The Pennsylvania State University The Graduate School College of Engineering

INFLUENCE OF STRAIN ON THE PHYSICAL PROPERTIES OF MATERIALS AT THE NANOSCALE

A Dissertation in Mechanical Engineering by

Mohan Prasad Manoharan

© 2011 Mohan Prasad Manoharan

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

August 2011 The dissertation of Mohan Prasad Manoharan was reviewed and approved* by the following:

M. Amanul Haque Associate Professor of Mechanical Engineering Dissertation Adviser Chair of Committee

Alok Sinha Professor of Mechanical Engineering

Adri van Duin Associate Professor of Mechanical Engineering

Tony Jun Huang Associate Professor of Engineering Science and Mechanics

Karen A. Thole Professor of Mechanical Engineering Head of the Department of Mechanical and Nuclear Engineering

* Signatures are on file in the Graduate School

ii Abstract

At the nanoscale, materials properties differ substantially from that at the bulk scale, opening new avenues for technological applications and basic science research.

Such size effects arise from dimensional and microstructural constraints, especially when specimen size coincides with the critical fundamental length scales for various physical properties. While the state of the art practice is to investigate the size effects on

„individual‟ properties (mechanical or electrical or thermal and so on), the focus of this research is to explore the size effects on the „coupling‟ among these domains. In particular, the effect of mechanical strain on various physical properties of materials at the nanoscale is studied. This is motivated by the hypothesis that very small elastic strain could be engineered in micro and nanoscale systems to „tune‟ materials properties, which is not possible at the bulk scale using strain as a parameter.

The objective of this research is to study the influence of strain on various material properties at the nanoscale, such as crystal structure, thermal and electrical conductivity, electronic bandgap and tribological properties through experimental characterization. While characterization of nanoscale materials in single domains remains the state of the art, coupled domain studies usher even stiffer challenges. This is because in addition to the difficulties in nanoscale specimen preparation, handling and properties measurement, meticulous attention has to be given to the boundary conditions for each of the domains. Another desired feature of the experimental setup is the capability for in situ high resolution microscopy so that microstructural details as well as experimental accuracy are achieved. A major contribution of this research is the development of

iii microfabricated integrated systems to perform coupled domain characterization of small scale specimens in situ in thermal (infra-red), micro-Raman and electron microscopes. In addition, conceptual modeling based on the experimental characterization was developed to explain the observed phenomena on the basis of existing nanoscale materials theories, or if none exist, suitable scientific hypothesis were proposed. The salient contributions of this research are summarized below.

a) Uniaxial tensile testing was performed on 4 - 6 nm thick amorphous carbon thin film

specimens in situ in a scanning electron microscope. The study revealed size effect on

the Young‟s modulus, which is traditionally a scale independent property. The size

effect is explained on the basis of the increased contribution of surface elastic

properties (surface stress) at the nanometer length-scale.

b) Significant stress-induced crystallization was observed in about 5 nm thick ion beam

deposited amorphous platinum thin films. At 3 % tensile strain, electron diffraction

patterns clearly show irreversible transformation to face-centered cubic (FCC)

structure even at room temperature. It is proposed that the externally applied stress, in

addition to the large tensile residual stress in the films provided the activation energy

needed to nucleate crystallization, while subsequent grain growth occurred through

enhanced atomic and vacancy diffusion as an energetically favorable route towards

stress relaxation at the nanoscale.

iv c) While it is widely accepted that amorphous materials do not exhibit any size or

deformation effects on thermal conductivity, about one order of magnitude reduction

in conductivity was experimentally observed at strains of up to 2.4 % for 50 nm thick

freestanding amorphous silicon nitride thin films. To explain this unusually strong

strain–thermal transport coupling, it is proposed that in silicon nitride, vibration

localization due to very strong Si-N bonds decreases hopping mode thermal transport.

d) The friction coefficient between individual zinc oxide nanowires and silicon substrate

in ambient conditions was measured to be about two orders of magnitude higher than

bulk values, even under zero externally applied normal loads. This anomalous

behavior is explained by the compliant nature of the nanowires and the presence of

molecularly thin surface moisture layers.

e) Effect of strain on the electronic band gap of single zinc oxide nanowires was studied

under a micro-Raman microscope by acquiring the photoluminescence spectra. The

bandgap of the nanowires was found to reduce by 25 meV per 1 % of tensile strain

applied. This red shift of the near-band-edge emission is largely due to the lowering

of the conduction band edge instead of valence band edge.

f) The thermal and electrical conductivity of polyaniline thin films was measured by the

3-omega method and four-point I-V method respectively. The conductivities were

found to reduce with increasing tensile bending strains, due to the appearance of

cracks in the film.

v Table of Contents

List of Figures viii

List of Tables xi

Acknowledgements xii

Chapter 1 Introduction 1 1.1 Material properties at the nanoscale ...... 2 1.2 Multi-domain coupling in nanoscale materials ...... 6 1.3 Challenges in materials characterization at the nanoscale ...... 8 1.4 Research contributions summary ...... 9 1.5 Outline of dissertation ...... 15

Chapter 2 Literature Review 16 2.1 Characterization of mechanical properties at the nanoscale ...... 16 2.2 Characterization of thermal conductivity at the nanoscale ...... 24 2.3 Characterization of electrical conductivity at the nanoscale ...... 30 2.4 Characterization of tribological properties at the nanoscale ...... 32

Chapter 3 Mechanical Properties of Glassy Carbon Thin Films 36 3.1 Introduction ...... 36 3.2 Properties of glassy carbon ...... 37 3.3 Synthesis of glassy carbon thin films...... 38 3.4 Experimental setup to measure Young‟s modulus ...... 39 3.5 Experimental results – Young‟s modulus ...... 44 3.6 Size effect at the nanoscale ...... 47

Chapter 4 Effect of Strain on Atomic Structure of Platinum Thin Films 49 4.1 Phase transformations ...... 49 4.2 Experimental setup for in situ TEM study ...... 51 4.3 Experimental results – amorphous to crystalline transformation ...... 55 4.4 Stress-induced crystallization in FIB-deposited platinum ...... 58

Chapter 5 Strain dependence of Thermal Conductivity of Silicon Nitride Thin Films 65 5.1 Introduction ...... 65 5.2 Device Design and Fabrication ...... 68 5.3 Experimental Procedure and Analysis ...... 72 5.4 Results and Discussion ...... 78

vi

Chapter 6 Tribological properties of individual Zinc Oxide Nanowires 86 6.1 Introduction ...... 86 6.2 Experimental setup...... 87 6.3 Experimental results and discussion ...... 92

Chapter 7 Strain dependence of Bandgap in individual Zinc Oxide Nanowires 101 7.1 Introduction ...... 101 7.2 Experimental setup and results ...... 103 7.3 Discussion of results ...... 105

Chapter 8 Strain dependence of Thermal and Electrical Conductivity of Polyaniline Thin Films 109 8.1 Introduction ...... 109 8.2 Experimental setup to measure thermal and electrical conductivity ...... 110 8.3 Measuring thermal and electrical conductivity as a function of strain ...... 112 8.4 Experimental results...... 117 8.5 Discussion of results ...... 119

Chapter 9 Conclusions and Directions for Future Research 123 9.1 Scientific and technical contributions ...... 123 9.2 Directions for future research ...... 126

References 133

vii List of Figures

Figure 1-1: Size dependence of Young's modulus in nanowires and thin films ...... 3 Figure 1-2: Size dependence of thermal conductivity in nanowires and thin films...... 3 Figure 1-3: Size dependence of electrical resistivity in nanowires and thin films ...... 3 Figure 1-4: Length scales for various physical phenomena...... 4 Figure 1-5: Freestanding glassy carbon thin film (a) before and (b) after loading to fracture ...... 10 Figure 1-6: Applied tensile strain causes platinum thin films to undergo irreversible transformation from amorphous to face-centered cubic (FCC) structure ...... 11 Figure 1-7: Experimental setup to measure strain - thermal conductivity coupling in silicon nitride thin films ...... 12 Figure 1-8: Coefficient of friction between a single zinc oxide nanowire and silicon substrate was measured ...... 12 Figure 1-9: Strain – electronic bandgap coupling was measured from photoluminescence spectra ...... 13 Figure 1-10: Effect of strain on thermal and electrical conductivity of thin films was studied ...... 14

Figure 2-1: Schematic of AFM-based three-point bending test...... 17 Figure 2-2: Schematic of a nanoindenter ...... 18 Figure 2-3: Schematic of the vibrating-reed technique ...... 20 Figure 2-4: MEMS devices that use post- buckling beam deformation for very high displacement resolution ...... 21 Figure 2-5: MEMS devices that use thermal actuator beams to apply stress on the specimen ...... 22 Figure 2-6: MEMS device with freestanding thin film specimen attached to force sensor beam and a central backbone ...... 23 Figure 2-7: Various thermal conductivity characterization techniques ...... 25 Figure 2-8: Schematic to illustrate the 3ω method for freestanding thin films ...... 26 Figure 2-9: Schematic to illustrate the membrane method ...... 29 Figure 2-10: Schematic to illustrate the bridge method ...... 29 Figure 2-11: Schematic to illustrate the photoreflectance method ...... 30 Figure 2-12: Schematic of setup for (a) 2-point and (b) 4-point probe configuration ...... 31 Figure 2-13: Equivalent electric circuit to illustrate AC complex impedance technique. 32 Figure 2-14: Schematic of friction force microscopy setup...... 34 Figure 2-15: Torsion loops observed in (a) NaCl (100) (b) polymer thin films ...... 35

viii

Figure 3-1: Schematic of the nanoscale uniaxial tensile testing device...... 40 Figure 3-2: (a) Raman spectra and (b) TEM image of freestanding GC film ...... 41 Figure 3-3: Schematic of GC specimen preparation steps ...... 42 Figure 3-4: Schematic of fabrication steps for the MEMS device...... 43 Figure 3-5: Pick-and-place technique in situ in the FIB-SEM ...... 44 Figure 3-6: SEM image of GC film (a) before and (b) after loading to fracture ...... 45 Figure 3-7: Stress-strain diagram for a 5 nm-thick freestanding glassy carbon film...... 46

Figure 4-1: Schematic showing the device fabrication steps...... 52 Figure 4-2: SEM image of MEMS device and Raman spectra of thin film specimen ..... 54 Figure 4-3: TEM image of FIB-deposited platinum before application of tensile stress. 55 Figure 4-4: SAED patterns of platinum thin film at increasing strain levels ...... 56 Figure 4-5: TEM micrograph of platinum specimen at 3% strain ...... 57 Figure 4-6: Thermal scanning microscope image of device at max. deformation...... 62 Figure 4-7: SAED pattern (a) initially, and (b) after 45 minutes of e-beam exposure ..... 63

Figure 5-1: Schematic of setup to measure thermal conductivity of Si3N4 thin films..... 69 Figure 5-2: Fabrication processing for the device integrating the actuator, specimen and heater for thermal conductivity characterization ...... 71 Figure 5-3: Multi-physics simulation model for the device...... 74 Figure 5-4: Comparison between experimental results and multi-physics simulation ..... 77 Figure 5-5: Comparison of experimental and simulation results on the temperature profile of the silicon nitride specimens with fitted values of thermal conductivity...... 77 Figure 5-6: Thermal conductivity of 50 nm thick Si3N4 films as a function of strain ...... 79 Figure 5-7: Conceptual diagram to illustrate phonon-mediated energy hopping from one fracton to another (a) at 0 % strain and (b) when tensile strain is applied ...... 83 Figure 5-8: Density of vibrational states of amorphous silicon ...... 84

Figure 6-1: Schematic of setup to measure friction and adhesion forces ...... 88 Figure 6-2: Schematic of the various stages in the experiment ...... 91 Figure 6-3: Finite element analysis of the adhesion-friction force sensor...... 93 Figure 6-4: Typical friction loading and unloading curve for ZnO nanowire on silicon . 94 Figure 6-5: Effect of nanowire contact compliance on friction-adhesion coupling...... 96 Figure 6-6: Nanowire suspended on two global peaks of a silicon substrate ...... 97 Figure 6-7: AFM scan of silicon substrate surface ...... 99 Figure 6-8: Restoring force as a function of nanowire radius ...... 100

ix

Figure 7-1: Schematic of experimental setup to strain individual nanowires ...... 104 Figure 7-2: Energy shift in NBE emission versus strain for ZnO nanowires ...... 106 Figure 7-3: Strain-dependent PL spectra in two individual ZnO nanowires ...... 108

Figure 8-1: Schematic of PANI/PET sheet subject to increasing bending strains ...... 113 Figure 8-2: Strain measurement of the bent PANI/PET sheet ...... 113 Figure 8-3: Schematic of the 3-omega setup for thermal conductivity measurement. ... 114 Figure 8-4: Conductivity as a function of strain for 20 nm thick PANI film ...... 118 Figure 8-5: Conductivity as a function of strain for 100 nm thick PANI film ...... 118 Figure 8-6: Conductivity as a function of strain for 250 nm thick PANI film ...... 119 Figure 8-7: FE-SEM images of PANI thin film under increasing bending strain ...... 120

Figure 9-1: Experimental setup to measure the effect of strain on thermal conductivity of VA-CNT ...... 127 Figure 9-2: Thermal microscope image of VA-CNT at zero strain; peak temperature is about 43 0C ...... 128 Figure 9-3: Thermal microscope image of VA-CNT at 2.8 % tensile strain; peak temperature has increased to about 66 0C ...... 128 Figure 9-4: Thermal microscope image of VA-CNT at 3.3 % compressive strain; peak temperature has increased to about 56 0C ...... 129 Figure 9-5: The silicon nanowire specimen is prepared by ion beam milling a 20 µm thick silicon beam ...... 130 Figure 9-6: Thermal microscope image to measure heat transport across the silicon nanowire ...... 130 Figure 9-7: Schematic of inter-digitated transducer array and heater patterned with 150 nm thick titanium on lithium niobate wafer ...... 132 Figure 9-8: Thermal microscope image of the inter-digitated transducers and metal heater at a frequency of 8 MHz ...... 132

x List of Tables

Table 5-1: Multi-physics modes and input parameters for the finite element model ...... 73

Table 5-2: Geometry parameters for the aluminum and silicon nitride structures ...... 73

Table 8-1: Thickness dependence of the reduction in thermal and electrical conductivity with strain in PANI thin films ...... 121

xi Acknowledgements

I take this opportunity to thank Dr. Aman Haque, my graduate advisor and mentor for his invaluable guidance and motivation throughout my time in graduate school. I thank the members of my doctoral committee for their constructive inputs and helpful insights on my research. I thank my colleagues Amit Desai and Benedict Samuel for mentoring me during my first stages of research and thank Sandeep Kumar, Md. Tarekul Alam and

Jiezhu Jin for their research collaboration that has resulted in state of the art research and several journal publications. I thank Dr. R. Rajagopalan and Dr. H. Lee of the MRI for their help in preparing the glassy carbon films and their helpful inputs on my research. I thank Bei Wang for her help with the micro-Raman measurements. The staff at the MRI nanofab – Guy Lavallee, Trevor Clark, Shane Miller and Bhangzhi Liu, warrants my sincere gratitude for their help and support with fabrication processes. I would like to thank my friends at Penn State and elsewhere (Sardi, Kushal, Ritwik, Goli, Chatty and

Chachu) for reminding me that „all work and no play make Jack a dull boy‟. Words cannot express my sincere thanks to my parents and my sister who have always been motivating and supportive of all my decisions.

The woods are lovely, dark and deep.

But I have promises to keep,

And miles to go before I sleep –

And miles to go before I sleep.

– Robert Frost

xii Chapter 1

Introduction

The key to the development of advanced microelectronics, optoelectronics, micro- electro-mechanical (MEMS) sensors and nanoscale energy conversion devices is the development of state-of-the-art materials synthesis, processing and characterization techniques that enable the use of materials at increasingly smaller length scales.

However, development of new characterization techniques suitable for lower dimensional materials has been outpaced by the explosive growth of new materials synthesis and processing techniques. This could result in questionable reliability and performance characteristics, especially for applications utilizing nanoscale materials. Strain, either externally applied or residual stress arising from synthesis methods has been found to affect various physical properties of materials, both at the bulk and nanoscale.

Researchers have long focused on methods to „tune‟ material properties using strain as a parameter. „Strained silicon‟ is a well known example used in modern microprocessors, where silicon grown epitaxially on silicon-germanium experiences tensile stresses. This increases electron mobility up to 70 % [1], providing a new route to faster electronics other than fabricating ever smaller transistors. Thus, an understanding of the influence of strain on the various physical properties of materials at the nanoscale would provide vital information necessary to ensure the performance and reliability of devices designed and fabricated based on these novel nanomaterials.

1.1 Material properties at the nanoscale

Nanoscale materials or nanomaterials can be defined as materials having features of the order of nanometers (10- 9 m) in at least one dimension. As the size of a material is reduced to the nanoscale, its properties differ significantly from that at the bulk scale.

This phenomenon has been well documented in literature for a range of material properties such as the elastic modulus [2-12], thermal conductivity [13-18] and electrical resistivity [18-22] in nanowires and thin films. Selected works from literature are shown in Figure 1-1, Figure 1-2 and Figure 1-3 to illustrate this size dependence. Such length scale dependence of material properties, known as size effect or length scale effect would seem to be in contradiction to the general understanding of material behavior at the bulk scale, where properties such as the Young‟s modulus or thermal conductivity are acknowledged to be size and mass independent. However, at the nanoscale, new phenomena begin to emerge that are typically predominant only at this scale because of a shift in the underlying physics at such small length scales. An excellent example of such a phenomenon is quantized conductance [23], which is observed only at the nanoscale. A more detailed explanation of the reasons behind this length scale dependence of Young‟s modulus, thermal and electrical conductivity at the nanoscale is discussed below.

2

Figure 1-1: Size dependence of Young's modulus in nanowires and thin films [2, 11]

Figure 1-2: Size dependence of thermal conductivity in nanowires and thin films [13, 18]

Figure 1-3: Size dependence of electrical resistivity in nanowires and thin films [18, 22]

3 As the size of a material is reduced from bulk to the micro and nanoscale, its size begins to coincide with the critical (or characteristic) length scales in materials [24], such as the phonon mean free path or Fermi wavelength (Figure 1-4) and hence its properties could be significantly different from that of the bulk because of this length scale effect.

When the size of the material and a characteristic length coincide, the configuration and energy of the atoms and molecules are different than if the atoms and molecules had been a part of the bulk [25] and this results in size dependent material properties.

Figure 1-4: Length scales for various physical phenomena [24]

4 The length scale dependence of Young‟s modulus, which increases with reducing thickness (of thin films) or decreasing diameter (in the case of nanowires) is primarily due to a surface stiffening effect accompanied by significant bond length contractions occurring at the surface of nanowires and thin films [2, 4, 5]. The surface atoms have a lower coordination number, which causes the remaining bonds of these surface atoms to relax, thus raising the binding energy. As a result, more energy is required to deform the surface layer of atoms, and is typically the predominant factor in increasing the elastic modulus in nanowires with smaller diameter [2]. Another reason is the effect of grain boundary compliance [26, 27], which scales up for nanocrystalline materials since the grain boundary area to grain volume ratio increases nonlinearly. In addition, grain boundary mediated processes (such as sliding, rotation) contribute significantly towards softening the material [28, 29].

Size effects on thermal conductivity become important when the thickness or diameter of the nanomaterials becomes comparable to the mean free path or wavelength of the primary heat carrier in the material - phonons in semiconducting and dielectric materials and electrons in the case of metals [15]. The probability of collision between phonons or phonon-phonon interaction increases with the reduction in thickness due to the confinement, which reduces the efficiency of heat conduction [30]. The enhanced surface-to-volume ratio at the nanoscale also increases the surface boundaries [14, 16], interfaces [30] and grain boundaries causing increased electron and phonon scattering, which inhibits thermal transport and reduces the thermal conductivity. In the case of amorphous films, where the phonon mean free path is on the order of mean inter-atomic

5 spacing, the microstructure, especially mass density and stoichiometry, which are dependent on processing conditions, play an important role in thermal conductivity [15].

In organic films, the volumetric heat capacity also decreases due to atomic-scale disorder, porosity, partial crystallinity and molecular orientation [30].

The thickness dependence of electrical conductivity arises due to increase in the number of electrons scattered by phonons, reflected by grain boundaries, or diffusely reflected by the film surface [31]. In addition, surface roughness also affects electrical conductivity [19]. Fuchs [32] provided the first theoretical analysis to characterize the influence of electron scattering from the surface on the electrical conductivity of metal thin films, which was extended to the case of wires by Dingle [33]. Mayadas and

Shatzkes [34] further generalized this model by adding the influence of grain boundaries on thermal conductivity and is known as the MS model.

1.2 Multi-domain coupling in nanoscale materials

A consequence of the length scale effect is enhanced „coupling‟ between different material properties at the nanoscale. While such coupling exists at the bulk scale, the overlap of material size and the characteristic length scale associated with different physical properties makes this coupling dominant at the nanoscale. Nanomaterials such as nanowires and ultra thin films have several important technological applications as nanogenerators [35], gas sensors [36], field emission transistors [37], optical memory devices, thin film transistors and nanoscale sensors [38], where the operating conditions would involve an interaction between different material properties. An understanding of

6 the coupling effect would help in designing better devices and discovering unique behavior that could lead to novel applications. „Strained silicon‟ used in modern microprocessors is the best known example of a practical application of such nanoscale coupling effects. Silicon grown epitaxially on silicon-germanium experiences tensile stresses; this increases electron mobility up to 70 % [39], providing a new route to faster electronics other than fabricating ever smaller transistors. While characterization of nanoscale material properties in single domains remains the state of the art in the literature, coupled domain studies pose even stiffer challenges. This is because in addition to the difficulties in nanoscale specimen preparation, handling and properties measurement, meticulous attention has to be paid to the boundary conditions for each of the domains.

Strain, either externally applied or residual stress arising from the synthesis methods, has been found to affect various physical properties of materials, especially semiconductors, both at the bulk and nanoscale. For instance, the size of interconnects and junctions used in current semiconductor-based chips is in the nanometer range [40] and thermal gradients present during typical operating conditions result in thermal stresses in the nanowire components. An understanding of the thermo-mechanical response of the nanowire interconnects would provide guidelines to a better design.

Despite its importance, there are very few comprehensive studies available in literature on the influence of strain on material properties at the nanoscale. Available literature is largely limited to computational simulations, such as the effect of strain on the thermal conductivity of silicon nanowires [41], germanium nanowires [42], carbon nanotubes

7 [43] and graphene [44]. The main contribution of this research is the experimental characterization of the influence of strain on various material properties at the nanoscale, such as crystal structure, thermal and electrical conductivity, electronic bandgap and tribological properties.

1.3 Challenges in materials characterization at the nanoscale

The primary technological contribution of this research was developing a framework and methodology for experimental characterization of multi-domain coupling at the nanoscale, specifically, to study the influence of strain on various material properties of thin films and nanowires. At the nanoscale, specimen fabrication and manipulation, especially of single nanowires or ultra thin films is challenging, in addition to the stringent requirements on resolution imposed on the equipment used to measure material properties. While characterization of material properties at the nanoscale in general has its set of challenges, coupled domain studies add further layers of complexity.

This is because, in addition to the difficulties in specimen preparation, handling and high measurement resolutions, meticulous attention has to be paid to the boundary conditions for each of the domains. For instance, when studying the piezoelectric, piezoresistive or thermo-mechanical properties of thin films and nanowires, the proper strain mode needs to be applied. For the above mentioned coupled field interactions, uniaxial tensile loading is the preferred experimental technique, since it excludes the effects of non-planar stress, strain fields and strain gradients [25]. The length scale associated with nanowires and thin films, however demands a complex experimental setup that can maintain specimen

8 alignment and gripping during uniaxial tensile loading, in addition to high resolution force and displacement sensing and actuation capabilities.

Typically, for experiments at the nanoscale, it is important for the specimen to be monitored in real-time for specimen integrity and boundary conditions. In situ experiments provide real-time visualization of the experiment and present both qualitative and quantitative information. However, in situ experiments pose constraints in terms of space available inside or under microscopes, especially, in the case of transmission electron microscopes. A conscious effort was therefore made to design experimental setups such that the experiments could be performed in situ in microscopes, whether it be electron, micro-Raman, thermal or optical microscope.

1.4 Research contributions summary

In this research, the effect of strain, either uniaxial tensile or bending tensile strain, on the crystal structure, thermal and electrical conductivity, electronic bandgap and tribological properties of thin films and nanowires was studied. The scientific contributions of this research are as follows:

a) Uniaxial tensile testing was performed on 4 - 6 nm thick amorphous carbon thin film

specimens in situ in a scanning electron microscope (Figure 1-5). The study revealed

size effect on the Young‟s modulus, which is traditionally known to be scale

9 independent. The size effect is explained on the basis of the increased contribution of

surface elastic properties (surface stress) at the nanometer length-scale.

Figure 1-5: Freestanding glassy carbon thin film (a) before and (b) after loading to fracture

b) Significant stress-induced crystallization was observed in about 5 nm thick ion beam

deposited amorphous platinum thin films. At 3 % tensile strain, electron diffraction

patterns clearly show irreversible transformation to face-centered cubic (FCC)

structure even at room temperature. It is proposed that the externally applied stress, in

addition to the large tensile residual stress in the films provided the activation energy

needed to nucleate crystallization, while subsequent grain growth occurred through

enhanced atomic and vacancy diffusion as an energetically favorable route towards

stress relaxation at the nanoscale.

10

Figure 1-6: Applied tensile strain causes platinum thin films to undergo irreversible transformation from amorphous to face-centered cubic (FCC) structure

c) Thermal conductivity of 50 nm thick freestanding amorphous silicon nitride thin

films was found to reduce by about one order of magnitude at strains of up to 2.4 %.

This finding contradicts the literature, where it is believed that amorphous materials

do not exhibit any size or deformation effects on thermal conductivity. To explain

such strong coupling with mechanical deformation, vibration localization in the

disordered medium needs to be taken into account. Here, heat transfer is possible only

through hopping (from one localized frequency to other) based mechanisms. The very

strong Si-N bonds make the localization even stronger, and mechanical deformation

is proposed to decrease the overlap of the vibrational mode localization. This reduces

the hopping mode thermal transport.

11

Figure 1-7: Experimental setup to measure strain - thermal conductivity coupling in silicon nitride thin films

d) The friction coefficient between individual zinc oxide nanowires and silicon substrate

in ambient conditions was measured to be about two orders of magnitude higher than

bulk values, even under zero externally applied normal loads. This anomalous

behavior is explained by the compliant nature of the nanowires and the presence of

molecularly thin surface moisture layers.

Figure 1-8: Coefficient of friction between a single zinc oxide nanowire and silicon substrate was measured

12 e) Effect of strain on the electronic band gap of single zinc oxide nanowires was studied

under a micro-Raman microscope by acquiring the photoluminescence spectra. The

bandgap of the nanowires was found to reduce by 25 meV per 1 % of tensile strain

applied. This red shift of the near-band-edge emission is largely due to the lowering

of the conduction band edge instead of valence band edge.

Figure 1-9: Strain – electronic bandgap coupling was measured from photoluminescence spectra

f) The thermal and electrical conductivity of polyaniline thin films was measured by the

3-omega method and four-point I-V method respectively. The conductivities were

found to reduce with increasing tensile bending strains, due to the appearance of

cracks in the film.

13

Figure 1-10: Effect of strain on thermal and electrical conductivity of thin films was studied

The technological contributions of this research were in developing a framework and methodology for experimental characterization of the influence of strain on various material properties of thin films and nanowires. Experimental setups were developed to:

a) Study the influence of strain on the crystal structure of thin films in situ inside a

transmission electron microscope b) Measure thermal conductivity of thin films using thermal microscopy c) Measure the tribological properties of individual nanowires d) Measure the strain dependence of electronic bandgap in individual nanowires e) Measure strain - thermal conductivity coupling in thin films using 3-omega method

14 1.5 Outline of dissertation

In the following chapter, current experimental techniques reported in literature for material characterization at the nanoscale are introduced along with their advantages and limitations. An experimental setup to measure the Young‟s modulus of thin films with thickness of few nanometers is introduced in the third chapter and demonstrated for glassy carbon films of thickness 5 nm and the observed size effect is explained. In the fourth chapter, an experimental setup developed to study the influence of strain on the crystal structure of thin films in situ in a transmission electron microscope is introduced and demonstrated for ion beam-deposited platinum thin films. In the subsequent chapter, a technique developed to measure thermal conductivity of thin films using thermal microscopy is explained and the effect of strain on the thermal conductivity of silicon nitride thin films is presented. A unique setup developed to measure the tribological properties of individual nanowires is presented in the sixth chapter and is demonstrated for zinc oxide nanowires. In the seventh chapter, the strain dependence of bandgap in individual zinc oxide nanowires is discussed. Thermal conductivity measurement of thin films using the 3-omega method is introduced in the eighth chapter and the effect of strain on the thermal and electrical conductivity of polyaniline thin films is discussed. In the final chapter, conclusions from this research and directions for future research are presented.

15 Chapter 2

Literature Review

2.1 Characterization of mechanical properties at the nanoscale

At the bulk scale, the most straightforward and popular method used to measure the mechanical properties of materials such as Young‟s modulus, yield strength, ultimate strength, is uniaxial tensile testing with dog-bone shaped specimens. However, experimental characterization of mechanical properties at the nanoscale poses several challenges due to the stringent requirements of high resolution force and displacement sensing, the need to perform in situ experiments and the lack of reliable and robust techniques for specimen preparation [25]. The various techniques for characterization of thin film mechanical properties available in literature are discussed in this chapter.

2.1.1 Atomic force microscope-based techniques

Atomic force microscope (AFM)-based techniques have been the workhorse for mechanical characterization studies due to their high force and displacement resolution.

An AFM has a low stiffness microscale cantilever with a sharp tip at its end. When the tip is in contact with a surface, its displacement is measured by focusing a laser beam on the tip and tracking the reflected beam using a four-quadrant photodiode (Figure 2-1). To test the mechanical properties of a thin film, the film is suspended across a trench and deflected downwards using the AFM tip (Figure 2-1), subjecting the film to a three-point

16 bending loading. By monitoring the tip deflection, the force and displacement modulus of the film can be calculated.

Figure 2-1: Schematic of AFM-based three-point bending test

This technique has been successfully applied to thin films [45, 46] and nanowires

[47-51]. AFM-based techniques provide superior force and displacement resolution, but the technique in its basic form lacks in situ capabilities. In situ experiments provide for direct visualization and description of the events as they happen, and give qualitative information about the mechanics of deformation along with quantitative data. In addition in situ experimentation also ensures integrity and accuracy of the experimental procedure and boundary conditions, which is critical in nanoscale mechanical characterization.

17 2.1.2 Nanoindentation

Indentation is a standard technique for estimating mechanical properties of materials at the bulk scale and has been used for measuring hardness of materials like

Brinell hardness and Vickers hardness. In a typical indentation test, a hard tip, generally made of diamond, is pressed into the sample with a known load, and then the load is removed. The material hardness is estimated from the residual indented area and the maximum applied load. This technique has been adapted for mechanical characterization of nanostructures, and is known as „nanoindentation‟. The schematic of a nanoindenter is shown in Figure 2-2. A sharp indentation tip is driven into a substrate and the forces and displacements are captured during loading and unloading. A controlled load is applied using magnets and coils and the indenter displacement is measured by capacitive sensors.

The mechanical properties of the substrate indented are then estimated based on the loading and unloading curves.

Figure 2-2: Schematic of a nanoindenter [52]

18 This technique has been used to measure the Young‟s modulus of thin films [53,

54] and nanowires [55-59]. The technique as described above lacks in situ capabilities, but a modified setup was developed [60] to observe material deformation inside a TEM.

The technique‟s main limitations are sensitivity to the substrate, known as substrate effect and gradient-dominant deformation, which makes data interpretation and modeling difficult [61]. It also introduces highly localized compressive deformation that may not be representative of the entire specimen [62].

2.1.3 Resonance-based techniques

The vibrating-reed method is a popular resonance-based technique used to measure the elastic modulus of thin films [63-66]. In this technique, a bi-layer of the thin film material and the substrate is fabricated in the form of a cantilever, which is then electrostatically or magnetically vibrated. The change in the resonant frequency of the cantilever due to the presence of the thin film coating can be used to calculate the

Young‟s modulus of the thin film. The main limitations of this technique are that it cannot provide data to determine mechanical properties such as yield stress and ultimate stress, the complex fabrication procedure for the cantilevers and wrinkling of the thin film due to residual strains between the film and the substrate [63], which adversely affects the data.

19

Figure 2-3: Schematic of the vibrating-reed technique [63]

2.1.4 MEMS-based techniques

Micro-electro-mechanical systems (MEMS) based experimental techniques are ideally suited for mechanical characterization of nanoscale materials in general, because their small size enables in situ experimentation inside a scanning or transmission electron microscope. They can be designed to apply pure uniaxial loading on the specimen, which can be challenging to achieve with the other techniques discussed previously in this chapter. Uniaxial tensile testing is a preferred technique for determining the elastic modulus as the data interpretation is straightforward. Researchers have used a wide variety of MEMS-based devices to study the mechanical properties of thin films [67-71].

The major challenges in applying this technique at the nanoscale are fabrication of a freestanding specimen, gripping and accurate alignment of the specimen along the axis of force application and generation and measurement of forces and displacements with a high resolution [67]. Actuation principles commonly used in MEMS devices for measuring elastic modulus and other mechanical properties are discussed below.

20 MEMS devices that employ post-buckling deformation of beams for very high displacement resolution were developed by Desai et al. [72-74]. The sensing and actuation scheme of the device is purely mechanical in nature and hence can be used for studying strain effects on the electrical and thermal properties of nanowires. The main disadvantage of this technique is the need to pick-and-place the specimen on to the device, typically in situ in a SEM.

Figure 2-4: MEMS devices that use post- buckling beam deformation for very high displacement resolution [72-74]

21 MEMS devices that use thermal actuators to apply stress on the specimen have been used to measure the elastic properties of thin films [75, 76]. Here, the specimen is mounted between a load sensor and a central shuttle that is attached to a set of beams inclined at a small angle to the shuttle. The beams are micromachined from heavily doped silicon-on-insulator wafers. When a current is applied across the thermal actuator beams, they expand due to Joule heating and the geometry of the beams results in a uniaxial stress on the specimen and the force sensor. In this device type, the specimen can be co-fabricated with the device or can be integrated by the pick-and-place technique after the device is fabricated.

Figure 2-5: MEMS devices that use thermal actuator beams to apply stress on the specimen [75, 76]

22 In another category of devices [67, 70], the freestanding thin film specimen is co- fabricated with a force sensor beam made of single crystal silicon and the other end of the specimen is attached to a central backbone with a supporting beam assembly. The two ends of the device are connected by the central backbone and a pair of U-springs and the chip is attached to a piezo-actuator at either end. As the piezo-actuator applies a load on end of the chip, quasi-static displacements are transmitted to the specimen and the force sensor. The adhesion between the specimen and silicon acts as the gripping mechanism.

The supporting beams attached to the central backbone prevent rotation of the specimen ends and thereby minimize bending moment on the specimen.

Figure 2-6: MEMS device with freestanding thin film specimen attached to force sensor beam and a central backbone [67, 70]

23 2.2 Characterization of thermal conductivity at the nanoscale

With the trend towards miniaturization in electronics, the use of conducting thin films as components is increasing exponentially. The operating conditions of these devices include varying thermal conditions and heat transfer in thin film components plays a critical role in the performance and reliability of these devices. Hence it is important to study the heat transfer characteristics of ultra thin films that are expected to be in use in light of the continuous reduction of size in microelectronics. Current literature on the thermal properties of such ultra thin films is rather limited in literature.

Thermal conductivity measurements of thin film are often complicated by the presence of a substrate which provides mechanical or structural stability. Typically, in such cases, the conductivity of the combined system is measured and the properties of the substrate are

„subtracted‟ in order to ascertain the properties of the specimen film [30]. If a steady state conduction method is used to measure conductivity, errors arise due to parasitic heat flow through the substrate and radiation losses from the specimen. If the conductivity of the substrate is much larger than the specimen, then total heat flow through the substrate will be larger than that through the specimen and subtracting the substrate‟s contribution to heat conduction will significantly magnify errors in measurement. On the other hand, if the conductivity of the substrate is low, radiation losses from the specimen surface could dominate heat flow through the specimen and uncertainty of this heat transfer component will introduce errors in the conductivity measurement of the combined substrate – specimen system [77, 78]. The techniques used to study the thermal properties of nanomaterials in general are discussed in this section. For the sake of brevity, only techniques used/adapted for in-plane thermal conductivity (Figure 2-7) measurements

24 will be discussed here. In an in-plane thermal conductivity experiment, heat flow parallel to the film plane is measured while cross-plane thermal conductivity techniques measure the heat transfer perpendicular to the film plane.

Figure 2-7: Various thermal conductivity characterization techniques

The techniques are categorized based on the heating and temperature sensing methods. The symbols adjacent to each method indicate the direction - in-plane (||), cross- plane (┴) or both along which thermal conductivity can be measured [79]).

2.2.1 The 3-omega (3ω) technique

The 3-omega method is a widely implemented technique used to measure the thermal conductivity of thin films [80-83], usually in the cross-plane direction, but has been adapted for in-plane conductivity measurements of freestanding membranes [79].

For ultra-thin films, heat transfer can be approximated to a model of one-dimensional

25 heat conduction and in-plane thermal conductivity is the relevant parameter. In a typical

3ω experiment for an electrically insulating specimen, a thin, electrically conductive wire, usually metallic is deposited onto the specimen whose thermal conductivity needs to be measured [84-86]; the wire serves as heater and temperature sensor. In the case of an electrically conductive specimen, the specimen itself serves as both heater and temperature sensor. When an alternating current, I = I0 sin(ωt) is applied across the specimen, it causes a temperature fluctuation with frequency 2ω and consequently, a resistance fluctuation of 2ω. This, in turn leads to a voltage fluctuation of 3ω across the specimen, which can be used to calculate the thermal conductivity of the specimen [87].

Figure 2-8: Schematic to illustrate the 3ω method for freestanding thin films

Cahill [84] popularized the 3ω method for measuring the cross-plane thermal conductivity of thin films. The cross-plane conductivity, κ of the specimen is given by:

3  f  V ln  2   f1  dR   2  (1) 4lR V3,1 V3,2  dT

where, V is the voltage across the metal line at frequency ω, and V3ω,1 and V3ω,2 are the in- phase third harmonic of the voltages at frequencies f1 and f2 respectively, l is the length of

26 the metal heater line and R is the average resistance of the metal heater line. dR/dT is the resistance derivative of temperature. The temperature oscillation is given by [84]

dT R T  4  V (2) dR V 3

Lu et al. [87] developed a model which applies the 3ω principle to the 1D heat conduction equation, which has been successfully applied to the study of thermal properties of silicon nanowires [88] and carbon nanotubes [89]. Jin et al. [90] further generalized this model for the case of thin films on a substrate. In this model, the relationship between the third harmonic of the voltage, V3ω and in-plane thermal conductivity, κ is given by [90]

2 2I 3 R R ' L V  0 0 (3) 3  2 LA  4S   Rt

The average temperature change of the specimen [90] can be expressed as

8I 2 R L T  0 0 (4)  2 LA  4S   Rt where I = I0 sin(ωt) is the sinusoidal current applied across the specimen, R0 is the initial electrical resistance of the specimen at initial temperature T0, R’ is the resistance derivative of temperature, R' dR dT  . L and S are the length between the voltage T0 contacts and the cross-section of the specimen, respectively and A is the contact area between the specimen and substrate. The heat loss to the substrate is taken into account by considering the thermal resistance ΣRt, where Σ Rt = Rt,cont-int. + Rt,cond-sub, i.e., the sum of contact resistance at the interface (Rt,cont-int.) and conduction resistance within the

27 substrate (Rt,cond-sub). Thermal resistance from the substrate can be approximated

as, Rt,cond sub  s  s , where s   s / 2 , is the thermal penetration depth in the

substrate,  s is the thermal diffusivity and  s is the thermal conductivity of the substrate.

Widespread application of this model is limited by the challenge of measuring the relatively small 3ω signals that are typically three orders of magnitude lower than the amplitude of the applied voltage [79].

2.2.2 Membrane and Bridge methods

A schematic to illustrate the membrane method for in-plane thermal conductivity characterization is shown in Figure 2-9. A membrane is supported around its boundaries or edges by a frame, usually much larger than the dimensions of the membrane.

Typically, this frame is the substrate, which also acts as a heat sink. Thin, narrow strips of electrically conductive material, usually a metal, are deposited on the membrane, which acts as a heater and temperature sensor when a current is passed through it. The heat generated from the heater spreads from the middle of the membrane toward its edges and the temperature profile is detected by one or more metal strips which act as thermometers because of their temperature-dependent electrical resistance. The experiments are performed in vacuum to minimize convection losses. The temperature response of the membrane under steady-state, pulsed, and modulation heating, coupled with appropriate heat transport modeling, can be used to determine the thermal conductivity, thermal diffusivity, and heat capacity of the membrane [79, 91].

28

Figure 2-9: Schematic to illustrate the membrane method [79]

When the thin film specimen to be tested is electrically conductive, it can serve both as a heater and temperature sensor when current is passed through it. This technique, called the bridge method to measure in-plane thermal conductivity is illustrated by a schematic in Figure 2-10. The thin film is patterned as a thin strip bridging the gap between two heat sinks, typically the substrate. The temperature rise of the heater is determined by measuring the change in its electrical resistance. Similar to the membrane method, experiments are performed in vacuum to minimize convection losses. The temperature response of the strip under steady-state, pulsed and modulation heating, coupled with appropriate heat transport modeling, can be used to determine the thermal conductivity, thermal diffusivity, and heat capacity of the thin film [79, 92].

Figure 2-10: Schematic to illustrate the bridge method [79]

29 2.2.3 Photoreflectance method

In this frequency domain method, a continuous-wave heating laser, such as argon or diode laser (the pump) is periodically modulated while focused on the thin film. The small periodic changes in the intensity of the reflected beam of another continuous wave laser (the probe) are monitored continuously. This modulation in the reflectance arises from the temperature dependence of the refractive index of the specimen [79]. Typically, the modulation is slow such that the probe laser and pump laser sources are different and the pump laser signal can be filtered out before the signal reaches the detector (Figure

2-11). This method has been used to measure the thermal diffusivity of thin films [93].

Figure 2-11: Schematic to illustrate the photoreflectance method

2.3 Characterization of electrical conductivity at the nanoscale

2.3.1 DC two-point and four-point probe methods

The DC two-point and four-point probe measurement techniques are the most widely used techniques to characterize electrical conductivity of thin film structures. In the two-point technique (Figure 2-12a), a direct current is passed across the length of the

30 specimen (at two probes) and the voltage is measured across the same length (same probes). Electrical resistivity can then be calculated by plotting the I-V curves. This is a relatively simple and straightforward technique that has been widely used for thin films

[94-97]. In a four-point probe experiment (Figure 2-12b), direct current is applied across two outer probes in the specimen, while the voltage across the specimen is measured across two inner probes. Electrical resistivity can then be calculated by plotting the I-V curves. The probes are made of high conductivity materials (metal coatings) to minimize electrical contact resistance between the probe and leads. The advantages of this method over the traditional two-point probe technique, viz. insensitivity to contact resistances is well documented [98, 99]. This technique has been applied to measure the electrical resistivity of thin films [97, 100-102].

Figure 2-12: Schematic of setup for (a) 2-point and (b) 4-point probe configuration

2.3.2 AC complex impedance technique

The experimental setup for the AC complex impedance technique is similar to the

DC two-point probe technique in that current, in this case, alternating current is passed across the length of the specimen and the voltage measured across the same length of the

31 specimen. This is illustrated in Figure 2-13, where an equivalent circuit diagram is used in lieu of the usual schematic diagrams. The specimen is represented by its impedance Zs.

This technique is not as widely applied [102, 103] as the DC probe techniques, but is useful in certain cases, such as asymmetric metal-insulator configurations, which may have rectifying characteristics or for ferroelectric composite materials that may exhibit polarization reversal [104].

Figure 2-13: Equivalent electric circuit to illustrate AC complex impedance technique. The specimen is represented by its impedance Zs.

2.4 Characterization of tribological properties at the nanoscale

Friction measurements at the macroscopic scale employ averaging methods and are highly dependent on the smoothness and disorder of the contacting surfaces. At the nanoscale, contacts are typically atomically smooth and highly ordered, and averaging methods do not provide as complete a picture as measurements on individual nanoscale systems. Probing friction at atomically smooth contacts also eliminates effects such as roughness and wear and can thus help in better understanding the fundamental origins of friction [105]. For instance, in nanowires (length scale, l), surface forces such as adhesion

32 and friction forces (scales as l 2) are more dominant than bulk forces such as gravity

(scales as l 3) [106] and thus provide an ideal testing platform to better understand the underlying physics. Researchers have studied particle-surface interactions by measuring the force required to displace a particle from its adsorbed location [107-109] and the relationship between adhesion and friction at the molecular level by studying nanoscale particle moving along a surface [110, 111]. Experimental techniques to measure the coefficient of friction at the nanoscale can be broadly categorized into two categories:

1) methods based on the atomic force microscope (AFM) [112-116], friction force

microscope (FFM) [117, 118], surface force apparatus [119, 120] and

nanoindentation [121]

2) custom micro-machined friction and adhesion characterizing tools [122-125]

Among the first group of methods, FFM and AFM-based methods are the most widely adopted for thin film friction characterization. The principle of AFM has been explained in section 2.1.1. A typical experimental setup using FFM will be discussed in this section. Also, the second group of methods that use custom micro devices is too broad a research area to be able to summarize here.

Friction force microscopy is based on a modified-AFM that can be used to measure both the vertical (normal) and lateral (friction) forces in contact mode imaging.

To measure friction forces, the specimen is „imaged‟ in contact mode, usually with constant force and the lateral deflections are recorded (Figure 2-14) which corresponds to

33 the „friction image‟. Typically, a topographic image is also recorded simultaneously by measuring the feedback signal needed to maintain constant force. This is done to compare the topographical and tribological features from the friction image [126].

Figure 2-14: Schematic of friction force microscopy setup [126]

A characteristic feature of friction force images is the friction or „torsion‟ loop

(Figure 2-15), which is caused by the stick-slip motion of the tip and the hysteresis effect depending on the scanning direction. This is because, while “sticking” occurs at the same locations on the surface, the location of „slip‟ is dependent upon the direction of motion of the tip [126]. The torsion loop is used to calculate the friction force and when combined with information on normal load (known from the topographic image), the coefficient of friction can be calculated.

34

Figure 2-15: Torsion loops observed in (a) NaCl (100) [127] (b) polymer thin films [128]

The accuracy of results from this technique are largely dependent on proper characterization of the stiffness or spring constants of the cantilever tip, as this is used to calculate both the normal and friction forces. Typically, to calibrate the bending stiffness

(normal loads) and torsional rigidity (friction forces) of the cantilever, the tip dimensions are measured in a SEM and the thickness from the resonance frequency [126].

35 Chapter 3

Mechanical Properties of Glassy Carbon Thin Films §

3.1 Introduction

Glassy carbon is a class of non-graphitizing carbon [129] and in bulk form has been commercially used as an electrode material for over half a century due to its excellent thermal stability and chemical resistance. Glassy carbon (GC) prepared by the pyrolysis of certain polymeric precursors are nanoporous and can act as molecular sieves leading to potential applications in air separation [130] and catalysis [131]. These properties also make it more suitable than zeolite molecular sieves for applications such as catalyst supports and as selective adsorbents in high temperature [132] and corrosive environments [133]. Its thermal stability has led researchers to suggest it as a possible material for capture and sequestration of carbon dioxide from industrial processes [134].

At the bulk scale, glassy carbon has the electrical properties of an intrinsic semiconductor with „impurity levels‟ and its conductivity increases with increasing temperature [135].

Glassy carbon derived by pyrolysis of the polymer precursor polyfurfuryl alcohol

(PFA) is nanoporous [133], with a pore width in the range of 0.4 – 0.5 nm [136].

Pyrolysis of PFA results in a highly disordered structure, resulting in porosity. The material has regions of crystalline order, which are typically of short range and on a

§ Contents of this chapter are based on the following journal publication; Manoharan, M. P., Lee, H., Rajagopalan, R., Foley, H. C., Haque, M. A., Elastic properties of 4-6 nm-thick Glassy Carbon Thin Films, Nanoscale Research Letters, 2009

36 global scale it can best be described as amorphous. The disorder causes the material to be non-graphitizing since it resists transformation to long-range graphitic structures even at temperatures as high as 2000 0C [133]. This non-graphitic nature has been attributed to the extensively cross-linked structure of the polymer precursor, which results in a kinetically frozen disorder due to a chaotic misalignment of defective graphene sheets upon pyrolysis [137].

3.2 Properties of glassy carbon

Due to their unique application potentials, the thermo-physical properties of glassy carbon have been extensively studied, but only in their bulk form [10-12].

However, nanoporous glassy carbon can also be synthesized in the form of thin films with thickness of few nanometers by choosing an appropriate concentration of the polymer precursor; in this study PFA has been used. Such ultra-thin films are expected to exhibit pronounced size effects on their physical properties because of the large fracture of unccordinated surface atoms and the inherent porosity, yet only a few studies are available for micro [138] and nanoscale [139] glassy carbon structures, with the smallest size around 150 nm. This is because, at a length-scale of 5 nm, specimen fabrication, manipulation, gripping and alignment of the specimen required to achieve the desired boundary conditions for mechanical testing are challenging, not to mention the stringent resolution requirements on force and displacement application and measurement.

While no such study exists for glassy carbon at this length-scale, literature contains a few investigations on the mechanical properties of single [45] and multi-layer

37 [46] graphitic carbon (graphene) films. These studies use nano-indentation and atomic force microscope (AFM) tip-based three-point bending, respectively. Both these techniques are popular tools used by researchers to measure the Young‟s modulus of nanoscale materials. However, nano-indentation on such ultra-thin specimens requires complex data de-convolution [140-142]. It also introduces highly localized deformation that may not be representative of the entire specimen [62]. AFM tip-based three-point bending requires an extensive understanding of the tip-thin film interaction for accurate and reliable experimental studies. For example, friction (due to slipping) and van der

Waals forces between the thin film and tip will introduce errors in measurement of mechanical properties. The influence of these surface forces on the mechanical properties have been shown to be very significant in the case of small diameter nanowires (less than

30 – 40 nm) [106] and can be expected to have the same effects while measuring the elastic properties of ultra-thin films. Also, in the above experiments a fixed-fixed beam boundary condition was assumed, even though only van der Waal‟s forces were used to provide the gripping on the substrate.

3.3 Synthesis of glassy carbon thin films

Glassy carbon can be synthesized in the form of thin films whose thickness can be controlled by choosing an appropriate concentration of the polymer precursor [116]; in this research, PFA-derived films are used. Films with thickness as low as 4-6 nm have been obtained with three different precursors – PFA, photoresist and coal-tar pitch [116].

As outlined in chapter 1, the objective of this research is to study the strain dependence of

38 nanoscale material properties; in these respects, ultra thin films of glassy carbon have all the desirable qualities needed for this study.

3.4 Experimental setup to measure Young’s modulus

Nano-indentation and atomic force microscope (AFM) tip-based three-point bending are popular techniques to measure the elastic properties of materials at the nanoscale, but have significant shortcomings as described in chapter 2. In this study, uniaxial tensile testing is used to measure the elastic properties of glassy carbon thin films under uniform deformation. The technique is relatively straightforward as no assumptions or complicated models are needed to measure the Young‟s modulus, fracture stress and fracture strain of the material.

A micro-electro-mechanical device was designed and fabricated to apply uniaxial tensile stresses on the freestanding thin film specimen. Figure 3-1a shows the device design, where the specimen is mounted between a flexure beam force sensor and a set of

1 inclined thermal actuator beams. The beams are micromachined from heavily doped silicon-on-insulator wafers with resistivity of 0.001-0.005 Ω-cm. The thermal actuator beams expand due to Joule heating upon application of a DC voltage, which loads the specimen and the force sensing beam. The force on the specimen can be obtained from the force equilibrium diagram shown in Figure 3-1b. If the stiffness values of the force sensor and the specimen are kfs and ksp respectively, then the elongation (δspecimen) and force (Fspecimen) in the specimen are given by,

39  24       ; F  k     (3.1) specimen 1 2 specimen fs 2  3  2  L fs  where δ1 and δ2, are displacements in the thermal actuator and force sensing beams respectively and κ is the in-plane flexural rigidity of the force sensing beam. Figure 3-1c shows a scanning electron microscope (SEM) image of a fabricated device.

(c)

Figure 3-1: Schematic of the nanoscale uniaxial tensile testing device.

Figure (a) shows the thermal actuator and integrated force and displacement sensing beams (not to scale) (b) spring equivalent of the specimen-device system and (c) SEM image of the device.

To test specimens with different aspect ratios (length-to-width ratio), the specimens are fabricated separately from the device. The 4 - 6 nm thick glassy carbon thin film specimens used in this study were synthesized by pyrolyzing PFA precursor at

800 0C on a silicon substrate coated with a 500 nm thick thermally grown silicon dioxide

(silica) layer. Details of the synthesis and thickness characterization are given elsewhere

[3, 9, 22]. The Raman spectrum was measured for a 5 nm thick freestanding glassy

40 carbon film to verify the structural characteristics of the carbon film. Figure 3-2a shows the results, where the prominent peaks in the spectrum are the G peak at 1580 cm-1 and D peak at 1350 cm-1, which confirms the formation of polyaromatic domains. In polyaromatic structures, the G peak represents the Raman-active E2g in-plane vibration mode and the presence of disorder in the structure is indicated by the D peak, which represents the A1g in-plane breathing mode [116]. The ratio of the intensity of these peaks, ID/IG, is called the relative peak intensity ratio and can be correlated to the reciprocal of the crystalline size along the basal plane, La , which was measured to be 7.5 nm. A transmission electron micrograph (Figure 3-2b) reveals the disordered structure of the polyaromatic domains in glassy carbon.

Figure 3-2: (a) Raman spectra and (b) TEM image of freestanding GC film Scale bar is 20 nm

3.4.1 Specimen preparation

Tensile testing specimens, 100 µm long and 10 µm wide, were patterned using photolithography (Figure 3-3a). The glassy carbon layer was etched by oxygen plasma

(Figure 3-3b), exposing the underlying silica layer, which was then anisotropically etched

41 by the reactive ion etching tool (Figure 3-3c). Next, the silicon substrate was isotropically etched using xenon difluoride, resulting in freestanding bi-layer beams of glassy carbon and silica (Figure 3-3d). The silica layer provides structural support to the ultra-thin glassy carbon film until the specimen is transferred to the device.

Figure 3-3: Schematic of GC specimen preparation steps

Step (a) photoresist is patterned in the form of 100 µm long, 10 µm wide beams (b) oxygen plasma is used to etch the glassy carbon layer (c) anisotropic plasma etching to pattern silicon dioxide and (d) silicon substrate isotropically etched using XeF2 to make freestanding bi-layer beams

3.4.2 MEMS device fabrication

The micro-scale uniaxial tensile testing device was fabricated from a SoI wafer with a highly doped silicon device layer (resistivity of 0.001-0.005 Ω-cm) using conventional nanofabrication processes. Patterned photoresist is used as a template

(Figure 3-4a) to transfer patterns to the silicon device layer using deep reactive ion etching (DRIE) (Figure 3-4b). Isotropic vapor-phase hydrofluoric (HF) acid etch was

42 then used to selectively release beams from the substrate, making them freestanding and mobile (Figure 3-4c).

Figure 3-4: Schematic of fabrication steps for the MEMS device

Step (a) photoresist patterned using photolithography (b) pattern transferred to silicon by DRIE (c) vapor phase HF etch of silicon dioxide to release beams for mobility

3.4.3 Specimen integration with MEMS device

The glassy carbon-and-silica freestanding beam-specimen was then transferred to the device using a microscale version of the conventional pick-and-place technique inside a dual beam focused ion beam-scanning electron microscope (FIB-SEM). The

Omniprobe® attachment of the FIB-SEM – a 100 nm resolution three axis piezo stage – fitted with a very sharp tungsten probe tip was “glued” to the freestanding beam at one end using platinum deposition and the ion beam was used as a milling tool to release the beam from the substrate. The probe tip was then moved to the device area, oriented along the device‟s axis (Figure 3-5a) and the beam brought in contact with pads on the device, to which it is then securely “glued” using platinum (Pt) deposition. Vapor phase hydrofluoric acid (HF) etch was used to remove the supporting silica layer, resulting in a

5 nm glassy carbon thin film securely anchored on the device (Figure 3-5b). The advantage to using such a three step procedure of preparing the specimen, fabricating the

43 testing device and then integrating them, is that specimens of lengths up to 100 µm can be easily fabricated and tested.

Figure 3-5: Pick-and-place technique in situ in the FIB-SEM

Step (a) Omniprobe® attachment of FIB-SEM used to pick and place bi-layer specimen on device and (b) platinum deposition used to secure specimen on the device, followed by vapor phase HF etching to remove the silica support layer

3.5 Experimental results – Young’s modulus

After integration of the specimen with the MEMS device, the device is wire bonded and placed inside the SEM with electrical feed-through for in situ testing. The specimens were loaded quasi-statically by applying a DC voltage across the thermal actuator beams. The device is equipped with sensors measuring displacements of the thermal actuator and the force sensing beams (δ1 and δ2 respectively, as shown in Figure

3-1b). After each step of the voltage increment, these displacements were measured to obtain the force and elongation in the specimen using equation (1). The applied voltage

44 was increased in small steps until the film fractured. Figure 3-6a shows the specimen mounted on the two mechanical jaws, bridging the thermal actuator and the force sensor beams. Figure 3-6b shows the specimen slightly curling up after brittle fracture. In situ testing in the SEM not only provides direct visual observation of the deformation in the specimen, but also enhances the resolution of the quantitative study. For example, SEM imaging allows the thermal actuator and force sensor beam displacements to be measured with a resolution of 50 nm, which results in 0.05% strain resolution for the 100 µm long specimens used in this study. The force resolution of the device would depend on the stiffness of the force sensing beam; for example, a beam 250 microns long (Lfs), 2 microns wide and 10 microns deep has a stiffness of 1.75 N/m, which results in 85 nN force and 1.75 MPa stress resolution for a nominally 5 nm thick specimen. The in situ

SEM experiments also enhance the consistency and repeatability of the experiments and the maximum deviation of the data (from the spread of 5 experiments) is about 10% from the mean trend-line.

Figure 3-6: SEM image of GC film (a) before and (b) after loading to fracture Scale bar is 50 µm

45 Figure 3-7 shows a representative stress-strain data for a 5 nm thick freestanding glassy carbon specimen. The fracture mode is brittle and none of the specimens showed signs of plasticity or necking. The average Young‟s modulus for the five specimens was measured to be about 62 GPa and the average tensile strength and strain values are 870

MPa and 1.3% respectively. The corresponding values for bulk glassy carbon are about

30 GPa [135], 240 MPa and 0.5-0.7% respectively [143], which show significant size effect on the stress-bearing capability of the material at the nanoscale, even though conventional elasticity theory is size independent.

Figure 3-7: Stress-strain diagram for a 5 nm-thick freestanding glassy carbon film

46 3.6 Size effect at the nanoscale

The observed size effect can be explained by taking into consideration the effect of surface elastic properties on the mechanical properties of materials. Atoms at the surface have a lower coordination number (i.e. fewer neighboring atoms) than bulk atoms. Consequently, the nature of the chemical bond and the equilibrium inter-atomic distances are different at the surface compared to the bulk. This difference leads to surface stresses and surface energy [144], resulting in different mechanical properties for the surface and bulk material. As the length scale of the material under study is reduced, the proportion of surface atoms to that of the bulk increases; and at the nanoscale, this ratio is large enough for surface properties to significantly affect the overall properties of the material. This surface effect can be accounted for by introducing the concept of surface elastic constant S (units of N/m) [145], which is a measure of the variation of surface stress (η) with strain (ε). This can be expressed as [145, 146]

        0 S  , i.e., S  where α , β = 1 – 3 (3.2)     0

At the nanoscale, the contributions from the surface elastic properties (ηαβ and Sαβ) are significant and need to be taken into account in addition to the bulk elastic properties. For the case of tensile loading, this can be expressed as [145]

S Emeasured  Ebulk  4 t (3.3)

47 where Emeasured is the measured Young‟s modulus, Ebulk is the modulus at the bulk scale and t is the critical size for the material under study, in this case, t being the thickness of the thin film. This equation illustrates the effect of length-scale of the material on the measured modulus value.

However, glassy carbon is not crystalline as assumed in the above equations, and there is no reported value for the surface elastic constant for glassy carbon in the literature. The surface elastic constant can be approximated as S = Ebulk * r0, where r0 is a characteristic length-scale representative of the material structure. Since glassy carbon does not have a long range order in atomic arrangement, a representative length scale can be determined by considering the misalignment of the polyaromatic domains in glassy carbon. It has been experimentally determined that the coherence length (atomic pair distribution function) of the domains in glassy carbon tapers off beyond a distance of about 1.2 nm [147]. Using r0 = 1.2 nm and Ebulk = 30 GPa gives a surface elastic constant of S = 36 N/m and a measured modulus value of 59 GPa, which is close to the experimentally determined value of 62 GPa.

48 Chapter 4

Effect of Strain on Atomic Structure of Platinum Thin Films §

4.1 Phase transformations

Crystalline materials, especially nanocrystalline materials, typically exhibit enhanced mechanical, electrical and chemical properties in comparison to their amorphous counterparts. For instance, polycrystalline materials typically have higher ductility and are used in structural applications. The brittle nature of most amorphous materials makes it difficult to use them in load bearing applications as there is no indication of the onset of failure. The driving force for crystallization of amorphous solids (a thermodynamically meta-stable state) to form stable polycrystalline states is the

Gibbs free energy difference between the amorphous and crystalline states. Classical thermodynamic theory can be used to formulate crystallization as a solid state phase transformation [148]. Typically, crystallization takes place when external energy is supplied to the amorphous phase to overcome the potential barrier for the disordered atoms to attain lower and more stable energy states – crystalline or polycrystalline. This can be achieved by heat treatment, irradiation or mechanical attrition [148]. Heat treatment is the most commonly used technique in crystallization of amorphous solids but it requires temperatures comparable to half of the melting point to initiate any diffusion- based atomic restructuring process. Mechanical strain energy is less effective than heat

§ Contents of this chapter are based on the following journal publication; Manoharan, M. P., Kumar, S., Haque, M. A., Rajagopalan, R., Foley, H. C., Room temperature amorphous to nano-crystalline transformation in ultra-thin films under tensile stress: an in-situ TEM study, Nanotechnology, 2010

49 treatment in promoting crystallization because of its lower energy density. However, literature shows evidence of the significance of mechanical stress on the dynamics of such phase transformation when applied in conjunction with heat treatment [149-151].

Phase transformation in such systems is usually of three types – amorphous to crystalline (a-c), crystalline to amorphous (c-a) and transition from one (poly) crystalline state to another (c-c). The focus of this chapter is on the first type (a-c), which so far has not been reported to be observed at room temperature or under the application of tensile stress. Tensile stress is known to facilitate crystallization in polymeric materials only

[152-154], where the driving force for crystallization in polymers is deformation induced reorientation of the polymer chains, which increases the melting temperature of the polymer and leads to super-cooling [154]. All other classes of materials, such as metals, ceramics, carbon etc., require very high temperature and controlled cooling. Unlike polymers, these materials do not have relatively flexible chained molecular structures and tensile stress will only increase the inter-atomic distance of an assembly of disordered, amorphous atoms. This is the reason there is no evidence or attempts in the literature to study the crystallization of non-polymeric materials when subjected to tensile stress.

Literature contains evidence of stress-induced amorphization (c-a) in NiTi intermetallic compounds [155, 156] as well as crystallization [157] and phase transition [158] in bulk metallic glasses. However, purely stress-induced crystallization (a-c) in amorphous metals is rarely reported in literature. The only evidence of room temperature a-c transformation in metals involved very high compressive loading [159, 160].

50 In this chapter, the first experimental evidence of tensile stress induced crystallization at room temperature in 4 – 6 nm thickness focused-ion beam (FIB) deposited amorphous platinum films is presented. The experiments were performed in situ inside a transmission election microscope (TEM) at room temperature using a custom-designed micro-electro-mechanical (MEMS) device. The experimental setup and results are discussed in the following sections.

4.2 Experimental setup for in situ TEM study

The primary challenge for in situ testing in the TEM is its limited space for experimental setup – typically only a 3 mm diameter grid is allowed. This raises opportunities for miniaturization of experimental techniques using nanofabrication. For this experiment, a custom-designed and micro-fabricated 3mm x 5mm sized device was used to apply and measure uniaxial tensile stress/strain on electron transparent freestanding films inside the TEM. The devices are fabricated on silicon-on-insulator wafers with a highly doped device layer (0.001 - 0.002 Ω-cm). Figure 4-1 describes the fabrication processes schematically. An essential feature of the device is a through-the- wafer hole that allows transmission electrons of the TEM through the specimen. This hole is first patterned on the back side using photolithography (Figure 4-1a), followed by etching vertically through the entire handle layer by DRIE (Figure 4-1b). In the next step, the device design is patterned on the device layer using a Karl Suss MA-BA6 mask aligner (Figure 4-1c). The device pattern is then etched vertically by DRIE (Figure 4-1d).

The device beams are then released from the handle layer using hydrofluoric acid vapor etching (Figure 4-1e).

51

Figure 4-1: Schematic showing the device fabrication steps.

Step (a) Through the wafer hole for transmission electrons is patterned using photolithography and (b) the pattern is etched vertically through the handle layer using DRIE. Next, (c) the device design is patterned on the device layer side using front side alignment photolithography, followed by (d) DRIE etching of the device pattern. (e) The beams are then released using HF vapor etching. (f) A three-dimensional model to illustrate the device.

The custom-designed and fabricated micro-electro-mechanical device is used to apply uniaxial tensile stress on an ultra-thin freestanding film. The uniqueness of the experimental setup is its in situ quantitative (through micromechanical sensors) transmission electron microscopy (TEM) capabilities [161-164] that go beyond the conventional qualitative (high resolution imaging and diffraction patterns) observations.

The principle of operation of the device has been described in detail in chapter 3.4. The

52 specimen preparation and integration steps are the same as that for measurement of

Young‟s modulus and are described in chapters 3.4.1 and 3.4.3 respectively. The thin film specimen used in this study is a bi-layer structure, comprised of an ultra-thin glassy carbon film acting as the substrate for another layer of ultra-thin platinum film, but deposited at only the two ends of the GC layer (Figure 4-2b). The synthesis and material properties of the GC film are detailed by Lee et al. [116]. The role of the 4 - 6 nm thick glassy carbon layer is two fold; firstly, to support the platinum layer, because it is very difficult to obtain electron transparent specimens of focused ion beam-deposited platinum using wet or dry micro-electronic etching techniques. Secondly, it unambiguously shows

TEM evidence of any phase transformation in the platinum layer. For example, the middle (glassy carbon) portion of the specimen serves as a reference structure for electron diffraction based phase transformation detection. Since the atomic structure of the glassy carbon layer does not change with stress, the phase transformation of the

(initially amorphous) platinum layer can be captured readily. It is very well known that the focused ion beam deposited platinum has excellent adhesion with most micro- electronic materials. Nevertheless, since the experiments are performed in situ in the

TEM, any indication of poor adhesion at the glassy carbon-platinum interface would be readily identified.

53

Figure 4-2: SEM image of MEMS device and Raman spectra of thin film specimen

(a) Scanning electron image of a thermal-actuator device for applying uniaxial tensile stress on the thin film (b) A detailed view of the bilayer thin film – the areas in green (false color added for highlight) indicate the FIB-deposited platinum thin film over the glassy carbon layer. (c), (d) are electron dispersive spectroscopy (EDS) data taken at the platinum-free glassy carbon film region and the ends where platinum deposition has taken place respectively. The EDS spectra were obtained before the silicon dioxide support structure was removed by HF vapor etching.

FIB-induced platinum deposition was used to secure the specimen to the device at either ends of the film; this platinum deposit is the material under study (Figure 4-2b).

During ion beam-induced deposition in the FIB–SEM, the precursor trimethyl- cyclopentadienyl platinum (IV) (MeCpPtIVMe3) is dissociated by gallium ions, causing platinum to be deposited on to the substrate. Ideally, the volatile organic components of the precursor are pumped out the system. However, the precursor is never completely dissociated and the deposited material contains mostly platinum and a negligible amount of carbon-containing amorphous material [165-167]. The exact composition of the platinum is a still a matter of debate – ranging from 2 nm [166] to 6 – 8 nm crystalline

54 [168] to completely amorphous [169] structures. In the specimen under study, a composite structure consisting of amorphous and sub-nano (less than 1 nm) crystals of platinum was observed. This is evident from the Selected Area Electron Diffraction

(SAED) patterns and the bright field image as shown in Figure 4-3.

Figure 4-3: TEM image of FIB-deposited platinum before application of tensile stress.

Inset shows SAED pattern suggesting that the platinum is a mixture of amorphous and sub-nano crystalline structures.

4.3 Experimental results – amorphous to crystalline transformation

The thin film specimen was loaded quasi-statically by applying a DC voltage across the thermal actuator beams, causing the beams to expand due to Joule heating and apply a uniaxial tensile force on the thin film [170]. The applied voltage is increased in

55 small steps and the TEM image and SAED pattern was recorded at each step. Up to 3% strain was applied on the specimen, which was the threshold limit for neglecting any specimen heating effect contributed by the thermal actuators. Neither the glassy carbon nor the platinum film segments fractured at this level of strain.

Figure 4-4: SAED patterns of platinum thin film at increasing strain levels (a) At 0% strain, the diffuse rings indicate a composite structure consisting of amorphous and sub-nano (less than 1 nm) crystals of platinum (b) At less than 0.1 % strain, grain nucleation begins (c) At 2% strain, significant grain growth is observed and (d) at 3% strain, further grain growth indicated by highly defined and discrete rings

Before application of stress, the specimen material is a composite structure consisting of amorphous and sub-nano (less than 1 nm) crystals of platinum (Figure 4-3,

56 Figure 4-4a). As tensile stress is applied, grain growth is observed at about 2% (Figure

4-4b). Further application of stress results in significant grain growth, as seen by the appearance of discrete rings in the SAED pattern (Figure 4-4d) for a strain of 3%. The grain size increases to about 10 nm (Figure 4-5) at this strain. The phase transformation is irreversible as indicated by no change in crystalline structure as the stress was gradually reduced to zero. This observation is remarkable since the transformation process took place at room temperature and tensile loading, whereas high temperature, high

(compressive) pressure conditions are typically known to be key requirements for such structural changes.

Figure 4-5: TEM micrograph of platinum specimen at 3% strain Extensive grain growth results in nanocrystalline platinum with grain size of 10 nm. Inset shows SAED pattern.

57 4.3.1 Effect of strain on the glassy carbon film

When the freestanding film is loaded in situ inside the TEM, the glassy carbon film is subject to uniaxial tensile stresses. The strain values were measured by the displacement sensor in the device. As mentioned earlier in this chapter, glassy carbon is a disordered, nanoporous form of carbon that resists transformation to graphite even at temperatures as high as 3,000 °C [133]. Our in situ observations did not show any change in the glassy carbon structure for tensile strains up to 3%. However, there is also evidence to the contrary in the literature, where carbon fibers embedded in a glassy carbon matrix and annealed to temperatures of 2300 – 2800 °C [171, 172] or at 1500 °C under very high

(on the order of a few GPa) pressure [173, 174] show a graphitic structure at the fiber- matrix interface due to residual stress.

4.4 Stress-induced crystallization in FIB-deposited platinum

The reported crystal structure of FIB-deposited platinum varies from nanocrystalline [168, 175] to amorphous [169], although in the specimen under study, a composite structure consisting of amorphous and sub-nano (less than 1 nm) crystals of platinum (Figure 4-2) was observed. It is proposed that this structure can best be described by the „amorphous cement‟ model proposed by Rosenhain [176, 177] almost a century ago. The possibility of a two-phase microstructure in nanocrystalline materials comes from the comprehensive simulations done by Gleiter and co-workers [177, 178] though is model is still disputed by van Swygenhoven et al. [179, 180] and others [181].

Schiøtz et al. have also shown through simulations [182] that unlike coarse-grain materials where the volume fraction of material in the grain boundaries is small, in

58 nanocrystalline materials, this could be as high as the theoretical [183] estimate of 50%.

It has also been observed that below a critical grain size, the amorphous and nanocrystalline phases can undergo a reversible, free-energy based phase transition. This critical size is 1.4 nm in general for a nanocrystalline fcc metal [184] and 2 nm for nanocrystalline silicon [185].

The crystal spacing in bulk platinum for {111} plane is 2.265 Å [186]. The radius of the first diffraction ring (corresponding to the {111} plane) at zero or negligible loads

(0.2 % strain) was measured to show an atomic spacing distance of 2.376 Å (Figure 4-4a, b). This indicates that the platinum specimen experiences large (about 5%) tensile residual strain upon deposition. However, in about 30 minutes after the application of the additional 3% strain through the thermal actuator, the crystal spacing measured from the electron diffraction (Figure 4-4d) was found to be 2.328 Å. Therefore, the effective stress in the platinum layer is about 2.7%, which corresponds to an overall stress relaxation of about 5.3% (from 8% to 2.7% strain) in the crystal structure. Such large initial strain

(about 8%) and fast stress relaxation lays down the foundation for the following hypothesis,

a) The mechanical strain energy in the sample provides the activation energy for the

nucleation of crystallization.

b) The stress relaxation is mediated by both atomic and vacancy diffusion driven

deformation.

59 The overall effect for the above two processes is the reduction in vacancy concentration (the initial amorphous structure is meta-stable with very large vacancy concentration) or, in other words, an increase in the grain size takes place as result of the mechanical deformation. This is supported by other studies on nanoscale deformation in the literature. When a two-phase composite structure, such as the specimen used in this study, is subjected to stress, it is found that stress-induced crystallization is the dominant mechanism of plastic deformation in the amorphous phase and the deformation in turn was observed to enhance the crystallization process [187]. Similarly, grain growth is the dominant mechanism for reducing the overall energy of the system by reducing the total grain boundary energy [163, 188]. The underlying mechanism for the observed grain nucleation and growth is therefore diffusion driven deformation, which dominates over the conventional dislocation based mechanisms at the extremely small length scales [189,

190]. It is therefore proposed that when subjected to tensile stress, the amorphous/sub- nano-crystalline phase accommodates the deformation by stress-induced crystallization as a means to achieve stress relaxation in the thin film. The mechanical strain energy from the overall strain (residual and applied) in the specimen provides the activation energy necessary to nucleate crystallization.

Although the magnitude of strain energy is independent of whether the stress applied is compressive or tensile, for amorphous materials, such as the platinum in this study, the nature of stress is important. This is because, in amorphous materials, the average interatomic distance is higher than the interatomic distance in a perfect crystal.

Under compressive stress, the interatomic distance is reduced, bringing order to the

60 system and under tensile stress, the interatomic distance increases, increasing the disorder in the atomic arrangements. Hence, crystallization processes in the literature typically involves very high compressive stresses. It is therefore hypothesized that the tensile strain in the present study is relaxed by atomic and vacancy diffusion driven deformation mechanisms. Since the lowest possible energy configuration also involves the lowest fraction of grain boundaries, the energetically favorable route for the meta-stable amorphous platinum is to grow or increase the grain size. This process can take place at room temperature because of the strong length scale dependence of diffusion at the nanoscale. In comparison, very high temperature is needed at the bulk scale to initiate diffusion and/or annihilation of vacancies in amorphous materials. Also, mechanical deformation based crystallization processes require very high compressive pressure to reduce the average inter-atomic spacing in the disordered atomic structure. The mechanism proposed in this study does not attempt to crystallize by reducing the inter- atomic spacing. Rather, it suggests that grain growth through atomic diffusion processes is an energetically favorable process to relax stress in the material. This is feasible only at the nanoscale, where the diffusion limited processes dominate over the dislocation limited process (bulk characteristics) in mechanical deformation of materials [191].

The experimental setup itself raises two different possibilities that could provide sufficient energy to cause crystallization other than the mechanisms discussed above – thermal energy from the Joule heating in the thermal actuators and the high energy electron beam used in the TEM. Although Joule heating raises the temperature of the thermal actuator beams significantly, the presence of cooling fins dissipates the heat and

61 the specimen is maintained at or near room temperature throughout the course of the experiment. To verify this, the experiment was repeated under an infrared thermal microscope and the specimen‟s temperature was found to remain constant near the room temperature as indicated by a thermal micrograph of the actuated device (Figure 4-6).

Figure 4-6: Thermal scanning microscope image of device at max. deformation Heat dissipation by the cooling fins ensures that the specimen is always maintained at or near room temperature.

Local heating of the specimen due to prolonged exposure to a high energy electron beam such as in a TEM (200 keV) has been reported in literature [192, 193].

Thermal activation helps in the diffusion process required for grain growth. Localized heating due to electron beam exposure has been found to typically occur only in semiconductor or insulator specimens while metallic specimens do not show localized

62 heating under normal TEM operation if they are suitably grounded. A local temperature rise of 10-100°C has been observed to occur, depending upon the electron beam current

[193]. To alleviate this effect, exposure to the electron beam was limited to only when needed and the focus spot was moved by a few microns between recording each SAED pattern. In order to ascertain the effect of electron beam heating on the amorphous platinum, the specimen was exposed to direct and intense beam at 200 keV and no crystallization was observed even after 45 minutes of exposure as shown in Figure 4-7.

Thus, Joule heating of the actuator beams and exposure to high energy electron beams did not appreciably contribute towards the crystallization of the amorphous platinum film.

Figure 4-7: SAED pattern (a) initially, and (b) after 45 minutes of e-beam exposure Crystallization due to localized electron beam heating was not observed

63 The strain applied on the specimen was limited only by the deformation that can be achieved using the thermal actuator-based testing device. For comparison, a similar setup was used to study the elastic properties of glassy carbon thin films (chapter 3.7). In that experiment, the extent of the platinum deposition was carefully controlled so that the platinum precursor did not reach the gauge section of the tensile testing specimen and glassy carbon was observed to undergo brittle fracture at a fracture strain of 1.3%. For the specimen under study here, the platinum deposition extends over more than 60 % of the specimen length and the film does not fracture at strains as high as 3%. The strain energy of the specimen was measured to be about 150 J/mol. Unfortunately, this could not be quantitatively compared to the activation energy of platinum recrystallization, because of the lack of data in the literature on amorphous platinum (similar to the specimens in the current study) with thickness on the order of nanometers.

64 Chapter 5

Strain dependence of Thermal Conductivity

of Silicon Nitride Thin Films §

5.1 Introduction

Multi-domain (electrical, mechanical and thermal, to name a few) coupling is an essential feature of micro and nanoscale electromechanical and systems (MEMS/NEMS)

[194]. The same is true for other applications in micro-electronics [195, 196], opto- electronics [197, 198], flexible-electronics [199, 200] and energy conversion [201, 202].

These devices are commonly fabricated using thin films, whose mechanical reliability is as important as transport (electrical and thermal) properties. While the electro-mechanical coupling is commonly exploited in microelectronic and MEMS devices, the thermal domain is also pervasively prevalent in these devices, either by intentional design or undesirable coupling (for example, excessive heat generation in chip devices [203]).

Thermo-mechanical coupling in thin films is typically studied as temperature effects on mechanical properties [204-206] and not from a thermal transport perspective. Thermal transport in solids is mediated by electrons and/or phonons, which are scattered by the strain fields associated with the micro-structural features such as free surfaces, grain boundaries, dislocations and point or volume defects. At the bulk scale, thermal transport is minimally influenced by mechanical strain unless the strain is large enough to nucleate

§ Contents of this chapter are based on the following manuscript; Alam, M. T., Manoharan, M. P., Haque, M. A., Muratore, C., Voevodin, A., Can Elastic Deformation Influence Thermal Transport in Amorphous Materials?, (Submitted) 2011

65 and grow defect structures. However, this may not be true for ultra-thin films or nanostructures for which strong size effect in thermal transport [207] is observed even without any externally applied strain. Size effects in thermal transport are due to the pronounced proportions of defects, surfaces and interfaces [208] as well as spatial confinement [209]. Since mechanical strain influences defects, interfaces and grain boundaries as well as the lattice dynamics [210-212], it can be hypothesized thermal transport will be strongly coupled with externally applied strain at the nanoscale. This hypothesis gives rise to the concept of tuning thermal transport with mechanical strain, which would significantly impact nanoscale device design.

The role of mechanical stress or strain on thermal conductivity has been explored by only a few researchers [41, 213-216]. It is interesting to note that all these studies are computational; experimental efforts are appearing in the literature only very recently

[217-219]. Another aspect of the literature is that most of the existing studies involve crystalline or polycrystalline semiconductors, where phonon confinement effects are noticeably large. Therefore, the stringent test of the strain based tuning concept should involve metals (electron dominated) or insulators (phonon dominated). In this chapter, the role of mechanical strain on the thermal conductivity of low pressure chemical vapor deposited silicon nitride (LPCVD Si3N4) was investigated. Silicon nitride thin films are prevalently used in isolation, passivation and etch masking as well as structural and optical layers for various micro-electronic, optoelectronic and micro-electro-mechanical systems [220-223]. Further, there is no computational or experimental study exploring the strain dependent thermal conductivity coupling in silicon nitride, even though the

66 material is well known to withstand unusually high elastic strain (up to 3%) before fracture [224, 225]. This has led researchers to propose silicon nitride as the substrate to engineer the strain in microelectronic devices [226, 227].

Mastrangelo et al. [228] measured thermal conductivity of few microns thick silicon nitride films to be around 3.2 W/m-K. Zhang & Grigoropuolos [229] observed anomalous thickness dependence and suggested that microstructural defects may strongly influence thermal conductivity. Jain & Goodson [230] measured in-plane thermal conductivity of 1.5 micron thick specimens to be about 5 W/m-K. At the nanoscale,

Sultan et al. [231] reported thermal conductivity of 500 nm thin films as 3 - 4 W/m-K for a temperature range of 77 to 325K. For 180 - 220 nm thick low stress nitride, Zink &

Hellman [232] observed stronger temperature effects with thermal conductivity varying from 0.07 to 4 W/m-K in a temperature range of 3 - 300 K. The cross-plane thermal conductivity measured by Lee & Cahill [233] and Shin et al. [234] for less than 100 nm thickness were in the range of 0.4 - 0.7 W/m-K, showing very strong size effects which were ascribed to the interfacial thermal resistance. Stojanovich et al. [235] measured thermal conductivity of 180 nm thick freestanding specimens to be about 2.1 W/m-K. Bai et al. [236] measured thermal conductivity of stoichiometric silicon nitride to be about

1.2 - 2.0 W/m-K for 37 to 200 nm thick films. The literature consistently indicates size dependence of thermal conductivity for films thinner than 100 nm. However, the phonon mean free path of the amorphous material is on the same order of the mean inter-atomic spacing, which suggests that thickness is not the influential factor. Rather, the growth

67 chemistry, temperature range and experimental techniques could contribute to the observed apparent size effect.

5.2 Device Design and Fabrication

The experimental challenge in the strain – thermal conductivity characterization of silicon nitride lies in the brittleness of the material. Also, in the stoichometric composition, it develops very high tensile residual stress. Therefore, the common approaches are to synthesize low stress, silicon rich nitride (SiNx, x = 1 - 1.1) or to study the film on a rigid substrate. Because the interfacial thermal resistance is extremely difficult to measure, studies on freestanding specimens is more desirable. However, none of the existing studies attempt to control the amount of residual stress or strain in the specimen. This is difficult because the residual stress is uniform in a single wafer and irrespective of the specimen cross-section or length, conventional uniaxial tensile specimens fabricated from a single wafer will experience the same value of tensile strain.

To obtain specimens with different values of strain, the deposition parameters need to be varied from wafer to wafer, which unfortunately changes the specimen composition and density. This issue is addressed with a novel concept, where the tensile residual stress in the material is exploited for actuation. In other words, both the actuator and specimen are designed in the same film plane with an innovative actuator design that allows excellent control of stress/strain. As shown in Figure 5-1a, the design involves co-fabrication of an array of actuator strips with length La and cross sectional area Aa in series with the tensile specimen with length Ls and cross sectional area As. While both the specimen and actuator are patterned on the same film, the total force in the actuator array (more strips

68 in parallel compared to the single strip specimen) is greater than that in the specimen.

Therefore, the specimen will experience a net tensile force on the specimen that can be controlled by the number and geometry of the actuator strips. Figure 5-1a and b show the design philosophy with three and seven actuator strips respectively.

Figure 5-1: Schematic of setup to measure thermal conductivity of Si3N4 thin films

(a) Schematic diagram showing a single layer silicon nitride actuator and specimen, (b) SEM image of a 7-legged actuator showing aluminum thin film heater, (c) Strain is measured through post-experiment fracture of the specimen.

Once the actuator and specimen are released from the substrate, force distribution is re-organized according to their respective cross-sectional areas. While the net force acting remains the same, the amount of tensile forces on the actuator and specimen could be obtained from the force equilibrium condition as follows,

F  ka a  ks s (1) where k is stiffness, δ is net displacement and the subscripts a and s denote the actuator and specimen respectively. The equilibrium equation can thus be written as a function of

69 the length (L), cross-sectional area (A) and Young‟s modulus (E) of the actuator and specimen.

Ea Aa Es As n  a   s (2) La Ls where n is the number of legs in the actuator. The total displacement in the fabricated structure, δ, is the sum of the actuator and specimen displacement (δa + δs = δ). This displacement can be measured by tracing the discontinuity in the heater line on the substrate and on the nitride specimen. Figure 5-1c shows the measurement of d by intentionally fracturing specimen when the experiment is over. Using the force equilibrium equation, the specimen displacement can be related with the total displacement as follows,

 Es As La   s 1    (3)  nEa Aa Ls 

The strain in the specimen, εs, is then given by,

 s   nEa Aa  s   (4) Ls nEa Aa Ls  Es As La 

For the present study, the actuator and the specimen are fabricated from the same material. The specimen strain is therefore given by,

  nAa  s  (5) nAa Ls  As La 

The device fabrication process is schematically described in Figure 5-2. The process starts with deposition of 50 nm thick freestanding LPCVD Si3N4 using ammonia

70 and dichlorosilane at 820 ºC (Figure 5-2a). The residual stress in the deposited film is about 1.2 GPa. The device design showed in Figure 5-1a is then patterned on the nitride layer using lithography, after which the exposed nitride is etched with reactive ion etching using CF4/O2 plasma, shown in Figure 5-2b. Using front side alignment, a negative lithography is performed to pattern a beam perpendicular to the silicon nitride line and 170 nm thick aluminum is evaporated to complete the lift-off process. Figure

5-2c shows the aluminum and nitride beams patterned on the silicon wafer, which are still attached to the substrate. The next step is to release the two beams by etching the underlying silicon substrate using isotropic XeF2 etching. Figure 5-2d shows the freestanding nitride specimen and the aluminum heater beams schematically, and a scanning electron micrograph is shown in Figure 5-1b.

Figure 5-2: Fabrication processing for the device integrating the actuator, specimen and heater for thermal conductivity characterization

71 5.3 Experimental Procedure and Analysis

To measure thermal conductivity of the freestanding nitride specimens, DC voltage is applied across the aluminum heaters. Since the heater beam is also freestanding, Joule heating develops a parabolic temperature profile with the highest temperature at the middle section, which intersects the silicon nitride specimen and supplies a heat flux to it. In a typical experiment, from 4 to 10 milliamps of current is passed to raise the mid-section of the heater (and the silicon nitride) from 310 to 375 K.

The temperature distribution along the length of the heater is measured using an infrared microscope (Quantum Focus Instruments, MWIR-512 InSb IR FPA camera) with 0.1 K temperature and 2 microns spatial resolution. The inset in Figure 5-1b shows a thermal micrograph of the heater during operation. At the same time, the temperature profile along the length of the silicon nitride specimen is measured. However, calculation of the thermal conductivity requires the heat flux in the specimen, which can be approximated by the power supply to the heater, or more accurately by performing finite element simulation [235].

Commercially available software COMSOL Multiphysics™ was used to carry out the finite element solution of the described problem. Among the various application modes, electro-thermal application mode is used for modeling as this problem incorporates Joule heating of the material. This mode presents the coupling of three different basic application modes which are conductive media DC application, heat transfer application and solid mechanics application modes. Heat loss through convection and conduction (through the air to the etched substrate below the specimen) were

72 included in the model. Table 5-1 and Table 5-2 describe the primary input parameters for the model.

Table 5-1: Multi-physics modes and input parameters for the finite element model

Application Properties Silicon nitride Aluminum mode Resistivity (Ω-m) 1.72 e-8 3.75 e-7 Conductive media Temperature coefficient of 0.0038 0.0030 DC mode resistance (1/K) Reference temp (K) 300 300 Varied to match Thermal conductivity measured 237 Heat transfer (W/m-K) temperature profile mode Density (kg/m3) 3100 2700 Heat capacity, Cp (J/kg K) 700 904 Young‟s modulus (Pa) 250 e9 70 e9 Poisson‟s ratio 0.23 0.35 Solid mechanics Thermal expansion mode 2.3 e-6 23.1 e-6 coefficient (1/K) Density (kg/m3) 3100 2700

Table 5-2: Geometry parameters for the aluminum and silicon nitride structures

Material Length (µm) Width (µm) Thickness (µm)

Aluminum 35 3 0.175

Silicon nitride 100 5 0.050

Figure 5-3 shows the finite element model, where the four boundaries are numbered for ease of identification. The conductive media DC mode solves the following equation,

e .V  J  Qj (6)

73 where, ζ is the electrical conductivity, V is the potential, Je is the external current density and Qj is the current source. This mode assumes that the model has symmetry and electric potential varies only in the X and Y direction and is constant in Z (film thickness) direction. For Joule heating, the electrical conductivity is temperature dependent and maintains the following relationship,

1   (7) 0 1T T0  where, ρo is the resistivity at reference temperature T0 and α is the temperature coefficient of resistance. One end of the aluminum heater (boundary 3) is provided with an electric potential (V = Vo) and the opposite end (boundary 4) is electrically grounded, as shown in

Figure 5-3. All other boundaries of aluminum and silicon nitride are chosen to be electrically insulated (n.J = 0).

Figure 5-3: Multi-physics simulation model for the device

74 The heat transfer mode solves the following governing equation:

 kT   Q  qsT (8) where, k is the thermal conductivity,  T is the temperature gradient, Q is the heat generation and qs is the production/absorption coefficient. The four ends of the aluminum and silicon nitride films (boundaries 1, 2, 3 and 4) are kept at constant temperature (T =

T0). This is because the thermal mass of the substrate is enormous compared to the aluminum and nitride films. For all other boundaries, the heat flux boundary condition is applied through the following equation,

 n.q  q0  hT0 T  (9) where, n is the outward normal, q is the conductive heat flux vector, qo is the inward heat flux from external sources (such as radiation) and h is the convection heat transfer coefficient. Here, To was taken to be 300 K and radiation losses were neglected because of the relatively lower temperatures involved. The role of convective heat transfer coefficient of air was found to be negligible at this length scale. This is because buoyancy, the driving force for natural convection becomes very small at the length scales under study here. So, a typical value of h = 10 W/m2K was used. At the same time, heat conduction loss through air (from the bottom surface of the nitride specimen to the device floor) is known to be dominant in the literature [237]. Zhang et al. [238] measured

2 the „effective convective heat transfer coefficient‟, which gives hair = 500 W/m K for an etch depth of about 15 microns in this case, which is due to the reduced thermal capacitance and the increased surface to volume ratio at the microscale.

75 The solid mechanics mode employs the governing equation,

  E (10) where ζ is the stress, E is the Young‟s modulus and ε is the net strain. The net strain includes elastic strain, thermal strain and initial strain. Boundaries 1, 2, 3 and 4 are constrained with fixed boundary condition (displacement is zero in all directions) while all other boundaries are considered as constraint free. No external load is applied to the boundaries.

To validate the model, the simulated temperature profile along the aluminum heater beam was compared with that obtained from simulation for different values of input current. Figure 5-4 shows the excellent agreement between the actual and simulated heater temperature profile. It also shows the heat flux values from the simulation. Since the governing equations of the finite element model do not have any strain - thermal conductivity coupling, the temperature profile along the specimen length was measured for various levels of mechanical strain. To extract the thermal conductivity of the specimen for each strain value, the heat flow for the calculated heat flux values and various trial values of thermal conductivity was simulated until the simulated temperature profile closely matched that obtained from thermal microscopy. Figure 5-5 shows this procedure for two different values of strain.

76

Figure 5-4: Comparison between experimental results and multi-physics simulation

Experimental and multi-physics simulation results on the maximum temperature at the midpoint of the thin film heater as a function of input current. The corresponding heat flux at the specimen midpoint is also shown.

Figure 5-5: Comparison of experimental and simulation results on the temperature profile of the silicon nitride specimens with fitted values of thermal conductivity.

77 5.4 Results and Discussion

Steady state thermal conductivity measurements were performed on nominally 50 nm thick freestanding silicon nitride specimens about 100 microns long and 5 microns wide at strains up to 2.4%. The specimen was heated using a 35 microns long, 5 microns wide and 170 nm thick freestanding aluminum thin film heater. A novel device design exploiting intrinsic tensile residual stress in the silicon nitride was used to apply mechanical strain in the specimens. Combining infrared thermal microscopy and multi- physics simulation, the thermal conductivity of the specimens was extracted as a function of strain. The experimental results for room temperature are shown in Figure 5-6. Since the applied strains are in the elastic range for silicon nitride, the experimental results support the concept of tuning thermal conductivity with mechanical strain as an external stimulus. The zero strain thermal conductivity was obtained after intentionally fracturing the specimen at the edge to relieve the stress entirely. Figure 5-6 also compares the experimental results with the data available in the literature for similar specimen thicknesses. Since the LPCVD Si3N4 composition is associated with the highest residual strain, the literature predominantly involves LPCVD or PECVD SiNx (also known as hydrogen-rich or low stress silicon nitride) with x varying from 1 to 1.1. Even though none of the existing studies measure the mechanical strain in the specimens, the highest possible strain in these compositions is about 0.3 % [239], which is used in Figure 5-6 to present the literature data. When interpolated between 0 and 0.6 % strain, the results obtained are in excellent agreement with the literature except two instances involving cross-plane thermal conductivity. This is quite expected since cross-plane measurements

78 involve nanoscale length of heat flow path (L = specimen thickness) and two interfacial thermal resistances (th), which pronounce the pseudo-size effects as given below [240],

1 1 A   th (11) T, L T, L   L where, A is the cross-section of the specimen. Lee and Cahill [233] explained their observed size effect with the above argument, while Bai et al. [236] corrected their data after developing a technique to measure the interfacial thermal resistance.

Figure 5-6: Thermal conductivity of 50 nm thick Si3N4 films as a function of strain

The letters corresponding to 0.3 % strain denote experimental data available from the literature (inset). The symbol () denote cross-plane thermal conductivity data before consideration of the interfacial thermal resistance.

79 Two concerns related to the experimental technique deserve further scrutiny. The first concern is on the role of interfacial thermal resistance, which is typically not critical for in-plane thermal conductivity measurements. This is verified by plugging in representative values from the experiments in equation 11. For heater-specimen

-12 2 -8 2 interfacial area A = 25x10 m , ρth = 2 ~ 3x10 m -K/W [233, 236] and L is about

15x10-6 m), the size dependent term is only about 6.25x10-14 , which clearly shows that interfacial thermal resistance is not a critical concern for this study. The second concern arises from the amount of strain developed in the aluminum heater due to the strain in the silicon nitride specimen, which may change the electrical and thermal properties of the heater and introduce experimental errors. For 125 nm thick aluminum on silicon dioxide, such strain effects have been shown to be pronounced [241], which calls for a detailed analysis. Since the freestanding aluminum heater is attached to the nitride specimen at the mid-point, the maximum strain it experiences is the same as the net strain in the width direction of the nitride specimen. This is given by,

       x y  (12) Al y E residual where x and y directions are along the length and width of the silicon nitride specimen respectively and Poisson‟s ratio  = 0.22. The residual strain is about 0.4 % for the specimens and is bi-axial and tensile in nature. The actuation method applies uniaxial tension in the nitride specimens with stress (x) of about 6 GPa for about 2.4 % strain

(the fracture stress of silicon nitride varies from 6 - 10 GPa). For these values, the net strain in the aluminum heater is -0.5 %, i.e., there is no appreciable strain developed in the aluminum heater for the actuated nitride specimens. This was also verified by measuring the electrical resistance of the aluminum heater before and after release from

80 substrate, which did not show any appreciable change in the resistance due to the loading of the heater beam. For zero strain thermal conductivity measurements, the tensile strain in the heater segment overlapping the nitride specimen is about 0.4 %, for which the thermal conductivity was assumed to be 100 W/m-K [241].

To understand the physics behind the pronounced strain - thermal conductivity coupling (Figure 5-6), we note that commonly cited phonon confinement phenomenon for low dimensional materials [41, 209] and hetero-structures [211, 212] cannot be used because of the amorphous microstructure of the specimens. Amorphous materials typically have very low thermal conductivity because the phonon mean free path is on the same order of the structural disorder [242] or the inter-atomic spacing, rendering bulk thermal conductivity of amorphous materials size independent. This is in agreement with our results, which are comparable with data for thicker specimens in the literature. While the mechanism of heat transfer in amorphous solids is still debated, the original Einstein model appears to be a popular approach at higher temperatures. Here, the phases of the atomic vibrations are incoherent and the oscillators are damped strongly enough to pass their energy to the neighbors within half the period of oscillation yet the states are not localized. Or in other words, heat transfer in amorphous solids is a random walk of energy between localized oscillators of varying sizes and frequencies. The Cahill model

[243] for thermal conductivity of amorphous materials is a rigorous implementation of the Einstein approach given as an integration of the specific heat (C), phonon velocity (v) and the mean free path (l) over the entire range of frequencies,

1  dC     l  d (13) diff      3 0 d

81 It is important to note that such diffusive mode heat transfer does not require anharmonicity in the oscillation of the atoms. In real amorphous materials, the inherent aperiodicity gives rise to strong localization of high frequency vibrations or „fractons‟.

Orbach and co-workers therefore suggested an alternative mode of heat transfer, modeled by hopping energy through highly localized vibrational modes (fractons) that are coupled to phonons via the anharmonic interaction [244]. While fractons in a harmonic system are believed not to be contributing in thermal transport, it has been shown in the literature that anharmonicity induces interaction between phonons and fractons that allows transfer of energy from one localized excitation to another, resembling spatial overlapping of localized modes [245]. It is proposed that such spatial overlap is extremely marginal, otherwise amorphous materials would exhibit large thermal conductivity. Therefore, slightest reduction of this overlap, through tensile mode mechanical deformation can be expected to produce significant reduction in the phonon-fracton interaction (Figure 5-7).

This is supported by experimental observation of about one order of magnitude reduction in thermal conductivity at about 2.4% strain. It is hypothesized that the strain sensitivity of thermal conductivity is strongest only for tensile deformation, for which the „barely‟ overlapping localized modes are further isolated with applied strain. According to the conceptual model proposed here, compressive deformation would increase such overlap and weaken the localization effect. By increasingly the overlap in the localized modes, compressive deformation is expected to increase thermal conductivity only at pressures large enough to change the elastic properties, which is consistent with theory and experiments [219]. Next, the role of bond energy of stiffness on the strain sensitivity of thermal conductivity is discussed.

82

Figure 5-7: Conceptual diagram to illustrate phonon-mediated energy hopping from one fracton to another (a) at 0 % strain and (b) when tensile strain is applied Tensile stress decreases such hopping and thus decreases the thermal conductivity

Unlike crystalline materials, where all the modes are non-localized (diffusive), amorphous materials show the spectra of both localized (fracton) and diffusive (phonon) modes [246]. Therefore, the thermal conductivity can be expressed as,

T    diff T   hop T  (14)

The proposed conceptual model suggests that the strain thermal conductivity coupling would depend on the relative contribution of these two modes, which in turn, depends on the lack of long range order and atomic bond energy.

83

Figure 5-8: Density of vibrational states of amorphous silicon [247]

Crystalline or polycrystalline materials exemplify diffusion-dominated thermal transport, for which very large strain (~10% [41]) or stress (~ 20 GPa [248]) is shown to produce only modest reduction in thermal conductivity at the extremely small (< 10 nm) length-scales. The lack of long range order in amorphous materials gives rise to the predominance of fractons in the vibrational density of states. For example, the sharpest peak for amorphous silicon is at frequency of 66 meV (Figure 5-8), which is very close to the cut-off value of 72 meV, below which localization effect is too strong to transport heat [247]. It is hypothesized that the relative contribution of fractons in thermal transport of amorphous materials is dependent on the bond energy of the atoms. While the vibrational density of states of silicon nitride is not available in the literature, the peak frequency is expected to be higher than amorphous silicon because the Si-N bond energy

84 (78.32 kcal/mol) is much higher than Si-Si bond (53.31 kcal/mol) [249]. Amorphous silicon nitride is therefore expected to show stronger vibration localization compared to amorphous silicon. This implies that strain-thermal conductivity coupling in amorphous solids will also depend on the bond type and energy.

85 Chapter 6

Tribological properties of individual Zinc Oxide Nanowires §

6.1 Introduction

Nanowires have received considerable attention in materials and device physics research because of their unique length-scale dependent physical properties [250, 251].

Typically, these one-dimensional structures are synthesized using bottom–up approaches while the rest of the devices (such as electrodes) are nanofabricated top–down [252, 253].

After their integration, the nanowire-substrate shear strength plays a critical role in both electrical performance and mechanical reliability of the device. It is important to note that in spite of the abundant literature on nanowire-based devices, only a few studies are available on the shear strength of nanowire contacts, or in general, the physics of adhesion-dominated friction in nanowires on substrates [106, 254]. This is because of two fundamentally different aspects of the physics and the geometry of nanowire–substrate interfaces when compared with other interfaces, namely (i) contact strength is due to pure adhesion only, as no externally applied normal force is applied on the nanowires in almost all nanowire-based devices and (ii) one of the bodies (the nanowire) is extremely compliant because of its unusually high aspect ratio. These features make popular tools such as the atomic force microscope (AFM), the surface force apparatus (SFA) or other custom micro-machined friction and adhesion characterizing tools [122, 255, 256]

§ Contents of this chapter are based on the following journal publication; Manoharan, M. P., Haque, M. A., Role of adhesion in shear strength of nanowire-substrate interfaces, Journal of Physics D: Applied Physics, 2009

86 difficult to apply directly to nanowire-based interfaces. Using a novel experimental setup that effectively decouples adhesion and friction forces, the friction coefficient for a zinc oxide nanowire and silicon system was measured to be about two orders of magnitude higher than the bulk values, even under zero externally applied normal loads. The nanowire bending compliance and capillary line tension were modeled as competing mechanisms to explain the observed anomalous adhesion–friction coupling and establish a criterion for contact area dependence in friction in one-dimensional interfaces.

6.2 Experimental setup

An experimental setup was developed that can decouple and measure adhesion and friction forces at a nanowire- substrate interface. Figure 6-1a shows a schematic diagram of the experimental setup, where a nanofabricated adhesion and friction force sensor is mounted on a three-degrees-of-freedom piezo-electric actuator. The commercially available actuator (Tritor®) has a travel of 100 µm in the x, y and z directions. The nanowire is attached to the end of the cantilever using focused ion beam deposited platinum. Single crystal ZnO nanowires about 30 – 40 µm long and 100 nm in radius were used as specimens. The nanowires with (0001) crystallographic orientation in the length direction were synthesized using the vapor-liquid-solid (VLS) technique as described in [257]. Single crystal silicon with the (100) crystallographic orientation was used as the substrate because of its prevalence in the micro- and nano-electronic devices.

The substrate was mounted on a manual micromanipulator with 1 µm positioning accuracy. The setup is shown for ambient experiments in Figure 6-1b, where a minimum

87 positioning resolution of 0.5 µm was achieved with an optical microscope using a 100X long working distance objective.

Figure 6-1: Schematic of setup to measure friction and adhesion forces

(a) The nanofabricated adhesion-friction force sensor is mounted on a Tritor® piezo-actuator and the silicon substrate (not to scale), (b) the setup under a 100X optical microscope objective, (c) schematic of the adhesion-friction force sensor (not to scale) and (d) SEM image of the adhesion-friction force sensor (inset: zoomed view of the displacement markers).

The design and working principles of the adhesion friction force sensor are shown in Figure 6-1c. The sensor is essentially a U-shaped spring with a cantilever beam attached to its end. The lateral (friction) force is measured by multiplying the displacement in the U spring with its stiffness. The U spring structure is made of (100) single crystal silicon with 1 µm width and 2 µm depth. This aspect ratio allows only in-

88 plane (X–Y plane) deformation of the U spring. Figure 6-1d shows the scanning electron micrograph of the sensor. The inset shows a zoomed view of the reference gap, which is constantly monitored to measure the friction force. At all points in time, the displacement of the friction force spring is directly measured by recording the extension of the reference gap, which makes the measurement free from the piezo-actuator hysteresis. As shown in Figure 6-1c, the U spring also acts as the support for the cantilever beam, whose deflection multiplied by stiffness measures the adhesion force. The cantilever beam is about 5 µm wide, 2 µm deep and 500 µm in length and can only move in the vertical (Z- axis) direction.

Figure 6-2 shows a schematic of the various stages in a typical experiment.

Initially the calibrated piezo-actuator was set up such that the nanowire hangs freely above the silicon substrate (Figure 6-2a). The X-axis of the piezo was then actuated to position the nanowire over the silicon substrate for a desired contact length. Under an optical microscope, such positioning for contact length is repeatable with 0.5 µm resolution. The piezo was then actuated to lower the force sensor until a snap-in event was observed. At this stage, the nanowire was bent like a cantilever and its entire length was not in focus (Figure 6-2b). The deflection of the cantilever was then measured by either (i) using the manual micromanipulator with 1 µm resolution or (ii) actuating the piezo so that the entire nanowire moves into focus (Figure 6-2c). This zero deflection position implies zero externally applied normal load, which is applicable to this study.

Optionally positive or negative normal load can be applied on the nanowire-substrate interface by actuating the piezo-actuator towards and away from the substrate,

89 respectively. The nanowire was then loaded in friction by actuating the piezo in the X- direction (Figure 6-2c). Finally, after the friction loading and unloading cycle, the snap- out or pull-off force was measured in a similar way to the snap-in force, as shown in

Figure 6-2d. Figure 6-2e shows an optical micrograph of the nanowire specimen and the substrate position as rendered in Figure 6-2c. Here the entire nanowire is in focus and the contact length can be repeatedly positioned with a 0.5 µm resolution. It is important to note that the adhesion force was approximated with the measured pull-off force, which arises from a range of contributions such as van der Waals force, electrostatic force, meniscus force and other interaction forces, originating from the physics and chemistry of the surfaces [258, 259].

90

Figure 6-2: Schematic of the various stages in the experiment

(a)-(d) Schematic of the nanowire–substrate contact shear strength measurement, and (e) optical micrograph showing the nanowire positioned on the substrate with desired contact length.

The friction–adhesion force sensor can be calibrated by deforming the structure with a factory calibrated AFM cantilever structure. This was performed inside a scanning electron microscope with a 100 nm displacement measurement resolution. Further calibration can be performed using a tribo-indenter [70]. The stiffness values for the friction–adhesion force sensor were found from the force-displacement profiles as shown in Figure 6-3, which also shows finite element analysis results. Since the flexible U

91 spring serves as the support for the cantilever, the force-displacement profile for the cantilever is slightly non-linear. Also, its stiffness is about two orders of magnitude smaller than the friction force sensor, which virtually eliminates any appreciable cross talk between the friction and adhesion forces.

6.3 Experimental results and discussion

Shear strength of the nanowire–substrate contacts were carried out on ZnO nanowires on a silicon substrate. Zero normal load friction experiments were performed by actuating the piezo in-plane, thereby loading the nanowire–substrate interface by shear. The resulting friction forces were obtained by multiplying the U-spring deflection with its in-plane stiffness as described in the previous section. The loading on the nanowire was done quasi-statically, even though the actuator can be programmed for desired sliding velocities. The hysteresis of the piezo actuator was accounted for in the displacement data to obtain a friction force versus piezo actuator displacement curve as shown in Figure 6-4. After unloading, the nanowire was retracted from the substrate by reducing the voltage on the actuator. This takes the „released‟ part of the nanowire out of focus, while the adhesion force maintains some extent of overlap. Continued retraction of the piezo-actuator results in snap-out of the nanowire from the substrate. The snap-out distance (measured with a 600 nm resolution by a 100X objective) multiplied by the sensor stiffness in the bending (out-of-plane) direction gives the adhesion force.

92

Figure 6-3: Finite element analysis of the adhesion-friction force sensor. Top: stiffness of friction force sensor. Bottom: stiffness of adhesion force sensor.

For the experimental data shown in Figure 6-4, the initial contact length was 31

µm and the snap-in and snap-out forces were 17.6 nN and 158.4 nN, respectively. This results in a large adhesion hysteresis and, accordingly, the coefficient of friction using adhesion as the effective normal force model was found to be 43.6. Five experiments were performed with different contact lengths and the coefficient of friction was obtained to be between 25 and 45, which is about two orders of magnitude larger than the macro- scale values. Assuming the true contact area is equal to the apparent contact area

93 (explained in the next paragraph), the shear strength of the nanowire-substrate contact area was found to be about 1MPa, which is in very close agreement with the only available measurement [254] in the literature.

Figure 6-4: Typical friction loading and unloading curve for ZnO nanowire on silicon The experiment is performed in ambient conditions.

To trace the origin of the two orders of magnitude higher friction force, it needs to be noted that the experiments were performed in ambient conditions, where all surfaces are conformally covered with adsorbed hydrocarbon and water molecules [110, 260].

These molecularly thin liquid films exert very high meniscus forces that can, depending on the surface chemistry, significantly influence the magnitude of the friction force [261].

For example, the snap-out forces measured in vacuum (SEM) was on the order of 80 -

100 pN only, which highlights the dominant role of meniscus forces. However, meniscus

94 force induced adhesion alone cannot explain the large friction force. It is therefore hypothesized that the compliance of the nanowire plays a critical role by drastically increasing the true area of contact at the interface. Because of the ultra-high aspect ratio

(about 150 - 300), the nanowires resemble compliant beams in fixed– fixed support conditions on the silicon substrate asperities. The effect of such compliance is shown schematically in Figure 6-5. Macro or microscopic systems typically involve mating bodies (Figure 6-5a) whose large stiffness values prevent any appreciable deformation due to adhesion forces only. Hence, at this scale, a normal force, N, is necessary to make a contact. This force, however, is still small to remove the gaps between the asperities and thus the true contact area is always a very small percentage (less than 10%) of the apparent contact area (Figure 6-5b). The overall effect is the predominance of the normal force and the friction force which is given as F = μN, where μ is the static friction coefficient.

Figure 6-5c-e show the corresponding scenario for compliant structures, such as nanowires or nanotubes, on a substrate. Figure 6-5c highly exaggerates the surface profile of an ultra-compliant nanowire approaching a rigid substrate (the VLS-grown ZnO nanowires used in this study were atomically smooth). Upon contact, the nanowire at first makes multi-asperity contacts with the silicon substrate, which is shown in Figure 6-5d.

At this stage, the adhesion force between the two bodies is compounded by the meniscus force at the interface, which applies a pull-in force on the nanowire, whose elastic stiffness resists the pull-in force. However, the meniscus force dominates the restoring force from the nanowire, resulting in a conformal contact (Figure 6-5e), even without the

95 application of any external normal load (N = 0). In the absence of any externally applied normal force and because of the conformal contact, the classical law of friction (F = μN) ceases to be valid, and experimental observations indicate F = σA type behavior [105,

262]. Here μ and σ are the coefficient of friction and shear strength, respectively.

Figure 6-5: Effect of nanowire contact compliance on friction-adhesion coupling.

(a), (b) For rigid macro-scale bodies adhesion alone cannot make the elastic– plastic contacts and externally applied force N is essential for friction. (c) - (e) For ultra- compliant nanoscale structures, adhesion force alone can make conformal contact, shifting the friction mechanism to F = σA type.

96 The conceptual adhesion–friction coupling model in Figure 6-5 can be verified quantitatively using the scaling analysis of surface tension and linear elasticity theories.

The total attractive force between the nanowire and the substrate is a combination of the capillary force due to Laplace pressure and the van der Waals force [263].

 1 1    2 Fattractive     RA  nRA (1)  RA RB  where γ is the surface tension, RA is the inner radius of the capillary neck, RB is the local meniscus radius (shown in Figure 6-6) and n is a factor that depends on the adhesion and elastic contact mechanics (n = 4 for Derjaguin-Muller-Toporov and n = 3 for Johnson-

Kendall-Roberts models, respectively). The contribution of the capillary force clearly dominates the van der Waals force and their combined effect is to pull in the nanowire towards the rigid substrate. The nanowire can be modeled as a clamped beam between two asperities, as shown in Figure 6-6.

Figure 6-6: Nanowire suspended on two global peaks of a silicon substrate Inset shows zoomed view of the contact

97 To completely pull in the nanowire to make a conformal contact as shown in

Figure 6-5e, the attractive force must dominate the restoring force due to the nanowire bending stiffness, which can be expressed as

192 E 5 3a 4 F  h (2) restoring 16 L3

where E is Young‟s modulus of the nanowire, a is the length of the one face of the hexagonal nanowire cross-section, L is the distance between the two asperities and h is the maximum separation between the two surfaces. The nominal radius of the ZnO nanowires used in this study was 100 nm and its Young‟s modulus was measured to be about 30 - 40 GPa [257]. It is important to note that marginally accurate values of the interfacial contact area can be obtained by considering the true hexagonal cross-section of the nanowires. AFM scans were performed to determine the substrate surface roughness

(Ra) to be about 0.254 nm (Figure 6-7). Since the ZnO nanowires are grown by self- assembly, they have smoother surfaces. The term L denotes the average length between global peaks in the surface, which varies from 3 to 4 µm for a commercially available polished silicon wafer [264]. The value of the nanowire- substrate separation distance h is obtained from the Rmax values from the AFM scans, which is about 1.093 nm.

98

Figure 6-7: AFM scan of silicon substrate surface

Figure 6-8 shows the restoring force in the nanowires as a function of the basal unit length of the hexagonal nanowire cross-section. The experimentally obtained value of the adhesion for the nanowires with a nominal basal unit length of 100 nm varied from

155 to 175 nN and the average value is shown. Three different cases of global peaks (L =

1, 2 and 3 µm) are shown, with L = 1 µm being the most conservative value. According to this model, conformal contact was established and the F = σA type friction mechanism was dominant as long as the adhesion (attractive) force is greater than the restoring force.

As the nanowire cross-sectional area increases, so does its bending stiffness and beyond a critical value (about 110 nm for the ZnO–silicon system), the nanowire rather makes only non-conformal, multi-asperity contact like any other macroscopic rigid bodies as shown in Figure 6-5b. This is shown by the shaded region in Figure 6-8.

99

Figure 6-8: Restoring force as a function of nanowire radius

100 Chapter 7

Strain dependence of Bandgap in individual

Zinc Oxide Nanowires §

7.1 Introduction

Zinc oxide (ZnO) is a direct bandgap semiconductor and a piezoelectric material with several important technological applications at the nanoscale such as nanogenerators

[265, 266], field emission transistors [267, 268], chemical and strain sensors [269-272] and in biomedical systems [273, 274]. The recent focus on using ZnO nanostructures in nanoscale energy conversion devices as well as conventional micro-electronic devices requires a detailed understanding of how strain affects the electrical and electronic properties. The electrical properties of ZnO nanowires [275-277] and nanobelts [278] have been studied as a function of strain and the conductance was observed to change significantly with applied strain. However, studies on the variation of electronic properties (bandgap) of zinc oxide as a function of strain have been largely limited to thin films and the strain applying mechanism has always been intrinsic or residual stresses arising from growth of ZnO films on substrates [52, 279-281]. In comparison, literature on the nanowire form is limited to the studies by Han et al. [282] and Xue et al. [283], in which the authors induced curvatures in nanowires fixed on substrates and observed

§ Contents of this chapter are based on the following manuscript; Manoharan, M. P., Wang, B., Haque, M. A., Electronic-mechanical coupling in Zinc Oxide nanowires, 2011 (In preparation)

101 significant red shift under tensile stress [282, 283] and blue shift under compressive stress

[283] in the cathodoluminescence spectra.

Understanding the effect of mechanical strain on the bandgap and carrier mobility of semiconductors bears enormous technological implications, especially with the potential applications of novel nanostructured materials such as nanowires. Such strain dependence of bandgap can prove beneficial if the bandgap of a semiconductor can be

„tuned‟ controllably for specific applications. Strain control is primarily achieved by two methods, (i) modifying the residual stresses arising from mismatched lattice parameters when the semiconductor is epitaxially grown on a substrate or (ii) by applying an external stress to the material. For instance, lattice mismatch-induced strain has been used to tune the bandgap of CdTe quantum dots [284], Ge nanocrystals [285] and CdS thin films

[286], while an externally applied stress has been observed to change the bandgap in silicon nanowires [287], GaAs quantum well structures [288] and also in carbon nanotubes [289] and graphene [290]. „Strained silicon‟ is another well known example used in faster and smaller modern microprocessors, where tensile stresses in silicon

(grown epitaxially on silicon germanium) significantly increases electron mobility, providing a new route to circumvent the effects of miniaturization. It has been observed that the bandgap linearly decreases (increases) with applied tensile (compressive) strain, hence very little or no strain engineering is possible by simply bending a nanowire. As shown in Figure 7-1a, bending introduces linearly variable strain across the cross-section of the nanowire, where the integral of the bandgap change over the cross-section would equal to zero. For analogy, piezo-resistivity in semiconductors is also dependent on the

102 direction of the applied strain [291], which is the reason piezo-resistive layers in sensors are never deposited throughout the thickness in bending structure. For fundamental studies on electronic-mechanical coupling, uniform strain field is more relevant (shown in Figure 7-1b) and accurate over bending because photo or cathodoluminescence techniques essentially involve spatial averaging, which may be difficult to avoid because of the considerable electron scattering and exciton diffusion (the length of exciton diffusion in ZnO is about 110 nm [292]) in the nanowires.

7.2 Experimental setup and results

Uniform tensile stress is applied on individual zinc oxide nanowires with average diameter of 200 nm using a custom-designed and fabricated micro-electro-mechanical device. The tensile testing device was fabricated using bulk micromachining techniques from a silicon-on-insulator wafer with a highly doped silicon device layer. The device uses thermal actuator beams to apply displacements between two freestanding micromachined silicon structures, which act as mechanical grips. The fabrication and working principle of this MEMS device is explained in chapter 3.4. Figure 7-1c shows a scanning electron micrograph of the testing device, with the specimen barely visible.

Figure 7-1d shows the zoomed view of a freestanding nanowire specimen mounted on the testing device. When mounted on these grips as shown in Figure 7-1d, the nanowires experience uniform tensile deformation, which can be characterized through the input power in the thermal actuator beams and the mechanical stiffness of the actuator structure as described in [293]. The single crystal zinc oxide nanowire specimens were grown using the vapor-liquid-solid (VLS) mechanism using ultrathin gold film as a catalyst

103 [257]. The growth of the nanowires took place in the 0001] direction, which is also the mechanical loading axis. Individual nanowires were manipulated to the testing device inside a dual gun focused ion beam – electron microscope (FEI Quanta 3D 200

FIB/SEM) using a tungsten probe tip attached to an Omniprobe ® nanomanipulator. Ion beam induced platinum deposition in the FIB-SEM was used to attach the two ends of the nanowires on the testing device.

Figure 7-1: Schematic of experimental setup to strain individual nanowires

Strain field in a nanowire cross-section under (a) bending and (b) uniaxial loading, (c) scanning electron micrograph of the MEMS loading device, (d) zoomed in view of the freestanding ZnO nanowire specimen, (e) schematic diagram of the experimental setup for acquiring photoluminescence spectra as a function of uniaxial strain

104 After integrating the nanowire with the device, the testing device was packaged and positioned under a Raman microscope. The experimental setup is shown schematically in

Figure 7-1e. DC voltage applied across the actuator beams causes thermal expansion of the beams, while the geometry of the device ensures that the nanowire is subjected to uniform tensile stress. The voltage applied was increased in small steps till the nanowires fractured. The device has built in displacement sensors to measure the strain on the nanowire, which was recorded in conjunction with the photoluminescence spectrum at each voltage step. Image analysis was then used to determine the strain on the nanowire and the position of the peaks in the corresponding photoluminescence spectrum. The specimens are freestanding, which eliminates any concern on laser reflections from the substrate. Also, the applied strain field is uniform, which eliminates any concern on the spatial averaging of the photoluminescence signal throughout the specimen cross-section.

7.3 Discussion of results

To probe the strain effect on near-band-edge (NBE) emission of ZnO nanowires, the MEMS device was actuated while the photoluminescence (PL) spectra were acquired.

The collected PL spectra on ZnO nanowires typically consisted of a UV emission at

~3.24 eV, a green emission at ~2.25 eV and an IR emission at ~1.62 eV. Studies carried out on the origin of the PL emission bands have shown that the UV emission is associated with band-edge excitons and is commonly referred to as NBE emission. The green and IR emissions are due to defects in the crystal [294-296]. Figure 7-2 shows the NBE emission as a function of strain and a comparison with the only two experimental studies on ZnO nanowires available in the literature. Here, the scatter in the experimental data is because

105 of the inherent brittleness of the material and not due to size effect. Especially at higher strains, some point-defect structures might evolve, even though the fracture pattern is brittle. The trend in the experimental data suggests that electronic bandgap linearly decreases with applied tensile strain with a measured sensitivity of 25 meV per % of strain. Such linearity is predicted by density functional theory and plane-wave pseudo- potential techniques [297]. The measured strain-bandgap sensitivity was also consistent in magnitude with previously reported results for ZnO thin films [298] and with computational predictions [299, 300].

Figure 7-2: Energy shift in NBE emission versus strain for ZnO nanowires

As the nanowires were subject to tensile strain from the device, a downshift of the

NBE emission energy was observed. To further study the mechanism, the PL spectra of two different ZnO nanowires subject to uniaxial strain up to ~1.3 % is highlighted in

Figure 7-3. Each emission spectrum is normalized to the highest intensity. The value of the strain was calculated from the displacement recorded in the photos and is labeled next

106 to the corresponding spectrum. The emission profiles in Figure 7-3a consist of a relatively broad band with no sharp features. The wavelength of this emission band exhibits up shift with increasing strain. The emission profile in Figure 7-3b, on the other hand, shows sharp peaks within the overall broad emission, which shows the same trend as illustrated in Figure 7-3a with a larger energy downshift. The sharp features, however, possess relatively invariant energy positions (3.265 eV and 3.122 eV) with increasing strain (up to 1.34%) within instrumental resolution. These sharp features can be attributed to the phonon replicas of the transition of excitons bound to neutral donors (DX). The DX emission and its phonon replica are normally observed in high quality ZnO materials under low temperature (< 20 K). The energy positions of these features are slightly downshifted from their usual observations at lower temperatures by ~20 meV. This is probably due to the temperature induced change of band structure. The relative invariance of the energy of DX emission probably suggests that the red shift of NBE emission is largely due to the lowering of conduction band edge instead of valence band edge. That is, the energy of the conduction band edge is more sensitive to the external strain than the valence band edge. This observation conforms with the effective-mass- envelope function theory predictions, where the applied strain is known to broaden the gaps between the quantized states of the sub-bands in the conduction band minima [282].

107

Figure 7-3: Strain-dependent PL spectra in two individual ZnO nanowires

108 Chapter 8

Strain dependence of Thermal and Electrical Conductivity

of Polyaniline Thin Films §

8.1 Introduction

Polyaniline is the most widely studied conductive polymer because of its simple synthesis and doping chemistry which allows its electrical conductivity to be easily customized for any application [30]. While applications for conducting polymers in organic electronics [301, 302] and solid state energy conversion devices [39, 303] have been the subject of extensive research in recent years, studies on thermal and electrical conductivity of such films at the nanoscale are limited. In the case of thermal properties in conducting polymer thin films, for instance, existing studies focus on the thermal conductivity in the direction of the film thickness which is usually different from the current flowing (in-plane) direction due to anisotropy. Thermal transport properties of electrically conductive polyaniline (PANI) films (40 µm thickness) were first investigated over a wide range of temperatures by Yan et al. [304]. Thermal conductivities of various protonic acid-doped polyaniline films were measured by a combination of a laser flash method and a differential scanning calorimeter and results indicate that doped polyaniline films have extremely low thermal conductivity.

§ Contents of this chapter are based on the following journal publication; Manoharan, M. P., Jin, J., Wang, Q., Haque, M. A., Thermo-electro-mechanical Characterization of Nanoscale Conducting Polymer Films, Journal of Nanoscience and Nanotechnology Letters, 2010

109 Albuquerque et al. [305] applied photo-thermal spectroscopy to measure the thermal conductivity of 20 µm thick polyaniline films and found no significant difference between undoped and doped films with regards to thermal parameters. Recently, Kaul et al. [306] applied the three-omega method to 110 nm and 5 µm thick conducting polyaniline films, and a strong length-scale effect on electrical and thermal conductivity was found. The effect of doping [30] and length scale or thickness [18] on the thermal and electrical conductivity of PANI thin films has been studied recently in much greater detail.

In this chapter, the development of a unique characterization tool that enables the measurement of thermal and electrical conductivity of polyaniline thin films as a function of tensile stress applied on the films is reported. The thin films tested had thickness in the range of 20 nm – 250 nm, thus also demonstrating the length-scale dependence of the effect of mechanical strain on thermal and electrical conductivity.

8.2 Experimental setup to measure thermal and electrical conductivity

In this work, PANI in the emeraldine base form (EB) was synthesized by the chemical oxidative polymerization of aniline. Camphor-10-sulfonic acid (CSA) powders and EB in a 0.5 molar ratio of CSA to phenyl-N repeat unit were mixed using a mortar and pestle and then added to the m-cresol while stirring. To obtain a thin film, the filtered

PANI solution was spin coated on to a polyethylene terephthalate (PET) sheet (the blue

110 layer in Figure 8-1a) followed by heat treatment. The thickness of the PANI/CSA specimens was measured using an atomic force microscope.

For the thermal conductivity measurements, a modified 3-omega technique was used where the PANI layer acts as both heater and temperature sensor. The PANI thin film was patterned lithographically in the form of four pads that connect to a 100 µm long and 10 µm wide filament (the green layer in Figure 8-1a). Oxygen plasma reactive ion etching was used to transfer this pattern to the PANI layer. The four pads act as electrodes for the thermal and electrical conductivity measurements. To reduce contact resistance between the electrical probes and the specimen, a thin layer of aluminum (the grey layer in Figure 8-1a) was sputtered on to the four electrode pads using a shadow mask. Small diameter silver wires were attached to these aluminum pads using electrically conductive epoxy to further minimize contact resistance. The specimen was placed inside a vacuum chamber to minimize convection losses and the temperature was maintained at 300 K. For the thermal conductivity measurements, a sinusoidal current I =

I0 sin ωt was supplied across the outer two pads and the third harmonic of the voltage signal was measured by a lock-in amplifier. This signal (V3ω) can be used to evaluate the in-plane thermal conductivity of the PANI thin film. The electrical conductivity was determined by measuring the four-point current-voltage characteristics of the specimen.

111 8.3 Measuring thermal and electrical conductivity as a function of strain

The PANI thin film was spin coated on a PET (polyethylene terephthalate) sheet with 0.5 mm thickness. To subject the PANI film to strain, the PET sheet was bent in an arc using a custom made mechanical manipulator. The thickness of the PANI film varies between 20 nm and 250 nm, which is much smaller compared to the thickness of the PET sheet. Thus, the PET sheet can be bent such that the PANI film experiences uniform tensile stresses across the entire thickness of the film. Increasing the curvature of the PET sheet increases the tensile stresses on the PANI film as illustrated in Figure 8-1a-d. The thermal and electrical conductivity are measured by 3-omega method and four point I-V respectively. The low-resistance silver wires (not shown in Figure 8-1) attached to the four aluminum pads enable measurements to be made even when the PET sheet is bent in a high curvature arc (Figure 8-1d).

Once the PET sheet has been bent and clamped, its outline was traced on to a sheet of paper. The curvature of the arc was then determined as illustrated in Figure 8-2.

The strain on the PANI thin film is then given by,

t  T t   2  2 R R

where, ε is the strain on the PANI thin film, t is the thickness of the PET sheet (t = 0.5 mm), T is the thickness of the PANI film (varies between 20 nm and 250 nm) and R is the

112 radius of curvature of the PET sheet. Since, t >> T, the error resulting from the approximation used above is negligible.

Figure 8-1: Schematic of PANI/PET sheet subject to increasing bending strains

The PANI thin film (green layer) is spin coated on a PET substrate (blue) with aluminum (grey) sputtered to form low resistance electrical contacts.

Figure 8-2: Strain measurement of the bent PANI/PET sheet

113 8.3.1 Thermal conductivity measurement

Lu et al. [87] extended the 3-omega (3ω) method to measure the in-plane thermal properties of a rod- or filament-like specimen, including specific heat and thermal conductivity. The experimental technique used here is a modified version of the original

3-omega method, which has been applied to measure the in-plane thermal conductivity of polyaniline thin films that have a temperature-dependent electrical resistance. A conducting filament-like polyaniline specimen is considered in a four-probe configuration deposited on the surface of the electrically insulating PET substrate (Figure

8-1a). The two outer electrodes (1 and 4) are used to supply an alternating current, and the two inner electrodes (2 and 3) are used to measure the voltage across the specimen

(Figure 8-3). The applied sinusoidal current source (I = I0 sint) leads to Joule heating

2 equal to I (R0+R), where R is the resistance fluctuation of the specimen and is proportional to the temperature oscillation.

Figure 8-3: Schematic of the 3-omega setup for thermal conductivity measurement.

The same four-probe configuration is also used for electrical conductivity measurements. A sinusoidal current is passed across the outer two pads (1 and 4) and the resulting third harmonic voltages across the two inner pads (2 and 3) are measured by a lock-in amplifier

114 The heat loss to the substrate was taken into account by considering the thermal resistance ΣRt, where Σ Rt = Rt,cont-int. + Rt,cond-sub, i.e., the sum of contact resistance at the interface (Rt,cont-int.) and conduction resistance within the substrate (Rt,cond-sub). Thermal

resistance from the substrate can be approximated as, Rt,cond sub  s  s , where

s   s / 2 , is the thermal penetration depth in the substrate,  s is the thermal

diffusivity and  s is the thermal conductivity of the substrate. The heat generated by the specimen, and transported to the substrate are expressed by the one dimensional heat conduction equation [30],

Txt(,) 2 TxtI (,)sin 2 2  t ((,)) TxtTA C 00[ R  R ( T ( x , t )  T )]  p t x2 LS00 LS R  t (1) where T(x, t) is temperature at time t and position x along heat flow direction. L and S are the length between the voltage contacts and the cross-section of the specimen, respectively. ρ, Cp and κ are the density, specific heat and thermal conductivity of the specimen. R0 is the initial electrical resistance of the specimen at initial temperature T0.

R’ is the temperature coefficient of resistance at T0, R' dR dT  and A is the contact T0 area between the specimen and substrate.

At low modulation frequencies, the thermal conductivity (κ) can be determined from the following relation between the root-mean-square values of the 3ω voltage (V3ω), thermal conductivity, and thermal resistance. The low frequency range can be obtained by measuring V3ω as a function of frequency; this is explained in detail in [18],

115 2I 3 R R' L V  0 0 (2) 3  2 LA  4S   Rt

The average temperature change of the specimen [18] can be expressed as

4I 2 R L T  0 0 (3)  2 LA  4S  Rt

3 The linear relationship between V3ω and I0 can be extracted by measuring the applied current dependence of V3ω, and inserting equations (2) and (3) into the heat balance equation,

2 I0 ' TA R0  R T   C pT (4) 2LS LSRt

-1 κ and ΣRt can be simultaneously determined, where λ is the thermalization time,

 2 A   2  (5) L C p LSRt C p

The PANI/PET sheet is subjected to strain by bending the sheet in a two-point fixture as described in the preceding section. The thermal conductivity of the PANI film was then measured at each strain step using the 3-omega described above.

116 8.3.2 Electrical conductivity measurement

The electrical conductivity of the spin-coated PANI thin films was measured by the standard four-point I-V characterization technique (Figure 8-3). A current source is used to supply a steady current across the outer two pads 1 and 4 while a high sensitivity voltmeter (Keithley 2400 sourcemeter) measures the voltage across the inner pads 2 and

3. The PET sheet was then bent and clamped as described in the preceding section to apply a strain on the PANI thin film and the I-V measurements were repeated to determine the strain dependence of electrical conductivity.

8.4 Experimental results

The strain dependence of electrical and thermal conductivity of PANI thin films was measured for films with thickness of 20 nm, 100 nm and 250 nm and tensile bending strains up to 10%. The results of the experiments are presented in Figure 8-4, Figure 8-5 and Figure 8-6. As explained in the preceding sections, the PET sheet was bent and clamped in an arc resulting in a uniform tensile stress across the thickness of the PANI film. The electrical and thermal conductivity of the PANI films was measured while the strain was progressively increased (labeled as loading in Figure 8-4, Figure 8-5 and

Figure 8-6) and then gradually reduced (labeled as unloading in Figure 8-4, Figure 8-5 and Figure 8-6). A general trend observed for different thickness of the PANI film is that during loading, both electrical and thermal conductivity decrease monotonically as the strain was increased. However, during unloading, electrical and thermal conductivity remain nearly constant (i.e. have the same value as during the highest tensile strain applied) until the strain is reduced to about 3%. As the strain was further reduced, the

117 electrical and thermal conductivities begin to decrease monotonically with reducing strain.

Figure 8-4: Conductivity as a function of strain for 20 nm thick PANI film

Thermal conductivity (, solid blue line) and electrical conductivity (, dotted black line) of PANI thin film with 20 nm thickness as a function of the bending strain in a complete loading and unloading cycle

Figure 8-5: Conductivity as a function of strain for 100 nm thick PANI film

118

Figure 8-6: Conductivity as a function of strain for 250 nm thick PANI film

8.5 Discussion of results

To further understand the observed trend in the thermal and electrical conductivities of PANI films, scanning electron microscope (FE-SEM) images of the

PANI film surface were taken as the PANI/PET sheets were subjected to increasing bending strains. The images (Figure 8-7a-d) clearly show a trend of crack initiation and growth as the bending strain on the PANI film was increased – the „loading‟ phase.

Cracks began to appear in the PANI film at a strain of about 3% (Figure 8-7b), irrespective of the film thickness and can be considered as fracture strain for the PANI thin films. The cracks are oriented in a direction perpendicular to the direction of the applied tensile stresses. As the bending strain on the film was further increased, the cracks grow in length and depth; and at 4.5 % strain, the cracks had propagated through the entire depth of the PANI thin film (Figure 8-7c). Further bending of the PANI/PET sheet resulted in extensive crack growth across the PANI film surface (Figure 8-7d).

119

Figure 8-7: FE-SEM images of PANI thin film under increasing bending strain

(a) PANI film under zero strain, (b) at 2.7 % strain, cracks begin to appear and at (c) 4.5 % strain, the cracks widen with the crack propagating through the entire thickness of the film and (d) at maximum applied strain of 10.3 %, the length and number of cracks has increased significantly. Inset for each image shows a schematic of the PANI/PET sheet subjected to the corresponding bending strain.

The length and number of cracks that appeared in the PANI film surface was found to increase continuously with increasing strain. This provides a qualitative explanation to the observed trend of electrical and thermal conductivity of the PANI film with bending strain (Figure 8-4, Figure 8-5 and Figure 8-6). As the length and number of cracks increases, the voids created by the presence of cracks in the PANI film increases resistance to the flow of electrons and phonons which are responsible for electrical and thermal transport in conducting polymers such as PANI. At the maximum applied bending strain of 10.3 %, the electrical and thermal conductivity had reduced by as much as 36% and 13% respectively for the 20 nm thick PANI film. The reduction in conductivity is also a function of the thickness of the PANI film as listed in Table 8-1.

120 Table 8-1: Thickness dependence of the reduction in thermal and electrical conductivity with strain in PANI thin films

Reduction in Reduction in Reduction in Reduction in Thickness thermal thermal electrical electrical of PANI conductivity conductivity conductivity conductivity film during loading during unloading during loading during unloading 20 nm 12.8 % 6.2 % 35.5 % 15.6 %

100 nm 4.0 % 1.5 % 26.9 % 20.7 %

250 nm 2.1 % 0.9 % 22.7 % 20.1 %

Further crack growth did not occur as the strain was reduced – the „unloading‟ phase, and therefore, the electrical and thermal conductivity remain nearly constant

(Figure 8-4, Figure 8-5 and Figure 8-6). This trend was observed until the strain was reduced to about 3 %; further reduction in bending strain was typically accompanied by a reduction in both electrical and thermal conductivity of the PANI films (Figure 8-4,

Figure 8-5 and Figure 8-6). Crack initiation or fracture observed at a strain of 3 % during the loading phase has important implications for the unusual behavior of conductivity observed during the unloading phase. During the loading phase, as the bending strain was progressively increased, cracks begin to appear at a strain of about 3 % and continue to grow in length and depth as the strain was increased to a maximum of 10.3 %. Thus, during the unloading phase when the bending strain was gradually reduced, the crack faces along the length of the crack begin to “close” and there was no additional void created that could have affected electron or phonon transport and thus, the thermal or electrical conductivity. It is important to note here that crack formation is an irreversible process in PANI thin films. There was no crack „healing‟ occurring as the bending strain was reduced, only the width of the crack reduces to almost zero such that the when the

121 strain was reduced to the fracture strain of 3 %, the two faces of the crack surface were in contact with each other. Further reduction in bending strain resulted in the crack faces being pressed against each other, resulting in new contact areas. These new contact points cause electron and phonon scattering, thereby reducing the thermal and electrical conductivity of the PANI films. The reduction in thermal and electrical conductivity during the unloading phase is always lower than that during the loading phase and was also a function of the PANI film thickness as detailed in Table 8-1.

122 Chapter 9

Conclusions and Directions for Future Research

9.1 Scientific and technical contributions

In this research, the effect of strain, either uniaxial tensile or bending tensile strain, on the crystal structure, thermal and electrical conductivity, electronic bandgap and tribological properties of thin films and nanowires was studied. The scientific contributions of this research are summarized below.

a) The uniaxial tensile testing study on 4 - 6 nm thick amorphous carbon thin film

specimens in situ in a SEM revealed size effect on the Young‟s modulus, which is

traditionally known to be scale independent. The size effect was explained on the

basis of the increased contribution of surface elastic properties (surface stress) at the

nanometer length-scale.

b) Significant stress-induced crystallization was observed in 4 - 6 nm thick ion beam

deposited amorphous platinum thin films. At 3% tensile strain, electron diffraction

patterns clearly showed irreversible transformation to face-centered cubic (FCC)

structure even at room temperature. It is proposed that the externally applied stress, in

addition to the large tensile residual stress in the films provided the activation energy

needed to nucleate crystallization, while subsequent grain growth occurred through

123 enhanced atomic and vacancy diffusion as an energetically favorable route towards

stress relaxation at the nanoscale.

c) While it is widely accepted that amorphous materials do not exhibit any size or

deformation effects on thermal conductivity, about one order of magnitude reduction

was experimentally observed at strains of up to 2.4 % for 50 nm thick freestanding

amorphous silicon nitride thin films. To explain such strong coupling with

mechanical deformation, the vibration localization in the disordered medium was

taken into account. In silicon nitride, heat transfer is possible through hopping (from

one localized frequency to other) based mechanisms. The very strong Si-N bonds

make the localization even stronger, and mechanical deformation is proposed to

decrease the overlap of the vibrational mode localization, which reduces the hopping

mode thermal transport.

d) The coefficient of friction between individual zinc oxide nanowires and silicon

substrate in ambient conditions was measured to be about two orders of magnitude

higher than bulk values, even under zero externally applied normal loads. This

anomalous behavior was explained on the basis of the compliant nature of the

nanowires and the presence of molecularly thin surface moisture layers.

e) Effect of strain on the electronic band gap of single zinc oxide nanowires was studied

under a micro-Raman microscope by acquiring the photoluminescence spectra. The

bandgap of the nanowires was found to reduce by 25 meV per 1 % of tensile strain

124 applied. This red shift of the near-band-edge emission is largely due to the lowering

of the conduction band edge instead of valence band edge.

f) The thermal and electrical conductivity of polyaniline thin films was measured by the

3-omega method and four-point I-V method respectively. The conductivities were

found to reduce with increasing tensile bending strains, due to the appearance of

cracks in the film.

The technological contributions of this research were in developing a framework for the overarching concept of length-scale induced multi-domain coupling. Particularly, a broad set of experimental methodology was developed and demonstrated on thin films and nanowires. Experimental setups were developed to:

a) Study the influence of strain on the crystal structure of thin films in situ inside a

transmission electron microscope b) Measure thermal conductivity of thin films using thermal microscopy c) Measure the tribological properties of individual nanowires d) Measure the strain dependence of electronic bandgap in individual nanowires e) Measure strain - thermal conductivity coupling in thin films using 3-omega method

125 9.2 Directions for future research

In addition to the above mentioned studies on thin films and nanowire materials, experiments are currently being performed to study the influence of strain on the thermal conductivity of vertically aligned carbon nanotubes and silicon nanowires. Also, the possibility of using surface acoustic waves to alter thermal conductivity is being investigated using a lithium niobate substrate. These studies are thematically described below.

9.2.1 Strain – thermal conductivity coupling in vertically aligned carbon nanotubes

The influence of strain on the thermal conductivity of vertically aligned carbon nanotubes (VA-CNT) is measured using thermal microscopy imaging. The experimental setup used here is similar to that used for the study on polyaniline thin films (Chapter 8).

The vertically aligned carbon nanotubes are synthesized on a silicon substrate. A polyethylene terephthalate (PET) sheet is used as the „test‟ substrate and a 500 - 600 µm wide strip of Scotch tape with adhesive on both sides is placed in the center of the PET sheet. This sheet is then pressed against the VA-CNT, causing the nanotubes to adhere and transfer to the Scotch tape as shown in Figure 9-1. The PET sheet can be bent such that the nanotubes experience tensile (Figure 9-3) or compressive (Figure 9-4) stresses.

Increasing the curvature of the PET sheet increases the tensile or compressive bending stresses on the nanotubes. Joule heating is generated in the nanotubes by passing a direct current across the electrical wires attached to the nanotubes. Thermal transport in the nanotubes and the PET substrate is then obtained for different strains (Figure 9-2, Figure

126 9-3 and Figure 9-4) by measuring the temperature profile in the thermal microscope.

Thermo-mechanical modeling and simulation are currently underway to determine the thermal conductivity value needed to generate the experimentally observed temperature profiles.

Figure 9-1: Experimental setup to measure the effect of strain on thermal conductivity of VA-CNT

127

Figure 9-2: Thermal microscope image of VA-CNT at zero strain; peak temperature is about 43 0C

Figure 9-3: Thermal microscope image of VA-CNT at 2.8 % tensile strain; peak temperature has increased to about 66 0C

128

Figure 9-4: Thermal microscope image of VA-CNT at 3.3 % compressive strain; peak temperature has increased to about 56 0C

9.2.2 Strain – thermal conductivity coupling in silicon nanowires

The influence of strain on the thermal conductivity of silicon nanowires is measured using thermal microscopy imaging. Nanowires with a cross-sectional dimension of 150 nm X 150 nm and 12 µm in length (Figure 9-5) were prepared by ion beam milling of a silicon beam, initially with a cross-section of 10 µm X 20 µm. This beam is attached to the heater beam at one end and the central beam at the other. The central beam has cooling fins for heat dissipation to reduce the influence of heating in the thermal actuator beams (Figure 9-5). Joule heating is generated in the heater beam by passing a direct current across it and the thermal transport in the silicon nanowire is then calculated (Figure 9-6) by measuring the temperature profile in the thermal microscope.

Thermo-mechanical modeling and simulation are currently underway to determine the

129 thermal conductivity value needed to generate the experimentally observed temperature profiles.

Figure 9-5: The silicon nanowire specimen is prepared by ion beam milling a 20 µm thick silicon beam

Figure 9-6: Thermal microscope image to measure heat transport across the silicon nanowire

130 9.2.3 Can thermal transport be affected by Surface Acoustic Waves?

The possibility of using ultrasonic flexural waves for convective heat transfer

[307] has been studied and here the feasibility of enhancing thermal transport using surface acoustic waves (SAW) is investigated. The experimental setup consists of an array of inter-digitated transducers and a heater patterned with 150 nm thick titanium on a

0 Y + 128 X-propagation lithium niobate (LiNbO3) piezoelectric wafer with thickness of

500 µm. This material was chosen for its high coupling coefficient in SAW generation

[308]. The transducers are powered by alternating current supplied by a radio frequency function generator (Wavetek model 145), while the heater is powered by a DC power supply (Keithley 6221). Thermal transport in the lithium niobate wafer is then obtained by measuring the temperature profile in the thermal microscope. Thermo-mechanical modeling and simulation are currently underway to determine the thermal conductivity value needed to generate the experimentally observed temperature profiles.

131

Figure 9-7: Schematic of inter-digitated transducer array and heater patterned with 150 nm thick titanium on lithium niobate wafer

Figure 9-8: Thermal microscope image of the inter-digitated transducers and metal heater at a frequency of 8 MHz

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152 VITA MOHAN PRASAD MANOHARAN

317 Leonhard Building, Pennsylvania State University, University Park, PA 16802 http://www.personal.psu.edu/mxm1002 E-mail: [email protected]

Research Expertise

In situ experimental studies of coupled fields in nanoscale materials – interaction between mechanical, thermal, electrical and electronic properties in thin films and nanowires

Studying thermo-mechanical properties of graphene (synthesized by CVD), vertically aligned carbon nanotube arrays and silicon nanowires

Design and fabrication of MEMS devices for force and displacement actuation and sensing and five years experience in microfabrication in class 10/100 cleanroom

Education

PhD in Mechanical Engineering, Pennsylvania State University, Summer 2011 Dissertation title: Influence of strain on the physical properties of materials at the nanoscale

Master of Science in Mechanical Engineering, Pennsylvania State University, 2009

Bachelor of Technology in Mechanical Engineering, Indian Institute of Technology Roorkee, Roorkee, India, 2006

Awards & Honors

Rustum & Della Roy Innovation in Materials Research Award, Pennsylvania State University, 2009

University Graduate Fellowship, Pennsylvania State University, 2008-09

Kulakowski Travel Award, Department of Mechanical & Nuclear Engineering, Pennsylvania State University, 2008

Representative Publications

Manoharan, M. P., Kumar, S., Haque, M. A., Rajagopalan, R., Foley, H. C., “Room temperature amorphous to nano-crystalline transformation in ultra-thin films under tensile stress: an in situ TEM study”, Nanotechnology, 21, 505707, 2010

Manoharan, M. P., Lee, H., Rajagopalan, R., Foley, H. C., Haque, M. A., “Elastic Properties of 4-6 nm-thick Glassy Carbon Thin Films”, Nanoscale Research Letters, 10.1007/s11671- 009-9435-2, 2009

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