Investigation of Pile-Up and Delamination of Au Thin Films on Various Substrates and the 
Behavior of the Films Described by a Discontinuous Elastic Strain Model 
 
by 
 
James Brandon Frye 
 
 
 
 
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 
May 6, 2012 
 
 
 
 
Keywords: nanoindentation, thin films, pile-up,  
delamination 
 
 
Copyright 2012 by James Brandon Frye 
 
 
Approved by 
 
Barton Prorok, Committee Chair, Associate Professor of Material Engineering 
Dong-Joo Kim, Associate Professor of Material Engineering 
 Ruel Overfelt, Professor of Material Engineering 
 
 
 
 
ii 
 
 
 
Abstract 
 
 
 A new method of accurately and reliably extracting the actual Young?s modulus of a thin 
film on a substrate has been developed. The method is referred to as the discontinuous elastic 
interface transfer model. The method has been shown to work exceptionally well with films and 
substrates encompassing a wide range of elastic moduli and Poisson ratios. The advantage of the 
method is that it does not require a continuous stiffness method and can use the standard Oliver 
and Pharr analysis and the use of a predictive formula for determining the modulus of the film as 
long as the film thickness, substrate modulus and bulk Poisson ratio of the film are known. 
However, when there is much pile-up during the indentation process in a softer film, the 
experimental data does not follow the predictive formula but instead follows a similar model 
with a single Poisson ratio between the film and the substrate. 
  
 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. Kim 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, Kevin, Nicole, Shakib, Madhu, MariAnne, Danny, Naveed 
and Dong. Thanks to all of the faculty and staff members past and present in Materials 
Engineering at Auburn University including Steve, Allison, Jenny and LC. I would also like to 
acknowledge and thank all of my friends in Auburn for their support. And lastly I would like to 
thank my family for all of the support and love they have shown me throughout my time here at 
Auburn University. 
  
 iv
 
 
 
 
 
Table of Contents 
 
 
Abstract ........................................................................................................................................... ii?
Acknowledgments ......................................................................................................................... iii?
List of Tables ................................................................................................................................. vi?
List of Illustrations ......................................................................................................................... vi?
List of Abbreviations ...................................................................................................................... x?
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 ....................................................................................... 7?
2.3 Erroneous Contact Area ...................................................................................................... 10?
2.4 Modeling Thin Film Substrate Effects ................................................................................ 12?
Chapter 3: Material Selection ....................................................................................................... 20?
3.1 Material Selection and Their Mechanical Properties .......................................................... 20?
Chapter 4: Experimental Setup and Fabrication ........................................................................... 21?
4.1 Film Deposition ................................................................................................................... 21?
4.2 Nanoindentation .................................................................................................................. 26?
 v
Chapter 5: Results and Discussions .............................................................................................. 28?
5.1 Experimental Nanoindentation Analysis ............................................................................. 28?
Chapter 6: Conclusions ................................................................................................................. 50?
References ..................................................................................................................................... 52?
 
  
 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.
[7]
??????????......4 
 
Table 3.1.1 Material selections for film and substrates with desirable Young?s modulus and 
Poisson?s ratio?????????????????????????????20 
 
Table 4.2.1 Sputtering parameters of 480 nm Au film with Ti adhesion layer??...???.?.24 
 
  
 vii
 
 
 
List of Illustrations 
 
Figure 2.1.1 Schematic of nanoindentation system. ....................................................................... 3?
Figure 2.1.2 Micrograph of a Berkovich indenter tip ..................................................................... 5?
Figure 2.1.3 (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.
[7]
 ........................................................ 6?
Figure 2.2.1 Load-Displacement curve during the continuous stiffness method.
[8]
 ....................... 7?
Figure 2.2.2a Young?s Modulus verses Displacement into surface for a bulk material 
[9]
 ............. 8?
Figure 2.2.2b Young?s Modulus verses Displacement into surface for a compliant film on hard 
substrate 
[9]
 .............................................................................................................................. 9?
Figure 2.2.2c Young?s Modulus verses Displacement into surface for a hard film on compliant 
substrate. 
[9]
 ........................................................................................................................... 10?
Figure 2.3.1 Schematics of the pile-up and sink-in effect. ........................................................... 11?
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.
[11]
 ........................... 14?
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]
 ................................ 15?
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) SiO
2
, (b), Ge, (c) Si, (d) 
MgO, and (e) Sapphire .......................................................................................................... 17?
Figure 2.4.4 E-h curves of AlO
x
 films on SiO
2
, Ge, Si, MgO and Al
2
O
3
 showing a flat region at 
low indentation depths .......................................................................................................... 18?
Figure 2.4.5 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. ............................................................................................................ 19?
 viii
Figure 4.1.1 Schematic of sputtering method ............................................................................... 22?
Figure 4.1.2 Denton Vacuum Inc. DC & RF sputtering system. .................................................. 23?
Figure 4.1.3 Tencor Instruments "Alpha-Step 200" profilometer. ............................................... 25?
Figure 4.2.1 Image of MTS Nano Indenter XP nanoindentation system. ..................................... 27?
Figure 5.1.1 E-h curve of arbitrary film on substrate with varying film Modulus ....................... 29?
Figure 5.1.2 E-h curve of arbitrary film on substrate with varying substrate modulus ................ 30?
Figure 5.1.3 E-h curve of arbitrary film on substrate with varying film Poisson ratio ................. 32?
Figure 5.1.4 E-h curve of arbitrary film on substrate with varying substrate Poisson ratio ......... 33?
Figure 5.1.5 E-h curve of arbitrary film on substrate showing combined effect of varying Poisson 
ratios of film and substrate .................................................................................................... 34?
Figure 5.1.6a E-h curve for Al
2
O
3
 substrate. ................................................................................ 36?
Figure 5.1.6b E-h curve for MgO substrate. ................................................................................. 36?
Figure 5.1.6c E-h curve for Si substrate. ...................................................................................... 37?
Figure 5.1.6d E-h curve for SiO
2
 substrate. .................................................................................. 37?
Figure 5.1.6e E-h curve for Ge substrate. ..................................................................................... 38?
Figure 5.1.7 E-h curve for Au on 5 different substrates. .............................................................. 39?
Figure 5.1.8 E-h curve with discontinuous model and film E for 500nm Au on Ge with Ti 
adhesion layer. ...................................................................................................................... 40?
Figure 5.1.9 ?-h curve for 500nm Au on Ge with Ti adhesion layer. ........................................... 40?
Figure 5.1.10 E-h curve with discontinuous model and film E for 500nm Au on Si with Ti 
adhesion layer. ...................................................................................................................... 41?
Figure 5.1.11 ?-h curve for 500nm Au on Si with Ti adhesion layer. .......................................... 41?
Figure 5.1.12 E-h curve with discontinuous model and film E for 500nm Au on MgO with Ti 
adhesion layer. ...................................................................................................................... 42?
Figure 5.1.13 ?-h curve for 500nm Au on MgO with Ti adhesion layer. ..................................... 42?
Figure 5.1.14 E-h curve with discontinuous model and film E for 500nm Au on Al
2
O
3
 with Ti 
adhesion layer. ...................................................................................................................... 43?
 ix
Figure 5.1.13 ?-h curve for 500nm Au on Al
2
O
3
 with Ti adhesion layer. .................................... 43?
Figure 5.1.15 E-h curve with Z-P model, film E, and film alpha for 2000nm Au on SiO
2
. ......... 44?
Figure 5.1.16 E-h curve with discontinuous model and D-N model for 2000nm Au on SiO2. ... 45?
Figure 5.1.17 JEOL JSM 7000F Scanning Electron Microscope. ................................................ 46?
Figure 5.1.18 Micrograph of 2000nm Au on SiO
2
 370nm indention ........................................... 47?
Figure 5.1.19 Micrograph of 2000nm Au on SiO
2
 500nm indention ........................................... 47?
Figure 5.1.20 Micrograph of 2000nm Au on SiO
2
 800nm indention ........................................... 48?
Figure 5.1.21 Micrograph of 2000nm Au on SiO
2
 1000nm indention ......................................... 48?
Figure 5.1.22 Micrograph of 2000nm Au on SiO
2
 1500nm indention ......................................... 49?
Figure 5.1.23 Micrograph of 2000nm Au on SiO
2
 1700nm indention ......................................... 49?
 
 
 
 
 
 
 
 
 
 
 
 
 
 x
 
 
 
List of Abbreviations 
 
null 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 
Z-P In relation to Zhou and Prorok Model 
S-N In relation to Saha and Nix Model 
null As subscript: of the film 
null As subscript:?of?the?indenter 
? Angstrom 
nm Nanometer 
null Weighting factor 
null As subscript: of the substrate 
null Shear Modulus 
null Poisson?s Ratio 
SEM Scanning Electron Microscope 
CSM Continuous Stiffness Method 
MEMS Microelectromechanical systems 
 
 
1 
 
Chapter 1: Introduction 
1.1 Overview 
 Over the past several decades, Instrumented Indentation Testing (IIT) has become a 
heavily researched topic in both bulk and nano-scale material testing. From indentation tests, 
researchers can measure physical properties of materials such as the hardness and young's 
modulus. The areas of micro and nano-scale indentation has certainly gained more attention and 
focus in a world becoming more and more dependent and fascinated with smaller scale devices 
such as nanoparticles, nanowires, MEMS and NEMS devices. The computer and technology 
boom of the past several decades have led scientists and researchers to explore the properties and 
behavior of thin films. However, there are still several areas in thin film indentation that present 
problems in current measurement techniques. One of the main issues being investigated in micro 
and nano scale thin film indentation is the effect the substrate has on the measurements of the 
film. As a thin film becomes increasingly thin, the substrate's interaction with the properties and 
measurements of the film increases.  
 In the following work, the workings of Doerner, Nix, Gao, Oliver and Pharr were studied 
in order to build off of their findings and understand the behavior of thin films more clearly. The 
complexity of thin film Nanoindentation experimental and theoretical methods arise from many 
different phenomena including pile-up and sink-in of the film during Nanoindentation as well as 
microstructural effects such as grain size and orientation of thin films. In order to eliminate such 
microstructural problems in the experiments, a nanocrystaline film was used in the research to 
understand the substrate effect on the film and the resulting composite modulus. Five different 
substrates were chosen for the experiment with a range of Poisson ratios and Young?s moduli.  
 
 2
1.2 Thesis Structure 
 Chapter 2 includes a literature review of all of the work related to this Thesis. It includes; 
instrumented indentation testing, continuous stiffness measurement, erroneous contact area, pile-
up/sink-in effects during nanoindentation and major models that have been developed to extract 
the film?s intrinsic properties. Chapter 3 discusses the selection of materials used in the research 
and why they were chosen. Chapter 4 details the experimental setup of the research including; 
how the samples were prepared, thin film deposition via sputtering techniques as well as the 
parameters used in the deposition process and overview of the Nanoindentation set-up. Chapter 5 
presents the results of the experiments and discusses the meaning of the results and Chapter 6 
gives a summary of the research.  
 
  
 3
Chapter 2: Literature Review of Instrumented Thin Film Indentation 
 
2.1 Instrumented Indentation Testing 
 
 Nanoindentation, or Instrumented Indentation Testing (IIT), is a high-resolution process 
of mechanically measuring a material?s properties by driving an indenter tip made of diamond 
into the surface of a sample. During Nanoindentation, the indenter tip penetrates the sample as 
the load and displacement of the tip are recorded by positional sensors. From the measured 
recordings, the mechanical properties of the sample can be extracted. A schematic of a general 
Nanoindentation set-up is shown in Figure 2.1.1. The load from the tip is generated by a magnet 
and coil, and the displacement of the indenter is measured by a capacitive displacement gauge
[8]
. 
 
Figure 2.1.1 Schematic of nanoindentation system.
[8]
 
 
 There are several different types of indenter tips commonly used in Nanoindentation. 
However, the most common tip used is a Berkovich tip, or three sided pyramid. The advantage 
 4
 of this tip is that it can be easily fabricated to a very sharp point by simple grinding techniques. 
In the case of the Vickers tip, or four sided pyramid, it is extremely hard to fabricate a sharp 
point and instead results in a wedge shape tip, which is used in some indentation experiments. 
Also, the Berkovich tip is geometrically self-similar, meaning that the geometry of the tip?s cross 
section, normal to the sample being indented, remains unchanged as the tip penetrates further 
into the sample. Table 2.1.1 shows schematics of various tips used in indentation as well as their 
projected contact areas as a function of indent depth. 
[7]
 
 
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.
[7]
 
 
 
 
 
 
 5
Figure 2.1.2 Micrograph of a Berkovich indenter tip 
 
 As the indenter penetrates the sample, there are two things happening congruently, plastic 
deformation and elastic deformation. As the tip is extracted from the sample, there is only the 
elastic response resulting in a force on the tip from the elastic recovery of the material being 
indented. This elastic recovery is related to how stiff the material is and the magnitude of the 
force on the tip is proportional to the elastic recovery. As the tip retracts from the sample, the 
elastic deformation is isolated from the total deformation and thus a curve of load versus 
displacement is used to determine the stiffness of the material. Equation 1 shows the relationship 
between the Stiffness, S, and the Reduced Young?s modulus, E
r
, with A being the projected 
contact area of the indenter tip.  
 
 
nullnull
nullnull
nullnull
null
2
?
null
null
null
?null 
 
(1)
 
 
 From the equation, it can be seen that the stiffness of the material can be obtained by 
taking the instantaneous slope at the point of unloading, which is dP, or change in load, over dh, 
the change in indent depth. Using the model developed by Doerner and Nix, the modulus of the 
film can be extracted by relating the effective Young?s modulus to the following equation:  
 
 
1
null
null
null
null1nullnull
null
null
null
null
null1 null null
null
null
null
null
null
 
 
(2)
where E is the modulus of the film, E
i
 is the modulus of the indenter tip, ? is the Poisson ratio of 
the film and ?
i
 is the Poisson ratio of the indenter tip. Figure 2.1.3 represents load versus 
 6
displacement plots for a material that is relatively soft as well as a plot of a material that is 
relatively hard, or stiff. 
[7]
 
 
 
 
 
 
 
Figure 2.1.3 (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.
[7]
 
 
 
 7
2.2 Continuous Stiffness Measurement 
 The Continuous Stiffness Measurement, or CSM, is an indentation method where the 
indenter oscillates up and down onto the sample with an increasing load. This method is useful in 
Nanoindentation of thin films in that the method can accurately extract the modulus of the 
sample at a finite number of indentation depths. The result of the continuous stiffness 
measurement is that the test gives a curve of the modulus at each depth as the indenter pulls 
away from the sample and measures the force from the samples elastic spring back, or elastic 
recovery. CSM allows for the separation of the film and the substrates corresponding properties 
such as hardness and modulus. Figure 2.2.1 shows a load versus displacement curve of a 
theoretical indentation test, where each spike in the curve represents a single oscillation and 
measurement of stiffness.  
 
Figure 2.2.1 Load-Displacement curve during the continuous stiffness method.
[8]
 
 
 In the case of the CSM method, instead of getting a single value for the modulus, it is 
possible to get a progressive measurement at each individual indent depth. The result of the plot, 
for a thin film on a substrate, shows that at lower depths, the value of the recorded modulus is 
 8
more characteristic of the film while at higher indent depths, the recorded modulus is 
characteristic of the substrate. At intermediate depths, the modulus is a mixture of the film and 
the substrate moduli as the two components interact with each other. When indenting that of a 
bulk material, the resulting plot will exhibit a horizontal line representing the value of the 
modulus. As for a compliant film on a hard substrate, the corresponding plot will exhibit an 
increase in modulus as the indenter?s depth increases. Conversely, in the case of a hard film on a 
soft substrate, the plot will exhibit a decreasing trend as the elastic recovery against the indenter 
decreases the closer it gets to the substrate. Figure 2.2.2a-c represents CSM indentation plots of a 
bulk material, soft film on a hard substrate and a hard film on a soft substrate respectively. 
 
 
 
Figure 2.2.2a Young?s Modulus verses Displacement into surface for a bulk material 
[9] 
 9
 
 
Figure 2.2.2b Young?s Modulus verses Displacement into surface for a compliant film on hard 
substrate 
[9] 
 
 10
 
 
Figure 2.2.2c Young?s Modulus verses Displacement into surface for a hard film on compliant 
substrate. 
[9] 
2.3 Erroneous Contact Area 
 There exists a great problem in Nanoindentation tests due to a physical concept known as 
erroneous contact area. Since the measured modulus and hardness values of a sample are 
dependent on the projected contact area of the indenter?s tip, any deviation away from an 
increase in contact area as described by a known function of indentation depth will result in a 
misrepresentation of the measured stiffness. In the case of a soft film on a relatively hard 
substrate, the film material has a tendency to ?pile-up? around the edges of the indenter tip, 
resulting in an underestimation of the projected contact area and an overestimation of the 
calculated modulus and hardness. The reason for the overestimation, in this case, is due to more 
 11
material providing elastic recovery than what the projected contact area would suggest. On the 
other hand, in the case of a hard material on a relatively soft substrate, there exists a ?sink-in? 
effect. The sink-in effect arises from the harder film material projecting its strain into the 
substrate causing an underestimation in the projected contact area from what the function of the 
indent depth would suggest. An underestimation of the projected contact area leads to an 
underestimation in the modulus and hardness due to less material contributing to the elastic 
recovery at a given indent depth. Figure 2.3.1 depicts a schematic of both a pile-up effect and 
sink-in effect as well as what the corresponding cross-sectional area, A
i
, of the indenter looks 
like. 
[10]
 
 
Figure 2.3.1 Schematics of the pile-up and sink-in effect.
[10]
 
 
 
 12
2.4 Modeling Thin Film Substrate Effects  
 Instrumented indentation testing has become increasingly difficult to characterize and 
model as the science has become more focused on the nanoscale regime. The problem arises 
from the influence that the substrate has on the thin film at the nanoscale. Because of the 
interactions between the thin film and substrate, it becomes a difficult task to isolate and extract 
the film?s properties at such shallow indentation depths. Many researchers have formulated 
theories and models in order to deal with the underlying problem of the thin film/substrate 
interaction.
[1, 2, 5, 7, 11, 12]
 Some of the models do a good job of explaining certain combinations of 
films and substrates, however, there hasn?t been a specific model that can describe the behavior 
of most thin film/substrate combinations accurately. 
 Oliver and Pharr found there to be a power law function describing the stiffness curve 
which states for most materials, the unloading load-displacement curve is not linear:  
 
nullnullnullnullnullnullnull
null
null
null
 
 
(3)
where P is the load, B and m are empirically determined constants and h
f
 is the final 
displacement after the elastic recovery of the material. 
[11] 
 With the stiffness measurements and projected contact area, at a certain indentation 
depth, the reduced modulus and hardness can be calculated using the following relationship: 
 
 
 
null
null
null
?
null
2
null
?null
 
 
(4)
And 
 
 13
 
nullnull
null
null
 
 
(5)
Where S is the stiffness, E
r
 is the reduced modulus and A is the projected contact area at a peak 
load and a function of h
c
, or the indentation depth: 
 
 
null null 24.5null
null
null
 
 
(6)
The area function in the form of A = f (h
c
), assumes a perfect Bercovich indenter tip. However, 
there cannot be such a perfect tip and so the following equation more accurately describes the 
projected contact area as a function of indent depth: 
  
 
null null 24.5null
null
null
nullnull
null
null
null
null
nullnull
null
null
null
null/null
nullnull
null
null
null
null/null
null.....nullnull
null
null
null
null/nullnullnull
 
 
(7)
Where C
1
 ? C
8
 are constants, with the leading term describing that of an unblounted Bercovich 
indenter.  
 
 14
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.
[11]
 
  
Doerner and Nix developed a model to extract the film modulus from the composite 
modulus. 
[1]
 In their model, they suggested that there is a continuous transfer of energy between 
the film and the substrate at the interface. A continuous transfer of energy suggests that the strain 
at the interface on the film side is equal to the strain at the substrate side. Figure 2.4.2a shows a 
schematic of a completely continuous transfer of energy from the film to the substrate and equal 
magnitudes of strain at the interface. Due to a continuous transfer of energy, their model uses a 
single weighting factor, 
 
 
 1
null
null
null
1
null
null
null
nullnull
1
null
null
null
null
1
null
null
null
nullnull
nullnullnull
 
 
 
(8)
Where E? is the composite modulus, null
null
null
nullnull
null
null1 null null
null
null
null?  is the film modulus, null
null
null
nullnull
null
null1nullnull
null
null
null?  is 
the substrate modulus and null
nullnullnull
 is the Doerner and Nix weighting factor. The weighting factor 
describes that the substrates effect on the composite modulus increases as the indenter penetrates 
further into the film, approaching the substrate, 
 
null
nullnullnull
nullnull
nullnullnullnull null
nullnullnull
? null
 
 
(9)
 
Where null is suggested to be an empirically determined constant, t is the film?s thickness and h
eff
 
is the effective indentation depth, or depth at which the projected contact area represents. 
Doerner and Nix suggested that for most materials, null can be assumed to be equal to around 0.25. 
 15
   
 
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] 
 
However, Zhou and Prorok found that there is not a continuous transfer of energy 
between the film and the substrate. Finite element analysis was used to show that the transfer of 
energy at the interface is discontinuous. Figure 2.4.3 show simulations of AlOx films on various 
substrates, and how the strain fields change across the film substrate interface. As described by 
the discontinuous model, there has to be two weighting factors accounted for in the composite 
 16
modulus. Building from the models of Doerner and Nix and Gao, the discontinuous model has 
the following form, 
 1
null
null
null
1
null
null
null
null1nullnull
null
null null
1
null
null
null
null
null
 
(10)
where, 
 
null
null
nullnull
nullnull
null
nullnullnull?null
 and  null
null
nullnull
nullnull
null
nullnullnull?null
 
(11)
 
Here null
null
 and null
null
 represent the weighting factors of the film and substrate respectively, which 
account for the effects of the film on the substrate as well as the substrate on the film. The 
weighting factors? physical meanings are represented in figure 2.4.2c. The terms ?
f  
and ?
s 
are the 
film and substrate constants, which are equal to the Poisson?s ratios of the film and substrate 
respectively.  
 
 
SiO
2
Ge Si
Al
2
O
3
MgO
 17
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) SiO
2
, (b), Ge, (c) Si, (d) 
MgO, and (e) Sapphire 
 
However, Zhou et. al. found that there was a flat region at very shallow indentation 
depths where the initial value of the modulus at low indentation depths is believed to be 
representative of the Young?s modulus of the film. Further investigation shows that upon 
increasing indentation depth, the value of the composite modulus increases or decreases as the 
effect of the substrate increases with depth. In the flat region, or E?
flat
, the modulus is highly 
dependent on the substrate modulus, increasing with increasing substrate moduli. Figure 2.4.3 
shows E-h curves of AlO
x
 films on SiO
2
, Ge, Si, MgO and Al
2
O
3
 showing a flat region at low 
indentation depths. 
[7]
   
 
 
1
E
null
null
1
E
null
null
null1null?
null
nullnull
E
null
null
E
null
null
null
null.null
null
1
E
null
null
?
null
 
(12)
 18
 
Figure 2.4.4 E-h curves of AlO
x
 films on SiO
2
, Ge, Si, MgO and Al
2
O
3
 showing a flat region at 
low indentation depths  
Displacement into Surface (nm)
0
75
25 50 75
100
125
175
150
AlO
x
-on-SiO
2
AlO
x
-on-Ge
AlO
x
-on-Si
AlO
x
-on-MgO
AlO
x
-on-Al
2
O
3
M
easu
red
 Y
o
u
n
g
?
s M
o
d
u
l
u
s 
(
G
P
a
)
 19
 
Figure 2.4.5 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. 
 20
Chapter 3: Material Selection 
 
3.1 Material Selection and Their Mechanical Properties 
 The substrates that were investigated in this work were chosen based upon a couple of 
different parameters. A list of the selected substrates is shown in Table 3.1.1. In order to explore 
how the composite modulus of a film on a substrate behaves, the substrate candidates needed to 
have a range of properties differing from that of the Au film. Since the discontinuous model was 
being investigated, the chosen substrates had Young?s moduli ranging from near the value of 
gold?s modulus to several times that. The Poisson?s ratios of the chosen substrates were all 
chosen to be less than or equal to that of gold. MgO was chosen due to it having a bulk Poisson 
ratio equal to the value of Au, but has a higher Young?s modulus. Si was chosen based off of it 
having a higher Poisson ratio as well as a higher Young?s modulus relative to Au as well as the 
fact that the properties of Si are widely known and would serve as a benchmark for other tests. 
Al
2
O
3
 had a Poisson ratio close to that of Si but a much higher Young?s modulus. And finally, 
SiO
2
 was investigated due to having a similar Young?s modulus relative to Au, but a much lower 
Poisson?s ratio. The Au/SiO
2
 combination would become the main focus of this work, as its 
Nanoindentation data would result in a very unique trend compared to the rest of the data.  
 
Table 3.1.1 Material selections for film and substrates with desirable Young?s modulus and 
Poisson?s ratio 
Film Substrates 
Material E (GPa) ? Material E (GPa) ? 
Au 78 0.44 MgO 270-330 0.18
 Si 165 0..27 
Al
2
O
3
 430-460  0.21-0.27 
Ge 135 0.26 
 SiO
2
 78 0.18
 
 21
Chapter 4: Experimental Setup and Fabrication 
 
4.1 Film Deposition 
 There are many ways to deposit or grow materials on substrates such as sputtering, e-
beam lithography, plasma enhanced chemical vapor deposition (PECVD), low pressure chemical 
vapor deposition (LPCVD) and so on. In this work, magnetron sputtering was chosen for the film 
deposition method. Magnetron sputtering is a physical deposition process in which ion 
bombardment is the primary mechanism for the film growth. In this method, argon gas is 
introduced into the chamber and either an RF or DC power supply is used to create an argon 
plasma. The argon plasma sputters a graphite electrode, where the target material is located, and 
a magnetic field is applied in order to increase the mean free path of the electrons by spiraling 
the electrons. The increase in mean free path increases the deposition rate of the target material. 
A voltage bias can be applied to the substrate to increase the ion bombardment, and hence 
increase the deposition rate. When sputtering, there are several parameters than can affect the 
quality of the deposited film such as chamber pressure, RF or DC wattage and argon flow rate, to 
name a few, which make sputtering a highly useful method of film deposition. Figure 4.1.1 
shows a schematic of a magnetron sputtering systems method.  
 22
 
Figure 4.1.1 Schematic of sputtering method 
 
Double side polished substrates of MgO, Si, Al
2
O
3
, Ge and SiO
2
, or Quartz, of 0.5mm 
thick and 25x25mm or larger and at least 99.99% pure were obtained from MTI Corporation, 
Richmond, Ca. 
Once the substrates were in order, a thin film of gold 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 gold was first 
sputtered onto a cleaned fused silica microscope slide, or SiO
2
.  The parameters initially used 
were extracted from the sputtering system's log book, recorded when gold was previously 
sputtered by other users when running this system as shown in Table 4.1.1.  From these values it 
was chosen to go with a sputtering power of 100 watts as it was used for the film that most 
closely resembles the desired thickness of 500nm.  To compensate for the original film being 
 23
400nm, the sputtering time was increased to 1500 seconds in line with the deposition rate to 
reach an expected thickness of 500nm. 
 
 
 
 
Figure 4.1.2 Denton Vacuum Inc. DC & RF sputtering system. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 24
 
Table 4.2.1 Sputtering parameters of 480nm Au film with Ti adhesion layer. 
 
Base Pressure (Torr) 5?x?10
?6
?
Magnetron Type DC? DC?
Target Material Au? Ti?
Pre-Sputtering Power (W) 100? 400?
Pre-Sputtering Time (sec) 60? 25?
Sputtering Power (W) 100? 400?
Sputtering Time (sec) 1500? 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) 500? 10?
Actual Film Thickness (nm) 480? 10?
 
 
After deposition, the film thickness was measured using a Tencor Instruments "Alpha-
Step 200" profilometer shown in Figure 4.1.3. For each deposited film, 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 480nm; 20nm less than expected.  
 25
 
Figure 4.1.3 Tencor Instruments "Alpha-Step 200" profilometer. 
 
 
 
 
 
 
 
 
 
 
 
 26
 
4.2 Nanoindentation 
Nanoindentation was performed using TestWorks 4 to drive an MTS Nanoindenter XP 
(Agilent Technologies, Santa Clara, CA), as shown in Figure 4.2.1. A Berkovich type diamond 
tip was used during the experiments in a depth controlled test. The harmonic displacement, or the 
distance the tip travelled during each oscillation, was set to 2nm and the allowable drift rate of 
the indenter head was 0.05 nm/s. During each indentation test, twenty five indents were 
performed on a fused silica reference in order to calibrate the area coefficients of the tip. Next 
five indents were performed on an aluminum reference material to both clean any debris off of 
the surface of the indenter and calibrate the position between the camera and indenter head. 
When setting up the experiment for each film-substrate combination, the value of the bulk film 
Poisson ratio was input into TestWorks 4. Also, the depth of each indentation test was entered to 
be 500 nm in order to fully penetrate the film and test the behavior of the film throughout the 
entirety of the thin film. Twenty five indents were performed on each film-substrate combination 
in a five by five array separated by 50 ?m in both the x and y direction. The average value of the 
entire array was calculated using the program Analyst and plotted for the composite modulus 
versus indentation depth for each sample. The data gathered was acquired using the standard 
Oliver and Pharr analysis.  
 
 
 27
 
Figure 4.2.1 Image of MTS Nano Indenter XP nanoindentation system. 
  
 28
Chapter 5: Results and Discussions 
 
5.1 Experimental Nanoindentation Analysis 
 
 Before running any indentation tests, the discontinuous model was examined to 
determine what changing various film and substrate properties would result in. Figures 3.1.1- 
3.1.5 show E-h curves of arbitrary films on substrates with varying film moduli and Poisson 
ratios. Figure 3.1.1a shows that as the substrates modulus is held constant at 100 GPa, changing 
the film?s modulus results in an increase or decrease in the composite modulus upon further 
indentation depth with decreasing or increasing substrate modulus respectively. The trends of the 
composite moduli suggest that the substrates effect on the composite modulus increases upon 
further indentation depth. When varying the substrate modulus, the effect of the composite 
modulus was inverted. As the substrate modulus was increased, relative to that of the film?s 
modulus, the resulting composite modulus trend line increased upon further indentation depth 
and vice versa.  
 
 
 29
 
Figure 5.1.1 E-h curve of arbitrary film on substrate with varying film modulus 
 30
 
Figure 5.1.2 E-h curve of arbitrary film on substrate with varying substrate modulus 
 
 
 
 
 
 
 
 
 
 
 31
 After varying the film and substrate?s moduli with respect to each other, the Poisson?s 
ratios were changed to observe the resulting trends. Figure 3.1.3 shows that keeping all the 
parameters constant while varying the film?s Poisson ratio resulted in an initial increase or 
decrease in composite modulus. A film with a Poisson ratio of 0.50 on a substrate having a 
Poisson ratio of 0.30 resulted in an increase of the composite modulus at first but leveled off to 
that of the substrates modulus upon further indentation depth. Conversely, a film with a Poisson 
ratio of 0.10 on a substrate with a Poisson?s ratio of 0.30 results in a dip in the composite 
modulus and approaches the substrates modulus eventually. In Figure 3.1.6, it was seen that as 
the differences in the film and substrates Poisson ratios became increasingly far apart, the effect 
of the increase in composite modulus was intensified.  The expected behavior of the gold film on 
a SiO
2
 substrate can be seen in figure 3.1.6 where the Poisson ratios of the two are very different. 
According to the discontinuous theory, the film with a Poisson ratio of 0.44 ?wants? to spread 
out during compression while the SiO
2
 substrate with a Poisson ratio of 0.18 shows minimal 
displacement in the z and y direction, thus resulting in a temporary increase in the composite 
modulus. The increase in the composite modulus arises from the substrate restricting the 
expansion of the film during the indentation test.  
 32
 
Figure 5.1.3 E-h curve of arbitrary film on substrate with varying film Poisson ratio 
 
 33
 
Figure 5.1.4 E-h curve of arbitrary film on substrate with varying substrate Poisson ratio 
 
 
 
 
 
 
 
 
 
 34
 
The combined effect of changing the substrate and film Poisson ratios is shown in Figure 
5.1.5. Here, it can be seen that as the differences in Poisson ratios increase, the substrate effect 
becomes larger. 
 
 
Figure 5.1.5 E-h curve of arbitrary film on substrate showing combined effect of varying Poisson 
ratios of film and substrate 
 
 Nanoindentation tests at indentation depths of 500nm were performed on substrates 
Al
2
O
3
, MgO, Ge, Si and SiO
2
 in order to get the values of the bulk moduli. These tests were 
 35
performed in order to get the actual values of the substrates Young?s moduli rather than referring 
to the literature for the reported moduli, since the values could be slightly different due to 
various factors such as crystal orientation. 
Raw CSM Nanoindentation data of all the film substrate combinations were put into 
Analyst software, which is a program used with the MTS-Nano Nanoindenter XP system to 
process the data. The Analyst software calibrated the data from each CSM test. The results 
showed a horizontal line throughout the indentation tests representing the bulk moduli of the 
substrates. At very low indentation depths, the measured values were lower than that of the 
values at deeper depths due to the indenter tip initially losing contact with the surface of the 
substrate during the tip oscillation of the CSM method. Figures 5.1.6a-e show the results of the 
indentation tests on the five substrates. It should be noted that the data for the SiO
2
 substrate 
indentation test showed a slight variation at lower indentation depths eventually leveling out at 
larger depths. 
 
 
  
 36
 
Figure 5.1.6a E-h curve for Al
2
O
3
 substrate. 
 
 Figure 5.1.6b E-h curve for MgO substrate. 
0
100
200
300
400
500
600
0 100 200 300 400 500
Modulus (GPa)
Displacement Into Surface (nm)
0
50
100
150
200
250
300
350
0 100 200 300 400 500
Modulus (GPa)
Displacement Into Surface (nm)
 37
 
Figure 5.1.6c E-h curve for Si substrate. 
 
Figure 5.1.6d E-h curve for SiO
2
 substrate. 
0
50
100
150
200
250
300
0 100 200 300 400 500
Modulus (GPa)
Displacement Into Surface (nm)
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500
Modulus (GPa)
Displacement Into Surface (nm)
 38
 
Figure 5.1.6e E-h curve for Ge substrate. 
 
After the substrates were indented on, and it was known how they would behave with a 
film on them, the substrates were indented with Au films on them. Figure 5.1.7 shows the 
composite modulus versus displacement for all five film-substrate combination. The results of 
the indentation tests agree with the previous graphs of varying Young?s moduli and Poisson?s 
ratios. Figures 5.1.8 -5.1.15 show E-h curves of the data for each substrate along with several 
other areas of interest including the discontinuous model from equation (12), the Doerner and 
Nix model from equation (8), the extracted film?s Young?s  modulus from equation (12) and the 
film alpha, or film Poisson ratio, extracted from equation (10). The Doerner and Nix model was 
added in order to compare the fit with the composite modulus data to that of the discontinuous 
model. From the figures, it is noteworthy to add that the degree of flatness of the extracted film 
alpha and Young?s modulus is an indication of how well the data matched the model. In several 
0
20
40
60
80
100
120
140
160
180
200
0 100 200 300 400 500
Modulus (GPa)
Displacement Into Surface (nm)
 39
cases, the film?s alpha would start out at lower or higher values than expected and eventually 
level out to the correct values as the indenter went further into the film. The reason for the 
deviation at first could be due to indenter losing contact with the film at first and recording errant 
stiffness values, which would then translate to higher or lower Young?s moduli.  
 
 
Figure 5.1.7 E-h curve for Au on 5 different substrates. 
 
0
50
100
150
200
250
300
350
0 100 200 300 400 500
Modulus (GPa)
Displacement Into Surface (nm)
Au on MgO
Au on Si
Au on Al2O3
Au on Ge
Au on Quartz
 40
 
Figure 5.1.8 E-h curve with discontinuous model and film E for 500nm Au on Ge with Ti 
adhesion layer. 
 
Figure 5.1.9 ?-h curve for 500nm Au on Ge with Ti adhesion layer. 
0
20
40
60
80
100
120
140
160
180
200
0 100 200 300 400 500
Modulus (GPa)
Displacement Into Surface (nm)
Au on Ge (500nm)
Discontinuous Model
Film Modulus
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 100 200 300 400 500
Film
 Alpha
Displacement Into Surface (nm)
Au Film Alpha
 41
 
 
Figure 5.1.10 E-h curve with discontinuous model and film E for 500nm Au on Si with Ti 
adhesion layer. 
 
Figure 5.1.11 ?-h curve for 500nm Au on Si with Ti adhesion layer. 
0
20
40
60
80
100
120
140
160
180
0 100 200 300 400 500
Modulus (GPa)
Displacement Into Surface (nm)
Au on Si (500nm)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 100 200 300 400 500
Film
 Alpha
Displacement Into Surface
Au Film Alpha
 42
 
 
Figure 5.1.12 E-h curve with discontinuous model and film E for 500nm Au on MgO with Ti 
adhesion layer. 
 
Figure 5.1.13 ?-h curve for 500nm Au on MgO with Ti adhesion layer. 
0
50
100
150
200
250
300
0 100 200 300 400 500
Modulus (GPa)
Displacement Into Surface (nm)
Au on MgO (500nm)
Discontinuous Model
Film Modulus
0
0.1
0.2
0.3
0.4
0.5
0 100 200 300 400 500
Film
 Alpha
Displacement Into Surface
Au Film Alpha
 43
 
Figure 5.1.14 E-h curve with discontinuous model and film E for 500nm Au on Al
2
O
3
 with Ti 
adhesion layer. 
  
Figure 5.1.13 ?-h curve for 500nm Au on Al
2
O
3
 with Ti adhesion layer. 
0
50
100
150
200
250
300
350
0 100 200 300 400 500
Modulus (GPa)
Displacement Into Surface (nm)
Au on Al2O3 (500nm)
Discontinuous Model
Film Modulus
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 100 200 300 400 500
Film
 Alpha
Displacement into Surface (nm)
Au Film Alpha
 44
 
 
Figure 5.1.15 E-h curve with Z-P model, film E, and film alpha for 2000nm Au on SiO
2
. 
 
 In order to get a better picture of how the models matched the data for SiO
2
, A plot of an 
E-h curve is shown in 5.1.16. Here, it can be seen that the data matched the discontinuous model 
early on but then dropped back down to what the D-N model would predict. The composite 
modulus increased with indentation depth at shallow indentation depths higher than the bulk 
modulus of SiO
2
 or the Au film, and then rapidly decreased to the value of the substrates 
modulus. Due to the fact that Au and SiO
2
 have similar Young?s moduli but different Poisson 
ratios, the behavior of the composite modulus is greatly affected by the Poisson ratio mismatch. 
As the indenter penetrates deeper into the film surface, the Au thin film should spread out as 
described by the films Poisson ratio of 0.44. However, the substrate has a Poisson ratio of 0.18 
which is much lower than that of Au. The discontinuity in the Poisson ratio would suggest that 
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0
20
40
60
80
100
120
0 500 1000 1500 2000
Poisson'
s Ratio
Modulus (GPa)
Displacement Into Surface (nm)
Au on SiO2
Z-P Model
D-N
Film Modulus
Film Alpha
 45
the lateral movement of the film material upon loading should be restricted by the relatively low 
ratio of the substrate. This behavior would suggest that the film could be losing adhesion with 
the substrate and delaminating from the substrate. 
 
 
Figure 5.1.16 E-h curve with discontinuous model and D-N model for 2000nm Au on SiO2. 
 
From the previous results from the Au film on SiO
2
, micrographs of the indents were 
necessary to understand how the film was behaving during indentation. A JEOL JSM 7000F 
Scanning Electron Microscope was used to gather images of indents on various indentation 
depths of Au on SiO
2
. Figure 5.1.17 shows a picture of the scanning electron microscope used to 
image the indents. 
 
 
60
70
80
90
100
110
120
0 500 1000 1500 2000
Modulus (GPa)
Displacement Into Surface (nm)
Au on SiO2
Z-P Model
D-N Model
 46
 
 
 
 
Figure 5.1.17 JEOL JSM 7000F Scanning Electron Microscope. 
 
 Images of Au films of on SiO
2 
are shown in figures 5.1.18 ? 5.1.23. The thickness of the 
Au film was approximately 2000nm and indents were made at depths of 370nm, 500nm, 800nm, 
1000nm, 1500nm and 1700nm. From the images, it can be seen that as the indenter went deeper 
into the film, the amount of pile-up around the indenter increased. At the relatively shallow depth 
of 370nm, the bowing around the edge of the indenter profile is minimal. However, as the 
indentions were made at progressively larger depths the bowing around the tip increased.  
 47
 
Figure 5.1.18 Micrograph of 2000nm Au on SiO
2
 370nm indention 
 
Figure 5.1.19 Micrograph of 2000nm Au on SiO
2
 500nm indention 
 48
 
Figure 5.1.20 Micrograph of 2000nm Au on SiO
2
 800nm indention 
 
Figure 5.1.21 Micrograph of 2000nm Au on SiO
2
 1000nm indention 
 49
 
Figure 5.1.22 Micrograph of 2000nm Au on SiO
2
 1500nm indention 
 
Figure 5.1.23 Micrograph of 2000nm Au on SiO
2
 1700nm indention 
 50
Chapter 6: Conclusions 
 
 Nanoindentation was used to investigate the substrate effect of five different substrates, 
Al
2
O
3
, MgO, Ge, Si and SiO
2
 with the same Au film on each one. The CSM method was used in 
the Nanoindentation experiments to acquire Young?s modulus versus indent depth for each film-
substrate combination. Sputtering was used in order to achieve 500 nm nanocrystaline Au thin 
films on each substrate. Upon running the indentation experiments on each film-substrate 
combination, the resulting composite modulus versus indent depth curves were compared to the 
discontinuous model to confirm the effect of the substrate on the composite modulus. When 
comparing the data with the model, the film?s modulus and Poisson ratio was extracted to 
determine how well the experimental data fit the theoretical prediction by looking at what degree 
the two parameters remained constant throughout the tests.  
 Upon comparing the experimental data with the model, it was found that the model was 
able to predict the composite modulus quite well for Au on Al
2
O
3
, MgO, Ge and Si. The 
extracted film modulus and Poisson ratio also remained flat through most of the indentation tests, 
which would suggest that the model fit with the data. However, in the case of Au on SiO
2
, the 
discontinuous model suggests that there should be an increase in the composite modulus initially, 
which the experimental data did not coincide with. The Au film on SiO
2
 did exhibit a small 
increase in composite modulus at first, but quickly dropped back down to that of the substrate?s 
bulk modulus. Upon further indentation depth, the behavior of the film-substrate combination 
returned to what the Doerner and Nix single alpha model predicted. It was concluded that Au 
film experienced delamination during indentation just after a very shallow depth. The 
delamination of the film resulted in the discontinuity at the interface not restricting the total 
strain of the film on the substrate and thus the experimental composite modulus was not as high 
 51
as expected after the initial indent depth. SEM micrographs were taken of the indents to see the 
morphology of the indents. In the case of Au on SiO
2
, it was seen that the Au film piled up 
around the indenter as the displacement increased. 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 52
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