Substrate Effect, Pile-Up and Sink-In Factors during Thin Film Nanoindentation 
 
by 
 
Kevin Russell Schwieker 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
December 12th, 2011 
 
 
 
 
Keywords: Nanoindentation, Thin Films, Erroneous Contact Area, Instrumented Indentation 
Testing, Continuous Stiffness Measurement 
 
 
Copyright 2011 by Kevin Russell Schwieker 
 
 
Approved by 
 
Barton Prorok, Chair, Associate Professor of Materials Engineering 
 Ruel Overfelt, Professor of Materials Engineering 
Robert Jackson, Associate Professor of Mechanical Engineering 
 
 
 
 
 
 
2 
 
 
 
 
 
 
Abstract 
 
 Theoretical and experimental models continue to be developed for thin-film 
nanoindentation that attempt to account for substrate effects in differing film-substrate 
combinations.  While many models have been developed to extract film properties independent 
of the substrate through simple instrumented indentation testing, it is important for a sufficient 
model that correctly predicts the behavior in a wide range of materials.  One recent model 
developed by Zhou et al. has shown a more developed understanding of the interface between the 
substrate and film, and shows promise to better describe many material combinations, but has not 
been sufficiently vetted for films on substrates that more easily plastically deform.  The focus of 
this work is to apply the aforementioned model to situations that it has not been before, and to 
evaluate its ability to accurately extract the film?s Young?s modulus and Poisson?s ratio from the 
experimental composite modulus.  
 
  
 iii 
 
 
 
 
Acknowledgments 
 
 I would like to thank Dr. Prorok for his support and guidance throughout this process.  I 
would like to thank my committee members, Dr. Overfelt and Dr. Jackson for their time and 
suggestions toward my thesis and research.  I would also like to thank both the current and 
previous members of my group; Bo, Brandon, Nicole, Shakib, Madhu, Naveed and Dong as well 
as all of the other faculty, staff and students at Auburn University who have helped me during 
the course of my work; especially Jacob and Steve.  I would like to thank my family for their 
love and unwavering support throughout my time at Auburn University, as always having you 
behind me has been a pillar of support that I have needed and will always be thankful for.  And 
finally I would like to thank Brian for all of the early morning coffee and conversation 
throughout the years.   
 
 
 
  
 iv 
 
 
 
Table of Contents 
 
 
Abstract ........................................................................................................................................... ii 
Acknowledgments.......................................................................................................................... iii 
List of Tables ................................................................................................................................. vi 
List of Figures ............................................................................................................................... vii 
List of Abbreviations .................................................................................................................... xii 
Chapter 1: Introduction ....................................................................................................................1 
1.1 Overview ....................................................................................................................... 1 
1.2 Thesis Structure ............................................................................................................ 2 
Chapter 2: Literature Review of Instrumented Thin Film Indentation ............................................3 
2.1 Instrumented Indentation Testing ................................................................................. 3 
2.2 Continuous Stiffness Measurement .............................................................................. 6 
2.3 Erroneous Contact Area ................................................................................................ 8 
2.4 Modeling Thin Film Substrate Effects .......................................................................... 9 
Chapter 3: Material Selection ........................................................................................................18 
3.1 Material Selection and Their Mechanical Properties .................................................. 18 
Chapter 4: Experimental Setup and Fabrication ............................................................................20 
4.1 Substrates .................................................................................................................... 20 
4.2 Film Deposition .......................................................................................................... 26 
4.3 Nanoindentation .......................................................................................................... 37 
Chapter 5: Results and Discussions ...............................................................................................39 
 v 
5.1 Experimental Nanoindentation Analysis .................................................................... 39 
5.2 Validity of Zhou-Prorok Model in Investigated Materials ......................................... 65 
Chapter 6: Conclusions ..................................................................................................................71 
References ......................................................................................................................................72 
 
  
 vi 
 
 
 
 
List of Tables 
Table 2.1.1 Geometries of different indenter tips; C-f = centerline to face angle, d = indentation 
depth, and a = tip radius for cone and spherical indenters. ....................................................4 
Table 3.1.1 Material candidates for film and substrates with desirable Young?s modulus and 
Poisson?s ratio.  Highlighted materials were chosen to be substrates or deposited as a film 
due to having the most favorable mechanical properties, being safe to work with and their 
availability. ...........................................................................................................................19 
Table 4.1.1 Spectrum analysis of energy-dispersive X-ray spectroscopy of indium substrate after 
polishing; all results in weight %. ........................................................................................22 
Table 4.2.1 Sputtering parameters for Al film from Denton sputtering system log book. ............27 
Table 4.2.2 Sputtering conditions for Al films to evaluate how changing sputtering power 
influences Hillock grain formation and density. ..................................................................30 
Table 4.2.3 Sputtering conditions for Al films to evaluate how varying film thickness influences 
Hillock grain formation and density. ....................................................................................32 
Table 4.2.4 Sputtering parameters of 230nm Pt film with Ti adhesion layer. ...............................35 
Table 4.2.5 Film thickness of sputtered platinum films.................................................................36 
Table 5.1.1 Values of films? Young?s moduli and alphas from Eq. (15) and (17) for each Pt film 
on substrate combination, as well each substrate?s Young?s Modulus obtained from 
nanoindenting directly into the substrate..............................................................................51 
 
  
 vii 
 
 
 
 
List of Figures 
 
Figure 2.1.1 Schematic of nanoindentation system. ........................................................................3 
Figure 2.1.2 (a) Load verses displacement plots for a typical, a relatively soft, and a relatively 
hard material. (b) Cross-sectional schematic of certain stages of the loading-unloading 
curve as shown in the typical load verses displacement plot.[9] .............................................6 
Figure 2.2.1 Load-Displacement curve during the continuous stiffness method. ...........................7 
Figure 2.2.2 Young?s Modulus verses Displacement into surface for (a) bulk material, (b) 
compliant film on hard substrate and (c) hard film on compliant substrate.[11] .....................8 
Figure 2.3.1 Schematics of the pile-up and sink-in effect. ..............................................................9 
Figure 2.4.1 Schematic of a indentation's cross section showing h, hf, hc, and hs and how they 
relate to indention depth and elastic recovery after removal of load P.[13] ...........................11 
Figure 2.4.2 (a) Schematic illustrating the concept of continuous transfer of strain between the 
film and substrate, (b) simulation indicating that strain discontinuously transferred between 
the film and substrate, and (c) schematic showing how the film and substrate components 
are decoupled in the discontinuous elastic interface transfer model. ...................................13 
Figure 2.4.3 Finite element analysis of the AlOx film/substrate composites showing the elastic 
strain distribution for an indent penetrating 5nm into each film; (a) SiO2, (b), Ge, (c) Si, (d) 
MgO, and (e) Sapphire. ........................................................................................................16 
Figure 2.4.4 Zhou et al. demonstrating that the film?s modulus does not correspond to Eflat that 
their second model has the ability to accurately extract film modulus from the composite 
nanoindentation data. ...........................................................................................................17 
 viii 
Figure 4.1.1 Struers RotoPol-11 Surface Polisher. ........................................................................21 
Figure 4.1.2 JEOL JSM 7000F Scanning Electron Microscope. ...................................................21 
Figure 4.1.3 Location of spectrums for energy-dispersive X-ray spectroscopy of indium substrate 
after polishing. ......................................................................................................................22 
Figure 4.1.4 (a) Arbor press used to flatten both the indium and tin substrates for a smooth 
surface. (b) Illustration to show how force was evenly distributed across substrate surface.23 
Figure 4.1.5 Micrographs at 1,000 magnification of In (a) 0.5mm surface as received, (b) 0.5mm 
thick In compressed, (c,d) 2mm thick In compressed ..........................................................25 
Figure 4.1.6 Micrographs at 1,000 magnification of Sn (a) 2mm surface as received, (b) 0.5mm 
thick Sn compressed, (c,d) 2mm thick Sn compressed ........................................................26 
Figure 4.2.1 Denton Vacuum Inc. DC & RF sputtering system. ...................................................27 
Figure 4.2.2 Tencor Instruments "Alpha-Step 200" profilometer. ................................................28 
Figure 4.2.3 Hillock growth grains on film surface of 400nm Al on SiO2. ...................................29 
Figure 4.2.4 Micrographs of Al film surface as sputtered at different powers of 75, 125, 175, 300, 
400, 600 and 700W at 10,000 magnifications. .....................................................................31 
Figure 4.2.5 Micrographs of Al film surfaces as sputtered to different thickness of 250, 500, 750 
and 1000nm at 10,000 magnifications. ................................................................................33 
Figure 4.2.6 Micrographs of 250nm Al film on SiO2 at (a) 25x and (b) 1000x showing sporadic 
coverage. ..............................................................................................................................34 
Figure 4.2.7 Surface quality of platinum film on SiO2 substrate. .................................................36 
Figure 4.3.1 Image of MTS Nano Indenter XP nanoindentation system.......................................38 
Figure 5.1.1 E-h curve of an example erroneous indention that would be deleted before averaging 
indentation results. ...............................................................................................................40 
 ix 
Figure 5.1.2 Checking validity of changing Poisson?s ratio through Excel when compared to 
recalculating the sample through TestWorks. ......................................................................41 
Figure 5.1.3a E-h curve for In substrate after flattening with Arbor press. ...................................42 
Figure 5.1.3b E-h curve for Sn substrate after flattening with Arbor press. ..................................43 
Figure 5.1.3c E-h curve for Al single crystal substrate, orientation (100). ....................................43 
Figure 5.1.3d E-h curve for Cu single crystal substrate, orientation (100). ...................................44 
Figure 5.1.3e E-h curve for Ti substrate. .......................................................................................44 
Figure 5.1.3f E-h curve for Pt substrate. ........................................................................................45 
Figure 5.1.3g E-h curve for Ta substrate. ......................................................................................45 
Figure 5.1.3h E-h curve for Si single crystal substrate, orientation (100). ....................................46 
Figure 5.1.4a E-h curve for 230nm Pt on In with Z-P model, film E and film alpha. ...................47 
Figure 5.1.4b E-h curve for 230nm Pt on Sn with Z-P model, film E, and film alpha. .................48 
Figure 5.1.4c E-h curve for 230nm Pt on Al with Z-P model, D-N model, film E, and film alpha.48 
Figure 5.1.4d E-h curve for 230nm Pt on Cu with Z-P model, film E, and film alpha. ................49 
Figure 5.1.4e E-h curve for 230nm Pt on Ti with Z-P model, D-N model, film E, and film alpha.49 
Figure 5.1.4f E-h curve for 230nm Pt on Pt with Z-P model, film E, and film alpha ...................50 
Figure 5.1.4g E-h curve for 230nm Pt on Ta with Z-P model, film E, and film alpha. .................50 
Figure 5.1.4h E-h curve for 230nm Pt on Si with Z-P model, D-N model, film E, and film alpha.51 
Figure 5.1.5a 230nm Pt on In: 500nm indention ...........................................................................52 
Figure 5.1.5b 230nm Pt on Sn: 500nm indention. .........................................................................53 
Figure 5.1.5c 230nm Pt on Al: 500nm indention...........................................................................53 
Figure 5.1.5d 230nm Pt on Cu: 500nm indention. .........................................................................54 
Figure 5.1.5e 230nm Pt on Ti: 500nm indention. ..........................................................................54 
 x 
Figure 5.1.5f 230nm Pt on Pt: 500nm indention. ...........................................................................55 
Figure 5.1.5g 230nm Pt on Ta: 500nm indention. .........................................................................55 
Figure 5.1.5h 230nm Pt on Si: 500nm indention. ..........................................................................56 
Figure 5.1.6 500nm indentions into 230nm Pt on Indium have a larger radius of volume than 
indicated by sharp edges shown in the 20,000 magnification. .............................................57 
Figure 5.1.7 Stiff film plastically deforming a larger area than typical in a softer substrate, 
causing the readily visible residual indention to be much smaller than if deformation was 
localized to under the tip. .....................................................................................................58 
Figure 5.1.7a Micrograph of 230nm Pt on In. Left: secondary e-. Right: back-scattered e-. .........60 
Figure 5.1.7b Micrograph of 230nm Pt on Sn. Left: secondary e-. Right: back-scattered e-. ........60 
Figure 5.1.7c Micrograph of 230nm Pt on Al. Left: secondary e-. Right: back-scattered e-. ........61 
Figure 5.1.7d Micrograph of 230nm Pt on Cu. Left: secondary e-. Right: back-scattered e-. .......61 
Figure 5.1.7e Micrograph of 230nm Pt on Ti. Left: secondary e-. Right: back-scattered e-. .........62 
Figure 5.1.7f Micrograph of 230nm Pt on Pt. Left: secondary e-. Right: back-scattered e-. .........62 
Figure 5.1.7g Micrograph of 230nm Pt on Ta. Left: secondary e-. Right: back-scattered e-. ........63 
Figure 5.1.7h Micrograph of 230nm Pt on Si. Left: secondary e-. Right: back-scattered e-. .........63 
Figure 5.1.8 EDS of 500nm indention into 230nm Pt on Si. a) Spectrum locations for b) 
Spectrum 1, c) Spectrum 2 and d) Spectrum 3. ....................................................................64 
Figure 5.2.1 Eflat plotted against Es for all substrates as a means to suggest the Pt film?s actual 
Young?s modulus by where it crosses the line of plastic homogeneity indicated by the 
dashed line. ...........................................................................................................................66 
Figure 5.2.2 Plots of ?    verses the substrate modulus normalized by    . ...............................67 
Figure 5.2.3 Micrograph of 230nm Pt on Si 500nm indention at a 70? tilt. ..................................68 
 xi 
Figure 5.2.4 Micrograph of 230nm Pt on Al 500nm indention at a 70? tilt. .................................69 
Figure 5.2.5 Micrograph of 230nm Pt on Ti 500nm indention at a 70? tilt. ..................................69 
Figure 5.2.6 Micrograph of 230nm Pt on Ta 500nm indention at a 70? tilt. .................................70 
  
 xii 
 
 
 
 
 
List of Abbreviations 
 
  Composite Young?s Modulus 
DC Direct Current 
RF Radio Frequency 
D-N In relation to Doerner and Nix Model 
O-P In relation to Oliver and Pharr Model 
H-C In relation to Hay and Crawford Model 
Z-P In relation to Zhou and Prorok Model 
S-N In relation to Saha and Nix Model 
  As subscript: of the film 
  As subscript: of the indenter 
? Angstrom 
nm Nanometer 
  Weighting factor 
  As subscript: of the substrate 
  Shear Modulus 
  Poisson?s Ratio 
SEM Scanning Electron Microscope 
CSM Continuous Stiffness Method 
MEMS Microelectromechanical systems 
1 
 
Chapter 1: Introduction 
 
1.1 Overview 
 Indentations of materials on a macro and micro scale have been a cornerstone of 
determining mechanical properties, such as hardness, of materials for the last century.  During 
indentation, a tip with known geometric size and mechanical properties is pressed into a material.  
Once loading is complete, the hardness of the indented material is then calculated from the 
maximum load applied and the measured contact area from the remaining indent.  As the 
experimentation method has progressed, there has been a desire to make smaller and less 
intrusive indents on smaller and smaller scales.  Over the last few decades instrumented 
indentation on the nano-scale, nanoindentation, has gained attention as a method to extract the 
hardness and Young?s modulus of a samples that require higher precision and much lower loads 
that can be applied by direct human interaction.   
 With nanoindentation came the possibility to indent on a sample that consists of a thin 
layer, or film, of one material on the surface of a different bulk material, or substrate. The 
interest in thin films comes from their use in a wide range of material applications such as optical 
coatings, very large-scale integrated circuits, anti-corrosion, anti-wear and fuel cells.  Even when 
the applications are not centered on the mechanical behavior of the thin films, increasing their 
ability to withstand processing, and durability during their lifetime is still needed.  One current 
shortcoming of nanoindenting thin films being widely researched is that as the film?s thickness 
decreases, the substrate starts to play more of a role in the properties determined through 
indentation, even at very low penetration depths of the film.  Recent authors[1-7] have developed 
theoretical models based on both experimental and finite element analysis that attempt to extract 
 2 
the mechanical properties of the film, independent of the substrate.  While all of these models 
have their strengths, they also tend to only work for certain material combinations; such as 
compliant films on hard substrates, or hard films on compliant substrates.  
 The goal of this research is to thoroughly review one of the more recent models to of 
been developed that takes a new approach in describing the film and substrates composite 
behavior.  This model, developed by Zhou et al. takes into account that the transfer of energy 
across the film-substrate interface is not linear, but actually discontinuous; allowing it to better 
describe the film?s behavior for a broader range of material combinations.  A group of materials 
were selected for their similar Poisson?s ratio, but varying Young?s modulus, to have a single 
thin film layer sputtered on them which also has a similar Poisson?s ratio to the substrates.   The 
samples were then nanoindented, comparing the Young?s modulus verses indention depth to the 
behavior expected through the evaluated model. 
 
1.2 Thesis Structure 
 Chapter 2 includes a literature review of instrumented indentation testing, and looks at 
each of the major models that have been developed to extract the film?s intrinsic mechanical 
values.  Chapter 3 discusses the method and line of thought throughout the process of material 
selection for both the film and substrates used in terms of which mechanical properties were 
desired, and why.  Chapter 4 details the experimental setup of how the substrates were prepared, 
the parameters used for thin film deposition, and characterization of the resulting composite film-
substrate samples through SEM and nanoindentation.  Chapter 5 and 6 present the results, a 
discussion of their meaning, and a summary of the research. 
 
 3 
 
Chapter 2: Literature Review of Instrumented Thin Film Indentation 
 
2.1 Instrumented Indentation Testing 
 Instrumented Indentation Testing, or nanoindentation, is applying a measurable load on a 
sample through a tip of known geometry and mechanical properties, and then measuring the 
material?s response as the tip is withdrawn as well as the load required to displace the tip into the 
sample.  While there are a range of commercial available indentation systems that use their own 
methodology, a schematic of one of the most common implementations is shown in Figure 2.1.1; 
a magnet and coil in an induction force generation system to generate load, with the 
displacement being measured through a capacitance displacement gauge.[8]   
 
 
Figure 2.1.1 Schematic of nanoindentation system.[8] 
 
There are a range of indentation tips that can be utilized, each having their own area of 
purpose, and associated advantages and disadvantages. The most commonly used tips for 
 4 
indentation are spherical and Berkovich, a three sided pyramidal shape.  While conical tips are 
self-similar, meaning they have the same geometric relationship through a range of depths, and 
are good for defining mechanical properties, sufficiently hard specimens are increasing hard to 
manufacture at smaller scales.  The Berkovich tip also allows for a self-similar shape at 
increasing indent depth, but is able to be fabricated to an extremely sharp point through 
traditional grinding techniques on only three sides; making it the most commonly used indenter 
due to its low production costs.  A selection of available tips and their associated geometries are 
given in Table 2.1.1.[9] 
 
Table 2.1.1 Geometries of different indenter tips; C-f = centerline to face angle, d = indentation 
depth, and a = tip radius for cone and spherical indenters.[9] 
 
 
 Once the tip penetrates the surface of the sample, the deformation that occurs has both 
elastic and plastic components.  These two components are intertwined until the tip is unloaded, 
at which point only the elastic behavior is causing a force that pushes back on the tip as it moves 
out of the material.  As this mechanism is isolated from plasticity, the measured slope of the 
unloading curve is used to determine how elastic the material is.  The more stiff the material, the 
more energy that is able to be stored elastically between atoms, which is then applied back to the 
tip during unload; leading to an unloading curve that more closely follows the path of the loading 
 5 
curve.  Consequently, the less stiff the material, the more vertical the unloading curve is, as the 
energy has been dispersed as plastic behavior so there is less stored energy to be transferred back 
to the tip.  Load verses displacement plots for  typical, soft, and hard materials are given in 
Figure 2.1.2(a), and the resulting sample?s responses at different points are shown in Figure 
2.1.2(b).[9]  This unloading stiffness, S, can be related to Young?s modulus, E, of the material 
through the equation 
         ?   ?  (1) 
where dP is the change in load, dh is the change in displacement, A is the contact area, and Er is 
the effective modulus determined by 
   
 
 (    )  (    
 )
   (2) 
where E and Ei are the elastic moduli of the sample and indenter respectively, while ? and ?i are 
the Poisson?s ratio of the sample and indenter tip.[9] 
 6 
 
Figure 2.1.2 (a) Load verses displacement plots for a typical, a relatively soft, and a relatively 
hard material. (b) Cross-sectional schematic of certain stages of the loading-unloading curve as 
shown in the typical load verses displacement plot.[9] 
 
2.2 Continuous Stiffness Measurement 
 With thin films comes the desire to be able to show the Young?s modulus or hardness 
verses the indention depth into the sample as this allows for the separation of film and substrate 
properties.  A method used to accomplish this is the continuous stiffness method, or CSM.  Also 
known as the dynamic stiffness measurement, CSM applies an oscillatory force to the increasing 
load of a standard instrumented indentation test.  Shown in Figure 2.2.1 the oscillation of the 
load allows for the stiffness to be measured at many points as displacement increases. 
 7 
 
 
Figure 2.2.1 Load-Displacement curve during the continuous stiffness method.[10] 
 
 In the case of thin film nanoindentation, the advantage of CSM is the ability to the show 
mechanical properties for a range of displacement, not one set depth per indention, as it is with 
typical indentation methods.  At the earlier stage of the indention, the returned mechanical 
properties are mostly comprised of the thin film, and as the tip moves deeper into the film, the 
substrate?s effect starts to take over, eventually coming to dominate as the depth approaches, and 
surpasses, the thickness of the film.  If a bulk material is indented using CSM, the resulting 
Young?s modulus verses displacement plot will show a constant horizontal line, as the property 
of the material would not change with depth.  Indenting a sample that is composed of a soft, or 
compliant, film on a hard substrate, the Young?s modulus will start near the value of the film?s 
material in bulk, and rise toward that of the substrate.  When indenting a hard film on a 
compliant substrate the modulus-displacement curve starts near the value of the film and has a 
 8 
negative trending slope as you move deeper into the sample.   Summaries of each of these 
different occasions are given in Figure 2.2.2. 
 
 
Figure 2.2.2 Young?s Modulus verses Displacement into surface for (a) bulk material, (b) 
compliant film on hard substrate and (c) hard film on compliant substrate.[11] 
 
2.3 Erroneous Contact Area 
 One substantial challenge to nanoindentation is the difficulty in accurately measuring the 
contact area during displacement, due to how the material being indented can plastically deform 
around the indenter, causing a change in actual contact area between the sample and tip, also 
known as erroneous contact area.  If the material is soft it will tend to pile-up around the indenter 
tip, causing an increase in contact area, leading to an overestimation of the material?s modulus, 
 9 
and hardness, as there is more material providing elastic recovery.  Harder materials have the 
tendency to translate their strain further away from the tip, allowing for a greater volume of 
material to distribute the deformation, causing the area around the tip to sink-in, reducing the 
contact area of the tip.  The sink-in effect leads to an underestimation of the material?s modulus, 
and hardness.  A cross sectional schematic of both effects during indentation, and the resulting 
top-down view of the recovered material after unload is shown in Figure 2.3.1.[12] 
 
 
Figure 2.3.1 Schematics of the pile-up and sink-in effect.[12] 
 
2.4 Modeling Thin Film Substrate Effects  
As instrumented indentation has approached the nanoscale, a new issue has appeared that 
has been an area of research is how the mechanical properties of the substrate influence the 
 10 
experimental indentation data, even at very shallow depth.  As the field of nanoindentation has 
continued to develop, a range of approaches have developed different models that attempt to 
extract the film?s properties independent of the substrate.[1, 2, 5, 7, 13, 14]  While some of these 
models better describe certain material combinations, the goal is to have a model that describes 
the majority of film-substrate material combinations with a wide range of mechanical behavior.  
 Not satisfied with the underlying assumption that the unloading load-displacement curve 
is linear, Oliver and Pharr showed that for most materials the unloading curve relates to stiffness 
through a power law function 
    (    )  (3) 
where B and m are empirically determined constants and hf is final displacement after the 
material is allowed to elastically recover.[13] 
 With the stiffness data, S, the reduced Young's modulus and hardness, Er and H 
respectively can be calculated from 
     ?   ?  (4) 
and 
      (5) 
where A is the projected contact area at peak load and is a function of hc, the vertical distance 
along which contact is made, in the form        .  A schematic cross section of an indent 
before and after elastic recovery to show the related different depths is shown in Figure 2.4.1.  
For a perfect Berkovich tip, A is calculated as  
           (6) 
but in practice as a perfect tip cannot be obtained, another relationship 
 11 
                                                    (7) 
can be used where C1 through C8 are constants.  The lead term describes a perfect Berkovich tip, 
with the following terms representing changes to the tip's geometry due to blunting.  The Oliver 
and Pharr method to calculate mechanical properties from instrumented indention testing is 
currently the most common used in practice.   
 
 
Figure 2.4.1 Schematic of a indentation's cross section showing h, hf, hc, and hs and how they 
relate to indention depth and elastic recovery after removal of load P.[13] 
 
 
Doerner and Nix were the first to develop a model that allowed for the determination of 
the film?s modulus from the substrate affected Young?s modulus.[1]  In the Doerner-Nix model 
there is a continuous transfer of energy through the film-substrate boundary, meaning that the 
values of strain were equivalent on both sides of the interface, as shown in Figure 2.4.2(a).  This 
 12 
continuous transfer of energy through to the substrate allowed for a single weighting factor to be 
used in their model,  
       
  
 (  
  
   
  
)     (8) 
where,    is the composite modulus,       (     )? ,               ? , and      is the 
Doerner-Nix weighting factor.       accounts for the increasing contribution of the substrate to 
the composite modulus as the indenter moves deeper into the sample, and is given as,  
         (     ? ) (9) 
where, t is the film?s thickness,      is the effective indentation depth, and ? is the empirically 
determined constant suggested as 0.25 for most materials. 
 
 
 
 13 
 
Figure 2.4.2 (a) Schematic illustrating the concept of continuous transfer of strain between the 
film and substrate, (b) simulation indicating that strain discontinuously transferred between the 
film and substrate, and (c) schematic showing how the film and substrate components are 
decoupled in the discontinuous elastic interface transfer model.[7] 
 
 Modifying the Doerner and Nix model to work with a wider variety of substrate-film 
combinations, King et al. used numerical evaluation of a flat triangular punch to extend Eq. (8) 
and (9) to 
   
 
        
 
      
 
  (   
    )       
  ( 
    ) (10) 
where a is the square root of the projected contact area, t is the thickness of the film, and ? is a 
scaling parameter that differs for different tip geometries, as it is a function of the normalized 
 14 
punch size.[3]  This new equation allows for a term that is able to describe the substrate effect and 
extract the intrinsic film modulus, an attribute missing from the Doerner & Nix model.   
 Saha and Nix then made an effort to alter King model so that it allow for a Berkovich 
type indenter's geometry.[5] To do this they imagined that a flat punch was situated at the tip of 
the Berkovich indenter changing the effective film thickness, t, to be realized as t-h, where h is 
the total indenter displacement.  Substituting t-h for t in Eq. (10) leads to 
   
 
        
 
      
 
  (   
        )       
  ( 
        ). (11) 
As ? is a function of a/t, which of course also change with indenter geometry, it was also taken 
into consideration and extrapolated to larger ratios of a/t.  With the modified version of King's 
model, Saha and Nix plotted Ef  against displacement for several films of varying thickness; 
showing a reasonable match to the expected film modulus for indentions up to 50% of the film's 
thickness.   
 
Building upon the Song-Pharr model, the Hay-Crawford model better represents stiff 
films on compliant substrates.[2, 14] The Song-Pharr model assumes a column of the sample 
material; film and substrate, under the indenter as isolated from the surrounding material 
allowing it to be treated as springs in series; one for the film and one for the substrate.  The shear 
modulus of each spring is then weighted according to the tip?s contact area and film?s effective 
thickness through the transition function I0. Hay?s method takes into consideration an inherent 
problem of all models that treat the film and substrate as springs in series; that the material under 
the indenter cannot be isolated from the surrounding material, especially with stiff films, as there 
is a quite a bit of lateral support. 
 15 
 The Hay-Crawford model proposes to let the film also act as a spring in parallel with the 
substrate, not just in series. Having the film also behave as if in parallel allows for the 
consideration of several mechanisms. First, as the film becomes stiff, it dominates the response 
of the material. Second, as the film becomes thin and stiff, the deformation in the top layer of the 
substrate approaches that of the film; coinciding with two different stiffness springs acting in 
parallel when they experience equal deformation.  Third, when there is significant lateral support 
from the film then it behaves as the leaf springs that support the indenter column, which are well 
modeled by a parallel spring. As parallel springs are treated by adding their stiffness, Hay?s 
model is derived as: 
   
 
         
       
     
 
  (12) 
Where ?a, ?s and ?f are the apparent, substrate and film shear modulus respectively, I0 is the 
aforementioned Gao weighting factor, and F is a dimensionless constant used to moderate the 
influence of the film modulus; by finite-element analysis, F was determined to have the constant 
value 0.0626.  The shear modulus of the film is then calculated from the apparent value, which is 
then used along with the Poisson?s ratio to calculate the elastic modulus of the film. 
 Figure 2.4.3 illustrates that how through finite element analysis Zhou and Prorok showed 
that the transfer of strain between the film and substrate were not continuous, but instead 
discontinuous.[6]  Building upon Doerner-Nix, the Zhou-Prorok model allows for two weighting 
factors to account for the film and the substrate individually and is given as,  
       
  
         
  
     (13) 
where, 
           ?   and           ?   (14) 
 16 
Here    and    are the aforementioned weighting factors, with their physical meaning illustrated 
in Figure 2.4.2(b,c);    and    are the Poisson?s ratio of each the film and substrate respectively.  
 
 
Figure 2.4.3 Finite element analysis of the AlOx film/substrate composites showing the elastic 
strain distribution for an indent penetrating 5nm into each film; (a) SiO2, (b), Ge, (c) Si, (d) 
MgO, and (e) Sapphire. 
 
 The Zhou-Prorok model was further investigated for a wide variety of film, substrate 
combinations and Zhou et al. noted that the flat regions seen at shallow indents were not purely 
representative of the film alone and still had an influence from the substrate.[7]  Through 
application of a power law function to their model they were able to reliably extract the film?s 
Young?s modulus independent of indenter penetration through the equation 
       
  
      (    
  
)
   
   
  
    (15) 
 17 
employing the standard Oliver and Pharr method.  With this new model they were able to 
accurately extract the film?s Young?s modulus as determined through membrane deflection 
experiment, or MDE, demonstrated in Figure 2.4.4. 
 
Figure 2.4.4 Zhou et al. demonstrating that the film?s modulus does not correspond to Eflat that 
their second model has the ability to accurately extract film modulus from the composite 
nanoindentation data. 
  
 18 
Chapter 3: Material Selection 
 
3.1 Material Selection and Their Mechanical Properties 
 To explore the effects of the differences between the film and substrate?s Young?s 
modulus on the composite modulus and how it relates to errant contact area, a range of substrates 
were investigated that had equivalent Poisson?s ratio, but different Young?s modulus.  The films 
used not only needed to have a Poisson?s ratio that was near the substrates?, but also have a mid-
range Young?s modulus in order to facilitate substrates with both a lower and higher Young?s 
modulus.  As possibly creating sink-in with a soft film that usually exhibits pile-up behavior, the 
film?s modulus was kept in the lower portion of mid-range, specifically 70 to 90GPa.  Beyond 
their mechanical behavior, the materials must be available for purchase and safe to work with as 
they would be mechanically polished and exposed to a range of temperatures during film 
deposition.  A list of possible candidate materials first looked at for both the film and substrates 
are given in Table 3.1.1.  Aluminum and platinum were chosen as film candidates while In, Sn, 
Al, Ag, Cu, Pt and Ta were chosen for substrates as all of these materials have a Poisson?s ratio 
near 0.35, with Young?s moduli ranging from 11 to 186GPa.  Si was also added to the substrates 
as its mechanical behavior is widely known, and can serve as a substrate that does not plastically 
deform; a baseline to connect with the samples used in the creation of the Zhou-Prorok model.  
While In has a Poisson?s ratio a bit higher than the rest at 0.44, it was included as it has an 
extremely low Young?s modulus in comparison to Al and Pt.  
 
  
 19 
Table 3.1.1 Material candidates for film and substrates with desirable Young?s modulus and 
Poisson?s ratio.  Highlighted materials were chosen to be substrates or deposited as a film due to 
having the most favorable mechanical properties, being safe to work with and their availability. 
Films Substrates  
Material E (GPa) ? Material E (GPa) ? References 
Au 72 0.44 Se 10 0.33  
Al 70 0.35 In 11 0.44  
Ag 83 0.37 Mg 45 0.35 [15] 
Pt 168 0.36 Sn 50 0.36  
 Cd 50 0.30 [15] 
Al (100) 63-70  0.35 [13, 15, 16] 
SiO2 72 0.18 [11, 13, 15] 
Au 78 0.44 [15] 
Ag 83 0.37 [15] 
Zr 88 0.34  
Nb 105 0.40 [15] 
Ti 116 0.32 [15] 
Cu (100) 66.7-117 0.35 [15] 
Pd 121 0.39  
Pt 168 0.36 [17-19] 
Si 178 0.28 [9, 11, 13, 15, 20] 
Ta 186 0.34 [15] 
Ni 200 0.31 [15] 
Co 209 0.31  
Mo 329 0.31  
Re 463 0.30  
 
 
  
 20 
Chapter 4: Experimental Setup and Fabrication 
 
4.1 Substrates 
Unpolished metallic substrates of copper, aluminum, silver, tin, tantalum, platinum, 
titanium, and indium of 0.5mm thick and 25x25mm or larger and at least 99.99% pure were 
obtained from Alfa Aesar, Ward Hill, MA.  The substrates were then cut into smaller pieces 
using a Dremel rotary tool as opposed to shearing as to reduce bending and the resulting 
microstructural changes and internal stresses.  Once they were in 5 to 10mm squares, they were 
first rough polished using ANSI 2000 grit abrasive disc, and then polished to a mirror finish 
using 0.5?m, then 0.05?m alumina particle suspension with a Struers RotoPol-11 (Ballerup, 
Denmark), Figure 4.1.1.  Scanning Electron Micrographs obtained using a JEOL JSM 7000F 
(Tokyo, Japan), shown in Figure 4.1.2, indicated that the majority of substrates, specifically the 
softer materials of In, Sn, Al, and Cu had particles imbedded into their surface.  Figure 4.1.3 and 
Table 4.1.1 display the results of energy-dispersive X-ray spectroscopy, or EDS, that was 
performed on the In substrate to identify that the particles present were contaminates, AlOx and 
Si, from the polishing process. 
 
 21 
 
Figure 4.1.1 Struers RotoPol-11 Surface Polisher. 
 
Figure 4.1.2 JEOL JSM 7000F Scanning Electron Microscope. 
 22 
 
Figure 4.1.3 Location of spectrums for energy-dispersive X-ray spectroscopy of indium substrate 
after polishing.  
 
Table 4.1.1 Spectrum analysis of energy-dispersive X-ray spectroscopy of indium substrate after 
polishing; all results in weight %. 
Spectrum # O Al Si In Total 
1 51.40 34.97  13.63 100.00 
2   100.00  100.00 
3  4.75  95.25 100.00 
4 51.72 42.39  5.89 100.00 
 
To obtain these softer substrates with a mirror polish, <100> orientation single crystal 
substrates of aluminum and copper pre-polished by means of chemical-mechanical planarization 
to less than 100? roughness, were ordered from MTI Corporation (Richmond, CA).  No readily 
 23 
available polished substrates were found for the softest of the materials, indium and tin.  In order 
to create substrates of indium and tin with a smooth surface, they were mechanically flattened 
using pressure applied to their surface using an arbor press shown in Figure 4.1.4(a).  Aluminum 
pucks were used to distribute the force evenly across a polished sapphire substrate as illustrated 
in Figure 4.1.4(b), in order to maintain a smooth and uniform surface across the entire substrate.  
 
 
Figure 4.1.4 (a) Arbor press used to flatten both the indium and tin substrates for a smooth 
surface. (b) Illustration to show how force was evenly distributed across substrate surface. 
 
 At first, the results from using the arbor press were varied, and while the pressed 
substrates showed an improved flatness, they were still not suitable for film deposition and then 
nanoindentation.  The first attempt at flattening an indium sample resulted in what appeared to be 
a very smooth surface, but the sample was compressed into a foil no more than 150um thick 
 24 
which is not enough to ensure that during nanoindentation there is zero influence from the 
aluminum puck or bonding used to attach the substrate to the puck.  From this mistake, and the 
following attempts? inability to be smooth while maintaining a sufficient thickness, came the 
realization that if a substrate of original thickness of 2mm or more is compressed, it will allow 
for a larger degree of plastic deformation which will allow for a  flatter surface.  To that end, 
2mm thick indium and tin substrates were ordered.  These were then cut into 3 or 4mm squares 
and flattened through the same method as before.  SEM micrograph comparisons of the surfaces 
before being compressed and after the various attempts to make a smoother surface for In are 
shown in Figure 4.1.5, and in Figure 4.1.6 for Sn. 
 
 25 
 
Figure 4.1.5 Micrographs at 1,000 magnification of In (a) 0.5mm surface as received, (b) 0.5mm 
thick In compressed, (c,d) 2mm thick In compressed. 
 
 26 
 
Figure 4.1.6 Micrographs at 1,000 magnification of Sn (a) 2mm surface as received, (b) 0.5mm 
thick Sn compressed, (c,d) 2mm thick Sn compressed. 
 
4.2 Film Deposition 
 Once the substrates were in order, a thin film of aluminum was to be deposited using a 
Denton Vacuum Inc. DC & RF magnetron sputtering system, shown in Figure 4.2.1.  When 
depositing films for thin film nanoindentation it is crucial that the films are of uniform quality in 
terms of surface roughness and depth.  To measure the quality of film deposited, the aluminum 
was first sputtered onto a cleaned fused silica microscope slide, or SiO2.  The parameters initially 
 27 
used were extracted from the sputtering system's log book, recorded when aluminum was 
previously sputtered by other users when running this system as shown in Table 4.2.1.  From 
these values it was chosen to go with a sputtering power of 200 watts as it was used for the film 
that most closely resembles the desired thickness of 500nm.  To compensate for the original film 
being 400nm, the sputtering time was increased to 1125 seconds in line with the deposition rate 
to reach an expected thickness of 500nm. 
 
 
Figure 4.2.1 Denton Vacuum Inc. DC & RF sputtering system. 
 
Table 4.2.1 Sputtering parameters for Al film from Denton sputtering system log book. 
Date Base 
Pressure 
(Torr) 
Sputter 
Power 
(W) 
Sputter 
Time 
(s) 
Ar 
Flow 
(sccm) 
Deposition 
Pressure 
(mTorr) 
Deposition 
Temp 
(?C) 
Expected 
Thickness 
(nm) 
Deposition 
Rate 
(?/sec) 
03/15/07 5.0x10-5 400 1200 25 4.8 25 1500 12.5 
11/29/07 4.0x10-6 200 900 25 4.8 25 400 4.4 
11/08/08 2.7x10-6 100 435 25 4.8 25 100 2.3 
 
 28 
 After deposition, the film thickness was measured using a Tencor Instruments "Alpha-
Step 200" profilometer shown in Figure 4.2.2.  The profilometer?s tip was moved across the 
substrate to film edge in three locations across the tape pull, determining a uniform film 
thickness of 400nm; 100nm less than expected.  Also noted was that the film?s profile shows that 
the film lifted off near the edge before settling back to the true film?s thickness indicating there is 
a lack of adhesion which can be corrected with 10nm layer of titanium in future depositions.  
Upon viewing the film?s surface with SEM it was determined that while the film was uniformly 
thick, the surface roughness was inadequate due to grains that were protruding from the surface 
as shown in Figure 4.2.3.  These grains were determined to be Hillock growth formations that 
arise due to the internal stress of the film increasing, forcing the grains to the surface. 
 
 
Figure 4.2.2 Tencor Instruments "Alpha-Step 200" profilometer. 
 29 
 
 
Figure 4.2.3 Hillock growth grains on film surface of 400nm Al on SiO2. 
 
 It was determined that there are two main factors that facilitate internal film stress and 
consequently the growth of Hillock grains, both directly relating to sputtering power; chamber 
temperature and sputtering time.  While a lower sputtering power decreases the resulting 
temperature of the chamber, making the Hillock grains grow at a slower rate, it also gives them 
more time to grow as it takes longer to sputter an equivalent film than at higher sputtering power.  
In order to fully investigate the influence of sputtering power on Hillock growth a series of 
 30 
separate Al films, all with 10nm thick Ti layer for proper adhesion, were again deposited on SiO2 
substrates, each at a different sputtering power and time to maintain a consistent thickness of 
500nm.  The power ranged from a relatively low 75W to 700W which is the maximum allowed 
for this sputtering system.  The sputtering conditions used are listed in Table 4.2.2.  The actual 
film thickness was again determined using a profilometer across the film-substrate boundary 
averaged over three or four locations. 
 
Table 4.2.2 Sputtering conditions for Al films to evaluate how changing sputtering power 
influences Hillock grain formation and density. 
Sputter 
Power 
(W) 
Base 
Pressure 
(Torr) 
Sputter 
Time (s) 
Ar Flow 
Rate 
(sccm) 
Deposition 
Pressure 
(mTorr) 
Temp 
(?C) 
Expected 
Thickness 
(nm) 
Actual 
Thickness 
(nm) 
Deposit 
Rate 
(?/sec) 
75 8.2x10-6 4000 25 4.8 25 500 480 1.2 
125 7.7x10-6 2400 25 4.8 25 500 450 1.9 
175 7.6x10-6 1715 25 4.8 25 500 500 2.9 
300 8.0x10-6 1000 25 4.8 25 500 500 5.0 
400 5.0x10-6 750 25 4.8 25 500 500 6.7 
600 8.2x10-6 500 25 4.8 25 500 500 10.0 
700 7.7x10-6 428 25 4.8 25 500 505 11.8 
 
 Each film was then viewed using the SEM to determine the film quality and density of 
Hillock formations as shown in Figure 4.2.4.  As sputtering power increased, Hillock grain 
density decreased, improving the surface quality of the film which corresponds with literature.[21-
23]  It was decided to use 700W for all following Al depositions as it allowed for the lowest 
concentration of Hillock grains. 
 
 31 
 
Figure 4.2.4 Micrographs of Al film surface as sputtered at different powers of 75, 125, 175, 300, 
400, 600 and 700W at 10,000 magnifications. 
 32 
 
 Upon review of literature, the thickness of the aluminum film also has a large influence 
on Hillock growth grains as it allows them more time to grow due to the longer deposition 
time.[21-23]  To evaluate this, and determine the effect film thickness has using the Denton 
Sputtering system at 700W, another group of depositions were performed, with parameters listed 
in Table 4.2.3, to vary the film thickness as 250nm, 500nm, 750nm and 1000nm.   As before, all 
SiO2 substrates were first deposited with a 10nm layer of Ti for proper adhesion, and film 
thickness was measured in at three different locations using a profilometer to determine actual 
thickness. 
 
Table 4.2.3 Sputtering conditions for Al films to evaluate how varying film thickness influences 
Hillock grain formation and density. 
Sputter 
Power 
(W) 
Base 
Pressure 
(Torr) 
Sputter 
Time (s) 
Ar Flow 
Rate 
(sccm) 
Deposition 
Pressure 
(mTorr) 
Temp 
(?C) 
Expected 
Thickness 
(nm) 
Actual 
Thickness 
(nm) 
Deposit 
Rate 
(?/sec) 
700 3.9x10-6 215 25 5.0 25 250 243 11.3 
700 6.2x10-6 428 25 5.0 25 500 505 11.8 
700 5.5x10-6 645 25 5.0 25 750 743 11.5 
700 6.3x10-6 860 25 5.0 25 1000 1059 12.3 
 
 The samples were then viewed and compared using the SEM as shown in Figure 4.2.5.  
As expected through literature, the Hillock growths become much more prominent on the surface 
of the film as the thickness, and therefore sputtering time are increased.  On the 250nm film, 
Hillock formations were extremely sporadic, and even their average size had been reduced to 
less than 100nm, making the film surface more desirable than the other thickness evaluated, but 
possibly still not sufficient.  It was noted however that when viewing the film with the SEM, 
there are localized areas of the film that appeared to have a less uniform thickness.  Figure 4.2.6 
 33 
illustrates these areas, and this sporadic coverage originates from such a short sputtering time 
due to the high power required to avoid Hillock growth formations.  While it is believed that it 
would be possible to indent in areas that look to have consistent coverage through the 
nanoindentation systems optical microscope, the exact film thickness would not be known; 
which is unsuitable for thin film nanoindentation as film thickness is a required parameter used 
in the studied models. 
 
 
Figure 4.2.5 Micrographs of Al film surfaces as sputtered to different thickness of 250, 500, 750 
and 1000nm at 10,000 magnifications. 
 34 
 
 
Figure 4.2.6 Micrographs of 250nm Al film on SiO2 at (a) 25x and (b) 1000x showing sporadic 
coverage. 
 
Due to the inability to create a consistent thickness film of aluminum with adequate 
surface quality, it was determined to use another film, platinum, that has a similar Poisson?s ratio 
of 0.36, with widely understood deposition parameters and results due to its wide use in MEMS 
research.[18, 19]  While the Young?s modulus of platinum is a bit higher at 168 GPa, it still has a 
pile-up behavior when indented allowing for one of the same goals as the aluminum film.[18]  The 
sputtering parameters to obtain a 230nm thick layer of platinum with titanium adhesion layer are 
listed in Table 4.2.4.  
  
 35 
Table 4.2.4 Sputtering parameters of 230nm Pt film with Ti adhesion layer. 
Substrates Al, Si, Cu, In, Sn, Pt, Ti, Ta 
Base Pressure (Torr) 2.6 x 10-6 
Magnetron Type DC DC 
Target Material Pt Ti 
Pre-Sputtering Power (W) 100 400 
Pre-Sputtering Time (sec) 15 25 
Sputtering Power (W) 100 400 
Sputtering Time (sec) 800 25 
Gas 1 (Ar) flow rate (sccm) 25 25 
Gas 2 (O2/N2) flow rate (sccm) 0 0 
Deposition Pressure (mTorr) 4.7 4.7 
Deposition Temperature (?C) 23 23 
Soak Time (sec) 0 0 
Substrate holder rotation (%) 50 50 
Ignition Pressure (mTorr) 50 50 
Expected Film Thickness (nm) 250 10 
Actual Film Thickness (nm) 230 10 
 
 The resulting platinum film was observed with SEM and found to have consistent 
coverage and excellent surface quality, shown in Figure 4.2.7.  Table 4.2.5 shows that using the 
profilometer, the film thickness of each film-substrate combination was measured in three 
locations and then averaged to determine the film thickness of 230nm.  As the platinum film had 
a good surface quality with no disproportionally large protrusions over the film?s surface, this 
platinum film was determined to be the best candidate for indentations. 
 
 
 
 
 
 
 
 36 
Table 4.2.5 Film thickness of sputtered platinum films. 
Substrate Location 1 (nm) Location 2 (nm) Location 3 (nm) Average (nm) 
SiO2 220 235 220 225 
Si 235 236 231 234 
Pt 210 235 214 220 
Al 235 236 225 232 
Ta 232 225 240 232 
Ti 239 246 220 235 
In 210 233 243 229 
Sn 230 246 210 229 
Cu 231 243 228 234 
 
 
Figure 4.2.7 Surface quality of platinum film on SiO2 substrate. 
 
 37 
4.3 Nanoindentation 
Nanoindentation was performed using TestWorks 4 to drive an MTS Nanoindenter XP 
(Agilent Technologies, Santa Clara, CA), as shown in Figure 4.3.1, through a continuous 
stiffness measurement, or CSM.  The depth controlled tests used a Berkovich type diamond tip 
with a harmonic displacement of 2nm, and an allowable drift rate of 0.05nm/s.  Twenty-five 
indents were performed on a fused silica reference in order to calibrate the area coefficients of 
the tip.  For each sample tested, single crystal aluminum was first deeply indented to remove any 
debris or contamination from the tip, followed by a minimum of four indents in the silica 
reference to refine the tip calibration if needed.  The Poisson?s ratio used in testing film-substrate 
samples was the bulk value of the film.  For each film and substrate combination, twenty-five 
500nm CSM indents were run to fully cover behavior through the film, and then averaged for the 
composite, or apparent Young?s modulus verses indention depth using the standard Oliver-Pharr 
analysis.[13] 
 
 38 
 
Figure 4.3.1 Image of MTS Nano Indenter XP nanoindentation system. 
 
 39 
Chapter 5: Results and Discussions 
 
5.1 Experimental Nanoindentation Analysis 
 After twenty-five indents were run on each substrate, and film-substrate sample, 
erroneous tests were removed, and then an averaged Young?s modulus verses indention depth 
was plotted along with its correlating standard deviation error bars.  The erroneous tests result 
from the indenter believing it has made contact with the surface when it has usually due a sharp 
vibration causing the tip to momentarily make contact before withdrawing, reporting no Young?s 
modulus until it does eventually reach the surface again; resulting in a Young's modulus verses 
displacement plot similar to Figure 5.1.1.  While these tests are deleted, there is no possibility of 
them being confused with a legitimate, but unexpected result.   
 
 
 40 
 
Figure 5.1.1 E-h curve of an example erroneous indention that would be deleted before averaging 
indentation results. 
 
To further understand the methodology of how TestWorks arrives at its reported Young?s 
modulus of the sample and for a method to change the Poisson?s ratio on the fly, an Microsoft 
Excel worksheet was created that derives the raw modulus using the original Poisson?s ratio 
used, and then allows for a recalculation using a different Poisson?s ratio using Eq. (2).  To check 
validity, a sample was recalculated within TestWorks and Excel using a Poisson?s ratio of 0.10, 
0.20, 0.30, 0.40, and 0.50, and then compared in Figure 5.1.2 to show they match and that the 
Excel file correctly recalculates Young?s modulus, if a change of Poisson?s ratio is desired.   
 
0
5
10
15
20
25
30
0 100 200 300 400 500
Mod
ulu
s (G
Pa)
 
Displacement Into Surface (nm) 
 41 
 
Figure 5.1.2 Checking validity of changing Poisson?s ratio through Excel when compared to 
recalculating the sample through TestWorks. 
 
 The Young's modulus, E verses indention depth, h, or E-h curves, are shown in Figures 
5.1.3a through 5.1.3h.  These indentions were preformed, instead of relying on the values from 
literature, as the substrates? Young?s moduli can vary due to are a number of factors that can 
influence the elastic behavior such as crystal orientation, or large enough grain size that you can 
indent on that single grain?s different crystal structure.  It is notable that for very shallow 
displacement the Young?s modulus does not immediately start at the bulk value of the materials.  
This behavior is due to the loss of contact between the tip and material as the tip lifts from the 
surface during the oscillation cycle of the indenter in accordance to CSM.[4]  For the substrates 
that do not have pile-up around the indenter tip, Ti, Pt, Ta and Si the curves immediately rise to 
their Young's modulus and remain constant independent of indention depth.  A higher Young's 
60
80
100
120
140
160
180
0 100 200 300 400 500
Mo
du
lus
 (G
Pa)
 
Displacement Into Surface (nm) 
From Excel: 0.10 From TestWorks: 0.10
From Excel: 0.20 From TestWorks: 0.20
From Excel: 0.30 From TestWorks: 0.30
From Excel: 0.40 From TestWorks: 0.40
From Excel: 0.50 From TestWorks: 0.50
 42 
modulus is reported for the single crystal Al and Cu (100) as they readily plastically deform 
causing material to pile-up around the tip as it penetrates, leading to more elastic recovery than 
there would be otherwise.  Once the tip moves deep enough, the pile-up against the tip becomes 
less a less dominate factor, allowing for the Young's modulus to reduce toward its true value.  
Both the In and Sn substrates have relatively larger error bars due to their previously discussed 
inability to be polished and their resulting lack of surface quality.   
 
Figure 5.1.3a E-h curve for In substrate after flattening with Arbor press. 
0
2
4
6
8
10
12
14
16
0 100 200 300 400 500
Mo
du
lus
 (G
Pa)
 
Displacement Into Surface (nm) 
 43 
 
Figure 5.1.3b E-h curve for Sn substrate after flattening with Arbor press. 
 
Figure 5.1.3c E-h curve for Al single crystal substrate, orientation (100). 
0
20
40
60
80
100
0 200 400 600 800 1000
Mo
du
lus
 (G
Pa)
 
Displacement Into Surface (nm) 
0
20
40
60
80
0 500 1000 1500 2000
Mo
du
lus
 (G
Pa)
 
Displacement Into Surface (nm) 
 44 
 
Figure 5.1.3d E-h curve for Cu single crystal substrate, orientation (100). 
 
Figure 5.1.3e E-h curve for Ti substrate. 
0
25
50
75
100
125
150
0 200 400 600 800 1000
Mod
ulu
s (G
Pa)
 
Displacement Into Surface (nm) 
0
20
40
60
80
100
120
140
0 200 400 600 800 1000
Mo
du
lus
 (G
Pa)
 
Displacement Into Surface (nm) 
 45 
 
Figure 5.1.3f E-h curve for Pt substrate. 
 
Figure 5.1.3g E-h curve for Ta substrate.  
0
40
80
120
160
200
0 200 400 600 800 1000
Mo
du
lus
 (G
Pa)
 
Displacement Into Surface (nm) 
0
40
80
120
160
200
0 200 400 600 800 1000
Mod
ulu
s (G
Pa)
 
Displacement Into Surface (nm) 
 46 
 
Figure 5.1.3h E-h curve for Si single crystal substrate, orientation (100). 
 
 Once it was known how the substrates deposited on behaved when indented independent 
of films, the Pt film-substrate samples were indented and E-h curves shown along with several 
other variables of interest in Figures 5.1.4a through 5.1.4h; the Zhou-Prorok model from in Eq. 
(13), film's alpha extracted from Eq. (13), and film's Young's modulus extracted from Eq. (15). 
The film's alpha from Eq. (13) or Poisson's ratio, as described by Zhou et al. is useful as it lends 
credence to the Zhou-Prorok model when it remains constant through all indention depth as the 
film's Young modulus is independent of indention depth, pile-up or sink effects and substrate 
properties.  The film's Young's modulus is extracted from Eq. (15) as it also important since it 
should ideally remain constant independent of all other variables.  The film's alpha is obtained 
from Eq. (13) opposed to the film's Young's modulus from Eq. (15) as the latter was created to 
better describe the substrate's effect on the film's modulus, and does not more precisely 
0
40
80
120
160
200
0 200 400 600 800 1000
Mod
ulu
s (G
Pa)
 
Displacement Into Surface (nm) 
 47 
characterize the film's alpha.  Also included is the Doerner-Nix model in select cases to show 
how it compares to the Zhou-Prorok model in its ability to predict the composite modulus for the 
same parameters.  From this data, the previously mentioned extracted values for the film?s 
Poisson?s ratio and Young?s modulus match well with their expected values, and are shown in 
Table 5.1.1. 
 
Figure 5.1.4a E-h curve for 230nm Pt on In with Z-P model, film E and film alpha. 
0
0.1
0.2
0.3
0.4
0.5
0
50
100
150
200
0 0.2 0.4 0.6 0.8 1
Po
iss
on
's Rat
io Mo
du
lus
 (G
Pa)
 
Normalized Displacement (h/t) 
230nm Pt on In Experimental
Z-P Model
Film E
Film Alpha
 48 
 
Figure 5.1.4b E-h curve for 230nm Pt on Sn with Z-P model, film E, and film alpha. 
 
Figure 5.1.4c E-h curve for 230nm Pt on Al with Z-P model, D-N model, film E, and film alpha. 
0.2
0.3
0.4
0.5
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1
Po
iss
on
's Rat
io Mo
du
lus
 (G
Pa)
 
Normalized Displacement (h/t) 
230nm Pt on Sn Experimental
Z-P Model
Film E
Film Alpha
0.2
0.3
0.4
0.5
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1
Po
iss
on
's Rat
io Mod
ulu
s (G
Pa)
 
Normalized Displacement (h/t) 
230nm Pt on Al Experimental
Z-P Model
Film E
D-N
Film Alpha
 49 
 
Figure 5.1.4d E-h curve for 230nm Pt on Cu with Z-P model, film E, and film alpha. 
 
Figure 5.1.4e E-h curve for 230nm Pt on Ti with Z-P model, D-N model, film E, and film alpha. 
0
0.1
0.2
0.3
0.4
0.5
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1
Po
iss
on
's Rat
io Mo
du
lus
 (G
Pa)
 
Normalized Displacement (h/t) 
230nm Pt on Cu Experimental
Z-P Model
Film E
Film Alpha
0
0.1
0.2
0.3
0.4
0.5
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1
Po
iss
on
's Rat
io Mo
du
lus
 (G
Pa)
 
Normalized Displacement (h/t) 
230nm Pt on Ti Experimental
Z-P Model
D-N Model
Film E
Film Alpha
 50 
 
Figure 5.1.4f E-h curve for 230nm Pt on Pt with Z-P model, film E, and film alpha. 
 
Figure 5.1.4g E-h curve for 230nm Pt on Ta with Z-P model, film E, and film alpha. 
0.2
0.3
0.4
0.5
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1
Po
iss
on
's Rat
io Mod
ulu
s (G
Pa)
 
Normalized Displacement (h/t) 
230nm Pt on Pt Experimental
Z-P Model
Film E
Film Alpha
0.2
0.3
0.4
0.5
0.6
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1
Po
iss
on
's Rat
io Mo
du
lus
  (G
Pa)
 
Normalized Displacement (h/t) 
230nm Pt on Ta Experimental
Z-P Model
Film E
Film Alpha
 51 
 
Figure 5.1.4h E-h curve for 230nm Pt on Si with Z-P model, D-N model, film E, and film alpha. 
 
Table 5.1.1 Values of films? Young?s moduli and alphas from Eq. (15) and (17) for each Pt film 
on substrate combination, as well each substrate?s Young?s Modulus obtained from 
nanoindenting directly into the substrate. 
Substrate E?sub ?sub E?film ?film 
In 12 0.44 ? ? 
Sn 42 0.36 163 ? 5 0.36 
Al 60 0.35 157 ? 7 0.35 
Cu 100 0.35 158 ? 7 0.35 
Ti 116 0.32 162 ? 2 0.35 
Pt 168 0.36 167 ? 4 0.35 
Ta 153 0.34 171 ? 7 0.36 
Si 178 0.28 166 ? 2 0.36 
 
 While the majority of the film-substrate combinations' experimental data matched well 
with the Zhou-Prorok model, along with its derived film alpha and E, there are a few of 
0.2
0.3
0.4
0.5
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1
Po
iss
on
's Rat
io Mo
du
lus
 (G
Pa)
 
Noramlized Displacement (h/t) 
230nm Pt on Si Experimental
Z-P Model
D-N Model
Film E
Film Alpha
 52 
occasions where this is not true; mainly with In and Sn.  To further investigate why these cases 
don't hold true, it is best to have a better image of how the indents interact with the surface in 
terms of surface quality, and if erroneous contact area in the form of pile-up or sink in is a factor.  
Toward this end, SEM micrographs at 20,000 magnification were taken for each indent as shown 
in Figures 5.1.5a through 5.1.5h. 
 
 
Figure 5.1.5a 230nm Pt on In: 500nm indention  
 53 
 
Figure 5.1.5b 230nm Pt on Sn: 500nm indention. 
 
Figure 5.1.5c 230nm Pt on Al: 500nm indention. 
 54 
 
Figure 5.1.5d 230nm Pt on Cu: 500nm indention. 
 
Figure 5.1.5e 230nm Pt on Ti: 500nm indention. 
 55 
 
Figure 5.1.5f 230nm Pt on Pt: 500nm indention. 
 
Figure 5.1.5g 230nm Pt on Ta: 500nm indention. 
 56 
 
Figure 5.1.5h 230nm Pt on Si: 500nm indention. 
  It is obvious that for the Pt on In sample, the surface quality is not smooth enough for 
accurate nanoindentation data. Nonetheless, the indentation does show unusual behavior for the 
film's modulus from the Z-P model that may not be entirely resultant of the surface quality.  It 
was noticed that the residual indention in the Pt-In surface was much smaller than that of the 
other materials, so another micrograph at 1,000 magnification was taken, Figure 5.1.6.  In this 
micrograph there is a visible halo of deformation that spreads out wider than the readily 
identifiable indention shown in Figure 5.1.5a.  It is believed that since the film is so much more 
stiff that as the tip pushes down on the film, a larger area of the film than that just below the tip 
begins to push down on the substrate; as demonstrated in Figure 5.1.7 (b, c).  Shortly after the tip 
contacts the film's surface, the film's modulus as calculated through the Z-P model starts to rise 
toward its correct value, but once the previously mechanism becomes dominate, there is more 
plastic deformation than expected, allowing for less elastic recovery, so the film's modulus starts 
 57 
to drop toward that of the substrate as the substrate becomes the driving force for elastic 
recovery. 
 
 
Figure 5.1.6 500nm indentions into 230nm Pt on Indium have a larger radius of volume than 
indicated by sharp edges shown in the 20,000 magnification.   
 
 
 58 
 
Figure 5.1.7 Stiff film plastically deforming a larger area than typical in a softer substrate, 
causing the readily visible residual indention to be much smaller than if deformation was 
localized to under the tip. 
 
 In Figure 5.1.4b  the Sn sample showed a constant film E and alpha that correspond to the 
correct values, something dramatic happens to them near 0.6 to 0.8 normalized displacement, or  
140 to 190nm indention depth.  It is interesting to note that this depth roughly correlates to a 
large change in the substrate's Young's modulus in Figure 5.1.3b.  While this bump in the Sn 
substrate's E-h curve is partially attributed to pile-up, it is believed another mechanical behavior 
of Sn under deformation contributes to the change in E; twinning.   For the Pt-Sn sample the E-h 
curve behaves correctly until the load onto the sample allows for enough energy for the Sn 
substrate to start deformation twinning.  Once twinning occurs, the amount of energy available 
for elastic recovery diminishes, reducing the perceived Young's modulus.  
 There is an interesting question to be asked after looking at micrographs of the 500nm 
indentions into all of the film-substrate combinations; why is there no discernible penetration 
into the substrate except for the platinum on silicon sample?  The most reasonable answer would 
be that the films are not 230nm thick, but that is very unlikely to be the case as each sample had 
its film thickness measured in at least three, different, locations.  Another explanation is that 
there is penetration into the substrate, but the micrographs are not showing it because the atomic 
number, Z, of some the substrates are similar to that of Pt.  While this could possibly be the case 
 59 
of tantalum, where Z = 73, as it is fairly close to Pt's Z of 78, it is unlikely the case for any other 
substrates.  To follow up on that possibility more thoroughly, micrographs were taken of 500nm 
indentions into each sample using back-scattered electrons, as it is more dependent on the atomic 
number of the material.  From the micrographs shown in Figures 5.1.7a through 5.1.7h, it is clear 
that the only substrate that is directly penetrated by the tip is silicon.  To verify that what is being 
seen in Figure 5.1.7h is penetration into the Si substrate, EDS was performed on the surrounding 
film and indention, with results in Figure 5.1.8.  While it is established that the film thickness is 
indeed 230nm, and that the substrate is indeed not being penetrated, it is not completely 
understood why this is the case.  One possible explanation is that similar with the observed 
dispersed plastic deformation of indium, the substrates are plastically deforming in a wider 
volume than just under the indenter, allowing the film to bow out, absorbing some of the 
displacement. 
In terms of range of applicability for the Zhou-Prorok model, there is one limitation due 
to a shortcoming of CSM nanoindentation at very shallow depths; loss of contact between the tip 
and surface due to the oscillation of the tip.  While the current research could also indicate an 
inaccuracy with the model when there is a very large difference between the film and substrate?s 
modulus as shown with the In substrate, there isn?t enough information to confirm that 
assumption.  The Indium sample?s surface quality was not sufficient enough to draw conclusions 
about the Zhou-Prorok model?s ability to predict film behavior.  To either further understanding 
of the model?s behavior with such an extreme case, it would be necessary to properly prepare the 
In sample through a more systematic method of mechanical flattening through use of rough 
surface contact models and controlling the load.[24, 25] 
 
 60 
 
Figure 5.1.7a Micrograph of 230nm Pt on In. Left: secondary e-. Right: back-scattered e-. 
 
Figure 5.1.7b Micrograph of 230nm Pt on Sn. Left: secondary e-. Right: back-scattered e-. 
 61 
 
Figure 5.1.7c Micrograph of 230nm Pt on Al. Left: secondary e-. Right: back-scattered e-. 
 
Figure 5.1.7d Micrograph of 230nm Pt on Cu. Left: secondary e-. Right: back-scattered e-. 
 62 
 
Figure 5.1.7e Micrograph of 230nm Pt on Ti. Left: secondary e-. Right: back-scattered e-. 
 
Figure 5.1.7f Micrograph of 230nm Pt on Pt. Left: secondary e-. Right: back-scattered e-. 
 63 
 
Figure 5.1.7g Micrograph of 230nm Pt on Ta. Left: secondary e-. Right: back-scattered e-. 
 
Figure 5.1.7h Micrograph of 230nm Pt on Si. Left: secondary e-. Right: back-scattered e-. 
 64 
 
Figure 5.1.8 EDS of 500nm indention into 230nm Pt on Si. a) Spectrum locations for b) 
Spectrum 1, c) Spectrum 2 and d) Spectrum 3. 
 65 
5.2 Validity of Zhou-Prorok Model in Investigated Materials 
 Although the behavior of film E and alpha being constant is a good indication that the Z-
P model works well for the investigated stiff films on plastically deforming substrates, it is 
important to delve a bit deeper.  Once the circumstances surrounding amiss E-h curves were well 
understood, the same process was followed as utilized by Zhou et al. in their derivation of their 
second model.[7]  First, Eflat was plotted against Es as a means to establish an estimated film 
modulus at where the points cross a line of elastic homogeneity shown by the dashed line in 
Figure 5.2.1; showing the Young?s modulus of the film to be near the expected value of 168GPa.   
 
 
 66 
 
Figure 5.2.1 Eflat plotted against Es for all substrates as a means to suggest the Pt film?s actual 
Young?s modulus by where it crosses the line of plastic homogeneity indicated by the dashed 
line.  
 
The next pivotal step in their process was relating the ratios        ?  and       ?   through 
the equation 
    
 
      (
   
   )
   
   (14)  
In 
Sn Al 
Cu 
Ti 
Pt Ta Si 
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200
E fl
at 
(GP
a) 
Es (GPa) 
 67 
where all boundary conditions were well known, except for the 0.1.  This 0.1 was an empirically 
determined constant found by plotting the previously mentioned ratios against each other and 
creating a best fit line to describe their relationship; a power function of 0.1 as shown as the 
black X's in Figure 5.2.2.[7]  This was repeated for the currently evaluated film-substrate 
combinations, and the same relationship persisted shown by the solid black diamonds. 
 
Figure 5.2.2 Plots of ?    verses the substrate modulus normalized by    . 
 
 It is a worthy accomplishment that the Z-P model predicts behavior not only for their 
originally studied film-substrate combinations that were mostly compromised of substrates that 
do not plastically deform, but also for the currently investigated combinations with substrates 
In 
Sn 
Al Cu 
Ti 
Pt 
Ta Si 
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
-1E-15
0.1
0.2
0.3
0 2 4 6 8
?E
f/E
f 
Es/Ef 
Pt Film
Power Function
Zhou Data
 68 
that do.  To illustrate the wide variety of erroneous contact area that Z-P model works so well 
with, micrographs at a 70? tilt were taken for the 500nm indents into 230nm Pt on Si, Al, Ti, and 
Ta, as shown in Figures 5.2.3 through 5.2.6, in order to get a better perspective of pile-up and 
sink in, and the difference it will make on contact area and material behavior.  For the 230nm Pt 
on Si sample, the film plastically deforms quite a bit, since the substrate is unable to, leading to a 
large quantity of pile-up.  As the majority of film-sample combinations investigated by Zhou et 
al. have a similar behavior as Pt on Si, it is understandable or even expected that their model 
would predict the mechanical behavior well in this case.  The current investigation shows 
another group of materials that the Z-P model performs well at predicting; substrates that are 
able to plastically deform. With a progression of harder substrates from Al to Ta, there is an 
evident increase in the residual indention depth and decrease in sink-in as the substrate increases 
in stiffness. 
 
Figure 5.2.3 Micrograph of 230nm Pt on Si 500nm indention at a 70? tilt. 
 69 
 
Figure 5.2.4 Micrograph of 230nm Pt on Al 500nm indention at a 70? tilt. 
 
Figure 5.2.5 Micrograph of 230nm Pt on Ti 500nm indention at a 70? tilt. 
 70 
 
Figure 5.2.6 Micrograph of 230nm Pt on Ta 500nm indention at a 70? tilt. 
 
 
 
 
 
 
  
 71 
Chapter 6: Conclusions 
 
 Instrumented indentation testing was used with the continuous stiffness method in order 
to evaluate nine different substrates, with the same film toward the goal to further evaluate the 
Zhou-Prorok model?s ability to predict substrate effects during sink-in when the substrates are 
more willing to plastically deform.  This was achieved by selecting plastically deforming 
substrates that have a high Poisson?s ratio similar to that of the proposed film to be deposited 
onto them.  First a deposition of aluminum was evaluated, but was determined to not be the ideal 
candidate due to Hillock growth grains prevalent on the surface.  Even after optimizing the 
deposition parameters to reduce Hillock formation, the grains were determined to be much too 
large for nanoindentation data to be consistent or useful.  A second candidate, platinum, was then 
looked at as it has a similar Poisson?s ratio to aluminum, but is known to have a much better 
sputtered deposition surface quality.   
Once deposited, the platinum film was evaluated through SEM and was found that 
surface quality and consistency were ideal for nanoindentation.  The experimental data from 
indenting these samples was then compared to the model, and the associated extracted film?s 
Young?s modulus and Poisson?s ratio to see to what degree they remain constant through 
indentation.  The Zhou-Prorok model is adept at predicting substrate effect behavior for 
plastically deforming substrates, when sink-in is the dominating factor of erroneous contact area, 
not pile-up.   
 
 
  
 72 
 
References 
1. Doerner, M.F. and W.D. Nix, A method for interpreting the data from depth-sensing 
indentation. Journal of Materials Research, 1986. 1(4): p. 601-609. 
 
2. Hay, J. and B. Crawford, Measuring substrate-independent modulus of thin films. Journal 
of Materials Research, 2011. 26(06): p. 727-738. 
 
3. King, R.B., Elastic analysis of some punch problems for a layered medium. International 
Journal of Solids and Structures, 1987. 23(12): p. 1657-1664. 
 
4. Pharr, G.M., J.H. Strader, and W.C. Oliver, Critical issues in making small-depth 
mechanical property measurements by nanoindentation with continuous stiffness 
measurement. Journal of Materials Research, 2009. 24(03): p. 653-666. 
 
5. Saha, R. and W.D. Nix, Effects of the substrate on the determination of thin film 
mechanical properties by nanoindentation. Acta Materialia, 2002. 50(1): p. 23-38. 
 
6. Zhou, B. and B.C. Prorok, A Discontinuous Elastic Interface Transfer Model of Thin 
Film Nanoindentation. Experimental Mechanics, 2009. 50(6): p. 793-801. 
 
7. Zhou, B. and B.C. Prorok, A new paradigm in thin film indentation. Journal of Materials 
Research, 2010. 25(09): p. 1671-1678. 
 
8. MTS Commercial Nanoindentation. 2003  [cited 2011 June 11th]; Available from: 
http://www.nanoindentation.cornell.edu/pictures/schematic_nanoindenter.gif. 
 
9. Prorok, B.C., et al., Micro- and Nanomechanics. Encyclopedia of Nanoscience and 
Nanotechnology, 2004. 5: p. 555-600. 
 
10. Li, X. and B. Bhushan, A review of nanoindentation continuous stiffness measurement 
technique and its applications. Materials Characterization, 2002. 48(1): p. 11-36. 
 
11. Zhou, B., Exploration of the Origin of Substrate Effects and Elastic Strain Properties 
during Thin Film Nanoindentation, in Materials Engineering, 2009, Auburn University: 
Auburn. p. 144. 
 
12. McElhaney, K.W., J.J. Vlassak, and W.D. Nix, Determination of indenter tip geometry 
and indentation contact area for depth-sensing indentation experiments. Journal of 
Materials Research, 1998. 13(5): p. 7. 
 
13. Oliver, W.C. and G.M. Pharr, An improved technique for determining hardness and 
elastic modulus using load and displacement sensing indentation experiments. Journal of 
Materials Research, 1992. 7(6): p. 1564-1583. 
 73 
 
14. Rar, A., H. Song, and G.M. Pharr, Assessment of new relation for the elastic compliance 
of a film-substrate system. Thin Films: Stresses and Mechanical Properties IX, 2002. 695: 
p. 431. 
 
15. Hertzberg, R.W., Deformation and Fracture Mechanics of Engineering Materials. 4th 
ed1996: John Wiley & Sns, Inc. 
 
16. Kulkarni, A.V. and B. Bhushan, Nano/picoindentation measurements on single-crystal 
aluminum using modified atomic force microscopy. Materials Letters, 1996. 29(4-6): p. 
221-227. 
 
17. Branger, V., et al., Study of the mechanical and microstructural state of platinum thin 
films. Thin Solid Films, 1996. 275(1-2): p. 22-24. 
 
18. Fang, T.-H., W.-J. Chang, and C.-I. Weng, Nanoindentation and nanomachining 
characteristics of gold and platinum thin films. Materials Science and Engineering: A, 
2006. 430(1-2): p. 332-340. 
 
19. Qui?ones, C., W. Vallejo, and F. Mesa, Physical and electrochemical study of platinum 
thin films deposited by sputtering and electrochemical methods. Applied Surface Science, 
2011. 257(17): p. 7545-7550. 
 
20. Espinosa, H.D., B.C. Prorok, and M. Fischer, A methodology for determining mechanical 
properties of freestanding thin films and MEMS materials. Journal of Mechanics and 
Physics of Solids, 2003. 51: p. 46-67. 
 
21. Furukawa, M., et al., Surface morphologies of sputter-deposited aluminum films studied 
using a high-resolution phase-measuring laser interferometric microscope. Appl. Opt., 
1996. 35(4): p. 701-707. 
 
22. Herman, D.S., M.A. Schuster, and R.M. Gerber, Hillock Growth on Vacuum Deposited 
Aluminum Films. Journal of Vacuum Science and Technology, 1972. 9(1): p. 515-519. 
 
23. Voutsas, A.T., et al., Structure engineering for hillock-free pure aluminum sputter 
deposition for gate and source line fabrication in active-matrix liquid crystal displays. 
Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, 1998. 16(4): 
p. 2668-2677. 
 
24. Archard, J.F., Elastic Deformation and the Laws of Friction. Proceedings of the Royal 
Society of London. Series A, Mathematical and Physical Sciences, 1957. 243(1233): p. 
190-205. 
 
25. Jackson, R., An Analytical Solution to an Archard-Type Fractal Rough Surface Contact 
Model. Tribology Transactions, 2010. 53(4): p. 543-553.