Development of a Microcantilever Based MEMS Device for Biosensor Application 
 
by 
 
Shakib Morshed 
 
 
 
 
A dissertation submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Doctor of Philosophy 
 
Auburn, Alabama 
December 13, 2010 
 
 
 
 
Keywords: microcantilever, microelectromechanical systems (MEMS), biosensor, resonant 
frequency, finite element analysis (FEA) 
 
Copyright 2010 by Shakib Morshed 
 
 
Approved by 
 
Barton C. Prorok, Chair, Associate Professor of Materials Engineering 
Dong-Joo Kim, Associate Professor of Materials Engineering 
Robert Dean, Assistant Professor of Electrical and Computer Engineering 
Pradeep Lall, Professor of Mechanical Engineering 
Ruel A. Overfelt, Professor of Materials Engineering 
 
 
 
 
 
 
 ii
 
 
 
Abstract 
 
 In this project a microcantilever based MEMS device for biosensing application had been 
developed.  The geometrical aspects of the cantilever beam structure had been studied for 
increasing the sensitivity of the sensor devices.  Finite Element Analyses of different geometrical 
shapes were performed to compare the mass sensitivity of different shapes of microcantilever 
beam structures.  Microcantilever beam structures of the promising geometries were fabricated, 
and their resonant frequencies were measured optically for comparison.  Both the FEA results 
and the optical measurement results agreed that the trends of triangular and the modified shape 
geometries compared to the regular rectangular shape geometry, in terms of frequency shift 
performances of those geometries.  The triangular shaped geometry showed, approximately, an 
order of magnitude, and the modified shaped geometry showed more than three times the 
performance of the regular rectangular shape. 
Damping effects on these geometries were investigated by testing them in air at different 
pressure levels, ranging from the atmospheric pressure of 10
5
 Pa to 10
-2
 Pa.  The resulting 
responses of these geometries followed the same trend as the analytical plot for the rectangular 
shape structure.  As the relative resonant frequency of the structure is proportional to the intrinsic 
resonant frequency, measured at the lowest pressure levels achieved by the AFM system, 
different shapes showed different amount of responses as a function of pressure.  As the intrinsic 
 iii
resonant frequency of the triangular shape was the highest, its relative resonant frequency was 
the highest; the modified geometry showed intermediate responses among the three geometries. 
MEMS devices based on piezoresistive sensing element were designed and fabricated 
that included regular rectangular, triangular, and the modified geometrical shapes, based on their 
performances in terms of the mass sensitivities.  Piezoresistive measurements of these MEMS 
devices were performed to characterize the devices, which matched the optical measurement data 
of those structures.  Thus, this project showed the performances of the microcantilever MEMS 
devices can be improved in terms of sensitivity, by modifying the geometrical shapes of the 
regular rectangular shaped geometries.  Also, the modified shaped geometry showed lesser effect 
on their resonant frequency response due to damping effect than the triangular shaped geometry.  
Thus, by using these geometries, part of the reduction in performances of the microcantilever 
MEMS devices can be recovered. 
 
 iv
 
 
 
Acknowledgements 
 
 The author would like to thank his adviser Dr. Barton C. Prorok for his guidance 
throughout the project; without whose constant guidance and encouragements, this project would 
not have been completed.  Thus, the author is eternally grateful for the accomplishment of this 
degree, to him.  The author would, also, like to extend his gratitude towards the Auburn 
University Detection & Food Safety (AUDFS) Center for funding the project, which could not 
have been performed without the necessary funds.  Next, the thanks are due to the committee 
members Dr. Ruel A. Overfelt, Dr. Pradeep Lall, Dr. Robert Dean and Dr. Dong-Joo Kim for 
providing occasional guidance, and equipment necessary for the completion of this project. 
Special thanks are due to the Microelectronics Fabrication Laboratory of the Alabama 
Microelectronics Science & Technology Center (AMSTC), especially Charles Ellis for his 
constant support and advice.  Thanks are also due to William Baugh, Kieth Warren, Drew Sellers, 
Roger Lugo, Joe Haggerty and Mike Palmer for their help at different phases of the project.  
Thanks are, also, due to LC Mathison, Levar Odum, Roy Howard, Dave Lindahl and Steve 
Moore for their technical assistances throughout this project.  Thanks are due to Shirley Liles and 
Alison Mitchell for their administrative helps.  Thanks are due to numerous colleagues and group 
members; without their helps this project would not have been completed.  Among them Bo 
Zhou, Cai Liang, Nikhil Mehta, Madhumida Ramaswamy, Nicole Odum, Dong Liu, Kevin 
 v
Schwieker, Brandon Frye, Sang Hoon Yoon, J.-H. Park, Naved Siddiqui and Rajesh Guntupali 
are to name a few. 
Last but not least, the author would like to thank his family and friends who gave support 
and encouragement throughout the years during this time.  There were times when the obstacles 
seemed insurmountable; friends and family members near or far, always stood beside the author, 
literally or figuratively.  There are numerous others who have extended their helping hands 
during this project, whose names are not mentioned here but the author is eternally grateful to all 
of them for this achievement. 
 
 vi
 
 
 
Table of Contents 
 
Abstract???????????????????????????????????ii 
Acknowledgements?????????????????????????????.?iv 
List of Figures?????..???????????????????...?????.?..vii 
List of Tables??.?????..????????????????????????...xi 
List of Charts??????..????????????????????.......................xii 
Chapter 1 Introduction???????????????????...???.????..1 
Chapter 2 Theoretical Background?????????????..????????.....7 
Chapter 3 Numerical Analysis of Geometries?????????????????....25 
Chapter 4 Verification of the FEA Results???????????????...???..39 
Chapter 5 Damping Effect on the Geometries??????????????????50 
Chapter 6  Microfabrication Process of the MEMS Devices??????..??????69 
Chapter 7  Piezoresistive Measurement of the MEMS Devices??????????......97 
Chapter 8 Discussion and Conclusions???????????????????....106 
References?????????????????????????????????112 
Appendix A????????????????????????????????..117 
 vii
 
 
 
List of Figures 
 
Figure 1: Resonant frequency based detection scheme of microcantilever based biosensors?.....3 
Figure 2: (a) Conventional optical based frequency sensing, and (b) MEMS based sensor.??..6 
Figure 3: 1
st
 mode shape of natural frequency of vibration of a cantilever beam of l=50?m, 
w=0.5?m & t=200nm?????????????????????????...9 
 
Figure 4: 2
nd
 mode shape of natural frequency of vibration of a cantilever beam of l=50?m, 
w=0.5?m & t=200nm.?.???????????????????????...10 
 
Figure 5: 3
rd
 mode shape of natural frequency of vibration of a cantilever beam of l=50?m, 
w=0.5?m & t=200nm.??.??????????????????????...11 
Figure 6: 4
th
 mode shape of natural frequency of vibration of a cantilever beam of l=50?m, 
w=0.5?m & t=200nm.??.?????????????????????...?12 
 
Figure 7: 5
th
 mode shape of natural frequency of vibration of a cantilever beam of 
l=50?m, w=0.5?m & t=200nm.??.??????????????????.....13 
 
Figure 8: 3D plot of natural frequency of vibration (1
st
 mode shape) of microcantilever 
beam as a function of length & thickness???????????...........................14 
 
Figure 9: Wheatstone bridge configuration???????????????.......................19 
Figure 10: 3D plot of fractional change in piezoresistance on microcantilever beam as a 
function of length & thickness?????????????????????....21 
 
Figure 11: Schematic arrangement showing the sensing & the reference cantilevers of the 
MEMS device???????????...?????...????..?????.....24 
 
Figure 12: Arrangement showing the small mass attachment in the FEA simulations????.28 
Figure 13: Plot showing numerically calculated correction factor as a function of the width 
to length ratio of 50 ?m long rectangular shaped cantilever beams?...........................31 
 
 
 viii
Figure 14: Plot showing numerically calculated frequency shift vs. the width to length 
ratio of 50 ?m long rectangular shaped cantilever beams??????????......32 
 
Figure 15: Tetrahedral structural element SOLID187 with 10 nodes, each with 3 
translational DOF????????..?????????????..?????34 
 
Figure 16: SEM images showing fabricated AFM tip microcantilever of shape A?????...42 
Figure 17: SEM images showing fabricated AFM tip microcantilever of shape F?????...43 
Figure 18: SEM images showing fabricated AFM tip microcantilever of shape I??????44 
Figure 19: Frequency spectrums obtained by the AFM system of shape A; with & without 
attaching poly-bead at ambient pressure????????????????....?.45 
 
Figure 20: Frequency spectrums obtained by AFM of shape F; with & without attaching 
polybead at 75 mtorr pressure????????????????????.?....46 
 
Figure 21: Frequency spectrums obtained by AFM of shape I; with & without attaching 
polybead at 30 mtorr pressure??????????????????.???....47 
 
Figure 22: Schematic figure showing expected pressure dependence on different 
geometrical shapes??????????????????????????..51 
 
Figure 23: Frequency spectrum for the sample no. 1 of Shape A at 0.048 Pa pressure????54 
Figure 24: Frequency spectrum for the sample no. 1 of Shape F at 0.045 Pa pressure????.55 
Figure 25: Frequency spectrum for the sample no. 4 of Shape I at 0.053 Pa pressure????..56 
Figure 26: Relative resonant frequency as the function of pressure for shape A??????..62 
Figure 27: Relative resonant frequency as the function of pressure for shape F??????...63 
Figure 28: Relative resonant frequency as the function of pressure for shape I???????64 
Figure 29: Comparison of the relative resonant frequency vs. pressure plots for all three 
geometries??????????????????????????...............65 
 
Figure 30: Effect of mass addition on the relative resonant frequency vs. pressure plot for 
shape A??????????????????????????????....66 
 
Figure 31: Effect of mass addition on the relative resonant frequency vs. pressure plot for 
shape F??????????????????????????????....67 
 
 ix
Figure 32: Effect of mass addition on the relative resonant frequency vs. pressure plot for 
shape I????..??????????????????????????...68 
 
Figure 33: Picture of piezoresistance and metal connector arrangement in a rectangular 
shaped device.???...????????????????????????..74 
 
Figure 34: A close up picture of piezoresistive polysilicon pads and their metal 
connectors?????????????????????????????...75 
 
Figure 35: Picture of the sensing pad on a triangular shaped device???????????.76 
Figure 36: Picture of a cantilever beam structure with sputtered oxide as the passivation 
layer; after exposing it to KOH solution..?..??????????????..?...78 
 
Figure 37: Picture of the piezoresistors on a device with sputtered oxide as the passivation 
layer; after exposing it to KOH solution????????????..?????...79 
 
Figure 38: Picture of the piezoresistors on a device with reactively sputtered nitride as the 
passivation layer; after exposing it to KOH solution?????????????..80 
 
Figure 39: SEM images showing polysilicon layers were attacked during KOH etch, due to 
the thinning of SiC layer when regular PR is used as the etch mask for the DRIE 
process??????????????????????..???????...?83 
 
Figure 40: A close up SEM image, showing piezoresistor etched away during KOH etching 
due to the thinning of SiC layer when regular PR is used as the etch mask for the 
DRIE process???????????????????????????......84 
 
Figure 41: Resistance measurement after etching SiC & Si
x
N
y
 in the AOE system, 
without specifying time for the etching cycles ???????????????..86 
 
Figure 42: Resistance measurement after etching SiC & Si
x
N
y
 in the AOE system, with 
specific 15 seconds etching cycles??????????...????...??.??...87 
 
Figure 43: Resistance measurement after etching Si in KOH for bulk micromachining of 
the MEMS device???????????????????..??.....................89 
 
Figure 44: Resistance measurement after etching Si in TMAH for bulk micromachining of 
the MEMS device using conventional recipe??????????..?????...90 
 
Figure 45: Resistance measurement after etching Si in TMAH for bulk micromachining of 
the MEMS device using pH controlled recipe...??????????????.....91 
 
Figure 46: SEM images showing microcantilevers.?????????????????..92 
 
 x
Figure 47: SEM images showing microcantilevers with the Wheatstone bridge 
structures?????????????????????????????.....93 
 
Figure 48: Schematic diagram showing test setup for optical measurement of the 
resonant frequency of the microcantilever MEMS device??????????.....98 
 
Figure 49: Resonant Frequency characterization of a 150? length microcantilever 
MEMS device using the AFM photodetector???????????????.....99 
 
Figure 50: Resonant Frequency characterization of a 250? length microcantilever 
MEMS device using the AFM photodetector???????????????...100 
 
Figure 51: Schematic diagram showing test setup for piezoresistive measurement of the 
resonant frequency of the microcantilever MEMS device??????????...102 
 
Figure 52: Resonant Frequency Measurement of a 150? length microcantilever MEMS 
device using the Lock-in amplifier????????????????...............104 
 
Figure 53: Resonant Frequency Measurement of a 250? length microcantilever MEMS 
device using the Network Analyzer??????????????????..?105 
 
Figure 54: SEM image showing microcantilever MEMS device of triangular geometry??...110 
 
Figure 55: SEM image showing microcantilever MEMS device of the modified geometry......111 
 xi
 
 
 
List of Tables 
 
Table 1: Comparison of Acoustic Wave based sensors?..?.??.???????????...3 
Table 2: Correction factors for different width to length ratios...?.????.???................30 
Table 3: Comparison of numerical performances of different geometrical shapes....????...37 
Table 4: Comparison of experimental performances of different geometrical shapes..................49 
Table 5: Resonant frequency responses of shape A?????????????????...57 
Table 6: Resonant frequency responses of shape F?????????????????...58 
Table 7: Resonant frequency responses of shape I??????????????????59 
Table A1: Simulation results for different geometrical shapes performed using ANSYS 
software??????????????????????????????.117 
 xii
 
 
 
List of Charts 
 
Flow Chart 4.1: Microfabrication process flow chart for the AFM tip microcantilevers???..41 
Flow Chart 6.1: Microfabrication process flow chart for the microcantilever MEMS 
devices???????????????????????????????.94 
 1
 
 
 
CHAPTER 1 
 
INTRODUCTION 
 
In recent years, Microcantilever based sensors have been applied to detect different 
physical quantities, such as acceleration of automobiles to deploy airbags, and different chemical 
[1-8] and biological species [8-17] present in different environments.  Sensors consist of two 
elements: sensing and transduction elements.  The sensing element measures the measurand, 
which can be a physical quantity, property or a certain condition, from the input signal that can 
be magnetic, chemical, electromagnetic, mechanical, thermal etc.  Microcantilever based sensors 
use two types of detection schemes, one of them involves deflection of the cantilever beam 
structure due to the mass loading on the beam in static condition, while the other one involves 
the change in the resonant frequency of the cantilever beam structure due to the mass loading on 
the beam in dynamic condition.  In this study, the second kind of detection scheme had been 
employed, which is illustrated in figure 1.  In case of the frequency based detection scheme, the 
sensing element of the microcantilever based sensor is the cantilever beam structure with specific 
natural frequencies.  These sensors work on the principle of resonant frequency.  That is, 
resonance occurs when an imposed frequency of vibration matches the natural frequency of 
vibration of the structure.  This translates into the fact that the deflection of the beam structure 
tends to become infinite, compared to the normal conditions.  The transduction element 
 2
transduces the sensed signal into an output signal, preferably electrical, which is a quantity 
depending on the applied measurand.  In this experimental study, piezoresistive element was 
used as the transduction element.  Piezoresistive materials change their resistivity depending on 
the applied strain.  As the cantilever beam structure vibrates, it bends up and down or sideways.  
This translates into the straining of the piezoresistive sensing element, which is integrated into 
the beam structure.  This result into change in the resistivity of the material; thus, changes the 
total resistance (?R) of the piezoresistive element.  This change in resistance can be detected 
through the change in the measured voltage drop (?V) across these elements.  To amplify this 
output, usually, a Wheatstone bridge configuration is used. 
Biosensors usually use acoustic wave based sensing devices for detection.  They use elastic 
waves at frequencies well above the human audible range propagating through the sensing 
structures.  Microcantilever based sensor devices fall into this category. Datskos et al. [18], Oden 
[19] and Stern et al. [20] have compiled and compared performances of acoustic wave based 
sensors.  Table 1 lists the mass sensitivity, which can be expressed by the equation 1, and the 
minimum detectable surface mass density for this type of devices. 
 
)1(
1
min
s
m
m
f
f
S
?
?
?=  
Here, f: resonant frequency, 
        ?f: resonant frequency shift 
and, ?m
s
min
 : Minimum detectable surface mass density. 
 3
 
 
Figure 1: Resonant frequency based detection scheme of microcantilever based biosensors. 
 
Table 1: Comparison of Acoustic Wave based sensors 
 
Sensor type 
Resonant frequency, f 
(MHz) 
Mass sensitivity, 
S
m
 (cm
2
/gm) 
?m
s
min
(ng/cm
2
)
Microcantilever 0.005-5 991-1363 0.069-13.8 
Flexural Plate Wave (FPW) 2-7 951 0.4 
Surface Acoustic Wave 
(SAW) 
30-300 151 1.2 
Acoustic Plate Mode (APM) 25-200 65 1.0 
Quartz Crystal Microbalance 
(QCM) 
5 14 10 
 
 4
It shows that, by employing microcantilever based sensing device, the smallest amount of 
mass can be detected.  In recent years, researchers at the Cornell University have demonstrated 
attogram (x10
-18
 gm) level mass sensitivity [21].  However, they have employed AFM (atomic 
force microscopy) system for detection, which employs optical detection scheme.  Thus, the 
detection mechanism is bulky and expensive, and cannot be employed in liquid mediums. 
In order to apply a sensor device as a biosensor, it has to be compatible with the biological 
agent that needs to be detected.  Also, it has to be of low cost and easily operable, and has to 
have high specificity and selectivity to eliminate false signals.  To achieve the biocompatibility 
of the sensor, the sensing surface is coated with gold pads, which can be functionalized to 
capture a specific bacteria or other biological agent that needs to be detected.  As the biosensors 
are required to be operated at remote and numerous locations, such as in the food chains of 
humans and animals alike, it needs to be inexpensive and easily operable. On-chip MEMS 
devices allow us to achieve this goal.  As the MEMS devices are fabricated using the 
microelectronic fabrication processes, it enables us to fabricate the devices in batches, which 
lowers the fabrication cost.  Conventional microcantilever based sensors are operated using 
optical based sensing scheme to detect the shift in the resonant frequency due to the attachment 
of mass on the sensor surface, which is costly and not easily operable.  On the other hand, 
MEMS devices give electrical output signals that can be easily operated and inexpensively 
processed; thus, driving downs the cost of the operation and minimizing the expertise of the 
operator.  For biosensor applications, the sensor needs to operate in liquid media, as most 
pathogens are present in liquid based solutions.  Optical sensing schemes are not suitable for 
liquid media.  Thus, the MEMS devices with proper passivation layers can be effectively used in 
liquid based media.  Figure 2 shows both of these sensing schemes.  As the resonant frequency 
 5
of a structure depends on the mass and the stiffness of the structure, the sensitivity of the 
structure depends on the geometry of the microcantilever structures.  In recent years, different 
researchers are investigating effects of sizes and shapes of the microcantilevers to increase the 
sensitivity of the sensors.  In this study, the geometrical aspects of the microcantilever structures 
were investigated to increase the sensitivity.  To perform that task, finite element analyses (FEA) 
of different geometrical shapes were performed using ANSYS software to calculate the 
frequency shift for a small mass attached on the tip of the geometries, and then compared to the 
basic rectangular shapes.  Some of the promising geometrical shapes of microcantilever 
structures, found from the numerical analysis, had been designed and fabricated for MEMS 
based sensors.  In this experimental study, these geometrical shapes were studied, along with the 
basic rectangular shaped cantilever structures, and performance of those experimental results 
were compared with the numerical ones.  For initial evaluation, microcantilever beam structures 
were made of in the range of 100 ?m length of different geometrical shapes along with regular 
rectangular shape.  Also, the damping effects on these geometries were studied.  The other aspect 
of this study was to increase the mass sensitivity by reducing the length of the piezoresistive 
microcantilevers.  So far, researchers have reported piezoresistive microcantilever sensors in the 
dimensions of 100s of ?m length.  In this project, piezoresistive microcantilevers of 50, 150 and 
250 ?m lengths were fabricated; thus, increasing the mass sensitivity of the devices. 
 6
 
 
(a) 
 
 
(b)
 
Figure 2: (a) conventional optical based frequency sensing scheme, and (b) MEMS based sensor. 
Laser 
Detector 
Piezoresistive 
Element 
V
in
V
out 
 7
 
 
 
CHAPTER 2 
 
THEORETICAL BACKGROUND 
 
Microcantilever based sensors are usually operated on the basis of shift in the resonant 
frequency of the structure due to the attachment of mass to the target element on the beam.  The 
resonant frequency of undamped cantilever beam structure of a uniform rectangular cross section 
can be obtained from the solution of an undamped simple harmonic oscillator [22].  For a 
cantilever beam with a uniform rectangular cross section, and a negligible thickness compared to 
the other parameters, the natural frequency of vibration can be approximated from the following 
equation: 
 
)2(
122
2
2
d
E
l
t
f
i
i
?=
?
?
 
where, t: thickness of the beam, 
l: length of the beam,  
d: density of the material 
E: elastic modulus, 
     and, ?
i
: i-th root of the frequency equation; cos ? cosh ? + 1 = 0, which depends on the 
boundary conditions of the cantilever beam structure. 
 8
These roots represent the consecutive mode shapes of the natural frequency of vibrations 
of the beam structure. The first few roots for the cantilever beam structure are [23]: ?
1
 = 
1.87510407, ?
2
 = 4.69409113, ?
3
 = 7.85475744, ?
4
 = 10.99554073, ?
5
 = 14.92256510 etc.  Now 
the following Figures 3 through 7, show the first five mode shapes that are numerically 
calculated for a simple cantilever beam, using the ANSYS software for finite element analysis 
(FEA).  Here, it can be seen that the base of the cantilever, which is fixed on the extreme left side 
on each figure, is uniformly stressed only in the first mode of natural frequency of vibration.  As 
piezoresistive material had been used to detect the change in frequency through the voltage 
measurements, the transduction element of the sensor should be uniformly stressed during the 
measurements for reliable signal output.  So, in this project the sensor devices were designed for 
the application based on the 1
st
 mode shape of the natural frequency of vibration. 
Now, by using the equation (2) for the 1
st
 mode shape of vibration, the natural frequency 
of a regular shaped cantilever beam can be calculated as a function of both thickness and length.  
Figure 8 shows a three dimensional plot of natural frequency of vibration for the 1
st
 mode shape.  
From this plot, it is clear that the natural frequency of vibration of cantilever beam structure 
increases significantly at around 50 ?m of lengths.  Although, the natural frequency increases 
even further more for lengths below 50 ?m, the most important limitation for any MEMS device 
is imposed by the fabrication facilities that are available.  In this case, it is the Microelectronics 
fabrication Lab in Auburn University at the Alabama Microelectronics Science and Technology 
Center (AMSTC), where these MEMS devices were fabricated.  In addition to this, as the 
dimensions get smaller, the cost of fabricating them becomes higher. 
 9
 
 
Figure 3: 1
st
 mode shape of natural frequency of vibration of a cantilever beam of 
l = 50?m, w = 10?m & t = 200nm. 
 
 
 
 
 
 
 
 
 10
 
 
Figure 4: 2
nd
 mode shape of natural frequency of vibration of a cantilever beam of 
l = 50?m, w = 10?m & t = 200nm. 
 
 
 
 
 
 
 
 
 11
 
 
Figure 5: 3
rd
 mode shape of natural frequency of vibration of a cantilever beam of 
l = 50?m, w = 10?m & t = 200nm. 
 
 
 
 
 
 
 
 
 12
 
 
Figure 6: 4
th
 mode shape of natural frequency of vibration of a cantilever beam of 
l = 50?m, w = 10?m & t = 200nm. 
 
 
 
 
 
 
 
 
 13
 
 
Figure 7: 5
th
 mode shape of natural frequency of vibration of a cantilever beam of 
l = 50?m, w = 10?m & t = 200nm 
 
 
 
 
 
 
 
 
 14
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 8: 3D plot of natural frequency of vibration (1
st
 mode shape) of microcantilever beam as a 
function of length & thickness. 
 15
Although equation (2) holds quite well for a narrow cantilever beam structure for all the 
practical purposes, it neglects to take account the Poisson?s effect for wider beam structures, 
which were evident from the finite element analysis results.  As the width to length ratio of the 
beam structure increases, they start to behave more and more like a plate.  Thus, Yahiaoui et al. 
[24] have introduced a correction factor for the uniaxial elastic modulus to take account for the 
Poisson?s effect.  They have modified the equation (2), by using the effective elastic modulus 
Y
eff
, instead of the uniaxial elastic modulus E, which can be related by the following expression: 
 
)3(1
1
1
1
2 ?
?
?
?
?
?
?
?
?
?
?
?
?
?
+=
?
?EY
eff
 
where, ?: Poisson?s ratio, 
and ?: correction factor, depending upon the width to length ratio of the beam structure.  This 
correction factor can be calculated numerically by using finite element analysis for different 
width to length ratio of cantilever beam structures. Thus, the equation (2) takes the following 
form [24]: 
 
)4(
122
2
2
d
Y
l
t
f
eff
i
i
?=
?
?
 
  
The equation (2) can be, alternatively, expressed as follows [25, 26]: 
 
)5(
2
1
eq
i
i
m
k
f
?
=  
 16
where, k: flexural stiffness of the cantilever beam, which is the proportionality constant between 
the applied load and the resulting deflection, 
and, m
i
eq
 : the equivalent mass acting on the beam structure for the i-th mode shape. 
In the equation (5), the stiffness of the beam remains unchanged due to the attachment of 
the analytes on the surface of the cantilever beam while the equivalent mass changes.  Now, the 
change in resonant frequency of the cantilever beam can be approximated from the following 
expression [25]: 
 
)6(
222
eq
i
eq
ii
eq
i
eq
iii
i
m
mf
m
mf
k
kf
f
?
???
?
??
?
???  
 
 Thus, from the equation (4) it can be observed that the sensitivity of the microcantilever 
based sensor device is proportional to the natural frequency of the cantilever beam structure, and 
inversely proportional to the effective mass acting on the structure.  Also, from the equation (5), 
it is clear that the natural frequency of vibration is inversely proportional to the effective mass of 
the structure itself.  Thus, in this experimental study, different geometrical shapes of the 
cantilever beam structures were investigated to increase the sensitivity through increasing the 
natural frequency of vibrations of the structures, while keeping the length of the cantilever 
structure at the range of 50-150 ?m due to the limitations that were discussed earlier. 
 Now, let us discuss the piezoresistive phenomenon, through which this sensor devices 
transduce the input measurand signal into the electrical output signal.  Piezoresistive material 
changes its resistivity when it experiences stress, according to the following expression [27]: 
)7(???? ??=?  
 17
where, ?: resistivity of the material, 
?: applied stress, 
     and, ?: the piezoresistive coefficient that depends upon the doping type, n-type or p-type, and 
the doping level of the single crystal silicon or polycrystalline silicon material.  In this case, 
polysilicon were used for transduction.  Also, it depends on the crystallographic orientation of 
the silicon and in case of polysilicon it takes up an average value of the directional coefficients.  
The total resistance change of the piezoresistive element can be expressed by the following 
expression for the gage factor [27]: 
 
)8()(21
?
?????
?
E
R
R
G
ttll
?+++=
?
=  
where, ?: the Poisson?s ratio, 
?: strain applied on the element, 
R: resistance of the piezoresistor, 
?R: change in resistance, 
and, the subscript l and t: denotes the lateral and the transverse directions respectively.  In case of 
operating in the 1
st
 mode shape, ?
t
 becomes negligible.  Thus, the piezoresistive sensing elements 
in these sensors operate similarly as a strain gage.  Although, single crystal silicon of certain 
orientation gives higher gage factor [27] and better performances against certain noises present 
in the system, the temperature effect on the resistivity of the piezoresistive material is greater in 
single crystal silicon than that of the polycrystalline silicon.  The piezoresistive elements that had 
been used for these sensors are of high concentration (~10
19
-10
20
/cm
3
) of phosphorous doped 
polysilicon thin film of approximately 100nm thickness, and deposited in the Low Pressure 
 18
Chemical Vapor Deposition (LPCVD) system.  After depositing the polysilicon film, it was 
doped with phosphorous by drive-in technique performed at 1000?C.  These processes will be 
discussed further in details in the later chapter discussing the microfabrication process. 
As the changes in resistance of the piezoresistive element, due to small strain, and to 
compensate for the temperature effect on the resistivity of the piezoresistances, the strain gages 
are usually operated in a Wheatstone bridge configuration as shown in figure 9.  Here, the output 
voltage across the bridge can be calculated using the following expression [27]: 
 
)9(
31
3
42
4
inout
V
RR
R
RR
R
V ?
?
?
?
?
?
?
+
?
+
=  
 
 As in the most cases, including this one, the resistances R
1
 = R
2
 = R
3
 = R
4
 = R.  In the 
above expression and for a small change in resistance, ?R < < R; it reduces to: 
 
)10(
4
1
inout
V
R
R
V ?
?
??  
 
Here, the change in the resistance of the piezoresistive poly silicon strain gage of length 
l
gage
 on a microcantilever beam with length l, width w and thickness t, which is deflected by a 
static force of F, can be expressed as follows [27]: 
 
)11(
2
6
2
wt
F
l
l
R
R
gage
?
?
?
?
?
?
?
?
=
?
?
 
 19
 
 
Figure 9: Wheatstone bridge configuration. 
V
in
 
V
out
 
Sensing 
R
1
R
2 
R
3
R
4
 20
Figure 10 shows a representative 3D plot of equation (11).  From figures 8 and 10, it can be 
seen that the frequency of the beam increases with decrease in the length, while the fractional 
change in resistance; thus, the gage factor for the piezoresistor decreases.  Also, the frequency of 
the beam increases with the thickness, while the fractional change in resistance decreases.  These 
conflicting characteristics of the piezoresistor and the cantilever beam show a trade off between 
higher cantilever beam sensitivity and higher piezoresistive sensitivity.  As the cantilever beam 
becomes shorter and thicker, the frequency of the beam increases and it becomes stiffer; thus, 
reducing the detectable change in resistance of the piezoresistive element.  Therefore, a balance 
has to be established between theses two phenomena.  In this project, the cantilever beam 
structure dimensions were chosen to be of 50-150 ?m length and thickness of approximately 1 
?m.  These parameters are limited by the fabrication processes that are available in the facilities 
at Auburn University. 
The main problem with the piezoresistive sensing scheme arises from the thermal drift of 
the material, which introduces Johnson noise in the frequency measurements.  To take account 
for this phenomenon, reference cantilever beam had been introduced in the novel design of this 
experimental study.  These reference beams would be operating in the same environment as the 
sensing cantilevers.  This Johnson noise is the fundamental limitation of any piezoresistor 
application set by the thermal energy of the system.  This noise is independent of the frequency 
and depends upon the temperature and the resistance of the piezoresistors, which is a function of 
the geometry of the piezoresistive polysilicon element and its doping concentration [28-29].  The 
voltage noise power density (Volt
2
/Hz) can be calculated for the application range of frequency, 
?f by using the following expression: 
)12(4 fRTkS
BJ
????=  
 21
 
 
 
Figure 10: 3D plot of fractional change in piezoresistance on microcantilever beam as a function 
of length & thickness. 
 22
where, k
B
: Boltzman?s constant, 
    and, T: temperature of the piezoresistor (K). 
 As the reference cantilever is introduced with the sensing one, and both of them are 
operated in the same environment (i.e. temperature and external noise), it will facilitate to 
monitor and compare their responses during their applications.  Figure 7 shows schematic 
arrangement of a device with both the sensing and the reference cantilever beam structures 
integrated in a Wheatstone bridge configuration.  As the cantilever beams are right across each 
other in the figure, there is a possibility of harmonic waves, generated due to their vibration, 
which may interfere with each others response during their operations.  In this experimental 
study, to investigate this phenomenon, reference cantilevers are being fabricated right across the 
sensing cantilevers, at an offset distance from each other.  In addition to that, the piezoresistors 
integrated in the reference cantilever beam, can be either included as one of the resistances of the 
Wheatstone bridge configuration that consist of the piezoresistances integrated in the sensor 
cantilever beam, or can be fabricated as a part of another Wheatstone bridge configuration 
separate from the sensing side.  In this project both of these configurations are being investigated 
for better performances.  One plausible advantage of the 1
st
 type is that depending upon their 
arrangements, the sensitivity of the device can be increased; while the advantage of the 2
nd
 type 
is that their responses can be monitored at the same time, making it possible to read the 
frequency shift directly from their responses, provided that both of their basic frequencies are the 
same, eliminating the need for the base line frequency establishment.  To make sure both the 
sensing and the reference side cantilevers have the same basic frequencies, a mass balancing had 
to be performed for their designs.  In the sensing side of the device, the sensing pads are required 
to be exposed to capture the biological analytes that need to be detected, while in the reference 
 23
side of the device the metal pads need to be covered by the passivation layer, so that none of the 
analytes get captured on that side.  Therefore, to balance the extra amount of passivation layer 
material on the reference side, a mass balance needs to be performed, and the same amount of 
mass from the metal layer was removed from the middle of the designed pads on the tip of the 
cantilever beam structures. 
 24
 
Figure 11: Schematic arrangement showing the sensing & the reference cantilevers of the MEMS 
device. 
 25
 
 
 
CHAPTER 3 
 
NUMERICAL ANALYSIS OF GEOMETRIES 
 
 As previously discussed, the different geometrical configurations of microcantilever 
beam structures are being analyzed to increase the sensitivity of the microcantilever based 
MEMS devices.  ANSYS software was used to perform finite element analysis (FEA) on 
different shapes of cantilever beam structures to calculate the natural frequency of vibrations.  
Any vibrating structure can be assumed as a system consisting of components that possess 
distributed energy storage and dissipative characteristics.  In a vibrating structure, such as a 
cantilever beam, the inertial property or the effective mass of the beam, stiffness of the beam and 
the damping parameters vary with time and with respect to their spatial locations.  These 
parameters, spatial coordinates and time, can be represented by partial differential equations, 
which can be solved to represent their vibration responses.  In finite element method a vibrating 
system can be approximated by a set of properly interconnected lumped masses using discrete 
linear spring and linear viscous damping elements, which enable the system to be represented by 
ordinary differential equations.  These systems can be solved by using mode-frequency analysis 
or modal analysis [30], which is based on the assumption that these structural models have 
preferred frequencies or natural frequencies of vibration and geometric configurations or natural 
mode shapes.  This modal analysis provides an important tool to design the cantilever beam 
structures for the MEMS devices.  The resonant frequency of the designed structures, their mode 
 26
shapes and their response to the addition of mass, which needs to be detected, can be calculated 
by performing modal analysis of those structures.  As it was described before, to get a uniform 
and reliable response from the piezoresistive transducers, only the first mode shape of vibration 
of the beam structures are of concern for this project. 
 In modal analysis for a linear system, the free vibration of a mechanical structure can be 
represented by the following matrix equation [31]: 
 
 
 
This represents an eigenvalue problem that can be solved for n number of circular natural 
frequency of vibration ? from ?
i
2
 and n number of corresponding eigenvectors {?}
i
.  These 
circular natural frequencies are converted into the natural frequency of vibration for the outputs, 
by using the following expression: 
 
)14(
2?
?
i
i
f =  
  
To compare sensitivity of different geometrical shapes of cantilever beam structures, 
modal analysis on a number of different shapes of cantilever beams were performed with the 
same thickness and length.  Also, to compare the frequency shift due to the same amount of mass 
attached at the tip of the cantilever beams, modal analysis of those cantilever beam structures 
with an addition of a mass of sub picogram level were performed.  In this study, the length of the 
cantilever beams was chosen to be of 50? and the thickness of 0.5?m, and modal analyses were 
 27
performed to calculate the natural frequencies of the beam structures.  To compare the frequency 
shift, a small element of 1?m X 1?m X 0.1?m dimensions was chosen and attached on the top of 
the cantilever beam structures near the tip, and their modal analyses were performed to calculate 
the frequency of the changed structural masses.  Then, the new frequency was subtracted from 
the previous one, which provided the frequency shift for the corresponding geometrical shapes.  
The material properties, chosen for the attached mass are the same as that of the main cantilever 
beam structure, which contain the material properties of silicon rich-silicon nitride deposited in 
the LPCVD system.  The elastic modulus of the LPCVD nitride was conservatively chosen to be 
100 GPa, the density of the material was assumed 2850 kg/m
3
, and the Poisson?s ratio of 0.24 
[32].  To calculate the frequency shift due to the attachment of the mass, the small mass element 
was attached 5?m from the tip of the cantilever to simulate the realistic events for these sensor 
devices, as the sensing pads on these devices are not at the very tip of the cantilever beam 
structures due to the limitations imposed by the fabrication processes.  Figure 12 shows the 
arrangement of the small mass attachment on a rectangular shaped cantilever.  The resulting 
frequencies of the structures and their corresponding frequency shifts are tabulated in the Table 
A.1, for comparison. 
In Table A.1, the first three geometries included are for simple rectangular shaped 
microcantilevers with different widths.  Although, in the equation (2), which is only an 
approximation by itself, the width parameter is not represented, the simulation results show a 
little variations from the theoretical values calculated from the equation.  The FEA results for 
these widths are within 0.85% for the 10 ?m to 1.82% for the 30 ?m widths.  This small 
discrepancy between the theoretical and numerical results arose from the fact that the analytical 
solution does not take account for the Poisson?s effect.  Even though this equation approximates 
 28
 
 
Figure 12: Arrangement showing the small mass attachment in the FEA simulations. 
5?m
 29
quite well for all practical purposes, finite element results for different width to length ratios 
were investigated.  The FEA results of the natural frequency of vibrations and their 
corresponding frequency shifts for the attached small mass, as described earlier, are tabulated in 
the following Table 2. The corresponding correction factors were calculated by combining 
equations (3) and (4), and tabulated in the Table 2 with their corresponding width to length ratios. 
Figure 13 shows the plot of the correction factor as a function of width to length ratio. 
The curve was fitted by using the following expression: 
 
)15(exp1
?
?
?
?
?
?
?
?
?=
?
?
?
?
?
?
?
l
w
b
a?  
 
where, the curve fitting parameters a = 0.8662 and b = 1.9547 with the standard error estimate of 
0.005.  Figure 14 shows the plot of the frequency shift for the attached mass of 0.285 picogram 
as a function of the width to length ratio.  The curve was fitted by the 1st order inverse 
polynomial as follows: 
 
)16(
?
?
?
?
?
?
+=?
l
w
b
af
 
 
where, the curve fitting parameters a = 6.2806 and b = 22.4322 with the standard error estimate 
of 5.5477. 
 30
Table 2: Correction factors for different width to length ratios 
 
Width, 
w (?m) 
Width to length ratio, 
w/l 
Frequency, f 
(Hz) 
Frequency 
shift, ?f (Hz) 
Correction 
factor, ? 
1 0.02 191,517 1,127 0.0242 
5 0.1 192,248 234 0.1495 
10 0.2 192,997 125 0.2785 
20 0.4 194,124 53 0.4733 
30 0.6 194,858 46 0.6009 
40 0.8 195,336 32 0.6842 
50 1.0 195,666 29 0.7418 
 
 31
Width to length ratio, w/l
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Correcti
on f
a
ctor, 
?
0.0
0.2
0.4
0.6
0.8
 
 
Figure 13: Plot showing numerically calculated correction factor as a function of the width to 
length ratio of 50 ?m long rectangular shaped cantilever beams. 
 32
Width to length ratio, w/l
0.0 0.2 0.4 0.6 0.8 1.0
Frequency shif
t,
 
?
f (H
z
)
0
200
400
600
800
1000
1200
 
Figure 14: Plot showing numerically calculated frequency shift vs. the width to length ratio of 50 
?m long rectangular shaped cantilever beams. 
 33
From Figure 14 it can be seen that as the width of the beam decreases, the sensitivity of 
the device increases rapidly below 10 ?m width. As the MEMS based sensor devices require 
some type of transduction element on the beam structures for detection, such as piezoresistive 
elements, and these geometries do not offer enough area to define those features, researchers are 
investigating other kind of geometrical shapes, such as the triangular shaped ones.  The 
triangular shaped geometries increase the stiffness, while reducing the effective mass acting on 
the original beam structures.  Thus, it improves the resonant frequency of the structure which is 
evident from the equation (5). 
As the accuracy of the FEA results are strongly dependent on the type and number of 
elements that are used in the analysis.  In these simulations, SOLID187 element had been used 
which is supported by the ANSYS software.  It is a higher order 3 dimensional tetrahedral 
structural element with 10 nodes.  These elements, as shown in the Figure 15, have 3 degrees of 
translational degrees freedom at each node in x, y and z directions.  It is well suited for meshing 
irregular geometrical shapes, such as in these cases.  One disadvantage of using this element is 
that the size of these elements cannot be controlled manually; ANSYS software automatically 
generates mesh but it can be set to generate finer or coarser mesh size by using 1 to 10 scale.  In 
all of these simulations, the scale was set to 1, which is the finest mesh size.  One way to achieve 
finer meshes with a certain level of mesh size is by defining the thickness smaller.  This is due to 
the fact that SOLID187 element has a certain limit for maximum allowable aspect ratios.  This is 
why in these simulations, cantilever beam structure thicknesses were chosen to be 0.5?m, though, 
in reality the fabricated cantilever beam structures are approximately 1?m thick. 
 34
 
Figure 15: Tetrahedral structural element SOLID187 with 10 nodes, each with 3 translational 
DOF. 
 
2
3
4
5
6 
7
8 
9 
10
1
 35
 The initial FEA results are listed in the Table A.1 in the APPENDIX A section of this 
document.  From equations (5), it is clear that the frequencies of a certain beam structure, 
increases with the stiffness of the beam and decreases with the effective mass acting on it, while 
from equation (6) it is observed that the frequency shift is proportional to the ratio of the 
measurand mass to the effective mass acting on it.  Thus, for a constant measurand or the 
attached mass in the FEA simulations, the frequency shift should increase with lesser mass of the 
original beam structure, unless the stiffness is reduced, which is represented in the simulation 
results for the shapes 4 through 10 of Table A.1.  In the case of the triangular shapes, as the mass 
of the beam structure is reduced, while increasing the stiffness of them, it translates into higher 
frequencies and higher frequency shifts for the attached mass.  The main disadvantages with this 
type of geometries are that, due to the smaller areas near the tip of the beams, there is not much 
room available for fabricating the sensing pads to catch the measurands, such as bacteria, virus 
or DNA for biosensors.  Thus, triangular geometries with an added square or rectangular area at 
the tip of the beam structures, as shown in the cases for shapes 27 to 30 in the Table A.1, were 
investigated. 
 From the initial numerical results listed in the Appendix A section, it is clear that the 
resonant frequency of the geometries are dominated by 2 dominating parameters: the clamping 
width at the fixed end and the effective mass acting upon the cantilever beam structure at the free 
end.  As the minimum clamping width is limited by the geometry of the transduction element of 
the MEMS based sensing devices and the resolution of the microfabrication facilities available, 
in this case the minimum width is approximately 20-25 ?m.  So, to further investigate these 
dominating parameters, modal analysis were performed on some of the geometrical shapes, and 
compared with the regular rectangular shaped one.  Table 3 lists these geometries that have the 
 36
same length of 50 ?m and 0.5 ?m thicknesses as before, and a fixed clamped width of 25 ?m for 
comparison.  It lists the resonant frequency, their corresponding frequency shifts due to the 
attachment of a 0.285 picogram of mass on the tip of the beam structure, and their corresponding 
mass sensitivity of the geometries.  From the results listed in Table 3, it can be seen that the mass 
sensitivity of the triangular shape F shows an order of magnitude improvement than the regular 
rectangular shaped one. But, as it was mentioned before that the triangular shape does not offer 
enough area at the tip of the beam structure to capture the analytes, other geometries were also 
investigated.  The shape I, which provides enough area to fabricate sensing pads, shows more 
than 3 fold improvement in mass sensitivity over the regular rectangular shape. 
 37
Table 3: Comparison of numerical performances of different geometrical shapes 
 
Shape 
ID 
Shape geometry 
Shape 
Parameters 
(?m) 
Resonant 
frequency, 
f (Hz) 
Frequency 
shift, ?f 
(Hz) 
Mass 
sensitivity, 
?f/?m 
(Hz/pico-
gm) 
A 
l = 50, 
w = 25 
194,532 49 171.93 
B 
 
l = 50, 
w = 25, 
w
1
 = 30, 
l
1
 = 20 
179,588 41 143.86 
C 
 
l = 50, 
w = 25, 
w
1
 = 20, 
l
1
 = 20 
213,575 69 242.11 
D 
 
l = 50, 
w = 25, 
w
1
 = 15, 
l
1
 = 20 
125,295 36 126.32 
E 
 
l = 50, 
w = 25, 
w
1
 = 15, 
l
1
 = 20 
126,070 31 108.77 
 
 
w1
w 
1 
l 1
w1 
w
1 
l 
1 
w
w-w1 
-
l
w
l 
l 
1
w
w1
 38
Table 3: Comparison of numerical performances of different geometrical shapes 
 
Shape 
ID 
Shape geometry 
Shape 
Parameters 
(?m) 
Resonant 
frequency, 
f (Hz) 
Frequency 
shift, ?f 
(Hz) 
Mass 
sensitivity, 
?f/?m 
(Hz/pico-
gm) 
F 
l = 50, 
w = 25 
390,387 506 1775.44 
G 
 
l = 50, 
w = 25 
w
1
 = 10 
371,707 464 1628.07 
H 
 
l = 50, 
w = 25, 
w
1
 = 10 
251,691 123 431.58 
I 
 
l = 50, 
w = 25, 
w
1
 = 10, 
l
1
 = 10 
262,729 162 568.42 
 
w1 
w
l 
l1 
l 
w 
1
l 
w
l 
w
w1
 39
 
 
 
CHAPTER 4 
 
VERIFICATION OF THE FEA RESULTS 
 
In this section, the FEA results obtained from the previous chapter were verified by 
measuring the resonant frequency and their corresponding shifts due to the attachment of a 
known mass in the AFM system.  A simplistic experimental approach to simulate the same type 
of effect due to the addition of a known mass on the tip of the different geometrical shapes of 
cantilever beam structures, as used for the modal analyses of the geometries, was employed.  
Different shapes of cantilever beam structures had been fabricated using SOI (silicon-on-
insulator) wafer.  As the length of the AFM tip cantilever beam structures of the AFM system 
available in our facilities are of 125 ?m in length, the microcantilever beam structures of 
different geometries were fabricated of the same length of 125 ?m, and width and other 
geometrical parameters were similarly designed 2.5 times larger of the geometrical shape 
parameters investigated in the previous chapter.  The resonant frequencies of the beams were 
measured in the JEOL SPM 5200 (AFM) system.  Then polystyrene beads of 10 micron diameter 
were attached on the surface of the tip to simulate the mass addition, and the corresponding 
change in their resonant frequencies were measured in the AFM system; thus, calculating the 
resonant frequency shift of the corresponding cantilever beam structures. 
 40
A SOI (silicon-on-insulator) wafer of 4 inch diameter was used to fabricate different 
shapes of cantilever beams, by etching silicon in the Inductively Coupled Plasma (ICP) based 
Advanced Silicon Etcher (ASE) system from the Surface Technology Systems (STS).  The SOI 
wafers used in this process have a thin layer of silicon-oxide, called BOX layer, or buried oxide 
layer.  This oxide layer is of approximately 1 micron thickness in between the thinner device 
layer of silicon of approximately 4 microns and the thicker bulk handle layer of silicon of 
approximately 450 microns.  This oxide layer acted as an etch stop for the deep reactive ion 
etching (DRIE) process in the ASE system.  The microfabrication process flow chart is attached 
below in the Flow chart 4.1.  The three geometries; shape A, F and I that are listed in Table 3, 
were investigated by fabricating AFM tip microcantilevers.  The resonant frequency and their 
corresponding frequency shifts were measured and compared.  Figures 16 through 18 show these 
three geometries with poly-beads attached on their tips.  Figure 19 through 21 show sample 
responses of those geometries in the AFM system at three different pressure levels that were 
measured. 
 41
Flow Chart 4.1: Microfabrication process flow chart for the AFM tip microcantilevers 
 
Step 1: Bare double side polished SOI wafer
Step 2: Spin coat top surface with AZ5214E 
photoresist
Step 3: Expose with UV light using the top side 
mask & develop in AZ400K developer
Step 4: Etch device layer Si in ASE
Step 5: Strip off photoresist
Step 6: Spin coat photoresist to protect the top 
surface
Step 7: Spin coat  bottom surface with AZ4620
Step 8: Expose with UV light using the bottom 
side mask & develop in AZ400K develop
Step 9: Etch bulk substrate layer Si in ASE
Step 10: Strip off photoresist
Step 11: Etch silicon oxide in 10 : 1 HF solution to 
release free standing structure
 
 42
 
 
Figure 16: SEM images showing fabricated AFM tip microcantilever of shape A. 
 43
 
 
Figure 17: SEM images showing fabricated AFM tip microcantilever of shape F. 
 44
 
 
Figure 18: SEM images showing fabricated AFM tip microcantilever of shape I. 
 45
Shape A (in ambient pressure)
Frequency, f (Hz)
200x10
3
220x10
3
240x10
3
260x10
3
280x10
3
300x10
3
Ampl
itude
0
2
4
6
8
10
12
base frequency spectrum
frequency spectrum with polybead attached
 
 
Figure 19: Frequency spectrums obtained by the AFM system of shape A; with & without 
attaching poly-bead at ambient pressure. 
 46
Shape F (in 75 mTorr)
Frequency (Hz)
480x10
3
490x10
3
500x10
3
510x10
3
520x10
3
530x10
3
540x10
3
Am
pl
it
ude (V
ol
ts)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
baseline frequency spectrum
frequency spectrum with attached polybead
 
 
Figure 20: Frequency spectrums obtained by AFM of shape F; with & without attaching poly-
bead at 75 mtorr pressure. 
 47
Shape I (30 mTorr)
Frequency (Hz)
360x10
3
380x10
3
400x10
3
420x10
3
A
m
plit
ude (Volt
s
)
0
1
2
3
4
baseline frequency spectrum
frequency spectrum with attached polybead
 
 
Figure 21: Frequency spectrums obtained by AFM of shape I; with & without attaching poly-
bead at 30 mtorr pressure. 
 48
Table 4 lists the resonant frequency, frequency shift and mass sensitivity of the best 
performing geometries of shape F and I, along with the regular rectangular shape A, tested in 
different ambient pressures.  From these results, it can be seen that the performance of the shapes 
in terms of the mass sensitivity are almost the same as the ones obtained by the modal analysis 
results listed in Table 3.  Shape F has a mass sensitivity of an order of magnitude higher than the 
regular rectangular shape A, while shape I has a mass sensitivity of more than 3 times higher 
than the shape A.  These experimental results agreed quite well as the ones predicted by the FEA 
results.  Although, the baseline frequency spectrum of these structures should have higher q-
factor than the ones with the attached mass, but in some cases it showed otherwise.  This was due 
to the fact that more optical signal got reflected off of the poly beads than the surface of the 
cantilever tip and was detected by the laser detector.  This also made the q-factor data of the 
frequency spectrum listed on Table 4 unreliable. 
 49
Table 4: Comparison of experimental performances of different geometrical shapes 
 
Shape ID 
Ambient 
Pressure 
(Torr) 
Resonant 
Frequency,
f (kHz) 
Q factor 
Frequency 
Shift, ?f 
(kHz) 
Mass 
Sensitivity, 
?f/?m 
(Hz/pico-gm) 
A 
760 243.750 356.571 1.562 3.04 
7.5X10
-4
 244.336 250.200 1.465 2.85 
3X10
-4
 244.238 227.364 1.367 2.66 
F 
760 519.358 759.743 13.694 26.67 
7.5X10
-4
 520.630 592.133 13.989 27.24 
3X10
-4
 520.430 592.133 13.887 27.04 
I 
760 388.086 331.167 7.109 13.84 
7.5X10
-4
 389.160 664.167 7.402 14.41 
3X10
-4
 389.160 664.167 7.402 14.41 
 50
 
 
 
CHAPTER 5 
 
DAMPING EFFECT ON GEOMETRIES 
 
To investigate the damping effect on these geometries and their performances, same A, F 
and I shaped cantilevers, described in the previous two chapters, were tested in the same manner.  
The resonant frequency of these geometries was measured in air at different pressure levels, 
starting from atmospheric pressure to the lowest vacuum pressure attainable by the AFM system.  
Theoretically, since the triangular shape offers less area at the free end of the structure, it should 
show the least effect of damping on the structure, while rectangular shape should show the 
maximum damping effect among these three geometries.  As the modified geometry offers 
intermediate area between the rectangular and the triangular shapes, it should show an effect in 
the intermediate range between the other two geometries.  To investigate this phenomenon, this 
experiment was set up.  During the thought process behind this experiment, the results were 
expected to show the changes in resonant frequency for different geometries as a function of 
pressure as shown in the schematic plots attached in Figure 22. 
The resonant frequency of the cantilever beam structures of these geometrical shapes 
were measured at different pressure levels from the atmospheric pressure of 10
5
 pascal to 10
-2
 
pascal that can be achieved by the vacuum pumps of the JEOL SPM 5200 (AFM) system.  This 
range of pressures has been divided into three separate regions [33-38].  At low pressure levels  
 51
 
 
 
Figure 22: Schematic figure showing expected pressure dependence on different geometrical 
shapes. 
Pressure 
Resonant 
Frequency 
Shape F 
Shape I 
Shape A 
 52
the vibrating cantilever beam structure loses energy due to internal damping, known as the 
intrinsic regime.  At this pressure level air molecules can be considered non-interacting with the 
vibrating structure.  Thus, the damping effect due to the medium can be neglected.  At higher 
pressure levels, near the atmospheric pressure, the damping effect is dominated by the external 
effect imposed by the molecules present in the medium.  This region of external damping is 
referred to as the viscous regime.  In between these two regimes, there is a transition regime 
where both the internal and the external damping effects play roles. 
In this experiment, fabricated cantilever beam structures were tested in the AFM system 
available in the laboratory facilities at Auburn University.  Those test samples were put in the 
AFM tip holder and actuated by the system, while the chamber was pumped down by using the 
vacuum pumps of the system.  The JEOL SPM 52OO system has a roughing pump and a turbo 
pump connected in series to pump down the chamber in the range of 10
-2
 Pa.  To record 
intermediate pressure level data, the automatic control of the roughing pump and the turbo 
pumps were disabled.  This kept the system at two different pressure levels, namely 10
-2
 Pa and 
10
4
 Pa, by independently controlling those two pumps.  From the literatures [33-38], it was found 
that the transition regime starts around 10
4
 Pa and the viscous regime continues through the 
atmospheric pressure level.  Since the goal of this experiment was to investigate damping effect 
on the geometries due to the presence of air, data points at these pressure levels were required.  
So, to achieve that goal two leaks were introduced in the vacuum line of the AFM system.  One 
bigger, open and shut, valve with another micro-valve attached in series, were introduced into 
the vacuum line.  The micro-valve was adjusted manually to stabilize the pressure at certain 
levels, which was read from the pressure gage attached to the line near the valves.  This made it 
possible to record data at the pressure range from 10
4
 Pa to 10
5
 Pa. 
 53
During the experiment, at each pressure level, the system was kept for a few minutes to 
stabilize at the pressure level, and then a frequency scan was performed to record the resonant 
frequency and the Q-factor data.  Figures 23 through 25 show the typical responses of the shapes 
A, F and I consecutively.  Although some of the spectrum curves show better and cleaner plots 
than the others, they clearly show the resonant frequencies of the structures.  After measuring the 
resonant frequencies of the structures, 10 nm of Ti and 75 nm of Au layers were deposited to 
mimic the addition of mass on the structures.  These layers were deposited in the E-beam system 
available in the microfabrication lab of Auburn University.  After that the structures were tested 
again, and the corresponding resonant frequencies at each pressure levels were measured. 
All these resonant frequency and the corresponding Q-factor data are listed in Tables 5 
through 7 for the shape A, F and I respectively. Here, it can be seen that the Q-factor data for 
different samples did not follow a clear trend, except for increasing with the higher pressure level.  
This might be due to multiple factors; such as the noises introduced by the leaks that were 
incorporated to achieve intermediate pressure levels.  Also, the samples had a small amount of 
undercuts, approximately 10 to 15 microns on the backside of the SOI wafer.  This was due to 
the fact that when using the Bosch process in the ASE system to etch through 450 to 500 microns 
thickness of the wafer, it leaves approximately 10 to 15 microns of undercuts.  Because of this, 
the fixed ends of the cantilever beam structures were not exactly clamped; they experienced 
small displacement during actuation.  Thus, the Q-factor values were not exactly reliable for 
these experiments. 
 54
SHAPE A
Frequency f(Hz)
150x10
3
200x10
3
250x10
3
300x10
3
350x10
3
400x10
3
450x10
3
Amp
litude
 V(Volts)
0
1
2
3
4
5
6
7
Sample 1; P = 0.048 Pa
 
 
Figure 23: Frequency spectrum for the sample no. 1 of Shape A at 0.048 Pa pressure. 
 
 55
SHAPE F
Frequency f(Hz)
350x10
3
400x10
3
450x10
3
500x10
3
550x10
3
600x10
3
650x10
3
Amplitude V(Volts)
0
1
2
3
4
5
6
Sample 1; at P=0.045 Pa
 
 
Figure 24: Frequency spectrum for the sample no. 1 of Shape F at 0.045 Pa pressure. 
 56
SHAPE I
Frequency f(Hz)
300x10
3
350x10
3
400x10
3
450x10
3
500x10
3
550x10
3
600x10
3
Amplitude
 V(Volts)
0
1
2
3
4
5
6
7
Sample 4; at P=0.053 Pa
 
 
Figure 25: Frequency spectrum for the sample no. 4 of Shape I at 0.053 Pa pressure. 
 
 57
Table 5: Resonant frequency responses of shape A 
 
Sample 
No. 
Status Pressure (Pa) Frequency (kHz) Q-factor 
1 
Before 
metal 
deposition 
101324.7200 299.707 511.500 
79993.2000 300.000 512.000 
66661.0000 300.000 512.000 
57328.4600 300.000 512.000 
9999.1500 300.586 1026.000 
0.0480 300.58 1026.000 
After metal 
deposition 
101324.7200 285.3520 487.000 
77326.7600 285.3520 487.000 
66661.0000 285.3520 487.000 
53328.8000 285.6450 487.500 
8665.9300 285.6450 487.500 
0.0480 285.6450 487.500 
2 
Before 
metal 
deposition 
101324.7200 213.037 290.867 
79993.2000 213.281 291.200 
66661.0000 213.281 291.200 
57328.4600 213.525 291.533 
9999.1500 213.770 291.867 
0.0480 213.77 291.86
After metal 
deposition 
101324.7200 199.121 54.373 
78659.9800 199.121 58.257 
66661.0000 199.121 58.257 
55995.2400 199.365 58.329 
9332.5400 199.609 62.892 
0.0533 199.60 68.133 
3 
Before 
metal 
deposition 
101324.7200 270.410 461.500 
79993.2000 270.703 462.000 
66661.0000 270.996 462.500 
58661.6800 270.996 925.000 
7999.3200 271.289 926.000 
0.0613 271.28 926.00
After metal 
deposition 
101324.7200 254.980 435.667 
78659.9800 255.273 435.667 
66661.0000 255.273 435.667 
53328.8000 255.273 871.333 
7999.3200 255.566 872.333 
0.0507 255.859 872.33
 58
Table 6: Resonant frequency responses of shape F 
 
Sample 
No. 
Status Pressure (Pa) Frequency (kHz) Q-factor 
1 
Before 
metal 
deposition 
101324.7200 470.117 534.889 
81326.4200 470.410 535.222 
71993.8800 470.410 535.222 
61328.1200 470.410 535.222 
9332.5400 470.996 535.889 
0.0453 470.99 535.88
After metal 
deposition 
101324.7200 441.211 502.000 
78659.9800 441.504 502.333 
66661.0000 441.504 502.333 
55995.2400 441.504 502.333 
9999.1500 441.797 502.333 
0.0533 441.79 502.33
2 
Before 
metal 
deposition 
101324.7200 483.887 550.556 
75993.5400 484.180 550.889 
66661.0000 484.180 550.889 
53328.8000 484.180 826.333 
9332.5400 485.059 827.833 
0.0800 485.05 827.83
After metal 
deposition 
101324.7200 453.516 516.333 
75993.5400 453.809 516.333 
66661.0000 453.809 516.333 
50662.3600 453.809 516.667 
8665.9300 454.102 516.667 
0.0427 454.10 775.000 
3 
Before 
metal 
deposition 
101324.7200 499.707 189.519 
75993.5400 499.707 213.208 
66661.0000 500.000 213.333 
53328.8000 500.000 213.333 
8665.9300 500.586 244.095 
0.0733 500.879 244.238 
After metal 
deposition 
101324.7200 469.043 400.250 
75993.5400 469.336 400.500 
66661.0000 469.336 400.500 
55995.2400 469.336 400.500 
8665.9300 469.629 400.500 
0.0453 469.62 400.75
4 
Before 
metal 
deposition 
101324.7200 511.719 64.691 
75993.5400 512.012 64.728 
66661.0000 512.012 62.417 
53328.8000 512.012 62.417 
8665.9300 513.184 194.630 
0.0587 513.18 250.238 
After metal 
deposition 
101324.7200 480.078 74.485 
75993.5400 480.371 74.530 
66661.0000 480.664 74.576 
51995.5800 480.664 78.127 
8665.9300 480.957 78.127 
0.0613 480.95 78.175 
 59
Table 7: Resonant frequency responses of shape I 
 
Sample 
No. 
Status Pressure (Pa) Frequency (kHz) Q-factor 
1 
Before 
metal 
deposition 
101324.7200 392.3830 669.667 
75993.5400 392.3830 669.667 
66661.0000 392.3830 669.667 
53328.8000 392.3830 669.667 
7999.3200 392.9690 1341.333 
0.0533 392.9690 1341.333 
After metal 
deposition 
101324.7200 367.2850 626.833 
77326.7600 367.5780 627.333 
66661.0000 367.5780 1254.667 
55995.2400 367.5780 1254.667 
8665.9300 367.8710 1255.667 
0.0613 368.1640 1255.667 
2 
Before 
metal 
deposition 
101324.7200 393.2620 671.167 
78659.9800 393.2620 671.167 
66661.0000 393.5550 671.167 
57328.4600 393.5550 671.167 
8665.9300 393.8480 1344.333 
0.0533 394.1410 1345.333 
After metal 
deposition 
101324.7200 369.9220 420.889 
75993.5400 369.9220 631.333 
66661.0000 369.9220 631.333 
51995.5800 370.2150 631.833 
8665.9300 370.5080 631.833 
0.0427 370.8010 631.833 
3 
Before 
metal 
deposition 
101324.7200 296.7770 202.600 
75993.5400 296.7770 253.250 
66661.0000 296.7770 253.250 
53328.8000 297.0700 253.250 
8665.9300 297.3630 253.750 
0.0613 297.6560 254.000 
After metal 
deposition 
101324.7200 275.6840 313.667 
75993.5400 275.9770 471.000 
66661.0000 275.9770 471.000 
51995.5800 275.9770 471.000 
8665.9300 276.5630 944.000 
0.0453 276.5630 944.000 
4 
Before 
metal 
deposition 
101324.7200 448.8280 766.000 
79993.2000 449.1210 766.500 
66661.0000 449.1210 766.500 
57328.4600 449.1210 766.500 
8665.9300 449.7070 1535.000 
0.0533 449.7070 1535.000 
After metal 
deposition 
101324.7200 423.9260 723.500 
78659.9800 424.2190 724.000 
66661.0000 424.2190 724.000 
49329.1400 424.5120 724.500 
8665.9300 424.8050 1450.000 
0.0400 425.0980 1450.000 
 60
Sandberg et al. [38] had developed an analytical expression for pressure dependence of 
the resonant frequency of a regular rectangular shaped cantilever beam structure:  
 
)17(
4
1
2
1
0
?
?
?
?
?
?
?
?
?
+=
hRT
Mwp
ff
?
?
 
 
Here, f
0
: intrinsic resonant frequency, 
          M: molar mass of the medium (in this case 28.97 gm/mol for air), 
          p:  pressure, 
          R: gas constant (8.314 J/mol.K), 
          T: temperature (room temperature, approximated as 300 K), 
          ?: density of the beam material (for Si it is 2.329 gm/cm
3
), 
      & h: thickness of the beam. 
 From equation (17), the relative resonant frequency can be calculated using the following 
expression: 
 
)18(1
4
1
2
1
0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+=?
?
hRT
Mwp
ff
?
?
 
 
 Here, the intrinsic resonant frequency was assumed to be the same as the maximum 
resonant frequency that was measured at the lowest pressure attained by the system during 
testing for each samples.  To calculate the analytical results for a rectangular shape cantilever, 
the average value of the thickness of the samples and the average value of the intrinsic resonant 
 61
frequencies of the samples were used.  The relative resonant frequencies were calculated from 
the experimental data for each of the samples of all three geometries and plotted in Figures 26 
through 28.  To make a comparison, the analytical model for a rectangular cantilever was 
attached to each of the plots for different shapes.  Those plots are combined in the Figure 29 for 
better comparison.  From these plots it can be seen that there are no significant differences 
among the three geometries, in terms of relative resonant frequencies.  Proving the expectation to 
be wrong which was summarized in the schematic plots attached in Figure 21.  This may be due 
to the fact that the relative resonant frequency is highly dependent on the intrinsic resonant 
frequency, as can be seen from the Equation (18).  Although the damping effects on the 
triangular shape might be the smallest, its intrinsic resonant frequency was the highest.  Thus, the 
change in the resonant frequency became comparable to that of the other shapes.  On the other 
hand, the rectangular shape had the largest surface area for damping effect to take place, while it 
had the lowest intrinsic resonant frequency.  Thus, the change in the resonant frequency due to 
damping became comparable to the other shapes. 
Figures 30 through 32 show the relative resonant frequencies for each sample, with the 
deposited metal layers and without adding any metals on them.  From these figures it can be seen 
that the resonant frequency shifts due to the addition of mass on them were the highest for the 
triangular shapes, as expected.  The lowest level of resonant frequency shifts due to the mass 
addition were exhibited by the regular rectangular shape structures, while the modified shaped 
structure showed resonant frequency shifts intermediate to the other two shapes.  These results 
are in good agreement with the results listed in the previous chapters. 
 62
SHAPE A
Pressure P(Pa)
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Relative Resonant Frequency 
?
f(kHz)
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Sample 1
Sample 2
Sample 3
Analytical model
 
 
Figure 26: Relative resonant frequency as the function of pressure for shape A. 
 63
SHAPE F
Pressure P(Pa)
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Relative Resonant Frequency 
?
f
(
kHz)
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Sample 1
Sample 2
Sample 3
Sample 4
Analytical model
 
 
Figure 27: Relative resonant frequency as the function of pressure for shape F. 
 64
SHAPE I
Pressure P(Pa)
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Relat
i
ve Resonant Frequency 
?
f
(
kHz)
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Sample 1
Sample 2
Sample 3
Sample 4
Analytical model
 
 
Figure 28: Relative resonant frequency as the function of pressure for shape I. 
 65
COMPARSION OF DIFFERENT SHAPES
Pressure P(Pa)
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Relativ
e
 Resonant Frequency
 
?
f(k
H
z)
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Shape A; Sample 1
Shape A; Sample 2
Shape A; Sample 3
Shape F; Sample 1
Shape F; Sample 2
Shape F; Sample 3
Shape F; Sample 4
Shape I; Sample 1
Shape I; Sample 2
Shape I; Sample 3
Shape I; Sample 4
Anlytical model
 
 
Figure 29: Comparison of relative resonant frequency vs. pressure plots for all three geometries. 
 66
SHAPE A
Pressure P(Pa)
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Relative Resonant Fr
equenc
y 
?
f(kHz)
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
Sample 1; before metal deposition
Sample 1; after metal deposition
Sample 2; before metal deposition
Sample 2; after metal deposition
Sample 3; before metal deposition
Sample 3; after metal deposition
 
 
Figure 30: Effect of mass addition on relative resonant frequency vs. pressure plot for shape A. 
 67
SHAPE F
Pressure P(Pa)
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Rel
a
t
i
v
e
 Resonant
 Frequency 
?
f(
k
H
z
)
-35
-30
-25
-20
-15
-10
-5
0
Sample 1; before metal deposition
Sample 1; after metal deposition
Sample 2; before metal deposition
Sample 2; after metal deposition
Sample 3; before metal deposition
Sample 3; after metal deposition
Sample 4; before metal deposition
Sample 4; after metal deposition
 
 
Figure 31: Effect of mass addition on relative resonant frequency vs. pressure plot for shape F. 
 68
SHAPE I
Pressure P(Pa)
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Relative Resonant Frequency 
?
f
(
kHz)
-30
-25
-20
-15
-10
-5
0
Sample 1; before metal deposition
Sample 1; after metal deposition
Sample 2; before metal deposition
Sample 2; after metal deposition
Sample 3; before metal deposition
Sample 3; after metal deposition
Sample 4; before metal deposition
Sample 4; after metal deposition
 
 
Figure 32: Effect of mass addition on relative resonant frequency vs. pressure plot for shape I. 
 
 
 69
 
 
 
CHAPTER 6 
 
MICROFABRICATION PROCESS OF THE MEMS DEVICES 
 
 It was planned to etch silicon by using bulk micromachining techniques of wet etching to 
form the cantilever beam structures for the MEMS devices.  Thus, the process of fabricating 
these devices start with (100) oriented silicon wafers with an average thickness of 500 ?m.  The 
process flow chart is attached below in Flow Chart 6.1.  Single side polished p-type 500 ?m 
thick 4 inch wafers were used for the fabrication of the MEMS devices.  First, the wafers were 
cleaned by following a few steps.  The first step was to use B cleaning process of the RCA 
cleaning procedure [39] for cleaning organic and ionic contaminations, by using a solution made 
of deionized water (DI-H
2
O), ammonium hydroxide (NH
4
OH) and hydrogen peroxide (H
2
O
2
) in 
the ratio of 5:1:1 and at a temperature of 55 to 60?C for 10 minutes.  Although, it is 
recommended to use this cleaning solution at 70 to 80?C, it was found that at temperatures 
higher than 60?C, the solution tends to slightly attack the bare silicon surface.  After the wafers 
were rinsed in DI-H
2
O and dried with blowing N
2
 gas on them, they were kept in an oven at 
120?C for 20 minutes for dehydration bake in a nitrogen environment.  Then, two minutes of 
oxygen plasma cleaning in the MATRIX system was performed; at 300 watts power, 5 torr 
pressure and 40% O
2
 in N
2
 gas. 
 70
 Right after these cleaning and drying processes, silicon nitride layer was deposited in the 
Low Pressure Chemical Vapor Deposition (LPCVD) system.  This nitride layer forms the base of 
the cantilever beam structure and acts as an etch stop for the bulk micromachining of silicon, as 
it has a negligible etch rate compared to the etch rate of silicon in the [100] direction [40-41].  To 
reduce the residual stress in the silicon nitride layer grown in the LPCVD system, a low stress 
silicon nitride deposition recipe [42] had been used.  According to the literature [43], if the ratio 
of the gases used, dichlorosilane (SiH
2
Cl
2
) to ammonia (NH
3
), is 5:1 and the film is grown at 
850?C temperature, the deposited silicon rich silicon nitride (Si
x
N
y
) layer should have a residual 
stress lower than 100 MPa.  This low stress recipe was used and the silicon nitride was deposited 
at approximately 350 mtorr furnace pressure for 90 minutes.  This deposited nitride layers of 
approximately 300 to 400 nm thicknesses on the wafers, along the length of the furnace tube.  
After the deposition the same cleaning procedures were used, as discussed above.  Then low 
stress polysilicon layer was deposited in the same LPCVD system, by thermal decomposition of 
silane (SiH
4
) gas at 650?C and approximately 400 mtorr process pressure.  In this process, on 
average, a 100nm thick polysilicon layer was deposited across the furnace length for an 
approximately 17 minutes run.  After deposition, the polysilicon layer was doped with 
phosphorous by using phosphorous diffusant, which is a solution of phosphosilicate glass.  The 
wafer was then spun coated with the diffusant at 3000 rpm for 30 seconds and initially baked at 
150?C for two minutes on a hotplate. Then the phosphorous was driven into the polysilicon layer 
at 1000?C in a furnace, while N
2
 gas was flown inside the furnace at a flow rate of 5 sccm.  The 
wafers were kept at that temperature inside the furnace for ten minutes, which makes a doping 
concentration in the range of approximately 10
19
 to 10
20
/cm
3
. This gives piezoresistive 
characteristics to the polysilicon layer.  After performing this drive-in step, the phosphosilicate 
 71
glass layer was stripped-off from the wafer surface, by using 10:1 ratio solution of DI-H
2
O and 
HF.  Then the wafer was prepared for patterning the piezoresistive transduction element for the 
sensor devices. 
 At first, the wafer was cleaned with the B cleaning solution for ionic and organic 
contamination. Then it was rinsed, dried and dehydrated by the same methods mentioned earlier.  
The only step that was done differently at this point was no O
2
 plasma cleaning procedure was 
performed, which is due to the fact that the oxidation of the polysilicon layer should be kept at a 
minimum level.  Otherwise, the devices would show Schottky type contact characteristics, 
instead of ohmic contact between the polysilicon and the metal layers.  After dehydration bake at 
120?C for 20 minutes, the wafer was kept inside an evaporating environment of hexamethyl 
disilazane (HMDS) for 5 minutes, which acts as a primer for the photoresist.  Then it was spun 
coated with the AZ5214E IR positive photoresist at 3000 rpm for 30 seconds, which forms 
approximately 1.2 ? thick layer of photoresist.  After spin coating, the wafer was soft baked at 
105?C for 1 minute on a hotplate.  Then, the 1
st
 mask for the piezoresistors was aligned with the 
wafer flat for (100) orientation in the KARLSUSS MA6 mask aligner.  The photoresist was 
exposed in UV light for 6 seconds at approximately 6 mW/cm
2
 light intensity level; thus, 
resulting in a total dose of 36 mJ/cm
2
 (approximately).  After the exposure, the photoresist was 
developed in AZ400K developer solution of 1:2 ratio with DI-H
2
O for approximately 18 seconds.  
As on this mask, only small areas are defined for the piezoresistors, most of the photoresist from 
the wafer ended up in the developing solution.  When the wafer was pulled out of the solution it 
formed a very thin and optically undetectable layer of the photoresist on the surface.  This was 
evident from the fact that when the polysilicon was etched in the Advanced Silicon Etcher (ASE), 
it did not form well defined piezoresistors.  To resolve this issue a fresh batch of solution was 
 72
made and the wafer was dipped into the solution just for a moment to dissolve that undetectable 
monolayer of photoresist.  After that the photoresist was flood exposed for post-develop flood 
exposure in UV light for 5 seconds.  This helped to retain the small geometries of the devices, 
and after that the wafer was hard baked at 120?C for 1 minute on a hot plate. 
 The piezoresistors were defined by etching the polysilicon layer in the Advanced Silicon 
Etcher (ASE) system from the Surface Technology Systems (STS).  In this inductively coupled 
plasma (ICP) etching system, the etching process was performed using alternate etching and 
sidewall passivating cycle with a process pressure of 36 mtorr.  The etch cycle was of 8 seconds 
duration using sulfur hexafluoride (SF
6
) gas at a flow rate of 130 sccm and O
2
 gas at a flow rate 
of 13 sccm.  The power applied in the magnetic coil generator was 600 watts, while 10 watts of 
power was applied in the platen generator.  The passivation cycle was of 4 seconds duration 
using octafluorocyclobutane (C
4
F
8
) gas at a flow rate of 85 sccm with 600 watts of power in the 
magnetic coil only.  This etching process was closely monitored through a glass window at the 
top of the chamber.  After the etching process for the polysilicon layer was done, the photoresist 
was stripped off in acetone.  Then, it was washed in isopropyl alcohol (IPA) or alternatively 
known as isopropanol, and DI-H
2
0 in consecutive steps.  After that the wafer was dried with N
2
 
gas blowing on the surfaces of the wafer. 
The next step was to pattern the wafer for depositing metal pads and connectors of the 
MEMS devices.  At first, the wafer was cleaned, dried and dehydration baked, as it was done 
during patterning the polysilicon layer.  After that, it was put in HMDS evaporating environment 
for 5 minutes, and spun coated with the AZ5214 photoresist, as before.  Then it was soft baked at 
105?C for 1 minute on hotplate, and exposed in UV light using the metal layer mask, which was 
aligned in the mask aligner.  The exposure time and dose was the same as in the previous step.  
 73
After exposure it was developed in the same AZ400K developing solution of 1:2 ratio for 
approximately 18 seconds.  Then the photoresist was flood exposed for post-develop flood 
exposure, as before. 
 Now the wafer was ready for Cr-Au-Cr deposition in the E-beam system.  The Cr 
layers act as an adhesion layer for the Au layer to stick on the polysilicon and the silicon nitride 
layers at the bottom, and the passivation layer on the top, which could be silicon oxide, silicon 
nitride, diamond like carbon (DLC) or silicon carbide.  Just before depositing metals, the wafer 
was ion cleaned inside the E-beam chamber using Ar gas in a vacuum environment.  This 
ensures a cleaner surface for the metal film growth and oxide removal from the exposed 
polysilicon layer.  Thus, it ensured good ohmic contact between the polysilicon layer and the 
metal pads, and the removal of any residual photoresist from the exposed substrate.  During the 
E-beam run, the base pressure was kept at less than 3X10
-6
 torr.  Cr layer was deposited at 9.78 
kilovolts voltage and 0.029 amps current, while Au layer was deposited at 9.82 kilovolts voltage 
and 0.130 amps current.  The deposited thicknesses of the metal layers were 20nm of Cr, 180nm 
of Au and another 20nm of Cr, making the thickness of the metal layers approximately twice the 
thickness of the polysilicon layer.  This ensured good step coverage.  After that, the wafer was 
put in an ultrasonic bath, while submerged in acetone to perform lift-off technique, and thus, 
defining the metal pads.  Figure 33 through 35 show pictures of piezoresistors and metal pads 
defined at this stage. 
 74
 
 
Figure 33: Picture of piezoresistance and metal connector arrangement in a rectangular shaped 
device. 
 75
 
 
Figure 34: A close up picture of piezoresistive polysilicon pads and their metal connectors. 
 76
 
 
Figure 35: Picture of the sensing pad on a triangular shaped device. 
 77
The next stage was to put a passivation layer on the wafer.  The passivation layer should 
protect the device layers underneath from bulk micromachining process, and electrically insulate 
them during the insitu measurements in liquid media for application.  In addition, it has to be 
deposited at a lower temperature to avoid introducing stress inside the structures underneath, and 
it should be, preferably, done in the facilities available here in Auburn University.  To achieve 
those goals, a few materials had been tested: sputtered silicon oxide in both neutral (Ar only) and 
oxygen plasma environments, reactively sputtered silicon nitride and sputtered silicon carbide. 
Also, one of the group members had deposited and showed application of DLC film for the 
passivation layer [44].  The problem with the DLC film is that it has to be deposited in Argonne 
National Laboratories, not in the facilities available on campus.  Also, as the DLC film is etched 
in O
2
 plasma, which oxidizes Cr, and subsequently the exposed metal layer delaminates from the 
device structure during bulk micromachining process. 
Other films were investigated in campus facilities.  At first, silicon oxide film was 
sputtered using a SiO
2
 target at 5X10
-6
 torr base pressure with 25 sccm of Ar flow, 350 watts 
power and a sputter pressure of 5.3 mtorr.  The resulting film could not protect the polysilicon 
layers underneath against the bulk micromachining process with KOH etch solution, as seen in 
Figure 36.  Then, the oxide film was sputtered while using 5 sccm of O
2
 with both 20 and 25 
sccm of Ar gas flow rates, and 1X10
-6
 torr base pressure, 100 watts of power and sputter 
pressures of 5.1 and 5.3 mtorr respectively.  The results were the same; they could not protect the 
piezoresistors either, as seen in Figure 37.  Then sputtered silicon nitride film was investigated.  
It was deposited by reactively sputtering silicon in the presence of nitrogen in the plasma.  This 
time Si target was used, with a base pressure of 1X10
-6
 torr, 100 watts of power, 7 sccm of N
2
 
gas with 18 sccm of Ar gas and a sputter pressure of 5.5 mtorr.  The resulting passivation layer 
 78
 
 
Figure 36: Picture of a cantilever beam structure with sputtered oxide as the passivation layer; 
after exposing it to KOH solution. 
 79
 
 
Figure 37: Picture of the piezoresistors on a device with sputtered oxide as the passivation layer; 
after exposing it to KOH solution. 
 80
 
 
Figure 38: Picture of the piezoresistors on a device with reactively sputtered nitride as the 
passivation layer; after exposing it to KOH solution. 
 81
acted the same way as in cases of the oxide layers.  Figure 36 through 38 show the pictures of the 
devices with these trial passivation layers, after exposing them to the bulk micromachining 
process of KOH etching.  Although the reactively sputtered nitride layer performed better than 
the oxide layers, it failed to protect the polysilicon layer underneath. 
Finally, this problem was solved with sputtered SiC layer, which held up quite well and 
protected the structures underneath against the KOH etching solution.  The SiC layer is deposited 
at 5X10
-7
 torr pressure, 150 watts of power, 25 sccm Ar gas flow and 5.2 mtorr of sputter 
pressure.  The resulting passivation layer survived 6 hours of KOH (30 wt/wt %) etch at 65?C to 
release the cantilever structure.  Thus, the SiC layer, which is sputtered from a SiC target, was 
chosen as the passivation layer for the devices. 
Before and after sputtering of the SiC film, the wafer had to go through usual cleaning, 
drying, and dehydration bake processes without O
2
 plasma cleaning as before.  After that, to 
define the actual cantilever beam structure and making openings for the metal pads for both 
electrical connections and sensing pads for testing, the SiC layer needed to be patterned and 
etched.  In the beginning AZ5214 positive photoresist was used as the etching mask.  The 
carbide and the nitride etching recipes in Deep Reactive Ion Etching (DRIE) system contain 
oxygen in them to remove the polymer by-product; the gas chemistry attacks the photoresist 
during these processes.  As the carbide layer had to be thick enough for the step coverage of the 
underneath device layers, the photoresist did not survive all the way through for the etching 
process.  When these samples were micromachined in KOH or TMAH, they did not survive the 
etching process, as evident from the SEM pictures in Figures 39 and 40.  As the photoresist got 
etched away, thinning of the SiC layer occurred.  When these devices went through the bulk 
micromachining process, the passivation layer failed to protect the polysilicon layers underneath.  
 82
The carbide layer was approximately 600 nm thick as sputtered, twice the total thickness of the 
polysilicon and the metal layers combined.  Ensuring good enough step coverage for the layers 
underneath.  As re-patterning was not feasible either, for the small features like 2.5 to 4 ?m, 
alternative etching mask was investigated.  As Al can be etched in potassium borates based 
developers such as AZ400K, it was investigated as the etching mask for etching both carbide and 
nitride films together in the Advanced Oxide Etcher (AOE) system.  As the passivation layer 
mask was made for the positive photoresist, to use the same mask to define the Al layer as the 
etching mask, defined through lift-off technique, reverse patterning of the photoresist needed to 
be done.  In case of reverse patterning, AZ5214E IR photoresist performs better than the regular 
AZ5214E one.  Here, the IR stands for image reversal.  At first, the wafer was spun coated with 
this photoresist following the same procedures as the regular one, and then soft baked at 90?C for 
2 minutes.  After that, it was exposed in UV light for 5 seconds, while using the 3
rd
 mask in the 
mask aligner.  Then, a reversal bake was performed at 110?C for 2 minutes, and then allowed to 
cool down.  After it was cooled down, the wafer was flood exposed for 1 minute, and then 
developed in AZ400K developer using 1:4 ratio of DI-H
2
O solution for about 15 seconds.  Al 
was deposited on the wafer in the E-beam system with 2 minutes of ion cleaning performed right 
before the deposition.  The Al deposition process was performed at a base pressure of less than 
3X10
-6
 torr, with 9.75 kilovolts of voltage and 0.141 amps of current.  After deposition the wafer 
was put in an ultrasonic bath, while submerged in acetone to define the etching mask through 
lift-off technique. 
 83
 
 
Figure 39: SEM image showing polysilicon layers were attacked during KOH etch, due to the 
thinning of SiC layer when regular PR is used as the etch mask for the DRIE process. 
 84
 
 
Figure 40: A close up SEM image, showing piezoresistor etched away during KOH etching due 
to the thinning of SiC layer when regular PR is used as the etch mask for the DRIE process. 
 85
 The carbide and the nitride layers were etched in the AOE system from the STS, using 30 
sccm of CF
4
 and 3 sccm of O
2
 gas.  The base pressure for the process was 0.5 mtorr with 600 
watts in the magnetic coil and 75 watts in the platen generator.  It takes approximately 15 
minutes to etch through the carbide and the bottom nitride layers.  In the beginning, the etching 
was performed at cycles lasting from 1 minute to a few minutes at a time.  After the etching was 
done, the resistances measured between the exposed metal pads showed a Schottky type contact 
while the resistances measured right after depositing metal pads, showed an ohmic contact.  It 
was suspected that the local temperatures on the surface was reaching high enough to oxidize Cr, 
although the cooling water temperature was kept at 10?C.  So, to investigate this hypothesis, 
etching was performed in 15 seconds long cycles.  By using these short cycles, it was possible to 
conserve the ohmic contact during the etching process.  Plots of resistance measurements for 
both longer and shorter 15 seconds etching cycles are attached in Figures 41 and 42, respectively.  
These measurements were performed by a Semiconductor Parameter Analyzer.  After etching 
through the carbide and the nitride layers, the Al etching mask is removed in 2:1 ratio DI-H
2
O 
solution of AZ400K developer. 
At first, the bulk micromachining of Si was done in KOH etching solution, which always 
etched quite well and released the cantilever structures without much of a difficulty.  However, 
after the etching process the resistance measurements always showed 3 orders of magnitude of 
larger resistances with no ohmic contact, regardless of the concentration and the temperature 
(30?C, 60?C, 65?C or 80?C) of the solution.  Figure 43 shows the I-V characteristic curves for 
the devices after KOH etch.  Therefore, the use of other etching solutions was investigated.  The 
popular alternative method is to use tetramethylammonium hydroxide or TMAH solution.  A 
recipe consisting of 8.33% of TMAH solution was tried to etch Si to release the cantilever 
 86
Applied Voltage (Volts)
-10 -5 0 5 10
Measured Cur
r
ent (
A
mps)
-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
Between pads 1 & 2
Between pads 1 & 3
Between pads 1 & 4
 
 
Figure 41: Resistance measurement after etching SiC & Si
x
N
y
 in the AOE system, without 
specifying time for the etching cycles. 
 
 87
Applied Voltage (Volts)
-10 -5 0 5 10
Measured Current
 (Amps)
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
Between pads 1 & 2
Between pads 1 & 3
Between pads 1 & 4
 
 
Figure 42: Resistance measurement after etching SiC & Si
x
N
y
 in the AOE system, with specific 
15 seconds etching cycles. 
 88
structures.  In this recipe, to reduce the hillock structure formations on the etched Si surface, and 
to make the surface smoother, ammonium peroxydisulfate (APOD), an oxidizing agent, was 
added every 20 minutes at a concentration level of 0.1 wt/wt % of the total solution.  This recipe 
also increased the resistances 3 orders of magnitude, as shown in the plots attached in Figure 44. 
A few TMAH etch recipes have been investigated and published [45-48] over recent 
years for post CMOS compatible bulk micromachining techniques.  In one of the techniques 
described by Zhang et al. [48], a 5 wt% of TMAH solution is mixed with 1.6 wt % of Si powder 
and 0.5% of APOD, and heated up to about 80?C for micromachining of Si.  This solution 
enables etching of Si through a pH controlled method without attacking the piezoresistive 
polysilicon or the metal-poly junction integrated inside the device structures.  The I-V 
characteristic curves from the devices that survived during the bulk micromachining process 
performed on them, using the pH controlled TMAH etch recipe, is attached in Figure 45.  After 
the cantilevers were released, the devices were cleaned and dried in isopropanol.  The complete 
process flow is listed in the Flow Chart 6.1 which is attached at the end of this chapter.  Figure 
46 and 47 shows SEM pictures of the fabricated devices.  Here, from the SEM images, it can be 
seen that the cantilever beams were bent downwards.  This may be due to the fact that the 
LPCVD system and its Mass Flow Controllers (MFCs) had not been calibrated.  Thus, the gas 
ratio was not perfectly 5:1 ratio during the silicon nitride deposition process.  Another plausible 
explanation can be the stress induced from the repeated thermal cycling the structures 
experienced from the rest of the processes after deposition.  For the resonance mode application, 
as this should not effect the measurements, it was not of much concern for this project. 
 89
Applied Voltage (Volts)
-10 -5 0 5 10
Measured Current
 (Amps)
-3e-6
-2e-6
-1e-6
0
1e-6
2e-6
3e-6
Between pads 1 & 2
Between pads 1 & 3
Between pads 1 & 4
 
 
Figure 43: Resistance measurement after etching Si in KOH for bulk micromachining of the 
MEMS device. 
 90
Applied Voltage (Volts)
-10 -5 0 5 10
Measured Current (Amps)
-8e-6
-6e-6
-4e-6
-2e-6
0
2e-6
4e-6
6e-6
8e-6
Between  pads 1 & 2 
Between  pads 1 & 3
Between pads 1 & 4 
 
 
Figure 44: Resistance measurement after etching Si in TMAH for bulk micromachining of the 
MEMS device using conventional recipe. 
 91
Applied Voltage (Volts)
-10 -5 0 5 10
Measured Current (Amps
)
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
Between pads 1 & 2 (sensor side) 
Between pads 1 & 2 (reference side) 
Between pads 1 & 3 (sensor side) 
Between pads 1 & 3 (reference side) 
Between pads 1 & 4 (sensor side) 
Between pads 1 & 4 (reference side) 
 
 
Figure 45: Resistance measurement after etching Si in TMAH for bulk micromachining of the 
MEMS device using pH controlled recipe.
 92
 
 
Figure 46: SEM images showing microcantilevers.
 93
 
 
Figure 47: SEM images showing microcantilevers with the Wheatstone bridge structures. 
 94
Flow Chart 6.1: Microfabrication process flow chart for the microcantilever MEMS 
devices 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Step1: Take bare single side polished (100) oriented Si 
wafer. 
Step 3: Deposit poly-Si at 650
O
C in LPCVD, using  
Silane (SiH
4
) gas. 
Step 4: Spin coat with phosphorous diffusant 
(phosphosilicate glass), prebake @ 150
O
C and then 
drive in @ 1000
O
C. 
Step 6: Put in HMDS environment, spin coat with +ve 
photoresist (AZ5214) and soft-bake @ 105
O
C. 
Step 2: Deposit Si
x
N
y
 on it in the LPCVD system, 
using DCS (SiCl
2
H
2
) & NH
3
 gases at 850
O
C. 
Step 5: Deglaze the phosphosilicate glass in 10:1 = 
DI-H
2
O: HF solution. 
Step 7: Expose in UV light and develop in potassium 
borates based developer (AZ400K), and hard-bake @ 
120
O
C. 
 95
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Step 8: DRI Etch of poly-silicon in ASE system, using SF
6 
& 
O
2
 gas. 
Step 10: Expose in UV light and develop in AZ400K 
developer. 
Step 11: Ion clean and deposit Cr-Au-Cr layers in the 
E-beam system. 
Step 12: Put the wafer in ultrasonic bath, while submerged 
in acetone to define metal pads by the lift-off technique. 
Step 13: Sputter SiC in the Sputtering system. 
Step 14: Put in HMDS environment, spin coat  
with +ve photoresist (AZ5214 IR) and soft-bake @ 
90
O
C. 
Step 9: Put in HMDS environment, spin coat with 
+ve photoresist (AZ5214) and soft-bake @ 105
O
C. 
 96
 
 
 
 
 
 
 
 
 
 
 
 
Step 20: Etch Si in TMAH solution, using a pH 
controlled recipe, and dry them in IPA to release 
the cantilever beam structure. 
Step 15: Expose in UV light, reverse bake @ 105
O
C, flood 
expose in UV light & develop in AZ400K developer for 
reverse patterning. 
Step 16: Deposit Al in the E-beam system. 
Step 17: Put the wafer in ultrasonic bath, while  
submerged in acetone to define etching mask by 
lift-off technique. 
Step 18: DRI Etch of SiC & Si
x
N
y
 in the AOE system, 
using CF
4
 & O
2
. 
Step 19: Strip-off Al etch mask with potassium  
Borates based developer AZ400K. 
 97
 
 
 
CHAPTER 7 
 
PIEZORESISTIVE MEASUREMENT OF THE MEMS DEVICES 
 
 At first the microcantilever beams on the MEMS devices were characterized by optically 
measuring the resonant frequency of the beams.  To accomplish that task the photo detector of 
the JEOL SPM 5200 system was used.  The laser of the AFM system was shone on the tip of the 
cantilever beam, and the reflected signal was processed using the photodetector of the system.  
The signal output from the system was then fed to the Tektronix TDS 3014B Digital 
Oscilloscope.  The device was mounted on a modified sample holder for the AFM system, which 
had a spring loaded clamp to hold the sample on top of the piezoelectric ceramics bought from 
the Fuji Ceramics Corporation.  The sample holder was made out of aluminum.  The actuator is 
of thickness mode with a resonant frequency of 1.2 MHz.  The actuator was actuated by a 
sinusoidal signal from a function generator Agilent 33220A through the wideband amplifier 
Model 7600 from Krohn-Hite Corporation.  The schematic diagram of the test setup is shown in 
Figure 48. 
 Since the structure was vibrated with a signal from the function generator, the output 
signal showed a response at all times, at the same frequency as the input frequency of the 
function generator.  This output signal was traced while manually scanning the input signal 
through a range of frequencies.  At the resonant frequency of the microcantilever beam structure 
 98
 
 
Figure 48: Schematic diagram showing test setup for optical measurement of the resonant 
frequency of the microcantilever MEMS device. 
Piezoactuator 
Sensor 
Device 
Spring Loaded Clamp 
Teflon piece 
Protecting 
the Device 
Function 
Generator 
Wide-band 
Amplifier 
Photodetector 
Laser 
Digital O-scope 
with FFT 
Cantilever 
beam 
 99
OPTICAL FREQUENCY MEASUREMENT
Frequency, f (Hz)
0 50x10
3
100x10
3
150x10
3
200x10
3
P
D
 out
put
,
 V
out
 (V
o
l
ts
)
0
1
2
3
4
5
6
Act. freq. 105 kHz
Act. freq. 106 kHz
Act. freq. 107 kHz
Act. freq. 108 kHz
Act. freq. 109 kHz
Act. freq. 110 kHz
Act. freq. 111 kHz
Act. freq. 112 kHz
Act. freq. 113 kHz
 
 
Figure 49: Resonant Frequency characterization of a 150? length microcantilever MEMS device 
using the AFM photodetector. 
 100
OPTICAL FREQUENCY MEASUREMENT
Frequency f (Hz)
0 20x10
3
40x10
3
60x10
3
80x10
3
100x10
3
Amplitude V (Volts)
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
Actuating frequency = 36 kHz
Actuating frequency = 37 kHz
Actuating frequency = 38 kHz
Actuating frequency = 39 kHz
Actuating frequency = 40 kHz
Actuating frequency = 41 kHz
 
 
Figure 50: Resonant Frequency characterization of a 250? length microcantilever MEMS device 
using the AFM photodetector. 
 101
the output signal showed much higher response than the other frequencies that the input signal 
was operated at.  This can be seen in the frequency spectrum plots in Figures 49 and 50, which 
are the responses obtained for 150 ?m and 250 ?m length rectangular shaped microcantilever 
beams.  From these plots, it can be seen that the output response rose sharply around 109 kHz for 
the 150 ?m length device, and 38 kHz for the 250 ?m length device.  It was observed that the 
output signals dropped significantly from those responses when the input signals were moved 
away from those specific frequencies.  Thus, the resonant frequency of the 150 ?m length device 
is close to 109 kHz, and the resonant frequency of the 250 ?m length device is close to 38 kHz.  
Since the resolution of the FFT function of the digital oscilloscope is not that great, these values 
should be considered as approximations only. 
Once the device had been characterized by the optical measurements, the resonant 
frequency was measured by the piezoresistive Wheatstone bridge.  The piezoactuator that was 
used requires a quite high AC voltage to operate, in the range of 80 to 100 Volts.  Since this 
actuator was sitting right underneath the MEMS device and the output signal is supposed to be 
very small, in the range of microvolts, phase-lock loop was required for the measurement.  
Figure 51 shows the schematic diagram of the test setup for the frequency measurement through 
the piezoresistive Wheatstone bridge.  At first, SR844 ? 200 MHz RF Lock-in Amplifier from 
the Stanford Research Systems was used for the piezoresistive measurement of the devices.  A 
phase locked system, such as the Lock-in amplifier, synchronizes the input or the reference 
signal with the output signal that it generates, by comparing their amplitudes at corresponding 
phases.  In this case, the input signal for the SR844 was the output signal from the Wheatstone 
bridge.  The Lock-in amplifier matches the phase of that output with the signal that feeds the 
wideband amplifier to actuate the piezoactuator.  The outputs from the Lock-in amplifier were 
 102
 
 
Figure 51: Schematic diagram showing test setup for piezoresistive measurement of the resonant 
frequency of the microcantilever MEMS device. 
Piezoactuator 
Sensor Device 
Spring Loaded 
Clamp 
Teflon 
Protecting 
the Device 
Sensing 
cantilever 
Lock-in 
Amplifier/
Network 
Analyzer 
Wide-band 
Amplifier 
DC Power 
supply 
 103
monitored by manually scanning near the range of the resonant frequency obtained by the optical 
measurements.  For the device of 150 ?m length microcantilever, it was possible to get a large 
output signal from the Lock-in amplifier, at 104 kHz.  When the input signal was varied from the 
specific frequency or the phase the output signal dropped significantly.  In case of manual 
control, the frequency of the input signal could be varied for the SR844 at a step size of about 1 
kHz.  But, when the frequency scan was performed automatically and recorded, the resulting 
frequency spectrum response showed as depicted in Figure 52.  From these plots it was seen that 
the response from the device looked like noise only.  But, when the response from the device 
with an applied DC voltage across the Whetstone bridge was normalized against the response 
from the device without any voltage applied across the bridge, there was an amplitude difference 
in the range of 5 to 7 ?volts, approximately.  This difference in response does fall in the range of 
output voltage change expected from the piezoresistors made out of highly doped poly Si. 
 After that the test setup was modified by replacing the Lock-in amplifier with a Network 
Analyzer HP 8751A.  The frequency spectrum obtained from this setup for the 250 ?m length 
microcantilever device is attached in Figure 53.  This response showed its 1
st
 peak at 43.2 kHz.  
This was very close to the response that was measured by the photodetector.  Thus, the MEMS 
device based on the piezoresistive sensing element worked for the frequency measurements. 
 104
FREQUENCY SPECTRUM FROM THE LOCK-IN AMPLIFIER
Frequency f (Hz)
102x10
3
103x10
3
103x10
3
104x10
3
104x10
3
105x10
3
105x10
3
A
m
pl
i
t
ude V
out
 (V
o
l
t
s
)
-1e-5
0
1e-5
2e-5
3e-5
4e-5
5e-5
6e-5
7e-5
V
in
=0
V
in
=40% of 0.3 Volts
Subtracted Spectrum
 
 
Figure 52: Resonant Frequency Measurement of a 150? length microcantilever MEMS device 
using the Lock-in amplifier. 
 105
FREQUENCY SPECTRUM FROM THE NETWORK ANALYZER
Frequency, f (Hz)
20x10
3
40x10
3
60x10
3
80x10
3
100x10
3
Amplitude (dB)
-80
-60
-40
-20
0
20
V
in
 = 0
V
in
 = 40% of 0.5 V
subtracted spectrum
 
 
Figure 53: Resonant Frequency Measurement of a 250? length microcantilever MEMS device 
using the Network Analyzer. 
 106
 
 
 
CHAPTER 8 
 
DISCUSSION AND CONCLUSIONS 
 
In this project geometrical aspects of the microcantilever beam structures were 
investigated to develop a better performing microcantilever based MEMS device for biosensor 
application.  Different shapes of cantilever beam structures were studied by finite element 
analysis in ANSYS.  From this initial study it was found that the resonant frequency of the 
cantilever beam structures depends on two parameters.  One of them is the area of cross section 
that is clamped on the fixed end of the cantilever beam.  Larger clamped area, in other words the 
base of the cantilever beam structure, increases the stiffness of the structure.  This phenomenon 
increases the resonant frequency and the corresponding shift in resonant frequency of the 
structure.  The other one is the effective mass acting on the structure, in other words the mass of 
the structure that is being supported by the beam structure at the clamped end.  These phenomena 
are obvious from the Equation (5).  Since the shift in resonant frequency is proportional to the 
intrinsic resonant frequency of the cantilever beam structure, as seen from the Equation (6), the 
performance of the cantilever beam in terms of mass sensitivity depends on them. 
Now, from this discussion, it was clear that the triangular shaped cantilever structure 
should offer the best performance in terms of mass sensitivity.  The disadvantage associated with 
the simple triangular shape structure is that they do not offer large enough area at the free end of 
 107
the structure, where it has the highest sensitivity in terms of frequency shift, for the sensing pad 
that is required to capture the target species for biosensor applications.  On the other hand, the 
triangular shape offers more uniform bending stress near the clamped end, which translates into 
larger signal from the functional or transduction material of the sensor devices. 
To combine both of these phenomena, some modified geometries were investigated by 
FEA simulations done in ANSYS.  This geometry offers the advantages of the triangular shape at 
the clamped end of the structure, while combining a rectangular shape pad area at the free end to 
overcome the disadvantages associated with the triangular shape.  As the FEA results showed 
promising performance by the modified geometry, in terms of mass sensitivity, it was further 
studied by fabricating AFM tip cantilever structure for optical measurement.  The tips were made 
of three geometries: the regular rectangular shape, the triangular shape, and the modified 
geometry.  These three geometries namely shape A, F and I were studied by measuring their 
resonant frequency by the AFM system, and their corresponding shift in resonant frequency due 
to mass addition.  Their performances, in terms of mass sensitivity were characterized and 
compared with each other. 
It was observed that the mass sensitivity of the triangular shape F cantilever structure is 
almost an order of magnitude higher than the regular rectangular shape A; this was predicted as 
well by the FEA results.  Although the modified shape I did not perform as well as the shape F, it 
still showed an improvement of more than three times the mass sensitivity of the shape A.  These 
results agreed quite well with the FEA predictions.  Since, the triangular shape F does not offer 
much space for fabricating sensing pad to capture the target species that needs to be detected, the 
shape I offers a compromise for better performance in term of both of these phenomena.  To 
further investigate its performance, the damping effect on this shape was studied and compared 
 108
with the rectangular and the triangular shape cantilever structures.  The AFM tips were tested at 
different levels of air pressure, and their corresponding resonant frequencies were measured.  
The relative resonant frequencies were plotted and compared with each other in chapter 5.  
Theoretically, since the triangular shape has a smaller area at the free end, it should show a lesser 
damping effect on its performance than the regular rectangular shape.  Based on the same logic, 
the modified geometry should show an intermediate damping effect between those two 
geometries, as depicted in the schematic Figure 22. 
In reality these geometries did not show any discernable differences in their performances, 
in terms of relative resonant frequencies as observed from the plots in Figure 29.  This was due 
to the fact that the relative resonant frequencies are highly dependent on the intrinsic frequencies 
of the structures.  Since the intrinsic resonant frequency of the triangular shape is much higher 
than the rectangular shape, the relative resonant frequency becomes comparable to the 
rectangular shape as a function of pressure.  The modified geometry, also, followed the same 
trend as the other geometries.  The shift in relative resonant frequencies as a function of pressure, 
due to mass addition can be seen in Figures 30 through 32.  Although these plots showed the 
same trend as the basic structures, they showed a shift in plots as predicted from the previous 
results listed in chapter 4. 
Microcantilever based MEMS devices were fabricated with piezoresistive sensing 
elements.  These devices were characterized by measuring their resonant frequencies optically, 
and verified by the electronic measurement through the piezoresistors.  Since the devices needed 
to be actuated by using a piezoactuator that needed a very high voltage AC signal, it offered a 
tremendous challenge to discern the actual output signal from the devices, which is expected to 
be of a very small scale of microvolts regime.  From Figure 52, it can be seen that the scanned 
 109
frequency response from the Lock-in amplifier looked like noise that was picked up by the 
connectors attached to the device for the measurement.  But when this response spectrum was 
normalized against the scanned spectrum, without applying any voltage across the Wheatstone 
bridge, there was an amplitude difference of approximately 5 to 7 microvolts in the response 
from the device.  This amplitude difference was right in the range of the expected value for that 
particular device, which was approximately 15 microvolts.  After replacing the Lock-in amplifier 
with a Network analyzer, a better looking response curve was observed.  This response 
frequency spectrum from the Network analyzer is shown in Figure 53.  This response also 
showed a noise level picked up by the output signal.  This might be due to the fact that there was 
a noise level of charge carriers present in the device connected to the Network analyzer, and as 
the structure vibrated, it showed peaks at different modes of natural frequency of vibration.  
Once the output signal was normalized against the output without applying any voltage across 
the Wheatstone bridge, a clear peak appeared at the expected range of resonant frequency from 
the optical measurement. 
Based on these results MEMS devices were designed and fabricated of the modified 
geometry, along with the triangular and regular rectangular shaped microcantilevers.  Figure 54 
and 55 show the SEM images of the MEMS device based on the triangular and the modified 
geometry, consecutively.  Due to the problems faced during the fabrication processes lately, the 
devices did not work properly.  Thus, the frequency response data for those devices are not 
added here.  In the future, these devices need to be fabricated, characterized, and then tested for 
real time biological species detection. 
 110
 
 
Figure 54: SEM image showing microcantilever MEMS device of triangular geometry. 
 
 111
 
 
Figure 55: SEM image showing microcantilever MEMS device of the modified geometry. 
 
 112
References: 
1. Alvarez, M, Calle, A., Tamayo, J., Lechuga, L.M., Abad, A., Montoya, A.; Development of 
nanomechanical biosensors for detection of the pesticide DDT; Biosensors & Bioelectronics, Vol. 
18, 2003. 
2. Baselt, D.R., Fruhberger, B., Klaassen, E., Cemalovic, S., Britton, C.L., Jr., Patel, S.V., 
Mlsna, T.E., McCorkle, D, Warmack, B.; Design and performance of a microcantilever-based 
hydrogen sensor; Sensors & Actuators B, Vol. 88, 2003. 
3. Gunter, R.L., Delinger, W.D., Porter, T.L., Stewart, R., Reed, J.; Hydration level 
monitoring using embedded piezoresistive microcantilever sensors; Medical Engineering & 
Physics, Vol. 27, 2005. 
4. Ji, H.-F.,Thundat, T; In-situ detection detection of calcium ions with chemically modified 
microcantilevers; Biosensors & Bioelectronics, Vol. 17, 2002. 
5. Pinnaduwage, L.A., Thundat, T., Hawk, J.E., Hedden, D.L., Britt, P.F., Houser, E.J., 
Stepnowski, S., McGill, R.A., Bubb, D.; Detection of 2,4-dinitrotoluene using microcantilever 
sensors; Sensors & Actuators B, Vol. 99, 2004. 
6. Porter, T.L., Eastman, M.P., Macomber, C., Delinger, W.G., Zhine, R.; An embedded 
polymer piezoresistive microcantilever sensor; Ultramicroscopy, Vol. 97, 2003. 
7. Zhou, J., Li, P., Zhang, S., Huang, Y., Yang, P., Bao, M., Ruan, G.; Self-excited 
piezoelectric microcantilever for gas detection; Microelectronics Engineering, Vol. 69, 2003. 
8. Tamayo, J., Humphris, A.D.L., Malloy, A.M., Miles, M.J.; Chemical sensors and 
biosensors in liquid environment based on microcantilevers with amplified quality factor; 
Ultramicroscopy, Vol. 86, 2001. 
 113
9. Rodolphe, M., Jensenius, H., Thaysen, J., Christensen, C.B., Boisen, A.; Adsorption 
kinetics and mechanical properties of thiol-modified DNA-oligos on gold investigated by 
microcantilever sensors; Ultramicroscopy, Vol. 91, 2002. 
10. Baselt, D.R., Lee, G.U., Colton, R.J.; Biosensor based on force microscope technology; 
Journal of Vacuum Science & Technology B, Vol. 14, 1996. 
11. Raiteri, R., Grattarola, M., Butt, H.-J., Skaladal, P.; Micromechanical cantilever-based 
biosensors; Sensors & Actuators B, Vol. 79, 2001. 
12. Ilic, B. Czaplewski, D., Zalalutdinov, M., Craighead, H.G., Neuzil, P., Campagnolo, C., 
Batt, C.; Single cell detection with micromechanical oscillators; Journal of Vacuum Science & 
Technology B, Vol. 19, 2001. 
13. Gunter, R.L., Delinger, W.G., Manygoats, K., Kooser, A., Porter, T.L.; Viral detection 
using an embedded piezoresistive microcantilever sensor; Sensors & Actuators A, Vol. 107, 
2003. 
14. Kooser, A., Manygoats, K.,Eastman, M.P., Porter, T.L; Investigation of the antigen 
antibody reaction between anti-bovine serum albumin (a-BSA) and bovine serum albumin (BSA) 
using piezoresistive microcantilever based sensors; Biosensors & Bioelectronics, Vol. 19, 2003. 
15. Yan, X., Ji, H.-F., Lvoy, Y.; Modification of microcantilevers using layer ?by-layer 
nanoassembly film for glucose measurement; Chemical Physics Letters, Vol. 396, 2004. 
16. Ilic, B., Yang, Y., Craighead, H.G.; Virus detection using nanoelectromechanical devices; 
Applied Physics Letter, Vol. 85, 20004. 
17. Alvarez, M., Tamayo, J.; Optical sequential readout of microcantilever arrays for biological 
detection; Sensors & Actuators B, Vol. 106, 2005. 
 114
18. Datskos, P.G., Sauers, I., Detection of 2-mercaptoethanol using gold-coated 
micromachined cantilevers, Sensors and Actuators B, Vol. 61, 1999. 
19. Oden, P.I., Gravimetric sensing of metallic deposits using an end-loaded microfabricated 
beam structure, Sensors and Actuators B, vol. 53, 1998. 
20. Stern, R., Levy, M., Acoustic wave sensors, Academic Press, 1997. 
21. Ilic, B, Craighead, H.G., Krylov, S., Senaratne, W., Ober, C., Neuzil, P., Attogram 
detection using nanoelectromechanical oscillators, Journal of Applied Physics, vol. 75, 2004. 
22. Timoshenko, Stephen; Vibration problems in engineering; 2
nd
 edition; D. Van Nostrand 
Co., Inc.; New York; July, 1937. 
23. Blevins, R.D., Formulas for natural frequency and mode shape, Krieger Publishing Co., 
Malabar, Fl, 2001. 
24. Yahiaoui, R., Bosseboeuf, A., Cantilever microbeams: modeling of the dynamical 
behaviour and material characterization, 5th International conference on Thermal and 
Mechanical Simulation and Experiments in Micro-electronics and Micro-Systems, Europe, 2004 
25. Lochon, F., Dufour, I., Rebiere, D.; An alternative solution to improve sensitivity of 
resonant microcantilever chemical sensors: comparison between using high-order modes and 
reducing dimensions; Sensors and Actuators B; 2005. 
26. Sone, H., Fujinuma, Y., Hieida, T., Chiyoma, T., Okano, H., Hosaka, S.; Picogram mass 
sensor using microcantilever; SICE Annual Conference in Sapporo; August 4-6, 2004; Japan. 
27. Elwenspoek, M., Wiegerink, R.; Mechanical microsensors; Springer; Germany; 2001. 
28. Harley, J.A., Kenny, T.W.; 1/F noise considerations for the design and process 
optimization of piezoresistive cantilevers; Journal of Microelectromechanical Systems, Vol. 9, 
No. 2; 2000. 
 115
29. Nyquist, H.; Thermal agitation of electric charge in conductors; Physical Review, Vol. 32; 
1928. 
30. DeSilva, Clarence W., Vibration: fundamentals and practice, CRC Press LLC, Boca Raton, 
Florida, 2000. 
31. ANSYS Release 8.0 Documentation. 
32. Kiesewetter, L., Zhang, J.-M., Houdeau, D., Steckenborn, A.; Determination of Young?s 
moduli of micromechanical thin films using the resonant method; Sensors and Actuators A; 1992. 
33. Sader, J.E.; Frequency response of cantilever beams immersed in viscous fluids with 
applications to the atomic force microscope; Journal of Applied Physics, Vol. 84, 1998. 
34. Sandberg, R., Molhave, K., Boisen, A., Svendsen, W.; Effect of gold coating on the Q-
factor of a resonant cantilever; Journal of Micromechanics & Microengineering, Vol. 15, 2005. 
35. Southworth, D.R., Craighead, H.G., Parpia, J.M.; Pressure dependent resonant frequency of 
micromechanical drumhead resonators; Applied Physics Letters, Vol. 94, 2009. 
36. Ikehara, T., Lu, J., Konno, M., Maeda, R., Mihara, T.; A high quality-factor silicon 
cantilever for a low detection-limit resonant mass sensor operated in air; Journal of 
Micromechanics & Microengineering, Vol. 17, 2007. 
37. Bianco, S., Cocuzza, M., Ferrero, S., Giuri, E., Piacenza, G., Pirri, C.F., Bich, D., Merialdo, 
A., Schina, P., Correale, R.; Silicon resonant microcantilevers for absolute pressure measurement; 
Journal of Vacuum Science & Technology B, Vol. 24, No. 4, 2006. 
38. Sandberg, R., Svendsen, W., Molhave, K., Boisen, A.; Temperature and pressure 
dependence of resonant in multi-layer microcantilevers; Journal of Micromechanics & 
Microengineering, Vol. 15, 2005 
 116
39. Baginsky, T.; Microelectronics fabrication and design lab manual; Auburn University; 
2002. 
40. Williams, K.R., Gupta, K., Wasilik, M.; Etch rates for micromachining processing-Part II; 
Journal of Microelectromechanical Systems; Vol. 12, No. 6; 2003. 
41. Kovacs, G.T.A., Maluf, N.I., Petersen, K.E.; Bulk micromachining of silicon; Proceedings 
of the IEE, Vol. 86, No. 8, 1998. 
42. Miller, Eric; Low stress silicon nitride process development, Washington Technology 
Center; 2001. 
43. Madou, M.; Fundamentals of microfabrication; CRC Press LLC; 1997. 
44. Mehta, N.J. Study of hydrogenated diamond like carbon films and investigating its use in 
MEMS devices, MS Thesis, Auburn University, 2005. 
45. Tabata, Osamu; pH controlled TMAH etchants for silicon micromachining; The 8
th
 
International Conference on Solid-State Sensors and Actuators, and Eurosensors IX; 1995. 
46. Tea, N.H., Milanovic, V., Zincke, C.A., Suehle, J.S., Gaitan, M., Zaghloul, M.E., Geist, J.; 
Hybrid postprocessing etching for CMOS-compatible MEMS; Journal of 
Microelectromechanical Systems, Vol. 6, No. 4; 1997. 
47. Kovacs, G.T.A., Maluf, N.I., Petersen, K.E.; Bulk micromachining of silicon; Proceedings 
of the IEEE, Vol. 86, No. 8, 1998. 
48. Zhang, J., Hon, W.C., Leung, L.L.W., Chen, K.J.; CMOS-compatible micromachining 
techniques for fabricating high-performance edge-suspended RF/microwave passive components 
on silicon substrates; Journal of Micromechanics and Microengineering, Vol. 15, 2005. 
 117
Appendix A 
 
Table A1: Simulation results for different geometrical shapes performed using ANSYS 
software 
 
Shape 
ID 
Shape Geometry 
Shape 
Parameters
Frequency 
(Hz) 
Frequency 
Shift (Hz) 
1 
 
w = 10? 192,997 125 
2 w = 20? 194,124 53 
3 w = 30? 194,858 46 
4 
 
w
1
= 30? 
w
2
 = 10? 
l
1
 = 30? 
160,877 46 
5 
 
 
w
1 
= 20? 
w
2
 = 30? 
171,886 41 
6 
 
w
1
 = 20? 
w
2
 = 30? 
w
3
 = 10? 
w
4
 = 16? 
l
1
 = 30? 
118,461 31 
7 
 
 
w
1
= 20? 
w
2
= 30? 
l
1
 = 30? 
l
2
 = 20? 
162,002 36 
8 
w
1
= 20? 
w
2
= 30? 
l
1
 = 20? 
l
2
 = 30? 
161,451 34 
 
w
1 
w
2 
w
2 
w
1 
l
1 
w
w
1 
w
3 
w
2 
w
4 
l
1 
w
1 w
2 
l
1 
l
2 
 118
Table A1: continued? 
 
Shape 
ID 
Shape Geometry 
Shape 
Parameters 
Frequency 
(Hz) 
Frequen
cy Shift 
(Hz) 
9 
Same as above 
w
1
= 10? 
w
2
= 20? 
l
1
 = 30? 
l
2
 = 20? 
141,017 52 
10 
w
1
= 10? 
w
2
= 20? 
l
1
 = 20? 
l
2
 = 30? 
140,365 55 
11 
 
w =26.795? 
? = 30
O
 
390,010 462 
12 
w =41.421? 
? = 45
O
 
385,752 296 
13 
w =57.735? 
? = 60
O
 
379,027 211 
14 
w =100? 
? = 90
O
 
358,080 118 
15 
 
w
1
 = 26.795? 
w
2
 = 10? 
? = 30
O
 
361,458 436 
16 
w
1
 = 41.421? 
w
2
 = 10? 
? = 45
O
 
289,124 236 
17 
w
1
 = 41.421? 
w
2
 = 12? 
? = 45
O
 
314,751 252 
18 
 
w
1
 = 57.735? 
w
2
 = 10? 
? = 60
O
 
294,402 179 
19 
w
1
 = 57.735? 
w
2
 = 10? 
? = 60
O
 
320,591 185 
20 
w
1
 = 100? 
w
2
 = 10? 
? = 90
O
 
213,480 117 
21 
w
1
 = 100? 
w
2
 = 15? 
? = 90
O
 
251,421 93 
w
2 
w
2 
w
2 
w
1 
? 
w
1 
w
2 
w
2 
? 
w 
? 
 119
Table A1: continued... 
 
Shape 
ID 
Shape Geometry 
Shape 
Parameters 
Frequency 
(Hz) 
Frequen
cy Shift 
(Hz) 
22 
w
1
 = 26.795? 
w
2
 = 10? 
w
3
=20? 
? = 30
O
 
l
1
=20? 
186,860 69 
23 
 
w
1
 = 41.421? 
w
2
 = 12? 
w
3
=20? 
? = 45
O
 
l
1
=20? 
200,140 78 
24 
 
w
1
 = 57.735? 
w
2
 = 12? 
w
3
=23.094? 
? = 60
O
 
l
1
=20? 
221,182 60 
25 
 
w
1
 = 100? 
w
2
 = 10? 
w
3
=30? 
? = 90
O
 
l
1
=15? 
l
2
 = 50? 
161,737 56 
26 
w
1
 = 100? 
w
2
 = 10? 
w
3
=30? 
? = 90
O
 
l
1
=20? 
l
2
 = 55? 
134,920 44 
 
 
w
2 
w
2 
w
1 
w
3 
l
1 
? 
w
2 
w
2 
w
1 w
3 
l
1 
? 
w
1 
w
2 
w
2 
w
2 
w
3
l
1
? 
w
1 
w
2 
w
2 
w
2 
w
3 
l
1 
l
2 
? 
 120
 
Table A1: continued... 
 
Shape 
ID 
Shape Geometry 
Shape 
Parameters 
Frequency 
(Hz) 
Frequen
cy Shift 
(Hz) 
27 
 
w
1
 = 26.795? 
w
2
 = 20? 
? = 30
O
 
198,939 70 
28 
w
1
 = 41.421? 
w
2
 = 20? 
? = 45
O
 
240,018 79 
29 
 
w
1
 = 57.735? 
w
2
 = 23.094? 
? = 60
O
 
256,579 70 
30 
w
1
 = 100? 
w
2
 = 30? 
? = 90
O
 
272,354 51 
 
 
 
 
 
 
 
 
 
 
 
 
w
1 
w
2 
l
1 
? 
W
1 
l
W
2