercialization of MEMS . . . . 6
1.4 Micromachining: Description and In uences on MEMS Surface Char-
acteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.1 Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.2 Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.3 Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.4 Wafer Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.5 Chemical Mechanical Planarization (CMP) . . . . . . . . . . . 12
1.4.6 The LIGA Process . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.7 Bulk Micromachining . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.8 Surface Micromachining . . . . . . . . . . . . . . . . . . . . . 15
1.5 Reliability of MEMS: A Challenge for the MEMS Community . . . . 18
1.5.1 Interfacial Forces . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5.2 Stiction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.5.3 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.5.4 Wear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
ix
1.5.5 Fracture and Fatigue . . . . . . . . . . . . . . . . . . . . . . . 36
2 Previous Studies: A Review . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1 Stiction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.1 Release Stiction . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.2 In-Use Stiction . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.2 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3 Self Assembled Monolayers . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.1 Chlorosilane Based Self-Assembled Monolayers . . . . . . . . . 51
2.3.2 Limitations Imposed by the Chlorosilane Chemistry . . . . . . 56
2.3.3 Non-Chlorosilane Based Organic Coatings . . . . . . . . . . . 61
2.3.4 Issues Challenging the Viability of Self-assembled Monolayers 64
2.4 Surface Texturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.5 Wear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.6 Fracture and Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3 Motivations and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.1 The Need of an Easy-to-fabricate, Versatile Test Platform . . . . . . 74
3.2 The Variation in the Material Properties of the Structural Film . . . 76
3.3 The In uence of the Multi-grain Nature of the Polysilicon Structural
Films on the Topography of Polysilicon MEMS Surfaces . . . . . . . 77
3.4 Objectives of this Study . . . . . . . . . . . . . . . . . . . . . . . . . 81
4 The Test Platform: Design, Fabrication and Actuation . . . . . . . . . . 83
4.1 Design of the Test Platform . . . . . . . . . . . . . . . . . . . . . . . 83
4.1.1 Structural Film . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.1.2 The Layout of the Test Platform . . . . . . . . . . . . . . . . 84
4.2 Fabrication of the Test Platform . . . . . . . . . . . . . . . . . . . . . 90
4.2.1 Single Mask Scheme . . . . . . . . . . . . . . . . . . . . . . . 90
4.2.2 Polishing of the Test Surfaces . . . . . . . . . . . . . . . . . . 91
x
4.3 Actuation of the Test Platform . . . . . . . . . . . . . . . . . . . . . 95
5 Microinstruments: Design, Testing Procedure and Modeling . . . . . . . 97
5.1 Residual Stress Tester (RST) . . . . . . . . . . . . . . . . . . . . . . 97
5.1.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.1.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.1.3 Testing Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2 Mechanical Strength Tester (MST) . . . . . . . . . . . . . . . . . . . 101
5.2.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2.2 Testing Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.3 Resonator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.3.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.3.2 Testing Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.3.3 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.4 Cantilever Beam Array (CBA) . . . . . . . . . . . . . . . . . . . . . . 115
5.4.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.4.2 Testing Procedure and Analysis . . . . . . . . . . . . . . . . . 117
5.5 Sidewall Beam Array (SBA) . . . . . . . . . . . . . . . . . . . . . . . 119
5.5.1 Previously Reported Devices: A Review . . . . . . . . . . . . 120
5.5.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.5.3 Testing Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.5.4 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.6 Sidewall Friction Tester (SFT) . . . . . . . . . . . . . . . . . . . . . . 129
5.6.1 Previously Reported Devices: A Review . . . . . . . . . . . . 129
5.6.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.6.3 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.6.4 Testing Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.7 Sidewall Friction and Adhesion Tester (SFAT) . . . . . . . . . . . . . 148
xi
5.7.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.7.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
5.7.3 Testing Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 161
6 Processes and Techniques Used: Experimental, Analytical, Surface Char-
acterization & Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.1 Process Used to Release the Microinstruments of the Test Platform . 165
6.2 Process Used to Obtain Oxide-covered Test Surfaces . . . . . . . . . . 166
6.3 Preparation of the OTS SAM Coating Solution . . . . . . . . . . . . 166
6.4 Process Used to Obtain OTS SAM Coated Test Surfaces . . . . . . . 167
6.5 Gold Nanoparticle (AuNP) Synthesis . . . . . . . . . . . . . . . . . . 168
6.6 Process Used to Deposit the Dodecanethiol-capped Gold Nanoparticles
on the Test Surfaces of the Test Platform . . . . . . . . . . . . . . . . 170
6.7 Contact Angle Goniometry . . . . . . . . . . . . . . . . . . . . . . . . 173
6.8 Ellipsometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.9 Fourier Transform - Infrared Spectroscopy . . . . . . . . . . . . . . . 174
6.10 Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
6.10.1 Optical Microscopy . . . . . . . . . . . . . . . . . . . . . . . . 175
6.10.2 Atomic Force Microscopy . . . . . . . . . . . . . . . . . . . . . 175
6.10.3 Scanning Electron Microscopy . . . . . . . . . . . . . . . . . . 176
6.10.4 Transmission Electron Microscopy . . . . . . . . . . . . . . . . 176
6.11 Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
6.12 Image Analysis Technique Used for Determining the Surface Coverage
of the Interacting Asperities . . . . . . . . . . . . . . . . . . . . . . . 178
7 Experimental Requirement of the Phase Shifting Interferometry . . . . . 179
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
7.2 Five Frame Interferogram Collecting Sequence for PSI . . . . . . . . . 181
7.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 185
xii
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
8 Benchmarking the Microinstruments: Highlighting Key Features & Test-
ing Standard Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
8.1 The Pattern Matching Technique . . . . . . . . . . . . . . . . . . . . 188
8.2 Residual Stress Tester . . . . . . . . . . . . . . . . . . . . . . . . . . 189
8.3 Mechanical Strength Tester . . . . . . . . . . . . . . . . . . . . . . . 191
8.4 Resonator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
8.5 Cantilever Beam Array . . . . . . . . . . . . . . . . . . . . . . . . . . 196
8.5.1 Validating the Authenticity of the Actuation Method Used to
Actuate the Cantilever Beams . . . . . . . . . . . . . . . . . . 196
8.5.2 Stress Gradient at the Sacri cial Oxide-Device Layer Interface 201
8.5.3 Determining the Apparent Work of Adhesion of In-plane Sur-
faces Coated with Standard Coatings . . . . . . . . . . . . . . 206
8.6 Sidewall Beam Array . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
8.7 Sidewall Friction Tester . . . . . . . . . . . . . . . . . . . . . . . . . . 217
8.8 Sidewall Friction and Adhesion Tester . . . . . . . . . . . . . . . . . . 228
8.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
9 The E ect of Surface Topography . . . . . . . . . . . . . . . . . . . . . . 240
9.1 Obtaining Test Surfaces with Distinct Topographies . . . . . . . . . . 240
9.2 Characterization of the Tailored Test Surfaces . . . . . . . . . . . . . 244
9.2.1 Topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
9.2.2 Stiction and Friction . . . . . . . . . . . . . . . . . . . . . . . 252
9.3 Tribotopography Number ( topo) . . . . . . . . . . . . . . . . . . . . . 262
9.3.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
9.3.2 Determination of  for Silicon-type Surfaces . . . . . . . . . . 272
9.3.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
9.3.4 Signi cance of the Tribotopography Number ( topo) . . . . . . 282
9.4 In uence of the Geometry of the Contact Interface on the E ect of
Surface Topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
xiii
9.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
10 A Simple Experimental Technique to Estimate the Surface Coverage of the
Nanoparticle-based Monolayer Coatings Used to Texture MEMS Surfaces 289
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
10.2 Estimation of Surface Coverage . . . . . . . . . . . . . . . . . . . . . 290
10.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
10.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
11 Surface Texturing: A Potent Alternative to Reduce Stiction and Friction
Experienced by MEMS Surfaces . . . . . . . . . . . . . . . . . . . . . . . 297
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
11.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
11.2.1 Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
11.2.2 Microinstruments Used . . . . . . . . . . . . . . . . . . . . . . 300
11.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 302
11.3.1 Topographical Properties of the AuNP Coating . . . . . . . . 302
11.3.2 Tribological Properties of the AuNP Coating . . . . . . . . . . 305
11.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
12.1 The Test Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
12.2 Microinstruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
12.3 E ect of Surface Topography . . . . . . . . . . . . . . . . . . . . . . 316
12.4 Other Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
A Scripts Used for Actuating the Microinstruments . . . . . . . . . . . . . 338
A.1 Script Name: RST Analysis.stp . . . . . . . . . . . . . . . . . . . . . 338
A.2 Script Name: MST Actuation.stp . . . . . . . . . . . . . . . . . . . . 343
A.3 Script Name: CBA Actuation Method Validity Test.stp . . . . . . . . 345
xiv
A.4 Script Name: CBA Analysis.stp . . . . . . . . . . . . . . . . . . . . . 353
A.5 Script Name: SB Actuation and Analysis.stp . . . . . . . . . . . . . . 359
A.6 Script Name: Comb - drive Actuator Calibration.stp . . . . . . . . . 362
A.7 Script Name: SFT Normal Arm Comb - drive Actuator Calibration.stp 368
A.8 Script Name: SFT Friction Test.stp . . . . . . . . . . . . . . . . . . . 375
A.9 Script Name: SFAT Friction Test.stp . . . . . . . . . . . . . . . . . . 379
A.10 Script Name: SFAT Adhesion Test.stp . . . . . . . . . . . . . . . . . 382
A.11 Script Name: Pattern Matching Technique Uncertainty.stp . . . . . . 388
A.12 Macro Name: init.mac . . . . . . . . . . . . . . . . . . . . . . . . . . 390
B Derivations of the Equations Used to Determine  and   . . . . . . . . 393
B.1 Derivation of the Equation Used to Determine  : Sequence H . . . . 393
B.2 Derivation of the Equation Used to Determine  : Sequence NH . . . 393
B.3 Error Analysis of Sequence H . . . . . . . . . . . . . . . . . . . . . . 394
B.4 Error Analysis of Sequence NH . . . . . . . . . . . . . . . . . . . . . 396
C List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
xv
List of Figures
1.1 (a) A DMDTM commercially manufactured by Texas Instruments. (b) A
micro-accelerometer (model: ADXL193) commercially manufactured by
Analog Devices using the silicon based iMEMS surface micromachining
technology. This device senses acceleration up to 250g and costs about
$7 in 2011. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 (a) SEM image of a micro steam engine developed by Sandia National
Laboratories [14]. (b) SEM image of an electromechanical locking device
developed by Sandia National Laboratories [14]. . . . . . . . . . . . . . . 5
1.3 A simpli ed schematic illustrating the basic steps involved in surface mi-
cromachining. Notice that the \released" microstructure is a cantilever
beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4 A schematic diagram exhibiting the shape of the meniscus of a liquid
layer trapped between two (a) hydrophilic surfaces and (b) hydrophobic
surfaces. The arrows shown in the diagram indicate the direction of the
Laplace force acting on the upper (movable) plate with respect to the
lower ( xed) plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.5 A schematic diagram of (a) a hydrophilic surface and (b) a hydrophobic
surface. Also illustrated in both the diagrams, is the de nition of contact
angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.6 A plot illustrating how the Capillary, Van der Waals and Electrostatic
forces experienced by a pair of proximate atomically smooth silicon sur-
faces vary with the distance of separation between them. For reference,
the variation in the Casimir forces (i.e., vacuum energy level) experienced
by a pair of atomically smooth, perfectly conducting plates with the dis-
tance of separation between them is also shown in the plot. Additionally,
the range of magnitudes of the restoring forces that are typically generated
in most MEMS devices is also indicated on the plot [66]. . . . . . . . . . 32
2.1 A P-T diagram depicting the phase paths followed during the critical
point drying and the freeze sublimation drying processes. Notice that in
both the processes, a longer phase path is intentionally followed to avoid
crossing the liquid-vapor line. . . . . . . . . . . . . . . . . . . . . . . . . 42
xvi
2.2 A schematic diagram of a typical precursor molecule. The non-polar tail
shown in the diagram is a C18 hydrocarbon chain and the polar head group
is a trichlorosilane molecule. . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.3 A simpli ed, conceptual model illustrating the second step of the chlorosil-
ane-based SAM formation process. The  rst step (not shown) is the com-
plete hydrolysis of the precursor molecules, which results in the forma-
tion of 3 HCl molecules per precursor molecule as well as the trisilanol
forms (shown in this  gure) of the precursor molecules. In the second
step, which is shown in this  gure, water elimination (condensation) re-
actions result in Si-O-Si linkages between the adjacent hydrolyzed pre-
cursor molecules and/or the native oxide layer present on the substrate.
The precursor molecules shown in the  gure are octadecyltrichlorosilane
(CH3(CH2)17SiCl3) molecules. . . . . . . . . . . . . . . . . . . . . . . . . 53
2.4 (a) AFM image of an OTS coated Si(100) surface. The RMS roughness
of the surface based on image statistics is 25 nm. (b) Linescan along the
white line drawn across image a. Notice that some of the particulates
visible in image a are as wide as 2 micron and as high as 490 nm. . . . 60
3.1 (a) An AFM image of a typical in-plane polysilicon surface. The rms
roughness of the surface shown in image a is 3.71 nm. The z-scale of
image a is 30.7 nm. (b) Linescan along the white line drawn across image a. 78
3.2 An AFM image of a typical sidewall polysilicon surface [78]. The rms
roughness of the surface shown in image a is 13.8 nm. The z-scale of
image a is 158.7 nm. (b) Linescan along the white line drawn across
image a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.1 (a) An AFM image of the in-plane surface of the test platform. The rms
roughness of the surface shown in image a is 0.097 nm. The z-scale of
image a is 1.1 nm. (b) Linescan along the black line drawn across image a. 85
4.2 (a) An AFM image of the sidewall surface of the test platform. The rms
roughness of the surface shown in image a is 6.52 nm. The z-scale of image
a is 41.8 nm. (b) Linescan along the black line drawn across image a. . . 86
4.3 The layout of the mask used to fabricate the test platform. Notice that
the test platform is fabricated on a 1 cm 1 cm chip. It consists of seven
di erent types of microinstruments, all of which, are labelled in the above
 gure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.4 SEM images of (a) An unpolished sidewall surface. (b) A polished sidewall
surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.5 Photograph of the custom-built probing system used to actuate the mi-
croinstruments of the test platform. . . . . . . . . . . . . . . . . . . . . . 96
xvii
5.1 (a) Optical image of a released Residual Stress Tester. Notice that the
I-beam consists of a horizontal central beam that is connected to two
vertical  anges. (b) Magni ed optical image of the area that is enclosed
in the box in Fig. 5.1a. Notice the pair of movable and anchored patterns
labelled in this image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.2 (a) A schematic diagram (plan view) illustrating the clockwise rotation of
the I-beam of the Residual Stress Tester due to the tensile stress present
in the released structural  lm. (b) A schematic diagram (plan view) il-
lustrating the anti-clockwise rotation of the I-beam of the Residual Stress
Tester due to the compressive stress present in the released structural  lm.
Shaded regions shown in the diagrams are anchored to the substrate. A
ground plane (not depicted) is present underneath the entire device. . . . 100
5.3 Optical image of a released Mechanical Strength Tester. . . . . . . . . . 102
5.4 Photograph of the Micro-manipulator developed to actuate the Mechani-
cal Strength Testers. Notice the \bypass" connection used to electrically
ground the probe tip. The two main components of the Micro-manipulator
(i.e., the \coarse" manipulator and the \ ne" manipulator) are clearly la-
belled in the photograph. . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.5 Photograph showing the  ve components of the \ ne" manipulator. . . . 106
5.6 Orthographic projections (plan view) of the four machined components
of the \ ne" manipulator. The dimensions indicated in the orthographic
projections are in mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.7 Optical images illustrating the actuation of a Mechanical Strength Tester.
(a) The MST is shown in its pre-actuated state. (b) Optical image col-
lected during the actuation of the MST. Notice that all the six fracture
beams are pushed against their corresponding anchored stoppers. (c) Op-
tical image showing the MST in its post-actuated state. Notice that all
the fracture beams that were attached to the central shuttle are fractured. 109
5.8 Optical image of a released Resonator. . . . . . . . . . . . . . . . . . . . 111
5.9 An optical image showing two adjacent released Cantilever Beam Arrays. 116
5.10 A schematic diagram illustrating the actuation procedure of a cantilever
beam. (a) Free-standing (unactuated) cantilever beam. (b) Actuated can-
tilever beam. (c) Cantilever beam released after actuation (post-actuation
state). Notice that the cantilever beam is adhered over a length of L s
at its tip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
xviii
5.11 A schematic diagram of the sidewall adhesion test microinstrument (plan
view). Shaded regions shown in the diagram are anchored to the substrate.
A ground plane (not depicted) is present underneath the entire device. . 122
5.12 (a) Optical image of a released sidewall adhesion test microinstrument.
Anchors that anchor the sidewall test beams are not visible in the image.
The total length of the sidewall beams shown in the image is 750  m.
(b) Optical image of a released sidewall beam array. The shortest pair
of sidewall beams is 750  m long. The length of sidewall beam pairs is
increased in increments of 250  m and the longest pair of sidewall beams
is 2250  m long. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.13 A schematic diagram (plan view) illustrating the actuation procedure of
the sidewall adhesion tester. (Top) The sidewall beams are in the as-
fabricated position. (Center) The sidewall beams are in an actuated state,
contacting over almost the entire length of their  nal segments. (Bottom)
Final state of the sidewall beams post-actuation when the actuating volt-
age is reduced to zero. The beams are adhered over a length L s at their
tips. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.14 A schematic diagram of the Sidewall Friction Tester (plan view). Shaded
regions shown in the diagram are anchored to the substrate. A ground
plane (not depicted) is present underneath the entire device. The diagram
is not drawn to scale to better illustrate the important components of the
device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.15 Optical image of a released Sidewall Friction Tester (SFT). Notice the
ground plane present underneath the entire device. The total footprint of
the microinstrument is 2.8 mm2. . . . . . . . . . . . . . . . . . . . . . . 134
5.16 (a) A schematic diagram illustrating the segmental design of the anchored
comb  ngers of the SFT. The diagram is drawn using a scale of 127000:1.
In the as-fabricated (unactuated) position, the anchored and suspended
comb  ngers overlap over a length of 20  m (nominal). Notice that the
gap between them will decrease to 1  m (nominal) when their overlap
increases beyond 22.8  m (nominal). (b) Optical image showing a bank
of interdigitated anchored and suspended comb  ngers. The two segments
of the anchored comb  ngers are clearly visible in this image. (c) Magni ed
optical image of the area enclosed in the box in image b. The pointed tips
of the suspended comb  ngers are clearly visible in this image. . . . . . 137
5.17 Optical image showing the loading section of an unpolished, released Side-
wall Friction Tester. The loading section is in its as-fabricated (unactu-
ated) position. Notice that the anchored posts are not aligned with the
as-fabricated position of the normal arm (i.e., b is greater than a). The
gap between the anchored posts and the corresponding sidewall surfaces
of the loading beam is 6  m (nominal) in the as-fabricated position. . . . 139
xix
5.18 Optical image of a released Sidewall Friction and Adhesion Tester (SFAT).
Notice the ground plane present underneath the entire device. The total
footprint of the microinstrument is 0.47 mm2. . . . . . . . . . . . . . . . 149
5.19 (a) Optical image showing the normal arm of a released Sidewall Friction
and AdhesionTester (SFAT). (b) Optical image showing the tangential
arm of a released Sidewall Friction and AdhesionTester (SFAT). Notice
that both the normal and the tangential arm have one push drive and one
pull drive each. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.20 (a) Optical image showing one bank of interdigitated comb  ngers each
of the normal and tangential arms of a released Sidewall Friction and
Adhesion Tester (SFAT). The two segments of the anchored comb  ngers
are clearly visible in this image. (b) Magni ed optical image showing the
comb  ngers of the tangential arm of the SFAT, that are enclosed in the
box in Fig. 5.20a. (c) Magni ed optical image showing the comb  ngers
of the normal arm of the SFAT, that are enclosed in the box in Fig. 5.20a.
The pointed tips of the suspended comb  ngers are clearly visible in both
Fig. 5.20b and Fig. 5.20c. . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.21 Optical image showing the loading section of a released Sidewall Friction
and Adhesion Tester. The loading section is in its as-fabricated (unactu-
ated) position. Notice the gap between the loading block and the friction
block. It is designed to be 4 m (nominal) in their as-fabricated posi-
tions. The anchored and suspended patterns that are used to track the
displacements of the normal and tangential arms are clearly labelled in
the image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.1 AFM image of a 25  m2 area of the OTS SAM coated Si(100) monitor
chip, which is processed simultaneously with the OTS SAM coated Test
Platform chip. Notice that only four extremely small polymerized particles
are present in the 25  m2 area shown in the scan. The rms roughness of
the area shown in the image is 0.23 nm. . . . . . . . . . . . . . . . . . . 169
6.2 A TEM image showing the dodecanethiol-capped gold nanoparticles used
to tailor the surface topographies of the test surfaces investigated in this
study. The size of the dodecanethiol-capped gold nanoparticles shown in
the image is determined to be 5.48  1.16 nm. . . . . . . . . . . . . . . . 171
7.1 Error in  (  ) for di erent imposed percentage error (% ) in  . . . . . 186
8.1 A plot showing the experimentally determined axial and lateral displace-
ments of the central shuttle of one of the MSTs of the OTS SAM coated
Test Platform chip versus the corresponding voltage applied to the micro-
manipulator that is used to actuate it. Notice the discontinuities in the
plot that represents the axial displacement data. Also, the lateral dis-
placements of the central shuttle are negligible throughout the actuation
of the MST. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
xx
8.2 A plot of the square of the observed resonance frequency of the Resonators
investigated in this chapter versus their corresponding value of the term
that is written in brackets on the right hand side of Eq. 5.3.6. The ( )
represent the experimentally observed resonance frequencies and () is a
line  tted to the experimentally obtained data. Notice the high R2 value
of the linear  t. The slope of the  tted line is the experimentally obtained
value of E of the structural  lm of the native oxide covered Test Platform
chip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
8.3 (a) Interferogram of a polysilicon-based CBA, collected before actuation.
(b) Interferogram of the CBA shown in Fig. 8.3a, collected after actuation.
This CBA was actuated manually. . . . . . . . . . . . . . . . . . . . . . 198
8.4 (a) Interferogram of a polysilicon-based CBA, collected before actuation.
(b) Interferogram of the CBA shown in Fig. 8.4a, collected after actuation.
This CBA was actuated electrostatically. . . . . . . . . . . . . . . . . . . 199
8.5 (a) Interferogram showing a released cantilever beam array of the Test
Platform chip coated with OTS SAM. Notice the presence of fringes on
all the cantilever beams, which indicates that they are not parallel to the
substrate. (b) Height pro le of beam 5 labelled in Fig. 8.5a. The height
pro le is obtained experimentally, using phase shifting interferometry. It
indicates that beam 5 is inclined upwards, and has a convex shape. . . . 203
8.6 (a) Interferogram showing a released cantilever beam array of a Test Plat-
form chip, which is not polished. Notice that the number of fringes present
on the cantilever beams shown in this image is less, which indicates that
they are not parallel to the substrate. (b) Height pro le of beam 5 labelled
in Fig. 8.5a. The height pro le is obtained experimentally, using phase
shifting interferometry. It indicates that beam 5 is inclined upwards, and
has a convex shape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
8.7 (a) Interferogram showing released sidewall adhesion test microinstru-
ments. Notice the fringes on the sidewall beams, which clearly indicate
that the sidewall beams are freestanding and also not parallel to the sub-
strate (b) Height pro le of the initial segment of the topmost sidewall
beam shown in Fig. 8.7a. The height pro le is obtained using phase shift-
ing interferometry. It clearly indicates that the sidewall beam is inclined
upwards and exhibits a take-o angle of 1 mrad. . . . . . . . . . . . . . . 211
8.8 Interferogram showing the initial segment of an actuated sidewall adhe-
sion test microinstrument. Voltage applied to the actuation electrode is 52
V. Notice the increased number of fringes visible on the actuated sidewall
beams as compared to that of fringes visible on the unactuated sidewall
beams shown in Fig. 8.7a, which is a manifestation of levitation. Also no-
tice that the exact same number of fringes are visible on both the actuated
sidewall beams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
xxi
8.9 (a) Interferogram showing the  nal segment of an actuated sidewall ad-
hesion test microinstrument. Voltage applied to the actuation electrode
is 70 V. The two sidewall beams are stuck to each other over a length
of 50  m at their tips. Notice that while the fringes on the two sidewall
beams are equal in number, they are slightly mismatched in phase. (b)
Interferogram, showing the  nal segment of the same sidewall adhesion
test microinstrument that is shown in Fig. 8.9a, collected post-actuation.
Notice that no \scissoring" is visible on the two sidewall beams, which are
stuck over a length of 25  m at their tips. . . . . . . . . . . . . . . . . . 215
8.10 A plot showing the experimentally determined axial ( ) and lateral ( )
displacements of the tangential arm of the test device versus square of
the corresponding voltages (V2t ) applied to its pull drive. Notice that
the data representing the axial displacements is clearly divided into two
segments, which have signi cantly di erent slopes. The transfer functions
Gt1 and Gt2 are extracted from the corresponding linear  ts () of the
experimental axial displacement data.  a, which is determined optically,
is the distance by which the tangential arm should be pulled to its left to
align the normal arm with the anchored posts and Va is the corresponding
voltage that should be applied to the pull drive of the tangential arm. . . 219
8.11 A plot showing the experimentally determined axial ( ) and lateral ( )
displacements of the normal arm of the test device versus square of the
corresponding voltages (V2n) applied to its pull drive. Notice that the data
representing the axial displacements is clearly divided into three segments,
which have signi cantly di erent slopes. The transfer functions Gn1 and
Gn2 are extracted from the corresponding linear  ts () of the experimental
axial displacement data.  c is the distance by which the normal arm should
be axially displaced in order to bring the loading beam in contact with the
anchored post and Vc is the corresponding voltage that should be applied
to the normal comb-drive actuator. Notice that even at voltages greater
than Vc, the lateral displacements of the normal arm are negligible. . . . 221
8.12 An interferogram, showing the loading section of the test device, collected
after bringing the loading beam in contact with the anchored post. A
voltage of 45 V is applied to the pull drive of the normal comb-drive
actuator before collecting this interferogram. Notice the absence of fringes
on the normal arm as well as on the loading section. The step edge at the
sidewall interface is determined using HSI to be 20 nm. . . . . . . . . . . 223
xxii
8.13 A plot showing the onset of slip at an OTS SAM coated sidewall interface.
The displacement of the loading beam, which is determined by considering
its position when the normal arm is aligned with the anchored post as the
initial position, is plotted against the voltage applied to the tangential
comb-drive actuator. A normal load of 8.05  N, which corresponds to a
Hertzian contact pressure of 224 MPa, is applied at the sidewall interface.
Notice that the  rst slip occurred at Vt;s of 32.8 V and the second slip
occurred at Vt;s of 34.8 V. . . . . . . . . . . . . . . . . . . . . . . . . . . 225
8.14 A plot showing the experimentally determined axial ( ) and lateral ( )
displacements of the tangential arm of of one of the OTS SAM coated
Sidewall Friction and Adhesion Testers versus square of the corresponding
voltages (V2t ) applied to its push drive. Notice that the data represent-
ing the axial displacements is clearly divided into two segments, which
have signi cantly di erent slopes. The transfer functions Gt1 and Gt2 are
extracted from the corresponding linear  ts () of the experimental axial
displacement data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
8.15 A plot showing the experimentally determined axial ( ) and lateral ( )
displacements of the normal arm of one of the OTS SAM coated SFAT
versus square of the corresponding voltages (V2n) applied to its push drive.
Notice that the data representing the axial displacements is clearly divided
into three segments, which have signi cantly di erent slopes. The transfer
functions Gn1 and Gn2 are extracted from the corresponding linear  ts ()
of the experimental axial displacement data.  c is the distance by which
the normal arm should be axially displaced in order to bring the loading
block in contact with the friction block and Vc is the corresponding voltage
that should be applied to the normal comb-drive actuator. . . . . . . . . 232
8.16 An interferogram showing the sidewall interface formed in one of the OTS
SAM coated Sidewall Friction and Adhesion Testers. A voltage of 50 V
is applied to the push drive of the normal arm to bring the loading block
in contact with the friction block, before collecting this interferogram.
Notice the absence of fringes on the loading and friction blocks shown in
the interferogram. The step edge at the sidewall interface is determined
using HSI to be 75 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
8.17 A plot showing the onset of slip at an OTS SAM coated sidewall interface
investigated using the SFAT developed in this study. The displacement of
the friction block is plotted against the voltage applied to the tangential
comb-drive actuator. A normal load of 1.82  N, which corresponds to an
apparent contact pressure of 0.26 MPa, is applied at the sidewall interface.
Notice that the  rst slip occurred at Vt;s of 52 V and the second slip
occurred at Vt;s of 57 V. . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
xxiii
9.1 SEM images of the substrates of the  ve textured Test Platform chips
investigated in this chapter. The numbers indicated on the SEM images
are the sample numbers of the corresponding textured Test Platform chips.
Notice the monotonous increase in the amount of the nanoparticles present
on the textured surfaces shown in the SEM images from the image a to
image e. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
9.2 AFM images of the substrates of the Test Platform chips investigated in
this chapter. The numbers indicated on the AFM images are the sample
numbers of the corresponding textured Test Platform chips. . . . . . . . 251
9.3 Bar graph showing the rms roughnesses of the in-plane surfaces of the
Test Platform chips investigated in this chapter. . . . . . . . . . . . . . . 253
9.4 A schematic explaining the observed variations in the roughnesses of the
substrates of the Test Platform chips investigated in this chapter. The
red lines shown in all the diagrams represent the surface pro le of the
(untextured or textured) substrates shown in them. . . . . . . . . . . . . 254
9.5 A plot showing the variations in the apparent works of adhesion of the
in-plane as well as sidewall surfaces with the variations in their surface
topographies. The data points plotted in the plot are arithmetic means of
several measurements. The error bars shown in the plot indicate the max-
imum and minimum values of the apparent works of adhesion exhibited
by the in-plane and sidewall surfaces of that Test Platform chip. . . . . . 259
9.6 A plot showing the variation in the engineering coe cient of static friction
of a sidewall surface with the variation in its surface topography. The data
points plotted in the plot are arithmetic means of 225 measurements. The
error bars shown in the plot indicate the maximum and minimum values
of the engineering coe cient of static friction exhibited by the contacting
sidewall surfaces of that Test Platform chip. . . . . . . . . . . . . . . . . 263
9.7 (a) A SEM image showing the edge of a released cantilever beam of sample
no. 4. (b) A SEM image of a region of the substrate, which is underneath
the cantilever beam shown in Fig. 9.7a.The SEM image shown in this
image is collected after breaking the cantilever beam shown in Fig. 9.7a
apart using a probe tip (Signatone 20T). Notice that the surfaces shown in
both the image a as well as the image b have exactly identical nanoparticle
coatings on them. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
xxiv
9.8 A plot of the apparent works of adhesion exhibited by the six in-plane
surfaces investigated in this chapter versus their rms roughnesses. The
data points plotted in the plot are arithmetic means of 40 measurements.
The error bars shown in the plot indicate the maximum and minimum
values of the apparent work of adhesion exhibited by the in-plane surface
of that Test Platform chip. Notice that the plot indicates that there exits
an optimum rms roughness, at which, the in-plane surface experiences
minimum stiction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
9.9 A plot, in which, the ordinates of Eq. 9.3.23 are plotted against its ab-
scissae. The data points ( ) plotted in Fig. 9.9 are obtained using the
mean values ofW reported in Table 9.5. The error bars shown in the plot
indicate one standard deviation of the sample of 40 measurements used to
determine that data point. A line ()  tted to the data points ( ) is also
shown in the plot. Notice the high R2 value of the linear  t. . . . . . . . 278
9.10 A representative AFM image of the sidewall surface of the control (un-
textured) sample.The rms roughness of the surface shown in the image is
6.52 nm. The z-scale of the image is 41.8 nm. . . . . . . . . . . . . . . . 279
9.11 A plot showing the  s of the sidewall surfaces of all the six Test Platform
chips, determined using both the SFTs as well as the SFATs. The data
points plotted in the plot are arithmetic means of several measurements.
The error bars shown in the plot indicate the maximum and minimum val-
ues of the engineering coe cient of static friction exhibited by the sidewall
surfaces of that Test Platform chip. Notice the close agreements between
the  s determined using the SFTs and those determined using the SFATs. 286
10.1 (a) A high resolution AFM image of the top surface of one of the Res-
onators of the coated Test Platform chip. The rms roughness of the sur-
face shown in image a is 2.06 nm. The z-scale of image a is 13.8 nm. (b)
Linescan along the white line drawn across image a. . . . . . . . . . . . . 293
11.1 (a) AFM image of the native oxide covered uncoated substrate of the
control chip I. The rms roughness of the surface shown in image a is 0.097
nm. (b) Linescan along the white line drawn across image a. . . . . . . . 303
11.2 (a) AFM image of the AuNP coated substrate of the test chip. The rms
roughness of the surface shown in image a is 8.3 nm. (b) Linescan along
the white line drawn across image a. . . . . . . . . . . . . . . . . . . . . 304
11.3 (a) An interferogram showing a tested Cantilever Beam Array of the con-
trol chip I. (b) Experimentally determined height pro le of beam 2 labelled
in image a. The height pro le is determined using phase shifting interfer-
ometry. Notice that the crack of beam 2 labelled in image a is less than
100  m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
xxv
11.4 (a) An interferogram showing a tested Cantilever Beam Array of the test
chip. (b) Experimentally determined height pro le of beam 4 labelled in
image a. The height pro le is determined using phase shifting interferom-
etry. Notice that the crack of beam 4 labelled in image a is close to 850
 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
11.5 (a) Optical image showing the  ve longest sidewall beam pairs of a re-
leased Sidewall Beam Array of the test chip, collected before actuating
the Sidewall Beam Array. Notice that the sidewall beams of each of the
 ve sidewall beam pairs shown in this image are apart from each other.
(b) Optical image of the Sidewall Beam Array shown in image a, collected
after actuating it. Notice that the sidewall beams of the three shorter
sidewall beam pairs shown in this image peeled apart completely, while
those of the two longer sidewall beam pairs remained stuck, after actuation.308
11.6 A plot of the (mean)  s of the AuNP coated contacting sidewalls versus
the corresponding voltage applied to the comb-drive actuator of the nor-
mal arm. The arrows shown in the plot indicate the direction, in which,
the normal load applied at the sidewall interface of the SFAT used for this
study is changed. Notice that the (mean)  s of the AuNP coated contact-
ing sidewalls changed irreversibly when a voltage of 77 V is applied to the
normal comb-drive actuator. . . . . . . . . . . . . . . . . . . . . . . . . . 312
A.1 A screenshot of the user-interface of MEMScript. . . . . . . . . . . . . . 339
xxvi
List of Tables
2.1 A comparison between the  lm properties of OTS, FDTS and oxide surface
 lms [6,35,64,80,99]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
8.1 This table reports the measured lever arms as well as the measured dis-
placements of corresponding MSTs at the instant of fracture of the tested
fracture beams. It also reports the strains that exist in the tested fracture
beams at the instant of their fracture. Each value reported in the table is
an arithmetic mean of 16 measurements, and the corresponding std. dev.
is one standard deviation of the sample consisting of those measurements. 193
8.2 This table reports the drive signals used to actuate the Resonators of
the native oxide covered Test Platform chip along with their optically
observed resonance frequencies. Each resonance frequency reported in the
table is an arithmetic mean of  ve measurements, which are made using
 ve distinct Resonators having the same supporting beam length. . . . . 195
8.3 Comparison between the apparent work of adhesion of OTS SAM coated
in-plane surfaces calculated using di erent methods. The OTS SAM
coated cantilever beam used for this analysis exhibited a crack length
of 835.3  m. The method used for determining the apparent work of ad-
hesion of the in-plane surfaces investigated in this study is highlighted in
the table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
8.4 Comparison between the apparent work of adhesion of in-plane surfaces
of OTS SAM coated surfaces and that of surfaces with only native oxide
on them. The apparent works of adhesion of in-plane surfaces reported in
this table are determined using the CBAs. All the values reported in the
table are arithmetic means of 40 measurements and sd is one standard
deviation of the sample consisting of those measurements. . . . . . . . . 208
8.5 Comparison between the apparent work of adhesion of sidewall surfaces
of OTS SAM coated surfaces and that of surfaces with only native oxide
on them. The apparent works of adhesion of sidewall surfaces reported in
this table are determined using the SBAs. All the values reported in the
table are arithmetic means of several measurements and sd is one standard
deviation of the sample consisting of those measurements. . . . . . . . . 216
xxvii
8.6 Comparison between the engineering coe cients of static and kinetic fric-
tion of OTS SAM coated surfaces and those of surfaces with only native
oxide on them. The engineering coe cients of friction reported in this
table are determined using the Sidewall Friction Tester. All the values
reported in the table are arithmetic means of 200 measurements and the
std. dev. is one standard deviation of the sample consisting of those mea-
surements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
8.7 Comparison between the engineering coe cients of static and kinetic fric-
tion of OTS SAM coated surfaces and those of surfaces with only native
oxide on them. The engineering coe cients of friction reported in this
table are determined using the Sidewall Friction and Adhesion Tester. All
the values reported in the table are arithmetic means of 325 measure-
ments and the std. dev. is one standard deviation of the sample consisting
of those measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
9.1 This table lists the decrease in the resonance frequencies ( fR) and the
corresponding increase in the e ective masses ( Meff) of the Resonators
with 500  m long supporting beams, of each of the  ve textured Test
Platform chips. Each value reported in the table is an arithmetic mean of
 ve measurements, which are obtained using  ve distinct Resonators that
are fabricated at di erent locations on the corresponding Test Platform
chip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
9.2 Comparison between the mean apparent works of adhesion of the in-plane
surfaces of the six Test Platform chips investigated in this chapter to
study the e ect of topography. The apparent works of adhesion of in-
plane surfaces reported in this table are determined using the CBAs. All
the values reported in the table are arithmetic means of 40 measurements. 256
9.3 Comparison between the mean apparent works of adhesion of the sidewall
surfaces of the six Test Platform chips investigated in this chapter to study
the e ect of topography. The apparent works of adhesion of in-plane
surfaces reported in this table are determined using the SBAs. All the
values reported in the table are arithmetic means of several measurements. 257
9.4 Comparison between the mean engineering coe cients of static friction of
the sidewall surfaces of the six Test Platform chips investigated in this
chapter to study the e ect of topography. The engineering coe cients of
static friction reported in this table are determined using Sidewall Friction
Testers. All the values reported in the table are arithmetic means of 225
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
xxviii
9.5 This table reports the W (arithmetic mean), rrms,  rms and  of all the
 ve textured in-plane surfaces investigated in this study. The values of
 and  rms reported in this table are determined using the untextured
(control) in-plane surface as the reference surface. Accordingly, Wo and
rorms used are 38700  J/m2 and 0.14 nm, respectively. The rrms of each
of the  ve textured in-plane surfaces as well as the rorms are obtained
from their corresponding representative AFM images. nasperities for each
of the  ve textured in-plane surfaces as well as for the reference surface are
determined using the image analysis technique explained in section 6.12.
The threshold value used in the image analysis technique is the kelvin
radius of water at the relative humidity of 45%. . . . . . . . . . . . . . . 274
9.6 This table reports the rrms,  rms,  and  topo of the sidewall surface
of the control (untextured) sample. The rrms reported in this table is
obtained using the AFM image shown in Fig. 9.10. The  rms and the  
reported in the table are obtained using the in-plane surface of the control
(untextured) sample as the reference surface. The table also reports the
apparent works of adhesion of the sidewall surface of the control sample,
determined using its  topo and obtained experimentally. . . . . . . . . . . 281
10.1 This table reports the optically observed resonance frequencies of the two
sets of Resonators tested in this study. Each resonance frequency reported
in the table is an arithmetic mean of  ve measurements, which are made
using  ve distinct Resonators having the same supporting beam length. . 296
11.1 Comparison between the critical tribological properties of the native oxide
covered hydrophilic surfaces of the control chip I, the OTS SAM coated
hydrophobic surfaces of the control chip II and the AuNP coated surfaces
of the test chip. All the values reported in the table are arithmetic means
of several measurements and sd is one standard deviation of the sample
consisting of those measurements. . . . . . . . . . . . . . . . . . . . . . . 310
xxix
Chapter 1
MEMS Technology
1.1 Miniaturization: Exploring the Room at the Bottom
Miniaturization is extremely bene cial in many technological applications, in
all the branches of fundamental (i.e., physics, chemistry and biology) and applied
(i.e., engineering) sciences [1]. A good example, which substantiates this, is the
increased e ciency and speed of microprocessors used presently, which are direct
consequences of the miniaturization of transistors used in them [2]. While there are
several such useful consequences of miniaturization, as pointed out by Feynman half-
a-century ago in his historic lecture \There?s plenty of room at the bottom", the one
that has materialized most prominently over the last two decades is the evolution
of the  eld of Micro-electromechanical systems (MEMS) [1, 3]. However, although
MEMS technology has evolved signi cantly in the past few years, it has seen lim-
ited commercial success due to the poor reliability of most of the invented MEMS
prototypes. Since the primary motivation behind this study is to enhance our under-
standing of the tribological characteristics of MEMS interfaces so that an appropriate
strategy to improve the reliability and hence, enable the commercialization of useful
MEMS prototypes, could be devised, it is only logical to begin this report by answer-
ing the following questions: what are MEMS, why are they technologically attractive
and why is it important to enable their commercialization?
1
1.2 MEMS: A Technological Evolution
Micro-electromechanical systems (MEMS) are miniature devices, in which, me-
chanical components, with dimensions ranging from a few to a few hundred microns,
and electrical components are directly integrated together. They are used either in-
dividually to sense, control and activate mechanical processes at the micro-scale or in
arrays to generate e ects at the macro-scale. The idea of MEMS was  rst conceived
in the mid 1960?s, when Nathanson and colleagues at the Westinghouse Research
Laboratory devised a complete oscillator by combining a simple mechanical resonator
with an early electronic transistor on the same silicon wafer [3]. However, it took
a quarter of a century for the scienti c community to produce the  rst commercial
MEMS device and even to-date the technology has been used successfully in only
a few commercialized applications. The working of most of those applications is
based on the mechanical response of a MEMS device (with no contacting parts) to
an environmental change [4,5].
The  rst MEMS device that was commercialized was an iMEMS accelerometer,
which integrated a small, reliable MEMS sensor structure with a signal condition-
ing circuitry on a single chip [6]. It was produced in 1991 by Analog Devices [6].
Other MEMS devices that have been commercialized since then include relatively
simple sensing mechanisms like accelerometers, gyroscopes and pressure sensors [7,8].
Presently, the accelerometer technology, which is used in airbag-deployment systems,
anti-skid breaking systems and four-wheel drive systems in the automobile industry,
is on the order of a billion dollars-a-year industry, dominated by Lucas NovaSensor
and Analog Devices. The most recently commercialized MEMS device is the Digital
Mirror Device (DMDTM) developed by Texas Instruments, which has useful applica-
tions in digital light processing (DLP) equipments such as television sets and projec-
tors [9{11]. Figures 1.1a and 1.1b show two of the most widely used commercially
available MEMS devices.
2
(a)
(b)
Figure 1.1: (a) A DMDTM commercially manufactured by Texas Instruments. (b)
A micro-accelerometer (model: ADXL193) commercially manufactured by Analog
Devices using the silicon based iMEMS surface micromachining technology. This
device senses acceleration up to  250g and costs about $7 in 2011.
3
MEMS are technologically as well as commercially very attractive primarily be-
cause they are inherently smaller, lighter, faster and generally more precise than their
macro-counterparts. However, for some applications such as car airbag deployment
systems, RF switches and RF  lters, they are commercially attractive because of
their low cost [3]. While some these attributes that make MEMS technologically and
commercially attractive, such as low cost, small size and light weight, are direct con-
sequences of the micromachining processes and the relatively inexpensive structural
material (i.e., silicon) used to fabricate them, others, such as high speed and precision,
are consequences of their small size [9,12,13].
Leveraging the infrastructure of the integrated circuit (IC) industry and the ad-
vancements in the micromachining technologies, the MEMS community have devised
an extensively large number of useful MEMS prototypes. However, to-date, only a
few of those MEMS prototypes have been commercialized and the rest, such as those
shown in Figs. 1.2a and 1.2b, still remain in the category of potential MEMS due to
their poor reliability. Since those potential MEMS devices are also technologically
and commercially very attractive and have extremely useful applications in a wide
variety of electronically controlled equipments such as robots, industrial process con-
trollers and instruments, toasters, automobiles, bathroom scales, displays, printers
and storage devices, there is an urgent and serious need to devise strategies that
can enable their commercialization [4]. Figure 1.2a shows a SEM image of a micro
steam engine developed by Sandia National Laboratories, which has the potential to
be a breakthrough invention in the  eld of micro-scale power generation. Figure 1.2b
shows a SEM image of another MEMS prototype developed by Sandia National Lab-
oratories, which is a strong potential candidate for applications that involve precise
positioning.
Presently, the potential MEMS devices that are most promising and on the verge
of commercialization belong to the two emerging and exciting branches of Bio-MEMS
4
(a)
(b)
Figure 1.2: (a) SEM image of a micro steam engine developed by Sandia National
Laboratories [14]. (b) SEM image of an electromechanical locking device developed
by Sandia National Laboratories [14].
5
and Micro uidics. Bio-MEMS and Micro uidic devices are portable, potentially low
cost, integrated packages, which also o er an additional advantage of requiring only
small amounts of sample and reagents due to their small sizes. While the only com-
mercially available Bio-MEMS devices presently are Biosensors, which are used for
detecting from pH of a biological system to small molecules such as oxygen and glu-
cose, the range of applications in which potential Bio-MEMS can be used extends
from tools for molecular biology, cell biology and biochemistry to breakthrough med-
ical devices such as micromachined neural prostheses, micro-pumps and micro-needles
used for drug delivery [15{20]. Additionally, extensive research to develop Bio-MEMS
implants that can record from, sense, stimulate and deliver to biological systems, is
also being conducted [17,20]. A good example of this is the retinal implant reported
by Peachey et al., which employs a semiconductor based microphotodiode array to
restore the impaired visual function [19]. Microfabricated biocapsule reported by De-
sai et al. is also a promising possible application of potential Bio-MEMS [18]. It has
novel implications in the  eld of immunoisolation [18].
1.3 Tribology: Role in Hindering the Commercialization of MEMS
While at the laboratory scale, a wide variety of complex MEMS prototypes in-
cluding sensors, actuators, valves, nozzles, turbines, pumps and gear trains have been
conceptualized and tested, at the commercial scale, only the sensors have been exten-
sively employed [3]. The issues that have historically hindered the commercialization
of most useful MEMS prototypes include generation of low force/torque by the MEMS
prototype, unavailability of technology to couple the di erent micro-components of
the MEMS prototype to produce useful work and poor reliability of the MEMS pro-
totype [3]. While the  ve-level poly-crystalline silicon (polysilicon) micromachining
process (i.e., \SUMMiTTM V") developed recently at Sandia National Laboratories
6
has resolved the  rst two issues, which in turn has initiated the realization of the con-
cept of mechanical power transmission using MEMS as well as signi cantly increased
the number of possible applications of potential MEMS, poor reliability still remains
a major hindrance in the commercialization of most complex and useful MEMS pro-
totypes [3].
The poor reliability of most MEMS prototypes is generally attributed to their
susceptibility to failures induced by surface phenomena such as stiction, friction and
wear [9,12,21]. Indeed, stiction is responsible for hampering the functioning of several
micro - and nano - machines because their moving parts adhere spontaneously upon
contact [6]. This is a direct consequence of the fact that the relative signi cance of
surface forces increases drastically at the scale of MEMS (i.e., micro-scale). To better
understand the increase in the relative signi cance of surface forces at the micro-scale,
consider the adhesion force experienced by the stainless steel grinding media used in
ball mills. If the diameter of the grinding media is 10 cm and its surface is dirty (i.e.,
apparent work of adhesion of its surface is 0.1 Jm 2), it experiences an adhesion force
(i.e., 12 mN) that is three orders of magnitude smaller than the force of gravity (i.e.,
41000 mN) experienced by it. Contrastingly, if the diameter of the same grinding
media is 1  m, it experiences an adhesion force that is more than a million times
greater than the force of gravity experienced by it. The increased relative signi cance
of the adhesion force experienced by the stainless steel grinding media at the micro-
scale is a consequence of the fact that the adhesion force falls linearly with the size
of the grinding media whereas the gravitational force falls with its size cubed [22].
The stainless steel grinding media illustration also emphasizes that we cannot
always intuitively transfer our understanding of the macroscopic mechanical systems
to the micro-domain. Therefore, dedicated systematic investigations should be con-
ducted to understand the laws that govern the behaviour of objects at the micro-
scale. A complete understanding of the behaviour of micron-size objects requires
7
knowledge of all the factors that in uence it as well as in-depth understanding of
the mechanisms underlying them. However, although surface phenomena such as
stiction, friction and wear were identi ed as factors that dominate the behaviour of
micron-size objects half-a-century ago, the mechanisms underlying their manifesta-
tions at the micro-scale are still poorly understood [1]. Our current knowledge base
is so incomplete that it can neither reasonably accurately predict nor satisfactorily
explain all the interactions that occur between two micron-size surfaces when they
are brought together, separated and rubbed against each other (collectively called
as tribology) [6, 23{31]. Making this already dire situation worse is the demand for
sophisticated and compact MEMS, which is increasing with every passing day. There-
fore, an increasing number of scientists are now opting to investigate the factors and
the associated mechanisms that lead to stiction, friction, lubrication and wear at the
micro-scale. Understanding the tribology of micron-size surfaces is critical not only
for the commercialization of an astronomical spectrum of sophisticated, complex and
useful MEMS prototypes but also for  nding the solutions of many other basic and
applied problems in the  eld of micro- and nano-technology [6,23{31].
The factors that strongly in uence the tribological properties of MEMS surfaces
include environmental factors such as temperature, pressure and relative humidity of
the operating environment and surface characteristics such as topography and chem-
istry of MEMS surfaces [3, 6, 13, 32]. While the environmental factors are imposed
by the targeted application, the chemistry and topography of MEMS surfaces are de-
 ned by the treatments, to which, they are subjected to during and post-fabrication.
While the chemistry of MEMS surfaces can be manipulated signi cantly, their topog-
raphy can be changed only limitedly, and is mainly de ned by the micromachining
processes used to fabricate the MEMS. The following section will brie y describe the
various micromachining processes used in the fabrication of MEMS and elaborate
their in uences on the characteristics of the micromachined MEMS surfaces.
8
1.4 Micromachining: Description and In uences on MEMS Surface Char-
acteristics
The three processes that constitute the realm of micromachining are Deposition,
Lithography and Etching. They are usually used in conjunction with Wafer Bonding
and Chemical Mechanical Planarization (CMP) to enable fabrication of extremely
complex structures, which have useful applications in a wide variety of  elds. Each
of the above mentioned  ve processes are known to have a strong in uence on the
characteristics of MEMS surfaces [3,32,33].
1.4.1 Deposition
Deposition, which is one of the three key processes used in micromachining, is
used to deposit structural, sacri cial or protective  lms of di erent thicknesses and
di erent materials. The three most commonly used deposition processes are the
chemical vapor deposition (CVD) process, the ion beam sputtering (IBS) process
and the thermal oxidation process [30, 31, 34{36] . Examples of deposited structural
 lms include metallic copper  lms, which are deposited using ISB and poly-crystalline
silicon (polysilicon)  lms, which are deposited using CVD [3, 30, 31, 36]. Examples
of sacri cial  lms include metal oxide and silicon oxide  lms, which are generally
grown on the substrate thermally and phosphosilicate glass (PSG)  lms, which are
deposited using CVD [31,34]. Examples of deposited  lms that are used as protective,
lubricating or surface modifying layers in MEMS include  lms of organic precursors
such as octadecyltrichlorosilane (OTS), which are deposited using either a vapor phase
process such as CVD or a solution phase process [30,31,35,37,38].
The parameters of the deposition process as well as that of the subsequent an-
nealing process strongly in uence the structural characteristics of the deposited  lms
such as the type, size, shape and arrangement of its crystals [3,36]. These structural
9
characteristics, in turn, de ne the surface characteristics such as texture, topogra-
phy and roughness of the surfaces of the deposited  lms [3,36]. The same structural
characteristics also de ne some of the mechanical properties such as the Young?s mod-
ulus of the deposited  lms, the residual stress in the deposited  lms and the residual
stress gradient across the thicknesses of the deposited  lms [39,40]. These mechani-
cal properties, in turn, determine the usefullness of the deposited  lms in addition to
determining their mechanical strength and wear properties [39,40].
1.4.2 Lithography
Lithography is the second key process used in micromachining. It is an essential
component of all the micromachining techniques and is required in the fabrication
of every MEMS device [7, 41]. It is used to de ne the in-plane shapes of the various
components of a MEMS device [7, 41]. It consists of a series of steps, which begins
with, coating of the layer that is to be patterned with a  lm of radiation sensitive ma-
terial (resist). Next, the resist layer is exposed to a radiation of speci c wavelength,
through a pattern (mask). Exposure to radiation makes the exposed regions of the re-
sist layer either soluble or insoluble in the corresponding developing solution. Finally,
the soluble portions of the resist layer are dissolved in the corresponding developing
solution and the corresponding regions on the underlying substrate are exposed for
etching [7, 41{46]. All the steps involved in lithography signi cantly a ect the  nal
shape of the components of a MEMS device and the surface topography of their side-
wall surfaces. An under/over exposed resist layer, an under/over developed resist
layer and a non-uniform resist layer can all lead to formation of irregularities on the
sidewall surfaces of a MEMS device.
10
1.4.3 Etching
Etching is the third key process used in micromachining. Like lithography, etch-
ing is also an essential component of all the micromachining techniques and is re-
quired in the fabrication of every MEMS device [7,41]. It is used to de ne the three-
dimensional geometry of a MEMS device [33,45,47{56]. In some cases, it is also used
to release a MEMS device [45,55,56]. Etching processes can be broadly classi ed into
two categories: wet etching processes and dry etching processes. Each wet as well
as dry etching process can be further classi ed either as anisotropic or as isotropic
etching process. Anisotropic wet etching of polysilicon structural layers is commonly
accomplished using either aqueous potassium hydroxide (KOH) or ethylenediamine
pyrocatechol (EDP), and anisotropic dry etching of polysilicon structural layers is
commonly accomplished using gases such as oxygen (O2), sulfur hexa uoride (SF6)
and C4F8 [33,45,47{56]. Isotropic dry etching of silicon and polysilicon structural lay-
ers is commonly accomplished using Xenon di uoride (XeF2) vapors [57]. Hydrogen
Fluoride (HF) vapors, Hydro uoric acid (HF) solutions of various concentrations as
well as HF solution bu ered with ammonium  uoride (NH4F) are etchants commonly
used for isotropic etching of sacri cial layers [56]. In case of etchants with known
etching rates, the extent of etching is usually controlled using a timed etch [55]. For
etchants whose etch rates are not known precisely, an etch stop is used to terminate
the etching [7,45]. A silicon layer heavily doped with either boron or phosphorous is
a commonly used etch stop [7, 45]. Silicon nitride and silicon oxide layers are other
commonly used etch stops.
The type as well as the parameters of an etching process determine the mech-
anisms that are involved in it. Etching mechanisms vary from physical removal due
to bombardment, which is a directional mechanism to chemical reactions followed by
removal of the reaction products, which is either directional (e.g., selective etching of
particular crystal planes) or isotropic [33,47{55,57{62]. Both the etching mechanism
11
involved as well as the environment to which the MEMS surfaces are exposed during
etching strongly in uence their surface characteristics. A prime example of this is
the di erence between the chemistry as well as the topography of in-plane surfaces,
which are masked during etching, and the corresponding sidewall surfaces, which are
exposed to the etching environment, of every MEMS device.
1.4.4 Wafer Bonding
Wafer bonding is a technique that is used to adhere two or more wafers together.
It is almost always used with the three key micromachining processes, in the fabri-
cation of MEMS devices. While in some applications, it is used to join two silicon
substrates to provide mechanical support to, thermal isolation to, heat sink for or
make electrical connections to the microfabricated devices, in other applications, it
is used to create sealed chambers in the bulk-micromachined micro-valves and micro-
pumps [63]. Additionally, it is also used to manufacture silicon-on-insulator (SOI)
substrates, which are used to fabricate microelectronics as well as MEMS [63]. Wafer
bonding is usually carried out at elevated temperatures, exposure to which, alters
the physical as well as chemical characteristics of most thin  lm coatings, which are
deposited on MEMS surfaces to improve their reliability [6, 35, 37, 64]. Therefore,
depending on the thin  lm coating that is deposited on MEMS surfaces and the tem-
perature at which wafer bonding is performed, wafer bonding can also signi cantly
in uence the characteristics of MEMS surfaces.
1.4.5 Chemical Mechanical Planarization (CMP)
Chemical mechanical planarization is a technique that is used to planarize or
polish the in-plane surface of a wafer. It was originally used in the sub-micron cir-
cuit technology for globally planarizing the surface of the topmost layer of a substrate
wafer [3]. It was  rst employed in MEMS micromachining for smoothening polysilicon
12
 lm surfaces, to improve the optical quality of surface micromachined mirror devices
fabricated using them [3]. Presently, it is more extensively used in surface microma-
chining of MEMS that are fabricated using multiple structural layers [3]. The four
attributes that make CMP an integral component of the micromachining technology
are as follows: First, it can be used to polish and produce surfaces that can be used in
optical applications. Second, it can be used in surface micromachining of MEMS that
are fabricated using multiple structural layers to reduce polysilicon  lm-to- lm me-
chanical interference caused by topography introduced during the process  ow. Third,
it can be used in surface micromachining of MEMS that are fabricated using multi-
ple structural layers to eliminate several fabrication issues related to photolithography
and  lm de nition. Fourth, it enables monolithic integration of electronic components
and surface micromachined structures [3]. While CMP has no in uence on the char-
acteristics of sidewall surfaces, by de nition, it strongly in uences the characteristics
of in-plane surfaces.
It is clear from the discussion in this section that each of the  ve processes
discussed here, which are either essential or extremely useful components of the mi-
cromachining technology, signi cantly in uence the performance and reliability of
MEMS devices through the surface characteristics of their contacting surfaces [32].
Fairly complex microstructures are fabricated by performing several rounds of the
deposition-lithography-etching cycle in conjunction with CMP. Leveraging the mature
infrastructure for deposition, lithography and etching from the IC industry, the micro-
machining technology has rapidly expanded and branched into three major branches,
namely, the LIGA process, Bulk micromachining and Surface micromachining. For
the sake of completeness, a brief description of all the three micromachining tech-
niques is provided in the following sections.
13
1.4.6 The LIGA Process
LIGA is a German acronym for Lithographie, Galvanoformung (electrodepo-
sition) und Abformung (molding). The LIGA process was developed in the 1980?s
for the mass production of microstructures with high aspect ratios, since those could
not be fabricated using the other two micromachining techniques [42]. It employs the
combination of X-ray lithography, electroforming and molding to fabricate microstruc-
tures and can be used to fabricate a wide variety of high aspect ratio microstructures.
It enables fabrication of three dimensional microstructures, which have arbitrary lat-
eral shapes, lateral dimensions of few micrometers and structural heights of several
hundred micrometers [46]. It allows usage of any metal or alloy as the structural layer
since in principle all metals and alloys can be electroplated [42]. Additionally, it can
also be used to fabricate microstructures using ceramic as well as plastic structural
layers [46]. Titanium and SiO2, which can be easily etched using HF solution, are
commonly used as the sacri cial layers in the microstructures fabricated using the
LIGA process [42,46].
1.4.7 Bulk Micromachining
Bulk micromachining is a technique, using which, microstructures are fabricated
in the silicon substrate itself, rather than on top of it. Consequently, the technique
is also known as substrate micromachining [41]. It was developed in the 1960?s. It
can be used to fabricate both stationary structures as well as structures that can
move with respect to the frame of the substrate [7, 45]. A useful advantage of bulk
micromachining is that since it relies on undercutting rather than sacri cial layer
etching for releasing the microstructures, signi cantly larger gaps between the sus-
pended free-standing structures and the substrate can be created using it than those
created using the other two micromachining techniques [7,45]. Additionally, since it
14
obviates the use of SiO2 as sacri cial material, it can be used to fabricate devices that
employ silica as a functional material [7,45].
1.4.8 Surface Micromachining
Surface micromachining is a technique, which is used to fabricate microstructures
above the substrate, by selectively etching the sacri cial layer sandwiched between
the substrate and the deposited patterned structural  lm. The microstructures fabri-
cated using the surface micromachining technique are anchored to the substrate but
can move freely with respect to it. Their in-plane dimensions are de ned using the
lithography and the etching processes, their thickness is de ned by the thickness of
the deposited structural  lm and their o set from the substrate (i.e., gap between the
top surface of the substrate and the bottom surface of the microstructures) is de ned
by the thickness of the deposited or grown sacri cial  lm. Although surface micro-
machining was  rst demonstrated in the 1960?s, using deposited thin metal  lms,
its use by the MEMS community increased signi cantly only after the introduction
of polycrystalline silicon (polysilicon) as the structural material for MEMS, in the
1980?s [3,41]. Presently, it is the most extensively used of the three micromachining
techniques [6]. It is used to fabricate static and dynamic MEMS using low-pressure
chemical vapor deposited (LPCVD) polysilicon  lms, LPCVD silicon nitride  lms as
well as polyimide  lms as structural  lms [6,41]. One of the several advantages of sur-
face micromachining is that it enables fabrication of integrated micro-systems, which
couple surface micromachined sensors and actuators with integrated electronics, on
the same chip [3]. Figure 1.3 is a simpli ed schematic illustrating the basic steps
involved in surface micromachining. A brief description of the basic steps involved
in the surface micromachining of polysilicon-based microstructures is also presented
here to contrast them with, and impress the relative simplicity and facileness of, those
involved in the surface micromachining of the microinstruments used in this study.
15
wafer
Single crystal silicon
Native oxide
Substrate
(a)
Thermal oxide
Isolation layer
(typically silicon nitride)
Substrate
(b)
Poly0 layer
(typically deposited)
Substrate
(c)
Patterned Poly0 layer
(using DRIE)
Substrate
(d)
(typically deposited)Sacrificial layer
Substrate
(e)
Patterned sacrificial
layer (using DRIE)
Substrate
(f)
Poly1 (Device) layer
(typically deposited)
Substrate
(g)
Released   structure
(after wet isotropic
etching of the sacrificial
layer)Substrate
(h)
\ "
Figure 1.3: A simpli ed schematic illustrating the basic steps involved in surface
micromachining. Notice that the \released" microstructure is a cantilever beam.
16
The substrate, which is used most commonly in the fabrication of polysilicon-
based surface micromachined microstructures is single-crystal-silicon wafer. Surface
micromachining of polysilicon-based microstructures begins with cleaning of the sub-
strate, after which, the cleaned surfaces of the substrate are oxidized thermally. An
electrical isolation layer (typically silicon nitride) is then deposited on the SiO2 layer
grown thermally on the substrate. Next, the  rst structural layer (typically polysil-
icon) \poly0" is deposited on top of the electrical isolation layer. Then, using pho-
tolithography and etching, the poly0 layer is patterned to de ne the ground planes as
well as the actuation pads of the microstructures. After patterning the poly0 layer,
a sacri cial (spacer) layer (typically silicon oxide or PSG) is deposited over it. In the
next step, the sacri cial layer is also patterned using photolithography and etching,
to reveal access windows to the underlying ground plane. Then, the second structural
layer (typically polysilicon) \poly1" is deposited on top of the patterned sacri cial
layer. Since the deposition of poly1 layer is conformal, it results in the formation of
a link between the poly0 and the poly 1 layers, through the access windows etched in
the sacri cial layer. This connection between the poly0 and the poly1 layers not only
anchors the microstructures to the substrate but is also used to electrically ground
them through the ground plane. Finally, using photolithography and etching, the mi-
crostructures, of desired designs, are de ned in the poly1 layer. This step completes
the surface micromachining of polysilicon-based microstructures but the microstruc-
tures do not become functional until the sacri cial layer is completely removed from
underneath them, which is usually accomplished by etching the sacri cial layer using
an isotropic wet chemical etching process. The suspended free-standing microstruc-
tures obtained after the complete removal of the sacri cial layer from underneath
them are termed as \released" microstructures.
17
1.5 Reliability of MEMS: A Challenge for the MEMS Community
Commercialization of a MEMS device demands that the device should not only
operate predictably and reliably in a variety of commonly encountered environments
but also perform e ciently even when subjected to extreme operating conditions or
put to service after a prolonged storage. Therefore, despite of having several other
commercially and technically attractive attributes such as high surface area to volume
ratio, small and precise size and geometry, of getting batch (parallel) processed, of
getting fabricated in a high throughput, high yield process and of getting integrated
with the required electronic circuitry on the same chip, most MEMS prototypes fail
to be commercially viable. Their reliability issues, which take over from the point of
releasing of microstructures, overshadow all the attributes that are bestowed on them
by micromachining and limit the extension of bene ts of those attributes only up to
the point of their fabrication [16]. While usually, the commercialization of MEMS
prototypes is primarily hindered by the quality concern associated with their poor
reliability, in the case of MEMS prototypes, which have applications in life-critical
systems such as those used in space applications and car airbags, it is primarily
hindered by the safety concern, which is associated with their poor reliability in
addition to the quality concern associated with it [65].
As mentioned earlier, the reliability and lifetime of a MEMS device depend on
the operating environment to which it is exposed and the mode in which it is op-
erated as well as the surface characteristics of its contacting surfaces, which in turn
depend on its design, the processes used to fabricate it and the treatments to which
it is subjected [32]. All of these factors have a strong in uence on the magnitude of
surface phenomena that ensue at interfaces between MEMS surfaces and are known
to be the main causes behind the failure of most MEMS devices. The operating
environment and the mode of operation of a MEMS device are de ned/ xed by the
targeted application but the characteristics of the surfaces of a MEMS device can be
18
manipulated desirably, to improve its reliability. However, in order to be able to ef-
fectively improve the reliability of MEMS devices by manipulating the characteristics
of their surfaces, it is essential to know which of the characteristics of the surfaces
of a MEMS device have a strong in uence on the surface phenomena that ensue at
interfaces between them, as well as understand why they have that strong in uence.
While it is known that the two characteristics of MEMS surfaces that strongly a ect
the magnitude of surface phenomena that ensue at interfaces between them are their
topography and chemistry, the mechanisms underlying the e ects of topography and
chemistry of MEMS surfaces on the surface phenomena that ensue at interfaces be-
tween them are still poorly understood [31]. Therefore, improving its presently poor
understanding of the e ects of surface characteristics of contacting MEMS surfaces
on the surface phenomena that lead to failure of MEMS is the biggest challenge cur-
rently faced by the MEMS community in improving the reliability and enabling the
commercialization of most useful MEMS prototypes. A brief overview of the various
phenomena that lead to failure of MEMS is provided in the following section.
1.5.1 Interfacial Forces
As the size scale shrinks from macroscopic to microscopic, the increasing ratio of
surface area to volume also increases the ratio of magnitude of surface forces to that of
volumetric forces. As explained earlier using the stainless steel grinding media illustra-
tion, when the characteristic dimension of an object decreases from a few centimeters
to a few micrometers, its surface area and hence the associated surface forces such
as capillary forces, Van der Waals (VDW) forces and electrostatic forces experienced
by it, which are proportional to the square of its characteristic dimension, increase
from being several orders of magnitude smaller to being several orders of magnitude
larger than its volume and the associated volumetric forces such as inertial forces,
19
gravitational forces and electromagnetic forces experienced by it, which are propor-
tional to the cube of its characteristic dimension, respectively [21, 28]. Therefore, in
the micro-domain, the surface forces become interestingly critical and have a much
greater signi cance and dominance than the corresponding body forces. On the other
hand, due to the increasing demand for tinier, more compact and more sophisticated
gadgets and leveraging the signi cant advances made in the  eld of micromachining
over the last two decades, an increasing number of MEMS devices with even smaller
dimensions, which range from a couple to a few thousand microns, are being devel-
oped [6, 21]. While those MEMS devices are commercially and technologically very
attractive and have a wide variety of useful applications, the reduced/extremely small
kinetic energies, start-up forces and torques involved in their operation, and available
to overcome the retarding resistive forces experienced by them, make surface forces,
which already have a high relative signi cance at the micro-scale, an even major
threat to their reliability and lifetime [21,66].
Depending on the operational parameters (i.e., electrostatic signals used for ac-
tuation) used, the surface characteristics of contacting surfaces (i.e., topography, sur-
face chemistry), the material properties of contacting surfaces (i.e., Young?s modu-
lus, shear modulus, fracture strength, hardness) and the environmental properties
(i.e., temperature, humidity) of the operating environment, some of the various sur-
face forces that ensue at interfaces between the contacting surfaces of a MEMS device
will have a stronger in uence on the tribological properties of its contacting surfaces
than others [3, 67, 68]. The various surface forces that ensue at interfaces between
contacting MEMS surfaces include capillary forces, Van der Waals (VDW) forces and
electrostatic forces, which are long range attractive forces and can strongly in uence
the tribological properties of the interface even when the two surfaces forming it are
signi cantly apart, as well as short range interactions such as hydrogen bonds, chem-
ical bonds and metallic bonds, which are e ective only when the two surfaces forming
20
the interface are in close proximity [68]. Interfacial interactions originating from dif-
fusion and alloying are generally very slow and weak at room temperature and hence
do not have a signi cant e ect on the tribological properties of contacting surfaces of
MEMS operated at room temperature [68]. The following section provides an insight
into the di erent types of interfacial forces that in uence the tribological properties
of MEMS interfaces.
Capillary Forces
The capillary forces that ensue at interfaces between the contacting surfaces of
a MEMS device are a manifestation of the surface tension of the liquid, to which, the
MEMS device is exposed during the release procedure [68]. The surface tension forces
are nonexistent as long as the device is completely submerged in the liquid [36]. They
begin to ensue when the upper surfaces of the device are removed from the liquid
and the device is exposed to the liquid-vapor interface, and even after the released
free-standing device is completely removed from the liquid, a thin layer of the liquid
remains trapped between each pair of adjacent  xed and movable plates present in
the device and a pressure di erential known as \Laplace Pressure" (PL) exists across
both the meniscuses of each trapped layer of the liquid [31, 36, 69]. The Laplace
Pressure across any liquid meniscus is determined using the Laplace-Young equation
(i.e., Eq. 1.5.1) shown below, where,  l is the surface tension of the trapped liquid
(with respect to air), r1 is the radius of curvature of the liquid meniscus that is
perpendicular to the two plate surfaces, between which, the liquid is trapped and r2
is the radius of curvature of the liquid meniscus that is parallel to them [67].
PL = P1 P2 =  l
 1
r1  
1
r2
 
(1.5.1)
21
Water
(a)
Water
(b)
Figure 1.4: A schematic diagram exhibiting the shape of the meniscus of a liquid
layer trapped between two (a) hydrophilic surfaces and (b) hydrophobic surfaces.
The arrows shown in the diagram indicate the direction of the Laplace force acting
on the upper (movable) plate with respect to the lower ( xed) plate.
P1 d
Hydrophilic Surfaces (P1 > P2)
P2
P1 d
Hydrophobic Surfaces (P1 < P2)
P2
22
Since the lateral dimensions of most MEMS structures are signi cantly larger than
the spacings between them (i.e., r2 r1), Eq. 1.5.1 can be reduced to Eq. 1.5.2 [67].
PL =  l
 1
r1
 
(1.5.2)
Further using Eq. 1.5.3 shown below, where,  1 and  2 are the contact angles made
by the trapped liquid on the two surfaces, between which, it is trapped, and d is the
distance of separation between those two surfaces, Eq. 1.5.2 can be expressed in terms
of measurable quantities, as shown in Eq. 1.5.4 [67].
d = r1(cos 1 + cos 2) (1.5.3)
PL =  l
 1
r1
 
=  lcos 1 + cos 2d (1.5.4)
Depending on the contact angles made by the trapped liquid on the surfaces of the
 xed and movable plates (i.e.,  1 and  2), the Laplace pressure may either pull the
movable plate towards the  xed plate or push it away from it, as shown in Fig. 1.4.
Surfaces on which, the contact angle ( ) made by a droplet of water is less than
90 , are considered as hydrophilic, and those on which, it is greater than 90 are
considered as hydrophobic [6]. Figure 1.5 illustrates how a droplet of water resides,
and the corresponding contact angles it makes, on a hydrophilic surface as well as
on a hydrophobic surface. As evident from Fig. 1.4, capillary forces can lead to
failure of only those MEMS devices that have hydrophilic surfaces [68, 70]. A good
example of a hydrophilic surface is a silicon surface covered with a thin layer of native
oxide. Hydrophilic surfaces have high surface energies owing to the presence of free
hydroxyl groups on them [67]. Additionally, they are known to adsorb from one to
several monolayers of water from the ambience [68]. The water  lms physisorbed on
hydrophilic MEMS surfaces do not desorb even when the surfaces are exposed to dry
23
Water
Hydrophilic  Surface
(a)
Water
Hydrophobic  Surface
(b)
Figure 1.5: A schematic diagram of (a) a hydrophilic surface and (b) a hydrophobic
surface. Also illustrated in both the diagrams, is the de nition of contact angle.
 <90 
 >90 
24
or vacuum ambients. Their complete desorption is reported to require temperatures
as high as 600 C [68]. Owing to these surface characteristics, hydrophilic surfaces are
always completely wetted by the solvents used in the release procedure, due to which,
when a MEMS device that has hydrophilic surfaces is pulled out of the rinse liquid
used in the  nal rinse step of the release procedure, its surfaces that are adjacent to
each other experience a strong capillary force, which acts to pull them together [67].
The capillary force (Fcp) experienced by adjacent hydrophilic MEMS surfaces when
they are pulled out from a liquid, is given by Eq. 1.5.5 shown below, where, Al is the
overlapping surface area of the two surfaces, between which, the liquid is trapped [66].
Fcp = Al lr
1
(1.5.5)
In order to arrest the capillary pull that is exerted by the trapped layers of the
rinse liquid, MEMS devices are usually subjected to drying treatments to remove
the trapped rinse liquid, immediately after they are pulled out from the rinse liquid.
However, while on one hand, the lowering of the vapor pressure of the rinse liquid
caused by the pressure di erential that exists across the meniscuses of the trapped
rinse liquid and the concentrated soluble impurities that are dissolved in it, makes
it extremely di cult to completely remove the trapped rinse liquid from the narrow
gaps between adjacent hydrophilic MEMS surfaces, on the other hand, even when
the trapped liquid is dried completely, the capillary pull experienced by the adjacent
hydrophilic MEMS surfaces is not averted completely because liquid droplets from
the ambience condense into the narrow gaps between them and continue to exert a
capillary pull on them [68]. If the MEMS surfaces are extremely smooth, the capillary
forces exerted on them by the condensed liquid droplets show no dependence on
the partial pressure that the vapors of the condensed liquid have in the ambience.
However, if they are rough, the capillary forces exerted on them by the condensed
25
liquid droplets show a strong exponential dependence on the partial pressure that
the vapors of the condensed liquid have in the ambience [66, 71]. This is a direct
consequence of the exponential dependence of the Kelvin radius (rk) on the relative
partial pressure that the vapors of the condensed liquid have in the ambience, which is
illustrated by Eq. 1.5.6 shown below, where, Vl is the molar volume of the condensed
liquid, R is the universal gas constant (i.e., its value is 8.314 Jmol 1K 1), T is the
temperature of the ambience in  K, pi is the pressure inside the condensed drop of
the liquid and po is the pressure of its vapors in the ambience [66,71]. If the liquid is
water, then the ratio pi/po represents the relative humidity of the ambience [66].
rk =  lVlRT ln(p
i=po)
(1.5.6)
Van der Waals (VDW) forces
Van der Waals forces (Fvdw), which are exerted by proximate or contacting sur-
faces on each other, are a manifestation of the interactions that occur between the
dipoles that are either present or induced in the surface atoms of those surfaces [13,70].
Unlike capillary forces, which ensue only at interfaces formed by hydrophilic surfaces,
they ensue at all interfaces irrespective of the chemistries of the surfaces forming
them. They are attractive in nature, and act to bring the proximate surfaces in
contact. Depending on the distance of separation between two surfaces, the VDW
forces experienced by them are classi ed as either non-retarded (short-range) or re-
tarded (long-range) VDW forces. If the distance of separation between the two sur-
faces is 20 nm or less, the VDW forces experienced by them fall in the non-retarded
regime [13, 68]. The VDW forces exchanged between two surfaces can be estimated
using Eqs. 1.5.7, 1.5.8a and 1.5.8b, where, H1 and H2 are the Hamakar constants
corresponding to the retarded and non-retarded regimes respectively, for the pair of
those two surfaces, h is the distance of separation between them, w and l are the
26
overlapping width and length of the two surfaces respectively, hc is the hard-wall
spacing between them at contact and z(x) is an arbitrary function that depends on
the surface topographies of the two surfaces [68]. As evident from Eqs. 1.5.7, 1.5.8a
and 1.5.8b, roughness of a surface signi cantly complicates the estimation of VDW
forces experienced by it and a mathematical function that precisely represents its
topography is required to accurately estimate them.
Fvdw;retarded = 
Z l
0
H1w
[h z(x)]4dx h z(x) > 20 nm (1.5.7)
Fvdw;non retarded = 
Z l
0
H2w
6 [h z(x)]3dx h z(x) >hc (1.5.8a)
= 
Z l
0
H2w
6 hc3dx h z(x) hc (1.5.8b)
Electrostatic Forces
Like the capillary and VDW forces, the electrostatic forces (Fe) experienced
by proximate or contacting MEMS surfaces are also attractive in nature and act
to bring them in contact. They can be induced by the release procedure induced
electrostatic charging of the surfaces, the di erence in the material work functions of
the surfaces forming an interface or a voltage externally applied across the interface
[13, 68, 70]. While the di erence between the work functions of contacting MEMS
surfaces usually does not exceed 1 V at equilibrium, the potential di erences induced
by the electrostatic charging of MEMS surfaces, at the interfaces formed by them,
can be in kV range [68, 70]. MEMS surfaces can get electrostatically charged either
during the etching of the sacri cial layers or during the drying of the microstructures
[68,70]. Large electric  elds associated with electrostatic actuation can also result in
27
electrostatic charging of MEMS surfaces by causing a signi cant amount of charge to
get trapped in the thin insulator  lms (i.e., silicon nitride or silicon oxide) present
on them [70]. The thin physisorbed  lm of water present on MEMS surfaces also
acts as an insulating  lm and traps charges [68]. Additionally, it is known that
even in the absence of an externally applied electric  eld, charges present in the
ambience accumulate on, and migrate across, the insulating  lms present on MEMS
surfaces [13]. Electrostatic forces experienced by proximate or contacting MEMS
surfaces can be estimated using Eqs. 1.5.9a and 1.5.9b, where,  is the e ective
dielectric constant of the insulating  lm that is sandwiched between the two surfaces,
w and l are the overlapping width and length respectively of the two surfaces, V
is the potential di erence across the interface formed by them, h is the distance of
separation between them, z(x) is an arbitrary function that depends on their surface
topographies and hc is the hard-wall spacing between them at contact [68]. Again,
Eqs. 1.5.9a and 1.5.9b indicate that the roughnesses of contacting MEMS surfaces
signi cantly complicate the accurate estimation of electrostatic forces that exist at
interfaces formed by them.
Fe =  wV
2
2
Z l
0
dx
[h z(x)]2 h z(x) >hc (1.5.9a)
=  wV
2
2
Z l
0
dx
hc2 h z(x) hc (1.5.9b)
Hydrogen Bonding
Hydrogen bonds are formed between the surface groups of two surfaces only when
the distance of separation between them is extremely small. Accordingly, the attrac-
tive forces associated with hydrogen bonding are not involved in bringing MEMS
surfaces together as they begin to act only after the MEMS surfaces are already in
28
close proximity. However, they do contribute in keeping the MEMS surfaces adhered
to each other. Although, while like the VDW forces, hydrogen bonding occurs at all
interfaces irrespective of the chemistries of the surfaces forming them, like the capil-
lary forces, its contribution in the total interfacial force is signi cant only at interfaces
formed by hydrophilic surfaces. Hydrophilic surfaces have a high density of groups
that have a strong tendency to form hydrogen bonds, such as free or polarized -OH
groups [13]. A completely hydrated silica surface has 5 free silanol groups per nm2.
The strengths of most hydrogen bonds are in the range of 10-40 kJ/mol [13].
Solid Bridging
A Solid Bridge is a speci c type of interfacial bond. Unlike other interfacial
bonds, which are formed between the surface atoms/molecules or surface functional
groups of proximate surfaces, a solid bridge cements together proximate MEMS sur-
faces that are separated by narrow gaps by forming a bridge of solid residue between
them. The constituents of a solid bridge are the non-volatile impurities, which pre-
cipitate out of the rinse liquid when it is evaporated during the drying of microstruc-
tures [70]. Those non-volatile impurities get accumulated in the narrow gaps between
proximate MEMS surfaces, and act as an adhesive, which adheres them together [70].
The non-volatile impurities, which form a solid bridge between proximate MEMS sur-
faces, are either present in the rinse liquid itself and directly introduced with it when
it is used during the release procedure, or formed by the dissolution of particles, sacri-
 cial  lms or structural  lms in the rinse liquid, during the release procedure [13,70].
Formation of a silica residue by the dissolution of polysilicon structural  lms in deion-
ized (DI) water, which is used for rinsing during the release procedure, has been con-
 rmed by Alley et al. using Auger electron spectroscopy [13,70]. The silica residue is
formed by the reaction of oxygen dissolved in the DI water with H-terminated surfaces
of polysilicon structural  lms that are exposed during the etching of the sacri cial
29
layers. Additionally, formation of  uorocarbon containing residues during the etching
of silicon dioxide sacri cial layers using HF has been con rmed by Gould and Irene
using in-situ ellipsometry and contact angle measurements [36, 40, 70]. It is di cult
to estimate the adhesive strength of a solid bridge, since it depends on the amount
as well as the density of the residue forming the bridge, both of which, are highly
variable and very di cult to determine accurately [13,68,70].
In addition to the attractive interfacial forces discussed in this section, a repulsive
interfacial force, which is induced by the deformation of the contacting asperities of
the two surfaces forming the interface, also exists at the interface, and tries to push the
two surfaces forming the interface apart from each other [13,68]. Accordingly, the net
interfacial force (i.e., attractive or repulsive) experienced by the two surfaces forming
an interface is an outcome of the balance between the attractive and repulsive forces
acting concomitantly on them. A plot illustrating how the more dominant interfacial
forces vary with the distance of separation between the two surfaces forming the
interface is shown in Fig. 1.6. The plots shown in Fig. 1.6 represent the capillary,
VDW and electrostatic forces experienced by a pair of atomically smooth silicon
surfaces, which are completely wetted by DI water, at room temperature. The hc for
most materials is in the range of 2 - 7  A and speci cally for atomically smooth silicon
surfaces, it is 5  A [13,70]. The H1 and H2 for a system consisting of a pair of clean Si
surfaces with air sandwiched between them as the dielectric are 1.8 eVnm and 1.7 eV
respectively [68, 70]. For reference, the variation in the Casimir forces (i.e., vacuum
energy level) experienced by a pair of atomically smooth, perfectly conducting plates
with the distance of separation between them is also shown in Fig. 1.6. The Casimir
forces (i.e., vacuum energy level) plotted in Fig. 1.6 are determined using Eq. 1.5.10,
where, Ap is the overlapping area of the pair of plates that experience the Casimir
forces, ~ is the reduced Planck constant, c is the speed of light in vacuum and h is the
distance of separation between the two plates [72]. Figure 1.6 clearly indicates that
30
at small separations, the dominant attractive interfacial forces are several orders of
magnitude greater than the typical restoring forces that are generated in most MEMS
devices.
Fcas = Ap~c 
2
240h4 (1.5.10)
1.5.2 Stiction
Stiction, which is a term coined by the magnetic recording media industry, is
used in the MEMS community to refer to unintentional and undesirable adhesion of
compliant MEMS structures [73,74]. Since MEMS structures have lateral dimensions
that typically range from 50 - 500  m and thicknesses that typically range from 0.1
- 10  m, and are o set from the substrate typically by 0.1 - 5  m, they have large
surface-area-to-volume ratios, which as explained in section 1.3, signi cantly increases
the in uence of surface/interfacial forces on their tribological behaviour [6, 9, 32, 66,
74{77]. Particularly, the interfacial forces experienced by the proximate surfaces of
a MEMS device, whose microstructures have hydrophilic surfaces, are several orders
of magnitude greater than the forces required to bend and bring them in contact. In
essence, the combination of the increased relative signi cance of the interfacial forces
at the scale of MEMS devices, the compliant nature of MEMS structures and the
small internal restoring forces that can be typically generated by most MEMS devices
makes proximate MEMS surfaces extremely susceptible to severe stiction. Stiction
is encountered by MEMS devices during the release procedure, which is classi ed as
release stiction, as well as after it, which is classi ed as in-use stiction [67, 78, 79].
Practically, every MEMS device is susceptible to either release and/or in-use stiction.
31
10 -10
10 -7
10 -4
10 -1
10 2
 1  10  100
Force per unit area, F/A (
?N/
?m
2 )
Separation between surfaces, (nm)
Typical range of
restoring forces
Fcas
Fvdw
 (H
1  = 1.8 eV nm, H
2  = 1.7 eV)
Fe  (V = 1 Volt)
Fcp  (?
1  = ?2  = 0, ?
l = 72.48 dyne cm -1
)
Figure 1.6: A plot illustrating how the Capillary, Van der Waals and Electrostatic
forces experienced by a pair of proximate atomically smooth silicon surfaces vary with
the distance of separation between them. For reference, the variation in the Casimir
forces (i.e., vacuum energy level) experienced by a pair of atomically smooth, perfectly
conducting plates with the distance of separation between them is also shown in the
plot. Additionally, the range of magnitudes of the restoring forces that are typically
generated in most MEMS devices is also indicated on the plot [66].
32
Release Stiction
Release stiction, which limits the yield of MEMS devices, is encountered when
microstructures are dried following their release. It is usually the  rst reliability issue
encountered with all MEMS devices. After the MEMS devices are micromachined,
the sacri cial layers, which encompass their structural layers, are usually dissolved
in a liquid etchant (this step is called as the release step) to render their movable
microstructures free-standing (released). The released microstructures are oxidized,
subjected to a series of rinsing using di erent solvents and  nally removed from the
liquid used for the  nal rinse, and dried. During drying, the microstructures get
exposed to a liquid-vapor interface. Exposure of adjacent MEMS surfaces to the
liquid-vapor interface that is created by the evaporating rinse liquid during drying
induces strong capillary forces between them. The induced capillary forces act to
bring the two surfaces together, in the same manner as that illustrated in Fig. 1.4a,
and are usually stronger than the internal restoring forces that are generated by most
MEMS devices. As the separation between the two surfaces decreases, the strength
of other interfacial forces acting between them also increases, eventually causing the
two surfaces to adhere permanently and result in device failure [77].
In-use Stiction
In-use stiction, which limits the lifetime and reliability of MEMS devices, occurs
when during storage or normal operation, the MEMS surfaces come in close proximity
of each other and experience attractive surface forces that are greater than the inter-
nal restoring forces generated by the corresponding microstructures [9, 76]. During
normal operation, MEMS surfaces may come into contact either unintentionally due
to overdriving electrical signals or mechanical instabilities such as excess acceleration,
or intentionally such as in applications which employ MEMS devices that consist of
microstructures that impact or shear against each other [11,76]. Additionally, during
33
storage as well as normal operation, exposure of MEMS devices, which have compo-
nents that are designed to touch each other, to environmental factors such as high
relative humidity (RH) leads to the formation of liquid bridges between their prox-
imate surfaces, which in turn, leads to the induction of strong attractive interfacial
forces between the proximate surfaces [76]. Most of the engineering solutions used to
address release stiction do not prevent adhesion from occurring during the operation
or storage of MEMS devices, and therefore cannot be used to address in-use stiction.
In-use stiction is commonly quanti ed by measuring the apparent work of adhesion
employing cantilever beam arrays [76].
1.5.3 Friction
The contact loads experienced by most MEMS interfaces during operation are
comparable to the adhesive forces existing at them [35,37,80]. Owing to the compa-
rable magnitudes of the contact loads and the adhesive forces experienced by MEMS
interfaces, and the fact that the adhesive forces existing at MEMS interfaces also act
as normal loads, the total normal load experienced by a MEMS interface strongly
depends on the stiction between the surfaces forming it. Consequently, the friction
forces exerted by a pair of contacting MEMS surfaces on each other also show a
strong dependence on the stiction between them [35,37,80]. Friction, like the stiction
experienced by MEMS devices, poses a severe threat to the commercial viability of
several useful MEMS prototypes. However, understandably, unlike stiction, friction
a ects the performance and reliability, and limits the lifetime, of only those MEMS
devices, which consist of components that are designed to impact or rub against each
other during operation [81]. Friction between contacting surfaces is reported to nega-
tively impact the dynamical behaviour of MEMS actuators and result in undesirable
modes of operation, if the drive signals used to actuate the MEMS actuators are not
optimized [66,82]. It has also been reported to increase the power requirements and
34
decrease the power output as well as e ciency of MEMS actuators [66, 82]. MEMS
devices, which cannot generate su cient driving forces to overcome the friction forces
experienced by their contacting components, do not function at all [81]. Addition-
ally, in all MEMS devices that have contacting components, friction leads to wear of
contacting surfaces, which eventually results in device failure [66]. Although, the fric-
tion forces experienced by contacting MEMS surfaces signi cantly impact both the
reliability and the performance of MEMS devices that have contacting components,
relatively fewer investigations to determine the factors that in uence them, and study
the mechanisms underlying their manifestation, have been conducted to-date [64].
1.5.4 Wear
While stiction between proximate surfaces mainly determines the reliability of
MEMS devices and friction experienced by contacting surfaces mainly determines the
e ciency of MEMS devices, wear of contacting surfaces mainly determines the lifetime
of MEMS devices [12]. In order to leverage the highly matured infrastructure of the IC
industry, MEMS devices are predominantly fabricated using silicon-based structural
 lms. While, owing to (among other reasons) its high Young?s modulus and low
density, silicon (monocrystalline and polycrystalline) is a good structural material for
MEMS devices that do not have contacting components, silicon-based MEMS devices
that have contacting components have a very limited lifetime because silicon surfaces
that contact (either intermittently such as at rotor-stator interface or continuously
such as at rotor-hub interface) each other during operation exhibit severe wear even
under moderate contact loads [11, 81, 83{85]. The hubs on microgears get visibly
cluttered with wear debris after only a few hundred thousand cycles. MEMS devices
such as microgears, linear racks, rotating platforms and pop-up mirrors, which have
components that experience high shear during operation, seldom last for more than a
few million cycles before the build-up of wear debris and increased friction irreversibly
35
binds them [11, 83]. The high wearability of MEMS surfaces that are derived from
silicon-based structural  lms is attributed to their high roughness, which signi cantly
reduces the real area of contact between them, and is responsible for the generation of
enormous contact pressures (even at moderate contact loads) at the interfaces formed
by them [11,81,83{85]. Although, wear of contacting surfaces is what predominantly
limits the lifetime of MEMS devices, relatively fewer studies have been conducted
to-date to understand the mechanisms that result in the wear of contacting MEMS
surfaces.
1.5.5 Fracture and Fatigue
Although, silicon (monocrystalline and polycrystalline) is a hard and brittle ma-
terial, to-date, fracture (without wear) of silicon-based components has never been
reported as the cause of failure of a MEMS device. Fatigue, which is a phenomenon
due to which materials subjected to alternating stresses degrade and fail pre-maturely,
on the other hand, has been reported to cause pre-mature failure of silicon-based
MEMS devices. For example, it is being considered as one of the possible failure
mechanisms that may be responsible for the limited lifetime of Texas Instrument?s
DMD [11]. Fatigue results in initiation of new  aws and/or growth of existing  aws,
and limits the long-term durability of MEMS. Fatigue induced damage results in loss
of sti ness, which degrades the performance of MEMS devices such as  lters and
other timing critical MEMS devices as well as MEMS sensors such as accelerometers
that rely on the invariance of the compliance of microstructures. Given the unsus-
ceptibility of bulk silicon to stress-corrosion cracking (at measurable rates) in water
or moist air, the ideal brittle nature of silicon due to its low dislocation mobility, the
limited fracture toughness of silicon-based structural  lms and the apparent absence
of extrinsic toughening mechanisms in the popular types of silicon-based structural
 lms produced using Low Pressure Chemical Vapor Deposition (LPCVD), one would
36
expect to not observe cyclic fatigue in the thin structural  lms that are derived from
silicon. However, the thin silicon  lms that are used as structural layers in MEMS
are observed to be susceptible to both fatigue crack initiation as well as fatigue crack
growth in moist air [86{92].
37
Chapter 2
Previous Studies: A Review
2.1 Stiction
The term \stiction" is used by the MEMS community to refer to the deleterious
e ects associated with adhesion, and the associated static friction, experienced by
MEMS components [6]. While stiction between proximate surfaces itself causes the
failure of the majority of MEMS prototypes, the two surface phenomena that cause
the failure of most of the remaining MEMS prototypes, namely the friction experi-
enced by, as well as wear of, contacting MEMS surfaces, also strongly depend on the
stiction experienced by the contacting surfaces of those MEMS prototypes [35,37,80].
Therefore, stiction between proximate surfaces is considered as the biggest obsta-
cle in the commercialization of MEMS prototypes, and hence, the most challenging
reliability issue faced by the MEMS community. Accordingly, most of the studies
conducted to-date to improve the reliability of MEMS devices have focussed on in-
venting strategies that can signi cantly reduce the stiction experienced by proximate
MEMS surfaces. The following sections provide a summary of the technological ad-
vances aimed at alleviating the issue of stiction that plagues the commercialization
of MEMS.
2.1.1 Release Stiction
As mentioned previously, stiction (speci cally release stiction) is the  rst relia-
bility issue encountered by every MEMS device. The engineering solutions developed
to address the issue of release stiction involve the use of either release or drying
techniques that eliminate the exposure of MEMS components to the liquid-vapor
38
interface, such as polymer-support ashing, dry-release methods such as hydro uoric
acid (HF) vapor etching, critical point drying (CPD) and freeze sublimation drying
(FSD) [4, 56, 93, 94]. Polymer-support ashing and HF vapor etching are techniques
used to release the microstructures, and critical point drying and freeze sublimation
drying are techniques used following the release step, to dry the microstructures. All
the engineering solutions that are commonly used to eliminate release stiction add
either additional and/or non-standard processing steps to the release procedure.
Vapor HF etching is a dry-release process. It completely eliminates the possi-
bility of released MEMS structures getting exposed to the liquid-vapor interface as
well as the need of rinse cycles that are used in conventional release procedures to
displace solvents, by employing a gaseous isotropic etchant for etching the sacri cial
layers. Usually, the chips that are released using HF vapor etching are placed upside-
down about 5 - 10 cm above a solution of conc. Hydro uoric acid, and heated to
maintain a temperature di erence of about 10 - 11.5  C between the sacri cial layers
being etched and the etching solution. The sacri cial layers are etched by the HF
vapors that are present in the vapor space between the etching solution and the chip
being released [56, 95{97]. Polymer-support ashing is a fairly complex, wet-release
process. It consists of, in addition to the steps that constitute the conventional re-
lease procedure, additional steps, which involve deposition, patterning and eventual
removal of a polymer layer. The polymer-support ashing process begins with par-
tially releasing the microstructures, which is accomplished by etching the sacri cial
layer using a timed etch. Next, a thin polymer  lm is deposited onto the partially
released microstructures. The deposited polymer  lm is patterned into support posts
that can hold the microstructures in place when the remainder of the sacri cial layer
is also etched away. Next, the sacri cial layer is completely etched away and the
microstructures are pulled out of the liquid. The polymer-support posts fabricated
on the microstructures prevent the proximate surfaces of the microstructures from
39
adhering under the in uence of capillary forces, which are experienced by them when
the microstructures are exposed to the liquid-vapor interface. Finally, the polymer-
support posts are burned away, typically by ashing in an oxygen plasma [76,94]. The
microstructures left behind after the ashing of the polymer-support posts are com-
pletely released and free-standing. It is clear from the above description that the
microstructures released using the polymer-support ashing process do not experience
release stiction. In other words, the polymer-support ashing process eliminates the
need of using a special drying technique to avoid release stiction.
MEMS devices that are dried using either the critical point drying technique or
the freeze sublimation drying technique are  rst released by etching their sacri cial
layers using an isotropic wet etchant. After the devices are completely released, they
are rinsed with a series of solvents, and  nally stored (in a submerged state) under
the rinse liquid that is used in the  nal rinse cycle until they are subjected to the
drying process. If the released MEMS devices are to be dried using the critical point
drying technique, then, the rinse liquid, under which they are stored, is displaced with
a short-alcohol (i.e., methanol, ethanol, isopropanol). Next, the devices are carefully
removed from the short alcohol solution and placed in a high-pressure chamber that is
already  lled with the same short-alcohol, without exposing them to the liquid-vapor
interface. Next, the high-pressure chamber is sealed and the short-alcohol solution
present in it is completely displaced with liquid carbon dioxide (CO2). Following
this, the chamber is,  rst isothermally pressurized up to a pressure greater than the
critical pressure of CO2, and then, isobarically heated up to a temperature greater
than the critical temperature of CO2, to transform the liquid CO2 present in it into a
supercritical  uid. After the CO2 present in the high-pressure chamber is completely
transformed into a supercritical  uid, it is slowly vented out of the chamber until the
pressure of the chamber reduces to atmospheric pressure. The venting of CO2 from
the high-pressure chamber is performed isothermally to ensure that the physical state
40
of the CO2 present inside the chamber never crosses the vapor-liquid line. After the
high-pressure chamber is completely vented, it is opened and the dried free-standing
MEMS devices are removed [93]. The freeze sublimation drying technique is very
similar to the critical point drying technique. It also begins with released MEMS
devices that are kept submerged under the rinse liquid used in the  nal rinse cycle
until they are subjected to the drying process. The rinse liquid, in this case, is
displaced through a series of gradual dilutions, with a solvent (i.e., t-butyl alcohol,
cyclohexane, water/isopropanol mixture), which has a high solid pressure even at near
room temperatures (i.e., 10 - 28  C). Next, instead of heating, the solvent, in this
case, is frozen with the released MEMS devices submerged in it, and maintained in
that state until the drying process is complete. The vapor above the solidi ed solvent
is continuously pumped away, using a vacuum pump, until the entire solid solvent is
completely sublimated. This leaves behind dry free-standing MEMS devices [4,40,68].
An expected, well-known disadvantage of the freeze sublimation drying technique is
that certain solvents can undergo a signi cant volume change when they are frozen,
and in doing so, can exert a signi cant amount of stress on, and damage the MEMS
devices submerged in them [76]. Figure 2.1 is a P-T diagram, which depicts the phase
paths that are followed during the critical point drying and the freeze sublimation
drying processes.
In theory, all the techniques discussed in this section should be equally e ective
in eliminating release stiction. However, in practice, they exhibit varied degrees of
success. Additionally, the implementation of each of them is non-trivial, and requires
specialized and costly equipments. Moreover, since the mechanism underlying each of
them can be e ective only during either the release or the drying of microstructures,
all of them can only prevent release stiction. None of them have a lasting e ect,
which can prevent proximate device surfaces from adhering during MEMS storage or
operation. In other words, none of them can prevent in-use stiction. The techniques
41
FSD
Pressure
Critical Point
Temperature
CPD
Solid
Liquid
Vapor
Supercritical Region
Figure 2.1: A P-T diagram depicting the phase paths followed during the critical point
drying and the freeze sublimation drying processes. Notice that in both the processes,
a longer phase path is intentionally followed to avoid crossing the liquid-vapor line.
42
that are used to address the issue of in-use stiction are discussed in greater detail in
the following sections.
2.1.2 In-Use Stiction
As explained in section 2.1.1, since release stiction occurs only during the release
step, most of the engineering solutions used to address it, while eliminate it with
varying degrees of success, are not e ective beyond the point of release of MEMS
devices. Therefore, they do not address the issue of in-use stiction, which by de -
nition, is experienced by MEMS devices after their release, either during storage or
during operation. Engineering solutions that are used to address the in-use stiction
experienced by MEMS devices include approaches that permanently change either
the topography and/or the chemical composition of their surfaces, and have lasting
e ects. The approaches are broadly classi ed into two categories: physical modi ca-
tion approaches and chemical modi cation approaches. In the physical modi cation
approaches, which are used to alter the topography of MEMS surfaces, microstructure
surfaces are textured to reduce the area of contact of surfaces that may touch each
other during storage or operation [66, 80, 98]. The various methods that are used to
permanently alter the topography of MEMS surfaces are discussed in greater detail
in section 2.4. The chemical modi cation approaches, which are used to alter the
chemistry of MEMS surfaces, involve grafting of hydrophobic molecules to MEMS
surfaces to alter the shape of meniscus made by water droplets on them [64, 70, 99].
They are aimed at eliminating the most prominent cause of stiction (i.e., capillary
forces).
One of the  rst strategies investigated to address the in-use stiction experienced
by MEMS devices employed a combination of both physical as well as chemical sur-
face modi cation approaches [100, 101]. It involved treating the surfaces of silicon-
based MEMS devices with NH4F or HF [100, 101]. This treatment etches away the
43
hydrophilic native surface oxide and terminates the treated silicon surfaces with hy-
drogen [100, 101]. Since Si-H bond is essentially non-polar, the treated surfaces are
hydrophobic in nature. Additionally, since NH4F preferentially etches (111) crys-
tallographic planes slower than the others, the treated surfaces also have a rougher
topography, and hence, a reduced area of contact. The two factors combined together
result in them experiencing a reduced in-use stiction. While this strategy is viable
for MEMS encapsulated in an inert (non-oxidizing) ambient, the treatment does not
have lasting e ects on MEMS operated in oxidizing ambients (i.e., air). This is be-
cause the H-terminated silicon surfaces slowly re-oxidize in air, thereby leading to
a recurrence of in-use stiction several weeks after the treatment [100]. Therefore,
for MEMS operated in oxidizing ambients, this strategy only delays the occurrence
of in-use stiction. Another strategy, which employs only the chemical modi cation
approach, involves depositing a low surface energy plasma-polymerized  uorocarbon
 lm on MEMS surfaces. A conformal  uorocarbon  lm is deposited on all the MEMS
surfaces including those that are underneath the microstructures if the deposition is
performed in the  eld-free zone of the plasma reactors used for depositing the  uoro-
carbon  lms [76,102]. However, deposition of a thick  lm on the top surfaces of the
microstructures is required to obtain a uniform coating on the surfaces underneath
them, which, is highly undesirable, since a thick as well as unidentical coating alters
the mechanical characteristics of the coated MEMS devices [103]. Also, this strategy
requires the microstructures to be released using some other release process before
they can be coated with the  uorocarbon  lm, indicating that it does not address
the issue of release stiction. A more e ective chemical modi cation approach based
strategy is to deposit a hydrophobic molecular thin  lm on MEMS surfaces. Indeed, it
has been con rmed by many research groups that self-assembled monolayers (SAMs)
deposited using the solution-based process are very e ective in reducing both release
44
as well as in-use stiction experienced by MEMS, if the coating is performed prop-
erly [13, 28, 35, 37, 64, 67, 73, 78, 80, 99, 104{107]. Tribology-related characteristics of
several di erent SAMs are reported and compared in the literature. They will be
discussed in greater detail in section 2.3.
In-use stiction is in uenced by a wider spectrum of factors and has a larger
time frame to occur than release stiction. Consequently, researchers have a poorer
understanding of in-use stiction, and hence, have achieved lesser success in addressing
the issue of in-use stiction than in addressing the issue of release stiction. This is
evident from the fact that while atleast some of the engineering solutions devised
to address release stiction are able to completely eleminate it, all the engineering
solutions devised to address in-use stiction can at best only reduce it. Additionally,
none of the several treatments used to mitigate in-use stiction address all the factors
that strongly in uence it. Therefore, in-use stiction still remains the focus of intense
research in the MEMS community.
2.2 Friction
Friction was  rst studied in the late  fteenth century, by Leonardo de Vinci, who
postulated that friction between two contacting surfaces is proportional to the normal
load applied at their interface [108]. Later in 1699, a french engineer named Amonton
rea rmed Leonardo de Vinci?s postulate and further postulated that friction between
two surfaces is independent of the area of contact between them [108]. The distinc-
tion between static and dynamic friction was  rst made in 1781, by Coulomb, who,
in addition to verifying the postulates proposed by Amonton and Leonardo de Vinci,
proposed two explanations of the physics underlying the phenomena of friction [108].
One explanation suggested that the interlocking of the asperities present on the con-
tacting surfaces is the source of friction between them while the other suggested that
45
the molecular adhesion between the contacting surfaces is responsible for it [108]. Ow-
ing to the observed independence of the friction experienced by contacting surfaces
on the area of contact between them, initially, the former explanation was accepted
and the latter was rejected [108]. However, later in the 1940?s, due to the revelation
of the fact that the real area of contact between surfaces is signi cantly lesser than
the observed area of contact between them, the latter explanation was accepted and
the former was rejected, since the latter explanation no more contradicted the obser-
vation that the friction experienced by contacting surfaces does not depend on the
apparent area of contact between them [108]. Since then, several studies have been
conducted to better understand the physics underlying the phenomena of friction,
and determine the various factors that in uence it.
Despite of several studies conducted to understand the mechanisms underlying
the friction experienced by contacting MEMS surfaces, it still remains a relatively
poorly understood tribological property. Even today, the coe cient of friction of
contacting surfaces is determined using empirical models. While for materials with
known mechanical properties, the plastic deformation theory may be used to esti-
mate the coe cient of friction, for other materials, the coe cient of friction can only
be determined experimentally, using Coulomb?s friction model, which states that the
friction force between two surfaces is proportional to the normal load applied at their
interface and the constant of proportionality is their coe cient of static friction [65].
Therefore, even today, there is a need for in-depth understanding of the factors that
lead to friction between contacting surfaces so that the physics underlying it can be
quanti ed using an appropriate model. Further, most materials exhibit di erent fric-
tion behaviour at di erent scales. While the macro-scale experiments conducted using
a pin-on-disc tribometer con rm that at the macro-scale the friction force exerted by
most materials obeys the Amonton?s law, the nano-scale experiments conducted using
an atomic force microscope indicate that the friction force experienced by nanoscopic
46
contacts varies locally [109]. The local variations in the nano-scale friction directly
correspond to the local slopes of the contacting surfaces, and are attributed to the
anisotropy in their surface roughnesses, which are a direct consequence of the tech-
niques used to prepare them [109]. Additionally, studies conducted at the micro-scale
indicate that friction between microscopic contacts exhibits two regimes [109]. In one
regime, it obeys the Amonton?s law, and the corresponding coe cient of friction is
constant and shows no dependence on the normal load applied at the contact inter-
face, in the other regime, the coe cient of friction of contacting surfaces shows a
strong dependence on the normal load applied at their interface [109]. Therefore, to
better understand the mechanisms that lead to friction between contacting MEMS
surfaces, the investigations should be conducted at the micro-scale, using dedicated
test devices, which physically more appropriately represent the real MEMS devices.
Friction at MEMS interfaces, like stiction, is strongly in uenced by the character-
istics of the surfaces forming the interface. For example, the tribochemical reactions
(chemical reactions induced at an interface by the rubbing of the surfaces forming the
interface) between the surface molecules of contacting surfaces are reported to have
a strong e ect on the friction experienced by them [11]. Similarly, the native surface
oxide present on MEMS surfaces is observed to have a signi cant in uence on the
friction behaviour of contacting MEMS surfaces [65]. A study, which investigated the
e ect of ambience on the friction force exerted by contacting MEMS surfaces on each
other, reported that contacting MEMS surfaces experience less friction in air than in
vacuum [65]. The study attributed the observed results to the lubricating e ect of the
contaminants that deposit on the contacting surfaces from the ambience, since the
replenishment of contaminants, which may wear-o during sliding, is expected to be
less in vacuum than in air [65]. Other studies have reported that while at higher nor-
mal loads, the friction force experienced by contacting MEMS surfaces depends only
on the normal load externally applied at their interface, at lower normal loads, which
47
are more representative of the loads experienced by contacting MEMS surfaces dur-
ing operation, it also shows a strong dependence on the stiction between them. The
strong in uence that stiction between contacting MEMS surfaces has on the friction
experienced by them at lower normal loads is the reason why the structure of water
molecules physisorbed on contacting MEMS surfaces also has a strong in uence on
the friction between them [32,67]. It is also the reason why friction between contact-
ing MEMS surfaces is also strongly altered by the same factors (i.e., environmental
factors such as RH, surface modi cations, etc.) that alter the stiction between them.
Consequently, the same surface modi cations that are known to successfully address
in-use stiction are used to reduce the friction experienced by contacting MEMS sur-
faces, to improve the reliability of MEMS devices [44]. Although past studies have
revealed the various factors that in uence the friction force existing at MEMS inter-
faces, to-date, the mechanisms underlying the in uence of those factors are at best
only postulated.
2.3 Self Assembled Monolayers
As mentioned in section 2.1.2, one of the most e ective anti-stiction treatments
employs the chemical modi cation approach to successfully address both release as
well as in-use stiction, and involves deposition of a thin molecular  lm onto mi-
crostructure surfaces. The deposited molecular  lm is called a self-assembled mono-
layers (SAM) since during its deposition, the precursor molecules  rst attach them-
selves to the microstructure surfaces and then align and orient themselves with each
other, thereby forming a thin  lm with a certain degree of order at the molecular
level. The precursor molecules that are typically used to form anti-stiction SAMs
on microstructure surfaces have a polar head, which chemically binds to the mi-
crostructure surface and a non-polar tail, which points away from it. Figure 2.2 is
a schematic representation of a typical precursor molecule. The non-polar tails of
48
the precursor molecules that constitute a SAM align and orient themselves together,
thereby assembling a thin surface  lm that consists of close-packed non-polar chains,
which terminate with non-polar groups. Accordingly, the SAMs typically have a
very hydrophobic surface, due to which, they are very e ective in reducing stiction
experienced by MEMS surfaces.
Indeed, several studies have demonstrated that SAM coatings deposited using
a solution-based process successfully address several of the tribological issues that
plague MEMS, if the coating process is appropriately integrated with the MEMS
release process [6,64,80,99,107,110{113]. Speci cally, SAMs are reported to reverse
the shape of the meniscus formed, during the drying process that follows the release
process, by the liquid layer trapped between proximate microstructure surfaces. This
e ect, which is reported to completely eliminate release stiction, has been veri ed
by measuring the contact angle made by water droplets on SAM-coated surfaces.
Water contact angle is reported to increase from <30 on native oxide covered silicon
surfaces to 110 on SAM-coated surfaces [6]. SAMs are reported to also reduce
the in-use stiction (quanti ed by measuring the apparent work of adhesion using
CBAs) experienced by native oxide covered silicon MEMS surfaces by four orders
of magnitude [6]. Additionally, SAMs deposited on the contacting surfaces of the
microengines are reported to signi cantly reduce the friction experienced by them.
This has been qualitatively determined by monitoring the input signals (or mechanical
probing) required to start the microengines [6]. Moreover, some of the SAMs can
even survive the typical packaging processes (some SAMs are thermally stable up to
temperatures as high as 400 C in several, including oxygen containing, environments)
used in the MEMS industry [6]. This further enhances their usability for improving
the reliability of MEMS devices.
49
Non?polar tail group
Polar head group
Si
Cl ClCl
Figure 2.2: A schematic diagram of a typical precursor molecule. The non-polar
tail shown in the diagram is a C18 hydrocarbon chain and the polar head group is a
trichlorosilane molecule.
50
To-date, several di erent classes of precursor molecules have been explored for the
formation of SAMs on MEMS surfaces. Examples include alkyl- and per uoroalkyl-
trichlorosilanes (R-SiCl3), dichlorosilanes, alkane-thiols and several other classes of
organic molecules. Among the various explored classes of precursor molecules, the
class that is by-far the most widely used is chlorosilanes.
2.3.1 Chlorosilane Based Self-Assembled Monolayers
Coating a MEMS surface with chlorosilane-based SAMs requires the presence
of free hydroxyl groups on it. Formation of chlorosilane-based SAMs is a two-step
process. In the  rst step, which takes place in the precursor (coating) solution itself,
the precursor (i.e., chlorosilane) molecules are completely hydrolyzed. For example,
a trichlorosilane precursor molecule will react with three molecules of water (present
in the precursor solution) and get hydrolyzed into its trisilanol form along with pro-
ducing three molecules of hydrochloric acid. A balanced chemical reaction depicting
the  rst step of trichlorosilane-based SAM formation process is shown below.
RSiCl3 + 3H2O ! 3HCl + RSi(OH)3
The water molecules required to hydrolyze the chlorosilane precursor molecules are
usually supplied to the coating solution by exposing it to the ambient humidity (and
not added to it), since the organic solvents generally used to prepare the coating
solution are typically fairly hygroscopic and absorb su cient water molecules from
the ambient air. However, in order to obtain a good coating, it is necessary to
ensure that while the coating is being performed, the relative humidity (RH) of the
ambience is in the range of 40-70%. If the RH of the ambience is too low (i.e., <40%),
then the amount of water molecules that get absorbed in the coating solution is too
little to hydrolyze the entire amount of precursor molecules needed to obtain a SAM
with complete surface coverage. On the other hand, if the RH of the ambience is
too high (i.e., >70%), then more than required water molecules are taken up by
51
the solvent from the ambience. This results in bulk polymerization of the precursor
molecules, in the coating solution itself, which has detrimental e ects on the MEMS
being coated. In the second step of the chlorosilane-based SAM formation process,
the silanol forms of the precursor molecules interact with the hydrophilic surface
layer, such as the native oxide layer, present on the MEMS surfaces. Typically, the
hydrophilic surface layer (i.e., native oxide) present on the MEMS surfaces has a layer
of water molecules physisorbed on it. Therefore, the hydrolyzed precursor molecules
that interact with the MEMS surfaces orient themselves in such a way that their
polar head-groups are directed towards the surface, and interact with the polar water
layer present on it, while their non-polar tail-groups are isolated from the polar water
layer and directed away from it. The hydrolyzed precursor molecules then di use
along the microstructure surface and/or interact with the neighbouring hydrolyzed
precursor molecules until they lock themselves in a place by cross-linking with the
neighbouring hydrolyzed precursor molecules and/or the microstructure surface [114].
The cross-linking involves condensation reactions between the hydroxyl groups of the
neighbouring hydrolyzed precursor molecules or the hydroxyl groups of the hydrolyzed
precursor molecules and the hydroxyl groups of the hydrophilic layer present on the
MEMS surface, which eliminate water and result in the formation of Si-O-Si bonds
at the SAM-native oxide interface and between the precursor molecules adsorbed
adjacent to each other on the microstructure surface. Although the actual mechanism
of the second step of the chlorosilane-based SAM formation process is still debated
in the research community, the simpli ed conceptual model illustrating it, shown in
Fig. 2.3, is most widely accepted [115,116].
SAMs were  rst considered for alleviating the stiction experienced by proximate
MEMS surfaces by Alley et al., in the 1990?s [70]. In particular, Alley et al. examined
a SAM coating derived using octadecyltrichlorosilane (OTS) as the precursor, using
arrays of polysilicon cantilever beams. They reported that the OTS SAM signi cantly
52
OH OH OH OH
OH OHOH
Si
OH OHOH
Si
OH OHOH
Si
OH OHOH
Si
O O O
Native oxide
Substrate
O O O
Native oxide
Substrate
O
Si Si Si SiO
O
O
H OH
Figure 2.3: A simpli ed, conceptual model illustrating the second step of the chlorosil-
ane-based SAM formation process. The  rst step (not shown) is the complete hydrol-
ysis of the precursor molecules, which results in the formation of 3 HCl molecules per
precursor molecule as well as the trisilanol forms (shown in this  gure) of the pre-
cursor molecules. In the second step, which is shown in this  gure, water elimination
(condensation) reactions result in Si-O-Si linkages between the adjacent hydrolyzed
precursor molecules and/or the native oxide layer present on the substrate. The pre-
cursor molecules shown in the  gure are octadecyltrichlorosilane (CH3(CH2)17SiCl3)
molecules.
53
reduced release stiction. However, they could not quantity the reduction in the release
stiction due to the high sti nesses of the cantilever beams used in their study. Based
on the ability of the OTS SAM to reduce release stiction, Alley et al. further suggested
that OTS SAM can also be an e ective post-release (in-use) anti-stiction lubricant.
Since then, several other research groups have investigated the e ectiveness of OTS
SAMs in addressing the tribological issues of MEMS. Deng et al. demonstrated
that SAM-coated polysilicon wobble motors are less prone to release stiction and
additionally their contacting surfaces have signi cantly improved wear properties [110,
111]. They reported that motors coated with OTS SAM operated for nearly 80 million
cycles, over a period of nine months, indicating low wear and good durability of the
OTS SAM present on motor surfaces that were in continuous moving contact. Also,
Cl echet et al., who investigated the lubricating properties of an OTS SAM coated on
oxidized Si(100) surfaces using a conventional pin-on-disc tribometer, reported that
the coe cient of dynamic friction, which is typically 0.6 - 0.7 for silicon surfaces with
only native oxide on them, is reduced to about 0.12 when the same silicon surfaces are
coated with an OTS SAM [117]. Houston et al. were the  rst to integrate the steps
involved in the OTS SAM formation process with those involved in the process used
to release MEMS devices [13,64]. They reported that the release stiction experienced
by MEMS test devices was e ectively eliminated, and the apparent work of adhesion
(in-use stiction) exhibited by them was reduced by three orders of magnitude, by
coating their native oxide covered surfaces with an OTS SAM [13,64].
While OTS is the most widely investigated precursor molecule, many other pre-
cursor molecules of the forms RSiCl3, R,R SiCl2, R2SiCl2 and R,R ,R  SiCl have also
been investigated for the formation of ordered hydrophobic SAMs on oxidized silicon
surfaces, where, R, R and R represent distinct aliphatic hydrocarbon chains. In fact,
it has been demonstrated that the most hydrophobic SAMs are those that are derived
54
from  uorinated alkyltrichlorosilane precursors [118]. Indeed, the critical surface ten-
sion exhibited by a 1H,1H,2H,2H-per uorodecyltrichloro silane (FDTS) SAM (i.e., 6
mJ/m2) is signi cantly lesser than that exhibited by Te on (i.e., 15 mJ/m2) and OTS
SAMs (i.e., 22 mJ/m2) [119]. Therefore, a FDTS SAM coating is expected to be more
e ective in addressing the tribological issues of MEMS than an OTS SAM coating.
Indeed, the apparent work of adhesion exhibited by the FDTS SAM coated MEMS
surfaces is lower than that exhibited by the OTS SAM coated MEMS surfaces [80].
A comparison between the  lm properties of the most widely investigated SAMs is
shown in Table 2.1 [6,35,64,80,99].
Besides the alkyl- and per uoroalkyl- trichlorosilane precursor molecules, the
dialkyldichlorosilane class of precursor molecules has also been considerably explored
for the formation of SAMs on oxidized silicon surfaces. The most widely investigated
dialkyldichlorosilane precursor molecule is the dimethyldichlorosilane ((CH3)2SiCl2,
DDMS) molecule. Several studies comparing the  lm properties of the DDMS SAM
with those of the OTS SAM as well as their e ectivenesses as anti-stiction coatings
for MEMS have been reported in literature [35,105]. While the coating processes used
to deposit the DDMS and OTS SAMs are identical to each other, there are important
di erences in the properties of the SAMs formed. The main advantages of the DDMS
SAM over the OTS SAM are its higher thermal stability in air as compared to the
OTS SAM and the lesser tendency of its precursor molecules as compared to the OTS
precursor molecules to polymerize in the coating solution itself. The main drawbacks
of the DDMS SAM are the higher coe cient of friction and the higher apparent
work of adhesion (in-use-stiction) exhibited by the DDMS SAM coated surfaces as
compared to the OTS SAM coated surfaces. Other precursor molecules of the form
R2SiCl2 that have been investigated for the formation of SAMs on oxidized silicon
surfaces are dichlorodiethylsilane ((C2H5)2SiCl2, DDES) and dichlorodipropylsilane
((C3H7)2SiCl2, DDPS) [105]. Studies reported in the literature indicate that unlike
55
their trichlorosilane counterparts, an increase in the chain length of the symmetric
dialkyldichlorosilane precursor molecules neither increases the water contact angle
nor improves the anti-stiction properties of the SAMs formed using them. Moreover,
the thermal stabilities (in air) of the DDES and the DDPS SAMs are inferior than
that of the DDMS SAM. In essence, DDMS is clearly the most e ective member of
the symmetric dialkyldichlorosilane class of precursor molecules, for the formation of
anti-stiction SAMs.
2.3.2 Limitations Imposed by the Chlorosilane Chemistry
While on one hand, properly formed chlorosilane-based SAM coatings are very
e ective in improving the tribological behaviour of the MEMS surfaces coated with
them, on the other hand, their formation process has a number of limitations in-
trinsically related to the chemistry involved in their formation, which motivates the
MEMS community to search for an alternative to replace them. Irrespective of the
precursor used, the  rst step in the formation of any chlorosilane-based SAM is the
hydrolysis of one or more Si-Cl bonds of the precursor molecules. The hydrolysis
reaction generates one equivalent of HCl for each Si-Cl bond that is hydrolyzed in
this step. The presence of HCl, which is formed as a by-product in the  rst step of
the chlorosilane-based SAM formation process, in the chlorosilane-based SAM coating
solution makes it corrosive for integrated MEMS devices that have exposed metal-
lic components [10]. Therefore, integrated MEMS devices, which invariably contain
metallic components, cannot be exposed to chlorosilane-based SAM coating solutions,
and hence, chlorosilane-based SAMs are not a viable alternative to improve their re-
liability. Additionally, the formation of chlorosilane-based SAMs on MEMS surfaces
requires the presence of free -OH groups on them. Therefore, the surfaces of all MEMS
devices are always oxidized before coating them with a chlorosilane-based SAM. This
is usually accomplished by growing a thin layer of chemical oxide (i.e., 20  A thick)
56
Table 2.1: A comparison between the  lm properties of OTS, FDTS and oxide surface
 lms [6,35,64,80,99].
Surface Contact Angle App. Work Coe . of Thermal Degree of
Film Water Hexadecane of Adhesion Static Stability Particulate
(mJ/m2) Friction in Air ( C) Formation
OTS 110 38 0.012 0.07 225 High
FDTS 115 68 0.005 0.10 400 Very High
Oxide 0-30 0-20 20.000 1.10 - -
57
on them, by exposing the MEMS device to an oxidizing agent such as hydrogen per-
oxide during the release process. Since the oxide layer grown on MEMS surfaces is
electrically insulating, and conformally present on all them, it is a concern in case
of some MEMS devices because it can trap charges, which can lead to unpredictable
performance and/or failure of those MEMS devices [113].
The ability, and the tendency of the chlorosilane (precursor) molecules to poly-
merize in the coating solution itself (bulk polymerization) is another limitation of
the chlorosilane-based SAM formation process [107,120]. Polymerization of precursor
molecules in the coating solution results in the formation of large agglomerates in
it, which get deposited on the MEMS surfaces being coated during the coating pro-
cess. The agglomerates (i.e, polymerized clusters of SAM precursor molecules) can
be several microns in diameter, and can mechanically interfere with the operation of
a MEMS device, thereby a ecting its performance and reliability. Figure 2.4a is an
AFM image of an OTS coated Si(100) surface, which has polymerized agglomerates
of precursor molecules deposited on it [35]. The linescan shown in Fig. 2.4b con rms
that some of the agglomerates visible in Fig. 2.4a are as wide as 2  m and as high as
490 nm. Unfortunately, presently, there is no method available to satisfactorily remove
the polymerized clusters, once they are deposited on the substrate or the surfaces of
microstructures. However, since the ability/tendency of the precursor molecules to
polymerize stems from the presence of more than one functional groups in them, us-
ing precursor molecules that have only one Si-Cl bond reduces the likelihood of them
polymerizing in the coating solution itself. This is in fact the motivation behind the
exploration of precursor molecules of the form R,R SiCl2, R2SiCl2 and R,R ,R  SiCl
for the formation of chlorosilane-based SAM coatings on MEMS surfaces.
Besides the limitations discussed above, which are implicitly imposed by the
chemistry of the reactions involved in the formation of the chlorosilane-based SAM
coatings, the coating process is very cumbersome too. In order to obtain a good
58
quality chlorosilane-based SAM, the SAM coating solution must be freshly prepared
and appropriately conditioned immediately before the coating is performed. This
requirement is due to the sensitivity of the chlorosilane-based SAM coating solution
to the ambient relative humidity and the ability/tendency of the chlorosilane precursor
molecules to polymerize in the coating solution itself in the presence of excess relative
humidity. As mentioned earlier, a hydrolysis step is required for the formation of
the chlorosilane-based SAMs, and the water, which is a reagent, necessary for that
step is made available in the chlorosilane-based SAM coating solution through mass
transfer of the water vapor present in the ambient air. Therefore, it is necessary
to control the relative humidity of the ambience such that while the water present
in the chlorosilane-based SAM coating solution is su cient to hydrolyze the required
number of precursor molecules, it is insu cient to promote their bulk polymerization.
In essence, great care and control must be exercised during the coating process to
obtain a good quality chlorosilane-based SAM.
Some of the issues associated with the solution-phase process used to deposit the
chlorosilane-based SAMs can be eliminated by carrying out the deposition in the vapor
phase. It has been demonstrated that the tridecafuoro-1,1,2,2-tetrahydrooctyltrichlor-
osilane (CF3(CF2)5(CH2)2SiCl3, FOTS) SAMs deposited using the vapor-phase SAM
formation process exhibit a similar apparent work of adhesion as that exhibited by
the FOTS SAMs deposited using the solution-phase SAM formation process [38]. Al-
though the vapor-phase chlorosilane-based SAM formation process does not eliminate
the formation of HCl as the by-product, it reduces the threat that HCl poses to the
exposed metallic components of integrated MEMS devices. The HCl generated during
the vapor-phase deposition of chlorosilane-based SAMs is a gas, which does not cor-
rode metals. Additionally, the stoichiometry of precursor and water molecules can be
more precisely controlled in the vapor-phase SAM formation process. Accordingly,
59
(a)
 0
 200
 400
 600
 0  5  10  15  20  25  30
nm
?m
(b)
Figure 2.4: (a) AFM image of an OTS coated Si(100) surface. The RMS roughness
of the surface based on image statistics is 25 nm. (b) Linescan along the white line
drawn across image a. Notice that some of the particulates visible in image a are as
wide as 2 micron and as high as 490 nm.
60
the vapor-phase SAM formation process enables the suppression of the bulk poly-
merization of precursor molecules. Further, the vapor-phase chlorosilane-based SAM
formation process eliminates the use of organic solvents, the need of freshly preparing
and conditioning the SAM coating solution immediately before performing the coat-
ing and the need of controlling the relative humidity of the ambience. Accordingly,
it is relatively much simpler than the corresponding solution-phase SAM formation
process. Since the vapor-phase depositions of SAMs are performed in low pressure
CVD-style reactors, it is possible to perform in-situ plasma cleaning of the samples
before the deposition as well as in-situ measurements of the  lm growth during the
deposition. The monitoring capability provided by the vapor-phase SAM formation
process enables tuning of the process, which results in excellent process uniformity as
well as reproducibility [38]. However, the vapor-phase SAM formation process also
has a few drawbacks. It does not eliminate the need of an oxide layer to be present on
the surfaces to be coated with the chlorosilane-based SAM. Also, it necessitates the
use of an alternate process to release the microstructure before they can be coated
with a SAM. Additionally, the vapor-phase SAM formation process is a feasible al-
ternative only for those precursors that have su cient vapor-pressures at the desired
temperatures.
2.3.3 Non-Chlorosilane Based Organic Coatings
In order to eliminate the need of an oxide layer to be present on the surfaces
to be coated with a SAM, several non-chlorosilane-based organic coatings have been
investigated as potential surface modi cations, for addressing the tribological issues of
MEMS. None of those coatings require an inter-linking oxide layer. They attach alkyl
chains to the silicon surface either directly or through an intermediate head group. For
example, Bansal et al. utilized the surface reactions of alkyl-lithium (e.g., C18H37Li)
and alkyl-Grignard (e.g., C18H37MgBr) with Cl-terminated Si surfaces to form densely
61
packed alkyl monolayers on silicon surfaces, in a two step process [6, 121]. In the
 rst step, a H-terminated Si surface was transformed into a Cl-terminated Si surface
by exposing it to a solution of PCl5 in chlorobenzene at an elevated temperature,
and in the presence of a catalytic amount of a radical initiator [121]. The second
step was the surface reaction between the Cl-terminated Si surface and the chosen
reagent. When an alkyl-lithium reagent was used, LiCl was eliminated, forming
a direct alkyl-Si linkage. When an alkyl-Grignard reagent was used, MgBrCl was
eliminated, also forming a direct alkyl-Si linkage. Bansal et al. characterized the -
C18H37 functionalized Si surfaces by determining the asymmetric methylene stretching
peaks exhibited by them using Multiple-internal-re ection Fourier-transform infrared
spectroscopy (FTIR) [121]. They reported that the asymmetric methylene stretching
peaks exhibited by the -C18H37 coatings obtained using both the alkyl-Li as well as the
alkyl-Grignard reagents indicated the presence of highly crystalline environments of
packed alkyl chains on the corresponding coated Si surfaces [121]. Zhu and co-workers
have also developed a two step process, which attaches alkyl chains to a Cl-terminated
silicon surface via Si-O or Si-N linkages [122{124]. In particular, they explored the
surface reactions of molecules of the form R-NH2 and R-OH with Cl-terminated Si
surfaces, in vacuum as well as in a solution. Again, the  rst step was to produce
a Cl-terminated Si surface. Zhu and co-workers obtained Cl-terminated Si surfaces
by exposing the H-terminated Si surfaces to Cl2 gas in vacuum, while simultaneously
either heating them and maintaining their temperature at about 80  C or illuminating
them with a tungsten  lament. The second step was the surface reaction between the
Cl-terminated Si surface and the chosen precursor (i.e., R-NH2 or R-OH). The surface
reaction was accomplished either in the vapor-phase by exposing the Cl-terminated
Si surface to the vaporized precursor molecules (i.e., R-NH2 or R-OH) in vacuum or
in the solution-phase by keeping the Cl-terminated Si surface in the solution that
contains the desired precursor molecules. When a molecule of the form R-NH2 is
62
used as the precursor, the surface reaction results in bridge bonding of the -N- of the
precursor molecules to two adjacent Si atoms on the Si surface, and generation of two
HCl molecules from every molecule of the precursor that is attached to the Si surface.
When a molecule of the form R-OH is used as the precursor, the surface reactions
result in the formation of O-Si bonds between the precursor molecules and the Si
surface, and generation of one HCl molecule from every molecule of the precursor
that is attached to the Si surface. Zhu and co-workers used X-ray photoelectron
spectroscopy (XPS) and interfacial force microscopy (IFM) to characterize the coated
Si surfaces. They reported that the  lms obtained using both types of precursors (i.e.,
R-NH2 and R-OH) had packed alkyl chains and ordering, similar to those of the  lms
obtained using the methods discussed earlier in this section [125].
While all the non-chlorosilane-based organic coatings discussed up to this point
do seem to have a promising potential for addressing some of the tribological issues of
MEMS, none of them have yet been tested on test devices that are representative of
real MEMS. The only new class of non-chlorosilane-based organic coatings that has
been examined using MEMS test devices is the class that is derived using alkenes as
precursor molecules. The process to coat MEMS devices with alkene-based organic
coatings was developed by Ashurst et al., who in particular, investigated a coating
derived using 1-octadecene (C16H33CH=CH2) as the precursor molecule [37]. Ashurst
et al. reported that not only are the tribological properties of an octadecene coating
comparable to those of an OTS SAM, but also its formation process does not have
any of the drawbacks that are inherent in the chlorosilane-based SAM formation
process [37]. An alkene-based thin  lm is formed on the surfaces of a MEMS device by
free radical mediated reactions between the precursor molecules and the H-terminated
surfaces of the MEMS device [37,106]. The H-terminated surfaces are obtained prior
to keeping the MEMS device in the alkene-based coating solution, by etching away
the native oxide present on the surfaces of the MEMS device using a solution of either
63
conc. HF or NH4F. Accordingly, the formation of alkene-based thin  lm coatings on
MEMS surfaces does not result in the generation of HCl as a by-product. Also, it
does not require the presence of an inter-linking oxide layer on the surfaces that are to
be coated. Additionally, the limited functionality of the alkene molecules limits their
ability/tendency to polymerize in the coating solution itself (i.e., bulk polymerize).
Indeed, surfaces coated with a 1-octadecene-based coating are reported to have fewer
particulates (polymerized agglomerates of precursor molecules) deposited on them as
compared to those coated with chlorosilane-based SAMs [37]. Moreover, since water
does not play any role in the formation of alkene-based coatings, the coating process
used to coat MEMS surfaces with alkene-based coatings is essentially insensitive to
the relative humidity of the ambience. Therefore, there is no need to freshly prepare
and condition an alkene-based coating solution immediately before performing the
coating. In essence, the process used to form alkene-based coatings on MEMS surfaces
is much simpler and robust as compared to the chlorosilane-based SAM formation
process. An additional advantage in using alkene-based coatings is that they can be
formed selectively only on exposed silicon surfaces by generating the radicals required
for their formation using a radical initiator.
2.3.4 Issues Challenging the Viability of Self-assembled Monolayers
While reports introducing new SAMs, and con rming the e ectivenesses of the
already devised SAMs in addressing the tribological issues of MEMS, are abundant in
literature, a relatively inadequate amount of research has been devoted to addressing
the several challenges that limit the viabilities of the existing SAM coating processes
[6,35,37,38,64,67,73,80,99,102{107,111,113,117,121{127]. Although some progress
has been made in improving the viabilities of the existing SAM coating processes,
several basic issues remain unaddressed [6, 104]. The following sections provide a
64
brief introduction of the main issues that challenge the viability of self-assembled
monolayers.
Reproducibility
The \portability" of the SAM coating processes between di erent laboratories
has been an issue since the very conceptualization of the idea of SAMs [6]. While some
of the research groups have been consistently reporting good quality SAM coatings,
others have struggled to obtain even acceptable coatings [6]. This has been attributed
to the large number of process variables involved in the SAM coating processes, which
make them extremely susceptible to operator errors at many of their critical steps [6].
Indeed, recently developed SAM coating processes, which consist of fewer processing
steps, are reported to be more reproducible across laboratories and operators [6].
Additionally, the advancement in technology, which has enabled process automation
as well as sensing for real-time process monitoring, has also resulted in signi cant
improvement in the reproducibility of the SAM coating processes [6]. However, the
issue of \portability" of SAM coating processes is still not resolved completely [6].
While to address the issue of \portability" of SAM coating processes, the ideal process
would be a novel dry (vapor-phase) SAM coating process that is designed to eliminate
many of the steps required by any wet-chemistry-based SAM coating process, vapor-
phase SAM formation processes have their own drawbacks, as explained in section
2.3.2.
Scale-up
Another challenging issue, which limits the viability of the SAM coating pro-
cesses, is the scale-up of those processes from the scale of single dies to the scale of
whole wafers, and eventually to the scale of multi-wafer cassettes [6,104]. Presently,
65
most of the laboratory scale studies are conducted on 1 cm 1 cm size dies. Scaling-
up the release and the SAM coating processes from the scale of individual individual
dies to the scale of whole wafers and eventually to the scale of multi-wafer cassettes
is an extremely challenging engineering task. The main challenges include complete
displacements of the solvents from one step to the next, without exposing the MEMS
devices to the liquid-vapor interface as well as without excessive use of solvents and
excessive generation of the associated chemical waste [6,104]. Again, dry vapor-phase
SAM formation processes would be much easier to scale-up than the wet solution-
phase SAM formation processes.
Wear of Self-assembled Monolayer Coatings
The durability of the SAM coatings is also a concern [10, 126, 128]. All SAM
coatings are essentially physically thin (i.e., typically, few nm thick), and mechanically
softer than the surfaces they are deposited on. Therefore, they wear o , when the
surfaces coated with them are operated under high contact loads (i.e., typically, on
the order of MPa or higher) for an extended amount of time [10, 126, 128]. One
strategy that can be used to address this issue is to deposit thicker coatings (i.e.,
multi-layer coatings) on the microstructures. This would ensure that the underlying
microstructure surface will not get exposed even when the top layer of the coating
completely wears o . In other words, the presence of multiple layers will extend
the overall lifetime of the coating. For devices that are encapsulated in a sealed
environment, a more bene cial strategy is to  ll the vapor space above the devices
with an excess amount of vaporized precursor molecules. The equilibrium between
the precursor molecules present in the vapor-phase and those adsorbed on the device
surfaces causes a continuous mass transfer (of the precursor molecules) from the
vapor-phase onto the device surfaces, which ensures that a near-monolayer coverage
of the coating is maintained on the coated surfaces for a longer time even if the coating
66
keeps wearing o with time. This strategy is indeed employed in the DMDTM, which
is a commercialized MEMS device developed by Texas Instruments [10].
Undesired Electrical Properties of Self-assembled Monolayer Coatings
Depending on the electrical signals used to actuate the MEMS device, the SAM
coating deposited on its surfaces may act as an insulator and lead to stiction between
its contacting surfaces. The touch-mode electrostatic actuators studied by Cabuz et
al. are a prime example of the MEMS devices, whose contacting surfaces experience
severe in-use stiction due to the undesired insulating properties of the SAM deposited
on them [6, 112, 113]. The contacting surfaces of an OTS SAM coated touch-mode
electrostatic actuator studied by Cabuz et al. remained stuck even after the bias
voltages applied to it were turned-o [112,113]. Cabuz et al. reported that the charges
trapped in the OTS SAM coating were responsible for the in-use stiction experienced
by the OTS SAM coated touch-mode electrostatic actuator. Their conclusion was
based on the observation that the contacting surfaces of the touch-mode electrostatic
actuator, which was coated with a less insulating FDTS SAM, did not experience any
in-use stiction at all [112,113].
As evident from the discussion in this section, while every self-assembled mono-
layer coating has certain speci c advantages, due to which, it perfectly satis es the
requirements of certain speci c applications, no single self-assembled monolayer coat-
ing satis es the requirements of all the applications. Therefore, despite the availability
of a large number of monolayer coatings, no one coating can be identi ed as the best
surface coating. Infact, the SAM-based surface modi cation approach itself cannot
be claimed as the best approach to address all the tribological issues of MEMS.
67
2.4 Surface Texturing
Surface texturing was one of the  rst strategies devised by the MEMS community
to alleviate the stiction (both release as well as in-use) experienced by proximate
MEMS surfaces. The rationale behind devising a surface texturing based strategy
was that it will roughen the surfaces of a MEMS device and consequently reduce the
area of contact between its contacting surfaces. However, over the last two decades,
the MEMS community has shown a greater inclination towards the SAM-based surface
modi cation approaches, and very limited research has been conducted to investigate
the surface texturing based surface modi cation approaches. To date, no study has
investigated the e ect of surface texturing on the friction experienced by, and the wear
of, contacting MEMS surfaces, and only a few studies investigating the e ectiveness
of surface texturing in alleviating the (in-plane) stiction experienced by proximate
MEMS surfaces have been reported in literature.
Until recently, etching using an anisotropic wet etchant such as ammonium  u-
oride (NH4F) was the only method known to the MEMS community for texturing
MEMS surfaces. Anisotropic wet etchants preferentially etch certain crystal facets
faster than the others, and hence roughen the surfaces being etched using them. The
surface texturing accomplished using anisotropic wet etchants has been reported to
reduce the (in-use) stiction experienced by (in-plane) MEMS surfaces only by a mod-
erate factor of 20 [127]. In 2006, when DelRio et al. studied the e ect of the presence
of silicon carbide (SiC) particles (diameter ranging between 20-50 nm) on polysilicon-
based contacting MEMS surfaces on the (in-use, in-plane) stiction experienced by
them, and reported that the deposition of nanoparticles (NPs) on contacting MEMS
surfaces can signi cantly reduce the stiction between them, NPs emerged as a new
tool that can be used to texture MEMS surfaces [27]. However, the nanoparticles
that textured the MEMS test surfaces that were used in the investigations conducted
by DelRio et al. were adventitiously formed on them (i.e., the particles were not
68
deposited intentionally) by a side reaction during the sacri cial layer growth, and
a process to controllably deposit NPs on MEMS surfaces was not available at that
time [24, 27]. Therefore, in order to be able to use NPs for texturing MEMS sur-
faces, a process that would deposit a conformal and uniform nanoparticle coating on
MEMS surfaces was needed. The conventional drop-casting and solvent evaporation
techniques were not preferred because not only they do not result in the deposition
of conformal and uniform coatings but also their underlying mechanisms cause defor-
mation of the microstructures being coated, which ultimately leads to device failure.
Consequently, the unavailability of a process that could be used to deposit conformal
and uniform nanoparticle coatings on MEMS surfaces delayed the use of nanoparti-
cles for texturing MEMS surfaces till 2009. In 2009, extending the process developed
by the Roberts research group at Auburn University, which precipitates metallic NPs
dispersed in a solution using the gas-expanded liquid technique and deposits them
as uniform, conformal, wide area thin  lms, Hurst et al. developed a novel surface
texturing technique, which could be used to deposit a conformal and uniform coating
of gold nanoparticles (AuNPs) on MEMS surfaces [24, 129]. The surface texturing
technique developed by Hurst et al. was completely compatible with the techniques
conventionally used to fabricate and release MEMS devices, and hence, could be eas-
ily integrated with them [24, 130]. Additionally, it enabled engineering of both the
surface topography as well as the surface chemistry of MEMS surfaces, which was
not possible with the other surface texturing techniques used to-date [24]. Hurst et
al. studied the e ect of texturing polysilicon-based (in-plane) MEMS surfaces us-
ing dodecanethiol-capped AuNP (precipitated from CO2 expanded hexane) on the
stiction experienced by them, and reported that the native oxide covered polysilicon-
based (in-plane) MEMS surfaces exhibited a factor of 100 reduction in in-use stiction,
when they were textured using AuNPs [24].
69
2.5 Wear
Wear, in general, shortens the lifetimes of all the MEMS devices that have con-
tacting surfaces. The extent of wear dictates which of those devices are mechanically
and/or commercially viable. While the primary mechanisms (i.e., adhesion, abrasion,
corrosion, surface fatigue, deformation, impact and fretting) underlying the wear of
macroscopic mechanical systems are fairly well-understood, those underlying the wear
of MEMS surfaces are extremely poorly understood [32]. Therefore, all the studies
that have been conducted to investigate the wear of contacting MEMS surfaces were
aimed at deciphering the mechanisms that govern it. Legtenberg et al. studied the
wear characteristics of several structural  lms that are commonly used in the fabri-
cation of MEMS devices. They suggested that while asperity fracture could be the
dominating mechanism underlying the wear of structural  lms composed of brittle
materials such as diamond-like carbon (DLC), SiO2, Si3N4 and single-crystal silicon
(SCS), asperity deformation could be the dominating mechanism underlying the wear
of polysilicon structural  lms [44]. Inspite of two decades of research, the mechanisms
that govern the wear of MEMS surfaces are still not understood satisfactorily. How-
ever, the studies conducted have revealed the various factors that in uence it. In
addition to the details of the mechanical contacts between their contacting surfaces,
the environmental conditions, to which, the MEMS devices are exposed during oper-
ation have a strong in uence on the wear of their contacting surfaces. Several studies
have con rmed that the mechanism that leads to the wear of rubbing MEMS sur-
faces in dry air (i.e., <1% RH) is di erent from the mechanism that leads to the
wear of rubbing MEMS surfaces in humid air [65]. The tribochemical reactions that
occur at the interfaces between rubbing MEMS surfaces are also reported to have
a signi cant in uence on their wear [11]. Tanner reported that the tribochemical
reactions in uence both the wear rate as well as the mechanisms that lead to wear,
of MEMS surfaces [11]. Patton et al. reported that the native oxide layer present on
70
microstructure surfaces acts as a lubricant, and resists the wear of rubbing MEMS
surfaces [65, 131]. They additionally reported that even the contaminants that de-
posit on MEMS surfaces from the ambience have a lubricating e ect on the rubbing
MEMS surfaces [65,131]. Their conclusions were based on the observation that rub-
bing MEMS surfaces exhibited greater durability in air than in vacuum [65,131].
While a fraction of the current research addressing the issue of wear in MEMS
is still focussed on understanding the fundamental causes of the wear of contact-
ing MEMS surfaces, a signi cant amount of research is also devoted to searching
and integrating harder materials into the micromachining processes commonly used
to fabricate MEMS [6, 134{139]. Owing to its excellent performance in demanding
mechanical and high temperature applications, silicon carbide (SiC) has emerged as
the most promising hard material for MEMS applications [132, 133]. However, since
the current infrastructure of the MEMS industry is unable to enable the usage of
SiC structural  lms, most of the present studies that are aimed at exploring SiC for
MEMS applications investigate the e ectiveness of SiC thin  lms either deposited or
grown on silicon-based MEMS surfaces [6,134{139]. The methods commonly used for
forming thin SiC coatings on silicon-based MEMS surfaces are conventional chemical
vapor deposition (CVD) using separate sources for Si (i.e., SiH4) and C (i.e., C3H8),
reaction of buckminsterfullerene (i.e., C60) with silicon and low pressure CVD py-
rolysis of disilabutane (CH3SiH2CH2SiH3, DSB) [6, 134{139]. Of the three methods
that are commonly used to form SiC thin  lms, the method, which involves low pres-
sure CVD pyrolisis of disilabutane (CH3SiH2CH2SiH3, DSB), is the most preferred
for polysilicon-based MEMS devices because not only it results in a SiC coating,
which is continuous, pinhole free and conformally coated on all the surfaces of the
MEMS device (including undersides), but also the coating is formed at low pres-
sures and relatively moderate temperatures [6]. Several studies have investigated the
relevant  lm properties of SiC thin  lms, and reported that the thin SiC coatings
71
deposited on silicon surfaces exhibit the same desirable properties as exhibited by
the bulk SiC material, which include exceptional electrical properties, high corrosion
resistance and most importantly, excellent tribological properties such as high wear
resistance [6, 134]. The high wear resistance of the SiC thin  lm coatings was also
reported by Sundararajan et al., who determined it using an atomic force microscope
(AFM), and attributed it to the higher hardness and fracture toughness of the SiC
thin  lm coatings [140].
2.6 Fracture and Fatigue
As mentioned in section 1.5.5, fracture of the structural  lm has never been
reported as the cause of failure of a MEMS device. However, fatigue has been re-
ported to cause pre-mature failure of several silicon-based MEMS devices. The use
of strength-based design approach for developing MEMS fails to prevent their pre-
mature failure caused by fatigue, even at stresses as low as 50% of the strength of the
structural material, when they are cyclically loaded [86, 89]. Therefore, it is equally
important to understand the mechanisms that cause fatigue-related failure of the
structural  lms that are used to fabricate MEMS as it is to determine their mechanical
properties, to improve the reliability of MEMS. Presently, as in the case of wear, the
mechanisms that lead to fatigue-related failure of silicon-based MEMS are extremely
poorly understood. Therefore, the current research that addresses the fatigue-related
failures of MEMS is also focussed on understanding the mechanisms underlying them,
in addition to devising solutions to suppress them [86, 90{92]. Muhlstein et al. re-
cently proposed a mechanism to explain the fatigue exhibited by the silicon-based
MEMS that were cyclically stressed in the presence of air [86, 90{92]. According to
the mechanism proposed by Muhlstein et al., which is called as the reaction-layer fa-
tigue, subcritical environmentally-assisted cracks grow in the surface oxide (reaction)
layer, which is invariably formed on the silicon surfaces that are exposed to air, until
72
a crack of critical length is formed in it, after which, the critical crack instantly leads
to the rupture of the MEMS component. Muhlstein et al. additionally reported that
the formation of an alkene-based monolayer  lm on the surfaces of a MEMS device
prevents the formation of the oxide (reaction) layer on them, on exposure to air, and
hence, suppresses the fatigue failure of the MEMS device [92].
73
Chapter 3
Motivations and Objectives
3.1 The Need of an Easy-to-fabricate, Versatile Test Platform
Over the last two decades, while one hand, the advancements in micromachining
technologies and the increasing demand for more complex, compact and sophisti-
cated devices have prompted an increase in the development of MEMS prototypes
possessing contact-mode structures, such as microrelays, stepper motors, gas bear-
ings, micromotors and microengines, on the other hand, their poor reliability and
limited lifetime have hindered their commercialization and limited their usage to
laboratory-scale studies [78, 141{143]. As discussed in the previous chapters, owing
to the substantially increased in uence of surface forces at the micro-scale, the fac-
tors that are mainly responsible for the poor commercial viability of MEMS with
contacting surfaces are surface phenomena, such as stiction, friction and wear, that
govern the tribological behaviour of MEMS interfaces [78,126,141,143{145]. However,
despite over two decades of research encompassing the full spectrum from modeling
to experimental characterization, our knowledge of the factors that in uence, and
the mechanisms that govern, the tribological behaviour of MEMS interfaces is still
insu cient [141,145]. Indeed, not much has been achieved in terms of addressing the
tribological issues that are the major bottlenecks to the realization of the full poten-
tial of the MEMS technology, at the commercial scale. In essence, with the present
state-of-the-art in MEMS technology, a comprehensive understanding of the factors
that in uence, and the mechanisms that govern, the tribological behaviour of MEMS
interfaces and a prompt formulation and accurate evaluation of the strategies that
can improve the reliability of MEMS devices are still needed.
74
This requires development of dedicated microinstruments, which can be used
to carry out systematic investigations at the length scales representative of MEMS,
since the relative signi cance of surface forces changes drastically with the length
scale [141, 142, 144, 145]. Also, studies conducted using an atomic force microscope
(AFM) investigate the tribological characteristics of only single asperity contacts
while contacts between MEMS surfaces involve multiple asperities, and those con-
ducted using a surface force apparatus (SFA) investigate the tribological characteris-
tics of atomically smooth surfaces while contacting MEMS surfaces have  nite surface
roughnesses [145{147]. Further, a relatively large contribution to surface forces from
the regions outside the area of direct contact as well as mixed plastic/elastic contact
mechanics complicate matters even more in the case of MEMS interfaces [67,70,142].
Another motivation behind using MEMS devices to study tribology is that they can
reveal insights that are needed to decipher the fundamental di erences in the tribo-
logical behaviour of surfaces at di erent length scales. Many tribological e ects, such
as thermal activation induced reduction of friction (thermolubricity) and near-zero
friction among incommensurate atomic lattices (superlubricity), that are observed at
the nano-scale have never been observed at the macro-scale, which indicates that at
some point during the transition from the nano-scale to the macro-scale, the char-
acteristic tribological behaviour of surfaces changes radically [145]. MEMS devices
seem to operate at length scales that are precisely in the range where this change
occurs.
While the stiction and friction experienced by MEMS surfaces limit the yield
and worsen the reliability of MEMS devices, the wear of contacting MEMS surfaces
limits their lifetime. Therefore, it is equally important to understand the mechanisms
that lead to, and determine the factors that in uence, each of the three tribological
characteristics (i.e., stiction, friction and wear) of MEMS interfaces. Additionally, in
order to improve the reliability of MEMS devices, it is essential to also understand the
75
inter-play between the three prominent tribological properties (i.e., stiction, friction
and wear) of MEMS interfaces. This requires that the microinstruments that are used
to study each of them are fabricated on the same chip, so that, the inconsistencies
associated with the uncontrollable variations in the experimental conditions can be
eliminated. Further, in order to be able to accurately correlate the e ects that a
particular surface treatment has on the three prominent tribological properties of
MEMS surfaces too, the di erent microinstruments that are used to investigate the
e ects should be fabricated on the same chip, so that, the test surfaces that will be
tested using each of them will have identical surface characteristics. Therefore, there
is a need to develop a versatile test platform, which could be used to systematically
investigate all the more prominent tribological properties of MEMS surfaces on the
same chip, so that, a meaningful and reliable correlation between the e ects that a
particular factor has on all of them could be established.
Historically, the test platforms that have been used to study the tribological
properties of MEMS surfaces have had extremely complicated designs [6]. Addition-
ally, their fabrications have involved extremely sophisticated fabrication processes,
which were not only expensive but also time consuming [6]. However, the design
of a test platform should be such that it can be easily fabricated using a facile and
inexpensive fabrication scheme, in a reasonable, less amount of time. This is an im-
portant requirement because most researchers in university-scale settings are known
to be usually short of the two resources, namely, time and money. Besides, this would
also make the design of the test platform portable across di erent laboratories.
3.2 The Variation in the Material Properties of the Structural Film
Most of the MEMS test devices that have been previously used to study the
tribology of MEMS interfaces were fabricated using polysilicon structural layers. It
76
has been reported by several studies that the material properties, such as the resid-
ual stress and the elastic modulus (E), of the polysilicon structural layers as well
as the stress gradient across their thicknesses are extremely sensitive to the condi-
tions (i.e., temperature, pressure, precursor gas  ow rates, etc.) used to deposit and
anneal them [36, 39, 40, 148]. Consequently, they are known to vary from fabrica-
tion to fabrication, and sometimes, even from chip to chip. If the furnace used to
deposit and anneal the polysilicon structural  lms is not tuned properly, the mate-
rial properties of the polysilicon structural  lms vary even on the same chip [9,149].
Since the material properties of the structural  lms, such as their elastic modu-
lus, are used in the determination of the tribological properties of the test surfaces,
variation in them not only limits the  exibility of the design of the test platform
but also results in inconsistent and unreliable estimation of the tribological proper-
ties [23,85,126,141,143,145,150,151]. It makes it impossible to compare and correlate
the e ects of the di erent surface treatments that are tested as strategies to address
the tribological issues of MEMS. Therefore, a test platform should be fabricated us-
ing structural  lms, whose material properties do not vary at all, so that, consistent
and reliable results can be obtained. Consequently, such a test platform would en-
able meaningful comparisons between the results obtained using di erent chips. This
will not only allow us to establish a reliable correlation between the e ects of sev-
eral factors that in uence the tribological characteristics of MEMS interfaces but
also facilitate systematic investigations of the strategies that are proposed to improve
them.
3.3 The In uence of the Multi-grain Nature of the Polysilicon Structural
Films on the Topography of Polysilicon MEMS Surfaces
Since the taller asperities are the real points of contact between two surfaces,
the real area of contact between them is determined by their roughnesses, material
77
(a)
 0
 5
 10
 15
 0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8
nm
?m
(b)
Figure 3.1: (a) An AFM image of a typical in-plane polysilicon surface. The rms
roughness of the surface shown in image a is 3.71 nm. The z-scale of image a is 30.7
nm. (b) Linescan along the white line drawn across image a.
78
(a)
 0
 30
 60
 90
 120
 0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1
nm
?m
(b)
Figure 3.2: An AFM image of a typical sidewall polysilicon surface [78]. The rms
roughness of the surface shown in image a is 13.8 nm. The z-scale of image a is 158.7
nm. (b) Linescan along the white line drawn across image a.
79
properties and the shapes of the asperities present on them. Consequently, since
the topographies of the contacting surfaces have a strong in uence on the area of
contact between them, they also have a strong in uence on the tribology of the
interface formed by them [70, 148, 152]. However, as mentioned in section 2.4, very
limited research has been conducted to-date to understand the e ect that the surface
topography of MEMS surfaces has on their tribological characteristics. Further, it has
been reported that the topography of polysilicon MEMS surfaces not only depends
on the processes used in the fabrication of MEMS devices but also depends on the
orientations as well as the boundaries of the grains present in the structural  lms
[78]. The AFM images of the in-plane (rms roughness is 3.71 nm) and sidewall (rms
roughness is 13.8 nm) polysilicon MEMS surfaces shown in Fig. 3.1a and Fig. 3.2a,
respectively, also substantiate the grain boundary and grain orientation dependence
of the topography of polysilicon MEMS surfaces. The linescans shown in Fig. 3.1b
and Fig. 3.2b clearly indicate that while the relative heights of the adjacent grains
is the source of the topography of in-plane polysilicon surfaces, the grain boundaries
are the main source of the topography of sidewall polysilicon surfaces. Owing to its
dependence on the characteristics of the grains present in the structural  lm, the
topography of polysilicon MEMS surfaces varies locally, due to which, it is more
than often considered responsible for the scatter observed in the experimental results
[23, 85, 126, 143, 145, 150]. Indeed, the (grain-characteristic induced) variation of the
topography of MEMS test surfaces from device to device makes it really di cult
to obtain a statistically signi cant data-set. Therefore, not only is there a need
to understand the e ect that the surface topography of a MEMS surface has on
its tribological properties but also there is a need to develop test platforms using
structural  lms that are not composed of multiple grains. Such a test platform will
not only enable us to obtain statistically signi cant data-sets but also enable the
80
determination of the exact e ects of the various surface treatments that are used as
strategies to improve the reliability of MEMS devices.
3.4 Objectives of this Study
The  eld of MEMS undoubtedly has the potential of producing great techno-
logical innovations. However, a precise understanding of the tribological behaviour
of MEMS surfaces is needed for the realization of the full potential of a variety of
complex, sophisticated and extremely useful MEMS. Therefore, the main objective
of this study is to enhance our overall understanding of the factors that in uence the
tribological characteristics of MEMS surfaces.
Speci cally, the  rst main goal of this study is to develop a test platform, which
not only overcomes the limitations of the previously reported test platforms but is
also a versatile tool that can be used to systematically study the tribology of MEMS
surfaces. Achieving this goal will involve designing of several di erent microinstru-
ments, which will either be used to determine the material properties (i.e., residual
stress, fracture strength, elastic modulus ) of the structural  lm or be used to deter-
mine the tribological properties (i.e., work of adhesion, coe cient of friction) of the
test surfaces (i.e., in-plane as well as sidewall). It will also involve devising of a single
mask scheme to fabricate the designed test platform using a SOI wafer. The last part
of this goal will involve formulation of the actuation schemes that will be required to
actuate the various microinstruments of the developed test platform.
The second main goal of this study is to understand the e ect that the surface
topography of MEMS surfaces (in-plane as well as sidewall) has on the stiction and
friction experienced by them. Achieving this goal will involve tailoring of the topog-
raphy of the test surfaces of the test platform to obtain test surfaces with several
(speci cally, six) distinct surface topographies. Further, the apparent works of ad-
hesion and the coe cients of friction (i.e., static as well as dynamic) of the various
81
tailored test surfaces will be determined. Finally, correlations between the surface
topography of a MEMS surface and its apparent work of adhesion as well as its
coe cient of static friction will be established.
82
Chapter 4
The Test Platform: Design, Fabrication and Actuation
4.1 Design of the Test Platform
4.1.1 Structural Film
In order to address the issues of the grain-characteristic induced variation of the
topography of polysilicon MEMS test surfaces and the deposition-condition induced
variation of the material properties of the polysilicon structural  lms, I have designed
a test platform that can be fabricated using a silicon-on-insulator (SOI) wafer. The
SOI wafer, which is used to fabricate the microinstrument, consists of a 2  m (nomi-
nal) thick device layer, which is a n-type Si(100)  lm and has a resistivity of 0.001 -
0.005  -cm, a 2  m (nominal) thick sacri cial layer, which is a buried-oxide (BOX)
 lm and a substrate, which is a 500  m (nominal) thick n-type Si(100) wafer and
has a resistivity of 0.001 - 0.005  -cm. Accordingly, both the substrate as well as
the structural  lm (i.e., device layer) used to fabricate the test platform used in this
study are single crystal silicon  lms, which do not have the polysilicon structural
 lm-like multi-grain morphology. The absence of grain boundaries in the substrate as
well as the structural  lm used to fabricate the test platform is substantiated by the
AFM images of the in-plane (rms roughness is 0.097 nm) and sidewall surfaces (rms
roughness is 6.52 nm) of the test platform, which are shown in Fig. 4.1a and Fig. 4.2a,
respectively. The linescan (i.e., Fig. 4.1b) taken across the AFM image of the in-plane
surface (i.e., Fig. 4.1a) clearly indicates that unlike the in-plane polysilicon surfaces,
the in-plane surfaces of the test platform are extremely smooth, and exhibit a sig-
ni cantly small peak to valley ratio. In fact, a large fraction of this already small
83
peak to valley ratio is due to the inherent noise of the AFM. Although the linescan
(i.e., Fig. 4.2b) taken across the AFM image (i.e., Fig. 4.2a) of the sidewall surface
of the test platform indicates that it is rougher than, and exhibits a peak to valley
ratio higher than, the in-plane surface of the test platform, it must be noted that the
rougher topography of the sidewall surface of the test platform is not induced by the
grain boundaries, but is a consequence of the etching process used to fabricate the
test platform. Further, it is a known fact that the material properties of the single
crystal silicon  lms do not vary at all. Therefore, the use of a SOI wafer to fabricate
the test platform ensures that the material properties of its structural  lm does not
vary from chip to chip, not even from one fabricated batch to another.
4.1.2 The Layout of the Test Platform
In order to be able to systematically investigate, and establish a meaningful and
reliable correlation between, the e ects that a particular factor has on the di erent
tribological properties (i.e., stiction, friction and wear) of MEMS surfaces, I have
included seven di erent types of microinstruments in the test platform. Their dimen-
sions are determined keeping in mind that fabricating all of them on the same chip
should not cause any issues during the release of the test platform. Fabricating all the
microinstruments, which are used to determine the di erent properties (i.e., material
or tribological) of MEMS surfaces, on the same chip ensures that the test surfaces
examined using each of them have identical surface characteristics, and are exposed
to identical experimental conditions. Figure 4.3 is the layout of the mask used to
fabricate the test platform. As seen in Fig. 4.3, the test platform is fabricated on a 1
cm  1 cm chip. All the seven di erent types of microinstruments that are included
in the test platform are labelled in Fig. 4.3. The design, actuation procedure and
modeling of each of them is discussed in greater detail in the following chapter.
84
(a)
 0
 0.2
 0.4
 0.6
 0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8
nm
?m
(b)
Figure 4.1: (a) An AFM image of the in-plane surface of the test platform. The rms
roughness of the surface shown in image a is 0.097 nm. The z-scale of image a is 1.1
nm. (b) Linescan along the black line drawn across image a.
85
(a)
 0
 6
 12
 18
 24
 0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8
nm
?m
(b)
Figure 4.2: (a) An AFM image of the sidewall surface of the test platform. The rms
roughness of the surface shown in image a is 6.52 nm. The z-scale of image a is 41.8
nm. (b) Linescan along the black line drawn across image a.
86
The test platform (TP) has microinstruments that can be used to determine sev-
eral di erent material properties of the structural  lm. The Residual Stress Tester
(RST) can be used to determine the residual stress present in a released device layer
(structural  lm). The Mechanical Strength Tester (MST) can be used to determine
the fracture strength of the device layer. The \Resonator" can be used to determine
the elastic modulus of the device layer. Additionally, the test platform has a microin-
strument (i.e., Cantilever Beam Array (CBA)) that can be used to study the stiction
characteristics of the in-plane surfaces. Although, most of the tribological studies
reported to-date have been conducted using in-plane surfaces, in devices belonging to
several of the emerging classes of MEMS such as microgears and microsliders, more
vertical (sidewall) surfaces come into contact during operation than horizontal (in-
plane) surfaces [142]. Additionally, it is clearly evident from the AFM images shown
in Fig. 4.1a and Fig. 4.2a that the in-plane and sidewall surfaces are signi cantly dif-
ferent topographically. The rms roughness of the sidewall surface shown in Fig. 4.2a
is 6.52 nm, which is signi cantly higher than that of the single crystal silicon in-plane
surface shown in Fig. 4.1a, which is 0.18 nm. Linescans (Fig. 4.1b and Fig. 4.2b) taken
across the AFM images (Fig. 4.1a and Fig. 4.2a, respectively) along the white lines
shown in the images further highlight the di erence in the topography of in-plane
and sidewall surfaces. Owing to the di erent processing environments, to which, the
sidewall and in-plane surfaces are exposed during micromachining, they are expected
to be di erent, both topographically as well as chemically. The sidewall surfaces are
revealed using reactive ion etching (RIE), during which, they are exposed to reac-
tive gases and high energy ions unlike the in-plane surfaces, which are protected by
photoresist or other masking layers during the etching process. This results in the
formation of polymer-like materials on them, due to which, they exhibit a di erent
chemistry than the in-plane surfaces. The signi cantly di erent topographies of the
sidewall and in-plane surfaces are also a consequence of the same etching process.
87
Since topography strongly in uences the tribological behaviour of MEMS interfaces,
 ndings of investigations carried out using in-plane interfaces are not applicable to
sidewall interfaces [78, 79, 126, 142]. Therefore, microinstruments in which sidewalls
form the test interface are needed to study the tribological behaviour of sidewall in-
terfaces. The test platform developed in this study conveniently addresses this need.
It has di erent microinstruments for studying the stiction characteristics of in-plane
and sidewall surfaces. While, as mentioned before, the CBA can be used to study
the stiction characteristics of the in-plane surfaces, the stiction characteristics of the
sidewall surfaces can be studied using the Sidewall Beam Array (SBA). Lastly, the
test platform has two di erent microinstruments (i.e., the Sidewall Friction Tester
(SFT) and the Sidewall Friction and Adhesion Tester (SFAT)) that can be used to
study the friction as well as wear characteristics of the sidewall surfaces. The purpose
behind including two di erent microinstruments for studying the friction and wear
characteristics of sidewall surfaces is to determine the in uence of the geometries of
the surfaces forming the contact interface on the e ect of surface topography. While
in the SFT, the contact interface is formed between the plane (vertical) surface of a
suspended beam and the cylindrical surface of an anchored post, in the SFAT, it is
formed between the plane (vertical) surfaces of two suspended shuttles.
As seen in Fig. 4.3, the test platform is designed to have multiple copies of the
seven main microinstruments. The purpose behind including multiple copies of each
microinstrument in the test platform is to obtain statistically signi cant (experimen-
tal) data-sets. Further, the copies of each microinstrument are judiciously distributed
over the entire real estate of the test platform in order to determine the local vari-
ations in the experimentally obtained results. This enables the elimination of the
positional bias from the experimentally obtained results. Additionally, the copies of
each microinstrument are divided into two groups, which are oriented orthogonally to
88
Figure 4.3: The layout of the mask used to fabricate the test platform. Notice that
the test platform is fabricated on a 1 cm  1 cm chip. It consists of seven di erent
types of microinstruments, all of which, are labelled in the above  gure.
89
each other in the test platform. The purpose behind this is to determine the crystal-
plane induced variations in the experimental results. Lastly, all the microinstruments
of the test platform are judiciously organized in order to make the most e cient use
of the total real estate area of the test platform. In summary, the test platform de-
veloped in this study (i.e., TP) is a carefully designed, versatile tool, which enables
systematic and reliable studies of the tribology of MEMS interfaces.
4.2 Fabrication of the Test Platform
4.2.1 Single Mask Scheme
In order to be able to fabricate the TP using a facile, inexpensive and less time
consuming fabrication process, the microinstruments are designed in such a way that
they can all be fabricated in a single-mask scheme. The TP is fabricated using the
standard surface micromachining tools. The fabrication process begins with cleaning
of the SOI wafer using a RCA1 solution (i.e., consists of 5 parts by volume of deionized
H2O, 1 part by volume of NH4OH and 1 part by volume of H2O2). The cleaned
wafer is dehydrated at 120 C for about 30 min., so that, it can be primed with
hexamethylenedisilazane (HMDS). Priming of the device layer with HMDS, for 10
min., ensures good adhesion between the device layer and the photoresist layer, which
is used as a mask to pattern it. After priming, the device layer is spin coated with
a 2  m thick layer of positive photoresist AZ 5214 E-IR. Next, the photoresist layer
is patterned by exposing it through a hard (chrome on quartz) mask, to the h-line
(wavelength of the radiation is 404.7 nm) of the mercury vapor lamp and developing
the exposed photoresist layer in an aqueous solution of AZ 400K for 2 min. The
primary  at of the photoresist coated SOI wafer is placed at 45 to the edges of the
hard mask while exposing the photoresist layer to the UV-radiation. The exposure
energy used is 50 mJ/cm2 and the composition of the developing solution used is one
part by volume of AZ 400K in four parts by volume of deionized water. Patterning of
90
the photoresist layer (i.e., photolithography) transfers the layout of the test platform
from the hard mask onto it. Next, the SOI wafer with a patterned photoresist layer
on it is dipped in a 1:50 (v:v) solution of HF acid in deionized (DI) water for 10
sec. This etches away the native oxide present on the exposed regions of the device
layer. Next, using the patterned photoresist layer as the etch mask, the device layer is
etched using the Bosch process, in a deep reactive ion etching (DRIE) system. This
anisotropic etching of the device layer de nes the three dimensional geometries of
the microinstruments of the test platform. Since the Bosch process etches the silicon
relatively much faster than the SiO2, the sacri cial layer can be conveniently used as
an e ective etch stop. However, ine cient tuning of the DRIE system used by me
necessitated intermittent monitoring of the etched depth of the device layer. Finally,
after the entire thickness of the device layer is etched, the wafer is carefully diced into
individual test platforms (chips).
4.2.2 Polishing of the Test Surfaces
The Bosch process, which is used to de ne the three dimensional geometries of
the microinstruments of the test platform, is known to result in the formation of
scallops on the surfaces that are revealed by it [33, 48{50, 52, 53]. Accordingly, the
sidewall surfaces of the as-fabricated test platform have a scalloped pro le. However,
since the in-plane surfaces of the test platform are masked during the etching process,
either by the photoresist or by the sacri cial layer, they are not a ected by the Bosch
process. Figure 4.4a is a SEM image showing the edge of an as-fabricated cantilever
beam. A large number of scallops are clearly visible on the as-fabricated sidewall
surface shown in Fig. 4.4a. Fig. 4.4a also clearly indicates that the in-plane surfaces
(top surface of the cantilever beam in the  gure) of the test platform are not a ected
by the Bosch process. Since one of the objectives of this study is to study the e ect
that the surface topography of MEMS surfaces has on their stiction and friction
91
characteristics, it is essential to examine test surfaces, whose surface topographies
span the range that includes the surface topographies (i.e., from rms roughness 0.2
nm to rms roughness 15 nm) of the surfaces of most MEMS prototypes. However,
the scallops present on the as-fabricated sidewall surfaces of the test platform make
the sidewall surfaces signi cantly rougher (i.e., typical rms roughness is greater than
30 nm) than even the most rough MEMS surfaces. Therefore, a polishing process is
devised to smoothen the as-fabricated sidewall surfaces of the test platform.
Three di erent approaches were tried to polish the test surfaces of the test plat-
form. The  rst approach involved etching of the as-fabricated test platform in a wet
isotropic silicon etchant, which consisted of HNO3, HF and H2O. Several di erent
compositions of the etching solution were examined in order to determine the compo-
sition that etches the single crystal silicon structural  lm of the test platform at the
desired etching rate. After  nalizing the composition of the isotropic etching solution,
the test platform was etched using it. A timed etch was used to ensure that only a
thin layer of silicon gets etched from the test surfaces. Unfortunately, this isotropic
etching approach did not have any signi cant e ect on the roughness of the sidewall
test surfaces. On the contrary, the top surface of the device layer became rough after
this treatment. Therefore, this approach was discarded. In the second approach, the
test platform was subjected to multiple cycles of polishing, each of which consisted
of growing a layer of native oxide on the test surfaces by placing the test platform
in hot H2O2 for 10 min., and subsequently etching it by dipping the test platform in
conc. HF. Even this approach was found to be ine ective, since even after subject-
ing the test platform to 100 cycles of polishing, no signi cant change was observed
in the scalloped pro le of the sidewall test surfaces. Therefore, a third polishing
approach based on the thermal oxidation of silicon was investigated to smoothen
the as-fabricated sidewall surfaces of the test platform. Considering that the rate of
growth of the thermally grown SiO2 is signi cantly higher on the asperities than on
92
(a)
(b)
Figure 4.4: SEM images of (a) An unpolished sidewall surface. (b) A polished sidewall
surface.
93
the  atter surfaces and silicon from the surface layer is consumed by the growing ther-
mal SiO2  lm, it was expected that this approach would considerably smoothen the
scalloped sidewall surfaces. Indeed, 2 cycles of polishing using this approach yielded
relatively much smoother sidewall surfaces. A SEM image of a sidewall polished using
this approach is shown in Fig. 4.4b.
The thermal oxidation (i.e., third) approach based polishing process begins with
cleaning of the test platform in piranha (i.e., consists of 2 parts by volume of conc.
H2SO4 and 1 part by volume of H2O2), for 2 min., after which, the test platform is
dried by blowing it with a stream of N2. Next, a layer of thermal oxide is grown on
the exposed silicon surfaces of the test platform using the dry oxidation process, at
1100 C in laboratory air (i.e., pP of O2 is 0.21 atm) for 75 min. This results in the
formation of a 125 - 140 nm thick layer of SiO2 on the exposed silicon surfaces of the
microinstruments of the test platform. The thickness of the thermal oxide layer grown
on the exposed silicon surfaces of the test platform is measured using ellipsometry,
on a Si(100) monitor chip processed simultaneously with the test platform. Next,
the thermally grown oxide layer is completely etched away from the surfaces of the
test platform using a timed etch (i.e., 5 - 6 sec.), and conc. HF solution as the
etchant. The thickness of the residual thermal oxide left behind on the surfaces of
the test platform after this treatment is measured, on the simultaneously processed
Si(100) monitor chip using ellipsometry, to ensure that the timed etch is su cient to
completely etch way the entire layer of thermally grown oxide. This completes one
cycle of polishing. The scalloped sidewall surfaces of the test platform used in this
study are polished using two cycles of polishing. The parameters of the oxidation
process (i.e., temperature, time/cycle and no. of cycles) are optimized using the
following three criteria: One, the total amount of thermal oxide grown on the exposed
silicon surfaces of the test platform should su ciently smoothen its scalloped sidewall
surfaces. Two, the amount of thermal oxide grown in each cycle should be minimized
94
to avoid chipping of the edges of the microstructures as well as pit formation on
the surfaces of the microstructures. Three, the number of polishing cycles should be
minimized to avoid induction of stresses in the structural  lm due to exposure to
high-temperature cycling.
4.3 Actuation of the Test Platform
The TPs used in this study are actuated using a custom-built probing system
(Probe Station). A photograph of the probing system is shown in Fig. 4.5. The prob-
ing system is equipped with the long-working-distance, incoherent light interference
microscope similar to that reported by Sinclair et al. in [153], which is mounted on a
vibration isolation table (Newport Electronics, Inc., ST Series) to dampen the noise
associated with the ground vibrations. The Mitutoyo M Plan Apo objectives (10X -
100X) are used as the objective lens in the microscope and a green LED (with  max
of 525 nm, Nichia corp.) monochromated using a monochromator that transmits 532
nm is used as the illumination source. The probing system is also equipped with
a charge-coupled device (CCD)-IRIS camera (Sony, XCD-SX910) to collect digital
images. Additionally, it has six probe modules, which are used to establish mechan-
ical and/or electrical contacts with the microinstruments. Lastly, it has an in-built
vacuum pump, which is used to generate the vacuum suction that holds the probe
modules and the TP in place during the actuation of the microinstruments. To auto-
mate the actuation of the various microinstruments of the Test Platform, the testing
procedures are executed using a scripting environment called MEMScript. All the
scripts that are used for this study are reported in Appendix A. The scripts used
for testing the microinstruments not only actuate them but also collect and store the
required data.
95
CCD?IRIS camera
(Green LED)Illumination sourceProbe module
Test platform
Figure 4.5: Photograph of the custom-built probing system used to actuate the mi-
croinstruments of the test platform.
96
Chapter 5
Microinstruments: Design, Testing Procedure and Modeling
5.1 Residual Stress Tester (RST)
The Residual Stress Tester (RST) can be used to determine the residual stress
present in a released structural  lm.
5.1.1 Design
Figure 5.1a is an optical image of a released Residual Stress Tester (RST). As
seen in Fig. 5.1a, the main component of the Residual Stress Tester is an I-shaped
beam, which is suspended when released. The suspended I-shaped beam is supported
by the two thin cantilever beams that are labelled as \supporting beams" in Fig. 5.1a.
The two supporting beams are equidistant from the midpoint of the central arm, and
are connected to it at a distance d (designed to be 200  m) apart. Both the supporting
beams are 100  m (nominal) long and 5  m (nominal) wide. Two movable patterns
are made on each of the two  anges of the I-shaped beam. On each  ange, the
two movable patterns are located close to the two ends of the  ange, respectively.
An anchored pattern corresponding to each movable pattern is designed besides the
movable pattern, at a distance of 10  m (nominal) from it. A pair of movable and
anchored patterns can be clearly seen in Fig. 5.1b, which is a magni ed optical image
of the area that is enclosed in the box in Fig. 5.1a.
5.1.2 Modeling
Since the two supporting beams are connected to the I-shaped beam at points
that are o -axis, the forces exerted by them due to the residual stress present in the
97
d
Central arm Supporting beams
(a)
Movable pattern
Anchored pattern
(b)
Figure 5.1: (a) Optical image of a released Residual Stress Tester. Notice that the
I-beam consists of a horizontal central beam that is connected to two vertical  anges.
(b) Magni ed optical image of the area that is enclosed in the box in Fig. 5.1a. Notice
the pair of movable and anchored patterns labelled in this image.
98
structural  lm, on the I-shaped beam are also o -axis (although equal in magnitude
and opposite in direction). Therefore, a torque is induced at the center of the I-shaped
beam of the Residual Stress Tester, which causes the I-shaped beam to rotate in the
x y plane when the Residual Stress Tester is released. Depending on the nature
of the residual stress (i.e., tensile or compressive) present in the structural  lm, the
I-shaped beam will rotate either clockwise or anti-clockwise. If the residual stress
present in the structural  lm is tensile, the I-shaped beam will rotate clockwise, as
shown in Fig. 5.2a. If the residual stress present in the structural  lm is compressive,
the I-shaped beam will rotate anti-clockwise, as shown in Fig. 5.2b.
Since (see Fig. 5.1a) d=2  w, which is the width of each supporting beam,
the strain induced in both the supporting beams, when the Residual Stress Tester is
released, by the residual stress present in the structural  lm can be approximated by
Eq. 5.1.1.
 R =  d2 (5.1.1)
Here,  R is the strain induced in the supporting beams by the residual stress present
in the released structural  lm,  is the amount (in radians), by which, the I-shaped
beam of the Residual Stress Tester rotates, when it is released and d is the distance
between the two points, at which, the two supporting beams are connected to the I-
shaped beam of the Residual Stress Tester. The residual stress present in the released
structural  lm, that induces a strain of  R in the supporting beams can be given by
Eq. 5.1.3.
 R = E R (5.1.2)
E is the elastic modulus of the structural  lm. Substituting Eq. 5.1.1 in Eq. 5.1.2
gives Eq. 5.1.3, which can be used to determine the residual stress present in the
99
Tensile force
(a)
Compressive force
(b)
Figure 5.2: (a) A schematic diagram (plan view) illustrating the clockwise rotation
of the I-beam of the Residual Stress Tester due to the tensile stress present in the
released structural  lm. (b) A schematic diagram (plan view) illustrating the anti-
clockwise rotation of the I-beam of the Residual Stress Tester due to the compressive
stress present in the released structural  lm. Shaded regions shown in the diagrams
are anchored to the substrate. A ground plane (not depicted) is present underneath
the entire device.
100
released structural  lm of the TP.
 R = E d2 (5.1.3)
5.1.3 Testing Procedure
A Mitutoyo M Plan Apo 20 objective is used as the objective lens in the micro-
scope, during the testing of Residual Stress Testers. The d for each tested Residual
Stress Tester is optically determined, with a resolution of 0.23  m. The rotation (i.e.,
 ) of a released Residual Stress Tester is determined by determining the change in
the position of either of the four movable patterns relative its corresponding anchored
pattern, when the Residual Stress Tester is released. The change in the position of a
movable pattern relative to its corresponding anchored pattern is determined using a
pattern matching. The resolution of the pattern matching technique used to deter-
mine  is experimentally determined to be 10 nm. Accordingly,  can be determined
with a resolution of 20  rad. The script used to test the Residual Stress Tester is
given in Appendix A.1.
5.2 Mechanical Strength Tester (MST)
The Mechanical Strength Tester (MST) can be used to determine the fracture
strength of the structural  lm. It can also be used to investigate the e ect of a surface
treatment on the fracture strength of the structural  lm. Accordingly, it can be used
to determine the fracture strength of the composite structural  lm, which is formed
when the original structural  lm is coated with a uniform conformal coating.
101
Fracturebeams
w
Lc
Anchored patternCentral Shuttle
Corrugations
Movablepattern
Figure 5.3: Optical image of a released Mechanical Strength Tester.
102
5.2.1 Design
Test Device
The fundamental design of the Mechanical Strength Tester is inspired from that
of the fracture strength test device developed by Jones [154]. Figure 5.3 is an optical
image of a released Mechanical Strength Tester. As seen in Fig. 5.3, the Mechanical
Strength Tester has a symmetric design. It consists of a central suspended shuttle,
which is supported by two identical folded beam  exures. One folded beam  exure
is connected to each of the two longer edges of the central shuttle. The two shorter
edges of the central shuttle are designed to be corrugated in order to ensure that
the probe tip that is used to actuate the Mechanical Strength Tester does not slide
along the edge that is pushed by it. This ensures that throughout the actuation of
the Mechanical Strength Tester, the motion of its central shuttle is strictly restricted
only along the direction of actuation, and the lever arm (i.e., Lc) of each of the
actuated fracture beams stays constant. Further, the Mechanical Strength Tester
has two identical sets of three fracture beams each. One set of three fracture beams
is protruding out of each of the two longer edges of the central shuttle. The three
fracture beams that belong to same set all have di erent lengths. Their lengths are
50  m , 60  m and 70  m, respectively. The widths of all the six fracture beams of
the Mechanical Strength Tester are same. However, the TP has three distinct sets of
Mechanical Strength Testers. While the widths of all the fracture beams belonging
to a particular set are same, those of the fracture beams belonging to di erent sets
are di erent. The widths of the fracture beams belonging to the three distinct sets of
Mechanical Strength Testers that are included in the TP are 3  m (nominal), 4  m
(nominal) and 5  m (nominal), respectively. The Mechanical Strength Tester also has
an anchored scale, which is placed in the cavity of the central suspended shuttle. This
scale is included in the Mechanical Strength Tester to aid the measurement of the
103
displacement of the central shuttle during the actuation of the Mechanical Strength
Tester. However, in all the experiments conducted for this study, the displacement of
the central shuttle of the Mechanical Strength Tester is measured using the movable
and anchored patterns labelled in Fig. 5.3 and a pattern matching technique.
Micro-manipulator
A specialized micro-manipulator is developed to actuate the Mechanical Strength
Testers for this study. The micro-manipulator, in its assembled form, is shown in
Fig. 5.4. It consists of two main components: the \coarse" manipulator and the
\ ne" manipulator. The coarse manipulator is a micropositioner (Model # S - 926)
obtained from Signatone. It is used as the holder for the  ne manipulator as well as
for positioning the probe tip in contact with the Mechanical Strength Tester that is to
be actuated. The  ne manipulator consists of  ve components, which are taken apart
and shown clearly in Fig. 5.5. The probe holder is used to hold the probe tip that is
used to push the central shuttle, and (using a connector) is screwed into the front-
end of the open-loop piezo module. The open-loop piezo module (Melles Griot, travel
range is 0 - 30  m and operating voltage is 0 - 100 V) is used to generate the force
that is required to push the central shuttle. It is controlled using the MEMScript.
The use of a piezoelectric actuator to actuate the Mechanical Strength Tester enables
a controlled and precise pushing of the central shuttle. It allows the central shuttle
to be displaced in extremely small, precise and equal nanometer-scale steps. The
connecting shaft (using a connector) is screwed into the back-end of the open-loop
piezo module at one end, and inserted into the coarse manipulator at the other. It
is used as the connection between the  ne manipulator and the coarse manipulator,
which is used as the holder for the  ne manipulator. The probe holder and the
connecting shaft are made from a single holder (U-P style) bought from Signatone.
The orthographic projections (plan view) of the four machined components (i.e., the
104
Coarse manipulatorBypass connectionFine manipulator
Figure 5.4: Photograph of the Micro-manipulator developed to actuate the Mechani-
cal Strength Testers. Notice the \bypass" connection used to electrically ground the
probe tip. The two main components of the Micro-manipulator (i.e., the \coarse"
manipulator and the \ ne" manipulator) are clearly labelled in the photograph.
105
ProbeholderConnectingConnectorConnectorshaftOpen?loop piezo moduleProbetip
Figure 5.5: Photograph showing the  ve components of the \ ne" manipulator.
106
Probeholder
ConnectorConnector
Connectingshaft
Figure 5.6: Orthographic projections (plan view) of the four machined components
of the \ ne" manipulator. The dimensions indicated in the orthographic projections
are in mm.
107
probe holder, the two connectors and the connecting shaft) of the \ ne" manipulator
are shown in Fig. 5.6. The probe tip is electrically grounded using the \bypass"
connection shown in Fig. 5.4.
5.2.2 Testing Procedure
Mechanical Strength Testers are actuated using the Micro-manipulator shown in
Fig. 5.4. The probe tip used in the Micro-manipulator, to push the central shuttle
of the Mechanical Strength Tester, is a Signatone SE-20T probe tip. To actuate a
Mechanical Strength Tester,  rst, it is brought in contact with the anchored stopper
blocks using the \coarse manipulator", at which point, its position is considered as
the initial position, then, a DC voltage is applied to the open-loop piezo of the  ne
manipulator, and the substrate and the probe tip are electrically grounded. The volt-
age applied to the open-loop piezo is increased from 0 V at a rate of 0.5 V/s up to 100
V. This stimulates the  ne manipulator to push the central shuttle of the Mechanical
Strength Tester in the direction of the arrow shown in Fig. 5.3. As the displacement
of the central shuttle increases, the fracture beams that are protruding out of the
central shuttle are pushed against their corresponding anchored stopper blocks. The
central shuttle is pushed until all the fracture beams attached to it are broken. Op-
tical images illustrating the actuation procedure of the Mechanical Strength Tester
are shown in Fig. 5.7. The displacement of the central shuttle is determined at every
push, throughout the actuation of the Mechanical Strength Tester. An optical pat-
tern matching technique, which has a resolution of 20 nm (A Mitutoyo M Plan Apo
10 objective is used as the objective lens in the microscope), is used to determine the
displacement of the central shuttle. The script that is used to actuate Mechanical
Strength Testers is given in Appendix A.2.
The Mechanical Strength Tester developed in this study can be modeled using
an analysis similar to that reported in [154], by Jones. Accordingly, the fracture
108
(a)
(b)
(c)
Figure 5.7: Optical images illustrating the actuation of a Mechanical Strength Tester.
(a) The MST is shown in its pre-actuated state. (b) Optical image collected during
the actuation of the MST. Notice that all the six fracture beams are pushed against
their corresponding anchored stoppers. (c) Optical image showing the MST in its
post-actuated state. Notice that all the fracture beams that were attached to the
central shuttle are fractured.
109
strength ( f) of the structural  lm can be determined using Eq. 5.2.1, where, E is
the elastic modulus of the structural  lm, w is the width of the fractured beam,  f is
the distance, by which, the shuttle is displaced when the fracture beam gets fractured
and Lc is the distance between the shuttle and the anchored stopper corresponding
to the fractured beam [154].
 f = 3Ew f2L2
c
(5.2.1)
Rearranging Eq. 5.2.1 gives Eq. 5.2.2, which can be used to determine the strain
( f) induced in the structural  lm at the time of its fracture. The fracture strain of
a structural  lm is a fundamental property characteristic of its material, and more
often reported in literature than the fracture strength.
 f = 3w f2L2
c
(5.2.2)
5.3 Resonator
The Resonator can be used to determine the elastic modulus (E) of a structural
 lm. It can also be used to determine the surface coverage (i.e., projected surface
area) of nanoparticle-based thin  lm coatings, which are deposited on MEMS surfaces
to texture them.
5.3.1 Design
Figure 5.8 is an optical image of a released Resonator. As seen in Fig. 5.8, the
Resonator also has a symmetric design. It consists of two banks of interdigitated
movable and anchored comb  ngers. Each bank of comb  ngers has 30 movable comb
 ngers and 29 anchored comb  ngers. The movable comb  ngers of the two banks of
comb  ngers are connected through a shuttle, which is suspended when the Resonator
is released. The suspended shuttle is supported by two identical folded beam  exures,
one of which, is attached to each of its two sides. Each of the two folded beam  exures
110
Suspended
Pattern
Folded beamflexure
shuttle
Anchored comb?finger
Movablecomb?finger
Figure 5.8: Optical image of a released Resonator.
111
consist of four identical supporting beams, which are connected to each other by a
truss. The width of each of the eight supporting beams of the Resonator is 3  m
(nominal). However, the Test Platform has nine distinct sets of Resonators, and
the lengths of the supporting beams of the Resonators belonging to di erent sets
are di erent. The lengths of the supporting beams of the Resonators belonging to
those nine distinct sets are 100  m (nominal), 150  m (nominal), 200  m (nominal),
250  m (nominal), 300  m (nominal), 350  m (nominal), 400  m (nominal), 450
 m (nominal) and 500  m (nominal), respectively. The purpose behind including
Resonators with nine di erent supporting beam lengths in the Test Platform is to
have test devices, whose resonance frequencies span a wide range. A speci c pattern
(labeled in Fig. 5.8) is made on the shuttles of all the Resonators of the Test Platform
in order to monitor their displacements during actuation.
5.3.2 Testing Procedure
The Resonators are actuated electrostatically. Electrical contacts are made by
touching the actuation pads, which are fabricated in the microinstrument, with sharp
tungsten probe tips (Signatone SE-20T). The drive-signals applied to actuate a Res-
onator are generated using an arbitrary waveform generator (Keithley, Model # 3390,
50 MHz), and ampli ed using a high-voltage ampli er (TEGAM, 2350S). To actuate a
Resonator, an AC drive signal with a DC bias is applied across either of the two banks
of comb  ngers and the substrate, the movable structure and the other bank of comb
 ngers are electrically grounded. The DC biases used to actuate the Resonators with
di erent supporting beam lengths range from 25 V to 150 V. The corresponding AC
drive signals used to actuate the Resonators with di erent supporting beam lengths
range from 20 V to 40 V, respectively. In order to determine the resonance frequency
of a Resonator, the frequency of the AC drive signal applied to it is increased from
close to zero until it crosses the resonance frequency of the resonating structure. The
112
resonance frequency of a Resonator is detected optically, with a resolution of 5 Hz,
by monitoring the amplitude of the oscillation of the pattern made on the shuttle.
5.3.3 Modeling
The resonance frequency of a resonating structure such as the Resonator devel-
oped in this study is mathematically expressed by the harmonic oscillator equation,
which is given by below:
fR = 12 
s
kx
Meff (5.3.1)
Here, fR is the resonance frequency of the Resonator, kx is the combined sti ness of
both the folded beam  exures, which support the suspended shuttle, and Meff is the
e ective mass of the resonating structure. Solving the Euler-Bernoulii beam equation
for the supporting beams of the Resonator indicates that kx, which is the combined
sti ness of the two folded beam  exures that support the suspended shuttle, can be
given by Eq. 5.3.2.
kx = 24EIL3 (5.3.2)
Here, E is the elastic modulus of the structural  lm, I is the area moment of inertia
experienced by the supporting beams of the Resonator about the axis that is perpen-
dicular to their plane of bending and L is the length of the supporting beams of the
Resonator. Since the slopes of all the sidewalls of the Test Platform are close to 90 ,
the cross-sections of all the supporting beams of the Resonator can be considered as
rectangular. Therefore, I can be given by Eq. 5.3.3.
I = tw
3
12 (5.3.3)
113
Here, t is the thickness of the structural  lm and w is the width of the supporting
beams. Substituting Eq. 5.3.3 in Eq. 5.3.2 gives,
kx = 2Et
 w
L
 3
(5.3.4)
Substituting Eq. 5.3.4 in Eq. 5.3.1 gives,
fR = 12 
s
2E tw
3
MeffL3 (5.3.5)
Squaring Eq. 5.3.5 gives Eq. 5.3.6, which can be used to determine the elastic modulus
(i.e., E) of the structural  lm.
f2R = E
 tw3
2 2MeffL3
 
(5.3.6)
fR, which is the resonance frequency of the Resonator, is determined experimentally,
t, w and L, which are the thickness, width and length of the supporting beams of the
Resonator, respectively, are measured optically, with a resolution of  0.465  m (A
Mitutoyo M Plan Apo 10 objective is used as the objective lens in the microscope).
The e ective mass of the resonating structure (i.e., Meff) can be given by the Rayleigh
equation shown below:
Meff = Ms + 14Mt + 1235Mb (5.3.7)
Here, Ms, Mt and Mb are the masses of the shuttle, the two trusses and the eight
supporting beams of the Resonator, respectively. Ms, Mt and Mb are determined
using the dimensions of the corresponding components of the Resonator, which are
measured optically, with a resolution of  0.465  m (A Mitutoyo M Plan Apo 10
objective is used as the objective lens in the microscope).
114
5.4 Cantilever Beam Array (CBA)
The Cantilever Beam Array can be used to determine the apparent work of
adhesion of contacting in-plane surfaces.
5.4.1 Design
Cantilever beams were  rst used for determining the interfacial work of adhesion
of in-plane surfaces by Mastrangelo et al., in 1992 [155]. Since then, the cantilever
beam array is considered as the standard test device for studying the stiction charac-
teristics of in-plane surfaces [78]. It has been widely used by several researchers for un-
derstanding the mechanisms underlying the stiction experienced by proximate MEMS
surfaces as well as for studying the e ects of di erent surface treatments [6,13,24,25,
35, 37,38, 64, 67,69, 70, 70,71, 73, 78, 80, 93, 94, 99{103, 107, 111, 130, 149, 152,155{158].
Historically, the cantilever beam arrays that have been used for studying stiction con-
sisted of cantilever beams with increasing lengths [24, 37, 64, 78, 80, 94, 99{101, 158].
While the advantage of using cantilever beam arrays that consist of cantilever beams
with increasing lengths is that they eliminates the need of a metrology technique
to determine the detachment length, the drawback of using them is that each array
can be used to obtain only one data point [13, 64, 94, 100, 101]. Additionally, since
the purpose behind using cantilever beam arrays that consist of cantilever beams
with increasing lengths is to eleminate the need of a metrology technique, the appar-
ent work of adhesion of in-plane surfaces (Wip) is quanti ed by visually determining
the detachment length [6, 13, 35, 37, 64, 78, 94, 100, 101]. This method of quantify-
ing stiction involves determination of the shortest stuck cantilever beam (arc-shaped
beam) [6, 13, 35, 37, 64, 78, 94, 100, 101]. However, deBoer et al. reported that using
cantilever beams that are adhered over long attachments lengths to determine the
apparent work of adhesion of in-plane surfaces yields signi cantly more accurate re-
sults [152]. They demonstrated that quanti cation of stiction using S-shaped beams
115
Figure 5.9: An optical image showing two adjacent released Cantilever Beam Arrays.
116
is much less sensitive to variations in surface topography or to details of capillary
drying than that using arc-shaped beams [152]. Therefore, in order to overcome the
limitations of the cantilever beam array that consists of cantilever beams with increas-
ing lengths, the CBAs that are included in the TP are designed to have 10 cantilever
beams each, all of the same length. An optical image showing two adjacent released
CBAs is shown in Fig. 5.9. The crack length of each cantilever beam of the CBA
is determined using interferometry. Therefore, each cantilever beam of the CBA can
be used to obtain a data point. Accordingly, each CBA of the TP can be used to
obtain ten data points. This not only allows the collection of a statistically signi cant
data set but also enables the analysis of the local variation in the adhesion of studied
in-plane surfaces. Further, to be able to use the S-shaped cantilever beams, which
enable a more accurate estimation ofWip, for quantifying the entire spectrum ofWip,
three distinct sets of eight CBAs each are included in the TP. While all the cantilever
beams belonging to a particular set have the same length, those belonging to di er-
ent sets have di erent lengths. The three sets of CBAs that are included in the TP
consist of cantilever beams with lengths of 500  m (nominal), 1000  m (nominal)and
2000  m (nominal), respectively. The widths of all the cantilever beams of the TP
are 30  m (nominal).
5.4.2 Testing Procedure and Analysis
The cantilever beams (CBs) are actuated manually using a sharp tungsten probe
tip (Signatone SE-SMS). A schematic diagram illustrating the actuation procedure of
the cantilever beams is shown in Fig. 5.10. To actuate a cantilever beam,  rst, its tip
is brought in contact with the substrate by pushing with the probe tip and then, the
cantilever beam is pushed along its length progressively at points closer to its anchor
until it is in contact with the substrate over almost its entire length, leaving a length
between 50 - 60  m near the anchor, as shown in Fig. 5.10b. At this point, the probe
117
6
?t
h
L
?
Ground Plane (Substrate)
?
Anchor
?
Cantilever Beam
(a)
(b)
(c)
s
Figure 5.10: A schematic diagram illustrating the actuation procedure of a cantilever
beam. (a) Free-standing (unactuated) cantilever beam. (b) Actuated cantilever beam.
(c) Cantilever beam released after actuation (post-actuation state). Notice that the
cantilever beam is adhered over a length of L s at its tip.
118
tip is carefully and slowly retracted, which allows the cantilever beam to peel apart up
to a certain characteristic length called as the crack length s, under the in uence of its
restoring force (i.e., see Fig. 5.10c). The crack length exhibited by a cantilever beam
depends on the interfacial properties of the two contacting in-plane surfaces, which in
the case of the TP, are the bottom surface of the cantilever beam (i.e., device layer)
and the top surface of the substrate. The crack length of each actuated cantilever
beam is determined optically using phase shifting interferometry. The long-working-
distance, incoherent light interference microscope of the Probe Station is used to
collect the interferograms. The apparent work of adhesion of the in-plane surfaces of
the TP is determined using Eq. 5.4.1, which is derived by Hurst et al. in [175].
Wip = 3Et
3
2s4
 
a23 +a3a2 + 13a22
 
(5.4.1)
Here, E is the elastic modulus of the structural  lm (device layer), t is the thickness
of the cantilever beam (in the case of the TP, thickness of the structural  lm), s is
the crack length and a3 and a2 are parameters extracted from a 3rd order polynomial
 tted to the height pro le of the actuated cantilever beam, which is determined
experimentally using phase shifting interferometry. The script used to determine the
height pro le of an actuated cantilever beam is given in Appendix A.4. This script
also extracts the crack length of the actuated cantilever beam from its experimental
height pro le, and calculates the apparent work of adhesion of the tested in-plane
surfaces using it.
5.5 Sidewall Beam Array (SBA)
The Sidewall Beam Array can be used to determine the apparent work of adhesion
of contacting sidewall surfaces.
119
5.5.1 Previously Reported Devices: A Review
While the cantilever beam array (CBA) is widely used as a standard test device
to investigate stiction between in-plane surfaces, there is no consensus on a standard
device to study stiction between sidewalls. Historically, the devices that have been
used to study stiction between sidewalls can be primarily classi ed into two categories:
devices that measure adhesion force and devices that measure adhesion energy. The
 rst device that was designed to measure adhesion force between sidewall surfaces was
reported by Timpe et al. [142]. The device consisted of two suspended shuttles, each
connected to two comb drives. One comb drive connected to each shuttle was used to
bring the shuttles into contact while the other comb drive was used to pull them apart.
The di erence in the voltages applied to the two sets of comb drives at the instance of
contact and separation of shuttles, respectively were used to determine the adhesion
force between sidewalls. Since the instance of contact and separation of shuttles was
detected optically, the resolution with which the adhesion force between sidewalls
could be measured was limited [79, 159]. Also, the electrostatic forces generated by
the comb drives, which were used to determine the adhesion force between sidewalls,
were calculated theoretically and not obtained experimentally. In order to improve
the resolution of adhesion force measurement, van Spengen et al. and Friedrich et al.
used the change in the experimentally measured capacitance of the detection drive
to determine the instance of contact and separation of sidewall test surfaces [79,159].
While the test device designed by Friedrich et al. was similar to that reported by
Timpe et al., that designed by van Spengen et al. consisted of only one suspended
shuttle, which was made to contact and separate from the sidewall surface of a  xed
post [79,159]. While the devices reported by van Spengen et al. and Friedrich et al.
could measure sidewall adhesion force with a high resolution of few nN, both required
external and extremely sophisticated electronic capacitance readout system. Also,
120
both these devices are prone to levitation, which should be accurately accounted for
in the determination of sidewall adhesion force.
Considering the magnitude of adhesion force between MEMS sidewalls, which
ranges from few ten nN to few hundred nN, its sensitivity to sidewall topography and
the dependence of sidewall topography on the conditions used to deposit and anneal
the device layers, measuring the adhesion energy of contacting sidewalls seems to be
a better alternative. The  rst and only device reported to-date, which measures the
apparent adhesion energy needed to separate contacting sidewalls, was designed by
Ashurst et al. [78]. The device consisted of two suspended, parallel cantilevers, which
were electrostatically brought into contact along their sidewalls, and the apparent
adhesion energy was determined using the energy minimization approach suggested
by Mastrangelo et al. [78]. Although the device was successfully used to determine
the apparent adhesion energy of octadence coated as well as oxide coated sidewall
surfaces, it had two major design limitations [78]. First, owing to the residual stress
gradients in the polycrystalline (polysilicon) device layers, the test beams were curled
down [78]. As a result, the longer test beams were touching the substrate at their tips,
which made them unusable [78]. Second, the post-actuated beams that were stuck
together exhibited random and irreproducible \scissoring" (misalignment in the z
plane), which limited the accuracy with which the apparent adhesion energy could
be determined [78]. The microinstrument developed in this study for studying the
stiction characteristics of sidewall surfaces not only addresses some of the limitations
of the test microinstrument reported by Ashurst et al. but is also much easier to
fabricate. The details of the design, fabrication and modeling of the microinstrument
are described in the following sections.
121
CCCC
    
 
  
Electrode
 
 
  
Kink
 
 
  
Stopper
 
 
  
 
 
 
  
Bending Beams
Figure 5.11: A schematic diagram of the sidewall adhesion test microinstrument (plan
view). Shaded regions shown in the diagram are anchored to the substrate. A ground
plane (not depicted) is present underneath the entire device.
122
5.5.2 Design
The fundamental design of the sidewall adhesion test microinstrument developed
in this study is inspired from that of the microinstrument designed by Ashurst et al.
[78]. Accordingly, the same rationale that was used, by Ashurst et al. in [78], to justify
the use of two cantilever beams as the sidewall beams of their sidewall adhesion test
microinstrument also explains the design of the Sidewall Beam Array, in which too,
two cantilever beams are used as the sidewall beams. A schematic diagram (plan
view) to illustrate the microinstrument is shown in Fig. 5.11. The microinstrument
consists of two cantilever beams (sidewall beams), which are suspended parallel to
each other. Each sidewall beam (SB) consists of two segments; the initial segment,
which has a  xed length of 320  m and the  nal segment, which is connected to
the initial segment using a kink. The sidewall beams (SBs) are 3  m (nominal)
wide and, over their entire  nal segment, 10  m (nominal) apart from each other.
They are designed to contact along their sidewalls when an increasing voltage is
applied to the actuating electrode, which is located between their initial segments.
The actuating electrode is 40  m (nominal) wide and 295  m (nominal) long. It
is centered between the initial segments of the sidewall beams and anchored to the
substrate over the shaded region shown in Fig. 5.11. In order to accommodate the
electrode, the initial segments of the sidewall beams are spaced 52  m apart and,
are kinked inward so that the spacing between their  nal segments is small enough
to ensure that they contact over much of their lengths with the application of only
moderate voltages to the electrode. A stopper with nominal dimensions of 40  m
 40  m is fabricated, in front of the electrode between the initial segments of the
sidewall beams, to avoid short-circuit between the sidewall beams and the electrode
in the event of a catastrophic failure. An optical image of a released sidewall adhesion
tester is shown in Fig. 5.12a. In order to be able to accurately determine the crack
length of the actuated adhered sidewall beams, anchored scales are fabricated on
123
both the sides of the pair of sidewall beams. One of those anchored scales is clearly
visible, at the bottom, in Fig. 5.12a. The distance between the adjacent markers (i.e.,
protrusions) of the scale is 25  m. In order to ensure that surfaces with a wide range
of adhesion energies could be investigated using the sidewall adhesion tester, an array
(i.e., Sidewall Beam Array) consisting of seven sidewall adhesion testers is designed.
The length of the  nal segment of the sidewall beams varies from 420  m to 1920
 m in the array. An optical image of the Sidewall Beam Array (SBA) is shown in
Fig. 5.12b.
5.5.3 Testing Procedure
The sidewall adhesion test microinstrument is actuated electrostatically. Elec-
trical contacts are made by touching the actuation pads, which are fabricated in the
microinstrument, with sharp tungsten probe tips (Signatone SE-20T). The voltages
applied to the electrode of the sidewall adhesion test microinstrument are generated
using a digital-to-analog converter (DAC) and ampli ed using a high-voltage ampli-
 er (TEGAM, 2350S). A schematic diagram (plan view) illustrating the actuation
procedure of the microinstrument is shown in Fig. 5.13. To actuate the sidewall ad-
hesion test microinstrument, the sidewall beams and the ground plane (substrate)
are electrically grounded and, a DC voltage is applied to the electrode. The voltage
applied to the electrode is increased from 0 V at the rate of 1 V/s to 90 V. As the
applied voltage is increased, the two sidewall beams are drawn together like tweezers
and at 90 V, they are in contact over much of the length of their  nal segments, leav-
ing a length between 100 and 125  m near electrode not contacting. The actuation
voltage is then ramped down to 0 V at the rate of 1 V/s, which allows the sidewall
beams to peel apart under the in uence of their restoring forces. The sidewall beams
peel apart up to a certain characteristic length called as the crack length (s), which
depends on the interfacial properties of the two contacting surfaces. The crack length
124
(a)
(b)
Figure 5.12: (a) Optical image of a released sidewall adhesion test microinstrument.
Anchors that anchor the sidewall test beams are not visible in the image. The total
length of the sidewall beams shown in the image is 750  m. (b) Optical image of a
released sidewall beam array. The shortest pair of sidewall beams is 750  m long. The
length of sidewall beam pairs is increased in increments of 250  m and the longest
pair of sidewall beams is 2250  m long.
125
of each actuated adhered pair of sidewall beams is determined using the anchored
scales fabricated on both the sides of the pair of sidewall beams. Each division of the
anchored scale, which is 25  m long, is further divided into  ve sub-divisions using a
scale ruler and the crack length is determined optically with a resolution of 2.5  m.
To determine the crack length, the adhered beams are brought into focus successively
from their anchored ends to their tips. This real-time dynamic focussing of the ad-
hered beams accentuates the sharpness of the crack tip and enables the determination
of its location within 12 pixels. Once the crack length is known, the apparent work
of adhesion of the sidewall surfaces is determined using the same analysis as that
reported by Ashurst et al. [78]. The script used to actuate a pair of sidewall beams
is given in Appendix A.5. This script can also be used to determine the crack length
of the actuated sidewall adhesion tester, and calculate the apparent work of adhesion
of tested sidewall surfaces using it.
5.5.4 Modeling
In order to evaluate the interfacial adhesion between the sidewall surfaces, a
mechanical energy minimization model is employed. The objective of the model is
to minimize the energy of the system (UT), which is a sum of the mechanical strain
energy (UE) stored in each bending beam and the interfacial adhesion energy (US) of
the fractions of the sidewall beams adhered beyond the crack length.
UT = 2UE +US (5.5.1)
Each sidewall beam is considered as a cantilever beam, which bends (from side to
side) in the x-y plane. Accordingly,
UE = EI2
sZ
0
 d2u
dx2
 2
dx (5.5.2)
126
CCCC
    
6
?t
2h
L
?
CCCC
    
?
CCCC
    
s
Figure 5.13: A schematic diagram (plan view) illustrating the actuation procedure
of the sidewall adhesion tester. (Top) The sidewall beams are in the as-fabricated
position. (Center) The sidewall beams are in an actuated state, contacting over
almost the entire length of their  nal segments. (Bottom) Final state of the sidewall
beams post-actuation when the actuating voltage is reduced to zero. The beams are
adhered over a length L s at their tips.
127
where, u is the de ection of the sidewall beam in the x-y plane. Since in their  nal
state post-actuation, the sidewall beams are S-shaped, their de ection can be de ned
by Eq. 5.5.3.
u = hx
2
s2
 
3 2xs
 
(5.5.3)
I is the moment of inertia in the bending plane and for the sidewall beams is given
by Eq. 5.5.4.
I = wt
3
12 (5.5.4)
E is the elastic modulus of the structural  lm (device layer), which for the microin-
strument developed in this study, is a 2  m thick (nominal) Si(100)  lm. h is the
distance through which each beam bends (half the distance between the unactuated
sidewall beam pair in as-fabricated position), x is the position along the beam (the
anchor point corresponds to x = 0), s is the crack length, w is the width of the
sidewall beams (for the microinstrument developed in this study, w is the thickness
of the device layer), t, as indicated in Fig. 5.13, is the thickness of the sidewall beams.
As suggested by Ashurst et al. in [78], the kink can reasonably be neglected in the
modeling of the sidewall adhesion test microinstrument. Also, since the slopes of all
the sidewalls of the test platform are close to 90 , the torsional compliance of the
sidewall beams is also neglected in their modeling. US is given by Eq. 5.5.5.
US = Wsw(L s) (5.5.5)
Here, Ws is the apparent work of adhesion of the sidewall surfaces and L s is the
fraction of their lengths, over which, the sidewall beams are adhered post-actuation.
Minimizing UT with respect to crack length s and solving for W gives Eq. 5.5.6.
Ws = 3Et
3h2
s4 (5.5.6)
128
It should be noted that Eq. 5.5.6 yields the apparent work of adhesion, since, the
model uses the apparent area of contact (in Eq. 5.5.5), which is di erent from the
real area of contact due to the  nite roughness and topography of the contacting
sidewall surfaces.
5.6 Sidewall Friction Tester (SFT)
The Sidewall Friction Tester can be used to study the friction and wear charac-
teristics of contacting sidewall surfaces.
5.6.1 Previously Reported Devices: A Review
Initial studies that investigated the friction and wear behaviour of MEMS sur-
faces used polycrystalline silicon (polysilicon) based, surface micromachined rotat-
ing microinstruments such as microturbines, electrostatic micromotors and micro-
engines [82, 83, 147, 160, 161]. While studying the dynamic behavior of a rotating
microinstrument gave a good notion of the friction and wear behaviour of the sur-
faces of that particular device, the results could not be generalized because the con-
tact geometries and hence the contact pressures at the contact interfaces could not
be determined accurately [85, 143]. Therefore, Senft and Dugger designed and sur-
face micromachined a polysilicon based sidewall friction and wear test device, which
had a well-de ned contact geometry [85]. The device consisted of two orthogonal
comb-drive actuators, one of which was used to apply the normal load at the contact
interface, while the other was used to shear the contact interface [85]. The contact
interface was formed by bringing the  at sidewall surface of a suspended beam in
contact with the cylindrical sidewall surface of an anchored post [85]. Although Senft
and Dugger?s test device had a well-de ned contact geometry, the contact pressure
could still not be determined accurately because the device had an asymmetric design,
which resulted in moments that could not be accurately accounted for. Additionally,
129
the onset of slip was detected optically, which limited the resolution, with which, the
friction force could be measured [85]. In order to improve the accuracy of the esti-
mation of contact pressure, Tas et al. reported a polysilicon based sidewall friction
and wear test device, whose design did not induce any unaccounted moments [150].
As a result, the contact pressure at the interface, which was formed between two  at
sidewall surfaces in their device, could be determined accurately. However, even Tas
et al. detected the onset of slip optically [150]. Timpe et al. also reported two di er-
ent polysilicon based sidewall friction and wear test devices, which enabled accurate
estimation of the contact pressure owing to their symmetric designs [23,143,162]. The
contact geometry in one of their devices was  at-on- at, while that in the other was
 at-on-cylinder [23, 143, 162]. Timpe et al. too detected the onset of slip optically,
which limited the resolution of their measurements [79,159]. In order to improve the
resolution of measurements, Asay et al., who used a polysilicon microdevice similar
to that reported by Timpe et al., used a pattern-matching algorithm, which enabled
displacement measurements with a resolution of 40 nm, and van Spengen et al., who
used a polysilicon microdevice similar to that reported by Senft and Dugger, used
an external electronic capacitance readout system, which measured the change in
the capacitance of the detection drive during the experiment with a resolution of 10
aF [126, 128, 145]. While the device used by Asay et al. did not have any design
limitations, that used by van Spengen et al. encountered levitation and had a design
limitation, which precluded accurate determination of the normal load applied to the
contact interface [145]. Additionally, the electronic capacitance readout system em-
ployed by them necessitated averaging of 1000 measurements to obtain an acceptable
signal-to-noise ratio [145].
One common hitch of all the studies mentioned above is that in all of them
the sti nesses of the suspension springs and the electrostatic forces generated by
130
the actuators were calculated using the designed dimensions and not determined ex-
perimentally, which might have resulted in inaccurate determination of the friction
coe cients [23,85,126,143,145,150]. Additionally, the sidewall friction and wear test
devices used in all of them were fabricated using polysilicon structural  lms. There-
fore, owing to the variable material properties and surface roughness of polysilicon
structural  lms, the results obtained in all of the above mentioned studies showed
signi cant device to device scatter, which made it di cult to draw a meaningful con-
clusion [23,85,126,143,145,150]. Only four single-crystal-silicon (SCS) based friction
test devices have been reported to date [141, 151, 163{165]. The  rst single-crystal-
silicon (SCS) based friction test device was reported in 1995, by Prasad et al., who
used it to study the friction characteristics of oxide coated sidewalls [164]. Later in the
last  ve years, three more single-crystal-silicon (SCS) based friction test devices have
been reported by Hwang et al., who used it to study the friction characteristics of oxide
coated sidewalls, Guo et al., who also used it study the friction characteristics of oxide
coated sidewalls, and Wu et al., who used it to study the stick-slip behaviour of SCS
sidewalls, respectively [141,151,163,165]. The single-crystal-silicon (SCS) based fric-
tion test device reported by Guo et al. had an asymmetric design [163]. Accordingly,
it has the same limitations as the friction test device reported by Senft and Dug-
ger [85]. Additionally, all the single-crystal-silicon (SCS) based friction test devices
reported to date were fabricated using relatively complicated fabrication schemes.
The device reported by Prasad et al. was fabricated using SCREAM, those reported
by Guo et al. and Wu et al. were fabricated using the silicon on glass (SOG) fab-
rication process and that reported by Hwang et al. was fabricated using a two step
surface micromachining scheme [141, 151, 163{165]. Also, the sidewall test surfaces
of all the single-crystal-silicon (SCS) based friction test devices reported to date had
signi cant roughnesses [141, 151, 163{165]. The SCS based sidewall friction tester
developed in this study not only addresses some of the limitations of the previously
131
reported devices, but is also much easier to fabricate and has relatively smoother
sidewalls [78,141]. The details of the design, fabrication and modeling of the SFT are
described in the following sections.
5.6.2 Design
The fundamental design of the Sidewall Friction Tester (SFT) developed in this
study is inspired from that of the microinstrument designed by Senft and Dugger [85].
A schematic diagram (plan view) illustrating the SFT is shown in Fig. 5.14. The
SFT consists of two identical comb-drive actuators, which are integrated in such a
way that they can produce motion in orthogonal directions. One of the comb-drive
actuators (normal arm) is used to form the sidewall interface by bringing the  at
sidewall surface of a suspended beam in contact with the cylindrical sidewall surface
of an anchored post. The normal arm is also used to apply the normal load at the
sidewall interface. The other comb-drive actuator (tangential arm) is used to shear
the sidewall interface. Each of the two comb-drive actuators have one push drive
and one pull drive (see Fig. 5.14), which allows the loading beam that forms the
sidewall interface to be moved both forward as well as backward from its unactuated
positions in both the orthogonal directions. In both the arms of the SFT, the shuttles
are suspended using four identical folded beam  exures. Each folded beam  exure
consists of four identical supporting beams, which are connected to each other by a
truss. The supporting beams are 500  m (nominal) long and 3  m wide (nominal).
The SFT has two anchored posts, which are fabricated exactly opposite to each other
(see Fig. 5.14), so that, both the sidewall surfaces of the loading beam can be tested.
An optical image of a released SFT is shown in Fig. 5.15.
Each of the four drives (i.e., two push drives and two pull drives) have four
identical banks of interdigitated anchored and suspended comb  ngers. Each bank
has 44 suspended and 45 anchored comb  ngers, which are 45  m (nominal) long
132
A
A
A
A
A
AAU
@
@
@
@@R
-
?
 
 
  
  
 
 
HHHY
A
A
AK
C
C
CCO
?
Push drives
Pull drives
Loading section
Tangential armNormal
arm
Anchored
reference
patterns
Patterns tracked during experimemt
Figure 5.14: A schematic diagram of the Sidewall Friction Tester (plan view). Shaded
regions shown in the diagram are anchored to the substrate. A ground plane (not
depicted) is present underneath the entire device. The diagram is not drawn to scale
to better illustrate the important components of the device.
133
Figure 5.15: Optical image of a released Sidewall Friction Tester (SFT). Notice the
ground plane present underneath the entire device. The total footprint of the mi-
croinstrument is 2.8 mm2.
134
and 3  m (nominal) wide. Since the minimum feature size that could be resolved in
the fabrication process used to fabricate the TP was 3  m (nominal), the minimum
gap between the overlapping lengths of anchored and suspended comb  ngers that
could be resolved was also 3  m. However, since the electrostatic force generated by
a comb-drive actuator is inversely proportional to the gap between its anchored and
suspended comb  ngers, a smaller gap between the anchored and suspended comb
 ngers of the comb-drive actuators of the SFT developed in this study was desired so
that a larger maximum electrostatic force could be generated using them. Therefore,
the anchored comb  ngers of the SFT developed in this study are designed to have two
segments. The initial segments of adjacent anchored comb  ngers, which are 22.8  m
(nominal) long, are 9  m (nominal) apart from each other, while the  nal segments,
which are 22.2  m (nominal) long, have a gap of 5  m (nominal) between them. A
schematic diagram illustrating the segmental design of the anchored comb  ngers of
the SFT developed in this study is shown in Fig. 5.16a. As seen in Fig. 5.16a, in
the as-fabricated (unactuated) position, in which they overlap over a length of 20
 m (nominal), the gap between the suspended comb  nger and the initial segment of
the anchored comb  nger is designed to be 3  m (nominal). However, owing to the
segmental design of the anchored comb  ngers, during actuation, when the overlap of
the suspended and anchored comb  ngers will increase beyond 22.8  m (nominal), the
gap between them will decrease to 1  m (nominal). This will increase the electrostatic
force generating capacity of the comb-drive actuators of the SFT developed in this
study by a factor of three. In order to ensure that the gap between the tip of a
suspended comb  nger and the  nal segment of an anchored comb  nger is also 3  m
(nominal) in the as-fabricated position, the suspended comb  ngers are designed to
have unique pointed tips. Figure 5.16b is an optical image showing one of the sixteen
banks of comb  ngers of a released Sidewall Friction Tester (SFT). The segmental
designs of the anchored comb  ngers, which are in their as-fabricated (unactuated)
135
position, are clearly seen in this image. Figure 5.16c is a magni ed optical image of
the area enclosed in the box in Fig. 5.16b. The pointed tips of the suspended comb
 ngers, which are in their as-fabricated (unactuated) positions, are clearly seen in
this image.
Figure 5.17 is an optical image showing the loading section of a released (un-
polished) SFT in its as-fabricated position. Anchored and suspended patterns that
are used to track the normal and tangential displacements of the loading beam are
clearly labelled in Fig. 5.17. It is clearly visible in Fig. 5.17 that the anchored posts
are not aligned with the as-fabricated (unactuated) position of the normal arm (i.e., b
is greater than a by 8  m). This intentional misalignment is designed to ensure that
the overlap of the anchored and suspended comb  ngers of the pull drive of the tan-
gential arm is greater than 22.8  m when the normal arm is aligned with the anchored
posts during actuation. Also, in the as-fabricated position, both the anchored posts
are designed to be 6  m (nominal) apart from the corresponding sidewall surfaces
of the loading beam, which ensures that the overlap of the corresponding anchored
and suspended comb  ngers of the normal arm is also greater than 22.8  m when
the loading beam comes in contact with either of the two anchored posts. Since the
normal arm and the anchored posts are aligned before the loading beam is brought
in contact with a post, application of the normal load at the sidewall interface does
not induce an unbalanced moment at it. While the symmetric geometry of the U-
beam (see Fig. 5.17), which transfers the electrostatic force generated by the normal
arm to the loading beam, ensures that both the ends of the loading beam exert the
exact same amount force on the post (i.e., half of the total applied normal load), the
alignment of the normal arm with the anchored posts ensures that both the ends of
the loading beam are equidistant from the post. As a result, the moments induced at
the post by the loads applied at the two ends of the loading beam are exactly equal
in magnitude and opposite in direction. Therefore, since no unbalanced moment is
136
?
6
3  m
?65  m ?3  m
@@RC
C
C
C
CCW
Anchored comb  ngers
C
C
C
CCW
Suspended comb  nger
(a)
(b)
(c)
Figure 5.16: (a) A schematic diagram illustrating the segmental design of the anchored
comb  ngers of the SFT. The diagram is drawn using a scale of 127000:1. In the as-
fabricated (unactuated) position, the anchored and suspended comb  ngers overlap
over a length of 20  m (nominal). Notice that the gap between them will decrease to
1  m (nominal) when their overlap increases beyond 22.8  m (nominal). (b) Optical
image showing a bank of interdigitated anchored and suspended comb  ngers. The
two segments of the anchored comb  ngers are clearly visible in this image. (c)
Magni ed optical image of the area enclosed in the box in image b. The pointed tips
of the suspended comb  ngers are clearly visible in this image.
137
induced at the sidewall interface by the applied normal load, no counter-balancing
unaccounted additional normal load is applied at it by the tangential arm.
5.6.3 Modeling
Since the geometry of a set of interdigitated anchored and suspended comb  ngers
is identical to that of a set of parallel plate capacitors, the electrostatic force (F)
generated by a comb-drive actuator in the direction parallel to the length of the
comb  ngers is given by Eq. 5.6.1 [63].
F =   ntg V2 (5.6.1)
Here,  and  , which are in uenced by the design of the comb-drive, are parameters
that account for the e ects of fringing  elds and levitation,  is the dielectric constant
of the material between the anchored and suspended comb  ngers (in the case of our
study, it is air), n is the number of suspended comb  ngers in the comb-drive actuator,
t is the thickness of the comb  ngers, g is the gap between the anchored and suspended
comb  ngers and V is the applied voltage. For simplicity, the constants are lumped
into a geometric parameter c. Therefore,
c =   ntg (5.6.2)
Accordingly Eq. 5.6.1 becomes,
F = cV2 (5.6.3)
The anchored comb  ngers of the Sidewall Friction Tester developed in this study
have two segments. Therefore, to distinguish between them, subscripts 1 and 2 will be
used for the initial and  nal segments of the anchored comb  ngers, respectively. Sim-
ilarly, subscripts n and t will be used for the normal and tangential arms, respectively.
138
U?beam
Figure 5.17: Optical image showing the loading section of an unpolished, released
Sidewall Friction Tester. The loading section is in its as-fabricated (unactuated) po-
sition. Notice that the anchored posts are not aligned with the as-fabricated position
of the normal arm (i.e., b is greater than a). The gap between the anchored posts
and the corresponding sidewall surfaces of the loading beam is 6  m (nominal) in the
as-fabricated position.
139
Accordingly,
cn1 =  n1 ntg 
n1
(5.6.4a)
cn2 =  n2 ntg 
n2
(5.6.4b)
ct1 =  t1 ntg 
t1
(5.6.4c)
ct2 =  t2 ntg 
t2
(5.6.4d)
Since the normal and tangential comb-drive actuators of the Sidewall Friction Tester
are exactly identical to each other, therefore,
cn1 = ct1 = c1 (5.6.5a)
cn2 = ct2 = c2 (5.6.5b)
Combining Eq. 5.6.3 with Eqs. 5.6.5a and 5.6.5b gives,
Fn1 = c1V2n (5.6.6a)
Fn2 = c2V2n (5.6.6b)
Ft1 = c1V2t (5.6.6c)
Ft2 = c2V2t (5.6.6d)
Since in both (normal and tangential) arms, the push and pull drives are exactly
identical to each other, the electrostatic forces generated by both the (push as well
as pull) drives of the normal arm can be determined using the same Eqs. 5.6.6a and
5.6.6b and the electrostatic forces generated by both the (push as well as pull) drives
of the tangential arm can be determined using the same Eqs. 5.6.6c and 5.6.6d.
140
As seen in Fig. 5.17, the design of the loading section is such that the normal
arm is not aligned with the anchored posts (i.e., b is greater than a) in its unactuated
(as-fabricated) position. However, before bringing the loading beam in contact with a
post, the normal arm is aligned with the anchored posts. This is done by pulling the
loading section to the left (see Fig. 5.17) using the tangential comb-drive actuator.
The force (Fa) needed to align the normal arm with the anchored posts is given by
Eq. 5.6.7.
Fa = kt a (5.6.7)
where, kt is the combined e ective spring constant of the thin beam that connects the
normal arm to the loading section and all the folded beam  exures of the tangential
arm, and  a is the distance by which the suspended comb  ngers of the pull drive
of the tangential arm must be displaced to align the normal arm with the anchored
posts. Accordingly, from Fig. 5.17,
 a = b a2 (5.6.8)
The sti ness of the thin beam that connects the normal arm to the U-beam is designed
to be signi cantly lesser than the sti nesses of the U-beam and the shuttle of the
normal arm. Therefore, the U-beam and the shuttle of the normal arm are considered
as rigid and the bending of the thin beam only is considered in the model of the
Sidewall Friction Tester. Also, since  a (designed to be 4  m) is much smaller than
the lengths of the supporting beams, which are 500  m (nominal) long, and the
length of the thin beam that connects the normal arm to the U-beam, which is 140
 m (nominal) long, the treatment of the folded beam  exures and the thin beam
that connects the normal arm to the U-beam as linear elastic (Hookean) springs is
valid [35]. The design of the tangential comb-drive actuator is such that a fraction
of the length of suspended  ngers overlaps with the  nal segments of the anchored
141
 ngers when the tangential arm is displaced to a distance of  a in either direction
from its unactuated position. Therefore, the tangential electrostatic force utilized in
aligning the normal arm with the anchored posts is given by Eq. 5.6.9.
Fa = kt a = c2V2a (5.6.9)
where, Va is the voltage that is required to be applied to the tangential comb-drive
actuator to align the normal arm with the anchored posts. Rearranging Eq. 5.6.9
gives,
 a = c2k
t
V2a = Gt2V2a (5.6.10)
Accordingly, the transfer function Gt2 is given by Eq. 5.6.11,
Gt2 = c2k
t
(5.6.11)
Similarly, in the as-fabricated position, the sidewall surfaces of the loading beam and
the corresponding anchored posts are separated by a distance of  c. Therefore, the
force (Fc) required to bring the loading beam in contact with an anchored post is
given by Eq. 5.6.12.
Fc = kn c (5.6.12)
where, kn is the combined e ective spring constant of the thin beam that connects the
tangential arm to the loading section and all the folded beam  exures of the normal
arm. Again, the sti ness of the thin beam that connects the tangential arm to the
loading section is designed to be signi cantly lesser than the sti nesses of the loading
beam and the shuttle of the tangential arm. Therefore, the loading beam and the
shuttle of the tangential arm are considered as rigid and the bending of the thin beam
only is considered in the model of the Sidewall Friction Tester. Also,  c (designed to
be 6  m) is much smaller than the lengths of the supporting beams, which are 500
142
 m (nominal) long, and the length of the thin beam that connects the tangential arm
to the loading section, which is 115  m (nominal) long. Therefore, the treatment
of the folded beam  exures and the thin beam that connects the tangential arm to
the loading section as linear elastic (Hookean) springs is also valid [35]. Further, the
design of the normal comb-drive actuator is also such that a fraction of the length
of suspended comb  ngers overlaps with the  nal segments of the anchored comb
 ngers when the normal arm is displaced to a distance of  c in either direction from
its unactuated position. Therefore, the normal electrostatic force utilized in bringing
the loading beam in contact with an anchored post is given by Eq. 5.6.13.
Fc = kn c = c2V2c (5.6.13)
where, Vc is the voltage that is required to be applied to the normal comb-drive
actuator to bring the loading beam in contact with an anchored post. Rearranging
Eq. 5.6.13 gives,
 c = c2k
n
V2c = Gn2V2c (5.6.14)
Accordingly, the transfer function Gn2 is given by Eq. 5.6.15,
Gn2 = c2k
n
(5.6.15)
The coe cient of static friction ( s) of the contacting sidewall surfaces can be
determined using Eq. 5.6.16,
 s = Ft2;s FaF
n2;s Fc
(5.6.16)
where, Fn2;s and Ft2;s are the total normal and tangential forces generated, at the
instant of slip between the loading beam and the anchored post, using the normal
and tangential comb-drive actuators, respectively. Substituting Eqs. 5.6.6b, 5.6.6d,
143
5.6.9 and 5.6.13 in Eq. 5.6.16 gives,
 s = V
2
t;s V
2
a
V2n;s V2c (5.6.17)
After the initiation of slip at the sidewall interface, the loading beam continues to
slide in contact with the anchored post until the sum of the restoring force generated
by the folded beam  exures of the tangential arm and the thin beam that connects
the normal arm to the U-beam and the kinetic friction force becomes equal to the
tangential force generated using the tangential comb-drive actuator. Therefore, the
coe cient of kinetic friction ( k) of the contacting sidewall surfaces can be determined
using Eq. 5.6.18,
 k = Ft2;s Fa kt sF
n2;s Fc
(5.6.18)
where,  s is the distance for which the loading beam slides in contact with the anchored
post after the initiation of slip at the sidewall interface. Substituting Eqs. 5.6.6b,
5.6.6d, 5.6.9, 5.6.11 and 5.6.13 in Eq. 5.6.18 gives,
 k = V
2
t;s V
2
a  ( s=Gt2)
V2n;s V2c (5.6.19)
It should be noted that the additional normal load experienced by the sidewall in-
terface due to adhesion between the contacting sidewall surfaces is not considered
in Eqs. 5.6.16 and 5.6.18. Therefore, the coe cients of friction determined using
Eqs. 5.6.16 and 5.6.18 are engineering coe cients of friction.
5.6.4 Testing Procedure
To actuate the Sidewall Friction Tester (SFT), the electrical contacts are made by
touching the actuation pads that are fabricated in the Sidewall Friction Tester with
144
sharp tungsten probe tips (Signatone SE-20T). The voltages applied to the comb-
drive actuators of the Sidewall Friction Tester are generated using a digital-to-analog
converter (DAC) and ampli ed using a high-voltage ampli er (TEGAM, 2350S).
Before actuating each SFT, a and b (see Fig. 5.17) are measured for that SFT,
optically with a resolution of  0.465  m, to determine  t. The resolution, with
which the optical measurements are made, is limited by the size of the pixels in the
 eld of view, which is 0.465  m 0.465  m (objective lens used is Mitutoyo M Plan
Apo 10). Next, the restoring forces generated in the normal and tangential arms
in response of their displacements are calibrated in order to determine the transfer
functions Gn2 and Gt2, respectively. To calibrate the restoring forces generated in the
tangential arm, the ground plane (substrate), the suspended movable structure, the
anchored posts and the anchored comb  ngers of the push drive of the tangential arm
are electrically grounded and, a DC voltage is applied to the anchored comb  ngers
of the pull drive of the tangential arm. The applied voltage is ramped up from 0 V
at a rate of 1 V/s to 32 V and the corresponding displacements of the tangential arm
are determined using a pattern matching technique. The script used to calibrate the
tangential arm of the Sidewall Friction Tester is given in Appendix A.6. To calibrate
the restoring forces generated in the normal arm,  rst, the normal arm is aligned
with the anchored posts. This is done by electrically grounding the ground plane
(substrate), the suspended movable structure and the anchored post and, applying a
DC voltage, which is ramped up from 0 V at a rate of 1 V/s to Va, to the anchored
comb  ngers of the pull drive of the tangential arm. Then, the anchored comb  ngers
of the push drive of the normal arm are electrically grounded and a DC voltage
is applied to the anchored comb  ngers of the pull drive of the normal arm. The
voltage applied to the anchored comb- ngers of the pull drive of the normal arm is
ramped up from 0 V at a rate of 1 V/s to 40 V. The position of the loading beam
after the normal arm is aligned with the anchored posts is considered as the initial
145
position and the displacements of the normal arm for each voltage applied to its
pull drive are determined using the pattern matching technique. The script used to
calibrate the normal arm of the Sidewall Friction Tester is given in Appendix A.7.
The patterns that are used to track the positions of the normal and tangential arms
during the calibration of the restoring forces generated in them are shown in Fig. 5.14.
In addition to determining the Gt2, the plot of displacement (of the shuttle of the
tangential arm) versus V2t is also used to determine the voltage required to align the
normal arm with the anchored posts (i.e., Va). Similarly, in addition to determining
the Gn2, the plot of displacement (of the shuttle of the normal arm) versus V2n is also
used to determine the voltage required to bring the loading beam in contact with the
anchored post (i.e., Vc).
To study the friction characteristics of the contacting sidewall surfaces, the
ground plane (substrate), the suspended movable structure and the anchored posts
are electrically grounded and a DC voltage is applied to the anchored comb  ngers
of the pull drives of the tangential and normal arms. First, the voltage applied to
the pull drive of the tangential arm is ramped up from 0 V at a rate of 1 V/s to Va,
at which point, the normal arm becomes aligned with the anchored posts. Next, the
voltage applied to the pull drive of the normal arm is ramped up from 0 V at a rate
of 1 V/s to VN, which is the voltage that should be applied to the pull drive of the
normal arm so that it generates an electrostatic force that corresponds to the external
normal load that is desired to be applied at the sidewall interface. The position of the
tangential arm (loading beam) at this point is considered as the initial position. After
allowing the sidewall interface to equilibrate for 1 min., the voltage applied to the pull
drive of the tangential arm is increased beyond Va at a rate of 0.2 V/s until a slip is
initiated at the sidewall interface. The onset of slip between the contacting sidewall
surfaces is detected by monitoring the position of the loading beam using the pattern
matching technique. The pattern matching technique collects optical images of the
146
loading section at every increment of the voltage applied to the tangential comb-drive
actuator, and uses them to determine the position of the movable pattern relative to
its corresponding anchored pattern at every voltage applied to the tangential comb-
drive actuator. The pattern matching technique is also used to determine  s, which
is the distance for which the loading beam slides in contact with the anchored post
after the initiation of slip at the sidewall interface. The script used for studying the
friction characteristics of the contacting sidewall surfaces, using the SFT, is given in
Appendix A.8.
To study the wear characteristics of the contacting sidewall surfaces, the ground
plane (substrate), the suspended movable structure and the anchored posts are elec-
trically grounded, an AC voltage with a DC bias is applied to the anchored comb
 ngers of the pull drive of the tangential arm and a DC voltage is applied to the
anchored comb  ngers of the pull drive of the normal arm. First, a DC bias, which
is ramped up from 0 V at a rate of 1 V/s to Va, is applied to the pull drive of the
tangential arm. At this point, the normal arm becomes aligned with the anchored
posts. Next, a DC voltage is applied to the pull drive of the normal arm. The voltage
applied to the pull drive of the normal arm is also ramped up from 0 V at a rate of 1
V/s to VN, which is the voltage that should be applied to the pull drive of the normal
arm so that it generates an electrostatic force that corresponds to the external normal
load that is desired to be applied at the sidewall interface. After allowing the sidewall
interface to equilibrate for 1 min., an AC voltage is superimposed on the DC bias ap-
plied to the pull drive of the tangential arm. Wear of the contacting sidewall surfaces
can be qualitatively studied by determining the change in their friction coe cients
with the accumulation of wear cycles [126,128,144].
147
5.7 Sidewall Friction and Adhesion Tester (SFAT)
The Sidewall Friction and AdhesionTester can also be used to study the friction
and wear characteristics of contacting sidewall surfaces. Additionally, it can be used
to determine the adhesion force experienced by contacting sidewall surfaces.
5.7.1 Design
The fundamental design of the Sidewall Friction and Adhesion Tester (SFAT)
developed in this study is a modi ed version of that of the microinstrument designed
by Timpe et al. [23]. An optical image of a released SFAT is shown in Fig. 5.18. As
seen in Fig. 5.18, the SFAT mainly consists of two comb-drive actuators, which are
placed in such a way that their shuttles move in orthogonal directions. One comb-
drive actuators (normal arm) is used to form the sidewall interface by bringing the
 at sidewall surface of the \loading block" attached to its shuttle in contact with the
 at sidewall surface of the \friction block" protruding out of the shuttle of the other
comb-drive actuator. The normal arm is also used to apply the normal load at the
sidewall interface. The other comb-drive actuator (tangential arm) is used to shear
the sidewall interface. Each of the two comb-drive actuators have one push drive and
one pull drive (see Fig. 5.19), which allows both the \loading block" as well as the
\friction block" to be moved both forward as well as backward from their unactuated
positions.
In the normal arm of the SFAT, both the push drive as well as the pull drive have
two identical banks of interdigitated anchored and suspended comb  ngers. Each of
the four banks of comb  ngers of the normal have 26 anchored comb  ngers and 25
movable comb  ngers, all of which are 20  m (nominal) long and 3  m (nominal) wide.
The shuttle of the normal arm of the SFAT is suspended using two identical folded
beam  exures. Each folded beam  exure of the normal arm consists of four identical
supporting beams, which are connected to each other by a truss. All the supporting
148
Normal arm
Tangential arm
Loading section
Figure 5.18: Optical image of a released Sidewall Friction and Adhesion Tester
(SFAT). Notice the ground plane present underneath the entire device. The total
footprint of the microinstrument is 0.47 mm2.
149
beams, which suspend the shuttle of the normal arm, are 300  m (nominal) long and
3  m wide (nominal). In the tangential arm of the SFAT, both the push drive as well
as the pull drive have only one bank of 45 anchored comb  ngers and 44 movable
comb  ngers. All the comb  ngers of the tangential arm are 35  m (nominal) long
and 3  m (nominal) wide. The shuttle of the tangential arm of the SFAT is suspended
using only one folded beam  exure, which consists of four identical supporting beams
that are also connected to each other by a truss. All the supporting beams, which
suspend the shuttle of the tangential arm, are 250  m (nominal) long and 3  m wide
(nominal).
The same rationale that was used to explain the segmental design of the anchored
comb  ngers, and the unique pointed tips of all the comb  ngers, of the SFT is also
the reason behind the segmental design of the anchored comb  ngers, and the unique
pointed tips of all the comb  ngers, of the SFAT. The initial and  nal segments
of the anchored comb  ngers of the normal arm are 12.8  m (nominal) and 7.2
 m (nominal) long, respectively. The gap between the initial segments of adjacent
anchored comb  ngers of the normal arm is 9  m (nominal), which reduces to 5  m
(nominal) between their  nal segments. The initial and  nal segments of the anchored
comb  ngers of the tangential arm are 22.8  m (nominal) and 12.2  m (nominal) long,
respectively. The gap between the initial segments of adjacent anchored comb  ngers
of the tangential arm is also 9  m (nominal) and reduces to 5  m (nominal) between
their  nal segments. Further, similar to the comb  ngers of the SFT (as explained in
Fig. 5.16a), in the as-fabricated (unactuated) position, in which, they overlap over a
length of 10  m (nominal), the gap between a suspended comb  nger and the initial
segment of the corresponding anchored comb  nger of the normal arm is designed
to be 3  m (nominal), which reduces to 1  m (nominal) as the displacement of the
shuttle of the normal arm increases beyond 2.8  m (nominal). In the as-fabricated
(unactuated) position, in which, they overlap over a length of 20  m (nominal), the
150
Pull drivePush drive
(a)Pull drive
Push drive
(b)
Figure 5.19: (a) Optical image showing the normal arm of a released Sidewall Fric-
tion and AdhesionTester (SFAT). (b) Optical image showing the tangential arm of a
released Sidewall Friction and AdhesionTester (SFAT). Notice that both the normal
and the tangential arm have one push drive and one pull drive each.
151
gap between a suspended comb  nger and the initial segment of the corresponding
anchored comb  nger of the tangential arm is also designed to be 3  m (nominal),
and reduces to 1  m (nominal) as the displacement of its shuttle increases beyond
2.8  m (nominal). Accordingly, like the comb-drive actuators of the normal and
tangential arms of the SFT, as the displacements of the shuttles of the normal and
tangential arms of the SFAT increase beyond 2.8  m (nominal), the electrostatic
force generating capacities of their corresponding comb-drive actuators also increase
by a factor of three. Figure 5.20a is an optical image showing one bank of comb
 ngers each of the normal and tangential arms of a released Sidewall Friction and
Adhesion Tester (SFAT). The segmental designs of the anchored comb  ngers of both
the normal as well as tangential arms, which are in their as-fabricated (unactuated)
positions, of the SFAT are clearly seen in this image. Figure 5.20b is a magni ed
optical image showing the comb  ngers of the tangential arm of the SFAT, that are
enclosed in the box in Fig. 5.20a. Figure 5.20c is a magni ed optical image showing
the comb  ngers of the normal arm of the SFAT, that are enclosed in the box in
Fig. 5.20a. The pointed tips of the suspended comb  ngers, which are in their as-
fabricated (unactuated) positions, of the tangential and normal arms of the SFAT are
clearly seen in Fig. 5.20b and Fig. 5.20c, respectively.
Figure 5.21 is an optical image showing the loading section of a released (unpol-
ished) SFAT in its as-fabricated position. The anchored and suspended patterns that
are used to track the displacements of the normal and tangential arms are clearly
labelled in Fig. 5.21. Also, it is clearly visible in Fig. 5.21 that in their as-fabricated
positions, the \loading block" and the \friction block" are designed to be 4  m (nom-
inal) apart from each other, which ensures that the overlap of the anchored and
suspended comb  ngers of the push drive of the normal arm of the SFAT becomes
greater than 12.8  m when the sidewall interface is formed. The contact area of the
152
Tangential armNormal arm
(a)
(b) (c)
Figure 5.20: (a) Optical image showing one bank of interdigitated comb  ngers each of
the normal and tangential arms of a released Sidewall Friction and Adhesion Tester
(SFAT). The two segments of the anchored comb  ngers are clearly visible in this
image. (b) Magni ed optical image showing the comb  ngers of the tangential arm
of the SFAT, that are enclosed in the box in Fig. 5.20a. (c) Magni ed optical image
showing the comb  ngers of the normal arm of the SFAT, that are enclosed in the
box in Fig. 5.20a. The pointed tips of the suspended comb  ngers are clearly visible
in both Fig. 5.20b and Fig. 5.20c.
153
sidewall interface formed by the sidewall surfaces of the \loading block" and the \fric-
tion block" is de ned by the dimensions of the \friction block". The friction block
is 10  m (nominal) long, and protrudes 4  m (nominal) out, from the shuttle of the
tangential arm of the SFAT.
5.7.2 Modeling
As explained in section 5.6.3, the electrostatic force (F) generated by a comb-
drive actuator in the direction parallel to the length of its comb  ngers is given by
Eq. 5.7.1.
F = cV2 (5.7.1)
where,
c =   ntg (5.7.2)
Here,  and  , which are in uenced by the design of the comb-drive, are parameters
that account for the e ects of fringing  elds and levitation,  is the dielectric constant
of the material between the anchored and suspended comb  ngers (in the case of
our study, it is air), n is the number of suspended comb  ngers in the comb-drive
actuator, t is the thickness of the comb  ngers, g is the gap between the anchored
and suspended comb  ngers and V is the applied voltage. Also, since the anchored
comb  ngers of the Sidewall Friction and Adhesion Tester developed in this study
also have two segments, to distinguish between them, subscripts 1 and 2 will be used
for their initial and  nal segments, respectively. Similarly, subscripts n and t will be
154
Movable pattern (Tangential arm)
Anchored pattern (Tangential arm)
Anchored pattern (Normal arm)
Movable pattern (Normal arm)
Loading block
Friction block
Figure 5.21: Optical image showing the loading section of a released Sidewall Friction
and Adhesion Tester. The loading section is in its as-fabricated (unactuated) position.
Notice the gap between the loading block and the friction block. It is designed to be
4 m (nominal) in their as-fabricated positions. The anchored and suspended patterns
that are used to track the displacements of the normal and tangential arms are clearly
labelled in the image.
155
used for the normal and tangential arms, respectively. Accordingly,
cn1 =  n1 ntg 
n1
(5.7.3a)
cn2 =  n2 ntg 
n2
(5.7.3b)
ct1 =  t1 ntg 
t1
(5.7.3c)
ct2 =  t2 ntg 
t2
(5.7.3d)
Combining Eq. 5.7.1 with Eqs. 5.7.3a, 5.7.3b, 5.7.3c, and 5.7.3d gives,
Fn1 = cn1V2n (5.7.4a)
Fn2 = cn2V2n (5.7.4b)
Ft1 = ct1V2t (5.7.4c)
Ft2 = ct2V2t (5.7.4d)
Since in both (normal and tangential) arms, the push and pull drives are exactly
identical to each other, the electrostatic forces generated by both the (push as well
as pull) drives of the normal arm can be determined using the same Eqs. 5.7.4a and
5.7.4b and the electrostatic forces generated by both the (push as well as pull) drives
of the tangential arm can be determined using the same Eqs. 5.7.4c and 5.7.4d.
As seen in Fig. 5.21, the design of the loading section of the SFAT is such that in
the as-fabricated position, the sidewall surfaces of the loading block and the friction
block are separated by a distance of  c. Therefore, the force (Fc) required to bring
the sidewall surface of the loading block in contact with that of the friction block is
given by Eq. 5.7.5.
Fc = kn c (5.7.5)
156
Here, kn is the combined e ective spring constant of the two folded beam  exures of
the normal arm. Since  c (designed to be 4  m) is much smaller than the lengths of
the supporting beams, which are 300  m (nominal) long, the treatment of the folded
beam  exures of the normal arm as linear elastic (Hookean) springs is valid [35].
Further, the design of the normal comb-drive actuator is such that a fraction of the
length of suspended  ngers overlaps with the  nal segments of the anchored  ngers
when the shuttle of the normal arm is displaced by a distance of  c in either direction
from its unactuated position. Therefore, the normal electrostatic force utilized in
forming the sidewall interface is given by Eq. 5.7.6.
Fc = kn c = cn2V2c (5.7.6)
Here, Vc is the voltage that is required to be applied to the normal comb-drive actuator
to bring the sidewall surface of the loading block in contact with that of the friction
block. Rearranging Eq. 5.7.6 gives,
 c = cn2k
n
V2c = Gn2V2c (5.7.7)
Accordingly, the transfer function Gn2 is given by Eq. 5.7.8,
Gn2 = cn2k
n
(5.7.8)
Since in the as-fabricated position, the suspended comb  ngers of the tangential
arm overlap only with the initial segments of the corresponding anchored  ngers, the
coe cient of static friction ( s) of the contacting sidewall surfaces can be determined
using Eq. 5.7.9,
 s = Ft1;sF
n2;s Fc
(5.7.9)
157
Here, Fn2;s and Ft1;s are the total normal and tangential forces generated, at the
instant of slip between the loading block and the friction block, using the normal and
tangential comb-drive actuators, respectively. Substituting Eqs. 5.7.4b, 5.7.4c and
5.7.6 in Eq. 5.7.9 gives,
 s = ct1V
2
t;s
cn2(V2n;s V2c ) (5.7.10)
After the initiation of slip at the sidewall interface, the friction block continues to slide
in contact with the loading block until the sum of the restoring force generated by
the folded beam  exure of the tangential arm and the kinetic friction force becomes
equal to the tangential force generated using the tangential comb-drive actuator.
Therefore, the coe cient of kinetic friction ( k) of the contacting sidewall surfaces
can be determined using Eq. 5.7.11,
 k = Ft1;s kt sF
n2;s Fc
(5.7.11)
Here,  s is the distance, for which, the friction block slides in contact with the loading
block after the initiation of slip at the sidewall interface. Substituting Eqs. 5.7.4b,
5.7.4c and 5.7.6 in Eq. 5.7.11 gives,
 k = ct1V
2
t;s kt s
cn2(V2n;s V2c ) (5.7.12)
The restoring force generated in the folded beam  exure of the tangential arm in
response to the displacement of its shuttle to a distance of  s is given by Eq. 5.7.13.
Fr = kt s (5.7.13)
Here, kt is the combined e ective spring constant of the folded beam  exure of the
tangential arm. Again, since  s is usually much smaller (typically a few  m) than the
lengths of the supporting beams, which are 250  m (nominal) long, the treatment
158
of the folded beam  exure of the tangential arm as linear elastic (Hookean) springs
is valid [35]. The equivalent tangential electrostatic force required to displace the
shuttle of the tangential arm by a distance of  s can be given by Eq. 5.7.14.
Fr = kt s = ct1V2e (5.7.14)
Here, Ve is the voltage that is required to be applied to the tangential comb-drive
actuator to displace the shuttle of the tangential arm by a distance of  s. Rearranging
Eq. 5.7.14 gives,
 s = ct1k
t
V2e = Gt1V2e (5.7.15)
Accordingly, the transfer function Gt1 is given by Eq. 5.7.16,
Gt1 = ct1k
t
(5.7.16)
Substituting Eq. 5.7.8 and Eq. 5.7.16 in Eq. 5.7.10 gives,
 s =
 k
t
kn
  G
t1
Gn2
  V2
t;s
V2n;s V2c
 
(5.7.17)
Similarly, substituting Eq. 5.7.8 and Eq. 5.7.16 in Eq. 5.7.12 gives,
 k =
 k
t
kn
  G
t1V2t;s  s
Gn2(V2n;s V2c )
 
(5.7.18)
Referring to the derivation of Eq. 5.3.4, kt can be given by Eq. 5.7.19.
kt = Ett
 w
t
Lt
 3
(5.7.19)
Here, E is the elastic modulus of the structural  lm, tt is the thickness of the sup-
porting beams of the tangential arm, which in the case of the SFAT developed in this
159
study, is the thickness of the structural  lm, wn and Ln are the width and length of
the supporting beams of the tangential arm, respectively. Similarly, kn can be given
by Eq. 5.7.20.
kn = 2Etn
 w
n
Ln
 3
(5.7.20)
where, tn is the thickness of the supporting beams of the normal arm, which again in
the case of the SFAT developed in this study, is the thickness of the structural  lm,
wn and Ln are the width and length of the supporting beams of the normal arm,
respectively. Dividing Eq. 5.7.19 by Eq. 5.7.20 gives,
kt
kn =
1
2
 L
n
Lt
 3
(5.7.21)
Substituting Eq. 5.7.21 in Eq. 5.7.17 gives Eq 5.7.22, which can be used to determine
the coe cient of static friction of the contacting sidewall surfaces of the SFAT.
 s = 12
 L
n
Lt
 3 G
t1
Gn2
  V2
t;s
V2n;s V2c
!
(5.7.22)
Similarly, substituting Eq. 5.7.21 in Eq. 5.7.18 gives Eq 5.7.23, which can be used to
determine the coe cient of kinetic friction of the contacting sidewall surfaces of the
SFAT.
 k = 12
 L
n
Lt
 3" G
t1V2t;s  s
Gn2(V2n;s V2c )
#
(5.7.23)
The transfer functions Gt1 and Gn2 are determined experimentally. It should be
noted that the additional normal load experienced by the sidewall interface due to
adhesion between the contacting sidewall surfaces is not considered in Eqs. 5.7.9 and
5.7.11. Therefore, the coe cients of friction determined using Eqs. 5.7.22 and 5.7.23
are engineering coe cients of friction.
If the displacement of the shuttle of the tangential arm during the  rst slip event
causes a fraction of the length of its suspended comb  ngers to overlap with the  nal
160
segments of the corresponding anchored comb  ngers, then the coe cient of kinetic
friction of the contacting sidewall surfaces of the SFAT is given by Eq.5.7.24 shown
below:
 k = 12
 L
n
Lt
 3" G
t2V2t;s  s
Gn2(V2n;s V2c )
#
(5.7.24)
The transfer functionGt2, which is also determined experimentally, is given by Eq. 5.7.25
shown below:
Gt2 = ct2k
t
(5.7.25)
5.7.3 Testing Procedure
To actuate the Sidewall Friction and Adhesion Tester (SFAT), the electrical
contacts are made by touching the actuation pads that are fabricated in the Sidewall
Friction and Adhesion Tester with sharp tungsten probe tips (Signatone SE-20T). The
voltages applied to the comb-drive actuators of the Sidewall Friction and Adhesion
Tester are generated using a digital-to-analog converter (DAC) and ampli ed using a
high-voltage ampli er (TEGAM, 2350S).
Before actuating each SFAT, the lengths of the supporting beams of its normal
and tangential arms (i.e., Ln and Lt) are measured, optically with a resolution of  
0.465  m. The resolution, with which the optical measurements are made, is limited
by the size of the pixels in the  eld of view, which is 0.465  m 0.465  m (objective
lens used is Mitutoyo M Plan Apo 10). Next, the restoring forces generated in the
normal and tangential arms in response of the displacements of their shuttles are
calibrated in order to determine the transfer functions Gn2, Gt1 and Gt2, respectively.
To calibrate the restoring forces generated in the tangential arm, the ground plane
(substrate) and the suspended movable structure as well as the anchored comb  ngers
of the pull drive of the tangential arm are electrically grounded, and a DC voltage is
applied to the anchored comb  ngers of the push drive of the tangential arm. The
applied voltage is ramped up from 0 V at a rate of 1 V/s to 55 V and the corresponding
161
displacements of the shuttle of the tangential arm are determined using a pattern
matching technique. The script used to calibrate the tangential arm of the Sidewall
Friction and Adhesion Tester is given in Appendix A.6. To calibrate the restoring
forces generated in the normal arm, the ground plane (substrate) and the suspended
movable structure as well as the anchored comb  ngers of the pull drive of the normal
arm are electrically grounded, and a DC voltage is applied to the anchored comb
 ngers of the push drive of the normal arm. The voltage applied to the anchored
comb- ngers of the push drive of the normal arm is ramped up from 0 V at a rate of
1 V/s to 40 V. The displacements of the shuttle of the normal arm for each voltage
applied to its push drive are determined using the pattern matching technique. The
script used to calibrate the normal arm of the Sidewall Friction and Adhesion Tester is
given in Appendix A.6. The patterns that are used to track the displacements of the
normal and tangential arms during the calibration of the restoring forces generated in
them are shown in Fig. 5.21. The plot of displacement (of the shuttle of the tangential
arm) versus V2t is used to determine the transfer functions Gt1 and Gt2. Similarly,
the plot of displacement (of the shuttle of the normal arm) versus V2n is used to
determine the transfer function Gn2. In addition to determining the Gn2, the plot of
displacement (of the shuttle of the normal arm) versus V2n is also used to determine
the voltage required to bring the loading block in contact with the friction block (i.e.,
Vc).
To study the friction characteristics of the contacting sidewall surfaces of the
SFAT, the ground plane (substrate) and the suspended movable structures of the
normal and tangential arms are electrically grounded, and a DC voltage is applied
to the anchored comb  ngers of the push drives of the normal and tangential arms.
First, the voltage applied to the push drive of the normal arm is ramped up from 0
V at a rate of 1 V/s to VN, which is the voltage that should be applied to the push
drive of the normal arm so that it generates an electrostatic force that corresponds
162
to the external normal load that is desired to be applied at the sidewall interface.
The position of the tangential arm (i.e., friction block) at this point is considered as
the initial position. After allowing the sidewall interface to equilibrate for 1 min., the
voltage applied to the push drive of the tangential arm is increased from 0 V at a rate
of 1 V/s until a slip is initiated at the sidewall interface. The onset of slip between
the contacting sidewall surfaces of the SFAT is detected by monitoring the position
of the friction block using the pattern matching technique. The pattern matching
technique is also used to determine  s, which is the distance, for which, the friction
block slides in contact with the loading block after the initiation of slip at the sidewall
interface. The script used for studying the friction characteristics of the contacting
sidewall surfaces, using the SFAT, is given in Appendix A.9.
To study the wear characteristics of the contacting sidewall surfaces of the SFAT,
the ground plane (substrate) and the suspended movable structures of the normal and
tangential arms are electrically grounded, a DC voltage is applied to the anchored
comb  ngers of the push drive of the normal arm and an AC voltage is applied to the
anchored comb  ngers of the push drive of the tangential arm. First, a DC voltage
is applied to the push drive of the normal arm. The voltage applied to the push
drive of the normal arm is ramped up from 0 V at a rate of 1 V/s to VN, which is
the voltage that should be applied to the push drive of the normal arm so that it
generates an electrostatic force that corresponds to the external normal load that is
desired to be applied at the sidewall interface. After allowing the sidewall interface to
equilibrate for 1 min., an AC voltage is applied to the push drive of the tangential arm.
Wear of the contacting sidewall surfaces of the SFAT can be qualitatively studied by
determining the change in their friction coe cients with the accumulation of wear
cycles [126,128,144].
To determine the adhesion force experienced by the contacting sidewall surfaces
of the SFAT, the ground plane (substrate) and the suspended movable structures of
163
the normal and tangential arms are electrically grounded, and a DC voltage is applied
to the anchored comb  ngers of both the push as well as the pull drives of the normal
arm. First, the voltage applied to the push drive of the normal arm is ramped up from
0 V at a rate of 1 V/s to VN, which is the voltage that should be applied to the push
drive of the normal arm so that it generates an electrostatic force that corresponds to
the external normal load that is desired to be applied at the sidewall interface. Next,
after allowing the sidewall interface to equilibrate for 1 min., the DC voltage applied
to the pull drive of the normal arm is increased from 0 V at a rate of 0.2 V/s until the
two sidewall surfaces that form the sidewall interface are separated from each other.
The instant of separation of the contacting sidewall surfaces of the SFAT is detected
by monitoring the position of the loading block using the pattern matching technique.
The adhesion force experienced by the contacting sidewall surfaces of the SFAT is the
di erence between the electrostatic forces generated by the push and pull drives of
the normal arm at the instant of separation of the contacting sidewall surfaces. The
script used to determine the adhesion force experienced by the contacting sidewall
surfaces, using the SFAT, is given in Appendix A.10.
164
Chapter 6
Processes and Techniques Used: Experimental, Analytical, Surface Characterization
& Metrology
This chapter brie y discusses all the experimental, analytical, surface characteri-
zation and metrology processes/techniques that are used in this study. The processes
discussed in this chapter include those that are used for releasing the microinstru-
ments of the Test Platform, coating the surfaces of the microinstruments of the Test
Platform with OTS SAM, the synthesis of gold nanoparticles used for tailoring the
topography of the test surfaces of the Test Platform and depositing gold nanoparti-
cles on the test surfaces of the Test Platform to tailor their topography. The tech-
niques discussed in this chapter include those that are used for characterizing the
gold nanoparticles used to tailor the topography of the test surfaces that are investi-
gated in this study, characterizing the topography of the tailored test surfaces of the
Test Platform, characterizing the chemistry of the test surfaces of the Test Platform,
characterizing the thickness of the OTS SAM coating investigated in this study and
determining the height pro le of an actuated cantilever beam.
6.1 Process Used to Release the Microinstruments of the Test Platform
The  rst step in utilizing the microinstruments of the Test Platform to study
the tribology of MEMS interfaces is to \release" them. The microinstruments need
to be released before they can be used for testing. The microinstrument release
procedure begins with cleaning of the Test Platform chip to strip-o the patterned
photoresist layer from it. The microinstruments developed in this study are released
by etching the sacri cial layer underlying the device layer in a concentrated solution
165
of HF (Fischer Scienti c, Reagent A.C.S., 49 wt.%) for approximately 11 min., after
which, the etchant is completely rinsed away with deionized (DI) water. DI water,
with a resistivity of 18 M -cm, is obtained from a Millipak R Millipore system, which
has a 0.22  m  lter installed in-line. The released microinstruments are then placed
in hot H2O2 (75 - 80  C) for 10 minutes to oxidize the microstructure surfaces. The
H2O2 (Fischer Scienti c, Certi ed A.C.S., 30 wt.%) is also  nally rinsed away with
DI water.
6.2 Process Used to Obtain Oxide-covered Test Surfaces
To obtain test surfaces, which only have a layer of native oxide on them, the
DI water is rinsed away with isopropanol (IPA). Following this, the Test Platform
chip is supercritically dried in a Tousimis Autosamdri 815-B CPD system. Samples
dried using this CPD system have been known to have contaminated surfaces [78].
Therefore, the dried microinstruments are exposed to a low power (25 W), capacitively
coupled RF (13.56 MHz) plasma of oxygen (O2 pressure used is 300 mtorr) to clean
the test surfaces before testing. This treatment is similar to that reported by Mayer
et al., which resulted in clean, oxidized test surfaces, including the surfaces underneath
the microstructures [38]. DI water contact angle measured after this treatment on
a simultaneously processed Si(100) monitor chip is found to be <5 , indicating that
the cleaned surfaces are hydrophilic. The microinstruments are actuated immediately
after the plasma cleaning to minimize contamination from the ambience.
6.3 Preparation of the OTS SAM Coating Solution
All the glasswares that are used for preparing the OTS SAM coating solution are
 rst thoroughly cleaned using an elaborate cleaning procedure. Next, before preparing
the coating solution, the crystallizing dish, in which the coating solution is prepared,
is conditioned with the OTS precursor molecules. 100  l of OTS (Gelest, 97 %+) is
166
added to 50 ml of anhydrous hexane (Fisher Scienti c, Electronic grade, 98.5 %+), in
the conditioned crystallizing dish. The resulting 5 mM solution of OTS is thoroughly
mixed, after which, the crystallizing dish containing it is covered with a glass dish.
The OTS coating solution is kept standing for 45 min. (at room temperature of 22
 C and relative humidity of 46 - 48 %), during which, the trichlorosilane precursor
molecules present in the coating solution react with the water vapor present in the
ambience, and get hydrolyzed into the corresponding trihydroxy derivatives. Without
further delay, the Test Platform chip that is to be coated with OTS-SAM is placed
in the coating solution.
6.4 Process Used to Obtain OTS SAM Coated Test Surfaces
To obtain test surfaces coated with OTS SAM, the procedure outlined by Srini-
vasan et al. in [80] is slightly modi ed and used in this study. The process used in
this study begins with completely rinsing away the DI water with IPA (Fischer Sci-
enti c, Certi ed A.C.S.). The IPA is further thoroughly rinsed away with anhydrous
hexane (Fischer Scienti c, Electronic grade, 98.5 %+). Next, the test platform chip is
carefully removed from the anhydrous hexane and transferred into a conditioned OTS
(Gelest, 97 %+) coating solution, which is kept in a glass dish that was previously
treated with OTS. Care should be taken to ensure that the microinstruments are
not exposed to the liquid-vapor interface while transferring the Test Platform chip
into the coating solution. The time, for which, the microinstruments are kept in the
coating solution depends on the relative humidity of the ambience. The OTS SAM
coating investigated in this study is deposited at room temperature (i.e., 22  C), and
a relative humidity of 40 - 45 %, in laboratory air. Therefore, the Test Platform chip
is kept in the coating solution for 45 min., after which, it is transferred back to the
anhydrous hexane. The anhydrous hexane is subsequently displaced with IPA, and
the IPA is similarly displaced with DI water. The coated Test Platform chip is  nally
167
removed, from DI water, in one slow but continuous motion, in such a way that its
in-plane surface is perpendicular to the liquid surface. All the solvent displacements
are carried out using the  ll/drain approach suggested by Ashurst et al. [35]. The
DI water contact angle measured on a simultaneously coated Si(100) monitor chip is
found to be 110 , indicating that the coated surfaces are hydrophobic. Additionally,
the thickness of the OTS SAM deposited on the monitor chip, which is determined
using an ellipsometer (Rudolph Research, AutoEL-III), is found to be 2.8  0.2 nm,
indicating that the studied OTS SAM is a monolayer. The DI water contact angle
exhibited by, and the thickness of, the OTS-SAM deposited on the monitor chip, indi-
cate that it is well ordered and densely packed [80,166]. The crystal-like structure of
the OTS-SAM investigated in this study is additionally con rmed by determining the
peak frequencies of methylene vibrations exhibited by it, using FTIR spectroscopy.
The frequency of the symmetric methylene vibration peak exhibited by the OTS
SAM investigated in this study is 2850.52 cm 1 and that of the asymmetric methy-
lene vibration peak exhibited by it is 2917.97 cm 1. Further, the OTS-SAM coated
monitor chip is also inspected using AFM. The scan shown in Fig. 6.1 indicates that
the OTS-SAM coated test surfaces have very few polymerized particulates on them.
6.5 Gold Nanoparticle (AuNP) Synthesis
All the chemicals used to synthesize the dodecanethiol-capped gold nanoparticles,
which are used for tailoring the surface topographies of the test surfaces investigated
in this study, are purchased from Alfa Aesar (Ward Hill, MA). A two-phase liquid
arrested precipitation process similar to that reported by Sigman et al. is used to
synthesize the dodecanethiol-capped gold nanoparticles [167]. The process begins by
adding 36 ml of an aqueous solution containing 0.38 g of hydrogen tetrachloroaurate
to an organic solution containing 2.7 g of tetraoctylammonium bromide (phase trans-
fer catalyst) and 24.5 ml toluene. The mixture is stirred for an hour, after which,
168
Figure 6.1: AFM image of a 25  m2 area of the OTS SAM coated Si(100) monitor
chip, which is processed simultaneously with the OTS SAM coated Test Platform
chip. Notice that only four extremely small polymerized particles are present in the
25  m2 area shown in the scan. The rms roughness of the area shown in the image is
0.23 nm.
169
the aqueous phase is separated and discarded. Next, the gold ions present in the
organic phase that is left behind are reduced to ground state by adding 30 ml of
an aqueous solution containing 0.5 g of NaBH4. The resulting mixture is stirred for
8 - 10 h to allow the gold nanoparticles to grow, before removing and discarding
the aqueous phase. Next, 240  l of 1-dodecanethiol is added to the organic phase
that is left behind, and the mixture is stirred for 4 h to cap and stabilize the gold
nanoparticles. Finally, the excess 1-dodecanethiol and NaBH4 are removed by cen-
trifuging the dodecanethiol-capped gold nanoparticle dispersion with equal parts of
ethanol, at 4500 rpm for 5 min. After repeating the centrifugation step several times,
the dodecanethiol-capped gold nanoparticles are dispersed and stored in hexane. The
size of the dodecanethiol-capped gold nanoparticles used to tailor the surface topogra-
phies of the test surfaces investigated in this study is characterized using transmission
electron microscopy (TEM). A TEM image showing the dodecanethiol-capped gold
nanoparticles used in this study is shown in Fig. 6.2. Based on the sizing of 3041
particles, the size of the dodecanethiol-capped gold nanoparticles used in this study
is determined to be 5.5  1.2 nm.
6.6 Process Used to Deposit the Dodecanethiol-capped Gold Nanoparti-
cles on the Test Surfaces of the Test Platform
The process reported by Hurst et al. in [24] is used for depositing the dodecane-
thiol-capped gold nanoparticles on the test surfaces of the Test Platform. To coat
the test surfaces of the Test Platform with dodecanethiol-capped gold nanoparticles,
the Test Platform chip is carefully placed upside-down on top of a stainless steel
washer (which is 1.6 mm thick and has an inner diameter of 9.5 mm), inside a glass
vial (which is 10 mm deep and has an inner diameter of 14.3 mm), which is kept in-
side a large beaker  lled with hexane (Fischer Scienti c, Electronic grade, 98.5 %+),
without exposing it to the liquid-vapor interface. Another washer is placed on top
170
Figure 6.2: A TEM image showing the dodecanethiol-capped gold nanoparticles used
to tailor the surface topographies of the test surfaces investigated in this study. The
size of the dodecanethiol-capped gold nanoparticles shown in the image is determined
to be 5.48  1.16 nm.
171
of the Test Platform chip to hold it in place. Next, the vial is removed from the
hexane- lled beaker, after which, the hexane is carefully removed from the vial up to
a level just above the Test platform chip. Next, a known, pre-determined volume of
concentrated dodecanethiol-capped gold nanoparticle dispersion (in hexane) is added
to the vial and carefully mixed, after which, the vial is placed inside a 30 ml stainless
steel high pressure vessel, which is equipped with a quartz viewing window, a resistive
temperature detector (RTD), a heating rope and a pressure gauge. Approximately
400  l of pure hexane is also added alongside the vial, to saturate the vapor-space
of the high pressure vessel and prevent evaporation of the organic (hexane-based)
nanoparticle dispersion prior to sealing the high pressure vessel. After sealing the
high pressure vessel, its chamber is pressurized with CO2,  rst to approximately 23
bar at room temperature (i.e., 22  C) using a 500 ml Teledyne ISCO piston syringe
pump (Lincoln, NE), and then up to the vapor pressure of the gas (i.e., 58 bar at
22  C) by setting the pump  ow rate to 0.4 ml/min. During the pressurization, the
CO2 dissolves in the organic phase, e ectively expanding the volume and reducing
the solvent strength of the hexane/CO2 mixture, which results in the precipitation of
the suspended dodecanethiol-capped gold nanoparticles. Speci cally, dodecanethiol
stabilized AuNPs in the size range of 3 - 7 nm are reported to precipitate in the pres-
sure range of 34.5 - 55.2 bar [129]. Moreover, the precipitating dodecanethiol-capped
gold nanoparticles are reported to conformally coat all the surfaces of the microin-
struments being coated [24]. Pressurization is continued until the entire chamber of
the high pressure vessel is  lled with liquid CO2, after which, the mixture of liquid
CO2 and the organic solvent (i.e., hexane) is heated isochorically to 40  C, to trans-
form it into a supercritical  uid. Next, the chamber of the high pressure vessel is
 ushed with several volumes of pure supercritical CO2 (at 40  C and 90 bar) at a
rate of approximately 1.0 ml/min, to ensure the complete removal of the organic sol-
vent (i.e., hexane) from it. Finally, the chamber of the high pressure vessel is slowly
172
depressurized (at 40  C) to atmospheric pressure and the dry, dodecanethiol-capped
AuNP coated Test Platform chip is removed.
6.7 Contact Angle Goniometry
Contact angle goniometry is used for characterizing the chemistry (i.e., hydropho-
bicity) of the test surfaces investigated in this study. Speci cally, it is used to deter-
mine the hydrophobicity of the native oxide covered and the OTS SAM coated test
surfaces investigated in this study. Contact angle measurements are made using a
Ram e-Hart Standard goniometer (Ram e-Hart, Inc., Model # 200-00-115). The mea-
surement reproducibility of this instrument is 2 . To determine the hydrophobicity
of a test surface, the contact angle made by a droplet of DI water on it is determined
using the sessile drop technique [168]. DI water, with a resistivity of 18 M -cm, is
obtained from a Millipak R Millipore system, which has a 0.22  m  lter installed in-
line. The volume of the water droplet used to make the contact angle measurements
is 4  l.
6.8 Ellipsometry
Ellipsometry is used for characterizing the thicknesses of the surface  lms that
are investigated in this study. Speci cally, it is used to determine the thicknesses of
the native surface oxide  lm present on the test surfaces, the oxide  lm thermally
grown on the surfaces of the as-fabricated microinstruments to polish them and the
OTS SAM deposited on the microinstruments. The ellipsometer used for this study
is a Rudolph Research ellipsometer, which is equipped with a 1 mW (max.) HeNe
laser ( of radiation is 632.8 nm) and AutoEL-III software. This instrument can
measure  lm thicknesses up to 3  m and has a measurement reproducibility of 2 A.
A single  lm model is used to determine the thicknesses of the native surface oxide
 lm present on the test surfaces and the oxide  lm grown thermally on the surfaces
173
of the as-fabricated microinstruments [169]. A refractive index of 1.463 is used for
the oxide  lm, in the model. A lumped single  lm model is used to determine the
thickness of the OTS SAM deposited on the test surfaces [169]. A refractive index
of 1.45 is used for the organic OTS SAM  lm, in the model. The lumped single
 lm model determines the combined thickness of the OTS SAM and the underlying
native oxide  lm. Therefore, in order to determine the thickness of the OTS SAM,
the thickness of the underlying native oxide  lm is determined prior to depositing the
OTS SAM on it, using the single  lm model.
6.9 Fourier Transform - Infrared Spectroscopy
Fourier Transform - Infrared (FT-IR) Spectroscopy is used for characterizing the
structure (i.e., orderliness and packing density) of the OTS SAM  lm investigated in
this study [170]. Speci cally, attenuated total internal re ection FT-IR (i.e., ATR-
FTIR) spectroscopy is used in this study. A Si ATR crystal and a Spectrum 2000 FT-
IR spectrometer (PerkinElmer) is used for taking the FT-IR scans. The symmetric
(observed between 2850 - 2855 cm 1) and asymmetric (observed between 2918 - 2923
cm 1) methylene stretching peaks are used to qualitatively determine the packing
and orderliness of the OTS SAM investigated in this study.
6.10 Microscopy
Several microscopy techniques are used either as imaging or as analysis tools in
this study. Speci cally, optical microscopy is used for characterizing, and during the
actuation of, the microinstruments developed in this study, atomic force microscopy
is used for characterizing the surface topography of the test surfaces investigated in
this study, scanning electron microscopy is used for characterizing the tailored test
surfaces investigated in this study and transmission electron microscopy is used for
characterizing the dodecanethiol-capped gold nanoparticles that are used to tailor
174
the surface topography of the test surfaces investigated in this study. The following
sections brie y discuss the various microscopy techniques used in this study.
6.10.1 Optical Microscopy
In this study, optical microscopy is used for obtaining the optical images of the
microinstruments developed in this study. It is also used for determining the di-
mensions of the components of the various microinstruments developed in this study.
Further, along with a pattern matching technique, it is used to determine the dis-
placements of the various moving components of the microinstruments developed in
this study. Additionally, it is used for determining the resonance frequencies of the
various Resonators included in the Test Platform. The optical microscope used in
this study is custom-built by East Mountain Optomechanical, Inc. The optical mi-
croscope is equipped with a green LED (with  max of 525 nm, Nichia corp.), which
is monochromated using a monochromator that transmits 532 nm and used as the
illumination source, Mitutoyo M Plan Apo objectives (10X - 100X), which are used
as the objective lens, and a charge-coupled device (CCD)-IRIS camera (Sony, XCD-
SX910), which is controlled using the MEMScript and used for collecting the optical
images.
6.10.2 Atomic Force Microscopy
In this study, atomic force microscopy is speci cally used for quantitatively char-
acterizing the topographies of the native oxide covered in-plane as well as sidewall sur-
faces, and the the test surfaces, whose topographies are tailored using dodecanethiol-
capped gold nanoparticles. Additionally, it is used to ascertain the presence /absence
of polymerized particulates of precursor molecules on the OTS SAM coated test
surfaces. All the AFM images obtained for this study are obtained by operating
175
the atomic force microscope (Paci c Nanotechnology Nano-R SPM, Model # O-020-
0002) in the tapping mode. Details on the working principles and the usage of the
atomic force microscope can be found elsewhere [171, 172]. The tips that are used
for obtaining the AFM images are Si tips ( masch, Model # NSC35/NoAl), which
have a radius of curvature of 10 nm. The parameter that is extracted from an AFM
image to quantify the surface topography of the surface being analyzed is the rms
roughness of the area of that surface, that is scanned. Additionally, the ASCII data
associated with the AFM image of each test surface is processed using the image
analysis technique discussed in section 6.12 to determine the surface coverage of the
interacting asperities present in the area of that surface, that is scanned.
6.10.3 Scanning Electron Microscopy
In this study, scanning electron microscopy (SEM) is used for qualitatively char-
acterizing the topographies of the test surfaces, whose topographies are tailored by
depositing dodecanethiol-capped gold nanoparticles on them. A carbon tape is used as
the conducting path while collecting the SEM scans. The qualitative characterization
of the topographies of the tailored test surfaces is done in terms of the conformality
and uniformity of the dodecanethiol-capped AuNP-based coatings deposited on them
as well as the number density of the dodecanethiol-capped gold nanoparticles present
on them.
6.10.4 Transmission Electron Microscopy
In this study, transmission electron microscopy (TEM) is used for determining the
size of the dodecanethiol-capped gold nanoparticles that are used for tailoring the sur-
face topographies of the test surfaces investigated in this study. In order to determine
the size of the dodecanethiol-capped gold nanoparticles, a TEM image of a monolayer
of the dodecanethiol-capped gold nanoparticles is obtained. A TEM (carbon) grid
176
is used for obtaining the TEM image of the monolayer of the dodecanethiol-capped
gold nanoparticles. The TEM image is analyzed using an image analysis software
called ImageJ. The scale of the processed image obtained from ImageJ is determined
using the Eq. 6.10.1, where,  is the scale of the processed image obtained from Im-
ageJ (in pixels/nm),  s is the number of lateral pixels present in the TEM image
(in pixels) and M is the magni cation used to obtain the TEM image. The size of
the dodecanethiol-capped gold nanoparticles is determined from the processed image
obtained from ImageJ, using the procedure developed by Kitchens [173].
 = M s3:936 10 8 (6.10.1)
6.11 Interferometry
Two di erent interferometric techniques are used in this study. The phase shift-
ing interferometry (PSI) is used for determining the height pro les of all the can-
tilever beams actuated in this study. The horizontal scanning interferometry (HSI)
is used for determining the step edges present at the sidewall interfaces investigated
in this study. A custom-built long working distance, incoherent light interference
microscope similar to that reported by Sinclair et al. in [153] is used to produce
the interferograms. The interference microscope is equipped with a green LED (with
 max of 525 nm), which is monochromated using a monochromator that transmits
532 nm and used as the illumination source, a Mitutoyo M Plan Apo 10 objective,
which is used as the objective lens, a closed-loop PZT actuator (PI, PZT model #
PZ-70E, LVPZT controller model # E-610.SO) with a reference surface mounted on
it, which is controlled using the MEMScript and used for taking the phase steps,
and a charge-coupled device (CCD)-IRIS camera (Sony, XCD-SX910), which is also
controlled using the MEMScript and used for collecting the interferograms.
177
6.12 Image Analysis Technique Used for Determining the Surface Cov-
erage of the Interacting Asperities
The surface topographies of the test surfaces, whose topographies are tailored
using the dodecanethiol-capped gold nanoparticles, are additionally quanti ed by
determining the surface coverage of the interacting asperities present on them. In
order to determine the surface coverage of the interacting asperities present on a test
surface, the ASCII data associated with the AFM image of a representative area
of that surface is processed using a specially-written, elaborate C program, which
is written by Dr. W. R. Ashurst (Associate Professor, Department of Chemical
Engineering, Auburn University). The C program converts the AFM image into a
two-dimensional array of pixels, whose intensities vary on a discrete scale of 0 - 255.
The intensity of each pixel is directly proportional to the z-height of the corresponding
point in the AFM image. By inputting a threshold intensity in the C program, the
pixels, whose intensities are greater than the threshold value can be determined. The
fraction of the pixels, whose intensities are greater than the inputted threshold value,
is the output of the C program, and the surface coverage of the interacting asperities
present on the surface being analyzed.
178
Chapter 7
Experimental Requirement of the Phase Shifting Interferometry
Digital phase shifting interferometry (PSI), a technique widely used in optical
testing, requires interferograms collected at optical phase di erences separated by a
de nite phase step. The  ve frame interferogram collecting sequence suggested by
Hariharan et al. is extremely e ective in signi cantly reducing the errors in the height
pro les derived using PSI that are caused by phase step errors [176]. In this chapter,
I report on a class of  ve frame sequence which, due to its mathematical equivalence
with the one suggested by Hariharan et al. and ease of execution, is more commonly
used, but is much less e ective in reducing the height pro le errors caused by phase
step errors.
7.1 Introduction
Since its introduction in 1974 by Bruning et al., phase shifting interferometry
(PSI) has become a very useful tool and is presently widely used in several applications
[174]. In optical testing, PSI is frequently used to determine the  atness of optical
surfaces as well as to determine the optical quality of certain optical components
[174]. Combined with appropriately designed test structures and analysis routines,
it is commonly used by the micro-electromechanical systems (MEMS) community to
determine critical material properties such as residual stress, Young?s modulus and
stress gradient in structural layers used to fabricate useful micromechanisms [153].
Recently, Hurst et al. reported a technique, which also employs PSI to study stiction
between contacting in-plane MEMS surfaces [175].
179
In all of its applications, PSI is essentially used to determine the topography of a
particular surface by determining the height of every point on that surface. The only
experimental step involved in using PSI is the collection of interferograms at di erent
optical phase di erences separated by a de nite phase step for every point on the
surface. Consequently, it is also the only source of experimental errors in PSI derived
height pro les. Further, it is widely accepted that the most prominent experimental
error is the error in the phase steps taken during the collection of interferograms
[174,176]. Because nanometer scale precision is one of the requirements of the MEMS
and NEMS based applications, in which, PSI is used, it is essential to ensure that the
height pro les derived using PSI are extremely accurate. Therefore, it is necessary
to reduce the in uence of these phase step errors on the height pro les derived using
PSI.
In most of the commonly used interferometers, phase steps are taken using a
piezoelectric transducer (PZT), on which, one of the surfaces (i.e., reference or sam-
ple) is mounted. Error in the phase steps (i.e., deviation from predetermined nominal
value) is usually caused by the non-linearity, and dependence of the PZT on variables
such as its age and temperature. Various approaches presently used to reduce the
phase step error or its in uence on PSI derived height pro les can be broadly classi-
 ed into two categories: hardware-based and algorithm-based approaches. The addi-
tional hardware, and hence expense, associated with the hardware-based approaches,
which include actuator calibration schemes, novel shifting hardwares, etc., makes
them less attractive than the algorithm based approaches [174]. Algorithm-based
approaches focus on using either a speci c sequence for collecting the interferograms
or a self-correcting computational scheme to address the uncertainty associated with
the phase steps. Some strategies involving a combination of the two approaches have
also been reported in literature [174]. For example, the equistep algorithm requires
additional hardware to ensure that the phase steps are equal but does not require
180
them to be known accurately [174]. In contrast, a generalized algorithm suggested
by Greivenkamp allows unequal phase steps but requires additional hardware to ac-
curately determine them [174].
Examples of prominent algorithm-based approaches include the two algorithms
reported by Farrell et al., which do not require the phase steps to be known or equal
and hence do not require additional hardware [174]. However, the computational
e ort involved in them is signi cantly higher than that involved in the algorithm
suggested by Hariharan et al. [174, 176]. The algorithm suggested by Hariharan
et al., which implicitly evaluates the actual phase steps and uses them to calculate
the original optical phase di erence between the interfering beams, is one of the most
simple, robust and reliable algorithms for PSI [176]. The  ve frame interferogram
collecting sequence used by it signi cantly reduces the errors in the height pro les
derived using PSI, that are caused by phase step errors [176]. In this chapter, I report
on a class of  ve frame sequence, which due to its mathematical equivalence with the
one suggested by Hariharan et al. and ease of execution, is more commonly used,
but is contrastingly much less e ective in reducing the height pro le errors caused by
phase step errors.
7.2 Five Frame Interferogram Collecting Sequence for PSI
The self-calibrating  ve frame sequence (referred to as H) suggested by Hariharan
et al. is given by Eqs. (7.2.1a - 7.2.1e) shown below, where I1, I2, I3, I4 and I5 are the
intensity measurements made at phase steps of  2 ,   , 0,   ,  2 respectively
181
and  is the original optical phase di erence between the interfering beams [176].
I1 = A+B + 2pABcos(  2 ) (7.2.1a)
I2 = A+B + 2pABcos(   ) (7.2.1b)
I3 = A+B + 2pABcos( ) (7.2.1c)
I4 = A+B + 2pABcos(   ) (7.2.1d)
I5 = A+B + 2pABcos(  2 ) (7.2.1e)
The class of  ve frame sequence (referred to as NH), which is mathematically equiv-
alent to sequence H is represented by Eqs. (7.2.2a - 7.2.2e) shown below, where I1, I2,
I3, I4, I5 are the intensity measurements made at phase steps of 0,   ,  2 ,  3 ,
 4 respectively.
I1 = A+B + 2pABcos( ) (7.2.2a)
I2 = A+B + 2pABcos(   ) (7.2.2b)
I3 = A+B + 2pABcos(  2 ) (7.2.2c)
I4 = A+B + 2pABcos(  3 ) (7.2.2d)
I5 = A+B + 2pABcos(  4 ) (7.2.2e)
The mathematical equivalence of the two sequences H and NH is evident from the
fact that both of them consist of  ve frames, each separated by a phase step  . Also,
for both the sequences,  is given by the same Eq. (7.2.3) when the nominal phase
step (i.e.,  ) is 90 . For completeness, the derivations of Eq. (7.2.3) for sequences H
and NH are given in Appendices B.1 and B.2 respectively.
tan = 2(I2 I4)2I
3 I1 I5
(7.2.3)
182
This mathematical equivalence along with only a subtle di erence in the experimental
execution of the two sequences and the ease of experimental execution of sequence
NH are the reasons why sequence NH is more than often used instead of sequence
H. However, while sequence H is extremely less sensitive to a small error ( ) incurred
in each phase step, sequence NH is highly sensitive to it. This is substantiated by
Eq. 7.2.4a and Eq. 7.2.4b, which give a  rst order approximation of the error (  ) in
 due to  , for sequences H and NH respectively. Both Eq. 7.2.4a and Eq. 7.2.4b are
derived using an error analysis similar to that reported in [176]. For completeness, the
complete error analyses of sequences H and NH are provided in Appendices B.3 and
B.4 respectively. It is important to note that Eq. 7.2.4a di ers from the analogous
equation reported in [176] by a factor of 2. However, it is consistent with the data
obtained experimentally. The experiments conducted to substantiate Eq. 7.2.4a and
Eq. 7.2.4b are discussed in the following section.
  H =  
2
8 sin 2 (7.2.4a)
  NH = 2 (7.2.4b)
7.3 Experimental Details
A long working distance, incoherent light interference microscope is used to pro-
duce the interferograms. A green LED (with  max of 525 nm) is monochromated to
532 nm and used as the illumination source. A closed-loop PZT actuator (PI, PZT
model # PZ-70E, LVPZT controller model # E-610.SO) with the reference surface
mounted on it is used for taking the phase steps. Two 8 mm  8 mm Si(100) chips
are used as the re ecting surfaces (i.e., reference and sample) for all the experiments.
183
In order to collect the interferograms using sequence H, initially, a voltage of
1 V is applied to the PZT to move it to a position, from where, it can be moved
in both the directions (forward and backward) to collect the interferograms. At this
position (starting position), the path lengths of the two arms of the interferometer
are precisely matched, in order to obtain the 0th order fringe. Next, the  rst interfer-
ogram is collected by moving the PZT two phase steps forward. The remaining four
interferograms are collected by moving the PZT backwards, one phase step for each
interferogram. For collecting interferograms using sequence NH, the PZT is initially
moved four phase steps forward. This is the starting position for sequence NH, at
which, the path lengths of the two arms of the interferometer are precisely matched.
The  rst interferogram for sequence NH is collected at the starting position itself. The
remaining four interferograms are again collected by moving the PZT backwards, one
phase step for each interferogram.
The nominal phase step used in all the experiments is 90 . In the  rst experiment,
which is conducted to determine the inherent phase step error present in the closed-
loop PZT, the displacement of the reference surface in each phase step up to  ve phase
steps is experimentally determined by measuring the displacement of a speci c fringe
for those phase steps. The inherent phase step error is determined from the di erence
between the expected and the experimentally measured displacements of the reference
surface. Next, before investigating the e ectiveness of sequence NH in reducing the
height pro le errors caused by phase step errors, the error in the determination of  
due to the low frequency vibrations present in the experimental setup is determined.
For this purpose, the surface height pro le of the sample surface is determined  ve
times at intervals of 5 min., using sequence H. No intentional phase step error is
added to the nominal phase steps for these experiments. Each of the determined  ve
surface height pro les are then compared with each of the other four surface height
pro les and the di erences in the corresponding heights of all the points on the sample
184
surface are used to calculate the rms error (  ) in  . The e ectivenesses of the two
sequences H and NH in reducing the height pro le errors caused by phase step errors
are studied by using them to determine the surface height pro le of the sample surface
with di erent amounts of phase step errors intentionally added to the nominal phase
step for collecting the interferograms. The  rst surface height pro le is obtained with
zero intentional phase step error ( ) added to  . For obtaining the next  ve surface
height pro les,  is incremented in steps of 10% (of the nominal phase step) for each
subsequent pro le.   due to a particular  is determined by comparing the surface
height pro le obtained with that particular  added to  , with the one obtained with
zero phase step error added to  . The e ectivenesses of sequences H and NH are
studied using both positive as well as negative  .
7.4 Results and Discussion
The measured displacements of the reference surface were 5 nm greater than the
expected displacements in all the experiments. This indicates that the closed-loop
PZT has an inherent positive  of 7.5% (of  ). The maximum   due to the low
frequency vibrations present in the interferometer was about 6.77 , which corresponds
to a rms error of 5 nm in the surface height pro le of the sample surface.   , as
a function of percentage  (of  ), for both the sequences is shown in Fig. 7.1. In
Fig. 7.1, Hexp and NHexp represent the data obtained experimentally, while Hth and
NHth represent the   calculated using Eq. 7.2.4a and Eq. 7.2.4b, for sequences H
and NH respectively. As seen in Fig. 7.1, the experimentally determined   are
in good agreement with those calculated using Eq. 7.2.4a and Eq. 7.2.4b for both
the sequences. Also, it is clearly evident from Fig. 7.1 that sequence H makes PSI
extremely less sensitive to both positive as well as negative  , and its usage limits   
to small values even for  as large as 60% of  . For each of the di erent  investigated
except one, the resulting   in the case of sequence H is less than the maximum   
185
 30
 60
 90
 120
-70 -60 -50 -40 -30 -20 -10  0  10  20  30  40  50  60  70
??
 (degree)
Imposed error in phase step (%)
H exp NH exp H th NH th
Figure 7.1: Error in  (  ) for di erent imposed percentage error (% ) in  .
186
due to the low frequency vibrations present in the interferometer. Contrastingly, in
the case of sequence NH, PSI is highly sensitive to  and the height pro les derived
have signi cantly larger   , which increases linearly with the increase in  . A phase
step error of 60% results in   of 8.12 and 121.8 , when sequences H and NH
are used, respectively. These correspond to rms errors of 6 nm and 90 nm in the
surface height pro le of the sample surface, respectively. Further, Fig. 7.1 indicates
that positive  result in larger   than the corresponding negative  , for both the
sequences. This is attributed to the inherent positive  of the closed-loop PZT, which
gets added to the intentionally imposed positive  , thereby increasing them, and gets
subtracted from the intentionally imposed negative  , thereby decreasing them.
7.5 Conclusions
I analyzed two distinct classes of the  ve frame interferogram collecting sequence
used in PSI, both mathematically as well as experimentally. The results clearly sub-
stantiate the presence of signi cant errors in the PSI derived height pro les obtained
using a mathematically equivalent but experimentally di erent  ve frame interfero-
gram collecting sequence than that suggested by Hariharan et al.. A signi cantly high
rms error of 90 nm was observed in the height pro le derived using sequence NH when
 was 60% of  . In contrast, sequence H made PSI extremely less sensitive to  and
even for a high  of 60%, a rms error of 6 nm, which is only marginally greater than
the maximum rms error due to vibrational disturbances, was observed in the height
pro le derived using it. Therefore, the  ve frame interferogram collecting sequence
for PSI should be selected cautiously, otherwise, the height pro les derived can have
signi cant errors in them.
187
Chapter 8
Benchmarking the Microinstruments: Highlighting Key Features & Testing
Standard Surfaces
This chapter reports the benchmarking of the microinstruments developed in this
study. It illustrates the key features of each of the seven microinstruments developed
in this study. Further, in order to substantiate the consistency and reliability of the
the results obtained using them, it reports the results of the investigations conducted
to study the e ects of two standard surface treatments using the microinstruments
developed in this study, and compares them with the corresponding results reported
in literature. The two types of surfaces studied in this chapter, using the microinstru-
ments developed in this study are surfaces coated with n-OTS (C18H37SiCl3) SAM
coating (i.e., hydrophobic surfaces) and surfaces having only a layer of native oxide
on them (i.e., hydrophilic surfaces). These two surface treatments are considered as
standard surface treatments by the MEMS community. All the results reported in
this chapter are obtained in laboratory air, at 22  C and in 45% relative humidity
(unless otherwise stated).
8.1 The Pattern Matching Technique
First, in order to determine the uncertainty in the measurements made using
the pattern matching technique, the position of a movable pattern is determined
thousand times, without moving the pattern, using it. The script used to perform
this experiment is given in Appendix A.11. The rms error in the determination of
the position of the movable pattern is found to be 7.5 nm. This clearly indicates that
the pattern matching technique used in this study determines the displacements of
188
the movable components of the microinstruments developed in this study extremely
accurately. However, it must be noted that the overall resolution of the pattern
matching technique used in this study depends on, and is slightly decreased by, the
magni cation (depth of focus) of the objective lens used in the microscope.
8.2 Residual Stress Tester
Optical images of four Residual Stress Testers of each of the two Test Platform
chips investigated in this chapter are collected before and after releasing the Test
Platform chips. The magni cation of the objective lens used to collect the optical
images is 20X. Accordingly, the size of each pixel in the optical images is 0.234  m
 0.234  m. Careful analysis of all the optical images collected, using the pattern
matching technique, indicates that the central beams of all the RSTs investigated in
this chapter do not exhibit any rotation. This result implies that the structural  lms
of both the Test Platform chips investigated in this chapter (i.e., the one coated with
OTS SAM as well as the one, whose surfaces are covered with only native oxide) do
not have any residual stress in them, which is as expected because they are single
crystal silicon  lms. Also, the OTS SAM coating did not induce any stress in the
underlying Si(100) structural  lm. This indicates that either the OTS SAM coating
is conformal and uniform or it does not have any signi cant in uence on the stress
state of the Si(100) structural  lm. The former possibility is more likely considering
that the characterization of the OTS SAM coating deposited on a monitor Si(100)
chip processed simultaneously with the Test Platform chip indicated that the OTS
SAM coating investigated in this chapter is a densely-packed, well-ordered monolayer
of OTS (see section 6.4). As explained in section 5.2.2, the Mechanical Strength
Testers developed in this study are actuated by applying an increasing DC voltage
to the open-loop piezo of a specialized micro-manipulator (speci cally developed in
this study), which pushes the central shuttle of the Mechanical Strength Tester being
189
actuated in the direction of the arrow shown in Fig. 5.3. The magni cation of the
objective lens used during the actuation of the Mechanical Strength Testers investi-
gated in this chapter is 10X. Accordingly, the size of each pixel in the  eld of view
is 0.465  m  0.465  m. In order to determine the distances, by which, the central
shuttle is displaced at the point of fracture of each of the six fracture beams of the
Mechanical Strength Tester, the displacements of the central shuttle are determined
using the pattern matching technique, at every push, throughout the actuation of the
Mechanical Strength Tester. Figure 8.1 is a plot showing the experimentally deter-
mined axial and lateral displacements of the central shuttle of one of the MSTs of the
OTS SAM coated Test Platform chip versus the corresponding voltage applied to the
micro-manipulator that is used to actuate it. The widths of the fracture beams of the
OTS SAM coated MST used to obtain the data shown in Fig. 8.1 are measured op-
tically, to be 2.72  m (design width is 3  m). The axial displacements of the central
shuttle, at which, each of the three pairs of fracture beams of the OTS SAM coated
MST got fractured can be clearly seen as discontinuities in the plot representing the
axial displacement in Fig. 8.1. The jumps during the axial displacement of the central
shuttle, which appear as discontinuities in the plot representing the axial displace-
ment data in Fig. 8.1, are consequences of the decrease in the resistance o ered by
the OTS SAM coated MST to the extension of the open-loop piezo, at the point of
fracture of each pair of fracture beams. This is substantiated by the fact that after
each discontinuity, the axial displacement data shown in Fig. 8.1 exhibits an increased
slope. In Fig. 8.1, while the discontinuities associated with the fracture of 50  m and
70  m long beams are sharp and signi cant, that associated with the fracture of 60
 m long beams is blunt and relatively less signi cant. This is because while both the
50  m long as well as 70  m long fracture beams got fractured at the same instant,
the two 60  m long fracture beams got fractured individually at axial displacements
of 11.45  m and 11.97  m, respectively. Also, the plot that represents the lateral
190
displacements of the central shuttle in Fig. 8.1 indicates that during the entire actua-
tion, the motion of the OTS SAM coated MST is con ned to only the axial direction.
This con rms that throughout the actuation of the OTS SAM coated MST, the lever
arm (i.e., Lc) of each of its actuated fracture beams remained constant.
8.3 Mechanical Strength Tester
On each of the two Test Platform chips (i.e., the one that is coated with OTS
SAM as well as the one that has microinstruments, whose surfaces are covered with
only native oxide) investigated in this chapter, 16 distinct MSTs are tested. The
width of each of the tested fracture beams is measured optically, to be 3.72  m
(design width is 4  m). The lever arm of each of the tested fracture beams is also
measured optically. Table 8.1 reports the measured lever arms as well as the measured
displacements of corresponding MSTs at the instant of fracture of the tested fracture
beams. It also reports the (calculated) strains that exist in the tested fracture beams
at the instant of their fracture. Each value reported in Table 8.1 is an arithmetic mean
of 16 measurements, and the corresponding std. dev. is one standard deviation of the
sample consisting of those measurements. The mean values of the fracture strain
of the structural  lm reported in Table 8.1 indicate that the results obtained using
fracture beams, which have di erent lengths, are consistent with each other. Even
those obtained using MSTs of di erent Test Platform chips (i.e., OTS SAM coated
Test Platform chip and native oxide covered Test Platform chip) are also consistent
with each other. This authenticates the reliability of the results obtained using the
Test Platform developed in this study. Additionally, the results reported in Table 8.1
indicate that the OTS SAM coating does not alter the fracture strength of the Si(100)
structural  lm, which is as expected, because the thickness of the OTS SAM coating
investigated in this chapter, which is 2.8 nm, is signi cantly lesser than the thickness
of the structural  lm of the Test Platform developed in this study, which is 2  m
191
 0
 5
 10
 15
 20
 25
 30
 0  10  20  30  40  50  60  70  80  90  100
Displacement of the Central Shuttle, (
?m)
Voltage Applied to the Micro-manipulator, (V)
Pair of 50 ?m long
fracture beams
Pair of 60 ?m long
fracture beams
Pair of 70 ?m long
fracture beams
Axial displacement
Lateral displacement
Figure 8.1: A plot showing the experimentally determined axial and lateral displace-
ments of the central shuttle of one of the MSTs of the OTS SAM coated Test Platform
chip versus the corresponding voltage applied to the micro-manipulator that is used
to actuate it. Notice the discontinuities in the plot that represents the axial dis-
placement data. Also, the lateral displacements of the central shuttle are negligible
throughout the actuation of the MST.
192
Table 8.1: This table reports the measured lever arms as well as the measured dis-
placements of corresponding MSTs at the instant of fracture of the tested fracture
beams. It also reports the strains that exist in the tested fracture beams at the in-
stant of their fracture. Each value reported in the table is an arithmetic mean of
16 measurements, and the corresponding std. dev. is one standard deviation of the
sample consisting of those measurements.
Beam Lc Displacement at Fracture Strain at Fracture
Length  f  std. dev. ( m)  f  std. dev. (%)
( m) ( m) Oxide OTS Oxide OTS
50 41.85 5.99  0.43 6.03  0.35 1.91  0.14 1.92  0.11
60 51.62 9.22  0.62 9.17  0.91 1.93  0.13 1.92  0.19
70 61.38 13.57  0.27 13.57  0.33 2.01  0.04 2.01  0.05
193
(nominal). Lastly, the fracture strain of the Si(100) structural  lm determined using
the Test Platform developed in this study is in good agreement with that reported
in literature for Si(100)  lms [87,88,177,178]. This authenticates the validity of the
results obtained using the Test Platform developed in this study.
8.4 Resonator
As explained in section 5.3, the Resonator developed in this study can be used to
determine the elastic modulus (i.e., E) of the structural  lm used to fabricate the Test
Platform. Although the elastic modulus of the structural  lm of the Test Platform
can be determined using a single Resonator and Eq. 5.3.6, in order to eliminate the
error induced in the estimate of the elastic modulus by the errors (induced by the
resolution of measurement) in the measured dimensions of the Resonator, a set of
twenty  ve di erent Resonators, which are present at di erent locations on the Test
Platform chip, is used to determine the elastic modulus of its structural  lm. Five
Resonators each are chosen from  ve of the nine sets of Resonators included in the
Test Platform chip.
In this chapter, the elastic modulus of the structural  lm of the native oxide
covered Test Platform chip is determined. The  ve sets of Resonators that are used
for it include Resonators with supporting beam lengths of 200  m (nominal), 350  m
(nominal), 400  m (nominal), 450  m (nominal) and 500  m (nominal). Table 8.2
reports the drive signals that are used to actuate the  ve selected sets of Resonators
along with their optically observed resonance frequencies. Each resonance frequency
reported in Table 8.2 is an arithmetic mean of  ve measurements, which are made
using  ve distinct Resonators having the same supporting beam length. The square
of the observed resonance frequency of each of the  ve selected sets of Resonators is
plotted against their corresponding value of the term that is written in brackets on the
right hand side of Eq. 5.3.6. The plot is shown in Fig. 8.2. All the dimensions, which
194
Table 8.2: This table reports the drive signals used to actuate the Resonators of the
native oxide covered Test Platform chip along with their optically observed resonance
frequencies. Each resonance frequency reported in the table is an arithmetic mean
of  ve measurements, which are made using  ve distinct Resonators having the same
supporting beam length.
Supporting Beam DC Bias AC Drive Signal Observed
Length (Amplitude) Resonance Frequency
( m) (V) (V) (KHz)
200 100 30 13.50  0.005
350 50 20 6.14  0.005
400 40 20 4.72  0.005
450 30 20 3.92  0.005
500 25 20 3.64  0.005
195
are required to determine the value of the term that is written in brackets on the
right hand side of Eq. 5.3.6, of each of the Resonators tested are measured optically,
before actuating the Resonator. The experimentally observed resonance frequencies
are represented by ( ) in the plot. A line  tted to the experimentally obtained data
reported in Table 8.2 is also shown in the plot. The high R2 (i.e., 0.9991) of the linear
 t con rms that the resonance behaviour of the Resonators developed in this study
can be accurately modeled using the harmonic oscillator equation given by Eq. 5.3.6.
According to Eq. 5.3.6, the slope of the  tted line is the elastic modulus (E) of the
structural  lm used to fabricate the Resonators. Therefore, the elastic modulus of the
structural  lm of the native oxide covered Test Platform chip, which is the slope of
the  tted line shown in Fig. 8.2, is 130 GPa. This indicates that the elastic modulus
(E) of the Si(100)  lm obtained experimentally using the Test Platform developed in
this study is exactly the same as that (i.e., 130 GPa) accepted widely, and published
in literature [149]. This again validates the authenticity of the results obtained using
the Test Platform developed in this study.
8.5 Cantilever Beam Array
8.5.1 Validating the Authenticity of the Actuation Method Used to Ac-
tuate the Cantilever Beams
As explained in section 5.4.2, the cantilever beams (CBs) of the Test Platform
developed in this study are actuated (brought in contact with the substrate) man-
ually, by pushing them using a sharp tungsten probe tip (Signatone SE-SMS). The
manual force applied on a cantilever beam to bring it in contact with the underlying
substrate has the potential of altering the characteristics of the in-plane interface
formed between them. Accordingly, it can in uence the result obtained using that
cantilever beam. Further, if the manual force applied to actuate the cantilever beams
196
0.0e10 0
5.0e10 7
1.0e10 8
1.5e10 8
2.0e10 8
0.0e10
0
2.0e10
5
4.0e10
5
6.0e10
5
8.0e10
5
1.0e10
6
1.2e10
6
1.4e10
6
1.6e10
6
f R
2 , (Hz
2 )
(tw 3)(2 pi2M eff L3)-1, (GPa -1)
y = 129.87x
R 2 = 0.9991
Figure 8.2: A plot of the square of the observed resonance frequency of the Resonators
investigated in this chapter versus their corresponding value of the term that is written
in brackets on the right hand side of Eq. 5.3.6. The ( ) represent the experimentally
observed resonance frequencies and ( ) is a line  tted to the experimentally obtained
data. Notice the high R2 value of the linear  t. The slope of the  tted line is the
experimentally obtained value of E of the structural  lm of the native oxide covered
Test Platform chip.
197
(a)
(b)
Figure 8.3: (a) Interferogram of a polysilicon-based CBA, collected before actuation.
(b) Interferogram of the CBA shown in Fig. 8.3a, collected after actuation. This CBA
was actuated manually.
198
(a)
(b)
Figure 8.4: (a) Interferogram of a polysilicon-based CBA, collected before actuation.
(b) Interferogram of the CBA shown in Fig. 8.4a, collected after actuation. This CBA
was actuated electrostatically.
199
does in uence the results obtained using them, then the results obtained using a can-
tilever beam array will be inconsistent, since the manual force applied to actuate the
cantilever beams may vary from beam to beam in the same array. Therefore, in order
to ascertain that the manual force exerted on a cantilever beam to actuate it does not
have any in uence on the result obtained using it, two polysilicon-based cantilever
beam arrays fabricated side-by-side on the same chip are actuated, one manually and
the other electrostatically. The purpose behind using the polysilicon-based cantilever
beam arrays for this analysis is that the cantilever beam arrays of the Test Platform
developed in this study cannot be actuated electrostatically. Electrostatic actuation is
considered as the standard method for actuating cantilever beam arrays. Figures 8.3a
and 8.3b are interferograms showing the polysilicon-based cantilever beam array that
is actuated manually, collected before and after the actuation, respectively. Similarly,
Figs. 8.4a and 8.4b are interferograms showing the polysilicon-based cantilever beam
array that is actuated electrostatically, collected before and after the actuation, re-
spectively. It is clearly evident from Figs. 8.3b and 8.4b that the manual actuation
method yields the exact same results as the electrostatic actuation method. The can-
tilever beams that did not stick in the polysilicon-based CBA, which was actuated
electrostatically, also did not stick in the polysilicon-based CBA, which was actuated
manually. Further, the same eight longer cantilever beams are stuck, either at their
tips or over a fraction of their lengths, in both the CBAs (i.e., the one that is actuated
manually as well as the one that is actuated electrostatically). This validates the au-
thenticity of the manual actuation method used to actuate the cantilever beams for
this study. The script used for validating the authenticity of the manual actuation
method used to actuate the cantilever beams, in this study is given in Appendix A.3.
200
8.5.2 Stress Gradient at the Sacri cial Oxide-Device Layer Interface
When released, the cantilever beams of the Test Platform developed in this study
do not remain horizontal, but are inclined upwards. This is evident in Fig. 8.5a, which
is an interferogram showing a released cantilever beam array of the Test Platform
chip coated with OTS SAM. The presence of fringes on the cantilever beams shown
in Fig. 8.5a clearly indicates that they are not parallel to the substrate. The height
pro le of beam 5 (labelled in Fig. 8.5a), which is shown in Fig. 8.5b, further substan-
tiates that the cantilever beams shown in Fig. 8.5a are inclined upwards, and have a
convex shape. This type of upward-inclined and curved height pro le is exhibited by
all the cantilever beams of every Test Platform chip, irrespective of the treatments, to
which, the Test Platform chips are subjected. The upward inclination of the released
cantilever beams of the Test Platform developed in this study is a consequence of the
augmentation of the stress-gradient present at the interface of sacri cial oxide and
device layer in their anchors. The curvature in their shape is a consequence of the
internal moment induced in them by the stress gradient present in their anchors, at
the interface of sacri cial oxide and device layer. The stress gradient that exists at the
interface of sacri cial oxide and device layer in the anchors of the cantilevers beams
of the Test Platform developed in this study is augmented by the high temperature
cycling, to which, the Test Platform is exposed during the polishing of its scalloped
sidewall test surfaces. This is substantiated by the fact that the released cantilever
beams of the Test Platform chip, which is not polished (i.e., exposed to high temper-
ature cycling), are signi cantly less upward-inclined and curved as compared to those
of the Test Platform chip, which is polished. Figure 8.6a is an interferogram show-
ing a released cantilever beam array of a Test Platform chip, which is not polished.
The lesser number of fringes present on the cantilever beams shown in Fig. 8.6a as
compared to those present on the cantilever beams shown in Fig. 8.5a substantiate
their less upward-inclined height pro les as compared to the height pro les of the
201
cantilever beams shown in Fig. 8.5a. Figure 8.6b, which is the PSI derived height
pro le of beam 1 labelled in Fig. 8.6a, further provides a quantitative con rmation of
the less upward-inclined and less curved height pro les of the cantilever beams, which
are not exposed to high temperature cycling, as compared to the height pro les of
those, which are exposed to high temperature cycling.
In order to obtain an accurate estimate of the work of adhesion of in-plane sur-
faces using the cantilever beams of the Test Platform developed in this study, the
e ects that the stress gradient present at the interface of sacri cial oxide and de-
vice layer in their anchors has on their initial (pre-actuated) height pro les must
be appropriately accounted for. The stress gradient present at the interface of sac-
ri cial oxide and device layer in the anchors of the cantilever beams of the Test
Platform used in this study causes them to have an upward-inclined, convex initial
(pre-actuated) height pro le. Therefore, the additional work done in bringing the
tips of the upward-inclined cantilever beams in contact with the substrate must be
included in the estimate of the work of adhesion of in-plane surfaces. The additional
work done includes the work done to bend the cantilever beams through an additional
height due to their upward inclination, which is stored as an additional bending en-
ergy in them, as well as the work done to counter the resistance o ered by the stress
gradient induced internal moment present in them to their bending. Additionally,
the stress gradient present at the interface of sacri cial oxide and device layer in the
anchors of the cantilever beams of the Test Platform used in this study causes the
adhered (actuated) cantilever beams to have non-zero slopes at their boundary points
(i.e., the points, at which, they are connected to their anchors as well as the points,
at which, they are adhered to the substrate). The equation used in this study for
estimating the apparent work of adhesion of in-plane surfaces (i.e., Eq. 5.4.1) takes
into account both the non-zero boundary slopes of the adhered cantilever beams as
well as the additional work done to counter the e ects of the stress gradient present
202
Beam 5
(a)
 0
 0.5
 1
 1.5
 2
 2.5
 3
 3.5
 0  100  200  300  400  500
Vertical height, (
?m)
Lateral position, (?m)
(b)
Figure 8.5: (a) Interferogram showing a released cantilever beam array of the Test
Platform chip coated with OTS SAM. Notice the presence of fringes on all the can-
tilever beams, which indicates that they are not parallel to the substrate. (b) Height
pro le of beam 5 labelled in Fig. 8.5a. The height pro le is obtained experimentally,
using phase shifting interferometry. It indicates that beam 5 is inclined upwards, and
has a convex shape.
203
Beam 1
(a)
 0
 0.5
 1
 1.5
 2
 2.5
 3
 3.5
 0  100  200  300  400  500
Vertical height, (
?m)
Lateral position, (?m)
(b)
Figure 8.6: (a) Interferogram showing a released cantilever beam array of a Test
Platform chip, which is not polished. Notice that the number of fringes present on
the cantilever beams shown in this image is less, which indicates that they are not
parallel to the substrate. (b) Height pro le of beam 5 labelled in Fig. 8.5a. The height
pro le is obtained experimentally, using phase shifting interferometry. It indicates
that beam 5 is inclined upwards, and has a convex shape.
204
at the interface of sacri cial oxide and device layer in their anchors. An analysis to
support this claim is provided in Table 8.3, which lists the apparent work of adhesion
of OTS SAM coated in-plane surfaces calculated using di erent methods. Method
\S-H" considers that the adhered cantilever beam is S-shaped, and was perfectly par-
allel to the substrate in its initial (pre-actuated) state. Method \S-I" also considers
that the adhered cantilever beam is S-shaped, but uses its PSI derived, experimen-
tally obtained initial (pre-actuated) height pro le as the reference. Both the methods
\P-H" and \P-I" use the PSI derived, experimentally obtained height pro le of the
actuated adhered cantilever beam for estimating the apparent work of adhesion of
in-plane surfaces. However, while method \P-H" considers that the cantilever beam
was perfectly parallel to the substrate in its initial (pre-actuated) state, method \P-I"
uses its PSI derived, experimentally obtained initial (pre-actuated) height pro le as
the reference. The OTS SAM coated cantilever beam used for this analysis exhibited
a crack length of 835.3  m. It is clearly evident from the data reported in Table 8.3
that the apparent work of adhesion of in-plane surfaces estimated using methods \S-
H" and \S-I" is signi cantly lower than the actual value. This is attributed to the
fact that both the methods \S-H" and \S-I" do not consider the non-zero boundary
slopes of the adhered cantilever beams. Additionally, method \S-H" neither considers
the work done to bend the cantilever beams through an additional height due to their
upward inclination nor considers the work done to counter the resistance o ered by
the stress gradient induced internal moment present in them to their bending. While
method \S-I" does consider the work done to bend the cantilever beams through an
additional height due to their upward inclination, it still does not consider the work
done to counter the resistance o ered by the stress gradient induced internal moment
present in them to their bending. On the other hand, both the methods \P-H" and
\P-I" consider both the work done to bend the cantilever beams through an addi-
tional height due to their upward inclination as well as the work done to counter the
205
resistance o ered by the stress gradient induced internal moment present in them to
their bending. Therefore, the work of adhesion of OTS SAM coated in-plane sur-
faces estimated using them appear to be more believable. Table 8.3 additionally
indicates that while the work required to counter the resistance o ered by the stress
gradient induced internal moment present in the cantilever beams to their bending is
signi cantly greater than that required to overcome the restoring forces of the bent
(actuated) cantilever beams, and the major fraction of the apparent work of adhesion
required by the cantilever beams to remain adhered to the substrate, the work re-
quired to bend the cantilever beams through an additional height due to their upward
inclination is much lesser than that, and only a minor fraction of it. The method used
for determining the apparent work of adhesion of the in-plane surfaces investigated
in this study is highlighted in Table 8.3.
8.5.3 Determining the Apparent Work of Adhesion of In-plane Surfaces
Coated with Standard Coatings
For each type of surface studied in this chapter (i.e., OTS SAM coated and
surfaces with only native oxide on them), four CBAs (consisting of ten cantilever
beams each) are used for determining the apparent work of adhesion of in-plane
surfaces. The magni cation of the objective lens, which is used in the interference
microscope that is used to determine the height pro le of the actuated cantilever
beams, is either 10X or 20X. Accordingly, the size of each pixel in the  eld of view is
either 0.465  m 0.465  m or 0.234  m 0.234  m, respectively. Table 8.4 reports
the crack lengths and the apparent works of adhesion of in-plane surfaces for both
OTS SAM coated surfaces as well as surfaces with only native oxide on them. The
results are as expected. OTS SAM coated in-plane surfaces exhibit a much lower
apparent work of adhesion than the corresponding surfaces with only native oxide
on them. This is expected because the hydrophobic surface chemistry of OTS SAM
206
Table 8.3: Comparison between the apparent work of adhesion of OTS SAM coated
in-plane surfaces calculated using di erent methods. The OTS SAM coated cantilever
beam used for this analysis exhibited a crack length of 835.3  m. The method used
for determining the apparent work of adhesion of the in-plane surfaces investigated
in this study is highlighted in the table.
Calculation Wip
Method (  J/m2)
S-H 8.848
S-I 8.360
P-H 46.15
P-I 45.12
S-H: Considers that the adhered cantilever beam is S-shaped.
Considers that it was perfectly parallel to the substrate in its initial state.
S-I: Considers that the adhered cantilever beam is S-shaped.
Uses its PSI derived initial (pre-actuated) height pro le as the reference.
P-H: Uses the PSI derived height pro le of the actuated adhered cantilever beam.
Considers that it was perfectly parallel to the substrate in its initial state.
P-I: Uses the PSI derived height pro le of the actuated adhered cantilever beam.
Uses its PSI derived initial (pre-actuated) height pro le as the reference.
207
Table 8.4: Comparison between the apparent work of adhesion of in-plane surfaces of
OTS SAM coated surfaces and that of surfaces with only native oxide on them. The
apparent works of adhesion of in-plane surfaces reported in this table are determined
using the CBAs. All the values reported in the table are arithmetic means of 40
measurements and sd is one standard deviation of the sample consisting of those
measurements.
Coating Crack Length Apparent Work of Adhesion of In-plane Surfaces
sip  sd Wip  sd
( m) (  J/m2)
Oxide 99.0  5.5 38700  9300
OTS 833.5  5 45.46  1
208
coated surfaces signi cantly reduces the contribution of capillary forces to stiction
between them. Further, for both types of surfaces (OTS SAM coated and surfaces
with only native oxide on them), the in-plane surfaces exhibit a higher apparent
work of adhesion than the corresponding sidewall surfaces (The apparent works of
adhesion of sidewall surfaces are reported in Table 8.5). This is also expected because
the sidewall surfaces of the Test Platform have a much higher rms roughness (6.52
nm) than the in-plane surfaces (0.1 nm). Infact, this substantiates the fact that the
topographies of contacting MEMS surfaces have a strong in uence on the tribological
properties of the interface formed by them. Further evidence of the in uence of the
surface topographies of contacting MEMS surfaces on their tribological properties is
provided by the fact that the apparent works of adhesion of in-plane surfaces reported
by Ashurst et al., who used microinstruments fabricated using rougher polysilicon
surfaces (rms roughness of the in-plane surfaces tested was 5.9 nm and rms roughness
of the sidewall surfaces tested was 13.3 nm), is signi cantly lesser than those obtained
using the Test Platform developed in this study, for both the types of surfaces studied
in this chapter [6,35,104]. Even though their experiments were conducted at a higher
relative humidity (RH) of 50 %, Ashurst et al. reported a lower in-plane apparent
work of adhesion of 0.012 mJ/m2 and 13.1 mJ/m2 for OTS coated polysilicon surfaces
and polysilicon surfaces with only native oxide on them, respectively.
8.6 Sidewall Beam Array
Figure 8.7a is an interferogram showing released sidewall adhesion test microin-
struments. The fringes visible on the sidewall beams in Fig. 8.7a reveal two features
about the released sidewall beams. First, the released sidewall beams are freestand-
ing. Second, they are not parallel to the substrate. This is also substantiated by
Fig. 8.7b, which shows the height pro le of the initial segment of the topmost side-
wall beam shown in Fig. 8.7a. The height pro le shown in Fig. 8.7b clearly indicates
209
that the sidewall beams are inclined upwards and they exhibit a take-o angle of 1
mrad. This upward inclination of the released sidewall beams is attributed to the
stress gradient present at the sacri cial oxide/device layer interface in the anchor. It,
unlike the compliance of the sidewall adhesion tester reported in [78], obviates the
need to place a constraining clip over the ends of a sidewall beam pair to ensure that
the sidewall beams remain in place during the drying process.
Levitation, which is a critical phenomena that ensues in most of the electrostat-
ically actuated microinstruments, needs to be appropriately accounted for to ensure
the accuracy of the results obtained using those microinstruments. Historically, re-
searchers have either used an elaborate actuation scheme to account for the e ects
of levitation or a sophisticated electronic read-out system combined with a theoreti-
cal model to subtract the levitation induced contribution from the measured output
signal [142,159]. However, while levitation does ensue during the electrostatic actua-
tion of the sidewall adhesion test microinstrument developed in this study, it has no
in uence on the results obtained using the microinstrument. This is substantiated
by Fig. 8.8, which is an interferogram showing the initial segment of an actuated
sidewall adhesion test microinstrument. A voltage of 52 V is applied to the electrode
to actuate the sidewall adhesion test microinstrument, in this case. The number of
fringes visible on the actuated sidewall beams seen in Fig. 8.8 is much greater than
that of the fringes visible on the unactuated sidewall beams seen in Fig. 8.7a. This
clearly indicates that levitation ensues and increases the upward inclination of the
actuated sidewall beams. However, it has the exact same e ect on both the sidewall
beams of the microinstrument, which is evident from the presence of the same num-
ber of fringes on them. As a result, it has no in uence on the apparent interfacial
contact area of the two adhered sidewall beams and hence on the apparent work of
adhesion of the sidewall surfaces determined using the sidewall adhesion test microin-
strument developed in this study. In essence, the design of the sidewall adhesion test
210
(a)
 0
 50
 100
 150
 200
 250
 0  40  80  120  160  200  240  280  320
Vertical height, (nm)
Lateral position, ( ?m)
? = 1 mrad
(b)
Figure 8.7: (a) Interferogram showing released sidewall adhesion test microinstru-
ments. Notice the fringes on the sidewall beams, which clearly indicate that the
sidewall beams are freestanding and also not parallel to the substrate (b) Height pro-
 le of the initial segment of the topmost sidewall beam shown in Fig. 8.7a. The height
pro le is obtained using phase shifting interferometry. It clearly indicates that the
sidewall beam is inclined upwards and exhibits a take-o angle of 1 mrad.
211
microinstrument developed in this study obviates the need to account for the e ects
of levitation on the results obtained using it.
One of the limitations of the sidewall adhesion tester reported by Ashurst et al.
in [78] was that the sidewall beams that remained stuck to each other after actuation
were not perfectly aligned in the z plane, in spite of the measures taken to prevent
the misalignment. This e ect, which Ashurst et al. referred to as \scissoring", acted
to reduce the apparent interfacial contact area of the adhered sidewall beams, and
thereby, compromised the accuracy of the apparent work of adhesion determined
using the sidewall adhesion tester. Moreover, the amount of scissoring exhibited by
di erent sidewall adhesion testers fabricated on the same chip was random and even
that exhibited by the same sidewall adhesion tester was not reproducible [78]. While
the scissoring induced error in the determination of apparent work of adhesion of
sidewall surfaces is relatively small when stiction between sidewall surfaces is high,
it is substantial when the stiction between them is low [78]. Therefore, scissoring
makes it di cult to compare the e ects of the surface modi cation strategies used
to reduce stiction between MEMS sidewalls. However, the sidewall adhesion test
microinstrument developed in this study does not exhibit scissoring at all. This is
substantiated by Fig. 8.9a, which is an interferogram showing the  nal segment of
an actuated sidewall adhesion test microinstrument (developed in this study). A
voltage of 70 V is applied to the electrode to actuate the sidewall adhesion test
microinstrument in this case. Notice that the sidewall beams are adhered over a
length of 50  m at their tips. It is clearly evident in Fig. 8.9a that the adhered sidewall
beams are perfectly aligned in the z-plane since the fringes on the two of them exactly
match each other in number as well as phase. The small mis-match in the phase of the
fringes visible on the two adhered sidewall beams in Fig. 8.9a is due to the torsional
twisting of the sidewall interface. The sidewall interface formed by the two adhered
sidewall beams experiences a torsional twist because the contacting sidewall beams
212
Figure 8.8: Interferogram showing the initial segment of an actuated sidewall adhesion
test microinstrument. Voltage applied to the actuation electrode is 52 V. Notice the
increased number of fringes visible on the actuated sidewall beams as compared to
that of fringes visible on the unactuated sidewall beams shown in Fig. 8.7a, which is
a manifestation of levitation. Also notice that the exact same number of fringes are
visible on both the actuated sidewall beams.
213
do not have perfectly vertical sidewall surfaces. The torsional twisting of the sidewall
interface was con rmed using phase shifting interferometry. The sidewall angle of the
contacting sidewall beams was also determined using phase shifting interferometry
and is found to be 89 . However, since the torsional twisting of the sidewall interface
does not a ect the apparent interfacial contact area of the adhered sidewall beams,
it does not induce any error in the determination of the apparent adhesion energy of
sidewall surfaces. Figure 8.9b is the interferogram of the same sidewall adhesion test
microinstrument that is shown in Fig. 8.9a, collected post-actuation. In the post-
actuated state too, the fringes on the two sidewall beams are equal and in-phase, as
evident in Fig. 8.9b. In order to determine the reproducibility of the vertical alignment
of the adhered sidewall beams of the sidewall adhesion test microinstrument developed
in this study, the adhered sidewall beams were carefully pulled apart and re-actuated.
Comparing the interferograms of the actuated and re-actuated sidewall adhesion test
microinstruments did not reveal any discernible di erences in the vertical alignment
of the adhered sidewall beams.
For each type of surface studied in this chapter (OTS SAM coated and surfaces
with only native oxide on them), eight SBAs are used to determine the apparent work
of adhesion of the contacting sidewall surfaces. The magni cation of the objective
lens of the microscope, which is used to observe the microinstrument during actuation
and determine the crack length of each actuated adhered pair of sidewall beams, is
10X. Accordingly, the size of each pixel in the  eld of view is 0.465  m  0.465
 m. Table 8.5 reports the crack lengths and the apparent works of adhesion of the
contacting sidewall surfaces for both OTS SAM coated surfaces as well as surfaces
with only native oxide on them. The results are as expected. OTS SAM coated
sidewalls exhibit a much lower apparent work of adhesion than the corresponding
surfaces with only native oxide on them. This is expected because the hydrophobic
surface chemistry of OTS SAM coated surfaces signi cantly reduces the contribution
214
(a)
(b)
Figure 8.9: (a) Interferogram showing the  nal segment of an actuated sidewall ad-
hesion test microinstrument. Voltage applied to the actuation electrode is 70 V. The
two sidewall beams are stuck to each other over a length of 50  m at their tips.
Notice that while the fringes on the two sidewall beams are equal in number, they
are slightly mismatched in phase. (b) Interferogram, showing the  nal segment of
the same sidewall adhesion test microinstrument that is shown in Fig. 8.9a, collected
post-actuation. Notice that no \scissoring" is visible on the two sidewall beams, which
are stuck over a length of 25  m at their tips.
215
Table 8.5: Comparison between the apparent work of adhesion of sidewall surfaces of
OTS SAM coated surfaces and that of surfaces with only native oxide on them. The
apparent works of adhesion of sidewall surfaces reported in this table are determined
using the SBAs. All the values reported in the table are arithmetic means of several
measurements and sd is one standard deviation of the sample consisting of those
measurements.
Coating Crack Length Apparent Work of Adhesion of Sidewall Surfaces
ss  sd Ws  sd
( m) (  J/m2)
Oxide 660  10 1070  60
OTS 1550  10 37.65  1
216
of capillary forces to stiction between them. Further, for both the types of surfaces
studied (i.e., OTS SAM coated and surfaces with only native oxide on them), the
sidewall surfaces exhibit a lower apparent work of adhesion than that exhibited by the
corresponding in-plane surfaces (The apparent works of adhesion of in-plane surfaces
are reported in Table 8.4). This is also expected because the sidewall surfaces of the
Test Platform developed in this study have a much higher rms roughness (6.52 nm)
than its in-plane surfaces (0.1 nm). The di erence between the apparent work of
adhesion of sidewall surfaces and that of in-plane surfaces is greater in the case of
surfaces with only native oxide on them as compared to OTS SAM coated surfaces
because the capillary forces present at interfaces between surfaces with only native
oxide on them augment the e ect of topography on stiction between them.
8.7 Sidewall Friction Tester
As outlined in section 5.6.4, the  rst step in actuating a Sidewall Friction Tester
is to determine the a and b of that Sidewall Friction Tester. The optically measured
values of a and b of one of the Sidewall Friction Testers coated with OTS SAM (re-
ferred to as test device from now onwards) are 18.135  m and 26.505  m, respectively.
Therefore, according to Eq. 5.6.8,  a for the test device is 4.185  m. The magni ca-
tion of the objective lens that is used in the microscope during the actuation of the
Sidewall Friction Testers is 10X. Accordingly, the size of each pixel in the  eld of view
is 0.465  m 0.465  m. Figure 8.10 is a plot showing the experimentally determined
axial and lateral displacements of the tangential arm of the test device versus the
square of the corresponding voltages (V2t ) applied to its pull drive. As expected, the
data representing the axial displacements is clearly divided into two segments, which
have signi cantly di erent slopes. The segment with the smaller slope corresponds
to the initial segment and that with the higher slope corresponds to the  nal seg-
ment of the anchored comb  ngers of the tangential comb-drive actuator. Further,
217
it is evident in Fig. 8.10 that within each segment, the axial displacement of the
tangential arm increases linearly with the force generated by the tangential comb-
drive actuator. This substantiates the validity of our treatment of the folded beam
 exures and the thin beam that connects the tangential arm to the loading section
as linear elastic (Hookean) springs. The transfer functions corresponding to the two
segments (i.e., Gt1 and Gt2 respectively) of the anchored comb  ngers of the tangen-
tial comb-drive actuator, which are determined by  tting straight lines to the two
segments of the axial displacement data shown in Fig. 8.10, are 0.0046  m/V2 and
0.0128  m/V2 respectively. Accordingly, the ratio of the experimentally determined
Gt2 to the experimentally determined Gt1 is 2.78, which con rms that as expected,
the electrostatic force generated by the pull drive of the tangential comb-drive actua-
tor increases by close to a factor of 3 when a fraction of the length of suspended comb
 ngers overlaps with the  nal segments of the anchored comb  ngers. Va, which is
determined by identifying the voltage that corresponds to an axial displacement of  a
in Fig. 8.10, is 26.1 V. It should be noted that the data point corresponding to  a and
Va belongs to the segment of axial displacement data that has a higher slope, which
indicates that when the normal arm is aligned with the anchored posts, a fraction of
the length of suspended comb  ngers overlaps with the  nal segments of the anchored
comb  ngers. The data that represents lateral displacements indicates that during
the entire calibration, the motion of the tangential arm is con ned to only the axial
direction.
Figure 8.11 is a plot showing the experimentally determined axial and lateral dis-
placements of the normal arm of the test device versus the square of the corresponding
voltages (V2n) applied to its pull drive. Again as expected, the data representing the
axial displacements is clearly divided into three segments, which have signi cantly
di erent slopes. The  rst two segments correspond to the initial and  nal segments
218
 0
 2
 4
 6
 8
 10
 0  300  600  900  1200
Displacement (
?m)
V t2 (V 2)
V a = 26.1 V
?a = 4.185 ?m
G t1 = 0.0046 ?m/V 2
G t2 = 0.0128 ?m/V 2
Figure 8.10: A plot showing the experimentally determined axial ( ) and lateral ( )
displacements of the tangential arm of the test device versus square of the correspond-
ing voltages (V2t ) applied to its pull drive. Notice that the data representing the axial
displacements is clearly divided into two segments, which have signi cantly di erent
slopes. The transfer functions Gt1 and Gt2 are extracted from the corresponding lin-
ear  ts ( ) of the experimental axial displacement data.  a, which is determined
optically, is the distance by which the tangential arm should be pulled to its left to
align the normal arm with the anchored posts and Va is the corresponding voltage
that should be applied to the pull drive of the tangential arm.
219
of the anchored comb  ngers of the normal comb-drive actuator. Further, it is ev-
ident in Fig. 8.11 that within the  rst two segments, the axial displacement of the
normal arm increases linearly with the force generated by the normal comb-drive ac-
tuator. This substantiates the validity of our treatment of the folded beam  exures
and the thin beam that connects the normal arm to the loading section as linear elas-
tic (Hookean) springs. The transfer functions corresponding to those two segments
(i.e., Gn1 and Gn2 respectively), which are determined by  tting straight lines to the
corresponding data, are 0.0036  m/V2 and 0.0104  m/V2 respectively. The ratio
of the experimentally determined Gn2 to the experimentally determined Gn1 is 2.88,
which again, is close to the design value of 3. The third segment of the axial displace-
ment data indicates that the axial displacement of the normal arm does not increase
beyond 6.17  m. Therefore,  c, which is the distance by which the normal arm should
be axially displaced to bring the loading beam in contact with an anchored post, is
6.17  m. Accordingly, Vc, which is the voltage that should be applied to a normal
comb-drive actuator to bring the loading beam in contact with the corresponding
anchored post is 32.6 V. It is determined by identifying the voltage that corresponds
to an axial displacement of  c in Fig. 8.11. Additionally, it should be noted that even
at voltages (applied to the normal comb-drive actuator) greater than Vc, the lateral
displacements of the normal arm are negligible. This con rms that no unbalanced
moment is induced at the sidewall interface by the normal load applied at it.
Levitation, which is a critical phenomena that ensues in most of the electrostat-
ically actuated microinstruments, has been reported to reduce the apparent contact
area of the test sidewall interface of most of the sidewall friction and wear test mi-
croinstruments reported to date [23,85,143,159,179]. The reduction in the apparent
contact area of the sidewall interface results in inaccurate determination of the con-
tact pressures applied to it. Therefore, historically, researchers have either used an
elaborate actuation scheme or a sophisticated electronic read-out system combined
220
 0
 2
 4
 6
 0  300  600  900  1200  1500  1800
Displacement (
?m)
V n2 (V 2)
V c = 32.6 V
?c = 6.17 ?m
G n1  = 0.0036 ?m/V 2
G n2  = 0.0104 ?m/V 2
Figure 8.11: A plot showing the experimentally determined axial ( ) and lateral ( )
displacements of the normal arm of the test device versus square of the corresponding
voltages (V2n) applied to its pull drive. Notice that the data representing the axial
displacements is clearly divided into three segments, which have signi cantly di erent
slopes. The transfer functions Gn1 and Gn2 are extracted from the corresponding
linear  ts ( ) of the experimental axial displacement data.  c is the distance by
which the normal arm should be axially displaced in order to bring the loading beam
in contact with the anchored post and Vc is the corresponding voltage that should be
applied to the normal comb-drive actuator. Notice that even at voltages greater than
Vc, the lateral displacements of the normal arm are negligible.
221
with a theoretical model to account for the e ects of levitation [23, 143, 159, 179].
However, no additional measures are required to account for the e ects of levitation
in the case of the Sidewall Friction Tester developed in this study, since levitation
does not ensue in it. This is substantiated by Fig. 8.12, which is an interferogram,
showing the loading section of the test device, collected after bringing the loading
beam in contact with the anchored post. A voltage of 45 V is applied to the pull
drive of the normal comb-drive actuator before collecting this interferogram. The
absence of fringes on the normal arm as well as on the loading section in Fig. 8.12 is
a reliable evidence of the fact that levitation does not ensue in the Sidewall Friction
Tester developed in this study. However, due to the presence of a stress gradient at
the sacri cial oxide/device layer interface in the anchored post, the portions of the
device layer of the post that are not anchored to the substrate are inclined upwards
with a slope of 1 mrad. As a result, a step edge exists at the interface between the
sidewall surfaces of the loading beam and the anchored post. This step edge, which
is determined using horizontal scanning interferometry (HSI), is found to be 20 nm
high. Since the step edge is much smaller than the total height of the sidewall inter-
face, which is 2  m (nominal), it does not reduce the apparent contact area of the
sidewall interface signi cantly.
To determine the coe cients of static and kinetic friction of the OTS SAM
coated sidewall surfaces of the test device, a Vn;s of 60 V is applied to the pull drive
of its normal comb-drive actuator. The corresponding friction force is determined by
ramping up the tangential force applied at the sidewall interface using the tangential
comb-drive actuator. A plot showing the onset of slip at the sidewall interface of
the test device is shown in Fig. 8.13. In the plot, the displacement of the loading
beam, which is determined by considering its position when the normal arm is aligned
with the anchored post as the initial position, is plotted against the voltage applied
to the tangential comb-drive actuator. As seen in Fig. 8.13, the  rst slip occurs at
222
Figure 8.12: An interferogram, showing the loading section of the test device, collected
after bringing the loading beam in contact with the anchored post. A voltage of 45 V
is applied to the pull drive of the normal comb-drive actuator before collecting this
interferogram. Notice the absence of fringes on the normal arm as well as on the
loading section. The step edge at the sidewall interface is determined using HSI to
be 20 nm.
223
a voltage of 32.8 V. Accordingly, using Vt;s as 32.8 V, Vn;s as 60 V, Va as 26.1 V
and Vc as 32.6 V in Eq. 5.6.17 gives a  s of 0.16 for the OTS SAM coated sidewall
surfaces. Further, the distance for which the loading beam slides in contact with the
anchored post after the initiation of the  rst slip at the sidewall interface (i.e.,  s) is
determined from Fig. 8.13 to be 1.36  m. Accordingly, Eq. 5.6.19 gives a  k of 0.11
for the OTS SAM coated sidewall surfaces. The  s and  k of the OTS SAM coated
sidewall surfaces can also be determined using the second slip that occurs at the Vt;s
of 34.8 V (see Fig. 8.13).
For each type of surface studied in this chapter (i.e., OTS SAM coated and surface
with only native oxide on it),  ve Sidewall Friction Testers are used to investigate
the friction and wear characteristics of contacting sidewalls. Using each Sidewall
Friction Tester, the coe cients of static and kinetic friction are determined at normal
loads ranging from 2.4  N - 15.7  N, which correspond to Hertzian contact pressures
(calculated by considering cylinder on  at geometry) of 123 MPa - 312 MPa. This
range of normal load is representative of that experienced by most potential and
commercialized MEMS during operation. Additionally, in order to obtain statistically
signi cant results, the coe cients of static and kinetic friction are determined  ve
times for each investigated normal load. Table 8.6 reports the engineering coe cients
of static and kinetic friction of both OTS SAM coated surfaces as well as surfaces
with only native oxide on them. The results are as expected. Again, the coe cients
of friction of the oxide covered sidewall test surfaces of the Test Platform developed
in this study are greater than those reported in literature, which were obtained using
microinstruments that had rougher sidewall test surfaces [23,79,85,126,128,141,143,
147, 150, 151, 159, 162, 164]. The coe cients of both static as well as kinetic friction
of surfaces with only native oxide on them are greater than 1. This is attributed to
two factors. First, the coe cients of static and kinetic friction reported in Table 8.6
are engineering coe cients of friction and the additional normal load experienced by
224
 0
 0.5
 1
 1.5
 2
 2.5
 3
 25  26  27  28  29  30  31  32  33  34  35  36
Displacement (
?m)
V t (V)
V t,s  = 32.8 V
?s = 1.36 ?m
Figure 8.13: A plot showing the onset of slip at an OTS SAM coated sidewall interface.
The displacement of the loading beam, which is determined by considering its position
when the normal arm is aligned with the anchored post as the initial position, is
plotted against the voltage applied to the tangential comb-drive actuator. A normal
load of 8.05  N, which corresponds to a Hertzian contact pressure of 224 MPa, is
applied at the sidewall interface. Notice that the  rst slip occurred at Vt;s of 32.8 V
and the second slip occurred at Vt;s of 34.8 V.
225
the sidewall interface due to the adhesion between the contacting sidewall surfaces
is not accounted for in their determination. Second, owing to the hydrophilic nature
of the surfaces with only native oxide on them, adhesion between contacting sidewall
surfaces, which have only native oxide on them, is signi cantly high and comparable
to the externally applied normal loads. Further, the  s and  k of surfaces with only
native oxide on them also vary signi cantly. This is also attributed to the same two
factors as the relative signi cance of adhesion between contacting sidewall surfaces
changes with the externally applied normal load. On the other hand, the  s and  k of
the OTS SAM coated sidewalls are signi cantly lesser than 1 and they also vary much
less as compared to those of surfaces with only native oxide on them. The one factor
that is responsible for both of these attributes of the  s and  k of OTS SAM coated
sidewalls is the hydrophobic surface chemistry of the OTS SAM coated sidewalls,
due to which, the adhesion between them is signi cantly lesser than that between
the sidewalls with only native oxide on them. The hydrophobic surface chemistry of
OTS SAM coated sidewalls is also responsible for the smaller di erence between their
 s and  k as compared to that between the  s and  k of surfaces with only native
oxide on them because the relatively higher adhesion between the contacting sidewall
surfaces, which have only native on them, augments the e ect of sliding on friction.
After determining  s and  k, each Sidewall Friction Tester is used to study the
wear characteristics of its contacting sidewall surfaces. The wear characteristics of
the contacting sidewall surfaces are studied by rubbing the loading beam against the
anchored post under a normal load of 0.5  N, which corresponds to a VN of 35.5
V and a Hertzian contact pressure of 55.9 MPa (calculated by considering cylinder
on  at geometry). The reciprocating motion of the loading beam is achieved by
superimposing an AC voltage, which has a frequency of 10 Hz and a peak-to-peak
amplitude of 2 V, on Va, which is the DC bias applied to the pull drive of the tangential
arm to align the normal arm with the anchored posts. The change in the  s and  k
226
Table 8.6: Comparison between the engineering coe cients of static and kinetic fric-
tion of OTS SAM coated surfaces and those of surfaces with only native oxide on
them. The engineering coe cients of friction reported in this table are determined
using the Sidewall Friction Tester. All the values reported in the table are arithmetic
means of 200 measurements and the std. dev. is one standard deviation of the sample
consisting of those measurements.
Coating Coe cient of Static Friction Coe cient of Kinetic Friction
 s  std. dev.  k  std. dev.
Oxide 1.75  0.40 1.40  0.20
OTS 0.15  0.02 0.11  0.01
227
of the contacting sidewalls is used as a measure to qualitatively study their wear
characteristics. The  s and  k of OTS SAM coated sidewalls remained unchanged
even after 180 min. of operation (i.e., even after accumulating 108000 wear cycles).
However, a reliable conclusion about the wear characteristics of the sidewalls with only
native on them could not be drawn because, while in some microinstruments with
sidewall surfaces having only native oxide on them, the loading beam reciprocated for
a few cycles, during which, it exhibited a stick-slip type of motion, in the remaining
microinstruments, the loading beam did not reciprocate at all due to the signi cantly
high adhesion between the contacting sidewalls.
8.8 Sidewall Friction and Adhesion Tester
As mentioned in section 4.1.2, the purpose behind including SFAT along with
SFT in the Test Platform, for studying the friction and wear characteristics of sidewall
surfaces is to determine the in uence of the geometries of the surfaces forming the
contact interface on the e ect of surface topography. While in the SFT, the contact
interface is formed between the plane (vertical) surface of a suspended beam and the
cylindrical surface of an anchored post, in the SFAT, it is formed between the plane
(vertical) surfaces of two suspended shuttles. The magni cation of the objective lens
that is used in the microscope during the actuation of the Sidewall Friction Testers
is 10X. Accordingly, the size of each pixel in the  eld of view is 0.465  m  0.465
 m. Figure 8.14 is a plot showing the experimentally determined axial and lateral
displacements of the tangential arm of one of the OTS SAM coated Sidewall Friction
and Adhesion Testers (referred to as test device from now onwards) versus the square
of the corresponding voltages (V2t ) applied to its push drive. Again, as expected, the
data representing the axial displacements is clearly divided into two segments, which
have signi cantly di erent slopes. The segment with the smaller slope corresponds to
the initial segment and that with the higher slope corresponds to the  nal segment of
228
the anchored comb  ngers of the tangential comb-drive actuator. Also, it is evident
in Fig. 8.14 that within each segment, the axial displacement of the tangential arm
increases linearly with the force generated by the tangential comb-drive actuator. This
substantiates the validity of our treatment of the folded beam  exure of the tangential
arm as linear elastic (Hookean) springs. The transfer functions corresponding to the
two segments (i.e., Gt1 and Gt2, respectively) of the anchored comb  ngers of the
tangential comb-drive actuator, which are determined by  tting straight lines to the
two segments of the axial displacement data shown in Fig. 8.14, are 0.0011  m/V2 and
0.0032  m/V2, respectively. Accordingly, the ratio of the experimentally determined
Gt2 to the experimentally determined Gt1 is 2.91, which con rms that as expected, the
electrostatic force generated by the push drive of the tangential comb-drive actuator
increases by close to a factor of 3 when a fraction of the length of suspended comb
 ngers overlaps with the  nal segments of the anchored comb  ngers. Again, the data
that represents lateral displacements indicates that during the entire calibration, the
motion of the tangential arm of the test device is con ned to only the axial direction.
Figure 8.15 is a plot showing the experimentally determined axial and lateral dis-
placements of the normal arm of the test device versus the square of the corresponding
voltages (V2n) applied to its push drive. Again as expected, the data representing the
axial displacements is clearly divided into three segments, which have signi cantly
di erent slopes. The  rst two segments correspond to the initial and  nal segments
of the anchored comb  ngers of the normal comb-drive actuator. Further, it is evident
in Fig. 8.15 that within the  rst two segments, the axial displacement of the normal
arm increases linearly with the force generated by the normal comb-drive actuator.
This substantiates the validity of our treatment of the folded beam  exures of the
normal arm as linear elastic (Hookean) springs. The transfer functions corresponding
to the two segments of the anchored comb  ngers of the normal arm of the test device
229
 0
 2
 4
 6
 8
 0  400  800  1200  1600  2000  2400  2800  3200
Displacement (
?m)
V t2 (V 2)
G t1 = 0.0011 ?m/V 2
G t2 = 0.0032 ?m/V 2
Figure 8.14: A plot showing the experimentally determined axial ( ) and lateral ( )
displacements of the tangential arm of of one of the OTS SAM coated Sidewall Friction
and Adhesion Testers versus square of the corresponding voltages (V2t ) applied to its
push drive. Notice that the data representing the axial displacements is clearly divided
into two segments, which have signi cantly di erent slopes. The transfer functions
Gt1 and Gt2 are extracted from the corresponding linear  ts ( ) of the experimental
axial displacement data.
230
(i.e., Gn1 and Gn2 respectively), which are determined by  tting straight lines to the
corresponding data, are 0.0020  m/V2 and 0.0059  m/V2, respectively. Accordingly,
the ratio of the experimentally determined Gn2 to the experimentally determined Gn1
is 2.95, which again, is close to the design value of 3. The third segment of the ax-
ial displacement data of the test device indicates that the axial displacement of its
normal arm does not increase beyond 3.75  m. Therefore,  c, which is the distance
by which the normal arm should be axially displaced to bring the loading block in
contact with the friction block, is 3.75  m. Accordingly, Vc, which is the voltage that
should be applied to the normal comb-drive actuator of a SFAT to bring its loading
block in contact with its friction block, is 33 V. It is determined by identifying the
voltage that corresponds to an axial displacement of  c in Fig. 8.15. The lateral dis-
placements of the normal arm of the test device are also negligible, indicating that
during the entire calibration, the motion of even the normal arm of the test device is
con ned to only the axial direction.
While levitation does ensue in the Sidewall Friction and Adhesion Testers de-
veloped in this study during their electrostatic actuation, it has no in uence on the
results obtained using them. Although it leads to tilting of both the normal as well
as tangential arms of the SFATs, it has a similar e ect on both of them. Therefore,
it induces only a small step edge at the sidewall interface formed between their load-
ing and friction blocks. Fig. 8.12 is an interferogram showing the sidewall interface
formed in the test device. A voltage of 50 V is applied to the push drive of the normal
arm to bring the loading block in contact with the friction block, before collecting
this interferogram. The absence of fringes on the loading and friction blocks shown in
the interferogram substantiates the absence of a signi cant step edge at the sidewall
interface formed by them. The typical step edge that exists at the sidewall interfaces
formed in the SFATs developed in this study is determined using horizontal scanning
interferometry (HSI) to be about 75 nm high. Since this step edge is much smaller
231
 0
 1
 2
 3
 4
 0  300  600  900  1200  1500  1800
Displacement (
?m)
V n2 (V 2)
V c = 33 V
?c = 3.75 ?m
G n1  = 0.0020 ?m/V 2
G n2  = 0.0059 ?m/V 2
Figure 8.15: A plot showing the experimentally determined axial ( ) and lateral ( )
displacements of the normal arm of one of the OTS SAM coated SFAT versus square
of the corresponding voltages (V2n) applied to its push drive. Notice that the data
representing the axial displacements is clearly divided into three segments, which
have signi cantly di erent slopes. The transfer functions Gn1 and Gn2 are extracted
from the corresponding linear  ts ( ) of the experimental axial displacement data.
 c is the distance by which the normal arm should be axially displaced in order to
bring the loading block in contact with the friction block and Vc is the corresponding
voltage that should be applied to the normal comb-drive actuator.
232
than the total (nominal) height of the sidewall interface, which is 2  m (nominal),
it does not reduce the apparent contact area of the sidewall interface signi cantly.
Consequently, it does not induce any signi cant error in the estimation of the contact
pressures applied at the sidewall interface. Therefore, no additional measures are
required to account for the e ects of the levitation induced in the Sidewall Friction
and Adhesion Tester developed in this study during their actuation.
To determine the coe cients of static and kinetic friction of the OTS SAM
coated sidewall surfaces of the test device, a Vn;s of 60 V is applied to the push drive
of its normal comb-drive actuator. The corresponding friction force is determined by
ramping up the tangential force applied at the sidewall interface using the tangential
comb-drive actuator. A plot showing the onset of slip at the sidewall interface of
the test device is shown in Fig. 8.17. In the plot, the displacement of the friction
block is plotted against the voltage applied to the tangential comb-drive actuator.
Two slip events are clearly visible in the plot. One occurs at a voltage of 52 V and
the other occurs at a voltage of 57 V. Using the  rst slip event (i.e., using Vt;s as
52 V) and, Vn;s as 60 V, Vc as 33 V, Gt1 as 0.0011  m/V2, Gn2 as 0.0059  m/V2,
Ln as 300  m and Lt as 250  m in Eq. 5.7.22 gives a  s of 0.17 for the OTS SAM
coated sidewall surfaces. Further, the distance, for which, the friction block slides in
contact with the loading block during the  rst slip event (i.e.,  s) is determined from
Fig. 8.13 to be 0.57  m, which is less than the distance, by which, the tangential arm
should be displaced for the suspended comb  ngers of its push drive to overlap with
the  nal segments of the corresponding anchored comb  ngers. Therefore, Eq. 5.7.23
can be used to determine the kinetic friction experienced by the sidewall interface of
the test device during the  rst slip event. The  k of the OTS SAM coated sidewall
surfaces of the test device is determined to be 0.14. The displacement of the shuttle
of the tangential arm of the test device during the second slip event does cause a
fraction of the length of its suspended comb  ngers to overlap with the  nal segments
233
Figure 8.16: An interferogram showing the sidewall interface formed in one of the OTS
SAM coated Sidewall Friction and Adhesion Testers. A voltage of 50 V is applied
to the push drive of the normal arm to bring the loading block in contact with the
friction block, before collecting this interferogram. Notice the absence of fringes on
the loading and friction blocks shown in the interferogram. The step edge at the
sidewall interface is determined using HSI to be 75 nm.
234
of the corresponding anchored comb  ngers. This is the reason why the distance, for
which, the friction block slides in contact with loading block during the second slip
event is signi cantly greater than the distance, for which, it slides during the  rst slip
event. While theoretically, the second slip event exhibited by the SFAT developed
in this study can also be used to determine the  s and  k of the surfaces that form
the sidewall interface, the one that is shown in Fig. 8.13 cannot be used because
its termination is not caused by the balance between the sum of the restoring force
generated by the folded beam  exure of the tangential arm and the kinetic friction
force, and the tangential force generated using the tangential comb-drive actuator. It
is caused due to the lateral instability encountered by the push drive of the tangential
arm during the slip event.
For each type of surface studied in this chapter (i.e., OTS SAM coated and surface
with only native oxide on it),  ve Sidewall Friction and Adhesion Testers are used to
investigate the friction and wear characteristics of contacting sidewalls. Using each
Sidewall Friction and AdhesionTester, the coe cients of static and kinetic friction are
determined at normal loads ranging from 0.677  N - 7.97  N, which correspond to
apparent contact pressures (calculated by considering  at on  at geometry) of 0.098
MPa - 1.15 MPa. Additionally, in order to obtain statistically signi cant results, the
coe cients of static and kinetic friction are determined  ve times for each investigated
normal load. Table 8.7 reports the engineering coe cients of static and kinetic friction
of both OTS SAM coated surfaces as well as surfaces with only native oxide on them,
obtained using the SFATs. The results are as expected. Again, the coe cients of
friction of the oxide covered sidewall test surfaces of the Test Platform developed in
this study are greater than those reported in literature, which were obtained using
microinstruments that had rougher sidewall test surfaces [23, 79, 85, 126, 128, 141,
143, 147, 150, 151, 159, 162, 164]. Further, like in the case of the SFTs investigated
in this chapter, the coe cients of both static as well as kinetic friction of surfaces
235
 0
 1
 2
 3
 4
 5
 6
 7
 0  5  10  15  20  25  30  35  40  45  50  55  60
Displacement (
?m)
V t (V)
V t,s  = 52 V
?s = 0.57 ?m
Figure 8.17: A plot showing the onset of slip at an OTS SAM coated sidewall interface
investigated using the SFAT developed in this study. The displacement of the friction
block is plotted against the voltage applied to the tangential comb-drive actuator. A
normal load of 1.82  N, which corresponds to an apparent contact pressure of 0.26
MPa, is applied at the sidewall interface. Notice that the  rst slip occurred at Vt;s of
52 V and the second slip occurred at Vt;s of 57 V.
236
with only native oxide on them obtained using the SFATs are also greater than 1,
and vary signi cantly. The fact that owing to the smaller normal loads applied at
the sidewall interfaces tested using the SFATs as compared to those applied at the
sidewall interfaces tested using the SFTs, the absolute values of, and the variations
in, the  s and  k of the native oxide covered sidewall test surfaces obtained using the
SFATs are greater as compared to the  s and  k of the native oxide covered sidewall
test surfaces obtained using the SFTs supports the rationale that the change in the
relative signi cance of the adhesion experienced by contacting sidewall test surfaces
with the externally applied normal load is responsible for the greater than 1, and
signi cantly varying, values of the  s and  k of the native oxide covered sidewall test
surfaces obtained using the microinstruments developed in this study. The  s and  k
of OTS SAM coated sidewalls obtained using the SFATs investigated in this chapter
are also in good agreement with those obtained using the SFTs investigated in this
chapter.
Like the SFTs investigated in this chapter, each Sidewall Friction and Adhesion
Tester investigated in this chapter is also used for studying the wear characteristics of
OTS SAM coated and native oxide covered sidewall test surfaces. Using SFATs, the
wear characteristics of contacting sidewall surfaces are studied by rubbing the friction
block against the loading block under a normal load of 0.5  N, which corresponds
to a VN of 42.2 V and an apparent contact pressure of 0.072 MPa (calculated by
considering  at on  at geometry). The reciprocating motion of the friction block is
achieved by superimposing an AC voltage, which has a frequency of 10 Hz and a
peak-to-peak amplitude of 6 V, on a DC bias of 43 V applied to the push drive of
the tangential arm of the SFAT. Again, the change in the  s and  k of the contacting
sidewalls is used as a measure to qualitatively study their wear characteristics. The
 s and  k of the OTS SAM coated sidewalls investigated using the SFATs remained
unchanged even after 300 min. of operation (i.e., even after accumulating 180000 wear
237
Table 8.7: Comparison between the engineering coe cients of static and kinetic fric-
tion of OTS SAM coated surfaces and those of surfaces with only native oxide on
them. The engineering coe cients of friction reported in this table are determined
using the Sidewall Friction and Adhesion Tester. All the values reported in the table
are arithmetic means of 325 measurements and the std. dev. is one standard deviation
of the sample consisting of those measurements.
Coating Coe cient of Static Friction Coe cient of Kinetic Friction
 s  std. dev.  k  std. dev.
Oxide 1.98  0.45 1.35  0.20
OTS 0.16  0.03 0.13  0.01
238
cycles). The  s and  k of the native oxide covered sidewalls investigated using the
SFATs remained unchanged only for 8 min. (i.e., 4800 wear cycles), after which, the
friction block momentarily exhibited a stick-slip type of motion before its motion
ceased completely.
8.9 Conclusions
The details of the key features of all the microinstruments developed in this
study are successfully highlighted in this chapter. Additionally, some of the microin-
struments developed in this study are convincingly shown to overcome some of the
limitations of the previously reported corresponding microinstruments. Further, all
the microinstruments developed in this study are successfully used to investigate two
standard test surfaces, namely, surfaces coated with n-OTS (C18H37SiCl3) SAM coat-
ing (i.e., hydrophobic surfaces) and surfaces having only a layer of native oxide on
them (i.e., hydrophilic surfaces). The results obtained are compared with the corre-
sponding results reported in literature. The comparisons substantiate the consistency
and reliability of the results obtained using the Test Platform developed in this study.
Moreover, the apparent work of adhesion of the OTS SAM coated sidewalls, which
has never been reported to-date, is obtained in this chapter using the Sidewall Beam
Array. The apparent work of adhesion of the OTS SAM coated sidewalls is 37.65
 J/m2. Also, the engineering coe cients of static and kinetic friction of the OTS
SAM coated sidewalls, which have also never been reported to-date, are obtained in
this chapter using both the Sidewall Friction Tester as well as the Sidewall Friction
and Adhesion Tester. The mean engineering coe cients of static and kinetic friction
of the OTS SAM coated sidewalls are 0.15 and 0.11, respectively.
239
Chapter 9
The E ect of Surface Topography
The surfaces (in-plane as well as sidewall) of the Test Platform developed in this
study are the smoothest surfaces reported to-date for investigating the tribological
characteristics of MEMS interfaces [78,141,164]. Accordingly, their topographies can
be considered as baselines, and controllably tailored to enable a systematic study for
investigating the e ects that the surface topographies of contacting MEMS surfaces
have on the stiction and friction characteristics of the interface formed by them. This
chapter reports on a technique that is used to tailor the topographies of the surfaces
(in-plane as well as sidewall) of the Test Platform developed in this study. It further
reports on the methods used to characterize the surface topographies of the tailored
test surfaces. Additionally, the stiction and friction characteristics of the tailored test
surfaces are also reported in this chapter. This chapter also discusses a dimensionless
parameter (i.e., Tribotopography number ( topo)), which can be used to predict the
e ect that the surface topography of a MEMS surface has on its stiction and friction
characteristics. Lastly, this chapter reports on the in uence that the contact geometry
of an interface has on the e ect of surface topography.
9.1 Obtaining Test Surfaces with Distinct Topographies
Both the in-plane as well as sidewall surfaces of the Test Platform developed in
this study have fairly smooth topographies to begin with, as indicated by the AFM im-
ages shown in Figs. 4.1 and 4.2, respectively. Therefore, their surface topographies can
be tailored by texturing them. For this study, the surface topographies of the surfaces
of the Test Platform developed in this study are tailored by depositing nanoparticles
240
on them. The nanoparticles speci cally used for this study are dodecanethiol-capped
gold nanoparticles. The process used to synthesize the dodecanethiol-capped gold
nanoparticles used in this study is described in detail in section 6.5. Accordingly, an
untextured Test Platform chip consisting of native oxide covered test surfaces is used
as the control sample and  ve Test Platform chips, whose test surfaces are textured
using gold nanoparticles, are used as the test samples. The  ve test samples are
controllably textured in such a way that the surface topographies of the test surfaces
of each one of them are distinct and di erent than those of the test surfaces of each
of the others.
As explained in chapter 1, the stiction and friction characteristics of an interface
are determined by the various interfacial forces experienced by the two contacting
surfaces that form the interface. In the control sample, the examined interface is
formed between two native oxide covered silicon surfaces, and characterized by the
interactions between pairs of native-oxide covered silicon asperities. In the test sam-
ples, the examined interface is formed between gold nanoparticle coated, native oxide
covered silicon surfaces. Accordingly, the interfaces formed in the test samples are
characterized by the interactions between pairs of a gold asperity and a native-oxide
covered silicon asperity as well as between pairs of two gold asperities. The interfa-
cial forces that are reported to prominently exist at the type of interfaces that are
formed in the Test Platform chips investigated in this chapter include capillary forces,
which are attractive and depend on the contact angle that a droplet of water makes
on the surface of the asperities present on the surfaces forming the interface as well
as the relative humidity of the testing environment, VDW forces between the non-
contacting asperities of the two surfaces forming the interface, which are attractive
and depend on the Hamakar constants of the materials of the asperities present on the
two surfaces forming the interface, inter-atomic and inter-molecular forces between
the asperities that are in contact at the interface, which are attractive and depend
241
on the surface energies of the materials of the contacting asperities, and the elastic
forces exerted by the contacting asperities that are elastically deformed, which are
repulsive, depend on the elastic properties of the materials of the contacting asperities
and act to push the surfaces forming the interface apart from each other. Owing to
the comparable elastic moduli of native oxide and gold (i.e., 70 - 75 GPa and 79 GPa,
respectively), the material of the deforming asperties will have a negligible in uence
on the di erence in the elastic forces that will be experienced by the control (i.e., in-
terfaces formed in the control sample) and the test (i.e., interfaces formed in the test
samples) interfaces investigated in this study [180{182]. Similarly, owing to the com-
parable surface energies of native-oxide covered Si(100) and gold surfaces (i.e., 1.36
J/m2 and 1.25 J/m2, respectively), the material of the contacting asperties will have
a negligible in uence on the di erence in the inter-atomic and inter-molecular forces
that will be experienced by the control (i.e., interfaces formed in the control sample)
and the test (i.e., interfaces formed in the test samples) interfaces investigated in
this study [183,184]. Further, the overall Hamakar constant for the VDW interaction
between the native oxide covered silicon and gold (HSi Au) can be determined using
Eq. 9.1.1 shown below [185]:
HSi Au =
p
HSiHAu (9.1.1)
The Hamakar constants of native oxide covered silicon (HSi) and gold (HAu) are 1.7
eV and 1.9 eV, respectively [68, 70, 186]. Accordingly, the HSi Au determined using
Eq. 9.1.1 is 1.8 eV, which is comparable to the overall Hamakar constant for the VDW
interaction between two native oxide covered silicon surfaces (i.e., 1.7 eV) [68, 70].
Therefore, the material (or surface chemical composition) of the surfaces forming
the interface will have a negligible in uence on the di erence in the VDW forces
that will be experienced by the control (i.e., interfaces formed in the control sample)
242
and the test (i.e., interfaces formed in the test samples) interfaces investigated in
this study. Lastly, at a given relative humidity, the capillary pull experienced by
two hydrophilic surfaces forming an interface depends on the contact angle that a
droplet of water makes on them. The contact angle that a droplet of water makes
on a clean native oxide covered silicon surface is <5 (determined experimentally on
a clean native oxide covered Si(100) surface), and that it makes on a clean gold
surface is 12 - 18 (determined experimentally on a clean gold-coated Si(100) surface).
The experimentally determined values of the contact angles that a droplet of water
makes on clean native oxide covered silicon and gold surfaces are in extremely good
agreement with those reported in literature [6, 187]. Accordingly, since a droplet of
water makes extremely small contact angles on both the native oxide covered silicon
as well as the gold surface, and the contact angles made by it on them are comparable,
the material (i.e., elemental identity) as well as the surface chemistry of the interacting
asperities of the two surfaces forming the interface will have a negligible in uence on
the di erence in the capillary forces that will be experienced by the control (i.e.,
interfaces formed in the control sample) and the test (i.e., interfaces formed in the
test samples) interfaces investigated in this study. Indeed, it has been reported that
smooth surfaces coated with gold thin  lms experience a similar stiction as well as
friction as that experienced by the smooth (untextured) in-plane surfaces of the Test
Platform developed in this study. Therefore, it can be safely concluded that the
e ect, which the dodecanethiol-capped gold nanoparticle-based surface texturing will
have on the stiction and friction characteristics of the surfaces of the Test Platform
developed in this study, will be solely associated with the surface topography change
caused by it and will not depend on the chemistry or the material of the nanoparticles
used. Therefore, in theory, the results reported in this chapter do not depend on
the material of the nanoparticles used to tailor the surface topographies of the test
surfaces. For that matter, they also do not depend on the surface texturing technique
243
used to tailor the surface topographies of the test surfaces. The purpose behind using
the dodecanethiol-capped gold nanoparticles for tailoring the surface topographies
of the test surfaces investigated in this study is the availability of well established
processes for synthesizing gold nanoparticles, and depositing them on MEMS surfaces.
The process used for depositing the dodecanethiol-capped gold nanoparticles on the
test surfaces investigated in this study is developed by Hurst et al., and described in
detail in [24] and section 6.6.
The  nal surface topography of a surface that is textured using the surface tex-
turing process used in this study depends on the absolute amount of the nanoparticles
deposited on it. Therefore, in order to obtain test surfaces (for this study) with dis-
tinct surface topographies, the surface texturing process used in this study is tuned
to deposit di erent (distinct) amounts of nanoparticles on each of the Test Platform
chips investigated in this chapter. The amount of the nanoparticles that get de-
posited on the surface being textured can be controlled by controlling the number
density of the nanoparticle dispersion used in the surface texturing process used in
this study. Speci cally, test surfaces with  ve di erent (distinct) surface topogra-
phies, in addition to the untextured (referred to as control from now onwards) test
surfaces, are investigated in this chapter. Therefore, nanoparticle dispersions with
 ve di erent (distinct) number densities are used in this study. In order to burn-o 
the dodecanethiol capping ligands present on the gold nanoparticles deposited on the
 ve textured Test Platform chips investigated in this study, each of the  ve textured
Test Platform chips are exposed to an UV-ozone atmosphere for 1 hour before testing.
9.2 Characterization of the Tailored Test Surfaces
In order to understand the e ects that the surface topographies of contacting
MEMS surfaces have on the stiction and friction characteristics of the interface formed
244
by them, the test surfaces of all the six (i.e.,  ve tailored and one control) Test Plat-
form chips investigated in this chapter are characterized both topographically as well
as tribologically. The topographic characterization of the Test Platform chips inves-
tigated in this chapter is accomplished by characterizing the surface topographies of
their in-plane surfaces both qualitatively as well as quantitatively. The tribological
characterization of the Test Platform chips investigated in this chapter is accom-
plished by determining the apparent works of adhesion of their in-plane and sidewall
surfaces as well as the coe cients of static friction of their sidewall surfaces. The
following sections discuss the results of the topographical and tribological character-
izations of the Test Platform chips investigated in this study.
9.2.1 Topography
Qualitative Characterization
In order to validate our hypothesis that the amount of the nanoparticles that
get deposited on the surface being textured using the surface texturing process used
in this study can be controlled by controlling the number density of the nanoparti-
cle dispersion used, the test surfaces, whose topographies are tailored for this study,
are characterized to qualitatively determine the relative amounts of the nanoparti-
cles present on them. The qualitative characterization of the textured test surfaces
investigated in this chapter is accomplished using SEM. Figure 9.1 shows the SEM
images of the substrates of each of the  ve textured Test Platform chips investigated
in this chapter. The numbers indicated on the SEM images are the sample numbers
of the corresponding textured Test Platform chips. The nanoparticle dispersion used
to texture sample no.1 has the least number density, which is increased monotonously
from the nanoparticle dispersion that is used to texture sample no. 1 to the nanopar-
ticle dispersion that is used to texture sample no. 5. Therefore, it is expected that
245
1
(a)
2
(b)3
(c)
4
(d)5
(e)
Figure 9.1: SEM images of the substrates of the  ve textured Test Platform chips in-
vestigated in this chapter. The numbers indicated on the SEM images are the sample
numbers of the corresponding textured Test Platform chips. Notice the monotonous
increase in the amount of the nanoparticles present on the textured surfaces shown
in the SEM images from the image a to image e.
246
the amount of the nanoparticles present on the textured surfaces of the Test Plat-
form chips investigated in this study will monotonously increase from sample no. 1
to sample no. 5. The SEM images shown in Fig. 9.1 clearly indicate that the results
of tailoring the surfaces topographies of the Test Platform chips investigated in this
study are as expected. It is clearly evident in the SEM images shown in Fig. 9.1
that the amount of the nanoparticles present on the surfaces of the textured Test
Platform chips investigated in this study increases monotonously from sample no. 1
to sample no. 5. In order to further validate this observation, a qualitative measure
of the amounts of the nanoparticles deposited on each of the  ve textured Test Plat-
form chips investigated in this chapter is obtained using the Resonators on them. As
validated in chapter 8, the resonance frequencies of the Resonators included in the
Test Platform are inversely proportional to the e ective masses of their suspended
resonating structures (i.e., Eq. 5.3.1). Accordingly, the deposition of nanoparticles
on the surfaces of a Resonator increases the e ective mass of its resonating struc-
ture, and consequently decreases its resonance frequency. Therefore, by comparing
the resonance frequencies of the nanoparticle coated and uncoated Resonators having
the same supporting beam length, the increase in the e ective mass of the nanopar-
ticle coated Resonator (i.e.,  Meff), which is due to the mass of the nanoparticles
deposited on it, can be determined. The analysis used for determining the increase
in the e ective mass of a nanoparticle coated Resonator (i.e.,  Meff) due to the
mass of the nanoparticles deposited on it is elaborated in detail in chapter 10. By
comparing the increase in the e ective masses of Resonators having the same sup-
porting beam length, fabricated at di erent locations on a textured Test Platform
chip, the uniformity of the nanoparticle coating deposited on that Test Platform chip
can be determined. Similarly, by comparing the increase in the e ective masses of
the Resonators having the same supporting beam length, of each of the  ve textured
247
Test Platform chips, a qualitative comparison between the amounts of the nanopar-
ticles deposited on them can be made. Table 9.1 lists the decrease in the resonance
frequencies (i.e,  fR) and the corresponding increase in the e ective masses of the
Resonators with 500  m long supporting beams, of each of the  ve textured Test
Platform chips. Each value reported in table 9.1 is an arithmetic mean of  ve mea-
surements, which are obtained using  ve distinct Resonators that are fabricated at
di erent locations on the corresponding Test Platform chip. The results reported in
table 9.1 are a quantitative con rmation of the observation that the amount of the
nanoparticles present on the surfaces of the textured Test Platform chips investigated
in this study increases monotonously from sample no. 1 to sample no. 5. They along
with the SEM images shown in Fig. 9.1 indisputably validate my hypothesis that the
amount of the nanoparticles that get deposited on the surface being textured can be
controlled by controlling the number density of the nanoparticle dispersion used.
Quantitative Characterization
In order to be able to establish a mathematical correlation between the surface
topographies of the test surfaces of the Test Platform chips investigated in this chapter
and their stiction and friction characteristics, the surface topographies of the test
surfaces of the Test Platform chips investigated in this chapter must be quanti ed in
terms of measurable parameters. The quantitative characterization of the textured
test surfaces investigated in this chapter is accomplished using AFM. Figure 9.2 shows
the AFM images of the substrates of all the Test Platform chips investigated in this
chapter. Again, the numbers indicated on the AFM images are the sample numbers
of the corresponding textured Test Platform chips. The control sample is a Test
Platform chip, whose surfaces are polished, native oxide covered and not textured
with the dodecanethiol-capped gold nanoparticles. The AFM images of the substrates
of all the textured Test Platform chips investigated in this chapter, which are shown in
248
Table 9.1: This table lists the decrease in the resonance frequencies ( fR) and the
corresponding increase in the e ective masses ( Meff) of the Resonators with 500
 m long supporting beams, of each of the  ve textured Test Platform chips. Each
value reported in the table is an arithmetic mean of  ve measurements, which are
obtained using  ve distinct Resonators that are fabricated at di erent locations on
the corresponding Test Platform chip.
Sample #  fR  Meff 1012
(Hz) (Kg)
1 11.5 0.806
2 15.1 1.06
3 28.7 2.02
4 63.8 4.49
5 126 8.82
249
Figs. 9.2b - 9.2f, perfectly correlate their SEM images, which are shown in Figs. 9.1a
- 9.1f, in terms of the relative amounts of the nanoparticles present on them. The two
measurable parameters that are extracted from the AFM images of the substrates of
all the Test Platform chips investigated in this chapter are the rms roughnesses of, and
the surface coverages of the interacting asperities present on, the surfaces shown in
them. The image analysis technique used to process the ASCII data associated with
an AFM image, to extract the surface coverage of the interacting asperities present
on the surface shown in it, is discussed in detail in section 6.12. Details on the usage
of the surface coverage of the interacting asperities present on the in-plane surfaces
of the Test Platform chips investigated in this chapter is provided in section 9.3.1.
The rms roughnesses of the in-plane surfaces of each of the six Test Platform
chips investigated in this chapter are indicated on their corresponding AFM images,
which are shown in Figs. 9.2a - 9.2f. It was expected that the rms roughnesses of the
surfaces of the Test Platform chips investigated in this chapter will exhibit a direct
correspondence with the amounts of the nanoparticles deposited on them. However,
as evident from Figs. 9.2a - 9.2f, the results obtained are counterintuitive. A bar
graph showing the rms roughnesses of the in-plane surfaces of the Test Platform
chips investigated in this chapter is shown in Fig. 9.3. The direction, in which, the
amount of the nanoparticles deposited on the Test Platform chips investigated in this
chapter increases is indicated by the arrow in the bar graph. It is clearly evident
from the bar graph shown in Fig. 9.3 that the rms roughnesses of the surfaces of the
Test Platform chips investigated in this chapter do not exhibit a direct correspondence
with the amounts of the nanoparticles present on them. To explain this observation, a
schematic is shown in Fig. 9.4. Figure 9.4a shows a schematic diagram of the substrate
of the Test Platform developed in this study. The red line, which is covering the top
(in-plane) surface of the substrate, shown in Fig. 9.4a represents the surface pro le
of the substrate. Accordingly, Figs. 9.4b and 9.4c indicate how the rms roughness
250
RMS roughness = 0.1 nm
Control
(a)
1
RMS roughness = 8.3 nm
(b)
2
RMS roughness = 9.7 nm
(c)
3
RMS roughness = 6.1 nm
(d)
4
RMS roughness = 4.3 nm
(e)
5
RMS roughness = 13.0 nm
(f)
Figure 9.2: AFM images of the substrates of the Test Platform chips investigated in
this chapter. The numbers indicated on the AFM images are the sample numbers of
the corresponding textured Test Platform chips.
251
of the top (in-plane) surface of the substrate shown in Fig. 9.4a increases with the
deposition of nanoparticles on it. Again, the red lines in Figs. 9.4b and 9.4c represent
the surface pro les of the textured substrates shown in them. Further, Fig. 9.4d
indicates how, while initially the rms roughness of the top surface of the substrate
shown in Fig. 9.4a does increase with the increase in the amount (number) of the
nanoparticles deposited on it (i.e., Figs. 9.4b and 9.4c), beyond a certain amount, the
nanoparticles getting deposited begin to  ll up the surface, thereby decreasing its rms
roughness. Additionally, the rms roughness of a textured surface, determined from
the AFM image of a representative area on it, is not a function of the amount of the
nanoparticles present on it alone but also depends on their positions relative to each
other. This is because the resolution, with which the AFM images of the textured
surfaces are obtained, is limited by the radius and the tip-angle of the AFM tip used
to obtain them.
9.2.2 Stiction and Friction
In order to understand the e ects that the surface topography of a MEMS surface
has on its stiction and friction characteristics, three important tribological properties
of the surfaces of the Test Platform chips investigated are determined in this chapter.
The tribological properties that are investigated in this chapter include the appar-
ent work of adhesion of the in-plane surfaces, the apparent work of adhesion of the
sidewall surfaces and the coe cient of static friction of the sidewall surfaces. All the
experiments that are conducted for this study are performed in laboratory air, at 22
 C and in 45% relative humidity (unless otherwise stated).
The apparent works of adhesion of the in-plane surfaces of the Test Platform
chips investigated in this chapter are determined using the Cantilever Beam Array
developed in this study. The magni cation of the objective lens, which is used in the
interference microscope that is used to determine the height pro le of the actuated
252
 0
 3
 6
 9
 12
 15
Control 1 2 3 4 5  
RMS roughness (nm)
Sample #
Amount of AuNPs deposited
increases in this direction
Figure 9.3: Bar graph showing the rms roughnesses of the in-plane surfaces of the
Test Platform chips investigated in this chapter.
253
Substrate
(a)
Substrate
(b)
Substrate
(c)
Substrate
(d)
Figure 9.4: A schematic explaining the observed variations in the roughnesses of
the substrates of the Test Platform chips investigated in this chapter. The red lines
shown in all the diagrams represent the surface pro le of the (untextured or textured)
substrates shown in them.
254
cantilever beams, is either 10X or 20X. Accordingly, the size of each pixel in the  eld
of view is either 0.465  m  0.465  m or 0.234  m  0.234  m, respectively. On
each of the six Test Platform chips investigated in this chapter, four CBAs consisting
of ten cantilever beams each are actuated to obtain a statistically signi cant data set.
Table 9.2 reports the mean observed crack lengths as well as the corresponding mean
(calculated) apparent works of adhesion of the in-plane surfaces of all the six Test
Platform chips investigated in this chapter.
The apparent works of adhesion of the sidewall surfaces of the Test Platform
chips investigated in this chapter are determined using the Sidewall Beam Array
developed in this study. The magni cation of the objective lens of the microscope,
which is used to observe the microinstrument during actuation and determine the
crack length of each actuated adhered pair of sidewall beams, is 10X. Accordingly,
the size of each pixel in the  eld of view is 0.465  m 0.465  m. On each of the six
Test Platform chips investigated in this chapter, eight SBAs are actuated to obtain
a statistically signi cant data set. Table 9.3 reports the mean observed crack lengths
and the corresponding mean (calculated) apparent works of adhesion of the contacting
sidewall surfaces of all the Test Platform chips investigated in this chapter. Figure 9.5
is a plot showing the variations in the apparent works of adhesion of the in-plane as
well as sidewall surfaces with the variations in their surface topographies. The data
points plotted in the plot are the mean values of apparent work of adhesion, which
are reported in Table 9.2 and Table 9.3. The error bars shown in the plot indicate
the maximum and minimum values of the apparent works of adhesion exhibited by
the in-plane and sidewall surfaces of that Test Platform chip.
The coe cients of static friction of the contacting sidewall surfaces of the Test
Platform chips investigated in this chapter are determined using the Sidewall Friction
Tester developed in this study. The magni cation of the objective lens that is used in
the microscope during the actuation of the Sidewall Friction Testers for this study is
255
Table 9.2: Comparison between the mean apparent works of adhesion of the in-
plane surfaces of the six Test Platform chips investigated in this chapter to study the
e ect of topography. The apparent works of adhesion of in-plane surfaces reported
in this table are determined using the CBAs. All the values reported in the table are
arithmetic means of 40 measurements.
Sample # Crack Length Apparent Work of Adhesion of In-plane Surfaces
sip Wip
( m) (  J/m2)
Control 99.0 38700
1 855.2 32.16
2 266.6 543.6
3 351.5 1209
4 216.1 4780
5 379.5 1058
256
Table 9.3: Comparison between the mean apparent works of adhesion of the sidewall
surfaces of the six Test Platform chips investigated in this chapter to study the e ect of
topography. The apparent works of adhesion of in-plane surfaces reported in this table
are determined using the SBAs. All the values reported in the table are arithmetic
means of several measurements.
Sample # Crack Length Apparent Work of Adhesion of In-plane Surfaces
ss Ws
( m) (  J/m2)
Control 660.1 1070
1 1753 21.50
2 1683 25.33
3 1431 48.52
4 1122 128.2
5 1498 40.38
257
10X. Accordingly, the size of each pixel in the  eld of view is 0.465  m  0.465  m.
On each of the six Test Platform chips investigated,  ve Sidewall Friction Testers are
used to determine the coe cient of static friction of their sidewall surfaces. Using
each Sidewall Friction Tester, the coe cient of static friction is determined at normal
loads ranging from 2.4  N - 15.7  N, which correspond to Hertzian contact pressures
(calculated by considering cylinder on  at geometry) of 123 MPa - 312 MPa. This
range of normal load is representative of that experienced by most potential and
commercialized MEMS during operation. Additionally, in order to obtain statistically
signi cant results, the coe cient of static friction is determined  ve times for each
investigated normal load. Table 9.4 reports the (experimentally determined) mean
engineering coe cients of static friction of the contacting sidewall surfaces of all the
Test Platform chips investigated in this chapter. Figure 9.6 is a plot showing the
variation in the engineering coe cient of static friction of a sidewall surface with the
variation in its surface topography. The data points plotted in the plot are the mean
values of engineering coe cients of static friction, which are reported in Table 9.3.
The error bars shown in the plot indicate the maximum and minimum values of the
engineering coe cient of static friction exhibited by the sidewall surfaces of that Test
Platform chip.
Like the rms roughnesses of the substrates of the six Test Platform chips inves-
tigated in this chapter, the apparent works of adhesion of their in-plane as well as
sidewall surfaces and the engineering coe cients of static friction of their contacting
sidewall surfaces also do not show a direct correspondence with the amounts of the
nanoparticles deposited on them. However, all the three tribological properties inves-
tigated in this chapter (i.e., apparent work of adhesion of in-plane surfaces, apparent
work of adhesion of sidewall surfaces and the engineering coe cient of static friction
of contacting sidewall surfaces) exhibit identical variations with the variation in the
surface topographies of the surfaces exhibiting them. In other words, the variation
258
 1
 10
 100
 1000
 10000
Control 1 2 3 4 5  
Apparent Work of Adhesion, (
?J/m
2 )
Sample #
In-plane stiction
Sidewall stiction
Figure 9.5: A plot showing the variations in the apparent works of adhesion of the
in-plane as well as sidewall surfaces with the variations in their surface topographies.
The data points plotted in the plot are arithmetic means of several measurements.
The error bars shown in the plot indicate the maximum and minimum values of the
apparent works of adhesion exhibited by the in-plane and sidewall surfaces of that
Test Platform chip.
259
Table 9.4: Comparison between the mean engineering coe cients of static friction
of the sidewall surfaces of the six Test Platform chips investigated in this chapter to
study the e ect of topography. The engineering coe cients of static friction reported
in this table are determined using Sidewall Friction Testers. All the values reported
in the table are arithmetic means of 225 measurements.
Sample # Coe cient of Static Friction
 s
Control 1.75
1 0.076
2 0.221
3 0.337
4 0.443
5 0.332
260
in the engineering coe cient of static friction of a sidewall surface with the variation
in its surface topography, which is shown in Fig. 9.6, shows a high degree of corre-
spondence with the variation in the apparent work of adhesion of a sidewall surface
with the variation in its surface topography, which is shown in Fig. 9.5. This is an
experimental con rmation of the already believed theory that the friction experienced
by contacting MEMS surfaces shows a strong dependence on the stiction experienced
by them. Further, the variations in the apparent works of adhesion of in-plane and
sidewall surfaces with the variations in their surface topographies, which are shown
in Fig. 9.5, also exhibit a high degree of correspondence with each other. Therefore, I
hypothesized that the variations in the apparent works of adhesion of the in-plane and
sidewall surfaces investigated in this study are governed by the nano-scale variations
in their topographies induced by the nanoparticles deposited on them. However, for
my hypothesis to be valid, since the variation in the apparent work of adhesion of an
in-plane surface with the variation in its surface topography is identical to the vari-
ation in the apparent work of adhesion of a sidewall with the variation in its surface
topography, both the in-plane as well as sidewall surfaces of the Test Platform chips
investigated in this study should have identical nanoparticle coatings deposited on
them. Fig. 9.7a is a SEM image showing the edge of a released cantilever beam of
sample no. 4 and Fig. 9.7b is a SEM image of a region of the substrate, which is un-
derneath the cantilever beam shown in Fig. 9.7a. The SEM image shown in Fig. 9.7b
is collected after breaking the cantilever beam shown in Fig. 9.7a apart using a probe
tip (Signatone 20T). It is clearly evident in Figs. 9.7a and 9.7b that the surfaces
shown in them have exactly identical nanoparticle coatings on them, which substan-
tiates that the in-plane and sidewall surfaces of the Test Platform chips investigated
in this chapter have exactly identical nanoparticle coatings on them. This supports
my hypothesis that the variations in the apparent works of adhesion of the in-plane
261
and sidewall surfaces investigated in this study are governed by the variations in their
nano-scale topographies.
In order to explain the di erence between the absolute values of the apparent
works of adhesion of the in-plane and sidewall surfaces of the same Test Platform
chip, I hypothesized that the lower apparent works of adhesion of the sidewall sur-
faces of the Test Platform chips investigated in this study as compared to those of the
corresponding in-plane surfaces are due to their initial micro-scale surface topogra-
phies (i.e., the surface topographies of the underlying untextured sidewall surfaces).
The in-plane surfaces investigated in this chapter have extremely smooth initial sur-
face topographies (i.e., their initial (untextured) rms roughness is 0.14 nm), while the
sidewall surfaces investigated in this chapter have rougher initial surface topographies
(i.e., their initial (untextured) rms roughness is 6.52 nm). In other words, both the
micro-scale as well as the nano-scale topographies of a surface have a strong in uence
on its stiction and friction characteristics. In order to mathematically correlate the
surface topography of a surface with its stiction and friction characteristics, the fol-
lowing sections discuss the formulation of a dimensionless parameter, which can be
used to predict the e ect that the surface topography of a surface will have on its
stiction and friction characteristics.
9.3 Tribotopography Number ( topo)
In order to quantitatively understand the e ect that the surface topography of
a surface has on its tribological (i.e., stiction and friction) properties, the apparent
works of adhesion of the in-plane surfaces investigated in this chapter are plotted
against their rms roughnesses, which is one of the measurable parameters of their
surface topographies. The plot is shown in Fig. 9.8. It was expected that the in-
crease in the rms roughness of the in-plane surfaces investigated in this chapter
will either increase their surface area and hence the stiction experienced by them
262
 0
 0.4
 0.8
 1.2
 1.6
 2
Control 1 2 3 4 5  
Coefficient of Static Friction, (
? s
)
Sample #
Sidewall Friction
Figure 9.6: A plot showing the variation in the engineering coe cient of static friction
of a sidewall surface with the variation in its surface topography. The data points
plotted in the plot are arithmetic means of 225 measurements. The error bars shown
in the plot indicate the maximum and minimum values of the engineering coe cient
of static friction exhibited by the contacting sidewall surfaces of that Test Platform
chip.
263
(a)
(b)
Figure 9.7: (a) A SEM image showing the edge of a released cantilever beam of sam-
ple no. 4. (b) A SEM image of a region of the substrate, which is underneath the
cantilever beam shown in Fig. 9.7a.The SEM image shown in this image is collected
after breaking the cantilever beam shown in Fig. 9.7a apart using a probe tip (Signa-
tone 20T). Notice that the surfaces shown in both the image a as well as the image
b have exactly identical nanoparticle coatings on them.
264
or decrease the contact area of the interface formed by them and hence the stiction
experienced by them. In other words, it was expected that the apparent works of
adhesion of the in-plane surfaces investigated in this chapter will either increase or
decrease monotonously with their rms roughnesses. However, it is clearly evident in
the plot shown in Fig. 9.8 that there exists an optimum rms roughness, at which,
the in-plane surface exhibits minimum apparent work of adhesion. This observation
can be explained by considering the mathematics involved in the calculation of the
rms roughness of a surface. The absolute value of the rms roughness of a surface de-
pends on two independent variables, namely, the heights of the asperities present on
that surface and their frequencies. While an increase in the heights of the asperities
present on a surface, which increases the rms roughness of that surface, decreases
the stiction experienced by it, an increase in their frequencies, which also increases
the rms roughness of the surface, increases the stiction experienced by it. Therefore,
since the two components, which de ne the rms roughness of a surface, are indepen-
dent, and change the stiction experienced by it in opposite directions, there exits an
optimum roughness, at which, the stiction experienced by the surface is minimum.
Accordingly, in order to comprehensively quantify the surface topography of a surface,
both the components that de ne its rms roughness should be quanti ed individually.
The following sections discuss the formulation and validation of the Tribotopography
number ( topo), which is a dimensionless parameter that separately accounts for both
the components that de ne the rms roughness of a surface, and can be used to de-
termine the e ect of the surface topography of a surface on its stiction and friction
properties.
265
 1
 10
 100
 1000
 10000
 0  2  4  6  8  10  12  14
Apparent Work of Adhesion, (
?J/m
2 )
RMS Roughness of In-plane Surfaces, (nm)
In-plane Stiction
Figure 9.8: A plot of the apparent works of adhesion exhibited by the six in-plane
surfaces investigated in this chapter versus their rms roughnesses. The data points
plotted in the plot are arithmetic means of 40 measurements. The error bars shown in
the plot indicate the maximum and minimum values of the apparent work of adhesion
exhibited by the in-plane surface of that Test Platform chip. Notice that the plot
indicates that there exits an optimum rms roughness, at which, the in-plane surface
experiences minimum stiction.
266
9.3.1 Formulation
E ect of Surface Topography on Stiction
As mentioned earlier, the two components that de ne the rms roughness (i.e.,
surface topography) of a surface change the stiction experienced by it in opposite
directions. An increase in the heights of the asperities present on contacting sur-
faces increases the distance of separation between the contacting surfaces, and hence
as explained in section 1.5.1, decreases the attractive forces experienced by them.
Accordingly, it also decreases the stiction between them. Therefore, based on the
equations reported in section 1.5.1,
W_ 1d (9.3.1)
Here,W is the apparent work of adhesion of the contacting surfaces, d is the distance
of separation between the mean planes of the two contacting surfaces and index  
is a factor that is determined by the type (see section 1.5.1) of the interfacial force
that dominates their stiction behaviour. Further, an increase in the number of the
interacting asperities present on the two contacting surfaces increases the area of
interaction between them, and hence, the stiction experienced by them. Accordingly,
W_nasperities (9.3.2)
Here, nasperities is the number of interacting asperities present on one of the two
contacting surfaces forming an interface (i.e., a measure of the area of interaction
between the two contacting surfaces). Combining Eqs. 9.3.1 and 9.3.2 gives,
W_nasperitiesd (9.3.3)
267
Considering that the elastic moduli of both the native oxide as well as gold are
relatively high (i.e., 70 - 75 GPa and 79 GPa, respectively), and the radii of curvature
of the asperities present on all the surfaces investigated in this study are extremely
small (i.e., mean diameter of the gold nanoparticles used to tailor the topographies
of the surfaces of the test samples is 5.5 nm), the asperities that come in contact at
the control and test interfaces investigated in this study can be considered as rigid
[180{182]. Accordingly, it is safe to conclude that they undergo extremely insigni cant
elastic deformations. Additionally, the mechanics involved in the methods that are
used for determining the apparent works of adhesion of the interfaces investigated in
this study ensure that all the attractive forces that exist at an interface are completely
balanced by the restoring forces generated by the microinstrument that is used for
determining its apparent work of adhesion, instead of by the elastic forces generated
by the deformation of the asperities that come in contact at it. This further ensures
that the asperities that come in contact at the interfaces investigated in this study
do not undergo any elastic and/or plastic deformation. Accordingly, the distances of
separation between the mean planes of the two surfaces that form the interfaces that
are investigated in this study can be given by the expression shown below [188]:
d_2rrms (9.3.4)
The above mentioned expression can also be understood by considering that each of
the surfaces investigated in this study can be represented by a corresponding equiv-
alent surface such that the rms roughness of the investigated surface is equal to the
amplitude of the asperities present on the equivalent surface. The equivalent surfaces
are de ned by cube-shaped peaks and valleys, have equal number of peaks and valleys
and the heights of all the peaks present on each equivalent surface are equal to each
other as well as to the depths of all the valleys present on it. Substituting Eq. 9.3.4
268
in Eq. 9.3.3 gives,
W_nasperities(2r
rms) 
(9.3.5)
Re-writing the generalized Eq. 9.3.5 for a reference surface:
Wo_n
o
asperities
(2rorms) (9.3.6)
Here,Wo is the apparent work of adhesion of a reference surface, noasperities is the num-
ber of interacting asperities present on it and rorms is its rms roughness. It should be
noted that the reference surface should be a surface, whose tribological (i.e., stiction
and friction) behaviour is dominated by the same types (see section 1.5.1) of inter-
facial forces that dominate the tribological behaviour of the surface being analyzed.
Dividing Eq. 9.3.5 by Eq. 9.3.6 gives,
W
Wo =
 n
asperities
noasperities
  ro
rms
rrms
  
(9.3.7)
Combining similar terms in Eq. 9.3.7 gives,
W
Wo =
 
( rms) (9.3.8)
where,  , which can be considered as the relative surface coverage of the interacting
asperities present on the surface being analyzed, is given by Eq. 9.3.9 shown below:
 = nasperitiesno
asperities
(9.3.9)
and  rms, which can be considered as the relative rms roughness of the surface being
analyzed, is given by Eq. 9.3.10 shown below:
 rms = rrmsro
rms
(9.3.10)
269
The Tribotopography number (i.e.,  topo) of the surface being analyzed is given by
Eq. 9.3.11 shown below:
 topo =  ( 
rms)
 (9.3.11)
Substituting Eq. 9.3.11 in Eq. 9.3.8 gives,
W
Wo =  topo (9.3.12)
Rearranging Eq. 9.3.12 gives,
W =  topoWo (9.3.13)
Equation 9.3.13 is a mathematical correlation between the surface topography of a
surface and its apparent work of adhesion. It can be used to determine the apparent
work of adhesion of a test surface (i.e., a surface, whose apparent work of adhesion is
unknown) using its  topo and the apparent work of adhesion of a reference surface (i.e.,
a surface, whose tribological behaviour is governed by the same types of interfacial
forces that govern the tribological behaviour of the test surface). As indicated by
Eqs. 9.3.11, 9.3.9 and 9.3.10, the  topo of a test surface can be determined using the
rms roughnesses of, and the surface coverages of the interacting asperities present on,
the test and reference surfaces, all of which, can be obtained from the corresponding
representative AFM images of the two surfaces. In essence, Eq. 9.3.13 can be used
to determine the e ect that the surface topography of a surface has on the stiction
experienced by it.
E ect of Surface Topography on Friction
As indicated by the results shown in Figs. 9.5 and 9.6, the static friction experi-
enced by the contacting sidewall surfaces investigated in this chapter shows a strong
dependence on the stiction experienced by them. This is attributed to the fact that
owing to the hydrophilic nature of the sidewall surfaces investigated in this chapter,
270
the adhesion force experienced by contacting sidewall surfaces is signi cantly high and
comparable to the external normal loads applied at the interfaces formed by them.
Therefore, it acts as additional normal load applied at them. Accordingly, the static
friction force experienced by the contacting sidewall surfaces of the Test Platform
chips investigated in this chapter should be given by Eq. 9.3.14 shown below:
fs =  s;t (N +Wf) (9.3.14)
Here, fs is the static friction force experienced by the contacting sidewall surfaces,
N is the external load applied at the interface formed by them, Wf is the adhesion
force experienced by them and  s;t is their true coe cient of static friction, which is
a material constant, depends only the materials (i.e., surface energies) of the surfaces
forming the interface and shows no dependence on any external factor. Re-writing
the generalized Eq. 9.3.14 for a reference surface:
fos =  s;t N +Wof (9.3.15)
Here, fos is the static friction force experienced by contacting reference surfaces when
an external normal load N is applied at the interface formed by them and Wo is the
adhesion force experienced by them. Again, it should be noted that the reference
surface should be a surface, whose tribological (i.e., stiction and friction) behaviour is
dominated by the same types (see section 1.5.1) of interfacial forces that dominate the
tribological behaviour of the surface being analyzed (i.e., test surface). Subtracting
Eq. 9.3.15 from Eq. 9.3.14 gives,
fs fos =  s;t Wf Wof (9.3.16)
271
Utilizing Eq. 9.3.12, the Tribotopography number (i.e.,  topo) of the test surface can
also be given by Eq. 9.3.17 shown below:
 topo = WfWo
f
(9.3.17)
Applying dividendo to Eq. 9.3.17 gives,
 topo 1 = Wf W
o
f
Wof (9.3.18)
Rearranging Eq. 9.3.18 gives,
Wf Wof =Wof ( topo 1) (9.3.19)
Substituting Eq. 9.3.19 in Eq. 9.3.16 gives,
fs fos =  s;tWof ( topo 1) (9.3.20)
Equation 9.3.20 is a mathematical correlation between the surface topography of a
surface and the static friction force experienced by it at a given normal load. It can
be used to determine the static friction force experienced by a test surface at a given
normal load using its  topo and the static friction as well as adhesion forces experienced
by a reference surface (i.e., a surface, whose tribological behaviour is governed by the
same types of interfacial forces that govern the tribological behaviour of the test
surface) at the same normal load. In essence, Eq. 9.3.20 can be used to determine the
e ect that the surface topography of a surface has on the friction experienced by it.
9.3.2 Determination of  for Silicon-type Surfaces
In order to be able to use Eqs. 9.3.13 and 9.3.20 for a particular type of surface,
the value of index  for that type of surface must be determined  rst. Therefore,
272
this section will discuss the determination of index  for silicon-type surfaces (i.e.,
surfaces, whose tribological behaviours are governed by the same types of interfacial
forces that govern the tribological behaviour of silicon surfaces).
Comparing Eqs. 9.3.11 and 9.3.12 gives,
W
Wo =
 
( rms) (9.3.21)
Rearranging Eq. 9.3.21 gives,
 
W=Wo = ( rms)
 (9.3.22)
Taking natural log of both sides of Eq. 9.3.22 gives,
ln
  
W=Wo
 
=  ln ( rms) (9.3.23)
Equation 9.3.23 can be used to determine the value of index  . The values of  
and  rms of each of the  ve textured in-plane surfaces investigated in this chapter
are determined using the untextured (control) in-plane surface investigated in this
chapter as the reference surface. Accordingly, the values of Wo and rorms used for
determining the value of index  for silicon-type surfaces are 38700  J/m2 and 0.14
nm, respectively. nasperities for each of the  ve textured in-plane surfaces investigated
in this chapter as well as for the reference surface are determined using the image
analysis technique explained in section 6.12.
As explained in section 9.3.1, the asperities that come in contact at the interfaces
investigated in this chapter do not undergo any elastic and/or plastic deformation.
Accordingly, the interfaces investigated in this chapter do not experience any re-
pulsive elastic forces. Further, the insigni cant deformation of the asperities that
273
Table 9.5: This table reports the W (arithmetic mean), rrms,  rms and  of all the
 ve textured in-plane surfaces investigated in this study. The values of  and  rms
reported in this table are determined using the untextured (control) in-plane surface
as the reference surface. Accordingly, Wo and rorms used are 38700  J/m2 and 0.14
nm, respectively. The rrms of each of the  ve textured in-plane surfaces as well as
the rorms are obtained from their corresponding representative AFM images. nasperities
for each of the  ve textured in-plane surfaces as well as for the reference surface
are determined using the image analysis technique explained in section 6.12. The
threshold value used in the image analysis technique is the kelvin radius of water at
the relative humidity of 45%.
Sample # W rrms  rms  
( J/m2) (nm) (%)
1 32.16 8.3 59 0.62
2 543.6 9.7 69 6.1
3 1209 6.1 44 22.0
4 4780 4.3 31 75.0
5 1058 13.0 93 23.0
274
come in contact at the interfaces investigated in this chapter (as explained in sec-
tion 9.3.1) is also responsible for the signi cantly small real area of contact of the
interfaces investigated in this chapter as compared to their area of interaction. The
contacting asperities (determined using the image analysis technique explained in sec-
tion 6.12) present at the interfaces investigated in this chapter are small fractions of
the interacting asperties (determined using the image analysis technique explained in
section 6.12) present on them. Therefore, the inter-atomic and inter-molecular forces
experienced by the interfaces investigated in this chapter are only a small fraction
of the apparent works of adhesion exhibited by them. Accordingly, the interfacial
forces that contribute signi cantly to the apparent works of adhesion of the inter-
faces investigated in this chapter are the capillary pull experienced by the interacting
asperities and the VDW forces between the non-interacting asperities, of the two
surfaces forming the interface. However, it has been reported that the tribological
behaviour of silicon-type surfaces is dominated by the capillary forces experienced by
them [71, 189]. Accordingly, the threshold value, which needs to be inputted in the
image analysis technique to obtain the nasperities present on the surface being ana-
lyzed, used for each surface investigated in this chapter is the height value obtained
after subtracting the zinteraction (of that surface) from the z-scale of the AFM image
of a representative area of that surface. The zinteraction of a surface is the depth from
the highest point on it, up to which, the asperities present on it experience a capillary
pull at the relative humidity, at which, the experiments are performed. It depends
on the kelvin radius of water (rk) at the relative humidity, at which, the experiments
are performed and the contact angles that a droplet of water makes on the two con-
tacting surfaces that form the interface. It can be determined using Eq. 9.3.24, which
is shown below:
zinteraction = rkcos 1 + cos 22 (9.3.24)
275
Here,  1 and  2 are the contact angles that a droplet of water makes on the two con-
tacting surfaces that form the interface. In the control sample, the examined interface
is formed between two native oxide covered silicon surfaces, and characterized by the
interactions between pairs of native-oxide covered silicon asperities. Therefore, the
zinteraction of the surfaces of the control sample (i.e, zcinteraction) is determined using
Eq. 9.3.25 shown below:
zcinteraction = rk cos 1 (9.3.25)
Here,  1 is the contact angle that a droplet of water makes on a clean native oxide cov-
ered silicon surface. The value of  1 used for determining the number of interacting
asperities present on the surfaces of the control sample is 0 (mean of the experi-
mentally determined values). In the test samples, the examined interface is formed
between gold nanoparticle coated, native oxide covered silicon surfaces. Accordingly,
the interfaces formed in the test samples are characterized by the interactions be-
tween pairs of a gold asperity and a native-oxide covered silicon asperity as well as
between pairs of two gold asperities. Therefore, the zinteraction of the surfaces of the
test samples (i.e, ztinteraction) is determined using Eq. 9.3.26 shown below:
ztinteraction = rkcos 1 + 3 cos 24 (9.3.26)
Here,  1 and  2 are the contact angles that a droplet of water makes on clean native
oxide covered silicon and clean gold surfaces, respectively. The values of  1 and  2
used for determining the number of interacting asperities present on the surfaces of
the test samples are 0 (mean of the experimentally determined values) and 15 (mean
of the experimentally determined values), respectively. All the experiments reported
in this chapter are preformed at a relative humidity of 45%. The kelvin radius of water
(calculated using Eq. 1.5.6) at a relative humidity of 45% is 0.66 nm [189]. In order to
convert the threshold value (from length units) to its corresponding value on a scale
276
of 0 - 255, the z-scale of the AFM image being analyzed is converted to an intensity
scale ranging from 0 - 255. The rrms of each of the  ve textured in-plane surfaces
investigated in this chapter as well as the rorms are obtained from their corresponding
representative AFM images. Table 9.5 reports the W (arithmetic mean), rrms,  rms
and  of all the  ve textured in-plane surfaces investigated in this study. Figure 9.9
shows a plot, in which, the ordinates of Eq. 9.3.23 are plotted against its abscissae.
The data points plotted in Fig. 9.9 are obtained using the mean values ofW reported
in Table 9.5. The error bars shown in the plot indicate one standard deviation of
the sample of 40 measurements used to determine that data point. A line  tted to
the mean values of the ordinates of Eq. 9.3.23, plotted in Fig. 9.9, is also plotted in
Fig. 9.9. The high R2 value of the liner  t indicates that the mathematical correlation
(i.e., Eq. 9.3.13) between the surface topography of a surface and its apparent work
of adhesion developed in section 9.3.1 is in good agreement with the data obtained
experimentally. According to Eq. 9.3.23, the slope of the linear  t represents the value
of index  . Therefore, the experimentally obtained value of the index  for silicon-
type surfaces, which is extracted from the slope of the linear  t shown in Fig. 9.9, is
0.5.
9.3.3 Validation
In order to substantiate the validities of the mathematical correlation between
the surface topography of a surface and its apparent work of adhesion (i.e., Eq. 9.3.13)
developed in section 9.3.1 and the value of index  for silicon-type surfaces obtained
experimentally, it is essential to determine the apparent work of adhesion of a surface,
which is not used to determine the value of index  for silicon-type surfaces, using its
Tribotopography number and compare it with the corresponding value obtained ex-
perimentally. For this purpose, the apparent work of adhesion of the sidewall surface
of the control (untextured) sample is determined, using its Tribotopography number.
277
 0
 0.5
 1
 1.5
 2
 2.5
 3
 3  3.5  4  4.5  5
ln[
?/(W/W
o )]
ln ?rms
y = 0.4978x
R2 = 0.99046
Figure 9.9: A plot, in which, the ordinates of Eq. 9.3.23 are plotted against its
abscissae. The data points ( ) plotted in Fig. 9.9 are obtained using the mean values
of W reported in Table 9.5. The error bars shown in the plot indicate one standard
deviation of the sample of 40 measurements used to determine that data point. A
line ( )  tted to the data points ( ) is also shown in the plot. Notice the high R2
value of the linear  t.
278
Figure 9.10: A representative AFM image of the sidewall surface of the control (un-
textured) sample.The rms roughness of the surface shown in the image is 6.52 nm.
The z-scale of the image is 41.8 nm.
279
Figure 9.10 shows a representative AFM image of the sidewall surface of the control
(untextured) sample. The rrms and the nasperities of the sidewall surface of the control
sample are obtained using this AFM image. The  rms and the  of the sidewall
surface of the control (untextured) sample are obtained using the in-plane surface of
the control (untextured) sample as the reference surface and Eq. 9.3.25. Table 9.6
reports the rrms,  rms,  and  topo of the sidewall surface of the control (untextured)
sample. It also reports the apparent works of adhesion of the sidewall surface of the
control sample, determined using its  topo and obtained experimentally. The close
agreement between the apparent work of adhesion of the sidewall surface of the con-
trol sample determined using its  topo and that obtained experimentally substantiates
the vailidities of the mathematical correlation between the surface topography of a
surface and its apparent work of adhesion (i.e., Eq. 9.3.13) developed in section 9.3.1
and the value of index  for silicon-type surfaces obtained experimentally. Since the
mathematical correlation between the surface topography of a surface and the friction
force experienced by it, which is represented by Eq. 9.3.20, is based on the mathemat-
ical correlation between the surface topography of a surface and its apparent work of
adhesion (i.e., Eq. 9.3.13), the analysis reported in this section also substantiates the
validity of the former.
Like most mathematical correlations, the two mathematical correlations devel-
oped in this study (i.e., one between the surface topography of a surface and its ap-
parent work of adhesion (Eq. 9.3.13) and the other between the surface topography of
a surface and the friction experienced by it (Eq. 9.3.20)), also have some constraints.
While the generalized form of the Tribotopography number (i.e., Eq. 9.3.11) can be
used for any surface, the value of index  (i.e., 0.5) determined experimentally in
this study can be used only for silicon-type surfaces (i.e., surfaces, whose tribologi-
cal behaviours are governed by the same types of interfacial forces that govern the
tribological behaviour of silicon surfaces). Additionally, for hydrophobic silicon-type
280
Table 9.6: This table reports the rrms,  rms,  and  topo of the sidewall surface of
the control (untextured) sample. The rrms reported in this table is obtained using
the AFM image shown in Fig. 9.10. The  rms and the  reported in the table are
obtained using the in-plane surface of the control (untextured) sample as the reference
surface. The table also reports the apparent works of adhesion of the sidewall surface
of the control sample, determined using its  topo and obtained experimentally.
Parameter Unit Value
rrms nm 6.52
 rms - 46.6
 % 18.1
 topo - 0.027
Wtopo  J/m2 1040
Wexp  J/m2 1070
281
surfaces, the value of index  (i.e., 0.5) that is determined experimentally in this
study can be used only for d  20 nm. For d < 20 nm, the value of index  for
hydrophobic silicon-type surfaces increases to a value between 2.5 - 3.0. Further, for
hydrophilic silicon-type surfaces, the two mathematical correlations developed in this
study (i.e., Eq. 9.3.13 and Eq. 9.3.20) are valid for d rk(cos 1 + cos 2). For all d 
rk(cos 1 + cos 2), the value of  of the contacting hydrophilic silicon-type surfaces
is 1, and their topographies do not exhibit any in uence on their stiction and friction
characteristics.
9.3.4 Signi cance of the Tribotopography Number ( topo)
Historically, several mathematical models have been developed to correlate the
surface topography of a surface with its stiction characteristics [188, 190]. However,
each of those models were developed using a statistical surface pro le model, which
was required to represent the surface topographies of the surfaces being studied, and
an appropriate contact mechanics model (i.e., JKR, DMT, MD, etc.), which was re-
quired to represent the interfacial forces experienced by the two contacting surfaces
forming the interface [188, 190]. The statistical surface pro le models used assume
that the height distribution of the asperities present on the surfaces being investigated
can be comprehensively represented by the statistical probability distribution func-
tions such the Gaussian distribution (used in most of the previously reported models)
or the exponential distribution, and that all of them have spherical tips having the
exact same radius of curvature [188{190]. Both of these assumptions compromise the
accuracy of the typical statistical surface pro le models used, in representing the sur-
face topographies of MEMS surfaces. Further, the contact mechanics model that were
used for representing the interfacial forces existing at the interface being investigated
were determined by determining the Tabor adhesion parameter of the two surfaces
282
forming the interface [189]. The Tabor adhesion parameter of an interface is a dimen-
sionless parameter, which represents the statistical average of a competition between
the repulsive elastic forces exerted by the deformed taller asperities of the two surfaces
forming the interface that try to prize them apart, and the attractive adhesive forces
between their contacting asperities that try to hold them together [190]. The original
Tabor adhesion parameter, which was formulated by Fuller and Tabor, is calculated
using the standard deviation of the heights of the asperities present on a surface
as the characteristic length, and therefore, can be used only for those interfaces, at
which, the short-range solid-solid interactions (i.e., inter-atomic and inter-molecular
forces) are the dominant contribution of the total interfacial forces [189]. However, in
the case of interfaces that are formed between hydrophilic surfaces in humid environ-
ments, the interfacial interactions are dominated by the long-range capillary forces.
Therefore, Fogden et al., Maugis et al. and Xu et al. separately formulated a modi ed
Tabor adhesion parameter, which is calculated using the kelvin radius at the relative
vapor pressure, at which, the experiment is performed as the characteristic length,
and therefore, can be used for those interfaces, at which, the capillary forces are the
dominant interfacial force [189, 191, 192]. While both the original Tabor adhesion
parameter as well as the modi ed Tabor adhesion parameter are extremely useful
in understanding the interfacial interactions of single asperity contacts, for interfaces
that consist of multiple point contacts, they can be used only as a qualitative measure
of the e ect of surface topography, and require the use of an appropriate statistical
surface pro le model and an appropriate contact mechanics model for quantitatively
determining the e ect that the surface topography of a surface has on its stiction
characteristics. On the other hand, the Tribotopography number (i.e.,  topo) formu-
lated in this chapter eliminates the need of a statistical surface pro le model for
quantifying the e ect that the surface topography of a surface has on its stiction and
283
friction characteristics. Additionally, it, and hence, the two mathematical correla-
tions formulated using it, can be used for interfaces represented by the entire spectra
of the two Tabor adhesion parameters.
9.4 In uence of the Geometry of the Contact Interface on the E ect of
Surface Topography
In order to determine the in uence of the geometry of the contact interface on
the e ect that the surface topographies of the surfaces forming the interface have
on its tribological characteristics, the engineering coe cients of static friction of the
sidewall surfaces of all the six Test Platform chips investigated in this study are
determined using both the Sidewall Friction Testers (SFTs) as well as the Sidewall
Friction and Adhesion Testers (SFATs). In the SFT, the contact interface is formed
between the plane (vertical) surface of a suspended beam and the cylindrical surface of
an anchored post, and in the SFAT, it is formed between the plane (vertical) surfaces
of two suspended shuttles. On each of the six Test Platform chips investigated,  ve
Sidewall Friction Testers as well as  ve Sidewall Friction and Adhesion Testers are
used to determine the engineering coe cient of static friction of their sidewall surfaces.
While using each Sidewall Friction Tester, the engineering coe cient of static friction
is determined at normal loads ranging from 2.4  N - 15.7  N, which correspond to
Hertzian contact pressures (calculated by considering cylinder on  at geometry) of
123 MPa - 312 MPa, using each Sidewall Friction and AdhesionTester, the engineering
coe cient of static friction is determined at normal loads ranging from 0.677  N - 7.97
 N, which correspond to apparent contact pressures (calculated by considering  at
on  at geometry) of 0.098 MPa - 1.15 MPa. In order to obtain statistically signi cant
results, the coe cient of static friction is determined  ve times at each investigated
normal load, using both the SFTs as well as the SFATs. All the experiments that are
conducted for this study are performed in laboratory air, at 22  C and in 45% relative
284
humidity. The magni cation of the objective lens used in the microscope during the
actuation of SFTs and SFATs for this study is 10X. Accordingly, the size of each pixel
in the  eld of view is 0.465  m  0.465  m. Figure 9.11 is a plot showing the  s
of the sidewall surfaces of all the six Test Platform chips, determined using both the
SFTs as well as the SFATs. The data points plotted in the plot are arithmetic means
of several measurements. The error bars shown in the plot indicate the maximum
and minimum values of the engineering coe cient of static friction exhibited by the
sidewall surfaces of that Test Platform chip. The close agreements between each of the
 s determined using the SFTs and the corresponding  s determined using the SFATs
indicates that the geometry of the contact interface does not have any in uence on
the e ect that the surface topographies of the surfaces forming the interface have on
its tribological characteristics.
9.5 Conclusions
In this study, I have successfully used a dodecanethiol-capped gold nanoparticle-
based surface texturing technique to tailor the topographies of the surfaces (in-plane
as well as sidewall) of  ve Test Platform chips. Additionally, I have successfully
investigated six Test Platform chips ( ve textured using the dodecanethiol-capped
gold nanoparticle-based surface texturing technique and one untextured (control)) to
understand the e ect that the surface topography of a surface has on its tribological
(i.e., stiction and friction) characteristics. The surface topographies of the surfaces of
each of the six Test Platform chips investigated in this study are characterized qual-
itatively using SEM and quantitatively using AFM. The qualitative characterization
of the surface topographies of the surfaces of the six Test Platform chips investigated
in this study con rmed that while on the same Test Platform chip, both the in-plane
as well as sidewall surfaces have identical nanoparticle coatings on them, the surfaces
of di erent Test Platform chips have distinct surface topographies. Additionally, it
285
 0
 0.5
 1
 1.5
 2
 2.5
Control 1 2 3 4 5  
Coefficient of Static Friction, (
? s
)
Sample #
SFT
SFAT
Figure 9.11: A plot showing the  s of the sidewall surfaces of all the six Test Platform
chips, determined using both the SFTs as well as the SFATs. The data points plotted
in the plot are arithmetic means of several measurements. The error bars shown in
the plot indicate the maximum and minimum values of the engineering coe cient of
static friction exhibited by the sidewall surfaces of that Test Platform chip. Notice
the close agreements between the  s determined using the SFTs and those determined
using the SFATs.
286
validated my hypothesis that the amount of the nanoparticles that get deposited on
the surface being textured can be controlled by controlling the number density of
the nanoparticle dispersion used. The quantitative characterization of the surface
topographies of the surfaces of the six Test Platform chips investigated in this study
is successfully used to quantify them in terms of two measurable parameters, namely,
the rms roughness and the surface coverage of the interacting asperities present on
the surface. Further, in order to understand the e ects that the surface topography
of a MEMS surface has on its stiction and friction characteristics, three important
tribological properties of the surfaces of each of the six Test Platform chips investi-
gated in this study, which are the apparent work of adhesion of the in-plane surfaces,
the apparent work of adhesion of the sidewall surfaces and the coe cient of static
friction of the sidewall surfaces, are determined. The tribological characterization of
the surfaces of the six Test Platform chips investigated in this study provided an ex-
perimental con rmation of the already believed theory that the friction experienced
by contacting MEMS surfaces shows a strong dependence on the stiction experienced
by them. Additionally, it indicated that both the micro-scale as well as the nano-
scale topographies of a surface have a strong in uence on its stiction and friction
characteristics.
In order to mathematically correlate the surface topography of a surface with
its stiction and friction characteristics, a dimensionless parameter called Tribotopog-
raphy number (i.e.,  topo), which separately accounts for both the components that
de ne the rms roughness of a surface, and can be used to predict the e ect that the
surface topography of a surface will have on its stiction and friction characteristics,
is formulated in this study. Further, the Tribotopography number is successfully
used to develop two mathematical correlations, one between the surface topography
of a surface and its apparent work of adhesion, and the other between the surface
topography of a surface and the friction experienced by it. In order to use the two
287
mathematical correlations developed in this study for a particular type of surface, the
value of index  , which is the index of the denominator of the fraction that represents
the Tribotopography number, for that type of surface must be determined  rst. The
value of index  for silicon-type surfaces (i.e., surfaces, whose tribological behaviours
are governed by the same types of interfacial forces that govern the tribological be-
haviour of silicon surfaces) is determined in this study. This study also reports an
analysis (i.e., experimental validation), which substantiates the validities of the two
mathematical correlations developed to correlate the surface topography of a sur-
face with its stiction and friction characteristics, respectively. Additionally, it also
discusses the constraints, under which, the two mathematical correlations are valid.
The two mathematical correlations developed in this study can be used to quantita-
tively determine the e ect that the surface topography of a surface will have on its
stiction and friction characteristics. Lastly, in order to determine the in uence of the
geometry of the contact interface on the e ect that the surface topographies of the
surfaces forming the interface have on its tribological characteristics, the engineering
coe cients of static friction of the sidewall surfaces of all the six Test Platform chips
investigated in this study are determined using both the Sidewall Friction Testers
(SFTs) as well as the Sidewall Friction and Adhesion Testers (SFATs). The results
indicate that the geometry of the contact interface does not have any in uence on
the e ect that the surface topographies of the surfaces forming the interface have on
its tribological characteristics.
288
Chapter 10
A Simple Experimental Technique to Estimate the Surface Coverage of the
Nanoparticle-based Monolayer Coatings Used to Texture MEMS Surfaces
10.1 Introduction
As explained in section 1.3, commercialization of an extremely large number
of useful MEMS prototypes is hindered by their poor reliabilities, which are conse-
quences of the dominance of surface phenomena such as stiction, friction and wear,
at the micron scale. Therefore, a signi cant fraction of the research conducted by
the MEMS community is focussed on devising strategies that can be used to improve
the tribological characteristics of MEMS surfaces. One strategy that is being con-
sidered by the MEMS community for addressing the tribological issues that plague
most MEMS devices consists of altering the surface topographies of MEMS surfaces
by depositing nanoparticles on them [24, 27, 130]. Indeed, it has been demonstrated
that the gold nanoparticle-based coatings signi cantly reduce the stiction experienced
by in-plane polysilicon as well as silicon surfaces [24,27,130]. However, the reduction
in stiction achieved by the di erent studies reported in literature are signi cantly
di erent [24, 130, 156]. Based on the results obtained in the previous chapter, this
can be attributed to the di erence in the  topo of the test surfaces investigated in
those studies. Accordingly, the e ectiveness of a nanoparticle-based coating strongly
depends on the  topo of the coated surface. Therefore, the surface coverage of the coat-
ing can serve as an e ective parameter in the comparison between the e ectivenesses
of various nanoparticle-based (sub-)monolayer coatings. This study reports a simple
experimental technique to determine the surface coverage of the nanoparticle-based
monolayer coatings used to texture MEMS surfaces.
289
10.2 Estimation of Surface Coverage
The surface coverage of a nanoparticle-based (sub-)monolayer coating can be
determined using the Resonator developed in this study. Details on the designs and
actuation procedures of the Resonators included in the Test Platform developed in
this study are given in section 5.3. Also derived in section 5.3.3, is the equation that
can be used to determine the resonance frequencies of the Resonators included in the
Test Platform developed in this study. The equation is reproduced here as Eq. 10.2.1
for completeness.
fR = 12 
s
2E tw
3
MeffL3 (10.2.1)
Here, fR is the resonance frequency of the Resonator being tested, E is the elastic
modulus of the structural  lm, t is the thickness of the structural  lm and w and L are
the width and length of the supporting beams of the Resonator being tested, respec-
tively and Meff is the e ective mass of the resonating structure. By di erentiating
both sides of Eq. 10.2.1 with respect to Meff we get,
 fR = 
"
1
4 
r
2Et
 w
L
 3#
M 3=2eff  Meff (10.2.2)
Rearranging Eq. 10.2.2 gives,
 Meff = 4 M3=2eff
 
2Et
 w
L
 3  1=2
 fR (10.2.3)
Here,  fR is the amount, by which, the resonance frequency of a Resonator developed
in this study changes when the e ective mass of its resonating structure changes by
 Meff and Meff is the original e ective mass of its resonating structure.
The deposition of nanoparticles on the surfaces of the Resonator increases the
e ective mass of its resonating structure, and as indicated by Eq. 10.2.1, decreases
its resonance frequency. Therefore, by comparing the resonance frequencies of the
290
nanoparticle coated and uncoated Resonators having the same supporting beam
length, the increase in the e ective mass of the Resonator, which is due to the mass
of the nanoparticles deposited on it, can be determined using Eq. 10.2.3. The t, w
and L, which are the thickness, width and length of the supporting beams of the
Resonator, respectively, are measured optically and  fR is given by Eq. 10.2.4 shown
below:
 fR = fcoatedR  funcoatedR (10.2.4)
Here, fcoatedR , which is the resonance frequency of the Resonator coated with nanopar-
ticles is determined experimentally. The original e ective mass of the resonating
structure (i.e., Meff) of the Resonator being tested can be given by the Rayleigh
equation shown below:
Meff = Ms + 14Mt + 1235Mb (10.2.5)
Here, Ms, Mt and Mb are the masses of the shuttle, the two trusses and the eight
supporting beams of the Resonator being tested, respectively. Ms, Mt and Mb are
determined using the dimensions of the corresponding components of the Resonator,
which are measured optically.  Meff, which represents the increase in the e ective
mass of a Resonator caused by the deposition of nanoparticles on it can be further
decomposed into two components, as shown in Eq. 10.2.6 below:
 Meff = Mcoatedeff  Muncoatedeff (10.2.6)
Here, Muncoatedeff is the e ective mass of the resonating structure of the uncoated Res-
onator, which is the same as Meff. Mcoatedeff , which is the e ective mass of the resonat-
ing structure of the coated Resonator, can be given by Eq. 10.2.7 shown below:
Mcoatedeff = Muncoatedeff + 2dnp np3
 
As + 14At + 1235Ab
 
(10.2.7)
291
Here, As, At and Ab are the total surface areas of the shuttle, the two trusses and the
eight supporting beams of the Resonator being tested, respectively, are determined
using the dimensions of the corresponding components, which are measured optically.
dnp and  np are the mean diameter and density of the nanoparticles deposited on
the Resonator being tested, and  is the surface coverage of the coating consisting of
them. Substituting Eqs. 10.2.7 and 10.2.6 in Eq. 10.2.3 gives Eq. 10.2.8, which can
be used to determine the surface coverage of a nanoparticle-based (sub-)monolayer
coating.
 2dnp np3
 
As + 14At + 1235Ab
 
= 4 M3=2eff
 
2Et
 w
L
 3  1=2
 fR (10.2.8)
10.3 Results
In order to experimentally test the technique discussed in the previous section,
one Test Platform chip is released and coated with nanoparticles using the processes
reported in sections 6.1 and 6.6, respectively. Again, the nanoparticles speci cally
used for this study are dodecanethiol-capped gold nanoparticles. The process used to
synthesize the dodecanethiol-capped gold nanoparticles used in this study is described
in detail in section 6.5. In order to burn-o the dodecanethiol capping ligands present
on the gold nanoparticles deposited on the Test Platform chip before testing the
Resonators on it, the Test Platform chip is exposed to an UV-ozone atmosphere for
1 hour before testing. The coated Test Platform chip is  rst characterized, using
AFM. Figure 10.1a shows a high resolution AFM image of the top surface of one of
the Resonators of the coated Test Platform chip. A linescan taken across the AFM
image shown in Fig. 10.1a, which is shown in Fig. 10.1b, clearly con rms that the
nanoparticle coating deposited on the Test Platform chip being investigated in this
study is a sub-monolayer coating.
292
(a)
 0
 5
 10
 15
 0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8
nm
?m
(b)
Figure 10.1: (a) A high resolution AFM image of the top surface of one of the
Resonators of the coated Test Platform chip. The rms roughness of the surface
shown in image a is 2.06 nm. The z-scale of image a is 13.8 nm. (b) Linescan along
the white line drawn across image a.
293
In order to eliminate the error that is induced in the estimate of the surface
coverage of a nanoparticle coating, by the errors (induced by the resolution of mea-
surement) in the measured dimensions of the Resonator, two sets of  ve Resonators
each are used in this study. All the Resonators belonging to the same set have
supporting beams of the same length, and those belonging to di erent sets have sup-
porting beams of di erent lengths. The two sets of Resonators that are used in this
study include Resonators with supporting beam lengths of 200  m (nominal) and
350  m (nominal). Further, the  ve Resonators belonging to each of the two sets
of Resonators tested in this study are selected from di erent locations on the coated
Test Platform chip. All the Resonators are actuated in laboratory air, at 22  C and
in 45% relative humidity. The magni cation of the objective lens used in the micro-
scope for this study is 10X. Accordingly, the size of each pixel in the  eld of view is
0.465  m  0.465  m. The resonance frequencies of the Resonators tested in this
study are determined optically, with an accuracy of  5 Hz. Table 10.1 reports the
optically observed resonance frequencies of the two sets of Resonators tested in this
study. Each resonance frequency reported in Table 10.1 is an arithmetic mean of
 ve measurements, which are made using  ve distinct Resonators having the same
supporting beam length. In order to obtain the surface coverage of the nanoparti-
cle coating deposited on the Test Platform chip that is investigated in this study,
Eq. 10.2.8 is  tted to the two experimentally obtained resonance frequencies reported
in Table 10.1 using the elastic modulus (E) of the structural  lm and the surface
coverage of the nanoparticle coating (i.e.,  ) as the  tting parameters. The values
of  np and dnp used for obtaining the surface coverage of the nanoparticle coating
deposited on the Test Platform chip investigated in this study are 19300 Kg/m3 and
5.48 nm, respectively. The surface coverage of the nanoparticle coating represented
by the AFM image shown in Fig. 10.1a is determined to be 89 %, which appears to
be consistent with its appearance in the AFM image. The elastic modulus of the
294
AuNP coated structural  lm is determined to be 130 GPa, which is expected since
the AuNP coating is discontinuous and so is not expected to alter the elastic modulus
of the structural  lm of the Resonators used to determine its surface coverage.
The resolution, with which, the experimental technique presented in this study
can determine the surface coverage of nanoparticle coatings is  xed by the resolution,
with which, the resonance frequencies of the Resonators used to determine the surface
coverage of nanoparticle coatings are determined. The resonance frequencies of the
Resonators used in this study are determined by visually monitoring the amplitudes of
their oscillations. Therefore, the resolution, with which, the resonance frequencies are
determined in this study is  5 Hz. However, the use of a capacitance-measurement
based technique for detecting the resonance of the Resonators can enable the determi-
nation of surface coverage of nanoparticle coatings with signi cantly high resolution.
Further, it should be noted that the technique presented in this study can be used to
determine the surface coverage of only sub-monolayer nanoparticle coatings because
the derivation of Eq. 10.2.7 assumes that the entire change in the e ective mass of
the Resonator is caused by only a single layer of coating.
10.4 Conclusions
In this study, I have successfully demonstrated a simple technique based on
optically determined resonance for determining the surface coverage of sub-monolayer
nanoparticle coatings, which can be used to texture MEMS surfaces. The modeling as
well as the experimental validation of the technique are presented in the study. The
factor that de nes the resolution of the technique is also discussed in the study. The
surface coverage of the coating can serve as an e ective parameter in the comparison
between the e ectivenesses of various nanoparticle-based (sub-)monolayer coatings.
Unfortunately, the technique presented in this study can be used to determine the
surface coverage of only sub-monolayer nanoparticle coatings.
295
Table 10.1: This table reports the optically observed resonance frequencies of the two
sets of Resonators tested in this study. Each resonance frequency reported in the
table is an arithmetic mean of  ve measurements, which are made using  ve distinct
Resonators having the same supporting beam length.
Supporting Beam Observed
Length Resonance Frequency
( m) (KHz)
200 17.01  0.005
350 8.276  0.005
296
Chapter 11
Surface Texturing: A Potent Alternative to Reduce Stiction and Friction
Experienced by MEMS Surfaces
This chapter reports on a novel gold nanoparticle (AuNP) coating, which is de-
posited on micro-electromechanical systems (MEMS) surfaces using the gas-expanded
liquid technique, and has the potential to be used as an alternative of OTS SAM for
reducing the stiction and friction experienced by them. A complete characterization
of the AuNP coating is presented in this chapter. The AuNP coating is character-
ized using atomic force microscopy (AFM) and several microinstruments developed
in this study. Surface coverage of the AuNP coating, which is determined using the
Resonator developed in this study; and the tribological properties including the work
of adhesion, the coe cients of static and kinetic friction and the apparent rupture
strength of the AuNP coating, which are determined using the Cantilever Beam Array,
the Sidewall Beam Array and the Sidewall Friction and Adhesion Tester developed
in this study, respectively, are reported in this chapter.
11.1 Introduction
Despite years of research, the MEMS community is yet to  nd a solution that
su ciently addresses the reliability issues that limit the commercial success of a wide
spectrum of useful MEMS prototypes. Further, the continuously increasing number
of smaller, more complex and more useful new MEMS is making the already dire need
of improving the tribological behaviour of MEMS interfaces even more pressing. To-
date, while several approaches that alter the chemical composition of MEMS surfaces
have been signi cantly investigated, very little attention has been paid to approaches
297
that alter the topography of MEMS surfaces. This chapter reports a novel gold
nanoparticle (AuNP) coating that signi cantly reduces stiction and friction between
MEMS surfaces by texturing them.
Initial investigations that probed the potential of surface texturing to improve
MEMS reliability altered the topography of MEMS surfaces by etching them in wet
anisotropic etchants. These investigations, which only studied the e ect of surface
texturing on stiction between in-plane MEMS surfaces, reported that surface tex-
turing reduced the stiction experienced by in-plane surfaces by a moderate factor of
20 [127]. In 2006, when DelRio et al. studied the e ect of the presence of silicon
carbide (SiC) particles (diameter ranging between 20-50 nm) on polysilicon-based
contacting MEMS surfaces on the (in-use, in-plane) stiction experienced by them,
and reported that the deposition of nanoparticles (NPs) on contacting MEMS sur-
faces can signi cantly reduce the stiction between them, NPs emerged as a new tool
that can be used to texture MEMS surfaces [27]. However, the nanoparticles that
textured the MEMS test surfaces that were used in the investigations conducted by
DelRio et al. were adventitiously formed on them (i.e., the particles were not de-
posited intentionally) by a side reaction during the sacri cial layer growth, and a
process to controllably deposit NPs on MEMS surfaces was not available at that
time [24, 27]. A process to controllably deposit AuNPs on MEMS was only recently
reported by Hurst et al., who studied the e ect of dodecanethiol-capped AuNP-based
surface texturing on the stiction experienced by the in-plane polysilicon surfaces and
reported about 100X reduction in in-plane stiction [24].
Due to the fact that each of the past studies, which investigated the e ect of
nanoparticle (NP) based surface texturing, reported only moderate reduction in stic-
tion between textured in-plane surfaces, I postulated that the e ectivenesses of the
nanoparticle-based coatings investigated in them were reduced by the grain-boundary
induced inherent roughness of the polysilicon test surfaces used in them. Therefore,
298
I investigated the e ect of AuNP-based surface texturing on the stiction experienced
by relatively smooth single crystal silicon in-plane surfaces [130]. My investigations
revealed that the e ectiveness of AuNP-based surface texturing not only depends on
the inherent roughness of the test surfaces but also depends strongly on the surface
coverage of the coating (refer to results reported in Chapter 9). In this chapter, I
report the reduced stiction experienced by the relatively smooth single crystal silicon
in-plane MEMS surfaces textured using the AuNP coating with the most e ective
surface coverage. Further, the e ect of the same AuNP coating on the stiction as well
as friction experienced sidewall surfaces is reported. Surface coverage and apparent
rupture strength of the studied AuNP coating are also reported in the chapter.
11.2 Experimental Details
11.2.1 Coatings
The test chip (i.e., the Test Platform chip coated with the AuNP coating that
is investigated in this study) used in this study is released and coated with AuNPs
using the processes reported in sections 6.1 and 6.6, respectively. The amount of
concentrated dodecanethiol-capped AuNP dispersion (in hexane) added to the vial,
in which, the test chip is placed for coating, to obtain the AuNP coating investigated
in this study is 2.5  l. The dodecanethiol-capped gold nanoparticles used in this
study are also synthesized using the process described in detail in section 6.5. In
order to burn-o the dodecanethiol capping ligands present on the gold nanoparticles
deposited on the Test Platform chip, the Test Platform chip is exposed to an UV-
ozone atmosphere for 1 hour before testing.
Two di erent control chips are used in this study. While both of them are released
using the same process, which is reported in section 6.1, one of them (control chip
I) is further subjected to the process reported in section 6.2 while the other (control
chip II) is further subjected to the process reported in section 6.4. Accordingly, the
299
test surfaces of one control chip are covered with only native oxide, while those of the
other are coated with OTS SAM.
11.2.2 Microinstruments Used
The surface coverage of the AuNP coating investigated in this chapter is deter-
mined using the technique reported in chapter 10. The two sets of Resonators that
are used for determining the surface coverage of the AuNP coating investigated in
this chapter include Resonators with supporting beam lengths of 200  m (nominal)
and 350  m (nominal). Both the sets of Resonators used in this study consist of  ve
Resonators each, which are selected from di erent locations on the test chip. The
magni cation of the objective lens used in the microscope during the actuation of the
Resonators used in this study is 10X. Accordingly, the size of each pixel in the  eld
of view is 0.465  m 0.465  m. The resonance frequencies of the Resonators tested
in this study are determined optically, with an accuracy of  10 Hz.
The reduction in the stiction experienced by the in-plane surfaces of the Test
Platform due to the AuNP coating investigated in this chapter is determined by
determining the apparent works of adhesion of the in-plane surfaces of the test as
well as control chips. The apparent works of adhesion of the in-plane surfaces of
the Test Platform chips (i.e, the test chip and the two control chips) investigated
in this chapter are determined using the Cantilever Beam Array developed in this
study. Details on the design and actuation procedure of the Cantilever Beam Arrays
included in the Test Platform developed in this study are given in section 5.4. The
magni cation of the objective lens, which is used in the interference microscope that
is used to determine the height pro le of the actuated cantilever beams, is either
10X or 20X. Accordingly, the size of each pixel in the  eld of view is either 0.465
 m  0.465  m or 0.234  m  0.234  m, respectively. On each Test Platform chip
300
investigated in this chapter, four CBAs consisting of ten cantilever beams each are
actuated to obtain a statistically signi cant data set.
The reduction in the stiction experienced by the sidewall surfaces of the Test
Platform due to the AuNP coating investigated in this chapter is determined by
determining the apparent works of adhesion of the sidewall surfaces of the test as well
as control chips. The apparent works of adhesion of the sidewall surfaces of the Test
Platform chips (i.e, the test chip and the two control chips) investigated in this chapter
are determined using the Sidewall Beam Array developed in this study. Details on
the design and actuation procedure of the Sidewall Beam Arrays included in the Test
Platform developed in this study are given in section 5.5. The magni cation of the
objective lens of the microscope, which is used to observe the microinstrument during
actuation and determine the crack length of each actuated adhered pair of sidewall
beams, is 10X. Accordingly, the size of each pixel in the  eld of view is 0.465  m  
0.465  m. On each Test Platform chip investigated in this chapter, eight SBAs are
actuated to obtain a statistically signi cant data set.
The reduction in the friction experienced by the surfaces of the Test Platform due
to the AuNP coating investigated in this chapter is determined by determining the
engineering coe cients of static and kinetic friction of the sidewall surfaces of the test
as well as control chips. The engineering coe cients of static and kinetic friction of the
contacting sidewall surfaces of the Test Platform chips (i.e, the test chip and the two
control chips) investigated in this chapter are determined using the Sidewall Friction
and Adhesion Tester developed in this study. Details on the design and actuation
procedure of the Sidewall Friction and Adhesion Tester developed in this study are
given in section 5.7. The magni cation of the objective lens used in the microscope
during the actuation of the Sidewall Friction and Adhesion Testers for this study is
10X. Accordingly, the size of each pixel in the  eld of view is 0.465  m  0.465  m.
On each Test Platform chip investigated,  ve Sidewall Friction and Adhesion Testers
301
are used to determine the engineering coe cients of static and kinetic friction of its
sidewall surfaces. Using each Sidewall Friction and Adhesion Tester, the engineering
coe cients of static and kinetic friction are determined at normal loads ranging from
0.677  N - 3.28  N, which correspond to apparent contact pressures (calculated by
considering  at on  at geometry) of 0.098 MPa - 0.473 MPa. Additionally, in order
to obtain statistically signi cant results, the coe cients of friction are determined
 ve times at each investigated normal load.
11.3 Results and Discussion
11.3.1 Topographical Properties of the AuNP Coating
The topography of the AuNP coated surfaces of the test chip is characterized
using an atomic force microscope (AFM). Figures 11.1a and 11.2a are AFM images
of the native oxide covered (uncoated) substrate of the control chip I and the AuNP
coated substrate of the test chip, respectively. It is clearly evident from Figs. 11.1a
and 11.2a that the AuNP coating signi cantly increases the roughness of the surfaces
coated with it. While the substrate of the control chip I is extremely smooth (rms
roughness is 0.097 nm), the AuNP coated substrate shown in Fig. 11.2a has a sig-
ni cant rms roughness of 8.3 nm. The mean peak/valley ratio (obtained from the
linescan shown in Figure 11.2b) of the topography of the AuNP coated substrate,
which is shown in Fig. 11.2a, is about 5 nm, which compares well with the mean di-
ameter of the AuNPs used to coat the test chip. This indicates that the topmost layer
of AuNPs deposited on the surfaces of the test chip has a sub-monolayer coverage.
The surface coverage, which is determined using the Resonators, of the AuNP coating
deposited on the test chip is determined to be 16%, which appears to be consistent
with its appearance in the AFM image (i.e., Fig. 11.2)a.
302
(a)
 0
 0.2
 0.4
 0  1  2  3  4  5  6  7  8  9  10
nm
?m
(b)
Figure 11.1: (a) AFM image of the native oxide covered uncoated substrate of the
control chip I. The rms roughness of the surface shown in image a is 0.097 nm. (b)
Linescan along the white line drawn across image a.
303
(a)
 0
 4
 8
 12
 0  1  2  3  4  5  6  7  8  9  10
nm
?m
(b)
Figure 11.2: (a) AFM image of the AuNP coated substrate of the test chip. The rms
roughness of the surface shown in image a is 8.3 nm. (b) Linescan along the white
line drawn across image a.
304
11.3.2 Tribological Properties of the AuNP Coating
The tribological properties of the AuNP coating deposited on the test chip that
are characterized in this study include the apparent work of adhesion of coated in-
plane surfaces, the apparent work of adhesion of coated sidewall surfaces, the engi-
neering coe cients of static and kinetic friction of coated sidewall surfaces and its
apparent rupture strength. All the results reported in this study are obtained in
laboratory air, at 22  C and in 45% relative humidity. Figures 11.3a and 11.4a are
interferograms showing one tested Cantilever Beam Array of the control chip I and
the test chip, respectively. It is clearly evident from Figs. 11.3a and 11.4a that the
AuNP coating signi cantly increases the crack length exhibited by the in-plane sur-
faces. The increased crack length exhibited by the AuNP coated in-plane surfaces
is further substantiated by the experimentally obtained (PSI derived) height pro les
shown in Figs. 11.3b and 11.4b, which indicate that the uncoated in-plane surfaces of
the control chip I exhibit a crack length of less than 100  m, while the AuNP coated
in-plane surfaces of the test chip exhibit a crack length of close to 850 micron. The
apparent works of adhesion of the sidewall surfaces investigated in this study are de-
termined using the Sidewall Beam Array. Figures 11.5a and 11.5b are optical images
showing the  ve longest sidewall beam pairs of a released Sidewall Beam Array of the
test chip, collected before and after actuating the Sidewall Beam Array, respectively.
It is clearly evident from Figs. 11.5a and 11.5b that the crack length exhibited by the
AuNP coated sidewalls is also signi cantly large.
Table 11.1 lists the critical tribological properties of the native oxide covered
hydrophilic surfaces of the control chip I, the OTS SAM coated hydrophobic surfaces
of the control chip II and the AuNP coated surfaces of the test chip. All the values
reported in Table 11.1 are arithmetic means of several measurements and sd is one
standard deviation of the sample consisting of those measurements. It is clearly ev-
ident from the Wip reported in Table 11.1 that the AuNP coated in-plane surfaces
305
Beam 2
(a)
 0
 0.5
 1
 1.5
 2
 0  100  200  300  400  500
Vertical height, (
?m)
Lateral position, ( ?m)
(b)
Figure 11.3: (a) An interferogram showing a tested Cantilever Beam Array of the
control chip I. (b) Experimentally determined height pro le of beam 2 labelled in
image a. The height pro le is determined using phase shifting interferometry. Notice
that the crack of beam 2 labelled in image a is less than 100  m.
306
Beam 4
(a)
 0
 0.5
 1
 1.5
 2
 2.5
 0  100  200  300  400  500  600  700  800  900  1000
Vertical height, (
?m)
Lateral position, ( ?m)
(b)
Figure 11.4: (a) An interferogram showing a tested Cantilever Beam Array of the
test chip. (b) Experimentally determined height pro le of beam 4 labelled in image
a. The height pro le is determined using phase shifting interferometry. Notice that
the crack of beam 4 labelled in image a is close to 850  m.
307
1250 micron
Freestanding
(a)
s
Did not stick
Stuck
(b)
Figure 11.5: (a) Optical image showing the  ve longest sidewall beam pairs of a
released Sidewall Beam Array of the test chip, collected before actuating the Sidewall
Beam Array. Notice that the sidewall beams of each of the  ve sidewall beam pairs
shown in this image are apart from each other. (b) Optical image of the Sidewall
Beam Array shown in image a, collected after actuating it. Notice that the sidewall
beams of the three shorter sidewall beam pairs shown in this image peeled apart
completely, while those of the two longer sidewall beam pairs remained stuck, after
actuation.
308
exhibit a factor of 1000 reduction in the stiction experienced by the uncoated native
oxide covered in-plane surfaces of the control chip I. Further, the AuNP coated side-
walls also exhibit a factor of 50 reduction in the stiction experienced by the uncoated
native oxide covered sidewall surfaces of the control chip I. It should be noted that
although the reduction in Ws is less than that in Wip, the absolute value of the Ws
of the AuNP coated sidewalls is signi cantly low, and marginally lower than theWip
of the corresponding AuNP coated in-plane surfaces. The engineering coe cients of
both static as well as kinetic friction of the AuNP coated sidewalls, which are 0.08
(mean) and 0.07 (mean), respectively, are also signi cantly smaller than those of the
native oxide covered sidewalls of the control chip I, which are 1.98 (mean) and 1.35
(mean), respectively. Additionally, the results reported in Table 11.1 indicate that
the stiction and friction properties of the AuNP coated surfaces are marginally better
than those of the corresponding OTS SAM coated surfaces too.
In order to determine the rupture strength of the AuNP coating investigated in
this study, a SFAT is used to determine  s of the AuNP coated sidewalls at di erent
normal loads. The normal loads tested for this study range from 0.677  N - 4.43  N,
which correspond to apparent contact pressures (calculated by considering  at on  at
geometry) of 0.098 MPa - 0.64 MPa. The normal applied at the sidewall interface
is  rst increased from 0.677  N to 4.43  N and then decreased back to 0.677  N.
At each investigated normal load, the  s of the AuNP coated contacting sidewalls
is determined  ve times. The normal load, at which, the  s of the AuNP coated
sidewalls increases irreversibly is considered as the rupture strength of the AuNP
coating. Figure 11.6 shows a plot of the (mean)  s of the AuNP coated contacting
sidewalls versus the corresponding voltage applied to the comb-drive actuator of the
normal arm. The arrows shown in the plot indicate the direction, in which, the normal
load applied at the sidewall interface of the SFAT used for this study is changed. It
is clearly evident in the plot that the (mean)  s of the AuNP coated contacting
309
Table 11.1: Comparison between the critical tribological properties of the native oxide
covered hydrophilic surfaces of the control chip I, the OTS SAM coated hydrophobic
surfaces of the control chip II and the AuNP coated surfaces of the test chip. All the
values reported in the table are arithmetic means of several measurements and sd is
one standard deviation of the sample consisting of those measurements.
Coating Wip  sd Ws  sd  s  sd  k  sd
( J/m2) ( J/m2)
Oxide 38700  9300 1070  60 1.98  0.45 1.35  0.2
OTS 45.46  1 37.65  1 0.155  0.03 0.13  0.01
AuNP 32.16  3 21.50  3 0.081  0.02 0.072  0.01
310
sidewalls changed irreversibly when a voltage of 77 V (i.e., Vr) is applied to the comb-
drive actuator of the normal arm. The normal load applied at the sidewall interface
when the voltage Vr is applied to the normal comb-drive actuator is 3.5  N, which
corresponds to an apparent contact pressure (calculated by considering  at on  at
geometry) of 500 kPa. Therefore, the apparent rupture strength of the AuNP coating
investigated in this chapter is 500 kPa.
11.4 Conclusions
In this study, I have successfully characterized the topography and the critical
tribological properties of a AuNP coating that is extremely e ective in reducing the
stiction and friction experienced by MEMS surfaces. The AuNP coating investigated
in this study signi cantly increased the roughnesses of the surfaces coated with it. It
has a surface coverage of 16 % and an apparent rupture strength of 500 kPa. The
in-plane surfaces coated with the AuNP coating investigated in this study exhibit a
reduced apparent work of adhesion of 32.16  3  J/m2, and the sidewall surfaces
coated with it exhibit a reduced apparent work of adhesion of 21.50  3  J/m2 and
reduced engineering coe cients of static and kinetic friction of 0.081 0.02 and 0.072
 0.01, respectively. The AuNP coating reduces the stiction experienced by the native
oxide covered hydrophilic in-plane surfaces by a factor of 1000, and that experienced
by the native oxide covered hydrophilic sidewall surfaces by a factor of 50.
311
 0
 0.4
 0.8
 1.2
 1.6
 2
 45  50  55  60  65  70  75  80  85
Coefficient of Static Friction, (
? s
)
Voltage Applied to the Normal Arm (V)
V r = 77 V
Increasing
Decreasing
Figure 11.6: A plot of the (mean)  s of the AuNP coated contacting sidewalls versus
the corresponding voltage applied to the comb-drive actuator of the normal arm. The
arrows shown in the plot indicate the direction, in which, the normal load applied
at the sidewall interface of the SFAT used for this study is changed. Notice that
the (mean)  s of the AuNP coated contacting sidewalls changed irreversibly when a
voltage of 77 V is applied to the normal comb-drive actuator.
312
Chapter 12
Summary
12.1 The Test Platform
This study reports on the successful development of a test platform (TP), which
not only overcomes the limitations of the previously reported test platforms but is
also a versatile tool that can be used to systematically study the tribology of MEMS
surfaces. The details of the design and fabrication of the Test Platform are discussed
in the study. The Test Platform is fabricated using a SOI (silicon-on-insulator) wafer,
due to which, the material properties of its structural  lm do not vary at all. The
use of a single crystal structural  lm (i.e., Si(100)) for fabricating the Test Platform
also ensures that the topographies of the surfaces (in-pane as well as sidewall) of
the microinstruments included in it also do not vary from chip to chip. Further,
in order to be able to fabricate the TP using a facile, inexpensive and less time
consuming fabrication process, a single mask scheme is devised in this study for
fabricating the Test Platform. All the microinstruments of the Test Platform are
fabricated on a 1 cm  1 cm SOI chip. Additionally, in order to ensure that the
sidewall surfaces of the microinstruments included in the Test Platform are relatively
smooth so that a systematic investigation of the e ects that the surface topographies
of MEMS surfaces have on their stiction and friction characteristics can be conducted,
a polishing technique to smoothen the scalloped as-fabricated sidewalls of the Test
Platform is developed in this study. The polishing technique developed in this study
yields relatively much smoother sidewall surfaces.
313
In order to be able to systematically investigate, and establish a meaningful and
reliable correlation between, the e ects that a particular factor has on the di er-
ent tribological properties (i.e., stiction, friction and wear) of MEMS surfaces, seven
di erent types of microinstruments are included in the Test Platform. Their dimen-
sions are determined keeping in mind that fabricating all of them on the same chip
should not cause any issues during the release of the Test Platform. The test platform
(TP) has microinstruments that can be used to determine several di erent material
properties of the structural  lm. The Residual Stress Tester (RST) can be used to
determine the residual stress present in a released device layer (structural  lm). The
Mechanical Strength Tester (MST) can be used to determine the fracture strength
of the device layer. The \Resonator" can be used to determine the elastic modu-
lus of the device layer. Additionally, the Test Platform has a microinstrument (i.e.,
Cantilever Beam Array (CBA)) that can be used to study the stiction characteristics
of the in-plane surfaces. Although, most of the tribological studies reported to-date
have been conducted using in-plane surfaces, in devices belonging to several of the
emerging classes of MEMS such as microgears and microsliders, more vertical (side-
wall) surfaces come into contact during operation than horizontal (in-plane) surfaces,
and  ndings of investigations carried out using in-plane interfaces are not applicable
to sidewall interfaces [78,79,126,142]. Therefore, microinstruments in which sidewalls
form the test interface are needed to study the tribological behaviour of sidewall in-
terfaces. The Test Platform developed in this study conveniently addresses this need.
It has di erent microinstruments for studying the stiction characteristics of in-plane
and sidewall surfaces. While, as mentioned before, the CBA can be used to study
the stiction characteristics of the in-plane surfaces, the stiction characteristics of the
sidewall surfaces can be studied using the Sidewall Beam Array (SBA). Lastly, the
Test Platform has two di erent microinstruments (i.e., the Sidewall Friction Tester
(SFT) and the Sidewall Friction and Adhesion Tester (SFAT)) that can be used to
314
study the friction as well as wear characteristics of the sidewall surfaces. The purpose
behind including two di erent microinstruments for studying the friction and wear
characteristics of sidewall surfaces is to determine the in uence of the geometries of
the surfaces forming the contact interface on the e ect of surface topography.
12.2 Microinstruments
The designs, actuation procedures and modeling of each of the seven types of
microinstruments included in the Test Platform are explained in detail in this study.
The details of the key features of all the (seven types of) microinstruments are suc-
cessfully highlighted in this study. Additionally, some of the microinstruments de-
veloped in this study are convincingly shown to overcome some of the limitations
of the previously reported corresponding microinstruments. Further, all the (seven
types of) microinstruments developed in this study are successfully used to investi-
gate two standard test surfaces, namely, surfaces coated with n-OTS (C18H37SiCl3)
SAM coating (i.e., hydrophobic surfaces) and surfaces having only a layer of native
oxide on them (i.e., hydrophilic surfaces). The results obtained are compared with
the corresponding results reported in literature. The comparisons substantiate the
consistency and reliability of the results obtained using the Test Platform developed
in this study. Additionally, the apparent work of adhesion of the OTS SAM coated
sidewalls, which has never been reported to-date, is obtained in this study using the
Sidewall Beam Array. The apparent work of adhesion of the OTS SAM coated side-
walls is 37.65  J/m2. Also, the engineering coe cients of static and kinetic friction
of the OTS SAM coated sidewalls, which have also never been reported to-date, are
obtained in this study using both the Sidewall Friction Tester as well as the Sidewall
Friction and Adhesion Tester. The mean engineering coe cients of static and kinetic
friction of the OTS SAM coated sidewalls are 0.15 and 0.11, respectively.
315
12.3 E ect of Surface Topography
The investigation conducted to study the e ect of surface topography reports
the successful use of a dodecanethiol-capped gold nanoparticle-based surface tex-
turing technique for tailoring the topographies of the surfaces (in-plane as well as
sidewall) of  ve Test Platform chips. Additionally, it reports the successful investi-
gation of six Test Platform chips ( ve textured using the dodecanethiol-capped gold
nanoparticle-based surface texturing technique and one untextured (control)) con-
ducted to understand the e ect that the surface topography of a surface has on its
tribological (i.e., stiction and friction) characteristics. The surface topographies of
the surfaces of each of the six Test Platform chips investigated in this study are char-
acterized qualitatively using SEM and quantitatively using AFM. The qualitative
characterization of the surface topographies of the surfaces of the six Test Platform
chips investigated in this study con rmed that while on the same Test Platform chip,
both the in-plane as well as sidewall surfaces have identical nanoparticle coatings on
them, the surfaces of di erent Test Platform chips have distinct surface topographies.
Additionally, it validated the hypothesis proposed in this study that the amount of the
nanoparticles that get deposited on the surface being textured can be controlled by
controlling the number density of the nanoparticle dispersion used. The quantitative
characterization of the surface topographies of the surfaces of the six Test Platform
chips investigated in this study is successfully used to quantify them in terms of two
measurable parameters, namely, the rms roughness and the surface coverage of the
interacting asperities present on the surface. Further, in order to understand the
e ects that the surface topography of a MEMS surface has on its stiction and fric-
tion characteristics, three important tribological properties of the surfaces of each of
the six Test Platform chips investigated in this study, which are the apparent work
of adhesion of the in-plane surfaces, the apparent work of adhesion of the sidewall
surfaces and the engineering coe cient of static friction of the sidewall surfaces, are
316
determined. The tribological characterization of the surfaces of the six Test Platform
chips investigated in this study provided an experimental con rmation of the already
believed theory that the friction experienced by contacting MEMS surfaces shows a
strong dependence on the stiction experienced by them. Additionally, it indicated
that both the micro-scale as well as the nano-scale topographies of a surface have a
strong in uence on its stiction and friction characteristics.
In order to mathematically correlate the surface topography of a surface with
its stiction and friction characteristics, a dimensionless parameter called Tribotopog-
raphy number (i.e.,  topo), which separately accounts for both the components that
de ne the rms roughness of a surface, and can be used to predict the e ect that the
surface topography of a surface will have on its stiction and friction characteristics,
is formulated in this study. Further, the Tribotopography number is successfully
used to develop two mathematical correlations, one between the surface topography
of a surface and its apparent work of adhesion, and the other between the surface
topography of a surface and the friction experienced by it. In order to use the two
mathematical correlations developed in this study for a particular type of surface, the
value of index  , which is the index of the denominator of the fraction that represents
the Tribotopography number, for that type of surface must be determined  rst. The
value of index  for silicon-type surfaces (i.e., surfaces, whose tribological behaviours
are governed by the same type of interfacial forces that govern the tribological be-
haviour of silicon surfaces) is determined in this study. This study also reports an
analysis (i.e., experimental validation), which substantiates the validities of the two
mathematical correlations developed to correlate the surface topography of a sur-
face with its stiction and friction characteristics, respectively. Additionally, it also
discusses the constraints, under which, the two mathematical correlations are valid.
The two mathematical correlations developed in this study can be used to quantita-
tively determine the e ect that the surface topography of a surface will have on its
317
stiction and friction characteristics. Lastly, in order to determine the in uence of the
geometry of the contact interface on the e ect that the surface topographies of the
surfaces forming the interface have on its tribological characteristics, the engineering
coe cients of static friction of the sidewall surfaces of all the six Test Platform chips
investigated in this study are determined using both the Sidewall Friction Testers
(SFTs) as well as the Sidewall Friction and Adhesion Testers (SFATs). The results
indicate that the geometry of the contact interface does not have any in uence on
the e ect that the surface topographies of the surfaces forming the interface have on
its tribological characteristics.
12.4 Other Results
Owing to the fact that the surface coverage of the coating can serve as an e ective
parameter in the comparison between the e ectivenesses of various nanoparticle-based
(sub-)monolayer coatings, this study also reports a simple experimental technique
based on optically determined resonance that can be used for determining the sur-
face coverage of the nanoparticle-based monolayer coatings used to texture MEMS
surfaces. The modeling as well as the experimental validation of the technique are
presented in the study. The factor that de nes the resolution of the technique is also
discussed in the study. Unfortunately, the technique presented in this study can be
used to determine the surface coverage of only sub-monolayer nanoparticle coatings.
The results obtained during the investigation of the e ect of surface topography
on the stiction and friction characteristics of a surface revealed that the e ectiveness
of AuNP-based surface texturing not only depends on the roughness of the uncoated
test surfaces but also depends strongly on the surface coverage of the coating (refer to
results reported in Chapter 9). Accordingly, a chapter in this study (i.e., chapter 11)
reports on a novel gold nanoparticle (AuNP) coating, which is deposited on micro-
electromechanical systems (MEMS) surfaces using the gas-expanded liquid technique,
318
and has the potential to be used as an alternative of OTS SAM for reducing the stic-
tion and friction experienced by them. A complete characterization of the AuNP
coating is presented in that chapter. The characteristics of the AuNP coating that
are characterized in chapter 11 include its topography in terms of surface coverage
and rms roughness, the reduced stiction experienced by the relatively smooth single
crystal silicon in-plane MEMS surfaces textured using it, its e ect on the stiction as
well as friction experienced sidewall surfaces and its apparent rupture strength. The
topographical characterization of the AuNP coating, which is accomplished using an
atomic force microscope, revealed that it signi cantly increased the roughnesses of
the surfaces coated with it. The surface coverage of the AuNP coating, which is
determined using Resonators, is determined to be 16 %. Additionally, the apparent
rupture strength of the AuNP coating is determined to be 500 kPa. The in-plane
surfaces coated with the AuNP coating exhibit a reduced apparent work of adhesion
of 32.16  3  J/m2, and the sidewall surfaces coated with it exhibit a reduced ap-
parent work of adhesion of 21.50  3  J/m2 and reduced engineering coe cients of
static and kinetic friction of 0.081 0.02 and 0.072  0.01, respectively. The AuNP
coating reduces the stiction experienced by the native oxide covered hydrophilic in-
plane surfaces by a factor of 1000, and that experienced by the native oxide covered
hydrophilic sidewall surfaces by a factor of 50.
Lastly, one of chapters of this study (i.e. chapter 7) reports on an experimental
requirement of the phase shifting interferometry, which is a technique widely used in
optical testing, and used in this study for determining the height pro les of actuated
cantilever beams. The chapter reports on a class of  ve frame interferogram-collecting
sequence, which, due to its mathematical equivalence with the one suggested by
Hariharan et al. and ease of execution, is more commonly used, but is much less
e ective in reducing the height pro le errors caused by phase step errors. It presents
a mathematical as well as experimental analysis of two distinct classes of the  ve
319
frame interferogram-collecting sequence used in PSI. The results clearly substantiate
the presence of signi cant errors in the PSI derived height pro les obtained using
a mathematically equivalent but experimentally di erent  ve frame interferogram-
collecting sequence (i.e., NH) than that suggested by Hariharan et al. (i.e., H). A
signi cantly high rms error of 90 nm was observed in the height pro le derived using
sequence NH when  was 60% of  . In contrast, sequence H made PSI extremely
less sensitive to  and even for a high  of 60%, a rms error of 6 nm, which is only
marginally greater than the maximum rms error due to vibrational disturbances, was
observed in the height pro le derived using it. Therefore, the  ve frame interferogram
collecting sequence for PSI should be selected cautiously, otherwise, the height pro les
derived can have signi cant errors in them.
320
Bibliography
[1] R. P. Feynman, There?s Plenty of Room at the Bottom [Data Storage], Journal
of Microelectromechanical Systems, 1(1), 60{66, 1992.
[2] K. Olukotun and L. Hammond, The Future of Microprocessors, Queue, 7(3),
26{29, 2005.
[3] J. J. Sniegowski and M. P. deBoer, IC-compatible Polysilicon Surface Micro-
machining, Annual Review of Materials Science, 30, 299{333, 2000.
[4] K. E. Petersen, Silicon As a Mechanical Material, in: Proceedings of the IEEE,
70(5), 420{457, 1982.
[5] R. S. Muller, Microdynamics, Sensors and Actuators A - Physical, 21(1-3),
1{8, 1990.
[6] W. R. Ashurst, Surface Engineering for MEMS Reliability, Ph. D. Dissertation,
University of California, Berkeley, CA, 2003.
[7] Micromechanical Sensors, MESA+, 1{20.
[8] S. Shelley, Nanosensors: Evolution, Not Revolution...Yet, CEP, 8{12, 2008.
[9] M. P. deBoer and T. M. Mayer, Tribology of MEMS, MRS Bulletin, 302{304,
2001.
[10] S. A. Henck, Lubrication of Digital Micromirror DevicesTM, Tribology Letters,
3(3), 239{247, 1997.
[11] D. M. Tanner, Reliability of Surface Micromachined Micromechanical Actua-
tors, Invited Keynote in: Proceedings of the 22nd International Conference in
Microelectronics, 97{104, 2000.
[12] B. Bhushan and V. N. Koinkar, Microtribological Studies of Doped Single-
crystal Silicon and Polysilicon Films for MEMS Devices, Sensors and Actuators
A - Physical, 57, 91{102, 1996.
[13] M. R. Houston, Surface Treatments for Adhesion Reduction in Polycrystalline
Micromechanical Devices, Ph. D. Dissertation, University of California, Berke-
ley, CA, 1996.
[14] http://mems.sandia.gov/gallery/images.html
321
[15] A. H. Auerbach, B. R. Soller and R. A. Peura, Sources of Error in Measuring
Tissue pH with Microsensors, in: Proceedings of the 1994 20th Annual Northeast
Bioengineering Conference, 108{109, 1994.
[16] J. Voldman, M. L. Gray and M. A. Schmidt, Microfabrication in Biology and
Medicine, Annual Review of Biomedical Engineering, 1, 401{425, 1999.
[17] K. C. Popat, R. W.?Robert and T. A. Desai, Characterization of Vapor De-
posited Thin Silane Films on Silicon Substrates for Biomedical Microdevices,
Surface & Coatings Technology, 154(2-3), 253{261, 2002.
[18] T. A. Desai, W. H. Chu, J. K. Tu, G. M. Beattie, A. Hayek and M. Ferrari, Mi-
crofabricated Immunoisolating Biocapsules, Biotechnology and Bioengineering,
57(1), 118{120, 1998.
[19] N. S. Peachey and A. Y. Chow, Subretinal Implantation of Semiconductor-
Based Photodiodes: Progress and Challenges... Journal of Rehabilitation Re-
search & Development, 36(4), 371{376, 1999.
[20] R. Bhandari, S. Negi, L. Rieth, R. A. Normann and F. Solzbacher, A Novel
Method of Fabricating Convoluted Shaped Electrode Arrays for Neural and
Retinal Prostheses, Sensors and Actuators A - Physical, 145, 123{130, 2008.
[21] S. Sundararajan and B. Bhushan, Static Friction and Surface Roughness
Studies of Surface Micromachined Electrostatic Micromotors Using an Atomic
Force/Friction Force Microscope. Journal of Vacuum Science Technology A,
19(4), 1777{1785, 2001.
[22] K. Kendall, Adhesion: Molecules and Mechanics, Science, 263(5154), 1720{
1725, 1994.
[23] S. J. Timpe and K. Komvopoulos, Microdevice for Measuring Friction and
Adhesion Properties of Sidewall Contact Interfaces of Microelectromechanical
Systems, Review of Scienti c Instruments, 78(6), 065106, 2007.
[24] K. M. Hurst, C. B. Roberts and W. R. Ashurst, A Gas-expanded Liquid
Nanoparticle Deposition Technique for Reducing the Adhesion of Silicon Mi-
crostructures, Nanotechnology, 20(18), 185303(9pp), 2009.
[25] S. Basu, A. Prabhakar and E. Bhattacharya, Estimation of Stiction Force
from Electrical and Optical Measurements on Cantilever Beams, Journal of
Microelectromechanical Systems, 16(5), 1254{1262, 2007.
[26] T. Manifar, A. Rezaee, M. Sheikhzadeh and S. Mittler, Formation of Uni-
form Self-assembly Monolayers by Choosing the Right Solvent: OTS on Silicon
Wafer, A Case Study, Applied Surface Science, 254(15), 4611{4619, 2008.
322
[27] F. W. DelRio, M. L. Dunn, B. L. Boyce, A. D. Corwin and M. P. deBoer, The
E ect of Nanoparticles on Rough Surface Adhesion, Journal of Applied Physics,
99, 104304(9pp), 2006.
[28] B. Bhushan, H. Liu and S. M. Hsu, Adhesion and Friction Studies of Silicon
and Hydrophobic and Low Friction Films and Investigation of Scale E ects,
Journal of Tribology, 126, 583{590, 2004.
[29] A. D. Corwin and M. P. deBoer, E ects of Adhesion on Dynamic and Static
Friction in Surface Micromachining, Applied Physics Letters, 84(13), 2451{2453,
2004.
[30] R. Maboudian and C. Carraro, Surface Chemistry and Tribology of MEMS,
Annual Review of Physical Chemistry, 55, 35{54, 2004.
[31] R. Maboudian, W. R. Ashurst and C. Carraro, Tribological Challenges in
Micromechanical Systems, Tribology Letters, 12(2), 95{100, 2002.
[32] Z. Rymuza, Control Tribological and Mechanical Properties of MEMS Surfaces,
Part 1: Critical Review, Microsystem Technologies: Micro- and Nanosystems-
Information Storage and Processing Systems, 5(4), 173{180, 1999.
[33] R. Legtenberg, H. Jansen, M. P. deBoer and M. Elwenspoek, Anisotropic
Reactive Ion Etching of Silicon Using SF6/O2/CHF3 Gas Mixtures, Journal of
The Electrochemical Society, 142(6), 2020{2028, 1995.
[34] B. du Bois, G. Vereecke, A. Witvrouw, P. De Moor, C. Van Hoof, A. de Causse-
maeker and A. Verbist, HF Etching of Si-Oxides and Si-Nitrides for Surface
Micromachining.
[35] W. R. Ashurst, C. Yau, C. Carraro, R. Maboudian and M. T. Dugger,
Dichlorodimethylsilane As an Anti-stiction Monolayer for MEMS: A Compari-
son to the Octadecyltrichlosilane Self-assembled Monolayer, Journal of Micro-
electromechanical Systems, 10(1), 41{49, 2001.
[36] H. Guckel, J. J. Sniegowski, T. R. Christenson, S. Mohney and T. F. Kelly,
Fabrication of Micromechanical Devices from Polysilicon Films with Smooth
Surfaces, Sensors and Actuators, 20(1-2), 117{122, 1989.
[37] W. R. Ashurst, C. Yau, C. Carraro, C. Lee, G. J. Kluth, R. T. Howe and
R. Maboudian, Alkene Based Monolayer Films as Anti-stiction Coatings for
Polysilicon MEMS, Sensors and Actuators A - Physical, 91(3), 239{248, 2001.
[38] T. M. Mayer, M. P. deBoer, N. D. Shinn, P. J. Clews and T. A. Michalske,
Chemical Vapor Deposition of Fluoroalkylsilane Monolayer Films for Adhesion
Control in Microelectromechanical Systems, Journal of Vacuum Science &
Technology B, 18(5), 2433{2440, 2000.
323
[39] M. Orpana and A. O. Korhonen, Control of Residual Stress of Polysilicon Thin
Films by Heavy Doping in Surface Micromachining, in: Proceedings of the
6th International Conference on Solid -State Sensors and Actuators, Transduc-
ers?91, 957{960, 1991.
[40] H. Guckel, J. J. Sniegowski, T. R. Christenson and F. Raissi, The Application of
Fine-grained, Tensile Polysilicon to Mechanically Resonant Transducers, Sen-
sors and Actuators A - Physical, 21(1-3), 346{351, 1990.
[41] R. T. Howe, Surface Micromachining for Microsensors and Microactuators,
Journal of Vacuum Science & Technology B, 6(6), 1809{1813, 1988.
[42] H. Sotobayashi, The Liga Process: Micromachining Techniques, Journal of
Photopolymer Science and Technology, 7(1), 1{16, 1994.
[43] Y. Hirata, H. Okuyama, S. Ogino, T. Numazawa and H. Takada, Piezoelec-
tric Composites for Micro-ultrasonic Transducers Realized with Deep-Etch X-
ray Lithography, in: Proceedings of IEEE Micro Electro Mechanical Systems,
MEMS ?95, 191{196, 1995.
[44] R. Legtenberg, E. Berenschot, M. Elwenspoek and J. H. Fluitman, A Fabri-
cation Process for Electrostatic Microactuators with Integrated Gear Linkages,
Journal of Microelectromechanical Systems, 6(3), 234{241, 1997.
[45] R. R. A. Syms, B. M. Hardcastle and R. A. Lawes, Bulk Micromachined Sil-
icon Comb-drive Electrostatic Actuators with Diode Isolation, Sensors and
Actuators A - Physical, 63(1), 61{67, 1997.
[46] R. Kondo, S. Takimoto, K. Suzuki and S. Sugiyama, High Aspect-ratio Electro-
static Micro Actuators Using LIGA Process, Microsystem Technologies, 6(6),
18{221, 2000.
[47] R. Abdolvand and F. Ayazi, An Advanced Reactive Ion Etching Process for
Very High Aspect-ratio Sub-micron Wide Trenches in Silicon, Sensors and
Actuators A - Physical, 144(1), 109{116, 2008.
[48] C. P. Demic, K. K. Chan and J. Blum,. Deep Trench Plasma-etching of Single-
crystal Silicon Using SF6/O2 Gas-mixtures, Journal of Vacuum Science &
Technology B, 10(3), 1105{1110, 1992.
[49] H. Rhee, H. Kwon, C. K. Kim, H. Kim, J. Yoo and Y. W. Kim, Comparison
of Deep Silicon Etching Using SF6/C4F8 and SF6/C4F6 Plasmas in the Bosch
Process, Journal of Vacuum Science & Technology B, 26(2), 576{581, 2008.
[50] K. W. Kok, W. J. Yoo, K. Sooriakumar, J. S. Pan and E. Y. Lee, Investigation of
In-situ Trench Etching Process and Bosch Process for Fabricating High Aspect-
ratio Beams for Microelectromechanical Systems, Journal of Vacuum Science
& Technology B, 20(5), 1878{1883, 2002.
324
[51] C. J. D. Craigie, T. Sheehan, V. N. Johnson, S. L. Burkett, A. J. Moll and
W. B. Knowlton, Polymer Thickness E ects on Bosch Etch Pro les, Journal
of Vacuum Science & Technology B, 20(6), 2229{2232, 2002.
[52] T. Syau, B. J. Baliga and R. W. Hamaker, Reactive Ion Etching of Silicon
Trenches Using SF6/O2 Gas Mixtures, Journal of The Electrochemical Society,
138(10), 3076{3081, 1991.
[53] O. W. Purbo, C. R. Selvakumar and D. Misra, Reactive Ion Etching of SOI
(SIMOX and ZMR) Silicon in Nitrogen Containing CF4 + O2 and SF6 + O2
Plasmas, Journal of The Electrochemical Society, 140(9), 2659{2668, 1993.
[54] W. R. Buchwald and K. Vaccaro, Sidewall Pro le Control of Thick Benzo-
cyclobutene Reactively Ion Etched in CF4/O2 Plasmas, Journal of Vacuum
Science & Technology B, 23(1), 51{56, 2005.
[55] V. B. Svetovoy, J. W. Berenschot and M. C. Elwenspoek, Precise Test of
the Di usion-Controlled Wet Isotropic Etching of Silicon via Circular Mask
Openings, Journal of The Electrochemical Society, 153(9), C641{C647, 2006.
[56] J. Anguita and F. Briones, HF/H2O Vapor Etching of SiO2 Sacri cial Layer
for Large-area Surface-micromachined Membranes, Sensors and Actuators A -
Physical, 64(3), 247{251, 1998.
[57] N. H. Tea, V. Milanovic, C. A. Zincke, J. S. Suehle, M. Gaitan, M. E. Zaghloul
and J. Geist, Hybrid Postprocessing Etching for CMOS-Compatible MEMS,
Journal of Microelectromechanical Systems, 6(4), 363{372, 1997.
[58] H. Robbins and B. Schwartz, Chemical Etching of Silicon 1. The system
HF,HNO3 and H2O, Journal of The Electrochemical Society, 106(6), 505{508,
1959.
[59] M. Elwenspoek, On The Mechanism of Anisotropic Etching of Silicon, Journal
of the Electrochemical Society, 140(7), 2075{2080, 1993.
[60] R. Houbertz, U. Memmert and R. J. Behm, On The Potential-dependent Etch-
ing of Si(111) in Aqueous NH4F Solution, Surface Science, 396(1-3), 198{211,
1998.
[61] J. Acker and A. Henssge, Chemical Analysis of Acidic Silicon Etch Solutions
II. Determination of HNO3, HF and H2SiF6 by Ion Chromatography, Talanta,
72(4), 1540{1545, 2007.
[62] M. P. Suarez, D. A. Mirabella and C. M. Aldao, Dynamics of Hillocks Formation
During Wet Etching, Journal of Molecular Catalysis A - Chemical, 281(1-2),
230{236, 2008.
[63] W. C. Tang, Electrostatic Comb Drive for Resonant Sensor and Actuator Ap-
plications, Ph. D. Dissertation, University of California, Berkeley, CA , 1990.
325
[64] M. R. Houston, R. T. Howe and R. Maboudian, Self-assembled Monolayer Films
as Durable Anti-stiction Coatings for Polysilicon Microstructures, in Technical
Digest: Proceedings of the 1996 Solid-State Sensor and Actuator Workshop,
Hilton Head, 42{47, 1996.
[65] S. T. Patton and J. S. Zabinski, Failure Mechanisms of a MEMS Actuator in
Very High Vacuum, Tribology International, 35(6), 373{379, 2002.
[66] K. Komvopoulos, Surface Engineering and Microtribology for Microelectrome-
chanical Systems, Wear, 200(1-2), 305{327, 1996.
[67] R. Maboudian and R. T. Howe, Critical Review: Adhesion in Surface Microme-
chanical Structures, Journal Of Vacuum Science & Technology B, 15(1), 1{20,
1997.
[68] R. Legtenberg. Electrostatic Actuators Fabricated by Surface Micromachining
Techniques, Ph. D. Dissertation, University of Twente, Netherlands, 1996.
[69] T. Abe, W. C. Messner and M. L. Reed, E ects of Elevated-temperature Treat-
ments in Microstructure Release Procedures, Journal Of Microelectromechani-
cal Systems, 4(2), 66{75, 1995.
[70] R. L. Alley, G. J. Cuan, R. T. Howe and K. Komvopoulos, The E ect of Release
Etch Processing on Surface Microstructure Stiction, in: Proc. of IEEE Solid
State Sensor and Actuator Workshop, Hilton Head, SC, 202{207, 1992.
[71] M. P. de Boer, J. A. Knapp, T. A. Michalske, U. Srinivasan and R. Maboudian,
Adhesion Hysteresis of Silane Coated Microcantilevers, Acta Materialia, 48(18-
19), 4531{4541, 2000.
[72] H. B. G. Casimir, On the Attraction Between two Perfectly Conducting Plates,
in: Proc. K. Ned. Akad. Wet., 51, 793{795, 1948.
[73] R. Maboudian and R. T. Howe, Stiction Reduction Processes for Surface Mi-
cromachines, Tribology Letters, 3(3), 215{221, 1997.
[74] R. Maboudian, Adhesion and Friction Issues Associated With Reliable Opera-
tion of MEMS, MRS Bulletin, 23(6), 47{51, 1998.
[75] N. Tas, T. Sonnenberg, H. Jansen, R. Legtenberg and M. Elwenspoek, Stiction
in Surface Micromachining, Journal of Micromechanics and Microengineering,
6(4),385{397, 1996.
[76] C. H. Mastrangelo, Adhesion-related Failure Mechanisms in Micromechanical
Devices, Tribology Letters, 3, 223{238, 1997.
[77] R. Maboudian, Surface Processes in MEMS Technology, Surface Science Re-
ports, 30, 207{269, 1998.
326
[78] W. R. Ashurst, M. P. de Boer, C. Carraro and R. Maboudian, An Investigation
of Sidewall Adhesion in MEMS, Applied Surface Science, 212, 735{741, 2003.
[79] T. Friedrich, C. Raudzis and R. Muller-Fiedler, Experimental Study of In-
plane and Out-of-plane Adhesions in Microelectromechanical Systems, Journal
of Microelectromechanical Systems, 18(6), 1326{1334, 2009.
[80] U. Srinivasan, M. R. Houston, R. T. Howe and R. Maboudian,
Alkyltrichlorosilane-based Self-assembled Monolayer Films for Stiction Reduc-
tion in Silicon Micromachines, Journal Of Microelectromechanical Systems,
7(2), 252{260, 1998.
[81] W. Y. Wang, Y. L. Wang, H. F. Bao, B. Xiong and M. H. Bao, Friction and
Wear Properties in MEMS, Sensors And Actuators A-Physical, 97-8, 486{491,
2002.
[82] S. L. Miller, J. J. Sniegowski, G. LaVigne and P. J. McWhorter, Friction in
Surface-micromachined Microengines, in: Proceeding of the SPIE, 2722, 197{
204, 1996.
[83] D. M. Tanner, W. M. Miller, K. A. Peterson, M. T. Dugger, W. P. Eaton,
L. W. Irwin, D. C. Senft, N. F. Smith, P. Tangyunyong and S. L. Miller, Fre-
quency Dependence of the Lifetime of a Surface Micromachined Microengine
Driving a Load, Microelectronics Reliability, 39(3), 401{414, 1999.
[84] J. A. Williams, Friction and Wear of Rotating Pivots in MEMS and Other
Small-scale Devices, Wear, 251, 965{972, 2001.
[85] D. C. Senft and M. T. Dugger, Friction and Wear in Surface Micromachined
Tribological Test Devices, in: Proceedings of SPIE, 3224, 31{38, 1997.
[86] C. L. Muhlstein, S. B. Brown and R. O. Ritchie, High-cycle Fatigue and Durabil-
ity of Polycrystalline Silicon Thin Films in Ambient Air, Sensors And Actuators
A-Physical, 94(3), 177{188, 2001.
[87] R. Ballarini, R. L. Mullen, Y. Yin, H. Kahn, S. Stemmer and A. H. Heuer, The
Fracture Toughness of Polysilicon Microdevices: A First Report, Journal Of
Materials Research, 12(4), 915{922, 1997.
[88] H. Kahn, N. Tayebi, R. Ballarini, R. L. Mullen and A. H. Heuer, Fracture
Toughness of Polysilicon MEMS Devices, Sensors And Actuators A-Physical,
82(1-3), 274{280, 2000.
[89] J. A. Connally and S. B. Brown, Slow Crack-growth in Single-crystal Silicon,
Science, 256(5063), 1537{1539, 1992.
[90] C. L. Muhlstein, S. B. Brown and R. O. Ritchie, High-cycle Fatigue of Single-
crystal Silicon Thin Films, Journal Of Microelectromechanical Systems, 10(4),
593{600, 2001.
327
[91] C. L. Muhlstein, E. A. Stach and R. O. Ritchie, Mechanism of Fatigue in
Micron-scale Films of Polycrystalline Silicon for Microelectromechanical Sys-
tems, Applied Physics Letters, 80(9), 1532{1534, 2002.
[92] C. L. Muhlstein, E. A. Stach and R. O. Ritchie, A Reaction-layer Mechanism
for the Delayed Failure of Micron-scale Polycrystalline Silicon Structural Films
Subjected to High-cycle Fatigue Loading. Acta Materialia, 50(14), 3579{3595,
2002.
[93] G. T. Mulhern, D. S. Soane and R. T. Howe, Supercritical Carbondioxide
Drying of Microstructures, in: Proceedings of International Conference on Solid
State Sensors and Actuators, Transducers?93, 296{299, 1993.
[94] C. H. Mastrangelo and G.S. Saloka, A Dry-release Method Based on Polymer
Columns for Microstructure Fabrication, in: Proceedings of the IEEE Micro-
electroMechanical Systems Workshop, 77{81, 1993.
[95] M. O enberg, B. Elsner and F. Laermer, Vapor HF Etching for Sacri cial Oxide
Removal in Surface Micromachining, in: Technical Digest of the Electrochemical
(Fall Meeting),1056{1057, 1994.
[96] F. Kozlowski, N. Lindmair, T. Scheiter, C. Hierold and W. Lang, A Novel
Method to Avoid Sticking of Surface Micromachined Structures, in: Proceed-
ings of the 8th International Conference on Solid-State Sensors and Actuators
Transducers?95, 1, 220{223, 1995.
[97] J. H. Lee, H. H. Chung, S. Y. Kang, J. T. Baek and H. J. Yoo, Fabrication of
Surface Micromachined Polysilicon Actuators Using Dry-release Process of HF
Gas-phase Etching, in: Technical Digest of the International Electron Devices
Meeting, 761{764, 1996.
[98] R. L. Alley, P. Mai, K. Komvopoulos and R. T. Howe, Surface Roughness
Modi cation of Interfacial Contacts in Polysilicon Microstructures, in: Trans-
ducers?93, 288{291, 1993.
[99] U. Srinivasan, M. R.Houston, R. T.Howe and R. Maboudian, Self-assembled
Fluorocarbon Coatings for Enhanced Stiction Reduction, in: Proceedings of the
9th International Conference on Solid State Sensors and Actuators, Transduc-
ers?97, 2, 1399{1402, 1997.
[100] M. R. Houston, R. T. Howe and R. Maboudian, E ect of Hydrogen Termina-
tion on the Work of Adhesion Between Rough Polycrystalline Silicon Surfaces,
Journal of Applied Physics, 81(8), 3474{3483, 1997.
[101] M. R. Houston, R. Maboudian and R. T. Howe, Ammonium Fluoride Anti-
stiction Treatments for Polysilicon Microstructures, in: Proceedings of the 8th
International Conference on Solid State Sensors and Actuators, Transducers?95,
1, 210{213, 1995.
328
[102] P. F. Man, B. P. Gogo and C. H. Mastrangelo, Elimination of Post-release
Adhesion in Microstructures Using Conformal Fluorocarbon Coatings, Journal
of Microelectromechanical Systems, 6(1), 25{34, 1997.
[103] B. K. Smith, J. J. Sniegowski and G. LaVigne, Thin Te on-like Films for
Eliminating Adhesion in Released Polysilicon Microstructures, in: Proceedings
of International Conference on Solid State Sensors and Actuators, Transduc-
ers?97, 1, 245{248, 1997.
[104] W. R. Ashurst, C. Carraro, R. Maboudian and W. Frey, Wafer Level Anti-
stiction Coatings for MEMS, Sensors and Actuators A-Physical, 104(3), 213{
221, 2003.
[105] B. H. Kim, T. D. Chung, C. H. Oh and K. Chun, A New Organic Modi er for
Anti-stiction, Journal of Microelectromechanical Systems, 10(1), 33{40, 2001.
[106] M. R. Linford, P. Fenter, P. M. Eisenberger and C. E. D. Chidsey, Alkyl Mono-
layers on Silicon Prepared from 1-alkenes and Hydrogen-terminated Silicon,
Journal of the American Chemical Society, 117(11),3145{3155, 1995.
[107] R. Maboudian, W. R.Ashurst and C. Carraro, Self-assembled Monolayers as
Anti-stiction Coatings for MEMS: Characteristics and Recent Developments,
Sensors and Actuators A-Physical, 82(1-3), 219{223, 2000.
[108] M. G. Lim, J. C. Chang, D. P. Schultz, R. T. Howe and R. M. White, Polysilicon
Microstructures to Characterize Static Friction, in: Proceedings of the Micro
Electro Mechanical Systems ?1990: An Investigation of Micro Structures, Sen-
sors, Actuators, Machines and Robots, 82{88, 1990.
[109] B. Bhushan, Nanotribology and Nanomechanics of MEMS Devices, in: Pro-
ceedings of IEEE ?1996, 91{98, 1996.
[110] K. Deng, R. J. Collins, M. Mehregany and C. N. Sukenik, Performance Impact
of Monolayer Coating of Polysilicon Micromotors, in: Proceedings of IEEE
Micro Electro Mechanical Systems Workshop, 368{373, 1995.
[111] U. Srinivasan, J. D. Foster, U. Habib, R. T. Howe, R. Maboudian, D. C. Senft
and M. T. Dugger, Lubrication of Polysilicon Micomechanisms with Self-
assembled Monolayers, in Technical Digest: Proceedings of the 1998 Solid -
State Sensor and Actuator Workshop, Hilton Head ?98, 156{161, 1998.
[112] C. Cabuz, E. I. Cabuz, E. R. Ohnstein, J. Neus and R. Maboudian, High
Reliability Touch-mode Electrostatic Actuators (TMEA), in Technical Digest:
Proceedings of the Solid-State Sensor and Actuator Workshop, Hilton Head ?98,
296{299, 1998.
[113] C. Cabuz, E. I. Cabuz, T. R. Ohnstein, J. Neus and R. Maboudian, Factors
Enhancing the Reliability of Touch-mode Electrostatic Actuators, Sensors and
Actuators A-Physical, 79(3), 245{250, 2000.
329
[114] M. M. Sung, C. Carraro, O. W. Yauw, Y. Kim and R. Maboudian, Reversible
Liquid-liquid Transitions in the Early Stages of Monolayer Self-assembly, Jour-
nal of Physical Chemistry B, 104(7), 1556{1559, 2000.
[115] C. Carraro, O. W. Yauw, M. M. Sung and R. Maboudian, Observation of
Three Growth Mechanisms in Self-assembled Monolayers, Journal of Physical
Chemistry B, 102(23), 4441{4445, 1998.
[116] D. K. Schwartz, Mechanisms and Kinetics of Self-assembled Monolayer Forma-
tion, Annual Review of Physical Chemistry, 52, 107{137, 2001.
[117] P. Cl echet, C. Martelet, M. Belin, H. Zarrad, N. Ja rezicrenault and S. Fayeulle,
Lubrication of Silicon Micromechanisms by Chemical Grafting of Long-chain
Molecules, Sensors and Actuators A-Physical, 44(1), 77{81, 1994.
[118] R. Banga, J. Yarwood, A. M. Morgan, B. Evans and J. Kells, FTIR and
AFM Studies of the Kinetics and Self-assembly of Alkyltrichlorosilanes and
(Per uoroalkyl)trichlorosilanes onto Glass and Silicon, Langmuir, 11(11), 4393{
4399, 1995.
[119] J. B. Brzoska, I. Benazouz and F. Rondelez, Silanization of Solid Substrates -
A Step Toward Reproducibility, Langmuir, 10(11), 4367{4373, 1994.
[120] B. C. Bunker, R. W. Carpick, R. A. Assink, M. L. Thomas, M. G. Hankins,
J. A. Voigt, D. Sipola, M. P. de Boer and G. L. Gulley, The Impact of Solu-
tion Agglomeration on the Deposition of Self-assembled Monolayers, Langmuir,
16(20), 7742{7751, 2000.
[121] A. Bansal, X. L. Li, I. Lauermann, N. S. Lewis, S. I. Yi and W. H. Weinberg,
Alkylation of Si Surfaces Using a Two-step Halogenation Grignard Route, Jour-
nal of the American Chemical Society, 118(30),7225{7226, 1996.
[122] W. F. Bergerson, J. A. Mulder, R. P. Hsung and X. Y. Zhu, Assembly of
Organic Molecules on Silicon Surfaces via the Si-N Linkage, Journal of the
American Chemical Society, 121(2), 454{455, 1999.
[123] X. Y. Zhu and J. E. Houston, Molecular Lubricants for Silicon-based Microelec-
tromechanical Systems (MEMS): A Novel Assembly Strategy, Tribology Letters,
7(2-3), 87{90, 1999.
[124] X. Y. Zhu, J. A. Mulder and W. F. Bergerson, Chemical Vapor Deposition of
Organic Monolayers on Si(100) via Si-N Linkages, Langmuir, 15(23), 8147{8154,
1999.
[125] X. Y. Zhu, V. Boiadjiev, J. A. Mulder, R. P. Hsung and R. C. Major, Molecular
Assemblies on Silicon Surfaces via Si-O Linkages, Langmuir, 16(17), 6766{6772,
2000.
330
[126] D. B. Asay, M. T. Dugger and S. H. Kim, In-situ Vapor-phase Lubrication of
MEMS, Tribology Letters, 29(1), 67{74, 2008.
[127] Y. Yee, K. Chun, J. D. Lee and C. J. Kim, Polysilicon Surface-modi cation
Technique to Reduce Sticking of Microstructures, Sensors And Actuators A-
Physical, 52(1-3), 145{150, 1996.
[128] D. B. Asay, M. T. Dugger, J. A. Ohlhausen and S. H. Kim, Macro- to-nanoscale
Wear Prevention via Molecular Adsorption, Langmuir, 24(1), 155{159, 2008.
[129] M. C. McLeod, M. Anand, C. L. Kitchens C. B. Roberts, Precise and Rapid
Size Selection and Targeted Deposition of Nanoparticle Populations Using CO2
Gas Expanded Liquids, Nano Letters, 5(3), 461{465, 2005.
[130] N. Ansari, K. M. Hurst and W. R. Ashurst, Surface Texturing Using Gold
Nanoparticles to Reduce Adhesion in MEMS, in T. Proulx (Ed.), MEMS and
Nanotechnology, Volume 2: Proceedings of 2010 SEM Annual Conference on
Experimental and Applied Mechanics, Springer, New York, 1st edition, 181{
188, 2011.
[131] S. T. Patton, W. D. Cowan, K. C. Eapen and J. S. Zabinski, E ect of Surface
Chemistry on the Tribological Performance of a MEMS Electrostatic Lateral
Output Motor, Tribology Letters, 9(3), 199{209, 2001.
[132] N. Rajan, C. A. Zorman, M. Mehregany, R. DeAnna and R. Harvey, Perfor-
mance of 3C-SiC Thin Films as Protective Coatings for Silicon-micromachined
Atomizers, Thin Solid Films, 315(1-2), 170{178, 1998.
[133] M. Mehregany, C. A. Zorman, N. Rajan and C. H. Wu, Silicon Carbide MEMS
for Harsh Environments, Proceedings of the IEEE, 86(8), 1594{1610, 1998.
[134] C. R. Stoldt, M. C. Fritz, C. Carraro and R. Maboudian, Micromechanical
Properties of Silicon-carbide Thin Films Deposited Using Single-source Chem-
ical Vapor Deposition, Applied Physics Letters, 79(3), 347{349, 2001.
[135] C. R. Stoldt, C. Carraro, W. R. Ashurst, D. Gao, R. T. Howe and
R. Maboudian, A Low-temperature CVD Process for Silicon Carbide MEMS,
Sensors and Actuators A-physical, 97(8), 410{415, 2002.
[136] K. W. Lee, K. S. Yu and Y. Kim, Heteroepitaxial Growth of 3C-SiC on Si(001)
Without Carbonization, Journal of Crystal Growth, 179(1-2), 153{160, 1997.
[137] K. W. Lee, K. S. Yu, J. H. Boo, Y. Kim, T. Hatayama, T. Kimoto and H. Mat-
sunami, Epitaxial Growth of Cubic SiC Films on Si Substrates by High Vacuum
Chemical Vapor Deposition Using 1,3-disilabutane, Journal of the Electrochem-
ical Society, 144(4), 1474{1476, 1997.
331
[138] L. Moro, A. Paul, D. C. Lorents, R. Malhotra, R. S. Ruo , P. Lazzeri,
L. Vanzetti, A. Lui and S. Subramoney, Silicon Carbide Formation by An-
nealing C-60 Films on Silicon, Journal of Applied Physics, 81(9), 6141{6146,
1997.
[139] M. De Seta, N. Tomozeiu, D. Sanvitto and F. Evangelisti, SiC Formation on
Si(100) via C-60 Precursors, Surface Science, 460(1-3), 203{213, 2000.
[140] S. Sundararajan and B. Bhushan, Micro/Nanotribological Studies of Polysilicon
and SiC Films for MEMS Applications, Wear, 217(2), 251{261, 1998.
[141] J. Wu, S. Wang and J. M. Miao, A MEMS Device for Studying the Friction Be-
havior of Micromachined Sidewall Surfaces, Journal of Microelectromechanical
Systems, 17(4), 921{933, 2008.
[142] S. J. Timpe and K. Komvopoulos, Experimental Study of Sidewall Adhesion in
Microelectromechanical Systems, Journal of Microelectromechanical Systems,
14(6),1356{1363, 2005.
[143] S. J. Timpe, D. H. Alsem, D. A. Hook, M. T. Dugger and K. Komvopoulos,
Wear of Polysilicon Surface Micromachines Operated in High Vacuum, Journal
of Microelectromechanical Systems, 18(2), 229{238, 2009.
[144] D. H. Alsem, M. T. Dugger, E. A. Stach and R. O. Ritchie, Micron-scale Friction
and Sliding Wear of Polycrystalline Silicon Thin Structural Films in Ambient
Air, Journal of Microelectromechanical Systems, 17(5), 1144{1154, 2008.
[145] W. M. van Spengen and J. W. M. Frenken, The Leiden MEMS Tribometer:
Real-time Dynamic Friction Loop Measurements with an On-chip Tribometer,
Tribology Letters, 28(2), 149{156, 2007.
[146] D. Kim, D. Cao, M. D. Bryant, W. J. Meng and F. F. Ling, Tribological Study
of Microbearings for MEMS Applications, Journal of Tribology-transactions of
the ASME, 127(3),537{547, 2005.
[147] E. E. Flater, A. D. Corwin, M. P. de Boer and R. W. Carpick, In-situ Wear
Studies of Surface Micromachined Interfaces Subject to Controlled Loading,
Wear, 260(6), 580{593, 2006.
[148] L. M. Phinney, G. Lin, J. Wellman and A. Garcia, Surface Roughness Mea-
surements of Micromachined Polycrystalline Silicon Films. Journal of Microme-
chanics and Microengineering, 14, 927{931, 2004.
[149] B. D. Jensen, M. P. de Boer, N. D. Masters, F. Bitsie and D. A. LaVan, In-
terferometry of Actuated Microcantilevers to Determine Material Properties
and Test Structure Nonidealities in MEMS, Journal of Microelectromechanical
Systems, 10(3), 336{346, 2001.
332
[150] N. R. Tas, C. Gui and M. Elwenspoek, Static Friction in Elastic Adhesion
Contacts in MEMS, Journal of Adhesion Science and Technology, 17(4), 547{
561, 2003.
[151] J. Wu, S. Wang and J. M. Miao, Friction Characteristics of the Curved Side-
wall Surfaces of a Rotary MEMS Device in Oscillating Motion, Journal of
Micromechanics and Microengineering, 19(6),065020, 2009.
[152] M. P. de Boer and T. A. Michalske, Accurate Method for Determining Adhesion
of Cantilever Beams, Journal of Applied Physics, 86(2), 817{827, 1999.
[153] M. B. Sinclair, M. P. de Boer and A. D. Corwin, Long-working-distance
Incoherent-light Interference Microscope, Applied Optics, 44(36), 7714{7721,
2005.
[154] P. T. Jones, The Fracture Strength of Brittle Films for Micro-Electro-
Mechanical Systems (MEMS) Devices. PhD Dissertation, University of Cali-
fornia at Berkeley, 1999.
[155] C. H. Mastrangelo and C. H. Hsu, A Simple Experimental Technique for the
Measurement of the Work of Adhesion of Microstructures, in Technical Digest:
IEEE Solid-State Sensor and Actuator Workshop, 1992, 208{212, 1992.
[156] K. M. Hurst, N. Ansari, C. B. Roberts and W. R. Ashurst, Self-assembled
Monolayer-immobilized Gold Nanoparticles as Durable, Anti-stiction Coatings
for MEMS, Journal of Microelectromechanical Systems, 20(2), 424{435, 2011.
[157] Z. Rymuza, M. Misiak, L. Kuhn, K. Schmidt-Szalowski and Z. Rzanek-Boroch,
Control Tribological and Mechanical Properties of MEMS Surfaces, part 2:
Nanomechanical Behavior of Self-lubricating Ultrathin Films, Microsystem
Technologies, 5(4), 181{188, 1999.
[158] B. D. Jensen, F. Bitsie and M. P. deBoer, Interferometric Measurement for
Improved Understanding of Boundary E ects in Micromachined Beams, Mi-
cromachining and Microfabrication, 3875, 61{72, 1999.
[159] W. M. van Spengen, E. Bakker and J. W. M. Frenken, A ?nano-battering ram?
for Measuring Surface Forces: Obtaining Force-distance Curves and Sidewall
Stiction Data with a MEMS Device, Journal of Micromechanics and Micro-
engineering, 17(7), S91{S97, 2007.
[160] M. Mehregany, S. D. Senturia and J. H. Lang, Friction and Wear in Microfab-
ricated Harmonic Side-drive Motors, in Technical Digest: Solid-State Sensor
and Actuator Workshop, 17{22, 1990.
[161] S. L. Miller, G. LaVigne, M. S. Rodgers, J. J. Sniegowski, J. P. Waters and
P. J. McWhorter, Routes to Failure in Rotating MEMS Devices Experiencing
Sliding Friction, in: Proceedings of SPIE: Micromachined Devies and Compo-
nents III, 3224, 24{30, 1997.
333
[162] S. J. Timpe and K. Komvopoulos, The E ect of Adhesion on the Static Friction
Properties of Sidewall Contact Interfaces of Microelectromechanical Devices,
Journal of Microelectromechanical Systems, 15(6), 1612{1621, 2006.
[163] Z. Guo, Y. Meng, H. Wu, C. Su and S. Wen, Measurement of Static and Dy-
namic Friction Coe cients of Sidewalls of Bulk-microfabricated MEMS Devices
with an On-chip Micro-tribotester. Sensors and Actuators A: Physical, 135(2),
863{869, 2007.
[164] R. Prasad, N. MacDonald and D. Taylor, Micro-instrumentation for Tribolog-
ical Measurement, in: Proceedings of the Solid-State Sensors and Actuators
Workshop, 1995 and Eurosensors IX..Transducers ?95, 2, 52{55, 1995.
[165] I. H. Hwang, Y. G. Lee and J. H. Lee, A Micromachined Friction Meter for
Silicon Sidewalls with Consideration of Contact Surface Shape, Journal of
Micromechanics and Microengineering, 16, 2475{2481, 2006.
[166] S. Ren, S. Yang, Y. Zhao, J. Zhou, T. Xu and W. Liu, Friction and Wear
Studies of Octadecyltrichlorosilane SAM on Silicon, Tribology Letters, 13, 233{
239, 2002.
[167] M. B. Sigman, A. E. Saunders and B. A. Korgel, Metal Nanocrystal Superlattice
Nucleation and Growth, Langmuir, 20(3), 978{983, 2004.
[168] R. J. Good and R. R. Stromberg, editors, Surface and Colloid Science, volume
II - Experimental Methods, Plenum Press, New York, 1979.
[169] I. Ohl idal and D. Franta, Ellipsometry of Thin Film Systems, In Progress In
Optics, 41, E. Wolf (ed.), 181{282, 2000.
[170] P. R. Gri ths and J. A. DeHaseth, Fourier Transform Infrared Spectrometry,
in: Chemical Analysis: A Series of Monographs on Analytical Chemistry and
its Applications Series, J. D. Winefordner (ed.), John Wiley & Sons, Inc., New
Jersey, 2007.
[171] G. Binnig, C. F. Quate and C. Gerber, Atomic Force Microscope, Physical
Review Letters, 56(9), 930{933, 1986.
[172] D. Bonnell (ed.), Scanning Probe MIcroscopy and Spectrometry: Theory, Tech-
niques and Applications, John Wiley & Sons, Inc., second edition, 2000.
[173] C. L. Kitchens, Metallic Nanoparticle Synthesis Within Reverse Miscellar
Microemulsion Systems, Ph. D. dissertation, Auburn University, Auburn, 2004.
[174] C. T. Farrell and M. A. Player, Phase-step Insensitive Algorithms for Phase-
shifting Interferometry, Meas. Sci. Technol., 5, 648{652, 1994.
[175] K. M. Hurst, C. B. Roberts and W. R. Ashurst, A New Method to Deter-
mine Adhesion of Cantilever Beams Using Beam Height Experimental Data,
Tribology Letters, 35, 9{15, 2009.
334
[176] P. Hariharan, B. F. Oreb and T. Eiju, Digital Phase-shifting Interferometry:
A Simple Error-compensating Phase Calculation Algorithm, Applied Optics,
26(13), 2504{2506, 1987.
[177] C. P. Chen and M. H. Leipold, Fracture Toughness of Silicon, Ceramic Bulletin,
59(4), 1980.
[178] J. F. Nye, Physical Properties of Crystals, Oxford University Press, Oxford,
1985.
[179] S. J. Timpe, D. A. Hook, M. T. Dugger and K. Komvopoulos, Levitation Com-
pensation Method for Dynamic Electrostatic Comb-drive Actuators, Sensors
and Actuators A-physical, 143(2), 383{389, 2008.
[180] B. Halg, On a Non-volatile Memory Cell based on Micro-electro-mechanics, in:
Proceedings of Micro-electromechanical Systems, MEMS?90: An Investigation
of Microstructures, Sensors, Actuators, Machines and Robots, Napa Valley, CA,
172{176, 1990.
[181] B. Rashidian and M. G. Allen, Electrothermal Microactuators based on Di-
electric Loss Heating, in: Proceedings of Micro-electromechanical Systems,
MEMS?93: An Investigation of Micro-structures, Sensors, Actuators, Machines
and Systems, Florida, 24-29, 1993.
[182] M. Tae and Kim, In uence of Substrates on the Elastic Reaction of Films for
the Micro-indentation Tests, Thin Solid Films, 283(1-2), 12{16, 1996.
[183] D. J. Eaglesham, A. E. White, L. C. Feldman, N. Moriya and D. C. Jacobson,
Equilibrium Shape of Si, Physical Review Letters, 70(11), 1643{1646, 1993.
[184] R. J. Needs and M. Mans eld, Calculation of the Surface Stress Tensor and
Surface Energy of the (111) Surfaces of Iridium, Platinum and Gold. Journal
of Physics:Condensed Matter, 1, 7555{7563, 1989.
[185] J. N. Israelachvili, Van derWaals Forces Between Surfaces, Intermolecular and
Surface Forces, Academic Press, 2nd edition, 176{209, 1992.
[186] D. Bargeman and F. V. Vader, Van derWaals Forces Between Immersed Parti-
cles, Journal of Electroanalytical Chemistry, 37, 45{52, 1972.
[187] K. W. Bewig and W. A. Zisman, The Wetting of Gold and Platinum by Water,
The Journal of Physical Chemistry, 69(12), 4238{4242, 1965.
[188] C. Gui, M. Elwenspoek, N. Tas and J. G. E. Gardeniers, The E ect of Surface
Roughness on Direct Wafer Bonding, Journal of Applied Physics, 85(10), 7448{
7454, 1999.
[189] D. Xu, K. M. Liechti and K. Ravi-Chander, On the Modi ed Tabor Parameter
for the JKR-DMT Transition in the Presence of a Liquid Meniscus, Journal of
Colloid and Interface Science, 315, 772{785, 2007.
335
[190] K. N. Gui and T. Fuller, The E ect of Surface Roughness on the Adhesion
of Elastic Solids, in: Proceedings of the Royal Society of London, Series A:
Mathematical and Physical Sciences, 345, 327{342, 1975.
[191] A. Fogden and L. R. White, Contact Elasticity in the Presence of Capillary
Condensation: I. The Nonadhesive Hertz Problem, Journal of Colloid and
Interface Science, 138(2), 414{430, 1990.
[192] D. Maugis and B. Gauthier-Manuel, JKR-DMT Transition in the Presence of
Liquid Meniscus, Journal of Adhesion Science and Technology, 8(11), 1311{
1322, 1994.
336
Appendices
337
Appendix A
Scripts Used for Actuating the Microinstruments
The following sections present the various scripts that are used to automate the
actuation of the microinstruments of the test platform as well as to collect the data
needed to study the tribological characteristics of its test surfaces. A brief description
of the tasks performed by each script is given in quotes following the command desc,
at the beginning of that script. The statements preceded by \apostrophes" (i.e., \ ?
") in the scripts are not executed by the scripting environment. They are comments
that describe the actions taken by the set of commands following them. The scripting
environment used to execute the scripts is called MEMScript.
A screen shot of the user interface of MEMScript is shown in Figure A.1. The
prominent  elds of the user interface are clearly labelled in Fig. A.1. The  eld labelled
\Script Selection Window" allows the user to select and load the desired script into the
scripting environment. In Fig. A.1, the script named \MST Actuation.stp" is loaded
in the scripting environment. The  eld labelled \Description Window" displays a brief
description of the tasks performed by the script loaded in the scripting environment.
The  eld labelled \Status Window" displays the current status of the script being
executed. It also displays instructions for the user if the user is suppose to take any
action. The  eld labelled \Input Window" allows the user to assign values to the
variables that can be inputted for the script loaded in the scripting environment.
Figure A.1 indicates that the script \MST Actuation.stp" allows the user to input
the basename of the data  les created by it, the gain of the voltage ampli er used
and the no. of 0.5 V increments that should be applied to the open-loop piezo used to
actuate the MST. The  eld labelled \Image Window" displays either a live or a still
image of the microinstrument that is being actuated or analyzed. In Fig. A.1, a live
image of the MST that is being actuated is displayed in the \Image Window". The
 eld labelled \Output Window" displays the plots generated as well as the variables
determined or monitored by the script that is being executed. In Fig. A.1, a plot of
displacement of the MST that is being actuated versus voltage applied to the open-
loop piezo used to actuate it is displayed in the \Output Window". The exact values
of the voltages applied to the open-loop piezo as well as of the corresponding x (i.e.,
axial) and y (i.e., lateral) displacements of the actuated MST are also displayed in
the \Output Window".
A.1 Script Name: RST Analysis.stp
?The following set of commands declares the variables that can be
?inputted by the user
338
Description Window
Script Selection WindowStatus WindowInput Window
Output Window Image Window
Figure A.1: A screenshot of the user-interface of MEMScript.
339
ustring basename, "RST_samplereferenceno", "Base of filenames"
uglobal status, 0, "0_analy 1_BR_img 2_AR_img"
desc "This script determines the in-plane"
desc "rotation of the Residual Stress Tester"
desc "and calc. the associated residual stress"
desc "present in the device layer film."
desc " "
desc "Created by Naveed - 04/20/09"
include init.mac
begin
call init
?The following set of commands declares the variables used in the
?script
alloc x_disp
alloc y_disp
alloc x_pos_diff_ini
alloc y_pos_diff_ini
alloc x_pos_diff_final
alloc y_pos_diff_final
alloc substrate_x_pos
alloc substrate_y_pos
alloc device_x_pos
alloc device_y_pos
alloc arc
alloc theta_one_end
string fname
string msg
array data_x_pos
array data_y_pos
print "Scale = ", scale,"microns/pixel"
?The following section asks the user to focus on appropriate
?patterns of an unreleased RST and collects optical images of the
?same
if (status == 1)
{
let msg = "Place 1 end of RST in the FOV"
340
msgbox msg
let fname = basename, "_end1_before_release.tif"
wait
snap
wrtimgt fname
let msg = "Place other end in the FOV"
msgbox msg
let fname = basename, "_end2_before_release.tif"
wait
snap
wrtimgt fname
}
?The following set of commands asks the user to focus on the same
?patterns of the RST as used in the previous section but after
?releasing the RST and collects optical images of the same
if (status == 2)
{
let msg = "Place 1 end of RST in the FOV"
msgbox msg
let fname = basename, "end1_after_release.tif"
wait
snap
wrtimgt fname
let msg = "Place other end in the FOV"
msgbox msg
let fname = basename, "end2_after_release.tif"
wait
snap
wrtimgt fname
}
if (status == 0)
{
?The following set of commands asks the user to select the anchored
?and movable patterns at one end on the optical image of the
?unreleased RST and determines the initial position of the movable
?pattern
let fname = basename, "end1_before_release.tif"
rdimg fname
let msg = "Select ROI & then pattern on substrate"
msgbox msg
pattern substrate
let pname = basename,"_substrate.png"
pattern_save substrate, pname
341
let msg = "Select ROI & then pattern on the unreleased device"
msgbox msg
pattern device
let pname = basename,"_device.png"
pattern_save device, pname
match substrate, substrate_x_pos, substrate_y_pos
match device, device_x_pos, device_y_pos
let x_pos_diff_ini = substrate_x_pos - device_x_pos
let y_pos_diff_ini = substrate_y_pos - device_y_pos
print "x_pos_diff_ini1 =", x_pos_diff_ini, "micron"
print "y_pos_diff_ini1 =", y_pos_diff_ini, "micron"
?The following set of commands determines the final position of the
?movable pattern and the in-plane rotation of that end of the
?released RST
let fname = basename, "end1_after_release.tif"
rdimg fname
match substrate, substrate_x_pos, substrate_y_pos
match device, device_x_pos, device_y_pos
let x_pos_diff_final = substrate_x_pos - device_x_pos
let y_pos_diff_final = substrate_y_pos - device_y_pos
let x_disp = x_pos_diff_final - x_pos_diff_ini
let y_disp = y_pos_diff_final - y_pos_diff_ini
print "x_pos_diff_final1 =", x_pos_diff_final, "micron"
print "y_pos_diff_final1 =", y_pos_diff_final, "micron"
print "x_disp1 =", x_disp, "micron"
print "y_disp1 =", y_disp, "micron"
let arc = (((x_disp^2)+(y_disp^2))^0.5)
let theta_end1 = arc*360/2/3.1415/x_pos_diff_ini
print "theta_end1 =" arc, "degrees"
?The following set of commands select the anchored and movable
?patterns at the other end on the optical image of the unreleased
?RST and determines the initial position of the movable pattern
let fname = basename, "end2_before_release.tif"
rdimg fname
match substrate, substrate_x_pos, substrate_y_pos
match device, device_x_pos, device_y_pos
let x_pos_diff_ini = substrate_x_pos - device_x_pos
let y_pos_diff_ini = substrate_y_pos - device_y_pos
print "x_pos_diff_ini2 =", x_pos_diff_ini, "micron"
print "y_pos_diff_ini2 =", y_pos_diff_ini, "micron"
?The following set of commands determines the final position of the
?movable pattern and the in-plane rotation of that end of the
342
?released RST
let fname = basename, "end2_after_release.tif"
rdimg fname
match substrate, substrate_x_pos, substrate_y_pos
match device, device_x_pos, device_y_pos
let x_pos_diff_final = substrate_x_pos - device_x_pos
let y_pos_diff_final = substrate_y_pos - device_y_pos
let x_disp = x_pos_diff_final - x_pos_diff_ini
let y_disp = y_pos_diff_final - y_pos_diff_ini
let arc = (((x_disp^2)+(y_disp^2))^0.5)
let theta_end2 = arc*360/23.1415/x_pos_diff_ini
print "x_pos_diff_final2 =", x_pos_diff_final, "micron"
print "y_pos_diff_final2 =", y_pos_diff_final, "micron"
print "x_disp2 =", x_disp, "micron"
print "y_disp2 =", y_disp, "micron"
print "theta_end2 =", theta_end2, "degrees."
}
A.2 Script Name: MST Actuation.stp
?The following set of commands declares the variables that can be
?inputted by the user
ustring basename, "MST_samplereferenceno", "Base of filenames"
uglobal gaino, 20, "Gain of the voltage amplifier"
uglobal n, 200,"No. of 0.5 V increments"
desc "This script pushes the MST forward in"
desc "small discrete steps for n steps and"
desc "determines its position at every step"
desc "using the pattern matching technique."
desc " "
desc "Created by Naveed - 04/21/09"
include init.mac
begin
call init
?The following set of commands declares the variables used in the
?script
alloc scale
alloc device_x_init_pos
alloc device_y_init_pos
alloc device_x_pos
343
alloc device_y_pos
alloc substrate_x_init_pos
alloc substrate_y_init_pos
alloc substrate_x_pos
alloc subsrate_y_pos
alloc x_disp
alloc y_disp
string msg
let scale = 0.465*10/mag
print "Scale = ", scale
outv 0 : 3.45
fireset "shutter", 300
?The following set of commands asks the user to select the anchored
?and movable patterns that should be used to track the displacement
?of the actuated MST and determines their initial positions
snap
let msg = "Select ROI & pattern on the anchor"
msgbox msg
pattern substrate
let msg = "Select ROI & pattern on the shuttle"
msgbox msg
pattern device
match substrate, substrate_x_init_pos, substrate_y_init_pos
match device, device_x_init_pos, device_y_init_pos
?The following set of commands creates and opens a data file, in
?which, the positions to which the MST is displaced during actuation
?are stored
let fname = basename,".dat"
fopen fname
fprint fname| "Voltage (V)"; " x_disp (microns)"; " y_disp (microns)"
?The following set of commands pushes the MST forward in small
?discreet steps for n steps, determines the position of the actuated
?MST at every step using the pattern matching technique and stores
?it in the data file opened previously
for i = 0 to n i+1
{
outv 1: i*0.5/gaino
delay 0.5
snap
344
match device, device_x_pos, device_y_pos
match substrate, substrate_x_pos, substrate_y_pos
let x_disp = device_x_pos - substrate_x_pos + substrate_x_init_pos
- device_x_init_pos
let y_disp = device_y_pos - substrate_y_pos + substrate_y_init_pos
- device_y_init_pos
print "Voltage = ", i*0.5 " V, x_disp = ", scale*x_disp
" microns, y_disp = ", scale*y_disp " microns"
fprint fname| i*0.5; scale*x_disp; scale*y_disp
chart i*0.5, x_disp, 1
chart i*0.5, y_disp, 2
}
fclose fname
outv 1 : 0
fireset "shutter", 200
A.3 Script Name: CBA Actuation Method Validity Test.stp
?The following set of commands declares the variables that can be
?inputted by the user
ustring basename, "Samplerefno_date","Base of filenames"
uglobal actuation, 0, "1_electrostatic 0_manual"
uglobal analysis, 1, "0_no_analysis 1_analysis"
uglobal no_of_profiles, 1, "No. of beams to be compared"
uglobal maxv, 120, "Maximum actuation voltage"
uglobal minv, 0, "Minimum actuation voltage"
uglobal incr, 10, "Voltage increment"
uglobal gaino, 20, "Gain of the voltage amplifier"
uglobal 2v2pi, 0.029544, "Voltage that modulates the phase by 2pi"
uglobal gain, 1, "Gain of the piezo controller"
uglobal lambda, 532, "Wavelength of illumination source (in nm)"
desc "This script enables electrostatic actuation"
desc "of 1 & manual actuation of the other of 2"
desc "adjacent CBAs. It also enables comparison"
desc "between the final states of the"
desc "corresponding CBs in the two actuated CBAs."
desc "Created by NAVEED - 04/06/09"
include init.mac
begin
call init
345
grab_init
video_on
?The following set of commands declares the variables used in the
?script
alloc voltage
alloc readytomove 0
alloc increasing 1
alloc decreasing 1
alloc scale
al
alloc left
alloc height
alloc width
string filename
string chartname
string imgname
string fname
string profilename
string beamname
string msg
array out
array final
array position
array zfinal
?The following set of commands actuates a CBA electrostatically
?and collects the sets of five interferograms corresponding to the
?actuated and final states of the CBA
let voltage = minv
outv piezo_chan: 1
if (actuation == 1)
{
while (increasing > 0.5)
{
while (readytomove < 0.5)
{
print voltage
outv 1: voltage/gaino
select readytomove
346
}
if (voltage == maxv)
{
for i = 4 to 0 i-1
{
let filename = basename,"_actuated_",@dvoltage, "_", @di, ".tif"
print filename
outv piezo_chan: (1 + (i-2)*2v2pi/4)/gain
print "piezo voltage = ", (1 + (i-2)*2v2pi/4)," V"
delay 1
grab
wrtimgt filename
}
}
let readytomove=0
let voltage = voltage + incr
if (voltage > maxv)
{
let increasing = 0
}
}
let voltage = maxv-incr
while (decreasing > 0.5)
{
while (readytomove < 0.5)
{
print voltage
outv 1: voltage/gaino
select readytomove
}
if (voltage == minv)
{
for i = 4 to 0 i-1
{
let filename = basename,"_final_state_", @dvoltage, "_", @di,
".tif"
print filename
outv piezo_chan: (1 + (i-2)*2v2pi/4)/gain
delay 1
grab
wrtimgt filename
}
}
347
let readytomove = 0
let voltage = voltage - incr
if (voltage < minv)
{
let decreasing = 0
}
}
}
?The following set of commands collects the set of five
?interferograms required to determine the final state profiles
?of the cantilever beams of a manually actuated CBA
if (actuation == 0)
{
for i = 4 to 0 i-1
{
let filename = basename,"_manual_actuation_final_state_", @di,
".tif"
print filename
outv piezo_chan: (1 + (i-2)*2v2pi/4)/gain
delay 1
grab
wrtimgt filename
}
}
outv piezo_chan: 0
if (analysis == 1)
{
video_off
let scale = 0.465*10/mag
for u = 1 to no_of_profiles u+1
{
?The following set of commands determines the final state height
?profile of an electrostatically actuated cantilever beam
for i = 4 to 0 i-1
{
let fname = basename,"_final_state_0_",@di, ".tif"
rdimg fname
let msg = "Select Beam", @du
msgbox msg
if (i == 4)
348
{
moire_select test
}
linescanx test, out
}
psi out, final, lambda/1000/4/3.1415
?The following set of commands creates and opens two files, in
?which, the data and the plot of the final state height profile of
? the electrostatically actuated cantilever beam are stored. It
?also creates and opens an image file, in which, the corresponding
?electrostatically actuated cantilever beam is labelled
let filename = basename,"_final_state_beam_", @du, ".dat"
let chartname = basename,"_final_state_beam_",@du, ".bmp"
let imgname = basename,"_final_state.tif"
fopen filename
fopen chartname
fopen imgname
?The following set of commands stores the data and the plot of
?the final state height profile of the electrostatically actuated
?cantilever beam in the corresponding files. It also stores the
?labelled image of the corresponding electrostatically actuated
?cantilever beam in its corresponding file
for j = 0 to asize[final]-1 j+1
{
fprint filename | scale*j; final[j]
let position[j] = scale*j
let zfinal[j] = final[j]-final[0]
}
mchart Profile, position, zfinal
let profilename = "Final Profile of beam", @du, " actuated
electrostatically and released"
mtitle Profile, profilename
maxisx Profile, "Lateral Position in microns"
maxisy Profile, "Vertical Position in microns"
wrtmchart Profile, chartname
if (u==1)
{
rdimg fname
}
else
{
349
rdimg imgname
}
rect_dim test, top, left, height, width
drawr top, left, height, width, 2
let beamname = "Beam",@du
drawt left+width+25, top+height+10, 2, beamname
drawmerge
wrtimgt imgname
fclose filename
fclose chartname
fclose imgname
mchrtclr Profile
clr_array out
clr_array final
clr_array position
clr_array zfinal
?The following set of commands determines the actuated state height
?profile of an electrostatically actuated cantilever beam
for i = 4 to 0 i-1
{
let fname = basename,"_actuated_120_", @di, ".tif"
rdimg fname
linescanx test, out
}
psi out, final, lambda/1000/4/3.1415
?The following set of commands creates and opens two files, in
?which, the data and the plot of the actuated state height profile
?of the electrostatically actuated cantilever beam are stored. It
?also creates and opens an image file, in which, the
?corresponding electrostatically actuated cantilever beam is
?labelled
let filename = basename, "_actuated_beam_", @du,".dat"
let chartname = basename, "_actuated_beam_", @du,".bmp"
let imgname = basename, "_actuated.tif"
fopen filename
fopen chartname
fopen imgname
?The following set of commands stores the data and the plot of the
?actuated state height profile of the electrostatically actuated
?cantilever beam in the corresponding files. It also stores the
350
?labelled image of the corresponding electrostatically actuated
?cantilever beam in its corresponding file
for j = 0 to asize[final]-1 j+1
{
fprint filename | scale*j; final[j]
let position[j] = scale*j
let zfinal[j] = final[j]-final[0]
}
mchart Profile, position, zfinal
let profilename = "Final Profile of beam", @du, " actuated
electrostatically"
mtitle Profile, profilename
maxisx Profile, "Lateral Position in Microns"
maxisy Profile, "Vertical Position in Microns"
wrtmchart Profile, chartname
if (u == 1)
{
rdimg fname
}
else
{
rdimg imgname
}
rect_dim test, top, left, height, width
drawr top,left, height, width, 2
let beamname = "Beam", @du
drawt left+width+25, top+height+10, 2, beamname
drawmerge
wrtimgt imgname
fclose filename
fclose chartname
fclose imgname
mchrtclr Profile
clrrec test
clr_array out
clr_array final
clr_array position
clr_array zfinal
?The following set of commands determines the final state height
?profile of a manually actuated cantilever beam
351
for i = 4 to 0 i-1
{
let fname = basename, "_manual_actuation_", @di,".tif"
rdimg fname
let msg = "Select Beam",@du
msgbox msg
if (i == 4)
{
moire_select test
}
linescanx test, out
}
psi out, final, lambda/1000/4/3.1415
?The following set of commands creates and opens two files, in
?which, the data and the plot of the final state height profile of
?the manually actuated cantilever beam are stored. It also creates
?and opens an image file, in which, the corresponding manually
?actuated cantilever beam is labelled
let filename = basename, "_manual_actuation_beam_", @du,".dat"
let chartname = basename, "_manual_actuation_beam_", @du,".bmp"
let imgname = basename, "_manual_actuation.tif"
fopen filename
fopen chartname
fopen imgname
?The following set of commands stores the data and the plot of the
?final state height profile of the manually actuated cantilever beam
?in the corresponding files. It also stores the labelled image of the
?corresponding manually actuated cantilever beam in its
?corresponding file
for j = 0 to asize[final]-1 j+1
{
fprint filename | scale*j; final[j]
let position[j] = scale*j
let zfinal[j] = final[j]-final[0]
}
mchart Profile, position, zfinal
let profilename ="Final Profile of beam", @du, "actuated manually"
mtitle Profile, profilename
maxisx Profile, "Lateral Position in microns"
maxisy Profile, "Vertical Position in microns"
wrtmchart Profile, chartname
352
if (u == 1)
{
rdimg fname
}
else
{
rdimg imgname
}
rect_dim test, top,left, height, width
drawr top, left, height, width, 2
let beamname = "Beam", @du
drawt left+width+25, top+height+10, 2, beamname
drawmerge
wrtimgt imgname
fclose filename
fclose chartname
fclose imgname
mchrtclr Profile
clrrec test
clr_array out
clr_array final
clr_array position
clr_array zfinal
}
}
grab_stop
A.4 Script Name: CBA Analysis.stp
?The following set of commands declares the variables that can be
?inputted by the user
ustring basename, "Samplerefno", "Base of filenames"
uglobal status, 0, "0_offline 1_online"
uglobal analysis, 1, "0_no_analysis 1_analysis"
uglobal nobtba, 1, "No. of beams to be analyzed"
uglobal 2v2pi, 0.029544,"Voltage that modulates the phase by 2pi"
uglobal gain, 1,"Gain of the piezo controller"
uglobal lambda, 532,"Wavelength of illumination source (in nm)"
uglobal E, 130000000000, "Young?s modulus of device layer (in Pa)"
uglobal t, 1.901, "Cantilever beam thickness (in microns)"
desc "This script determines the height profiles"
353
desc "of selected cantilever beams, from which, it"
desc "determines their crack lengths, and uses the"
desc "determined crack lengths to determine"
desc "their apparent works of adhesion. "
desc "Modified by Naveed - 04/18/2009"
include init.mac
begin
call init
grab_init
?The following set of commands declares the variables used in the
?script
alloc scale
alloc h_error
alloc avg_error
alloc tempmin
alloc s
alloc s_found
alloc errv
alloc term1
alloc term2
alloc work
alloc m_bob
alloc m_me
string filename
string chartname
string profilename
string msg
array out
array final
array zfinal
array position
array x_fit
array y_fit
array eta
array coefs
array deflection
let scale = 0.465*10/mag
video_on
354
outv led_chan: 3.45
outv piezo_chan: 1
delay 3
?The following set of commands collects the set of five
?interferograms, which is required to determine the final state
?height profiles of the cantilever beams of the CBA being
?analyzed
if (status == 1)
{
for i = 4 to 0 i-1
{
let filename = basename, "_", @di, ".tif"
outv piezo_chan: (1 + (i-2)*2v2pi/4)/gain
delay 1
refresh
grab
wrtimgt filename
}
}
video_off
outv piezo_chan: 0
if (analysis == 1)
{
for u = 1 to nobtba u+1
{
?The following set of commands determines the final state height
?profile of the selected cantilever beam
for i = 4 to 0 i-1
{
let filename = basename, "_", @di, ".tif"
rdimg filename
let msg = "Select Beam", @du
msgbox msg
if (i == 4)
{
moire_select test
}
linescanx test, out
}
psi out, final, lambda/1000/4/3.1415
355
?The following set of commands creates and opens two files, in
?which, the data and the plot of the final state height profile of
?the selected cantilever beam are stored
let filename = basename, "_beam_", @du, ".dat"
let chartname = basename, "_beam_", @du, ".bmp"
fopen filename
fopen chartname
?The following set of commands stores the data and the plot of the
?final state height profile of the selected cantilever beam in the
?corresponding files
for j = 0 to asize[final]-1 j+1
{
let position[j] = scale*j
let zfinal[j] = final[j] + abs[final[asize[final]-1]]
fprint filename | position[j]; zfinal[j]
}
mchart Profile, position, zfinal
let profilename = "Profile of beam", @du
mtitle Profile, profilename
maxisx Profile, "Lateral Position in microns"
maxisy Profile, "Vertical Position in microns"
wrtmchart Profile, chartname
fclose chartname
?The following set of commands determines the crack length of the
?selected cantilever beam
print "Analysis of Beam", @du
let tempmin = 100
for i = 0 to asize[position]-1 i+1
{
let s = position[i]
let h_error = 0
clr_array x_fit
clr_array y_fit
for j = 0 to asize[position]-1 j+1
{
let x_fit[j] = position[j]
if (x_fit[j] < s)
{
let y_fit[j] = zfinal[0]*(2*position[j]^3/s^3
356
- 3*position[j]^2/s^2 + 1)
}
else
{
let y_fit[j] = zfinal[0]*(2*s^3/s^3 - 3*s^2/s^2 + 1)
}
let h_error = h_error + ((zfinal[j] - y_fit[j])^2)
}
let avg_error = h_error/asize[x_fit]
print "When s = ", position[i], " microns"
print "The error is ", avg_error
if (avg_error <= tempmin)
{
let tempmin = avg_error
let s_found = s
}
refresh
}
print "Crack length of Beam", @du, " = ", s_found, " microns"
?The following set of commands fits the final state height profile of
?the selected cantilever beam to a third order polynomial of eta
for i = 0 to s_found/scale i+1
{
let eta[i] = position[i]/s_found
let deflection[i] = zfinal[i]
}
poly_fit eta, deflection, coefs, errv, 3
print "The coefficients are: ", coefs[3], " ,", coefs[2], " ,",
coefs[1], " ,", coefs[0]
print "The polyfit error is: ", errv
clr_array x_fit
clr_array y_fit
for i = 0 to asize[eta]-1 i+1
{
let x_fit[i] = eta[i]
let y_fit[i] = coefs[3]*eta[i]^3 + coefs[2]*eta[i]^2
+ coefs[1]*eta[i] + coefs[0]
chart x_fit[i], y_fit[i], 2
chart x_fit[i], zfinal[i], 1
}
357
?The following set of commands determines the apparent work of
?adhesion of the selected cantilever beam and stores it and the
?corresponding crack length in the data file opened previously
let term1 = E*3*(t^3)/2/(s_found^4)
let term2 = (coefs[3]^2) + (coefs[3]*coefs[2]) + (1/3)*(coefs[2]^2)
let work = term1*term2/1000
let m_bob = 2 - coefs[3]/coefs[0]
let m_me = -coefs[2]/coefs[3]
print "m_bob = ", m_bob
print "m_me = ", m_me
print " "
print " "
print " "
print "The crack length of Beam", @du, " is ", s_found, " microns"
fprint filename| "The crack length of Beam", @du, " is ", s_found,
" microns"
if (s_found == position[asize[position]-1])
{
print "Beam", @du," is arc-shaped with m_bob = ", m_bob, ", m_me
= ", m_me, "."
fprint filename| "Beam", @du, " is arc-shaped with m_bob = ",
m_bob, ", m_me = ",m_me,"."
}
else
{
print "Beam", @du," is S-shaped with m_bob = ", m_bob, ", m_me =
", m_me"."
fprint filename|"Beam", @du," is S-shaped with m_bob = ", m_bob,
", m_me = ", m_me"."
}
print "The apparent work of adhesion of Beam", @du, " is: ", work,
" mJ/m^2."
fprint filename|"The apparent work of adhesion of Beam", @du, "is:
", work, " mJ/m^2."
fclose filename
mchrtclr Profile
clrrec test
clr_array out
clr_array final
clr_array position
clr_array zfinal
clr_array eta
clr_array coefs
358
clr_array deflection
}
}
grab_stop
A.5 Script Name: SB Actuation and Analysis.stp
?The following set of commands declares the variables that can be
?inputted by the user
ustring basename, "Samplerefno", "Base of filenames"
uglobal status, 1, "1_online 0_offline"
uglobal analysis, 0, "1_analysis 0_no_analysis"
uglobal nobtba, 1, "No. of beams to be analyzed"
uglobal maxv, 65, "Maximum actuation voltage"
uglobal minv, 0, "Minimum actuation voltage"
uglobal incr, 1, "Voltage increment"
uglobal gaino, 20,"gain of the TEGAM"
uglobal s_found, 1965, "Observed crack length (in microns)"
uglobal E, 130000000000, "Young?s modulus of device layer (in Pa)"
uglobal t, 3.255, "Sidewall beam thickness (in microns)"
uglobal h, 9.77, "As-fabricated distance between Sidewall beams"
desc "This script electrostatically actuates"
desc "a pair of sidewall beams as well as"
desc "determines the apparent of work of"
desc "adhesion between them."
desc " "
desc "Created by NAVEED - 04/21/09"
include init.mac
begin
call init
grab_init
video_on
?The following set of commands declares the variables used in the
?script
alloc voltage
alloc readytomove 0
alloc increasing 1
alloc decreasing 1
359
alloc scale
alloc xp1
alloc yp1
alloc xp2
alloc yp2
alloc work
string fname
string msg
let scale = 0.465*10/mag
outv 0 : 3.45
fireset "shutter", 300
if (status == 1)
{
?The following set of commands actuates a pair of sidewall beams
?electrostatically
let voltage = minv
while (increasing > 0.5)
{
while (readytomove < 0.5)
{
print voltage
outv 1: voltage/gaino
select readytomove
}
if (voltage == maxv)
{
let fname = basename, "_actuated_", @dvoltage, "V.tif"
fopen fname
grab
wrtimgt fname
fclose fname
}
let readytomove = 0
let voltage = voltage + incr
if (voltage > maxv)
{
let increasing = 0
}
}
let voltage = maxv-incr
while (decreasing > 0.5)
360
{
while (readytomove < 0.5)
{
print voltage
outv 1: voltage/gaino
select readytomove
}
if (voltage == minv)
{
let fname = basename, "_released_", @dvoltage, "V.tif"
fopen fname
grab
wrtimgt fname
fclose fname
}
let readytomove = 0
let voltage = voltage - incr
if (voltage < minv)
{
let decreasing = 0
}
}
}
if (a == 1)
{
?The following set of commands determines the apparent work of
?adhesion of an electrostatically actuated pair of sidewall beams
if (s_found == 0)
{
for u = 1 to nobtba u+1
{
let fname = basename, "_released_0V.tif"
rdimg fname
let msg = "Select starting pt. on Beam", @du
msgbox msg
point xp1, yp1
let msg = "Select end of crack length on Beam", @du
msgbox msg
point xp2, yp2
let s_found = scale*(xp2-xp1)
print "The crack length of Beam", @du,"is ", @ds_found,
" microns."
let work = E*3*(t^3)/(s_found^4)/1000*(h^2)/4
print "The work of adhesion of Beam", @du,"is: ", work,
361
" mJ/m^2."
}
}
if (s_found != 0)
{
print "The crack length of Beam", @d1, "is ", s_found, " microns."
let work = E*3*(t^3)/(s_found^4)/1000*(h^2)/4
print "The work of adhesion of Beam is: ", work, " mJ/m^2."
}
}
grab_stop
A.6 Script Name: Comb - drive Actuator Calibration.stp
?The following set of commands declares the variables that can be
?inputted by the user
ustring basename, "Samplerefno", "Base of filenames"
uglobal num, 50, "Number of 1V increments"
uglobal gaino, 20, "Gain of the voltage amplifier"
uglobal p, 1, "1_pull_cycle 0_no_pull_cycle"
uglobal pb, 0, "1_pullback_cycle 0_no_pullback_cycle"
uglobal E, 130000000000, "Young?s modulus of device layer (in Pa)"
uglobal t, 1.884632, "Thickness of restoring springs (in microns)"
uglobal w, 2.79, "Width of restoring springs (in microns)"
uglobal L, 300, "Length of restoring springs (in microns)"
uglobal n, 25, "No. of suspended comb fingers"
uglobal xo, 8.835, "Initial overlap (in microns)"
uglobal g, 2.79, "Initial gap (in microns)"
desc "This script applies an increasing DC voltage"
desc "to the comb-drive actuator and determines the"
desc "corresponding displacement of the suspended"
desc "shuttle using a pattern matching technique. It"
desc "can be used to calibrate a comb drive actuator."
desc "Created by Naveed - 05/27/2009"
include init.mac
begin
call init
?The following set of commands declares the variables used in the
?script
362
alloc scale
alloc voltage
alloc voltage_pb
alloc device_x_init_pos
alloc device_y_init_pos
alloc device_x_pos
alloc device_y_pos
alloc substrate_x_init_pos
alloc substrate_y_init_pos
alloc substrate_x_pos
alloc subsrate_y_pos
alloc x_disp
alloc y_disp
alloc kx
alloc ky
alloc ky_pb
alloc ke
alloc ke_pb
string fname
string msg
array voltage
array voltage_pb
array x_pos
array x_pos_pb
array y_pos
array y_pos_pb
let scale = 0.465*10/mag
print "Scale = ", scale
outv 0 : 3.45
fireset "shutter", 300
?The following set of commands asks the user to select the anchored
?and movable patterns that should be used to track the displacement
?of the suspended shuttle and determines their initial positions
snap
let msg = "Select ROI & pattern on the anchor"
msgbox msg
pattern substrate
let msg = "Select ROI & pattern on the shuttle"
msgbox msg
pattern device
match substrate, substrate_x_init_pos, substrate_y_init_pos
363
match device, device_x_init_pos, device_y_init_pos
if (p == 1)
{
?The following set of commands creates and opens a data file, in
?which, the voltages applied to one of the two comb-drive actuators
?and the corresponding displacements of the suspended shuttle are
?stored
let fname = basename,"_inc_disp.dat"
fopen fname
fprint fname| "Voltage (V)"; "sq. Voltage (sq. V)"; "x_disp
(microns)"; "y_disp (microns)"; "ky (N/m)"; "ke (N/m)"
?The following set of commands applies an increasing voltage to
?one of the two comb-drive actuators, determines the
?corresponding displacements of the suspended shuttle using the
?pattern matching technique and stores the applied voltage and
?shuttle displacements in the data file opened previously. It also
?determines the theoretical lateral mechanical and the theoretical
?lateral electrostatic stiffnesses of the suspension springs of the
?suspended structure, which change with the displacement of the
?shuttle, and stores them in the data file opened previously
for i = 0 to num i+1
{
outv 1: i/gaino
let voltage[i] = i
print "Voltage = ", i
delay 1
snap
match substrate, substrate_x_pos, substrate_y_pos
match device, device_x_pos, device_y_pos,
let x_disp = device_x_pos - substrate_x_pos + substrate_x_init_pos
- device_x_init_pos
let y_disp = device_y_pos - substrate_y_pos + substrate_y_init_pos
- device_y_init_pos
print "x_disp = ", x_disp*scale, " microns, y_disp = ",
y_disp*scale, " microns"
let x_pos[i] = x_disp*scale
let y_pos[i] = y_disp*scale
?For the tangential arm of SFAT
?let ky = E*w*t/L/1000000*((8*(t^2))/((3*(y_pos[i]^2)) +
(8*(t^2))))
?For the normal arm of SFAT and the comb-drive actuator of
?Resonator
let ky = 50/9*E*w/L/(x_pos[i]^2)*(t^3)/1000000
364
?For the tangential arm of SFAT
let ke = n*8.85/1000000000000*t*(y_pos[i] + xo)*(voltage[i]^2)
*1000000*((1/((g - x_pos[i])^3)) + (1/((g - x_pos[i])^3)))
?For the normal arm of SFAT and the comb-drive actuator of
?Resonator
let ke = n*8.85/1000000000000*t*(x_pos[i] + xo)*(voltage[i]^2)
*1000000*((1/((g - y_pos[i])^3)) + (1/((g - y_pos[i])^3)))
print "ky = ", ky, "N/m"
print "ke = ", ke, "N/m"
fprint fname| voltage[i]; voltage[i]^2; x_pos[i]; y_pos[i]; ky; ke
}
fclose fname
}
if (pb == 1)
{
?The following set of commands creates and opens a data file, in
?which, the voltages applied to the other of the two comb-drive
?actuators and the corresponding displacements of the suspended
?shuttle are stored
let fname = basename, "_dec_disp.dat"
fopen fname
fprint fname| "Voltage (V)"; "sq. Voltage (sq. V)"; "x_disp
(microns)"; "y_disp (microns)"; "ky (N/m)"; "ke (N/m)"
let msg = "Hit select to start the pull back cycle"
msgbox msg
wait
?The following set of commands applies an increasing voltage to the
?other of the two comb-drive actuators, determines the corresponding
?displacements of the suspended shuttle using the pattern matching
?technique and stores the applied voltage and shuttle displacements
?in the data file opened previously. It also determines the
?theoretical lateral mechanical and the theoretical lateral
?electrostatic stiffnesses of the suspension springs of the suspended
?structure, which change with the displacement of the shuttle, and
?stores them in the data file opened previously
for i = 0 to num i+1
{
outv 2: i/gaino
let voltage_pb[i] = i
print "Voltage_pb = ", i
delay 1
snap
match substrate, substrate_x_pos, substrate_y_pos
365
match device, device_x_pos, device_y_pos
let x_disp = device_x_pos - substrate_x_pos + substrate_x_init_pos
- device_x_init_pos
let y_disp = device_y_pos - substrate_y_pos + substrate_y_init_pos
- device_y_init_pos
print "x_disp = ", x_disp*scale, " microns, y_disp = ",
y_disp*scale, " microns"
let x_pos_pb[i] = x_disp*scale
let y_pos_pb[i] = y_disp*scale
?For the tangential arm of SFAT
?let ky_pb = E*w*t/L/1000000*((8*(t^2))/((3*(y_pos_pb[i]^2))
+ (8*(t^2))))
?For the normal arm of SFAT and the comb-drive actuator of
?Resonator
let ky_pb = 50/9*E*w/L/(x_pos_pb[i]^2)*(t^3)/1000000
?For the tangential arm of SFAT
let ke_pb = n*8.85/1000000000000*t*(y_pos_pb[i] + xo)
*(voltage_pb[i]^2)*1000000*((1/((g - x_pos_pb[i])^3))
+ (1/((g - x_pos_pb[i])^3)))
?For the normal arm of SFAT and the comb-drive actuator of
?Resonator
let ke_pb = n*8.85/1000000000000*t*(x_pos_pb[i] + xo)
*(voltage_pb[i]^2)*1000000*((1/((g - y_pos_pb[i])^3))
+ (1/((g - y_pos_pb[i])^3)))
print "ky_pb = ", ky_pb, "N/m"
print "ke_pb = ", ke_pb, "N/m"
fprint fname| voltage_pb[i]; voltage_pb[i]; x_pos_pb[i];
y_pos_pb[i]; ky_pb; ke_pb
}
fclose fname
}
outv 1: 0
outv 2: 0
for i = 0 to asize[voltage]-1 i+1
{
if (p == 1)
{
?The following set of commands plots the voltages applied to one of
?the two comb-drive actuators versus the corresponding x and y
?displacements of the suspended shuttle
chart voltage[i], x_pos[i], 1
chart voltage[i], y_pos[i], 2
}
366
if (pb == 1)
{
?The following set of commands plots the voltages applied to the
?other of the two comb-drive actuators versus the corresponding x
?and y displacements of the suspended shuttle
chart voltage_pb[i], x_pos_pb[i], 3
chart voltage_pb[i], y_pos_pb[i], 4
}
}
let msg = "Hit select to see the next chart"
msgbox msg
wait
chrtclr
for j = 0 to asize[voltage]-1 j+1
{
if (p == 1)
{
?The following set of commands plots the square of the voltages
?applied to one of the two comb-drive actuators versus the
?corresponding x and y displacements of the suspended shuttle
chart ((voltage[j])^2), x_pos[j], 1
chart ((voltage[j])^2), y_pos[j], 2
}
if (pb == 1)
{
?The following set of commands plots the square of the voltages
?applied to the other of the two comb-drive actuators versus the
?corresponding x and y displacements of the suspended shuttle
chart ((voltage_pb[j])^2), x_pos_pb[j], 3
chart ((voltage_pb[j])^2), y_pos_pb[j], 4
}
}
?The following set of commands determines the theoretical axial
?stiffness of the suspension springs of the suspended structure and
?stores it in the data file opened previously
?For the tangential arm of SFAT
?let kx = E*t/1000000*((w/L)^3)
?For the normal arm of SFAT and the comb-drive actuator of Resonator
let kx = 2*E*t/1000000*((w/L)^3)
print "kx_theoretical = ", kx, " N/m"
fprint fname| "kx_theoretical = ", kx, " N/m"
367
A.7 Script Name: SFT Normal Arm Comb - drive Actuator Calibra-
tion.stp
?The following set of commands declares the variables that can be
?inputted by the user
ustring basename, "Samplerefno", "Base of filenames"
uglobal Va, 40, "V req. to align the normal arm with the anch. post"
uglobal num, 50, "Number of 1V increments"
uglobal gaino, 20, "Gain of the voltage amplifier"
uglobal p, 1, "1_pull_cycle 0_no_pull_cycle"
uglobal pb, 0, "1_pullback_cycle 0_no_pullback_cycle"
uglobal E, 130000000000, "Young?s modulus of device layer (in Pa)"
uglobal t, 1.884632, "Thickness of restoring springs (in microns)"
uglobal w, 2.79, "Width of restoring springs (in microns)"
uglobal L, 300, "Length of restoring springs (in microns)"
uglobal n, 25, "No. of suspended comb fingers"
uglobal xo, 8.835, "Initial overlap (in microns)"
uglobal g, 2.79, "Initial gap (in microns)"
desc "This script 1st aligns the normal arm with"
desc " the anchored post, then applies an increasing "
desc "DC V to the normal arm and determines the"
desc "corresponding displacement of the suspended"
desc "shuttle using a pattern matching technique."
desc "Created by Naveed - 05/27/2009"
include init.mac
begin
call init
?The following set of commands declares the variables used in the
?script
alloc scale
alloc voltage
alloc voltage_pb
alloc device_x_init_pos
alloc device_y_init_pos
alloc device_x_pos
alloc device_y_pos
alloc substrate_x_init_pos
alloc substrate_y_init_pos
alloc substrate_x_pos
alloc subsrate_y_pos
368
alloc x_disp
alloc y_disp
alloc kx
alloc ky
alloc ky_pb
alloc ke
alloc ke_pb
string fname
string msg
array voltage_t
array voltage
array voltage_pb
array x_pos
array x_pos_pb
array y_pos
array y_pos_pb
let scale = 0.465*10/mag
print "Scale = ", scale
outv 0 : 3.45
fireset "shutter", 300
?The following set of commands asks the user to select the anchored
?and movable patterns that should be used to track the displacement
?of the suspended shuttle and determines their initial positions
snap
let msg = "Select ROI & pattern on the anchor"
msgbox msg
pattern substrate
let msg = "Select ROI & pattern on the shuttle"
msgbox msg
pattern device
match substrate, substrate_x_init_pos, substrate_y_init_pos
match device, device_x_init_pos, device_y_init_pos
?The following set of commands creates and opens a data file, in
?which, the voltages applied to the tangential comb-drive actuator
?to align the normal arm with the anchored posts and the corresponding
?displacements of the suspended shuttle are
?stored
let fname = basename,"_align.dat"
fopen fname
fprint fname| "Voltage (V)"; "sq. Voltage (sq. V)"; "x_disp
369
(microns)"; "y_disp (microns)"
?The following set of commands applies a voltage of Va to the
?tangential comb-drive actuator in order to align the normal arm with
?the anchored posts. It determines the corresponding displacement of
?the loading beam using the pattern matching technique and stores it
?in the data file opened previously
for i = 0 to Va i+1
{
outv 3: i/gaino
print "Vt = ", i
delay 0.5
snap
match substrate, substrate_x_pos, substrate_y_pos
match device, device_x_pos, device_y_pos
let x_disp = device_x_pos - substrate_x_pos + substrate_x_init_pos
- device_x_init_pos
let y_disp = device_y_pos - substrate_y_pos + substrate_y_init_pos
- device_y_init_pos
print "x_disp = ", scale*x_disp, " microns, y_disp = ",
scale*y_disp, " microns"
let voltage_t[i] = i
fprint fname| voltage_t[i]; voltage_t[i]^2; x_disp*scale; y_disp*scale
}
fclose fname
wait
fireset "shutter", 200
delay 0.5
?The following set of commands collects an interferogram showing the
?SFT after the normal arm is aligned with the anchored posts
snap
wrtimgt basename,"_normal_arm_aligned_fringes.tif"
wait
fireset "shutter",300
delay 0.5
?The following set of commands collects an optical image showing the
?SFT after the normal arm is aligned with the anchored posts
snap
wrtimgt basename,"_normal_arm_aligned.tif"
wait
370
fireset "shutter",200
delay 0.5
video_on
if (p == 1)
{
?The following set of commands creates and opens a data file, in
?which, the voltages applied to one of the two comb-drive actuators
?and the corresponding displacements of the suspended shuttle are
?stored
let fname = basename,"_inc_disp.dat"
fopen fname
fprint fname| "Voltage (V)"; "sq. Voltage (sq. V)"; "x_disp
(microns)"; "y_disp (microns)"; "ky (N/m)"; "ke (N/m)"
?The following set of commands applies an increasing voltage to
?one of the two comb-drive actuators, determines the
?corresponding displacements of the suspended shuttle using the
?pattern matching technique and stores the applied voltage and
?shuttle displacements in the data file opened previously. It also
?determines the theoretical lateral mechanical and the theoretical
?lateral electrostatic stiffnesses of the suspension springs of the
?suspended structure, which change with the displacement of the
?shuttle, and stores them in the data file opened previously
for i = 0 to num i+1
{
outv 1: i/gaino
let voltage[i] = i
print "Voltage = ", i
delay 1
snap
match substrate, substrate_x_pos, substrate_y_pos
match device, device_x_pos, device_y_pos,
let x_disp = device_x_pos - substrate_x_pos + substrate_x_init_pos
- device_x_init_pos
let y_disp = device_y_pos - substrate_y_pos + substrate_y_init_pos
- device_y_init_pos
print "x_disp = ", x_disp*scale, " microns, y_disp = ",
y_disp*scale, " microns"
let x_pos[i] = x_disp*scale
let y_pos[i] = y_disp*scale
?For the tangential arm of SFAT
?let ky = E*w*t/L/1000000*((8*(t^2))/((3*(y_pos[i]^2)) +
(8*(t^2))))
371
?For the normal arm of SFAT and the comb-drive actuator of
?Resonator
let ky = 50/9*E*w/L/(x_pos[i]^2)*(t^3)/1000000
?For the tangential arm of SFAT
let ke = n*8.85/1000000000000*t*(y_pos[i] + xo)*(voltage[i]^2)
*1000000*((1/((g - x_pos[i])^3)) + (1/((g - x_pos[i])^3)))
?For the normal arm of SFAT and the comb-drive actuator of
?Resonator
let ke = n*8.85/1000000000000*t*(x_pos[i] + xo)*(voltage[i]^2)
*1000000*((1/((g - y_pos[i])^3)) + (1/((g - y_pos[i])^3)))
print "ky = ", ky, "N/m"
print "ke = ", ke, "N/m"
fprint fname| voltage[i]; voltage[i]^2; x_pos[i]; y_pos[i]; ky; ke
}
fclose fname
}
if (pb == 1)
{
?The following set of commands creates and opens a data file, in
?which, the voltages applied to the other of the two comb-drive
?actuators and the corresponding displacements of the suspended
?shuttle are stored
let fname = basename, "_dec_disp.dat"
fopen fname
fprint fname| "Voltage (V)"; "sq. Voltage (sq. V)"; "x_disp
(microns)"; "y_disp (microns)"; "ky (N/m)"; "ke (N/m)"
let msg = "Hit select to start the pull back cycle"
msgbox msg
wait
?The following set of commands applies an increasing voltage to the
?other of the two comb-drive actuators, determines the corresponding
?displacements of the suspended shuttle using the pattern matching
?technique and stores the applied voltage and shuttle displacements
?in the data file opened previously. It also determines the
?theoretical lateral mechanical and the theoretical lateral
?electrostatic stiffnesses of the suspension springs of the suspended
?structure, which change with the displacement of the shuttle, and
?stores them in the data file opened previously
for i = 0 to num i+1
{
outv 2: i/gaino
let voltage_pb[i] = i
print "Voltage_pb = ", i
372
delay 1
snap
match substrate, substrate_x_pos, substrate_y_pos
match device, device_x_pos, device_y_pos
let x_disp = device_x_pos - substrate_x_pos + substrate_x_init_pos
- device_x_init_pos
let y_disp = device_y_pos - substrate_y_pos + substrate_y_init_pos
- device_y_init_pos
print "x_disp = ", x_disp*scale, " microns, y_disp = ",
y_disp*scale, " microns"
let x_pos_pb[i] = x_disp*scale
let y_pos_pb[i] = y_disp*scale
?For the tangential arm of SFAT
?let ky_pb = E*w*t/L/1000000*((8*(t^2))/((3*(y_pos_pb[i]^2))
+ (8*(t^2))))
?For the normal arm of SFAT and the comb-drive actuator of
?Resonator
let ky_pb = 50/9*E*w/L/(x_pos_pb[i]^2)*(t^3)/1000000
?For the tangential arm of SFAT
let ke_pb = n*8.85/1000000000000*t*(y_pos_pb[i] + xo)
*(voltage_pb[i]^2)*1000000*((1/((g - x_pos_pb[i])^3))
+ (1/((g - x_pos_pb[i])^3)))
?For the normal arm of SFAT and the comb-drive actuator of
?Resonator
let ke_pb = n*8.85/1000000000000*t*(x_pos_pb[i] + xo)
*(voltage_pb[i]^2)*1000000*((1/((g - y_pos_pb[i])^3))
+ (1/((g - y_pos_pb[i])^3)))
print "ky_pb = ", ky_pb, "N/m"
print "ke_pb = ", ke_pb, "N/m"
fprint fname| voltage_pb[i]; voltage_pb[i]; x_pos_pb[i];
y_pos_pb[i]; ky_pb; ke_pb
}
fclose fname
}
outv 1: 0
outv 2: 0
outv 3: 0
for i = 0 to asize[voltage]-1 i+1
{
if (p == 1)
{
?The following set of commands plots the voltages applied to one of
?the two comb-drive actuators versus the corresponding x and y
373
?displacements of the suspended shuttle
chart voltage[i], x_pos[i], 1
chart voltage[i], y_pos[i], 2
}
if (pb == 1)
{
?The following set of commands plots the voltages applied to the
?other of the two comb-drive actuators versus the corresponding x
?and y displacements of the suspended shuttle
chart voltage_pb[i], x_pos_pb[i], 3
chart voltage_pb[i], y_pos_pb[i], 4
}
}
let msg = "Hit select to see the next chart"
msgbox msg
wait
chrtclr
for j = 0 to asize[voltage]-1 j+1
{
if (p == 1)
{
?The following set of commands plots the square of the voltages
?applied to one of the two comb-drive actuators versus the
?corresponding x and y displacements of the suspended shuttle
chart ((voltage[j])^2), x_pos[j], 1
chart ((voltage[j])^2), y_pos[j], 2
}
if (pb == 1)
{
?The following set of commands plots the square of the voltages
?applied to the other of the two comb-drive actuators versus the
?corresponding x and y displacements of the suspended shuttle
chart ((voltage_pb[j])^2), x_pos_pb[j], 3
chart ((voltage_pb[j])^2), y_pos_pb[j], 4
}
}
?The following set of commands determines the theoretical axial
?stiffness of the suspension springs of the suspended structure and
?stores it in the data file opened previously
?For the tangential arm of SFAT
?let kx = E*t/1000000*((w/L)^3)
374
?For the normal arm of SFAT and the comb-drive actuator of Resonator
let kx = 2*E*t/1000000*((w/L)^3)
print "kx_theoretical = ", kx, " N/m"
fprint fname| "kx_theoretical = ", kx, " N/m"
A.8 Script Name: SFT Friction Test.stp
?The following set of commands declares the variables that can be
?inputted by the user
ustring basename, "Samplerefno, "Base of filenames"
uglobal Va, 40, "V req. to align the normal arm with the anch. post"
uglobal Vn, 60, "Max. V appl. to the norm. comb-drive actuator"
uglobal Vt, 200, "No. of 0.2V incr. appl. to the tang. comb-drive act."
uglobal gaino, 20, "Gain of the voltage amplifier"
desc "This script 1st aligns the normal arm with the"
desc "anchored post, then applies a normal load of Vn"
desc " at the sidewall interf., then applies an incr. tang."
desc "load to shear the interf. It detects the onset of"
desc "slip using the pattern matching tech. to study fric."
desc "Created by Naveed - 06/24/09"
include init.mac
begin
call init
?The following set of commands declares the variables used in the
?script
alloc scale
alloc device_x_init_pos
alloc device_y_init_pos
alloc device_x_pos
alloc device_y_pos
alloc substrate_x_init_pos
alloc substrate_y_init_pos
alloc substrate_x_pos
alloc subsrate_y_pos
alloc x_disp
alloc y_disp
string fname
string msg
375
array voltage
array x_pos
array y_pos
let scale2 = 0.465*10/mag
print "Scale = ", scale
outv 0 : 3.45
fireset "shutter",300
delay 0.5
?The following set of commands asks the user to select the anchored
?and movable patterns that should be used to track the tangential
?displacements of the loading beam and determines their initial
?positions
snap
let msg = "Select ROI & pattern on the anchor"
msgbox msg
pattern substrate
let msg = "Select ROI & pattern on the shuttle"
msgbox msg
pattern device
match substrate, substrate_x_init_pos, substrate_y_init_pos
match device, device_x_init_pos, device_y_init_pos
?The following set of commands creates and opens a data file, in
?which, the voltages applied to the tangential comb-drive actuator
?and the corresponding tangential displacements of the loading beam
?are stored
let fname = basename,"_fric_test.dat"
fopen fname
fprint fname| "Voltage (V)"; "x_disp (microns)"; "y_disp (microns)"
?The following set of commands applies a voltage of Va to the
?tangential comb-drive actuator in order to align the normal arm with
?the anchored posts. It determines the corresponding displacement of
?the loading beam using the pattern matching technique and stores it
?in the data file opened previously
for i = 0 to Va i+1
{
outv 2: i/gaino
print "Vt = ", i
delay 0.5
snap
match substrate, substrate_x_pos, substrate_y_pos
376
match device, device_x_pos, device_y_pos
let x_disp = device_x_pos - substrate_x_pos + substrate_x_init_pos
- device_x_init_pos
let y_disp = device_y_pos - substrate_y_pos + substrate_y_init_pos
- device_y_init_pos
print "x_disp = ", scale*x_disp, " microns, y_disp = ",
scale*y_disp, " microns"
let voltage[i] = i
let x_pos[i] = x_disp*scale
let y_pos[i] = y_disp*scale
fprint fname| voltage[i]; x_pos[i]; y_pos[i]
}
wait
fireset "shutter", 200
delay 0.5
?The following set of commands collects an interferogram showing the
?SFT after the normal arm is aligned with the anchored posts
snap
wrtimgt basename,"_normal_arm_aligned_fringes.tif"
wait
fireset "shutter",300
delay 0.5
?The following set of commands collects an optical image showing the
?SFT after the normal arm is aligned with the anchored posts
snap
wrtimgt basename,"_normal_arm_aligned.tif"
wait
fireset "shutter",200
delay 0.5
video_on
?The following set of commands applies an increasing DC voltage to
?the push drive of the normal comb-drive actuator in order to bring
?the loading beam in contact with the anchored post and apply the
?desired normal load Vn at the sidewall interface
for i = 0 to Vn i+1
{
outv 1: i/gaino
377
print "Vn= ",i
delay 1
refresh
}
video_off
?The following set of commands collects an interferogram showing the
?SFT after the loading beam is brought in contact with the anchored
?post and a normal load of Vn is applied at the sidewall interface
snap
wrtimgt basename,"_beam_post_contact_fringes.tif"
wait
fireset "shutter",300
delay 0.5
?The following set of commands collects an optical image showing the
?SFT after the loading beam is brought in contact with the anchored
?post and a normal load of Vn is applied at the sidewall interface
snap
wrtimgt basename,"_beam_post_contact.tif"
?The following set of commands applies an increasing voltage to the
?tangential comb-drive actuator, determines the corresponding
?tangential displacements of the loading beam using the pattern
?matching technique and stores the applied voltage and tangential
?displacements of the loading beam in the data file opened previously.
for i = 0 to Vt i+1
{
outv 2: Va + i/gaino/5
print "Vt = ", i
delay 0.5
snap
match substrate, substrate_x_pos, substrate_y_pos
match device, device_x_pos, device_y_pos
let x_disp = device_x_pos - substrate_x_pos + substrate_x_init_pos
- device_x_init_pos
let y_disp = device_y_pos - substrate_y_pos + substrate_y_init_pos
- device_y_init_pos
print "x_disp = ", scale*x_disp, " microns, y_disp = ",
scale*y_disp, " microns"
let voltage[Va + i] = Va + i/5
let x_pos[Va+i] = x_disp*scale
378
let y_pos[Va + i] = y_disp*scale
fprint fname| voltage[Va + i]; x_pos[Va + i]; y_pos[Va + i]
}
?The following command collects an optical image of the SFT showing
?the sidewall interface after the completion of the friction test
wrtimgt basename,"_final_state.tif"
fclose fname
outv 2: 0
delay 1
outv 1: 0
?The following set of commands plots the voltages applied to pull
?drive of the tangential comb-drive actuator versus the corresponding
?x and y displacements of the loading beam
for i = 0 to asize[voltage]-1 i+1
{
chart voltage[i], x_pos[i], 1
chart voltage[i], y_pos[i], 2
}
A.9 Script Name: SFAT Friction Test.stp
?The following set of commands declares the variables that can be
?inputted by the user
ustring basename, "Samplerefno", "Base of filenames"
uglobal Vn, 75, "Max. V appl. to the norm. comb-drive actuator"
uglobal Vt, 200, "No. of 1V incr. appl. to the tang. comb-drive act."
uglobal gaino, 20, "Gain of the voltage amplifier"
desc "This script applies a normal load of Vn at the "
desc "sidewall interf. using the norm. comb-drive act."
desc "& then applies an incr. tang. load at it using"
desc "the tang. comb-drive act. It detects the onset of"
desc "slip using the pattern matching tech. to study fric."
desc "Created by Naveed - 06/24/09"
include init.mac
begin
call init
?The following set of commands declares the variables used in the
379
?script
alloc scale
alloc device_x_init_pos
alloc device_y_init_pos
alloc device_x_pos
alloc device_y_pos
alloc substrate_x_init_pos
alloc substrate_y_init_pos
alloc substrate_x_pos
alloc subsrate_y_pos
alloc x_disp
alloc y_disp
string fname
string msg
array voltage
array x_pos
array y_pos
video_on
let scale2 = 0.465*10/mag
print "Scale = ", scale
outv 0 : 3.45
?The following set of commands applies an increasing DC voltage to
?the push drive of the normal comb-drive actuator in order to bring
?the normal arm in contact with the tangential arm and apply the
?desired normal load Vn at the sidewall interface
for i = 0 to Vn i+1
{
outv 1: i/gaino
print "Vn = ", i
delay 1
refresh
}
video_off
?The following set of commands collects an interferogram showing the
?SFAT after the normal arm is brought in contact with the tangential
?arm and a normal load of Vn is applied at the sidewall interface
snap
wrtimgt basename,"_normal_tangential_arm_contact_fringes.tif"
wait
380
fireset "shutter",300
delay 0.5
?The following set of commands collects an optical image showing the
?SFAT after the normal arm is brought in contact with the tangential
?arm and a normal load of Vn is applied at the sidewall interface
snap
wrtimgt basename,"_normal_tangential_arm_contact.tif"
?The following set of commands asks the user to select the anchored
?and movable patterns that should be used to track the displacement
?of the tangential arm and determines their initial positions
let msg = "Select ROI & pattern on the anchor"
msgbox msg
pattern substrate
let msg = "Select ROI & pattern on the shuttle"
msgbox msg
pattern device
match substrate, substrate_x_init_pos, substrate_y_init_pos
match device, device_x_init_pos, device_y_init_pos
?The following set of commands creates and opens a data file, in
?which, the voltages applied to the tangential comb-drive actuator
?and the corresponding displacements of the tangential arm are
?stored
let fname = basename,"_fric_test.dat"
fopen fname
fprint fname| "Voltage (V)"; "x_disp (microns)"; "y_disp (microns)"
?The following set of commands applies an increasing voltage to the
?tangential comb-drive actuator, determines the corresponding
?displacements of the tangential arm using the pattern matching
?technique and stores the applied voltage and displacements of the
?tangential arm in the data file opened previously.
for i = 0 to Vt i+1
{
outv 2: i/gaino
print "Vt = ", i
delay 0.5
snap
match substrate, substrate_x_pos, substrate_y_pos
match device, device_x_pos, device_y_pos
let x_disp = device_x_pos - substrate_x_pos + substrate_x_init_pos
- device_x_init_pos
381
let y_disp = device_y_pos - substrate_y_pos + substrate_y_init_pos
- device_y_init_pos
print "x_disp = ", scale*x_disp, " microns, y_disp = ",
scale*y_disp, " microns"
let voltage[i] = i
let x_pos[i] = x_disp*scale
let y_pos[i] = y_disp*scale
fprint fname| voltage[i]; x_pos[i]; y_pos[i]
}
?The following command collects an optical image of the SFAT showing
?the sidewall interface after the completion of the friction test
wrtimgt basename,"_final_state.tif"
fclose fname
outv 2: 0
delay 1
outv 1: 0
?The following set of commands plots the voltages applied to pull
?drive of the tangential comb-drive actuator versus the
?corresponding x and y displacements of the tangential arm
for i = 0 to asize[voltage]-1 i+1
{
chart voltage[i], x_pos[i], 1
chart voltage[i], y_pos[i], 2
}
A.10 Script Name: SFAT Adhesion Test.stp
?The following set of commands declares the variables that can be
?inputted by the user
ustring basename, "Samplerefno", "Base of filenames"
uglobal push, 30, "No. of 1V increments to form the interface"
uglobal pull, 45, "No. of 1V increments to break the interface"
uglobal gaino, 20, "Gain of the voltage amplifier"
desc "This script applies an incr. vol. to the push"
desc "drive of the norm. arm to bring it in contact"
desc "with the tang. arm and then applies an incr. vol."
desc "to its pull drive to break the sid. interf."
desc "Used to determine adhesion between sidewalls."
desc "Created by Naveed - 06/24/09"
include init.mac
382
begin
call init
?The following set of commands declares the variables used in the
?script
alloc scale
alloc device_x_init_pos_normal
alloc device_y_init_pos_normal
alloc device_x_pos_normal
alloc device_y_pos_normal
alloc substrate_x_init_pos_normal
alloc substrate_y_init_pos_normal
alloc substrate_x_pos_normal
alloc substrate_y_pos_normal
alloc x_disp_normal
alloc y_disp_normal
alloc device_x_init_pos_tangential
alloc device_y_init_pos_tangential
alloc device_x_pos_tangential
alloc device_y_pos_tangential
alloc substrate_x_init_pos_tangential
alloc substrate_y_init_pos_tangential
alloc substrate_x_pos_tangential
alloc substrate_y_pos_tangential
alloc x_disp_tangential
alloc y_disp_tangential
string fname
string msg
array voltage
array x_pos_normal
array y_pos_normal
array x_pos_tangential
array y_pos_tangential
array voltage_pb
array x_pos_pb_normal
array y_pos_pb_normal
array x_pos_pb_tangential
array y_pos_pb_tangential
let scale = 0.465*10/mag
print "Scale = ", scale
383
?The following set of commands asks the user to select the anchored
?and movable patterns that should be used to track the displacement
?of the normal arm and determines their initial positions
snap
let msg = "Select anchor on normal arm"
msgbox msg
pattern substrate_normal
let msg = "Select shuttle on normal arm"
msgbox msg
pattern device_normal
match substrate_normal, substrate_x_init_pos_normal,
substrate_y_init_pos_normal
match device_normal, device_x_init_pos_normal,
device_y_init_pos_normal
?The following set of commands asks the user to select the anchored
?and movable patterns that should be used to track the displacement
?of the tangential arm and determines their initial positions
let msg = "Select anchor on tangential arm"
msgbox msg
pattern substrate_tangential
let msg = "Select shuttle on tangential arm"
msgbox msg
pattern device_tangential
match substrate_tangential, substrate_x_init_pos_tangential,
substrate_y_init_pos_tangential
match device_tangential, device_x_init_pos_tangential,
device_y_init_pos_tangential
?The following set of commands creates and opens a data file, in
?which, the voltages applied to the push drive of the normal arm
?and the corresponding displacements of its suspended shuttle are
?stored. The displacements of the suspended shuttle of the
?tangential arm due to the voltages applied to the push drive of
?the normal arm are also stored in the data file
let fname = basename,"_push.dat"
fopen fname
fprint fname| "Voltage (V)"; "x_disp_normal (microns)";
"y_disp_normal (microns)"; "x_disp_tangential(microns)";
"y_disp_tangential (microns)"
?The following set of commands applies an increasing voltage to
?the push drive of the normal arm, determines the
?corresponding displacements of its suspended shuttle using the
384
?pattern matching technique and stores the applied voltage and
?shuttle displacements in the data file opened previously. It also
?determines the displacements of the suspended shuttle of the
?tangential arm caused by the voltages applied to the push drive
?of the normal arm and stores them in the data file opened
?previously
for i = 0 to push i+1
{
outv 1: i/gaino
delay 1
snap
match substrate_normal, substrate_x_pos_normal,
substrate_y_pos_normal
match device_normal, device_x_pos_normal, device_y_pos_normal
match substrate_tangential, substrate_x_pos_tangential,
substrate_y_pos_tangential
match device_tangential, device_x_pos_tangential,
device_y_pos_tangential
let x_disp_normal = device_x_pos_normal - substrate_x_pos_normal +
substrate_x_init_pos_normal
- device_x_init_pos_normal
let y_disp_normal = device_y_pos_normal - substrate_y_pos_normal +
substrate_y_init_pos_normal
- device_y_init_pos_normal
print "Voltage = ", i
print "x_disp_normal = ", scale*x_disp_normal, " microns,
y_disp_normal = ", scale*y_disp_normal,
" microns"
let voltage[i] = i
let x_pos_normal[i] = x_disp_normal*scale
let y_pos_normal[i] = y_disp_normal*scale
let x_disp_tangential = device_x_pos_tangential
- substrate_x_pos_tangential
+ substrate_x_init_pos_tangential
- device_x_init_pos_tangential
let y_disp_tangential = device_y_pos_tangential
- substrate_y_pos_tangential
+ substrate_y_init_pos_tangential
- device_y_init_pos_tangential
print "x_disp_tang = ", scale*x_disp_tangential, " microns,
y_disp_tang = ", scale*y_disp_tangential, " microns"
let x_pos_tangential[i] = x_disp_tangential*scale
let y_pos_tangential[i] = y_disp_tangential*scale
fprint fname| voltage[i]; x_pos_normal[i]; y_pos_normal[i];
x_pos_tangentia[i]; y_pos_tangential[i]
385
}
fclose fname
let msg "Hit select to start the pull back cycle"
msgbox msg
wait
?The following set of commands creates and opens a data file, in
?which, the voltages applied to the pull drive of the normal arm
?and the corresponding positions of its suspended shuttle are
?stored. The displacements of the suspended shuttle of the
?tangential arm due to the voltages applied to the pull drive of
?the normal arm are also stored in the data file
let fname = basename,"_pull.dat"
fopen fname
fprint fname| "Voltage_pb (V)"; "x_disp_pb_normal (microns)";
"y_disp_pb_normal (microns)"; "x_disp_pb_tangential
(microns)"; "y_disp_pb_tangential (microns)"
?The following set of commands applies an increasing voltage to
?the pull drive of the normal arm, determines the
?corresponding positions of its suspended shuttle using the
?pattern matching technique and stores the applied voltage and
?shuttle positions in the data file opened previously. It also
?determines the displacements of the suspended shuttle of the
?tangential arm caused by the voltages applied to the pull drive
?of the normal arm and stores them in the data file opened
?previously
for i = 0 to pull*5 i+1
{
outv 2: i/gaino/5
delay 1
snap
match substrate_normal, substrate_x_pos_normal,
substrate_y_pos_normal
match device_normal, device_x_pos_normal, device_y_pos_normal
match substrate_tangential, substrate_x_pos_tangential,
substrate_y_pos_tangential
match device_tangential, device_x_pos_tangential,
device_y_pos_tangential
let x_disp_normal = device_x_pos_normal - substrate_x_pos_normal
+ substrate_x_init_pos_normal
- device_x_init_pos_normal
let y_disp_normal = device_y_pos_normal - substrate_y_pos_normal
+ substrate_y_init_pos_normal
386
- device_y_init_pos_normal
print "x_disp = ", scale*x_disp_normal, " microns, y_disp = ",
scale*y_disp_normal, " microns"
let voltage_pb[i] = i/5
let x_pos_pb_normal[i] = x_disp_normal*scale
let y_pos_pb_normal[i] = y_disp_normal*scale
let x_disp_tangential = device_x_pos_tangential
- substrate_x_pos_tangential
+ substrate_x_init_pos_tangential
- device_x_init_pos_tangential
let y_disp_tangential = device_y_pos_tangential
- substrate_y_pos_tangential
+ substrate_y_init_pos_tangential
- device_y_init_pos_tangential
print "x_disp_tang = ", scale*x_disp_tangential, " microns,
y_disp = ", scale*y_disp_tangential, " microns"
let x_pos_pb_tangential[i] = x_disp_tangential*scale
let y_pos_pb_tangential[i] = y_disp_tangential*scale
fprint fname| voltage_pb[i]; x_pos_pb_normal[i]; y_pos_pb_normal[i];
x_pos_pb_tangential[i]; y_pos_pb_tangential[i]
}
outv 1: 0
outv 2: 0
fclose fname
?The following set of commands plots the voltages applied to push
?drive of the normal arm versus the corresponding x and y
?displacements of its suspended shuttle
for i = 0 to asize[voltage]-1 i+1
{
chart voltage[i], x_pos_normal[i], 1
chart voltage[i], y_pos_normal[i], 2
}
?The following set of commands plots the voltages applied to pull
?drive of the normal arm versus the corresponding x and y
?displacements of its suspended shuttle
for i = 0 to asize[voltage_pb]-1 i+1
{
chart voltage_pb[i], x_pos_pb_normal[i], 3
chart voltage_pb[i], y_pos_pb_normal[i], 4
}
387
A.11 Script Name: Pattern Matching Technique Uncertainty.stp
?The following set of commands declares the variables that can be
?inputted by the user
ustring basename, "Testno_obj_lens_mag", "Base of filenames"
uglobal n, 1000, "No. of measurements"
desc "This script measures the distance"
desc "between two fixed points in a live"
desc "image n times & calculates the"
desc "rms error in the measurement."
desc " "
desc "Created by Naveed - 11/21/2010"
include init.mac
begin
call init
?The following set of commands declares the variables used in the
?script
alloc scale
alloc device_x_pos
alloc device_y_pos
alloc substrate_x_pos
alloc subsrate_y_pos
alloc device_x_init_pos
alloc device_y_init_pos
alloc substrate_x_init_pos
alloc substrate_y_init_pos
alloc x_disp
alloc y_disp
alloc rms_err_x
alloc rms_err_y
string fname
string msg
array x_pos_err
array y_pos_err
let scale = 0.465*10/mag
print "Scale = ", scale
388
outv 0 : 3.45
fireset "shutter",300
?The following set of commands asks the user to select two anchored
?patterns and determines their initial positions
snap
let msg = "Select ROI1 & pattern1"
msgbox msg
pattern substrate
match substrate, substrate_x_init_pos, substrat_y_init_pos
let msg = "Select ROI2 & pattern2"
msgbox msg
pattern device
match device, device_x_init_pos, device_y_init_pos
?The following set of commands creates and opens a data file, in
?which, the errors in the determination of the relative x and y
?positions of the two anchored patterns are stored
let fname = basename,"_uncertainty_in_pattern_matching_technique_",
@dn,".dat"
fopen fname
fprint fname| "error_x (nm)"; "error_y (nm)"
?The following set of commands determines the relative x and y
?positions of the two anchored patterns n times, calculates the
?relative errors in their determination and stores the errors in the
?data file opened previously
for i = 0 to n i+1
{
snap
match substrate, substrate_x_pos, substrate_y_pos
match device, device_x_pos, device_y_pos
let x_disp = device_x_pos - substrate_x_pos + substrate_x_init_pos
- device_x_init_pos
let y_disp = device_y_pos - substrate_y_pos + substrate_y_init_pos
- device_y_init_pos
print "x_disp = ", scale*x_disp*1000," nm, y_disp = ",
scale*y_disp*1000," nm"
let x_pos_err[i] = x_disp*scale*1000
let y_pos_err[i] = y_disp*scale*1000
fprint fname| x_pos_err[i]; y_pos_err[i]
refresh
delay 1
}
389
outv 1:0
outv 2:0
?The following set of commands charts the relative errors in the
?determination of the relative x and y positions of the two anchored
? patterns, calculates the rms errors in the determination of their
?relative x and y positions and stores the rms errors in the data
?file opened previously
let rms_err_x = 0
let rms_err_y = 0
for i = 0 to asize[x_pos_err]-1 i+1
{
chart i, x_pos_err[i], 3
chart i, y_pos_err[i], 4
let rms_err_x = rms_err_x + (x_pos_err[i]*x_pos_err[i])
let rms_err_y = rms_err_y + (y_pos_err[i]*y_pos_err[i])
}
let rms_err_x = rms_err_x/asize[x_pos_err]
let rms_err_y = rms_err_y/asize[y_pos_err]
let rms_err_x = sqrt(rms_err_x)
let rms_err_y = sqrt(rms_err_y)
print "RMS error in the measurement of x =", rms_err_x" nm"
fprint fname| "RMS error in the measurement of x =", rms_err_x" nm"
print "RMS error in the measurement of y =", rms_err_y" nm"
fprint fname| "RMS error in the measurement of y =", rms_err_y" nm"
fclose fname
A.12 Macro Name: init.mac
macro init
{
?The following command inputs the default magnification of the
?objective lens
global mag
let mag=10
?The following commands record the date and time of the commencement
?of execution of a script
string startdate
getdate startdate
390
string starttime
gettimel starttime
?The following command determines the size (in microns) of a pixel
?in the field of view
global scale
?For Firewire Camera
let scale = (0.465)*10/mag
?For NTSC B/W (2/3" CCD) Camera
?let scale = (1.35)*10/mag
?For NTSC Color (1/2" CCD) Camera
?let scale = 0.98*10/mag
?The following commands input the maximum number of x and y pixels
?in the field of view
global npix_x
global npix_y
?For Firewire Camera
let npix_x = 1280
let npix_y = 960
?For NTSC camera
?let npix_x = 640
?let npix_y = 480
global pi
let pi = 3.14159
?The following command inputs the gain of the voltage amplifier,
?which is used in line with a DAC to generate the voltages required
?to actuate the microinstruments
global amp_gain
let amp_gain = 20
global inv_amp_gain
let inv_amp_gain = 1/20
?The following command assigns a name piezo_chan to channel 7,
?which is the channel used to actuate the close-loop piezo used to
?modulate the length of the reference arm of the interferometer
global piezo_chan
let piezo_chan = 7
outv piezo_chan:0
?The following command inputs the value of v2pi, which is the
?voltage that should be applied to the close-loop piezo to cause a
391
?phase shift of 2pi in the reference light beam
global v2pi
?For open-loop piezo
?let v2pi=1.51
?For close-loop piezo
let v2pi=0.029544
?The following command inputs the wavelength (in nm) of light that
?gets transmitted through the monochromator installed in the
?interferometer and, is used for phase shifting interferometry
global lambda
let lambda = 532
?The following command inputs the gain of the piezo-controller,
?which is used in line with the DAC used to generate the voltages
?required to actuate the close-loop piezo
global piezo_gain
let piezo_gain = 1
?The following command assigns a name "led_chan" to channel 0, which
?is the channel used to power the illumination source (a green LED)
global led_chan
let led_chan = 0
?The following command causes the DAC to output 3.45 V at channel 6,
? which is the channel used to power an indicator light that is used
?to indicate operational status of the probe station
outv 6=3.45
print "init.mac was called successfully."
}
392
Appendix B
Derivations of the Equations Used to Determine  and   
B.1 Derivation of the Equation Used to Determine  : Sequence H
The self-calibrating  ve frame sequence (referred to as H) suggested by Hariharan
et al. is given by Eqs. (B.1.1a - B.1.1e) shown below, where I1, I2, I3, I4 and I5 are
the intensity measurements made at phase steps of 2 ,  , 0,  , 2 respectively
and  is the original optical phase di erence between the interfering beams [176].
I1 = A+B + 2pABcos(  2 ) (B.1.1a)
I2 = A+B + 2pABcos(   ) (B.1.1b)
I3 = A+B + 2pABcos( ) (B.1.1c)
I4 = A+B + 2pABcos(   ) (B.1.1d)
I5 = A+B + 2pABcos(  2 ) (B.1.1e)
Subtracting Eq. B.1.1d from Eq. B.1.1b gives,
I2 I4 = 4pABsin ( ) sin ( ) (B.1.2)
Similarly,
2I3 I1 I5 = 4pABcos ( )[1 cos (2 )] (B.1.3)
Dividing Eq. B.1.2 by Eq. B.1.3 gives,
I2 I4
2I3 I1 I5 = tan ( )
sin ( )
1 cos (2 ) (B.1.4)
For  = 90 , Eq. B.1.4 gives,
tan ( ) = 2(I2 I4)2I
3 I1 I5
(B.1.5)
B.2 Derivation of the Equation Used to Determine  : Sequence NH
The class of  ve frame sequence (referred to as NH), which is mathematically
equivalent to sequence H is represented by Eqs. (B.2.1a - B.2.1e) shown below, where
I1, I2, I3, I4, I5 are the intensity measurements made at phase steps of 0,   ,  2 ,
393
 3 ,  4 respectively.
I1 = A+B + 2pABcos( ) (B.2.1a)
I2 = A+B + 2pABcos(   ) (B.2.1b)
I3 = A+B + 2pABcos(  2 ) (B.2.1c)
I4 = A+B + 2pABcos(  3 ) (B.2.1d)
I5 = A+B + 2pABcos(  4 ) (B.2.1e)
Subtracting Eq. B.2.1d from Eq. B.2.1b gives,
I2 I4 = 4pABsin (  2 ) sin ( ) (B.2.2)
Similarly,
2I3 I1 I5 = 4pABcos (  2 )[1 cos (2 )] (B.2.3)
Dividing Eq. B.2.2 by Eq. B.2.3 gives,
I2 I4
2I3 I1 I5 = tan (  2 )
sin ( )
1 cos (2 ) (B.2.4)
For  = 90 , Eq. B.2.4 gives,
tan ( ) = 2(I2 I4)2I
3 I1 I5
(B.2.5)
B.3 Error Analysis of Sequence H
If a small error  is present in the nominal phase step  , then, according to
Eq. B.1.4,
I2 I4
2I3 I1 I5 = tan ( )
sin ( + )
1 cos [2( + )] (B.3.1)
Following Eq. B.1.4 and Eq. B.1.5,
I2 I4
2I3 I1 I5 = 
tan ( 0)
2 (B.3.2)
From Eqs. B.3.1 and B.3.2,
tan ( 0)
2 = tan ( )
sin ( + )
1 cos [2( + )] (B.3.3)
Now,
sin ( + )
1 cos [2( + )] =
sin ( ) cos ( ) + cos ( ) sin ( )
1 [cos (2 ) cos (2 ) sin (2 ) sin (2 )] (B.3.4)
394
For  = 90 , Eq. B.3.4 becomes,
sin ( + )
1 cos [2( + )] =
cos ( )
1 + cos (2 ) (B.3.5)
= 12 cos ( ) (B.3.6)
Since  is small, neglecting  2 in Eq. B.3.6 gives,
sin ( + )
1 cos [2( + )] =
1
2 cos2 ( =2) (B.3.7)
= 12 sec2 ( =2) (B.3.8)
= 12(1 + tan2 ( =2)) (B.3.9)
Since  is small, tan ( =2) =  =2, therefore, Eq. B.3.9 becomes,
sin ( + )
1 cos [2( + )] =
1
2(1 +
 2
4 ) (B.3.10)
Substituting Eq. B.3.10 in Eq. B.3.3, we get,
tan ( 0)
2 =
tan ( )
2 (1 +
 2
4 ) (B.3.11)
Rearranging Eq. B.3.11 gives,
tan ( 0) tan ( ) =  
2
4 tan ( ) (B.3.12)
Rearranging Eq. B.3.12 and using Eq. B.3.11 gives,
tan ( 0  ) =  
2
4
tan ( )
1 + tan ( ) tan ( )( 2=4 + 1) (B.3.13)
Since  is small, neglecting  2=4 in Eq. B.3.13 gives,
tan ( 0  ) =  
2
4
tan ( )
1 + tan2 ( ) (B.3.14)
=  
2
8 sin (2 ) (B.3.15)
Since  0  is small, tan ( 0  ) =  0  , therefore, Eq. B.3.15 becomes,
  H =  0  =  
2
8 sin (2 ) (B.3.16)
395
B.4 Error Analysis of Sequence NH
If a small error  is present in the nominal phase step  , then, according to
Eq. B.2.4,
I2 I4
2I3 I1 I5 = tan [  2( + )]
sin ( + )
1 cos [2( + )] (B.4.1)
Following Eq. B.2.4 and Eq. B.2.5,
I2 I4
2I3 I1 I5 = 
tan ( 0)
2 (B.4.2)
From Eqs. B.4.1 and B.4.2,
tan ( 0)
2 = tan [  2( + )]
sin ( + )
1 cos [2( + )] (B.4.3)
For  = 90 ,
tan [  2( + )] sin ( + )1 cos [2( + )] = tan (  2 ) cos ( )1 + cos (2 ) (B.4.4)
= tan (  2 ) 12 cos ( ) (B.4.5)
Substituting Eq. B.3.10, Eq. B.4.5 in Eq. B.4.3, we get,
tan ( 0)
2 =
tan (  2 )
2 (1 +
 2
4 ) (B.4.6)
Rearranging Eq. B.4.6 gives,
tan ( 0) tan ( ) = tan (2 )[1 + tan
2 ( )
1 tan ( ) tan (2 ) +
 2
4 tan (  2 ) (B.4.7)
Rearranging Eq. B.4.7 gives,
tan ( 0  ) = tan (2 )[1 + tan
2 ( )
[1 tan ( ) tan (2 )][1 + tan ( ) tan ( 0)] +
 2
4
tan (  2 )
1 + tan ( ) tan ( 0)
(B.4.8)
Now since  is very small,
tan (2 )[1 + tan2 ( )
[1 tan ( ) tan (2 )][1 + tan ( ) tan ( 0)] = 2 (B.4.9)
396
Substituting Eq. B.4.9 in Eq. B.4.8 gives,
tan ( 0  ) = 2 +  
2
4
tan (  2 )
1 + tan ( ) tan ( 0) (B.4.10)
= cos2 ( )[ 2 cos2 ( ) +  
2
4 tan ( ) 
 3
2 ] (B.4.11)
Since 2 =cos2 ( ) ( 2=4) tan ( ) and  3=2, Eq. B.4.11 becomes,
tan ( 0  ) = 2 (B.4.12)
Since  0  is very small, tan ( 0  ) =  0  , therefore, Eq. B.4.12 becomes,
  NH =  0  = 2 (B.4.13)
397
Appendix C
List of Acronyms
AFM Atomic Force Microscope/Microscopy
AuNP Gold Nanoparticle
BOX Buried Oxide
CA Contact Angle
CAA Contact Angle Analysis
CBA Cantilever Beam Array
CPD Critical Point Drying/Dried
CVD Chemical Vapor Deposition/Deposited
DI Deionized
DRIE Deep Reactive Ion Etching
FTIR Fourier Transformed Infra-red
GXL Gas-expanded Liquid
HMDS Hexamethyldisilazane
iMEMS1 Integrated Micro-Electro-Mechanical Systems
IPA Isopropyl Alcohol
MST Mechanical Stress Tester
MEMS Microelectromechanical Systems
NP Nanoparticle
OTS Octadecyltrichlorosilane
RMS Root Mean Square
RPM Revolutions Per Minute
RST Residual Stress Tester
SEM Scanning Electron Microscope/Microscopy
SUMMiT2 Sandia Ultra-planar Multi-level MEMS Technology
SBA Sidewall Beam Array
SFAT Sidewall Friction and Adhesion Tester
SFT Sidewall Friction Tester
TEM Transmission Electron Microscope/Microscopy
UHV Ultra-high Vacuum
UVO Ultra-violet-Ozone
XPS X-ray Photoelectron Spectroscopy
1Registered trademark of Analog Devices
2Registered trademark of Sandia National Laboratories
398