I the Pennsylvania State University the Graduate School College Of

The Pennsylvania State University

The Graduate School

College of Engineering

SIZE EFFECTS ON MECHANICAL AND THERMAL PROPERTIES OF THIN FILMS

A Dissertation in

Mechanical Engineering

Md Tarekul Alam

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

August 2015

The dissertation of Md Tarekul Alam was reviewed and approved* by the following:

Aman Haque Professor of Mechanical Engineering Dissertation Advisor Chair of Committee

Zoubeida Ounaies Professor of Mechanical Engineering

Donghai Wang Associate Professor of Mechanical Engineering

Charles E. Bakis Distinguished 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

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ABSTRACT

Materials, from electronic to structural, exhibit properties that are sensitive to their composition and internal microstructures such as grain and precipitate sizes, crystalline phases, defects and dopants. Therefore, the research trend has been to obtain fundamental understanding in processing-structure-properties to develop new materials or new functionalities for engineering applications. The advent of nanotechnology has opened a new dimension to this research area because when material size is reduced to nanoscale, properties change significantly from the bulk values. This phenomenon expands the problem to ‘size-processing-structure-properties- functionalities’. The reinvigorated research for the last few decades has established size dependency of the material properties such as thermal conductivity, Young’s modulus and yield strength, electrical resistivity, photo-conductance etc. It is generally accepted that classical physical laws can be used to scale down the properties up to 25-50 nm length-scale, below which their significant deviation or even breakdown occur. This dissertation probes the size effect from a different perspective by asking the question, if nanoscale size influences one physical domain, why it would not influence the coupling between two or more domains? Or in other words, if both mechanical and thermal properties are different at the nanoscale, can mechanical strain influence thermal conductivity? The hypothesis of size induced multi-domain coupling is therefore the foundation of this dissertation. It is catalyzed by the only few computational studies available in the literature while experimental validations have been non-existent owing to experimental challenges. The objective of this research is to validate this hypothesis, which will open a novel avenue to tune properties and functionalities of materials with the size induced multi-domain coupling.

Single domain characterization itself is difficult at the nanoscale due to specimen preparation, setting up proper boundary conditions and the required resolution in measurement. The scope of this work requires multiple property characterization simultaneously, which makes it even more challenging. To accomplish this goal, several micro electro mechanical system (MEMS) based testing devices have been developed in this work. These devices can integrate sample, tiny heaters, electrodes, actuators and sensors to measure not just one property, but multiple properties, at the same time. An additional advantage of the setup is its inherently small size that allows high- resolution microscopy techniques such as transmission electron microscope (TEM) to visualize the

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events taking place inside the specimen during the experiments. These devices were then used to characterize both single and multi-domain studies as highlighted below.

As a first step towards multi-domain characterization, this research explored the mechanical behavior (microstructural effects on deformation and failure) of metallic thin films. For example, in-situ TEM study of aluminum thin films under fatigue loading showed that deformation mechanism in nanoscale is remarkably different from that of bulk scale. In bulk material, dislocation based activity due to fatigue loading leads to formation of persistent slip bands (PSB) and failure of material through crack formation. However, 200 nm thick aluminum specimens with average gain size of 80 nm showed no signs of dislocation activities. Instead, elastic or reversible rotation of the grains is observed; a deformation mechanism that is proposed to make the specimens insensitive to stress concentration and fatigue. Consequently, not a single sample failed even after a million cycle of loading at 0.1% and 0.4% tensile strain.

As a continuation of the single domain studies towards multi-domain characterization, influence of stress and temperature on the grain size of nickel thin films is studied next. Grain size plays a major role on the mechanical and thermal properties of thin films. Commonly, thermal annealing is used in the literature to control grain size. Irradiation also has strong effects on grain size. Less known is the phenomenon of mechanical stress assisted grain growth. The in-situ TEM experiments on 75 nm thick, 5-10 nm average grain size platinum specimens show rapid grain growth above 290 MPa stress and 0.14% strain. The associated strain energy is found to be higher than that required for stable interface motion but lower than the stress required for unstable grain boundary motion. This is attributed to geometrical incompatibility arising out of crystallographic mis-orientation in adjoining grains, or in other words, geometrically necessary grain growth. Since temperature plays a strong role in grain boundary mobility, this study was expanded to thermomechanical loading scenario. The experimental results suggest a unique synergy – as evident from large grain growth in 100 nm thick, 10 nm average grain size nickel at only 325 MPa stress and

373 K temperature. In comparison, the yield stress and melting point (Tm) are about 1.8 ± 0.1 GPa and 1730 K. Such low temperature – low stress synergy towards large grain growth is remarkably different from the literature, which involves high temperature (T/Tm > 0.5) to achieve any appreciable grain growth.

To study the thermal transport, a novel approach based on infrared microscopy is developed. This technique uses energy conservation principle to establish the mathematical model and combines the model with experimentally measured sample temperature to determine the

thermal conductivity of thin film. This method is used successfully to measure the thermal conductivity of ultra-thin films (10 nm and 20 nm thick hexagonal boron nitride) as well as regular thin films (200 nm amorphous silicon film, 200-500 nm thick carbon doped oxide). This work also presents an experimental technique to measure heat transfer coefficient in micro and nano scale. The heat transfer coefficient for air is roughly two orders of magnitude higher than the bulk value and found to be dependent on the size and temperature of sample. It is suggested that the dominant heat transfer mode in this case is solid to air heat conduction. This work gives an empirical relationship to predict the heat transfer coefficient for different sample size and temperature.

To investigate the central hypothesis, i.e. size induced coupling between mechanical strain and thermal conductivity of material, multi-domain experiments are carried out. A major contribution of this dissertation is the experimental validation of this hypothesis. It has been shown that thermal conductivity of material in nano scale can be tuned by mechanical stress. Thermal conductivity of 50 nm thick freestanding silicon nitride thin film is found to be decreased by an order of magnitude with 2.4% tensile strain. Classical thermal physics does not predict such change. It is hypothesized that energy transfer in amorphous insulating solids depends heavily on the vibration localization, i.e. hopping mode, which is sensitive to mechanical strain. Increased localization of vibrations under tensile strain is the cause of thermal conductivity reduction. Another work on 200 nm thick freestanding amorphous silicon thin film shows the opposite trend i.e. increase of thermal conductivity with applied tensile strain. This is also novel because amorphous materials are not predicted to show any such effect. A closer look in the microstructure of the material during the experiment indicates that stress induced grain growth or phase transformation might be the major contributor for this increase in thermal conductivity.

Another key contribution of this dissertation is the observation of the mechanical stress dependent dielectric breakdown behavior in carbon doped oxide thin film. When electrical voltage is applied across a dielectric film, a very small amount of leakage current is measured across the material. The amount of leakage current increases with the increase of applied electrical field. As applied electrical field is increased gradually, the material fails at some point, which is known as the “breakdown” of the dielectric material. In this research work, it has been shown that mechanical stress alone can influence the amount of leakage current of the material, even though the applied electrical field is kept same throughout the process. This behavior is ascribed to the de-trapping of electrons under mechanical strain.

This dissertation showed experimental evidence of length scale induced coupling between thermal, mechanical and electrical domains. The technological aspect of this research impacts micro and opto electronics, energy conversion, sensors and actuators and in general, nanotechnology applications. However, it is also very fundamental in nature, and the new phenomena that are explored will enrich knowledge of material behavior and lay foundation for the future work on multi-physics of material at nano scale.

TABLE OF CONTENTS

LIST OF FIGURES ……………………………………………………………………………..... x

LIST OF TABLES ……………………………………………………….……………...……… xiv

ACKNOWLEDGEMENTS …………………………………………………..……...…………. xv

CHAPTER 1 INTRODUCTION ...... 1

1.1 Length scale effect on mechanical and thermal properties of material ...... 1 1.2 Length scale induced Coupling ...... 3 1.3 Objective and scope of this work ...... 4

CHAPTER 2 SIZE EFFECTS ON MICROSTRUCTURE AND PROPERTIES OF METALLIC THIN FILMS ...... 9

2.1 Fatigue Insensitivity of Nanoscale Freestanding Aluminum Films ...... 9 2.1.1 Objective and motivation ...... 10 2.1.2 Experimental details ...... 11 2.1.3 Results and Discussion ...... 16 2.1.4 Conclusions ...... 18 2.2 Grain Growth in Nano-crystalline Nickel Films at Low Temperature and Stress ...... 19 2.2.1 Literature review ...... 19 2.2.2 Experimental Setup ...... 20 2.2.3 Result and Discussion ...... 21 2.2.4 Conclusion ...... 24

CHAPTER 3 A NEW APPROACH FOR THERMAL CONDUCTIVITY MEASUREMENT OF THIN FILMS ………………………………………………………………………………..25

3.1 Structural Size and Temperature Dependence of Solid to Air Heat Transfer ...... 26 3.1.1 Introduction ...... 26 3.1.2 Experimental Setup ...... 28 3.1.3 Experimental procedure ...... 30 3.1.4 Mathematical model for determination of heat transfer coefficient ...... 31 3.1.5 Experimental results and validation ...... 32 3.1.6 Discussion ...... 36 3.1.7 Conclusion ...... 39

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3.2 Characterization of Very Low Thermal Conductivity Thin Films ...... 40 3.2.1 Introduction ...... 40 3.2.2 Experimental technique ...... 45 3.2.3 Mathematical model ...... 48 3.2.4 Results and discussion ...... 52 3.2.5 Conclusion ...... 56 3.3 Thermal Conductivity of Ultra-thin CVD Hexagonal Boron Nitride ...... 57 3.3.1 Introduction ...... 57 3.3.2 Experimental Setup ...... 59 3.3.3 Mathematical model for thermal conductivity measurement ...... 60 3.3.4 Result and discussion ...... 61 3.3.5 Conclusion ...... 65

CHAPTER 4 EFFECT OF MECHANICAL STRAIN ON THERMAL CONDUCTIVITY OF THIN FILM ………………………………………………………………………………..66

4.1 Influence of Strain on Thermal Conductivity of Silicon Nitride Thin Films ...... 66 4.1.1 Introduction ...... 67 4.1.2 Device design and fabrication ...... 68 4.1.3 Experimental Procedure and Analysis ...... 71 4.1.4 Result and discussion ...... 76 4.1.5 Conclusion ...... 79 4.2 Mechanical Strain Dependence of Thermal Transport in Amorphous Silicon Thin Films .. 81 4.2.1 Introduction ...... 81 4.2.2 Experimental Setup ...... 83 4.2.3 Thermal Conductivity Measurement ...... 85 4.2.4 Experimental result and analysis ...... 88 4.2.5 Experimental uncertainty analysis ...... 91 4.2.6 Discussion ...... 92 4.2.6 Conclusion ...... 96

CHAPTER 5 DOMAIN ENGINEERING OF PHYSICAL VAPOR DEPOSITED TWO- DIMENSIONAL MATERIALS ...... 97

5.1 Introduction ...... 97 5.2 Sample preparation and experimental setup ...... 100 5.3 Result and discussion ...... 102

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5.4 Conclusion ...... 104

CHAPTER 6 MECHANICAL STRESS FIELD ASSISTED CHARGE DE-TRAPPING IN CARBON DOPED OXIDES ...... 105

6.1 Introduction ...... 105 6.2 Experimental setup ...... 108 6.3 Experimental results and discussion ...... 111 6.4 Conclusion ...... 116

REFERENCES ………………………………………………………………………………118

LIST OF FIGURES

Figure 1.1. Size dependent Young’s modulus of (a) carbon nanotubes [21] and (b) silver and lead nanowire [18] (Figures are adopted from original literature) ...... 2

Figure 1.2. Size dependent thermal conductivity of (a) silicon nanowires [31] and (b) silicon di oxide thin films [29] (Figures are adopted from original literature) ...... 2

Figure 1.3. Approximate characteristic length scales for various physical domains at 300 K...... 3

Figure 1.4. (a) In-situ transmission electron microscope (TEM) device and (b) In-situ scanning electron microscope (SEM) device...... 5

Figure 1.5. (a) Schematic diagram and (b) spring equivalent sample-device arrangement [44] of thermal actuator based transmission electron microscope (TEM) device...... 6

Figure 1.6. (a) Image of unpowered device, (b) emissivity correction map of unpowered device, (c) post emissivity correction temperature map of unpowered device, (d) temperature map of powered device after emissivity corrected...... 7

Figure 2.1. (a) TEM holder tip and microchip test device for in-situ TEM tensile fatigue test, (b) Thermo-electric actuator and freestanding specimen with a through hole below for electron transmission, (c) Closeup view of specimen and sensors, (d) TEM image of the notch on the specimen...... 12

Figure 2.2. Quasi-static stress-strain behavior in the 200 nm thick un-notched aluminum specimens...... 13

Figure 2.3. TEM micrographs showing the notch tip for nominal values of 0.1% strain, 125 MPa stress level, (a) start (b) after 20000 cycles (c) after 325000 cycles (d) after 1.2×106 cycles. No dislocation activity or damage is observed...... 14

Figure 2.4. TEM micrograph showing fatigue damage at nominal values of 0.4% strain, 450 MPa stress (a) start (b) after 3000 cycles. Discrete level dislocation activities were observed for this loading level without any signs of fatigue damage were observed even up to 1.2x106 cycles...... 15

Figure 2.5. Snapshots from the 0.4% strain, 250 MPa stress amplitude fatigue loading in-situ in the TEM. Grains labeled ‘a’ and ‘b’ demonstrate the appearance and disappearance of the discrete level dislocations depending on the magnitude and direction of fatigue loading...... 17

Figure 2.6. (a) Scanning electron micrograph showing various components of a MEMS device for quantitative in-situ TEM testing of thin films, (b, c) Bright-field and selected area electron diffraction pattern of the as-deposited nano-crystalline Ni specimen (d, e) room temperature grain growth in a span of 30 to 60 days. Scale bar represents 500 nm...... 21

Figure 2.7. TEM images of the specimens at (a) room temperature (b) 0.2 Tm with no applied stress, (c) no applied stress and (b) 1.7 GPa stress at room temperature. Scale bar is 500 nm...... 22

Figure 2.8. TEM and selected area diffraction images of a specimen loaded at (a) 0.2Tm, 0.2Y and (b) 0.2Tm, 0.5Y...... 23

Figure 3.1. (a) Scanning electron micrograph of the micro device with a T shaped heater and specimen, (b) Experimental setup showing the infrared microscope and vacuum chamber...... 29

Figure 3.2. Nanofabrication processing steps for the micro device containing the specimen and micro heater...... 29

Figure 3.3. (a) Infrared micrograph of the specimen, (b) temperature profile in the y-o-y’ direction, (c) determination of the exponent s in equation (2)...... 32

Figure 3.4. Temperature profile of the specimen showing the measure value of heat transfer coefficient at different locations...... 33

Figure 3.5. Temperature profile of the silicon specimen at two different pressures...... 34

Figure 3.6. Validation of the proposed empirical relationship given in equation (15) for three difference cases, (a) 5 micron wide and 50 nm thick free standing silicon nitride, (b) 10 micron wide and 20 micron thick silicon specimen with no neighboring surfaces and (c) 10 micron wide and 20 micron thick silicon specimen a neighboring surface at 2 microns distance...... 38

Figure 3.7. Schematic diagrams showing (a) conventional micro-bridge/3 setup for thin film thermal conductivity characterization, (b) proposed technique for very low thermal conductivity materials (not up to scale)...... 43

Figure 3.8. Schematic presentation of the micro-fabrication process steps for specimen preparation ...... 46

Figure 3.9. (a) SEM image of the freestanding specimen, (b) Infra-red image of the specimen showing temperature profile. (c) Experimental setup showing the thermal microscope and the vacuum chamber housing the specimen and the heater...... 47

Figure 3.10. (a) Energy balance in small specimen segments with length ∆x and width w at two different locations, A and B, (b) Temperature profile along the length of the specimen...... 48

Figure 3.11. Temperature vs. time profile for the specimen as well as the die containing the specimen...... 50

Figure 3.12. Experimental data (each marker represent 20 data sets) juxtaposed with model predictions for three trial values of thermal conductivity. The thermal conductivity of the specimen is about 0.24 W/m-K...... 53

Figure 3.13. Experimental data (each data marker represent 10 data sets) juxtaposed with model predictions for three trial values of thermal conductivity...... 55

Figure 3.14. (a) Schematic rendering of a h-BN film transferred on a micro-heater device (b) infrared thermography of the heater supporting the h-BN film (c) schematic rendering of a specimen with boundary conditions (d) energy balance scheme in the specimen ...... 60

Figure 3.15. (a) Thermal boundary layer around the micro-heater surface provides accurate heat loss from the specimen to the air (b) comparison of the experimental h-BN temperature profile with model predictions ...... 62

Figure 3.16. Combination of (a) spatial and (b) temporal temperature profile allows measurement of the thermal diffusivity ...... 63

Figure 3.17. High resolution cross-sectional TEM (a) provides evidence of the loss of uniform layer spacing as hBN thickness increases. Additionally, while plan-view TEM demonstrates that the atomic structure remains hexagonal (b), selected area electron diffraction (c) indicates nanocrystalline nature of the film microstructure ...... 64

Figure 4.1. (a) Schematic diagram showing a single layer silicon nitride three-strip actuator and a specimen, (b) Scanning electron micrograph of a specimen integrated with a seven-strip actuator and a thin film heater, (c) Strain is measured after post-experiment fracture of the specimen...... 70

Figure 4.2. Fabrication processing for the device integrating the actuator, specimen and heater for thermal conductivity characterization...... 71

Figure 4.3. Multi-physics simulation model for the device showing temperature profile at zero strain. Infrared microscopy shows the large drop in thermal conductivity at 2.4% strain (inset). . 73

Figure 4.4. Comparison of the experimental and simulation results on the heater temperature profile as a function of input current...... 75

Figure 4.5. Comparison of experimental and simulation results on the temperature profile of the silicon nitride specimens with fitted values of thermal conductivity...... 76

Figure 4.6. Thermal conductivity of 50 nm thick Si3N4 films as a function of mechanical strain. The letters corresponding to 0.3% strain represent data from the literature. The symbol () denote cross- plane thermal conductivity data...... 77

Figure 4.7. (a) The experiment setup including the testing device and external piezo actuation mechanism (b) schematic diagram of the testing device (c) zoomed micrograph of the testing device showing two specimens (d) side view of the experimental setup...... 84

Figure 4.8. Fabrication processing steps for freestanding amorphous silicon on a silicon wafer. . 85

Figure 4.9. (a) Micro-manipulation of a RTD heater near the freestanding specimen, (b) IR micrograph of the specimen, (c) schematic diagram showing energy balance in the specimen (d) temperature profile along the length of specimen (obtained from IR micrograph) ...... 86

Figure 4.10. (a) Thermal boundary layer around the specimen for calculation of the convective heat transfer coefficient and (b) extraction of thermal conductivity for calibration (thermal oxide) and amorphous silicon at zero strain by fitting the experimental temperature profile along the specimen length with model prediction. In both cases, excellent agreement between model and data is obvious from the overlapping curves...... 89

Figure 4.11. (a). Calibration data for the actuator. Model prediction and experimental values of specimen temperature profile for (b) 1.09%, (c) 1.81% and (d) 2.45% strain in the specimen. .... 90

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Figure 4.12. Thermal conductivity of a-Si specimens as a function of externally applied mechanical strain...... 91

Figure 4.13. (a) Uncertainty in the thermal conductivity with (a) relative error in length at T = 50° C and (b) temperature measurement ...... 92

Figure 4.15. Reflectivity on an a-Si specimen at various levels of tensile strains...... 95

Figure 5.1. Experimental details (a) PVD of specimen layers on oxide coated silicon wafer and a protective titanium over-layer (b) reactive ion etching of all the layers and additional isotropic etching of silicon after photolithographic patterning preparation (c) nano-manipulation of the a cleaved specimen on to a MEMS device and (d) securing it with carbon deposition (e) vapor phase hydro-fluoric acid etch to remove the protective titanium and oxide layers, (f) infrared image of the MEMS heaters and (g) experimental validation of a finite element model for heater temperature estimation in TEM...... 101

Figure 5.2. Experimental results on MoS2 (a) bright field TEM, (b) electron diffraction and (c) Raman spectroscopy of the as-deposited specimen while supported on the substrate measured with 10 mW excitation laser power. After in-situ TEM annealing at 600 C, (d) bright field TEM and (e) electron diffraction shows significant grain/domain growth, (f) comparison of the as-deposited and annealed Raman spectra with that for a single crystal MoS2. The power was reduced to 1 mW to avoid damage to the freestanding specimens, thus the intensity of the as-deposited film is significantly reduced...... 103

Figure 5.3. Experimental results for amorphous boron nitride (a) bright field TEM, (b) electron diffraction of the as-deposited specimen. After in-situ TEM annealing at 600 C, (c) bright field TEM and (d) electron diffraction shows significant grain/domain growth with hexagonal crystal structure...... 103

Figure 6.1. (a) Measured leakage current as a function of applied electrical field (b) Dielectric breakdown field strength for samples without any mechanical stress...... 109

Figure 6.2. (a) sample with two electrodes, (b) Four-point bending fixture in a universal testing machine, (c-d) schematic diagram of sample, (e) schematic diagram of tensile loading ...... 110

Figure 6.3. Leakage current as a function of applied tensile stress in at constant electrical fields of (a) 0.6 MV/cm (b) 1.0 MV/cm (c) 2.0 MV/cm (d) 2.4 MV/cm. The variability from sample to sample is dependent on pre-existing defect concentration...... 111

Figure 6.4. For unstressed specimens, (a) ln (J) vs. E1/2 shows good fit with SE from 1.4 to 2.7 MV/cm while (b) ln (J/E) vs. E1/2 shows good fit with PF beyond 2.7 MV/cm for SiOC:H samples. For mechanically stressed specimens (c) SE mechanism exhibited closest match, while (d) P-F mechanism did not appear to be a good fit...... 114

Figure 6.5. (a) Leakage current as function of mechanical loading and unloading under small electrical fields of (a) 0.6MV/cm and (a) 1.0 MV/cm. For higher fields, the leakage current remains unchanged upon mechanical load reversal...... 116

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LIST OF TABLES

Table 3.1. Comparison of micro and bulk scale convective heat transfer ...... 37

Table 3.2. Material properties for the low-k dielectric investigated in this study...... 45

Table 4.1. Multi-physics modules and input parameters...... 72

Table 4.2. Geometry parameters for the aluminum and silicon nitride structures...... 72

Table 6.1: Material properties for the low-k dielectric films investigated in this study...... 108

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ACKNOWLEDGEMENT

I would like to thank my graduate advisor Dr. Aman Haque, and mentor, for his constant guidance, encouragement and constructive criticism, throughout my graduate studies. His deep scientific knowledge combined with his inspiring way of student advising encouraged me to perform my research work with more passion and enthusiasm. Moreover, his emphasis on communication skill and valuable insight on scientific writing helped me to achieve my professional and personal career goals. I am truly indebted to him for giving me this tremendous opportunity and believing in me for the entire time. I would like to thank Dr. Zoubeida Ounaies, Dr. Donghai Wang, Dr. Charles E. Bakis and Dr. Karen A. Thole for agreeing to serve on my doctoral committee. Special thanks towards my colleagues, Mohan Manoharan, Sandeep Kumar, Jiezhu Jin, Raghu Pulavarthy and Baoming Wang for sharing their invaluable experience and giving me moral support during this time. I would like to thank MRI and MCL staff - Guy, Shane, Trevor and Bangzhi for helping me with difficulties regarding the nanofabrication process and microscopy techniques. I am grateful to my friends – especially, Faisal, Shafayet and Rajib for their tremendous support and encouragement throughout this work. Finally, my sincerest thanks to my wife - Samira, my parents, brothers – Farhad, Raihan and my sister - Rahnuma, who are always my source of inspiration, for their unconditional love and support.

DEDICATION

I would like to dedicate my dissertation to my family

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CHAPTER 1

INTRODUCTION

The concept of nanotechnology was introduced a few decades ago by R.P. Feynman in one of his memorable speeches [1]. Due to the technological improvement in material processing, microscopy and other instrumentation, researchers are now able to probe the realm of nanometer scale material. Investigation in this length scale has allowed not only study of fundamental physics but also numerous science and engineering applications. Nanotechnology has ushered a variety of new materials such as zero dimensional (0D) fullerene [2], one dimensional nanotube and nanowire [3] and 2D graphene [4] for fundamental research. It has produced technologies such as digital micro-mirror device (DMD) [5], accelerometer [6], scanning tunneling microscope [7] and atomic force microscope [8] to name a few. For reliability and performance, these applications require the materials to be strong with various degrees of thermal, mechanical and electrical capabilities, as well as other physical properties. Therefore, nanoscale characterization is very important for novel functionalities and applications.

1.1 Length scale effect on mechanical and thermal properties of material

When at least one of the three dimensions of a material approaches the nanometer scale (10-9 m), its properties are no longer the same as the bulk scale [9-12]. Mechanical properties of the material, such as the Young’s modulus [13-18], fatigue limit [19, 20], Poisson’s ratio [21], fracture strain [22] are reported to exhibit such size effect. Figure 1.1 shows the size dependence of Young’s modulus at the nanoscale. Depending on the material, the Young’s modulus can increase [14, 18] or decrease with physical dimensions [23, 24]. Even though it is an intrinsic (size independent) property, new deformation mechanism [25], microstructural constraints [26], surface to volume ratio of material [27] lead to such size effects.

Figure 1.1. Size dependent Young’s modulus of (a) carbon nanotubes [21] and (b) silver and lead nanowire [18] (Figures are adopted from original literature)

Length scale also significantly affects the thermal properties of the material such as melting temperature [9] and thermal conductivity [28-31]. Buffat et. al. experimentally found that melting temperature of gold particle drops from 1300 K to 700 K as particle diameter is reduced from 200 Å to 20 Å [9]. Thermal conductivity also shows a strong size effect as shown is Figure 1.2.

Figure 1.2. Size dependent thermal conductivity of (a) silicon nanowires [31] and (b) silicon di oxide thin films [29] (Figures are adopted from original literature)

Experimental studies reveal that thermal conductivity of thin films is a strong function of film thickness below a certain threshold value [32, 33]. For single crystal and polycrystalline materials thermal conductivity decreases with thickness and it is believed that the phonon and electron scattering at the boundary, grain boundaries or interfaces play the key role for this phenomenon [31]. For amorphous films, shorter mean free path, stoichiometry, mass density etc. are considered to govern thermal conductivity [29].

1.2 Length scale induced Coupling

It is well accepted in the literature that below a critical size materials show strong size effect. Some characteristic lengths for physical phenomena, such as phonon mean free path, electron mean free path, defect spacing are approximated in Figure 1.3 [34].When materials size becomes comparable or smaller than a particular characteristic length scale, significant deviation from the classical physics can be expected [35].

Figure 1.3. Approximate characteristic length scales for various physical domains at 300 K.

Length scale not only introduces the size effect in single domains (e.g., thermal) but also opens up the possibility of coupling among the properties of the material as multiple characteristic lengths can overlap in same length scale. Multi-domain coupling , such as magneto-resistance and biaxial strain [36], thermal conductivity and mechanical strain [37-40] also exist at the bulk scale, but for specific atomic structures. For example, the strain-electrical charge (piezo-electric) effect arise due to a special non centro-symmetric arrangement of atoms in the lattice. Semiconductors show strain sensitive electrical resistivity because their bandgap changes due to the applied mechanical strain energy. However, the foundation of this dissertation is not such specific atomic arrangement induced coupling. Instead, the focus is on metals (no band gap) and insulators (wide band gap) as well as amorphous microstructures, for which classical physics predict no coupling effects. The literature contains very little or no experimental work in this area, which motivates this research.

1.3 Objective and scope of this work

The core objective of this dissertation is to validate the hypothesis of size-induced coupling between mechanical and thermal domain in nanoscale materials. To measure multiple properties such as, mechanical strength, thermal and electrical conductivity simultaneously, micro electro mechanical system (MEMS) based testing devices have been developed according to the experimental requirements Figure 1.4a shows a 3 mm × 5 mm size device with thermal actuator, stress sensor, strain sensor and freestanding sample for in-situ transmission electron microscopy. One end of the sample is connected to the thermal actuator beams and other end is connected to the stress sensor beam. This device uses the thermal actuation technique where electrical current is passed through highly doped single crystal silicon beams. These beams are bent slightly in the direction of motion so that thermal expansion due to Joule heating of the beams develop the actuation. This is shown in Figure 1.5. The deflection of thermal actuator beams produces displacement (δ) in both the sample and stress sensor beam. These deflections can be recorded and measured accurately through high-resolution TEM micrographs. The equations [41] for measurement of displacement and applied force in sample is given below:

훿푠푝푒푐푖푚푒푛 = 훿1 − 훿2 (1)

192 퐸퐼 퐹푠푝푒푐푖푚푒푛 = 푘푓푠훿2 = 3 훿2 (2) 퐿푓푠

Where, kfs, E, I and Lfs are the spring constant, Young’s modulus, moment of inertia and length of force sensor beam respectively. The force sensor beam is fabricated from single crystal silicon with well-defined Young’s modulus [42, 43]. The force sensor beam dimensions can be measured easily from high-resolution scanning electron microscope images to obtain its stiffness. Stress and strain in the sample can be calculated from the displacements 1 and 2 after measuring the sample dimensions.

Figure 1.4. (a) In-situ transmission electron microscope (TEM) device and (b) In-situ scanning electron microscope (SEM) device.

The device for in-situ scanning electron microscopy (SEM), shown in Figure 1.4b, has no such size constraints. It uses a piezoelectric stack to apply the displacement in the sample that is a function of applied electric voltage. Devices with other actuation techniques are also used to meet the different experimental requirements of this study, which will be discussed in the later chapters.

Figure 1.5. (a) Schematic diagram and (b) spring equivalent sample-device arrangement [44] of thermal actuator based transmission electron microscope (TEM) device.

Chapter 2 of this dissertation presents the work on microstructural observation and deformation behavior of metallic materials under mechanical stress. Experimental results on aluminum thin film show the fatigue insensitivity of material in nanoscale as no samples failed in the fatigue testing even after million cycles of tensile loading. Next section presents the evidence of grain growth in nano-crystalline nickel thin film under low stress and temperature.

In Chapter 3, a setup for thermal conductivity measurement of thin film based on infrared microscopy is demonstrated. In Infrared thermography, actual temperature of a target surface is calculated by measuring the infrared radiant energy leaving a surface, isolating the emitted component of energy from transmitted and reflected component, and finally applying corrections to this energy component for the emissivity variation on the target surface. The temperature measurement is completed by a series of steps. First the unpowered sample is placed on a temperature controlled stage. Radiance from the unpowered sample is measured at two known temperatures by heating the sample uniformly. Then emissivity of every pixel is calculated and the resulting emissivity values are used as emissivity correction map for the whole sample surface. The emissivity for the sample surface is corrected so that unpowered sample exhibits the known uniform temperature. After emissivity correction, the infrared microscope can capture an accurate

temperature map of the sample at powered condition [45]. These four steps are illustrated in Figures 1.6a-d. Average emissivity of air is found as 0.85 – 0.95 [46]. Using this measurement technique, size and temperature induced heat transfer coefficient of air are presented in the first section of Chapter 3. It has been found that heat transfer coefficient and mode of heat transfer at nano and micro scale are different from the bulk scale. This work also presents an empirical model for the prediction of heat transfer coefficient at this scale based on sample size and temperature. In next two sections, thermal conductivity of 200 nm thick carbon doped oxide and 10nm thick hexagonal boron nitride films are studied. This technique is found to be uniquely suited for freestanding thin films with low (<1 W/m-K) thermal conductivity.

Chapter 4 highlights the major contribution of this dissertation; the dependence of thermal conductivity on mechanical strain in nanoscale thin films. In the first section, experiment on 50 nm thick silicon nitride thin film is presented. It showed an order of magnitude decrease of thermal conductivity with 2.4% tensile strain. As an insulating material, silicon nitride thin film already possess a very low thermal conductivity and is not expected to show such dependence. It is hypothesized that stress sensitive energy transfer mode in amorphous insulating thin film is the main reason for this decrease. In the next section, experimental result on amorphous silicon thin film is presented and it showed the opposite trend compared to silicon nitride. For amorphous silicon, thermal conductivity increased with applied tensile strain. Further experiments on this material showed that stress assisted grain growth or phase transformation of the material might be the cause of such anomalous behavior.

Chapter 5 presents an interesting observation of domain restructuring of two-dimensional materials at moderate temperatures. As the physical vapor deposited films are annealed at 600°C for 30 minutes, domain size of 40 layer thick initially amorphous molybdenum disulfide (MoS2) and 10 layer thick boron nitride (BN) transformed from amorphous to polycrystalline phase. This temperature is much lower than the range cited in the literature. Successful domain engineering can lead to grow these materials on desired substrates with preferred crystalline structure, hence desired material properties.

Finally, Chapter 6 shows the mechanical stress induced charge de-trapping in carbon- doped oxide. Dielectric reliability studies are mainly concerned with the breakdown of material under the electrical field only. This study shows that mechanical stress also can affect the reliability of the material. Leakage current across the thickness of the material is found to be increasing with the increasing tensile stress while the electric field was kept unchanged. It is observed that at lower electrical field the influence of mechanical stress is less pronounced, however at higher electric filed mechanical stress can increase the leakage current by 70%. This study suggest that role mechanical stress on reliability should not be ignored in the multi layered microelectronic devices.

CHAPTER 2

SIZE EFFECTS ON MICROSTRUCTURE AND PROPERTIES OF METALLIC THIN FILMS

Content of this chapter are based on the following journal articles:  Kumar, S., Alam, M. T. and Haque, M. A., Fatigue Insensitivity of Nanoscale Freestanding Aluminum Films, Journal of Microelectromechanical Systems, Vol. 20 Issue 1, pp. 53–58, 2011. Author of this dissertation performed the thin film and device preparation, experimentation, data analysis and corresponding manuscript writing. Sandeep Kumar designed the experiment, performed data analysis and prepared the manuscript.

 Wang, B., Alam, M. T. and Haque, M. A., Grain Growth in Nano-crystalline Nickel Films at Low Temperature and Stress, Scripta Materialia, Vol. 71, pp 1-4, 2014. Author of this dissertation performed the thin film and device preparation, experimentation, data analysis and corresponding manuscript writing. Baoming Wang designed the experiment, assisted in experiment and data analysis and prepared the manuscript.

2.1 Fatigue Insensitivity of Nanoscale Freestanding Aluminum Films

In this section, a micro-electro-mechanical system based setup for fatigue studies on 200 nm thick freestanding aluminum specimens in-situ inside the transmission electron microscope is demonstrated. The specimens did not show any sign of fatigue damage even at 1.2x106 cycles under nominal stresses about 80% of the static ultimate strength. Direct evidence is presented to propose that the conventional theory of fatigue crack nucleation through persistent slip bands does not work for nanoscale freestanding thin films, which gives rise to the anomalous fatigue insensitivity.

2.1.1 Objective and motivation

Thin films are prevalent in a wide range of applications like microelectronics, sensors, energy storage, optics and micro electro-mechanical systems (MEMS). In many cases, these applications involve dynamic mechanical loading. For example, fatigue performance is critical in the reliability of micro-pumps [47], micro engines [48] and resonators [49]. At the bulk scale, fatigue in metals starts with crack nucleation due to the generation of dislocation slip bands leading the development of persistent slip bands (PSB), extrusions and intrusions in the surface grains with favorable crystallographic orientation [50, 51]. Singularities and discontinuities such as pores and grain boundaries may also initiate fatigue cracks [52, 53]. However, bulk deformation mechanisms may not necessarily be the same as in nanoscale thin films [54, 55]. At the same time, the findings on static deformation mechanisms should not be directly extrapolated to fatigue loaded materials [56]. Nanoscale fatigue remains unexplored compared to bulk fatigue, which highlights the need for fundamental investigations in this area [57].

Fatigue properties of metal films have been investigated for different types of loading, test arrangement, geometry and growth chemistry of the specimen [58]. Copper has been the most studied specimen material [59-62]. The consensus of these studies is that grain size and film thickness govern the fatigue behavior primarily through influencing the dislocation arrangement in the thin films. Because of its widespread use in micro and nanoscale devices and systems, aluminum is another popular specimen material. Alaca et al. [63] conducted biaxial tensile test of 150 nm aluminum on 4.6 μm polyimide substrate, while Eberl et al. [64] performed fatigue test of 420 nm aluminum on piezoelectric substrate at ultra-high frequencies and suggested that formation of extrusion and voids in the grain boundaries is the primary cause of fatigue damage. Fatigue test on free standing aluminum thin film was first reported by Read et al. [65] on tension-tension testing of 2.25 μm aluminum specimen sandwiched by 0.1 μm titanium. In a recent study, Park et al. [66] used Al-3% Ti sample of 1 μm thickness for a high cycle tensile fatigue test. However, no clear fatigue mechanism is elaborated in these studies. Bae et al. [67] performed a high cycle feedback controlled fatigue test for 1.16 μm thick aluminum thin film with in-situ surface roughness monitoring capability and observed a clear change in average surface roughness of the specimen. It was predicted that plastic deformation in the material due to the cyclic loading and accumulation of the deformations on the surface is the primary factor behind the surface roughness change. Other metals that are reported in the literature for fatigue tests are silver, nickel, magnesium and gold [68- 71].

A rigorous overview of the length scale effects on fatigue shows that most of the existing studies in the literature consider specimens with thickness larger than 500 nm [72]. However, fundamentally different mechanisms may prevail at the smaller length scales. For example, discrete dislocations at the nanoscale replace the typical dislocation wall and cell structures found in bulk materials. Similarly, the typical surface damage of fatigued bulk metals, such as extrusions and cracks near extrusions, is gradually suppressed and replaced by damage that is localized at interfaces, such as cracks, grooves, and voids along grain and twin boundaries [73]. Therefore, fatigue studies at the nanoscale promises exciting opportunities in advancing the state of the art in length scale effects. However, nanoscale fatigue testing is more challenging than the bulk testing, due to the smaller force requirements with higher resolution, difficulties in freestanding specimen fabrication as well as their gripping and alignment. Since visualization of the deformation mechanisms is very critical in understanding the length scale dependence of fatigue damages and guiding the simulation studies, perhaps the ideal experimental setup is the one that involves in-situ microscopy. For example, the transmission electron microscope can visualize microstructures and defects with up to atomic resolution. However, obtaining the stress strain data is challenging because the TEM chamber can only accommodate area equal to a 3 mm diameter specimen holder grid. Nevertheless, the unique advantages of quantitative in-situ TEM technique overweigh these challenges as demonstrated in the literature [74-79].

2.1.2 Experimental details

In this study, a micro-device is developed where an electron transparent specimen, actuator (for tension-tension fatigue loading) and sensors (for stress and strain measurement) are integrated using nanofabrication techniques. The design methodology utilizing a thermal actuator to apply tensile force is described in detail in the literature [80] and the stress-strain measurement of sample is shown in the previous chapter. The micro-device is housed by a custom-made Hummingbird Scientific TEM specimen holder with electrical biasing capability. The tip of the electrical biasing TEM specimen holder (shown in Figure 2.1a) can accommodate the 3 x 5 mm2 microchip (Figure 2.1b) comprising a set of bent-beam electro-thermal actuator (Figure 2.1c), heat-sink (to avoid temperature rise in the specimen) and mechanical force and displacement sensors (Figure 2.1c). The specimen material is 99.99% pure evaporated aluminum lithographically patterned to be 100 micron long, 5.2 micron wide and 200 nm thick. Figure 2.1d shows another version of the specimen with a single edge notch. The specimens are co-fabricated with the device, hence there is no need for manual specimen gripping and aligning. A through-the-wafer hole beneath the specimens is etched using deep reactive ion etching to facilitate to transmission of the electron beam for TEM.

After fabrication, the micro-device is wire bonded to set the proper electrical connection and placed on the TEM specimen holder. The experiments are performed inside a JEOL 2010 TEM with operating voltage of 200 kV. The thermal actuator in the chip was supplied with a sine wave generated by Keithley 6220 AC/DC current source.

At first, quasi-static loading was applied on the specimens to determine their static failure properties. Figure 2.2 shows the experimental results. The thin film specimens fail at about 1.75% strain, which indicates only limited plastic deformation compared to the bulk behavior. The average yield strength is about 500 MPa, while the ultimate strength is about 550 MPa.

Figure 2.2. Quasi-static stress-strain behavior in the 200 nm thick un-notched aluminum specimens.

For fatigue testing, sinusoidal current output to the device was set to an amount such that it will produce about 0.1% for low strain amplitude and 0.4% strain for high strain amplitude experiments. The motivation for the low strain set of experiments was to nucleate a small crack without breaking the specimen completely since primary goal of this study is to understand the deformation mechanisms. The frequency for the tension-tension loading was varied from 1 to 10 Hz. To facilitate the nucleation of a fatigue crack at a predefined location, a focused ion beam is used to mill a 2.4 micron long notch at one edge of the specimen with notch radius of approximately 100 nm. Theoretically, this notch geometry yields a stress concentration factor of about 11 at the tip [81]. Even though applied far-field strain is uniform and relatively small, the localized stress at the notch tip is therefore is significantly large. During the test the notch is placed in the center of the computer screen and image, video were taken at different loading cycles to observe the deformation mechanisms in real time.

Figure 2.3 shows the in-situ TEM images of the notch tip at various loading cycles, which clearly does not indicate any plastic deformation zone. None of the specimens loaded at the 0.1% strain failed and no discernible signs of fatigue damage were observed in the TEM. At this strain value, the far field stress was approximately 70 MPa and the nominal stress at the cross-section through the notch is about 125 MPa. The stress concentration factor for the notch was calculated to be about 11, which indicates that the effective stress at the notch tip is about 770 MPa. From Figure 2.2, it is observed that the ultimate strength of similar specimens is about 550 MPa, which is much smaller than the notch tip stress of the fatigue loaded specimen. A careful observation of the acquired images and videos suggests that at 0.1% strain amplitude, the stress at the notch tip is still not large enough to initiate dislocation generation and motion in the grains. In a few relatively larger grains, dislocations are seen to generate and disappear quickly either on the free surface or in the grain boundaries. Rather, the most common event is the change in contrast of the grains upon loading, which is an outcome of out of plane grain rotation. Such dislocation starvation can be explained by comparing the average grain size with the minimum theoretically allowable distance (dc) between two dislocations. The underlying physics is that since a minimum of two dislocations is needed to build a dislocation pile-up, dc also represents the threshold grain size for dislocation-based plasticity.

Assuming that only lattice friction needs to be overcome to move a dislocation, the value for dc is calculated to be about 60 nanometers for aluminum [82], which is somewhat close to the average grain size in specimens of this study (80 nm).

In a separate set of experiments, the strain amplitude was increased to approximately 0.4%, so that fatigue crack nucleation could be initiated. At 0.4% strain, corresponding approximate far field stress is about 250 MPa. The nominal stress at the cross-section of the notch is about 450 MPa, which is 80% of the ultimate strength. According to classical mechanics, the notch tip, stress should exceed 2.5 GPa. Considering the nominal stress, mean and alternating stress values for the tension- tension loading mode are equal to about 225 MPa, which is about 45% of the static yield strength. Such significant increase in stress level resulted in more frequent and significant dislocation activity inside the grains. Bulk aluminum survives only about 1000 cycles at this loading level. Intriguingly, discrete dislocation activities were observed in the larger grain, but no fatigue crack nucleation was observed at or near the notch tip, where the effective stress is the highest. The specimens were loaded up to 1.2x106 cycles, without any discernible change in microstructure and none of the specimens failed.

Figure 2.4 shows the evidence of dislocation activities at the notch tip, accompanied by grain rotation. The most critical observation is that the appearance and disappearance of the dislocations with the loading cycles. None of the specimens showed any indication of slip band or persistent slip band formation. Since the specimens were free from any pores or voids, none of these alternate fatigue crack nucleation mechanisms [83-85] were active.

2.1.3 Results and Discussion

To explain the observed fatigue tolerance in the nanoscale freestanding aluminum specimens, it is first noted that the vacuum environment play significant role on enhancing the fatigue life [86]. 10 to 15 times increase in fatigue life under high vacuum is commonly cited, while the proposed hypotheses (effect of water vapor and oxygen, surface morphology, slip homogenization to name a few) are not conclusive yet. However, the effect of vacuum is not as prominent at the micro and nanoscale, which is obvious from the studied mentioned in the introduction section of this study. Many of these studies are performed inside the vacuum (electron microscope chambers), yet there has been no report on anomalous fatigue life enhancement.

From a mechanism point of view, deformation at or near the notch tip is considered first, where the stress levels theoretically exceed a few GPa. It is therefore expected that fatigue cracks would nucleate from these areas. Direct TEM observations show that dislocation based plasticity is not as extensive as in bulk specimens. Rather, grain rotation is observed to be the dominant deformation mechanism at this length scale. However, as the strain amplitude is further increased from 0.1% to 0.4%, grain rotation alone cannot accommodate the applied deformation and dislocation activities are observed. However, because of the small size (about 80 nm) of the grains, such activities are limited to statistically insignificant and discrete levels. This is shown in Figure 2.5, which is a collection of the frames captured from the video. Here, the appearance and disappearance of discrete are clearly seen in grains labeled ‘a’ and ‘b’ upon loading and unloading in the tension-tension fatigue mode. Since the grain rotation is reversible, deformation is completely recovered upon unloading and there is no damage accumulation even after millions of cycles as shown in Figures 2.3, 2.4 and 2.5. Not all the grains show such appearance and disappearance simultaneously because of the difference in grain orientation and location with respect to notch tip. Overall, figures 2.3 and 4 also show very low dislocation density indicating that compared to bulk specimens, the nanoscale specimens primarily remain dislocation starved. This is because the dislocations generate and then quickly disappear at the surface or the grain boundaries depending upon the magnitude and direction of the fatigue loading. Such dislocation starvation has been observed or modeled by other researchers [87-89] for monotonic loading. Experimental observation of dislocation starvation in nanoscale fatigue is yet to be reported. However, the findings of this study is supported by the only fatigue model available in the literature, which finds that the dislocation starvation mechanism dominates fatigue loading with no strain gradient (such as the cyclic tension–compression), while gradient dominated loading (such as bending) is dominated by geometrically necessary dislocations [90]. The absence of dislocation based slip band or persistent

slip bands (or other alternative mechanisms, such as pores and voids) inhibit the nucleation of a fatigue crack even at the notch tip, where the theoretical stress exceeds 2.5 GPa. As a result, none of the specimens failed from fatigue damage. It is important to note that the proposed hypothesis is relevant only for freestanding and thin structures, where image forces are strong enough to influence dislocation motion to the free surfaces. For films on a substrate, the dislocations can still be pinned at the interface, giving rise to a fundamentally different fatigue behavior [61]. Film thickness is also important for the proposed model, since dislocations may not leave the Nano grained interior for thicker specimens [91].

Another important observation in the present study is the absence of a conventional ‘plastic zone’ ahead of the notch tip, which is seen for the bulk metals. Experimental observation of dislocation starvation suggests that dislocations at the nanoscale do not relax the stress at the notch tip. It is therefore proposed that grain rotation could be a candidate mechanism to relax the stress. Grain rotation can reduce the stress concentration by having differential rotation in the ensemble

of grains, depending on their localized stress and crystallographic orientation. The implication is that wherever there is stress concentration, the grains will rotate more as compare to other grains in order to homogenize the strain field throughout the specimen. In other words, the absence of dislocation-based plastic zone implies the absence of stress concentration in the deformation field near flaws such as notches and voids. This observation is further supported by studies showing that nanoscale materials are more tolerant to the flaws. Naturally occurring hard and tough bio- materials, such as bone and teeth, are known to show flaw or fault tolerance that originates from the nanoscale constituents of their hierarchical structures [92]. These extremely small building blocks are insensitive to any stress concentration arising from structural flaws; rather they fail from a uniform rupture stress. In a recent study, flaw insensitive behavior was previously observed in aluminum thin films [93], albeit for monotonic loading.

2.1.4 Conclusions

In-situ TEM fatigue testing of 200 nm thick (average grain size 80 nm) aluminum specimens has performed. None of the specimens failed even after 10 million cycles due to the tension-tension loading for two different nominal stress and strain (0.1%, strain - 125 MPa stress and 0.4% strain - 450 MPa stress) at the cross-section through the notch, which are comparable to the fracture stress and strain (about 1.75% strain and 550 MPa stress) for similar specimens loaded monotonically. Similar results were obtained for single edge notched specimens, with notch lengths as large as 50% of the specimen width. To explain such unexpectedly high resistance to fatigue damage, it is pointed out from the in-situ TEM observations that the Nano grained specimens are essentially dislocation starved. This is because the grains are not large enough to accommodate statistically significant dislocation density. In addition, the dislocations are allowed to disappear through the surfaces and grain boundaries in the freestanding specimens. It is proposed that the absence of extensive dislocation activities prohibit the formation of slip bands in the grains and hence inhibit the nucleation of fatigue cracks. It is also hypothesized that the observed very high fatigue damage resistance may be absent in thicker specimens (dislocations will not be able to leave through the surface), or thinner specimens on substrates (dislocations might be pinned at the interface).

2.2 Grain Growth in Nano-crystalline Nickel Films at Low Temperature and Stress

Influence of temperature and stress on grain growth was investigated in nano-crystalline nickel thin films in-situ inside a transmission electron microscope. Independently, temperature and stress did not show any appreciable effect. However, concurrent loading at only 20% of melting temperature and 20% of yield stress resulted in significant grain boundary mobility and grain growth. We propose that grain growth in nano-crystals is a stress-heterogeneity relieving mechanism that may not necessarily be associated with plasticity as proposed in the literature.

2.2.1 Literature review

Grain size is undoubtedly the most influential microstructural parameter governing polycrystalline materials properties. Mechanical properties have been studied for grain sizes from a few nanometers to hundreds of microns [94, 95]. By directly controlling defect density and grain boundary volume fraction, grain size is known to govern both elastic [75, 96] and plastic [97-99] behavior. It is generally accepted that as grain size becomes smaller, materials exhibit higher yield strength and lower ductility, primarily because of the confining of dislocations [26]. The trend reverses below a critical size due to large fraction of grain boundaries at the nanoscale [100]. Grain size effects go beyond mechanical behavior, since defects and grain boundaries are also responsible for scattering electrons and phonons. At the nanoscale, grain size can significantly impact electrical and thermal conductivity [101] primarily because grain boundary scattering is stronger than that by dislocations and vacancies [102]. The literature contains similar evidence for optical, magnetic etc. properties [103]. Such multi-disciplinary impact of grain size has been instrumental in vigorous research in various disciplines.

In this study, we focus on grain size growth in thin metal films, which are prevalently used in a wide variety of devices such as microelectronics, sensors, energy conversion [104], to name a few. Classical ways of increasing grain size are thermal annealing, precipitate/impurities and irradiation [105]. For nano-crystalline materials, thermal annealing works primarily through surface diffusion, a reason why grain growth stagnates at temperatures far below the melting point

(0.2 - 0.3 Tm) [106, 107]. Here, the excess free volume associated with the grain boundaries are transformed in to vacancies as the grains grow. The atomic rearrangement in the grain boundaries decreases the grain-boundary mobility to effectively halt the grain growth. Increasing temperature decrease the activation energy barrier only temporarily since any atomic rearrangement lowers the grain boundary energy and slows down its mobility [107, 108]. A more recent study suggests that

in addition to grain boundary energy reduction complex interaction of the anisotropy of grain boundary energy, grain boundary grooving and solute/triple junction drag may contribute to stagnation in grain growth [109]. Stagnation is therefore a key impediment to grain growth in nanocrystalline films.

Externally applied stress can also act as a stimulus for grain growth in nano-crystalline materials [110, 111]. Here, the growth is viewed as a grain boundary mediated plastic deformation mode [100, 112, 113]. The phenomenon has been consistently observed at or near room temperature [77, 110, 114, 115], which is very intriguing because grain boundary mobility requires higher temperatures. In addition, diffusional flow does not necessarily imply grain growth. It is suggested that room temperature grain growth is associated with shear stress driven grain boundary migration [77]. The concept is borrowed from recent studies showing shear stress can initiate normal grain boundary migration [116] at high angle boundaries and is energetically more favorable than the pure migration of a grain boundary [117]. When such coupled migration occurs over numerous grains, the global effect is an increased average grain size.

2.2.2 Experimental Setup

In this work, we present experimental evidence of grain growth due to simultaneous action of low stress and low temperature. This is in stark contrast with the grain growth literature, which involves either high stresses and low temperatures or low stress and high temperatures [110, 118]. Since both temperature and stress play role in grain growth; intuitively, external stress applied in nano-crystalline materials could catalyze the temperature driven grain growth and vice versa. However, there is no concerted effort in the literature to investigate such synergy, if any. This motivates us to develop an experimental setup where independently controlled uniform stress and temperature could be applied to a freestanding nano-crystalline thin film in-situ inside a transmission electron microscope (TEM). Figure 2.6a shows a custom designed and fabricated micro-electro-mechanical system (MEMS) device with electro-thermal actuator and heater to apply uniaxial tensile stress and temperature on the specimen respectively. The 100 nm thick, 99.99% pure Ni films used in this study were first evaporated on a silicon-on-insulator wafer. Standard photo-lithography and deep reactive ion etching was performed on the wafer so that the actuator and heater structures are co-fabricated with the specimen. Such co-fabrication ensures perfect specimen alignment and gripping [75]. The electro-thermal actuator and heater were calibrated for various values of input current using an infrared microscope with 0.1oK resolution. After

calibration, the 3mm x 5mm MEMS devices are mounted on an electrical biasing TEM specimen holder so that the experiments could be performed in-situ in TEM.

2.2.3 Result and Discussion

In-situ TEM tensile tests on 100 nm thick freestanding nickel thin films measured Young’s modulus and yield stress about 120 ± 5 GPa and 1.8 ± 0.1 GPa respectively, which compare very well with the literature [119]. The as-deposited grain size was approximately 10 nm with a few grains as large as 50 nm. Figures 2.6b and 2.6c show the bright field TEM and selected area diffraction images respective. Figure 2.6d shows secondary grain growth to a bimodal distribution (first mode 25 nm and second mode 100 nm) at room temperature without any applied stress in 30 to 60 days. Grain growth is also evident from the distinct changes electron diffraction pattern (Figure 2.6e). Such growth has previously been reported on nano-crystalline Pd and Cu, but not on Ni [107, 111]. The grain growth stagnated at this point. In a set of in-situ TEM heating (no applied stress) experiments, the specimen temperature was raised to 373 K (about 0.2Tm) for several hours. This is shown in Figures 2.7a and 2.7b. No appreciable grain growth or grain boundary mobility was observed, which is expected because Ni is thermally stable below 473 K. In a separate set of experiments, room temperature mechanical loading was performed to investigate any stress-

assisted grain growth. The results around ultimate stress range (1.7 GPa) are shown in Figures 2.7c and 2.7d, where discernible grain growth is observed in a few hours.

Figure 2.7. TEM images of the specimens at (a) room temperature (b) 0.2Tm with no applied stress, (c) no applied stress and (b) 1.7 GPa stress at room temperature. Scale bar is 500 nm.

The third set of experiments comprised of applying stresses on heated (373 K or 0.2Tm for Ni) specimens. The experimental results are given in Figure 2.8, where clearly discernible grain growth started at about 325 MPa stress, which is only about 20% of the yield stress (Y). The growth rate at this low temperature-low stress loading configuration was rapid enough to be visualized in the quasi-statically (about minutes) captured images, which suggests that further growth might have occurred had longer time been allowed. Interestingly, majority of the growth was in normal (or uniform) mode, where the smaller grains grew appreciably with the larger ones.

Figure 2.8b shows further grain growth at 0.5Y, resulting in equi-axed grain structure with many grains larger than the thickness. This uniform growth pattern is just opposite to the non-uniform

growth as seen in individual temperature and stress loading and as predicted in the literature [120]. Interestingly, the relative magnitude of grain growth decreased with increased stress in the plastic deformation zone, where the in-situ TEM observations clearly show other modes (primarily grain rotation and dislocation) of plastic deformation. This is quite expected since according to the literature normal grain growth saturates once a columnar grain structure develops [120]. Also, for grain sizes larger than 100 nm, conventional plasticity is energetically more favorable than grain growth [121]. To the best of our knowledge, this is the first experimental evidence in the literature on large grain growth at low temperature-low stress loading.

Figure 2.8. TEM and selected area diffraction images of a specimen loaded at (a) 0.2Tm, 0.2Y and

(b) 0.2Tm, 0.5Y.

While the absence of grain growth at 0.2Tm is not surprising, the interesting features of this study are (i) weak stress-assisted growth at stresses close to failure and (ii) prominent growth at the combination of low stress and low temperature. The lack of similarity between the observed grain growth under simultaneous and independent stimuli indicate that none of the individual proposed mechanisms (temperature or stress assisted) are directly applicable for the present study. Since the magnitude of stress required for stress-assisted grain growth varies from material to material (a comprehensive list compiled by [111]), a better metric is the stress value normalized with yield stress. In this respect, we clearly observe that almost all the observations reported in the literature are made near or at plastic deformation region. This includes our recent study on nano-crystalline Pt, where the far field stress of 290 MPa actually resulted in yielding at the notch tip where grain growth was observed [122]. Therefore, the concept of grain growth as a plastic deformation mechanism seems to be well suited for the existing literature. Contrarily, in absence of temperature, we observed very little grain growth even around failure stresses. Clearly, the effects of temperature

and stress on grain growth are not additive or complementary in nature. Considering temperature alone, the magnitude of grain growth and the stagnation agrees with the literature, but it is difficult to ascribe the large and rapid grain growth at stresses below the yield point. This is because once stagnated, higher temperature (about 0.4Tm) is needed to re-initiate grain growth. This is a very large thermal energy value compared to the strain energy supplied through the external stress in this study [123].

2.2.4 Conclusion

Our observation of stress and temperature driven grain growth agrees with a very recent proposition that grain growth is a deformation-induced thermally activated process [111]. The difference is that we observe the growth at as low as 0.2Y, which suggests that grain growth is not necessarily associated with plastic deformation. It is known that grain boundaries in nanocrystalline Ni are mostly high angle type, except abnormally large grains [97]. We propose that externally applied stresses are first localized in these boundaries and triple points [124] and then resolved into shear stresses that promote normal migration of the boundary [125], a process that is facilitated by even low temperatures. This is supported by our observation of grain growth at 0.2Tm and 0.2Y, where smaller grains grew significantly more than the larger grains. The motivation for such growth is more geometric compatibility (to reduce stress concentration at the high angle boundaries and triple points) than plasticity, a reason the phenomenon is observed below the yield stress of the specimens.

CHAPTER 3

A NEW APPROACH FOR THERMAL CONDUCTIVITY MEASUREMENT OF THIN FILMS

Content of this chapter are based on the following journal articles:  Alam, M. T., Raghu, A. P., Haque, M. A., Muratore, C. and Voevodin, A., Size and Temperature Dependence of Solid to Air Heat Transfer, International Journal of Thermal Sciences, Vol. 73, pp 1-7, 2013. Author of this dissertation designed the experiment, performed the thin film and device preparation, experimentation, data analysis and manuscript writing. Raghu Pulavarthy assisted in experimentation, data analysis and corresponding manuscript writing. Aman Haque took part in experiment design, data analysis and manuscript writing. Chris Muratore and Andrey Voevodin helped in the manuscript preparation.

 Alam, M.T., King, S., and Haque, M. A., Characterization of Very Low Thermal Conductivity Thin Films, Journal of Thermal Analysis and Calorimetry, Vol. 115, Issue 2, pp 1541-1550, 2014. Author of this dissertation designed the experiment, performed the sample and device preparation, experimentation, data analysis and manuscript writing. Aman Haque took part in experiment design, measurement, data analysis and manuscript writing. Sean King prepared the thin film and helped in the manuscript preparation.

 Alam, M. T., Bresnehan, M, Robinson, J. A. and Haque, M. A., Thermal Conductivity of Ultra-thin Chemical Vapor Deposited Hexagonal Boron Nitride Films, Applied Physics Letters, Vol. 104, 013113, 2014 Author of this dissertation designed the experiment, performed the thin film and device integration, experimentation, data analysis and manuscript writing. Aman Haque took part in experiment design, data analysis and manuscript writing. Michael Bresnehan and Joshua Robinson prepared the thin film and helped in the data analysis and manuscript preparation.

3.1 Structural Size and Temperature Dependence of Solid to Air Heat Transfer

Accurate prediction of heat transfer from micro and nanoscale devices is very important for their operation and reliability. While the consensus is that the heat transfer coefficient increases at the smaller scales, the literature also indicates contradiction in the scaling across length scales. In this study, we present an experimental technique to characterize heat transfer from micro to nano scales using infrared microscopy on nanofabricated specimens integrated with micro heaters. The heat transfer coefficient for quiescent air is found to be about two orders of magnitude higher than its bulk counterpart. It also showed pronounced inversely proportional relationship with temperature and suggested that solid to air conduction is the dominant mode of heat transfer. It was found that pressure only indirectly influences heat transfer. Based on the experimental data, we present an empirical relationship for the heat transfer coefficient that depends on the ratio of the surface area to cross-sectional area, temperature of the heated body and its proximity to other solid bodies.

3.1.1 Introduction

The mechanism of heat transfer from hot solids to the surrounding environment is crucial in wide variety of thermal systems [126]. The literature is particularly rich for bulk scale free and forced convective heat transfer but comparatively very little is known at the micron and submicron scales. This is critical for operation and reliability of micro-electronic and micro-electro- mechanical systems, where rapid and ever continuing miniaturization results in very high power dissipation densities [127]. The physics of solid to gas heat transfer changes considerably at length scales [128-131] that are on the same order of certain characteristic length parameters of the medium of heat transfer. Devices at these lengths are now routinely designed for applications like integrated circuits, heated cantilever thermometry [129], gas based sensors [132, 133] and micro- actuators [131] for which accurate prediction of free convective heat transfer is of paramount importance.

At the macroscale, the bulk flow (either due to density variation or externally imposed) of the fluid surrounding a heated solid is responsible for convective heat transfer. At the bulk scale, the heat transfer coefficient is a weak function of the temperature of the heated solid, which diminishes at higher temperatures. Pressure also influences the heat transfer coefficient since the molecular density of air is pressure dependent. A second mode of heat transfer is through diffusion and/or conduction at the still boundary layers next to the solid. Maxwell [134] introduced the

concept of molecular conduction in gases. The thermal conductivity was derived to be proportional to the specific heat at constant volume, density, mean free path and the mean velocity of molecules. Since the density is directly and the mean free path is inversely proportional to the number of molecules per unit volume, the dependence of the mean velocity is decisive, if the specific heat can be taken as constant. Thus, thermal conductivity does not depend on pressure or density and is proportional to the square root of temperature. This is very different from the classical notion of advection dominated heat transfer. Therefore, the relative contribution from the two mechanisms, advection and molecular conduction, determines the nature of the temperature and pressure dependence of the heat transfer coefficient.

While for macro-scale objects, density difference drives the ﬂow associated with natural convection, the buoyancy forces at the smaller scales are too small to overcome the forces of viscous drag, which oppose the convective motion. When a heated microstructure is suspended in air, the dominant mode of heat transfer is conduction through the air, and natural convection at such micro-scale devices is less important as evident from literature [128, 135]. Due to the small size of the system, density variations are very small in the control volume, and thus gravitational forces do not become signiﬁcant. This shows that at the microscale, the classical notion of advection may not be dominant and conduction should be considered [136]. Hu et al. [135] studied heat transfer from an aluminum micro heater fabricated on a silicon nitride thin film using 3ω measurements. Guo et al. [128] focused on the size effect on heat transfer in micro devices. These studies suggest that larger surface area to volume ratio in the heated solid will have more impact on heat transfer coefficient. It is also argued that the natural convection is less significant in a micro-enclosure owing to very small buoyancy, which is the driving force. The Grashof number is estimated, assuming the side surfaces of the silicon beam as a vertical flat plate that is 20 µm long, to be in the order of 10-5, which again reinforces the observation that buoyancy forces can be neglected when compared to viscous forces.

The rapid advances in miniaturization, particularly in thermal sensors and actuators and all other heat dissipating devices, has resulted in renewed interest in the size effects on convective heat transfer. While solid to gas heat transfer at micron and submicron scales remains to an open area for research, the consensus is that the heat transfer coefficient (h) increases with decreasing length scale. The bulk value of h is generally within a range of 10-25 W/m2K. A simple scaling argument using the correlation between Nusselt, Rayleigh and Prandtl numbers let Peirs et al. [131] to suggest that the heat transfer coefficient (h) value in the order of 100 W/m2K for air at length scales around 100 µm. Kim et al. [129] studied heat transfer between a micro cantilever with an integrated heater

at the tip and surrounding air using continuum finite element simulations. The calculated effective heat transfer coefficient around the heater portion and cantilever leg is considerably large; around 7000 W/m2K near the heater and 1000 W/m2K near the cantilever base. Giani et al. [137] presented a thermal model of a silicon rich silicon nitride thin film anemometer with a platinum heater. It is shown that the convection is dominating compared to conduction and radiation. They calculated thermal conductance due to various modes of heat transfer and deducted the value of heat transfer coefficient to be as high as 200 W/m2K. Wang et al. [130] studied the heat transfer around a microwire using the 3ω method and reported heat transfer coefficient values ranging from 100-1000 W/m2K depending on the diameter of the micro-wire. The degree of variation (100-7000 W/m2K) in the literature suggests that the heat transfer coefficient is strongly influenced not only by size but also on other factors that may not have been addressed consistently across the existing studies, which provides motivation for the present study. Most of the existing literature attempts to measure microscale heat transfer coefficient as a unique value, whereas a comprehensive study should involve the influence of temperature and pressure. Cheng et al. [138] measured the heat transfer coefficient between a free-standing VO2 nano wire and quiescent surrounding air using laser thermography and found that the coefficient is strongly dependent on pressure above ~ 10 Torr unlike in macroscale solids, where it is pressure independent. Very little work has been done to measure the dependence of the heat transfer coefficient on parameters like temperature and pressure [139, 140] at micro and nanoscales. This provides the motivation for the present experimental study, which is aimed at measuring the heat transfer coefficient at small scales and explore its dependence on temperature and pressure.

3.1.2 Experimental Setup

In this study, we designed and fabricated a micro device that integrates a micro heater with a freestanding specimen using standard nanofabrication techniques. The specimen is essentially a heavily doped single crystal silicon beam, 10 m wide and 20 m thick. To study the dimensional sensitivity on the convective heat transfer, about 100 micron long segment was photo- lithographically reduced to 8 m × 20 m in cross-sectional size. Further reduction in cross section size to 8 m × 1 m was performed with focused ion beam milling. Figure 3.1 shows a scanning electron micrograph (SEM) image of the micro device, highlighting the different parts. The size of the entire device is 3 mm × 5 mm and is compatible with scanning electron, probe or infrared microscopy.

Figure 3.1. (a) Scanning electron micrograph of the micro device with a T shaped heater and specimen, (b) Experimental setup showing the infrared microscope and vacuum chamber.

Figure 3.2. Nanofabrication processing steps for the micro device containing the specimen and micro heater.

The nanofabrication process starts with patterning photo resist on a SOI wafer (20m thick highly doped single crystal device layer silicon, 2m buried oxide and 400 m handle layer silicon) by photolithography, as shown in Figure 3.2. After that, the device layer silicon is etched anisotropically by deep reactive ion etching (DRIE). Samples are then exposed to hydrofluoric acid vapor to remove the 2 m oxide between the device and handle layer silicon. This creates a 2 m gap between the silicon layers and eventually releases the device layer features from the floor, i.e. handle layer silicon. In a separate batch of devices, a backside lithography and DRIE was used to remove the entire handle layer beneath the specimen. Finally, the resist is stripped away by using oxygen plasma. The specimen was designed to have a narrower cross-section (8 × 20 m2) compared to the nominal values of 10 × 20 m2. After the device is fabricated, a small part of the 20 m thick silicon sample beam is milled away using a focused ion beam (FIB) to create 8 × 1 m2 cross-section and 12 micron long constricted region as shown in Figure 3.1a.

3.1.3 Experimental procedure

A typical experiment starts with the passage of known electrical current through the heater beam (Figure 3.1a) while the device is in atmospheric pressure and room temperature. As current is passed through the heater beam, due to the Joule heating, a parabolic temperature profile is formed along the length of the heater beam. The highest temperature is observed in the middle of the heater beam where at its intersection with the sample beam, thereby creating a temperature gradient along the length of sample beam. A temperature gradient perpendicular to the specimen also exists, with the high temperature at the specimen surface and exponentially decaying to the ambient temperature. The temperature profile in the heater and sample is measured with an Infrascope II thermal microscope (Quantum Focus Instruments Corporation) with the spatial and temperature resolutions of about 2 microns and 0.1 K, respectively. Once the temperature profile for the initial electrical current (starting with 20 mA) is recorded by the infrared thermal microscope, current is increased progressively by 5 mA and thermal images are recorded for each electrical current until it reaches 80 mA. We also developed a vacuum chamber with CaF2 viewport and electrical feed-through so that the experiments could be carried out in a controlled vacuum environment (Figure 3.1b). The height of the vacuum chamber is such that it will fit in between the microscope objective and stage. The device is placed inside the vacuum chamber and electrical connections are completed via feed-through. After the chamber is pumped down to a moderate vacuum pressure (3 Pa), thermal images are collected for same electrical currents. All the thermal images are recorded in the steady state limit.

3.1.4 Mathematical model for determination of heat transfer coefficient

The heat transfer coefficient in quiescent air medium can be obtained by two different ways. The first technique utilizes the heating (or cooling) timescale, in conjunction with mass (m), surface area (S) and specific heat cp, as given in the following equation [141],

푟푚푐 ℎ = 푝 (1) 푆

The term r is the inverse of the time constant for the object, which is obtained from curve fitting the time dependent temperature data that typically follows an exponential profile, 푇(푡) = −푟푡 푇∞ + (푇(0) − 푇∞)푒 . While the transient mode temperature measurement in our experimental setup can achieve micro-second resolution, the exact mass measurement is difficult for the present study. This is because the inherent temperature gradient in the specimen. The second technique is to perform an energy balance between conduction in the specimen accounting from the convective heat losses. This technique requires measurement of the temperature profile of the thermal boundary layer near the heated solid surface. In this study, we measured the temperature profile across the sample to infer the air temperature boundary layer temperature with infrared thermal microscopy. Infrared thermography has been a powerful tool for macroscopic convective heat transfer measurements [142, 143]. Figure 3.2a shows an image obtained from the thermal microscope. The lateral T(y) scan operation, done at any section of the silicon beam, gives the temperature variation with distance away from the surface. An exponential distribution in space is suggested as the best fitting function by Roldan et al. [144] to allow T (air temperature at position y) to approach the room temperature T∞ as y→∞

−푠푦 푇 = 푇∞ + (푇푤 − 푇∞) ∗ 푒 (2)

Where s is a constant determined by plotting the logarithm of the temperature against the distance

(y) from the specimen surface at temperature Tw,

푇−푇 ln ∞ = 푠 ∗ 푦 (3) 푇푤−푇∞

The boundary condition is that the air immediately above the surface is at rest and transfers heat by conduction. The conductive flux Q given by the Fourier’s law of conduction is

푑푇 푄 = −푘 | , (4) 푎푖푟 푑푦 푠푢푟푓푎푐푒

Where kair is the thermal conductivity of air. The local heat transfer coefficient is defined as

푄 ℎ = (5) (푇푤−푇∞)

On substituting the conductive flux at the surface we obtain the expression for the local heat transfer coefficient as[144],

ℎ = 푘푎푖푟 ∗ 푠 (6)

3.1.5 Experimental results and validation

Figure 3.3. (a) Infrared micrograph of the specimen, (b) temperature profile in the y-o-y’ direction, (c) determination of the exponent s in equation (2).

Figure 3.3a shows the image from the thermal microscope. The green line (y-y’) perpendicular to the length of the beam shows the section of the lateral scan for which the temperature variation with length is shown in Figure 3.3b. According to equation (3), the plot of ln (푇−푇 ) ∞ and y should be linear with slope s. This is shown in Figure 3.3c. Similar line scans are (푇푤−푇∞) performed at different sections along the length of the beam, which are at different temperatures because the specimen is heated from only one end. This allows us to measure the heat transfer coefficient at various specimen temperatures. Figure 3.4 shows a plot for both the temperature

profile of the specimen and the measured heat transfer coefficient at different locations labeled from A to E. The heat transfer coefficient thus obtained from this technique is about three orders of magnitude higher than that for macroscopic bodies. Also evident is the strong dependence of h with temperature, which varies by approximately ~25% within a very small temperature differential of 35 °C. The bulk motion of the fluid particles being the dominant contribution in the convection does not explain this. The results discussed in this section are for the experiments carried out at atmospheric pressure.

Figure 3.4. Temperature profile of the specimen showing the measure value of heat transfer coefficient at different locations.

The boundary layer thickness and the heat transfer coefficient obtained for the microstructure are compared with those for a bulk scale object and are calculated using the following correlations:

퐺푟 −1/4 훿 = 5퐻 ( 퐻) (7) 푡ℎ,퐻 4

1/4 ̅̅̅̅̅̅ 0.670푅푎퐻 푁푢퐻 = [0.68 + 4/9] (8) [1+(0.492/푃푟)9/16]

In order to observe the effect of pressure on the temperature dependence of the heat transfer coefficient, an experiment was conducted in a moderate vacuum (3 Pa) and the results are compared with that in ambient pressure. As seen in Figure 3.5, the temperature of the specimen is relatively higher in vacuum because of the reduced heat loss through convection. Nevertheless, the apparent temperature dependence of h remains the same. The higher temperatures of the specimen can be explained by the low molecular density and high inter-molecular space in the surrounding air. It makes the heat transfer through diffusion process less prominent and hence the reduced heat transfer coefficient values. The decrease of h varies approximately from 4 to 8% in the total length of the silicon beam.

Figure 3.5. Temperature profile of the silicon specimen at two different pressures.

In order to validate the experimentally obtained values of the heat transfer coefficients, a model is developed to evaluate the temperature of the silicon beam from the first law of thermodynamics. An energy balance is performed at the specimen surface to measure the heat transfer coefficient. These measurements are validated by using the values in calculating the thermal conductivity (or in other words, the temperature gradient along the specimen length), because the thermal conductivity of silicon is very well characterized in the literature [141].

휕퐸 퐶푉 = 퐸̇ − 퐸̇ + 퐸̇ (9) 휕푡 푖푛 표푢푡 푔푒푛

Since there is no internal heat generation in the specimen, at steady state, heat incoming to a control volume is balanced by the outgoing heat in form of conduction, convection and radiation,

4 4 푑푞표푢푡 = ℎ ∗ 푑푆 ∗ (푇 − 푇∞) + 휀 ∗ 휎 ∗ 푑푆 ∗ (푇 − 푇∞ ) (10)

For small temperature differences, equation (10) can be approximated as

3 푑푞표푢푡 = (ℎ + 휀 ∗ 휎 ∗ 4푇∞ ) ∗ 푑푆 ∗ (푇 − 푇∞) (11)

푑푞표푢푡 = (ℎ푎푝푝푟표푥) ∗ 푑푆 ∗ (푇 − 푇∞) (12)

Equation (12) with fixed temperature boundary conditions and experimentally obtained values of heat transfer coefficient is used to validate the temperature of the silicon beam along its length. The temperature distribution is then developed by approximating the silicon beam as an extended surface with a constant temperature boundary condition at x=L [141].

휃 퐿 sinh 푚푥+ sinh 푚(퐿−푥) 휃 휃 = 푏 (13) 휃푏 sinh 푚퐿

2 ℎ푎푝푝푟표푥푃 Where, θ = T-T∞, θb = θ(0), θL = θ(L) and 푚 = . The h values measured previously 푘퐴푐 (locations A-E in Figure 3.4) are used in the above expression. P is the perimeter of the cross- sectional area Ac of the beam. Figure 3.4 also shows the predicted temperature distribution along the length of the specimen for thermal conductivity of 140 W/m-K, which shows remarkable fit between the measured and predicted temperature profiles. Since thermal conductivity of silicon is very well characterized in the literature, Figure 3.4 convincingly validates the measured values of the heat transfer coefficient.

Using equations (3) and (6), the uncertainty analysis has been carried out. The expression for the uncertainty in the heat transfer coefficient due to the uncertainties in the measured quantities is

Δℎ Δ푦 2∆푇 1 푇−푇∞ = + 푇−푇∞ [1 − ] (14) ℎ 푦 ln( ) 푇−푇∞ 푇푤−푇∞ 푇푤−푇∞

The uncertainty in evaluating the heat transfer coefficient is given by Equation (14). It is to be noted that the spatial resolution mentioned earlier is not the uncertainty in measuring y. The output of the thermal microscope is a pixel-by-pixel temperature plot. For a certain magnification,

the pixel-to-pixel distance is a fixed number and is not the error bar of y. A relative error of 10% in y is assumed which is a reasonable approximation. This gives a relative uncertainty of 10 - 11% in the heat transfer coefficient as evaluated using Equation (14).

3.1.6 Discussion

In this study, we measured the heat transfer coefficient by performing experiments on microscale specimens. The experimental results are in the same order of magnitude with the values given by Kim et al. [129]. The results also show pronounced effects of specimen temperature previously not reported in the literature. The observed large values of the heat transfer coefficient can be related to the thickness of the thermal boundary layer developed near the specimen surfaces. Since the characteristic length of the device are in the order of tens of micrometer (Kn ~ 0.001), the assumption of flow continuum is valid.

Table 3.1 compares the heat transfer characteristics of a micro (present study) scale and a macro scale object. The Grashof number for the specimens in this study is very small, which reinstates the argument that the buoyancy forces are negligible at low length scales. The boundary layer is more compressed and the heat transfer coefficient obtained is in the same order of magnitude with that presented by Piers et al. [131]. Such a high heat transfer coefficient in the absence of bulk fluid motion (very little buoyancy) explains that the diffusion through conduction in air molecules is the major mechanism of energy transfer. It implies that these correlations are majorly dominated by thermal conduction and not affected by the advection and agrees with Kim et al. [129]. This also supports the observed pronounced temperature dependence. At lower temperatures, the air molecules in the thermal boundary layer have lower kinetic energy and consequently are capable of higher rates of heat transfer by diffusion. This phenomenon is pronounced by the relative thickness of the thermal boundary layer at the microscale. As seen in

Table 3.1, the ratio th/Hchar is more than one order of magnitude larger at the microscale compared to bulk. Considering the dominance of heat conduction through the air surrounding the specimen, the relative thickness of the boundary layer can play significant role in the effective heat transfer. In other words, the relative thermal boundary layer thickness at the bulk scale is too thin to show any appreciable effect of temperature on the kinetic energy of the air molecules inside the boundary layer. This explains the relative temperature insensitivity of the heat transfer coefficient at the macro scale.

Table 3.1. Comparison of micro and bulk scale convective heat transfer

2 Hchar [m] Grashof No. δth,H [m] Nusselt No. δth/ Hchar h [W/m K]

20.0E-02 (bulk) 2.0963E+07 2.348E-02 32.534 8.51 4.47

20.0E-06 (micro) 2.0963E-05 2.348E-03 0.711 117.43 979.54

The orders of magnitude higher heat transfer coefficient make convective heat transfer to the surrounding air comparable to that through the specimen. We therefore propose that at the micro scale, the ratio of specimen surface area S (solid to medium heat transfer) to the cross-section area

Ac (conduction in the solid) plays an important role in the relative contribution of these two channels of heat transfer. The ratio is very large at the microscale, which is directly related to the heat transfer coefficient. The pronounced temperature dependence observed in this study suggests that similar effect can be related to the temperature ratio Tm/Ts, where Tm is the temperature differential between the heated solid to the ambient medium (solid to medium heat transfer) and Ts is the temperature differential between the hot and cold end of the specimen (conduction in the solid). This enables us to propose the following empirical relationship for the size and temperature dependence of the heat transfer coefficient,

푆 Δ푇푚 푘푎𝑖푟 ℎ = ℎ푏푢푙푘 + (15) 퐴푐 ΔT푠 푑푔푎푝

Where, hbulk is bulk scale heat transfer coefficient, kair is the thermal conductivity of air and dgap is the distance of the specimen from the nearest solid surface. The second term of equation (15) is predominant for cases where the heated specimen is very closely spaced with a second solid surface. Keeping in mind that the above expression is empirical in nature, we performed three different experiments to determine its validity. Figure 3.6a shows the experimentally obtained temperature profile of a 50 nm thin, 5 microns wide silicon nitride specimen juxtaposed with the predicted values using the heat transfer coefficient given by equation (15). Figure 3.6b shows similar results for a 20 m thick and 10 m wide specimen, which is freestanding with no solid surfaces nearby. Figure 3.6c shows a different scenario for the specimen that is freestanding, but hangs 2 m above the device floor. The heat transfer coefficient obtained in this case is very high because of the conduction through small air gap plays a dominant role. For all these cases, the

remarkable agreement between the experimental and predicted temperature profiles suggest the effectiveness of equation (15).

It is important to note that, while the experimental results in this study shows remarkable size and temperature dependence, the most critical influencing factor remains to be the heater geometry. In this study, the heater is a 100 microns long, 10 microns wide and 20 microns deep silicon beam, whose thermal time constant is about tens of microseconds. According to equation (1), such small thermal time constant leads to the observed heat transfer characteristics for the specimen section. If the specimen were heated using a macro-heater instead, the thermal time constant would be very large, which would reduce the size effect on heat transfer coefficient.

3.1.7 Conclusion

This study reports the size and temperature dependence of the heat transfer coefficient and explains the dominating mechanism of the heat transfer process at such size scales. An infrared thermal microscope was used to measure the spatial temperature profiles perpendicular to the microscale specimens, which are integrated with micro heaters. Energy balance at the solid-air interface was used to calculate the heat transfer coefficient. The measured heat transfer coefficient varied from 4650 W/m2K in a 10 μm × 20 μm freestanding specimen to 16300 W/m2K for the same specimen with 2 μm away from a neighboring solid surface. The measured values were validated by using them to predict the temperature profile along the length of the specimens using the one- dimensional heat transfer and then compared the predicted values with the measured ones. The main contribution of this study is an empirical relationship to obtain the heat transfer coefficient for arbitrary specimen size and temperature. The study also investigates the effect of medium pressure to find that the temperature dependence remains the same at low pressures but the magnitude of the heat transfer coefficient decreases by ~ 4-8% in vacuum from the values in atmospheric pressure.

3.2 Characterization of Very Low Thermal Conductivity Thin Films

Determining the thermal conductivity of nanoscale thin films with very low thermal conductivity (< 1 W/m-K) is challenging due to the difficulties in accurately measuring spatial variations in temperature field as well as the heat losses. In this study, we present a new direct and steady state technique that mimics the phenomenon where a bridge with both surfaces exposed to wintry conditions typically ices before the pavement. Accordingly, the technique involves freestanding nanofabricated specimens that are anchored at the ends, while the entire chip is heated by a macroscopic heater. Measurement of the spatial map of temperature field as well as the natural convective heat transfer coefficient allows us to calculate the thermal conductivity of the specimen using an energy balance modeling approach. The technique is demonstrated on thermally grown silicon oxide and low dielectric constant carbon doped oxide films. The thermal conductivity of 400 nm silicon dioxide films was found to be 1.2 W/m-K, and is in good agreement with the literature. Experimental results for 200 nm thin low-k oxide films demonstrate that the model is capable of accurately determining the thermal conductivity for materials with values < 1 W/m-K.

3.2.1 Introduction

Thin films with very low thermal conductivity, such as oxides and nitrides are prevalently used in micro-electronic devices [145]. Other applications, such as, organic electronics and energy conversion essentially involve low thermal conductivity polymeric or nanostructured materials [146, 147]. These materials typically have amorphous microstructure, where the atomic scale disorder attenuates the vibrational waves that carry heat, resulting in the low thermal conductivity. In addition, surface and/or interface dominated scattering may also influence the thermal transport at the nanoscale. As the characteristic size (L) of the integrated circuits shrink, the power density of these devices increase nonlinearly (scaled as L-1), which makes thermal conductivity of thin films a critical concern regarding device performance and reliability [148]. For better thermal dissipation, larger values of the thermal conductivity are desired. The current trend is to lower the dielectric strength (k) to mitigate the increase in resistance-capacitance (RC) time delays and power consumption in integrated circuits [149]. The interlayer dielectrics (ILDs) in interconnects thus possess lower thermal conductivity because lowering the dielectric constant involves increasing of the pores and foreign atomic pose a challenge due to their inherently lower thermal conductivity. Therefore, thermal and mechanical characterization of these materials is important from performance and reliability perspectives.

Characterization of nanoscale thermal transport has been a very active area of research. This stems from the observation of the strong size, surface, geometry and microstructure effects [150-152] that can potentially lead to control of intrinsic properties such as thermal conductivity. Accordingly, the techniques utilized to investigate thermal conductivity at the nanoscale are significantly different from those traditionally used for bulk materials. Research in this area has primarily followed three distinct streams namely the 3, thermo-reflectance and steady state techniques. In the 3technique, a planar four-probe configuration is micro-fabricated on the thin film specimen to serve the dual purpose of heating and sensing. When an alternating current (AC) voltage signal is used to excite the heater at a frequency ω, the periodic heating generates oscillations in the electrical resistance of the metal line at a frequency of 2ω. In turn, this leads to a third harmonic (3ω) in the voltage signal, which is used to infer the magnitude of the temperature oscillations [153]. The frequency dependence of the oscillation amplitude and phase can be analyzed to obtain the thermal conductivity and specific heat of the specimen [154]. Further generalization [155] and analysis [156, 157] of the concept is available in the literature. As the specimen size decreases below micron scale, special attention needs to be given to the interfacial thermal resistance [158, 159] as well as heat loss to the substrate and the surrounding medium. Accordingly, alternate specimen geometries and heating schemes [160-162] have been proposed in the literature that also allows in-plane characterization. However, insulating specimens still need to be integrated with heaters, and the influence of the metallic heaters with finite thickness [163] may not be favorable, especially for <100 nm thick specimens.

The second stream for thermal conductivity characterization is also transient in nature, but does not require any complicated specimen/heater fabrication. An example of such a non-contact technique is time-domain thermo-reflectance (TDTR) which uses ultra-fast laser pulses to locally heat the surface of the specimen. The surface temperature of the specimen is inferred from the change in reflectance of the surface, which is linearly dependent on the temperature of the specimen for small temperature changes. The reflectivity is measured by another low power probing laser. The ultra-short heating pulses can limit the thermal penetration depth to tens of nanometers, thereby allowing accurate measurement on nanoscale thin films on a substrate [164]. An in-plane version of this technique also has been developed [165]. However, TDTR actually measures the thermal diffusivity of the specimen. To obtain thermal conductivity from TDTR, one needs to know the volumetric heat capacity of the specimen. Unfortunately, this value is not known for many thin film or nanoscale materials and assumptions must be made that limit the accuracy of the technique.

Furthermore, the experimental setup (laser and optical equipment) and the analysis required to include the interfacial thermal resistance make the TDTR technique non-trivial [166, 167].

The third stream of thermal conductivity characterization technique involves steady state heating and sensing on specimens that are deposited on a substrate or are freestanding. Here, the specimens are heated with micro-patterned metallic line heaters, while temperature is sensed by another set of metal lines using resistance thermometry. The advantage is that in-plane thermal conductivity can be measured. A representative case [168] in the literature measured both in and cross plane thermal conductivity of disordered layered WSe2 and (W)x(WSe2)y specimens. These specimens, about 140 and 160 nm, respectively, showed very low thermal conductivity (about ∼ 1 Wm-1K-1). The advantages of such steady state measurements are simpler and robust instrumentation and thermal transport modeling, but accurate characterization of heat losses to the medium and substrate is of critical concern.

The motivation of this study comes from the need for a technique that can measure thermal conductivity of low-k interlayer dielectrics with values of < 1 W/m-K that are lower than most of the materials studied in the literature. Here, the key challenges are to accurately measure the spatial temperature variation and the heat loss from the specimen [169, 170]. Since the temperature gradient is very sharp in low thermal conductivity thin films, the conventional technique of electrical resistance measurement of micro-patterned metal lines as a function of temperature is not favorable. The second challenge of heat loss measurement is particularly binding for nanoscale thin films for which loss components from both the substrate and the surrounding air must be included. For a thin-film specimen deposited on a substrate, analytical models exist [157] to account for the substrate, but the simplified models enforce a variety of constraints that are not well documented in literature and are difficult to satisfy in experiments. For example, the substrate should have lower thermal conductivity than the specimen [171], which is very hard to achieve for low thermal conductivity specimens studied in this work. Kodama et al. [172] performed experiments on both freestanding and on-substrate specimens to show that the effect of heat loss to the substrate on the experimental uncertainty can be as high as 80%. While specimen preparation is easy for any on- substrate configuration, the heat loss to the substrate becomes complicated due to the interfacial thermal contact resistance issue [173]. This problem is addressed in the literature using freestanding specimens [154, 160, 174-177], which also enables easier to model in plane and one-dimensional thermal transport. This is also schematically shown in Figure 3.7a as metal heater lines, patterned on the specimen to locally heat it. Similar heater line with four electrical pads allows use of the 3

technique on freestanding membranes [135, 158]. The other metal lines in Figure 3.7a are used to detect the temperature of the film by measuring the change in resistance in the metal lines.

Heat loss to the surrounding air is also complicated because the bulk scale value (5-15 W/m2-K) of natural convective heat transfer coefficient (h) is not directly applicable at the micro or nano scales. The convective heat transfer coefficient can be obtained from the heating (or cooling) timescale, in conjunction with mass (m), surface area (S) and specific heat cp, as given in the following equation,

푟푚푐 ℎ = 푝 (16) 푆

The term r is the inverse of the time constant for the object, which is obtained from curve fitting the time-temperature data that typically follows an exponential profile,

−푟푡 푇(푡) = 푇∞ + (푇(0) − 푇∞)푒 (17)

The thermal time constant scales a L2, where L is the length scale. It is important to note that L reflects the active heating element size and not the overall heat transfer area alone. For example, the thermal time constant of a macroscopic heater (with large time constant) may lead to smaller values of h, even for a small-scale specimen. Following the same argument, nanoscale specimens heated locally by integrated line type micro heater (with very small time constant) may

result in very large values of the effective convective heat transfer coefficient [135, 178]. While transient studies can be carefully designed to minimize the heat losses [179], a key concept of this study is to circumvent the uncertainty in the micro- or nanoscale convective heat losses by shifting from localized micro heating to global and uniform heating of the entire die containing the thin film micro bridge specimen. This is shown in Figure 3.7b. Heating up the entire substrate implies that the temperature of the specimen ends (anchored with the substrate) will be governed by the substrate’s thermal time constant. Therefore, even though the micro or nanoscale specimen itself has very fast thermal response, the effective thermal time constant is primarily that of the substrate. Therefore, the main advantage of heating the entire substrate, in contrast to the conventional practice of using a thin metal line micro (and local) heater, is that the bulk value of natural convective heat transfer coefficient can be used with reasonable accuracy. This has been demonstrated in this study.

It is very important to note that none of the direct thin film thermal conductivity measurement techniques in the literature takes advantage of the global heating as described above. This is because for materials with even low to moderate thermal conductivity, the substrate acts as an enormous constant temperature heat source, resulting in uniform temperature field in the specimen with essentially the same value as the substrate. In absence of any appreciable thermal gradient, it is not possible to measure the thermal conductivity using the Fourier heat conduction law. This is why all of the existing direct techniques use localized heating through micro-patterned heater lines. However, very low thermal conductivity materials are uniquely suited for this technique because even though the specimen ends have the same temperature as the substrate, they develop a large thermal gradient. An analogous phenomenon is the icing of bridges before pavements in wintry condition. It is therefore possible to develop an energy balance model that accounts for the temperature boundary condition at the specimen ends and the convective heat transfer losses to accurately measure the thermal conductivity.

To address the above-mentioned issues on temperature gradient and heat loss, we present a steady state and direct technique that employs freestanding micro-bridge specimens fabricated using standard micro-fabrication (photo-lithography and etching) techniques. Since the specimen is freestanding, the errors associated with heat loss and interfacial thermal resistance due to the substrate are completely eliminated. Specimen preparation is easier than conventional micro-bridge techniques because there is no need to integrate micro-heaters with the specimens. Rather, the entire die containing the specimen is uniformly heated, which also allows accurate account for the convective heat losses for the specimen. The difficult task of measuring the true natural convective

heat transfer of the specimen is indirectly yet accurately performed by measuring the cooling rate of the entire die containing the specimen. The technique is direct in nature and does not require complex modeling as other alternatives such as the 3 and thermo-reflectance techniques.

3.2.2 Experimental technique

The experimental setup consists of a small (15 cm x 15 cm) die mounted on a thin Kapton foil heater. The die contains a 50 microns long and 5 microns wide micro-bridge specimen that is formed from a dielectric film that is deposited on a silicon wafer with the desired thickness. The calibration specimen material in the present study was 400 nm thick thermally grown silicon oxide film. Further characterization was performed on a 200 nm thick low-k carbon doped oxide deposited by Plasma Enhanced Chemical Vapor Deposition (PECVD) [180]. The details of the PECVD deposition have been previously described. Briefly, an alkoxysilane precursor diluted in Helium was used to deposit the low-k film at temperatures on the order of 400C on 300 mm diameter Si (100) wafers using an industry standard high volume manufacturing PECVD tool [181]. Table I below summarizes some of the key material properties for the low-k film including low frequency (100 kHz) dielectric constant, refractive index (at 400 nm), intrinsic film stress, nanoindentation Young’s modulus, and x-ray reflectivity mass density[182, 183]. Although the low-k film is half the density of a typical thermal SiO2 film, no open or interconnected porosity was detected for this film using standard ellipsometric porosimetry techniques. Positronium annihilation lifetime spectroscopy (PALS), however, detected the presence of isolated pores with an average radius of approximately 0.94 nm [183].

Table 3.2. Material properties for the low-k dielectric investigated in this study.

Dielectric Refractive Intrinsic Film Young’s Mass Density Pore Constant “k” Index Stress Modulus Diameter (g/cm3) (MPa) (GPa) (nm)

3.1 1.46 50 11 1.35 0.94

Figure 3.8 shows the micro-fabrication process steps developed for this study. The first step is to deposit the specimen film on the wafer with desired thickness. The micro bridge pattern

is then formed in photoresist on the thin film surface using photo-lithography. The photo-resist pattern is then used as the etch mask for the underlying specimen film while removing the unwanted portion using a reactive ion etching (RIE) process using CF4 and O2 chemistry. This step results in the patterned specimen with the silicon substrate exposed. To remove the substrate under the specimen with minimal undercutting, highly anisotropic deep reactive ion etching (DRIE) using

SF6 based chemistry was used. The photoresist used in this study is about 1.2 micron thick when spin coated at 4000 rpm, which ensures that the specimen is not exposed during the RIE and DRIE processes. At this point, the remaining photoresist is removed with a photoresist stripper, and the silicon beneath the specimen is removed by a quick SF6-based isotropic reactive ion etch. We observed no measurable attack of the specimen material for the RIE process. The completeness of the silicon etch is confirmed by inspection using a scanning electron microscope (SEM). Since the silicon is etched isotropically, an incomplete etch shows a very narrow and thin line of silicon beneath and along the centerline of the specimen. Since the specimen is very thin, this line of silicon is clearly visible for under-etched specimens. We did not observe any indication of incomplete silicon etch in our specimens.

Figure 3.8. Schematic presentation of the micro-fabrication process steps for specimen preparation

Figure 3.9a below shows a scanning electron micrograph of a specimen captured with a FEI Company Quanta 200 eD microscope under 5 kV acceleration voltage. Once the specimen is fabricated, the die is then mounted on a 1″ × 3″ perimeter of the specimen cross Kapton foil heater [184] using thermally conductive adhesives. The Kapton heater itself is mounted on a glass slab in a cantilevered configuration so that convection remains to be the dominant heat loss mechanism. The die containing the specimen is attached to the free end of the heater with a carbon tape. This configuration uniformly heats the die, rendering the substrate as very large heat source with constant temperature therefore; two anchored ends of the micro-bridge specimen have constant temperature boundary conditions. However, the specimen temperature (Ts) drops very quickly away from the anchor and remains constant for most of the length. This is due to the low thermal conductivity of the specimen. The temperature profile is characterized using an Infrascope II thermal microscope (Quantum Focus Instruments Corporation). The optical head contains the liquid nitrogen-cooled Indium-Antimonide infrared detector. The focal plane array type detector measures the radiance from target objects to calculate the temperature with 0.1 K resolution. Post processing of the data allows the user to perform line scans of the temperature profile, which is presented by pixel numbers. In this study, a 15x objective was used, which provides pixel-to-pixel resolution of 1.66 μm. Figure 3.9b shows the infrared image of the specimen. Figure 3.9c shows the experimental setup including an optional vacuum chamber. For this study, the specimen was placed in the chamber without operating the pump to obtain quiescent ambient condition. The room temperature was controlled to 22 °C.

3.2.3 Mathematical model

An energy balance model can be developed to determine thermal conductivity of the specimen from the input of the specimen, substrate and ambient temperatures as well as specimen dimensions. Figure 3.10 shows a schematic diagram (not up to scale) of the specimen temperature and geometry to highlight different regions of interest and the energy equilibrium conditions. At thermal equilibrium, the rate at which heat energy is being convected away from the surface is the same as the rate at which heat is being extracted from substrate. This has two components, (i) heat conduction from the specimen end, which is maintained at a constant, higher temperature and (ii) convective heat from the substrate under the specimen.

Figure 3.10. (a) Energy balance in small specimen segments with length ∆x and width w at two different locations, A and B, (b) Temperature profile along the length of the specimen.

Assuming Newtonian cooling, we can write the energy balance equation for a small element of length ∆x located near the specimen edge, where the temperature varies along the length direction [185]. This is schematically shown as location A in Figure 3.10.

푑푇 푑푇 푃 푃 퐾퐴 | − 퐾퐴 | + ℎ푐 ∆푥(푇푠 − 푇) = ℎ푎 ∆푥(푇 − 푇∞) (18) 푑푥 푥 푑푥 푥+∆푥 2 2

Here, P is the perimeter of the specimen cross-section, T and Ts are the ambient and substrate temperatures respectively. This equation can be re-written as,

푑2푇 푃 푃 퐾퐴 ∆푥 + ℎ ∆푥(푇 − 푇) = ℎ ∆푥(푇 − 푇 ) (19) 푑푥2 푐 2 푠 푎 2 ∞

Next, we observe that the relationship between ha and hc can be determined by examining the middle portion of the specimen (location B in Figure 3.10), which remains at a steady but higher temperature TB than the ambient, but lower than the substrate. This is a direct evidence of heat flowing from the substrate underneath to the specimen. The energy balance equation for this segment yields,

ℎ푐푤∆푥(푇푠 − 푇퐵) = ℎ푎푤∆푥(푇퐵 − 푇∞) (20)

Here, ha is the natural convective heat transfer coefficient from specimen to ambient and hc is its counterpart for the substrate and w is the specimen width. Since all the temperatures are measured from thermal microscopy, we can write,

(푇퐵−푇∞) ℎ푐 = ℎ푎 = 푛ℎ푎 (21) (푇푠−푇퐵)

The depth of silicon etch (or in other words distance from the etched floor of the die to the specimen) is an important parameter that influences hc or ha. This value is about 20 microns for our

2- specimens, which according to the scaling analysis would yield hc around 1000 W/m K [135]. However, as given by equation 16, the convective heat transfer coefficient is governed by the thermal mass and time constant and not simply scaled by size. In this study, instead of using a micro heater (with very small mass and time constant), we used a macroscopic heater to heat up the entire specimen. Even though the freestanding specimen is nanoscale, it is heated through the substrate, which has a very large mass and time constant. Therefore, the heat transfer coefficients are forced to assume values close to the bulk. This is supported by the cooling characteristics of the specimen and the die as shown in Figure 3.11 below. Here, a movie file was created by acquiring thermal snapshots at 0.01 s interval. The TM Viewer® data processing software accompanying the Infrascope II thermal microscope is capable of selecting a user-specified area and plotting the average temperature of that area as a function of time. Figure 3.11 shows the cooling curve for a 5 μm × 5 μm area located on the specimen as well as an arbitrary position on the large die. The remarkable fit of the specimen cooling curve with that of the die suggests that the larger die governs the cooling characteristics.

Figure 3.11. Temperature vs. time profile for the specimen as well as the die containing the specimen.

To measure the natural convective heat transfer coefficients, it is necessary to measure the cooling rate (dT/dt), surface area (S), mass (m) and the specific heat (cp). In this regard, the quantity ha is difficult to measure, but hc can be measured accurately. This is because the cooling rate for the relatively large die (compared to the small specimen) can be measured from time resolved thermal microscopy and specific heat and mass of the silicon substrate can be obtained with greater accuracy using equation 16.

The data given in Figure 3.11 results in r = 0.01. For the 15 cm × 15 cm × 0.5 mm chip

2 placed in a quiescent air medium, this results in hc = 8.2 W/m -K. The maximum temperature in the present studies is about 40 °C, which is low for radiation losses to dominate. Nevertheless, radiation loss was accounted for by determining an effective radiation heat transfer coefficient (hrad) and adding it to the convective heat transfer coefficient. For small temperature difference between an object and the ambient(푇표푏푗 ≈ 푇푎푚푏), the following linearization can be performed,

4 4 3 (푇표푏푗 − 푇푎푚푏) ≈ 4푇푎푚푏(푇표푏푗 − 푇푎푚푏) (22)

The effective radiation heat transfer can be defined as,

4 ℎ푟푎푑 = 휀휎4푇푎푚푏 (23)

where ε is the emissivity (0.7 for silicon [186]) and σ is the Stefan-Boltzmann constant ( 5.670373

-8 -2 -4 × 10 W m K ). The total heat transfer (ℎ푒푓푓 = ℎ푟푎푑 + ℎ푎) value is then used in the following equation,

푑2푇 푃 푃 + 푛ℎ (푇 − 푇) = ℎ (푇 − 푇 ) (24) 푑푥2 푒푓푓 2퐾퐴 푠 푒푓푓 2퐾퐴 ∞

Which can be rearranged as,

푑2푇 − 푚2푇 = 푐 (25a) 푑푥2 (푛−1)ℎ 푃 ℎ 푃 푚2 = 푒푓푓 푎푛푑 푐 = − 푒푓푓 (푛푇 + 푇 ) (25b) 2퐾퐴 2퐾퐴 푠 ∞

Solution for this second order differential equation is

푐 푇(푥) = 퐶 sinh(푚푥) + 퐶 cosh(푚푥) + (26) 1 2 푚2

The integration constants C1 and C2 can be found from boundary conditions,

푑푇 푇(푥 = 0) = 푇 푎푛푑 = 0 푎푡 푥 = 퐿 (27) 푠 푑푥

From these boundary conditions and defining sample length such that dT/dx = 0 at x = L (no heat input by heat conduction), we get,

푐 퐶 = 푇 − 푎푛푑 퐶 = −퐶 tanh (푚퐿) (28) 2 푠 푚2 2 1

Next, using the infrared thermal microscope data, T(x), and Ts can be accurately measured. Equation 24, therefore, enables us to plot the measured T(x) with the modeled T(x) as function of thermal conductivity. Since all the parameters of the term c in equation 25a except for the thermal conductivity (K) are measured accurately, equation 26 reduces the problem to one parameter (thermal conductivity) curve fitting to extract the true thermal conductivity of the specimen. It is important to note that conventional micro-bridge techniques are essentially two parameter models (thermal conductivity and natural convective heat transfer coefficient) unless very high vacuum environments are used. The primary source of error in the proposed technique is the estimation of the convective heat transfer.

The uncertainty in measurement scales with the errors in measuring various parameters, which can be obtained from equations 25a, 25b and 26,

∆푘 ∆푛 ∆ℎ ∆푃 2∆푚 ∆퐴 = + 푒푓푓 + + + , where (29) 푘 푛−1 ℎ푒푓푓 푃 푚 퐴 ∆푛 1 1 = 2∆푇 [ + ], (30) 푛 (푇푠−푇퐵) (푇퐵−푇∞) 2 ∆ℎ푒푓푓 = ∆ℎ푎 + 12휀휎푇∞∆푇, (31) ∆ℎ푎 ∆푛 2∆푇 1 푇(0)−푇∞ = + 푇(0)−푇 [1 − ], (32) ℎ푎 푛 푙푛( ∞) (푇(0)−푇∞) 푇(푡)−푇∞ 푇(푡)−푇∞ ∆푃 = 2(∆푥 + ∆푤), (33) ∆퐴 ∆푥 ∆푤 = + and (34) 퐴 푥 푤 [{푐1푐표푠ℎ(푚푥)+푐2푠푖푛ℎ(푚푥)}(푚∆푥)−∆푇] ∆푚 = 2푐 , (35) [ −푥{푐 푐표푠ℎ(푚푥)+푐 푠푖푛ℎ(푚푥)}] 푚3 1 2

Temperature, width, length, and time are the only direct measurements. The specimen width and length are defined the resolution of the photolithography and subsequent etching processes. Thus, these errors (Δw and Δx) are less than 0.1μm. The resolution of the infrared microscope used is 0.1 K, which can be safely taken as ΔT. It is to be noted that the spatial resolution mentioned earlier is not the uncertainty in measuring x. The output of the thermal microscope is a pixel-by-pixel temperature plot. For a certain magnification, the pixel-to-pixel distance is a fixed number and is not the error bar of x. To evaluate the time constant, a movie has been captured. The thermal snapshots are acquired at every 0.01 s time interval and hence Δt = 0.01 s.

3.2.4 Results and discussion

The proposed experimental technique was demonstrated on two low thermal conductivity thin film materials. Thermally grown oxide served as a calibration material, while further characterization was performed on a carbon doped low dielectric constant oxide specimen. For each experiment, 20 data sets on spatial temperature distribution were obtained. Figure 3.12 shows the experimental data on the temperature profile of the low dielectric constant specimen at one end with a constant temperature (313.2 K) boundary condition. This data is juxtaposed with the analytical predictions (equation 24) for three trial values (K = 0.23, 0.24 and 0.25 W/m-K) of thermal conductivity. The fit between the analytical model and measurements is reflected by the very close match between the analytical (solid line) and the experimental (dashed line) data with R2 value of 0.9961. The statistical variation in measurements (about 0.1 K) is shown in form of error bars in the experimental data. With the experimental data closely following the analytical model, the accuracy of the technique is demonstrated by the spread between the predictions for various values of thermal conductivity. We plotted the temperature profile for two very close values of thermal conductivity (K = 0.23 and 0.25 W/m-K), which is about 4.1% deviation in terms

of the thermal conductivity. Considering that the error bars are significantly smaller than the variation in the temperature for these plots, we can ascertain that the experimental accuracy is 95% or higher. From the plot, we observe that the carbon doped low dielectric constant specimens has a thermal conductivity value of K = 0.24 W/m-K. It is important to note that the energy balance model is two dimensional, while the real specimen has a third dimension. However, the specimen thickness (200 nm) is very small compared to the width and length (about 5 and 80 μm respectively), which allows us to use the 2D energy balance model to measure the in-plane thermal conductivity.

The obtained value of thermal conductivity (0.24 W/m-K) is in close agreement with values reported in the literature for carbon doped oxide films with similar mass density [187]. The significantly lower thermal conductivity of the low-k carbon doped oxide relative to SiO2 is to be expected based on the other reduced material properties that this material exhibits (see Table 3.2). Of particular significance for thermal conductivity is the reduced mass density of the low-k

3 3 dielectric (1.35 g/cm ) relative to that of a-SiO2 (2.35 g/cm ). Differential effective medium (DEM) and minimum thermal conductivity (MTC) theories predict a thermal conductivity dependence on

1.4-1.5 density () of K  (/bulk) for porous and amorphous materials where bulk is the density of the fully dense form of the material [188]. One would accordingly expect the thermal conductivity

3/2 of the low-k dielectric material to be (1.35/2.35) = 0.43 that of SiO2 or 0.5 W/m-K. This is close but slightly higher than the value measured here. This perhaps indicates that additional factors are responsible for reducing the thermal conductivity of the low-k dielectric beyond density simple scaling.

The accuracy of the technique is further validated through follow-up experiments on materials with well-characterized thermal conductivity values. Figure 3.13 shows results for a calibration experiment on 400 nm thick thermally grown oxide film. This thickness is intentionally chosen to eliminate any size effects [189, 190] that might make the comparison difficult. The measured thermal conductivity of the thermal oxide specimen is about 1.2 W/m-K, which is in close agreement with the literature [191] for the given thickness. It is important to note that the accuracy of the proposed technique declines for thermal conductivity > 1 W/m-K, where the temperature gradient in the specimen (compared to the boundary conditions) diminish. This is obvious from the comparison of figures 3.12 (temperature differential of about 4.7 K) and 7 (temperature differential of about 2 K). We therefore note that the accuracy and suitability of the technique enhances with the lower values of thermal conductivity. The resolution of the technique depends on the spatial resolution of the IR microscope, which imposes a constraint on the achievable resolution. For thermal conductivity of 0.24 W/m-K, this results in about 5 data points before the temperature gradient diminishes. However, this is for low temperature (313 K) heating of the specimen. For even lower thermal conductivity, similar accuracy (>95%) can be achieved by driving the heater to higher temperatures, since the temperature coefficient of thermal conductivity of oxides is almost negligible above 300 K [190].

The technique does not suffer from any limitations on the specimen thickness as long as the deposition process results in uniform thickness and the RIE process for specimen release does not attack the specimen. In case of unwanted specimen etching due to the SF6-based RIE chemistry, non-plasma based etching of silicon can be used. For example, XeF2 has the highest selectivity for oxide materials for silicon etching. The residual stress, on the other hand, has more influence on the technique compared to film thickness. For compressive stress, the specimen will buckle upon release from the substrate, which will not affect thermal conductivity of any insulating specimen. The tensile stress can have debilitating effects on specimen fabrication since the released specimen can fracture if the stress level is too high.

Figure 3.13. Experimental data (each data marker represent 10 data sets) juxtaposed with model predictions for three trial values of thermal conductivity.

It is interesting to note that the proposed specimen configuration (clamped-clamped beam) also allows mechanical testing (Young’s modulus and fracture strength) without further modification. This is because the specimen can be directly applied to a three point bending test using a suitable force-displacement measuring instrument. This is not possible with most state of the art thermal conductivity measuring techniques. Mechanical properties are also important for the low dielectric constant materials because of reliability concerns. The same mechanisms that reduce the dielectric constant also reduce the specimen stiffness, ductility and fracture toughness. Further applications may also involve characterization of interfacial thermal resistance between two layers in a bi-layer after measuring thermal conductivity of individual layers separately. By choosing the power level of the Kapton heater, it is also possible to measure thermal conductivity at different temperatures. Combined thermal-mechanical characterization of these materials will be reported in the future.

3.2.5 Conclusion

We have developed an experimental technique for measuring thermal conductivity of thin film materials made from very poor thermal conductors. The technique mimics the phenomenon that a bridge (poor thermal conductor as well as two free surfaces) ices before pavement. We have developed a mathematical model that captures this phenomenon and have demonstrated the technique on the in-plane thermal conductivity of 200 nm thick carbon doped low dielectric constant and 400 nm thick thermally grown silicon oxide specimens. The experiments involved freestanding films to eliminate any substrate error. Yet, it requires minimal fabrication for sample preparation as no micro heaters are required to be integrated with the specimen and only one instrument is required for data acquisition. The most significant aspect of the technique is that the difficult task of measuring the heat loss from the specimen to the ambient is indirectly yet accurately performed by measuring cooling rate of the die containing the specimen. The technique is shown to work very well for specimens with thermal conductivity of 1.2 W/m-K and below.

3.3 Thermal Conductivity of Ultra-thin CVD Hexagonal Boron Nitride

Thermal conductivity of freestanding 10 nm and 20 nm thick CVD grown hexagonal boron nitride (h-BN) films was measured using both steady state and transient energy balance techniques. The measured value for both thicknesses, about 100 ± 10 W m-1K-1, is lower than the bulk basal plane value (390 W m-1K-1) due to the imperfections in crystallinity of the specimen microstructure and probable phonon suppression from polymer residues. Impressively, this value is still 100 times higher than conventional dielectrics. Furthermore, when considering scalability and ease of integration, CVD h-BN is an excellent candidate for thermal management in two-dimensional materials-based nanoelectronics.

3.3.1 Introduction

Often dubbed white graphite, hexagonal boron nitride (h-BN) is a III-V compound and an insulating isomorph to graphite consisting of sp2 hybridized bonding in layered hexagonal basal planes [192]. It is a unique material considering its very high thermal conductivity [193, 194] and electrically insulating behavior [194]. Because of its excellent thermal and chemical stability, it has been used as high temperature lubricant and heat sink for microelectronic packaging. It is also used in polymeric nanocomposites to improve overall thermal conductivity [195]. Advent of two- dimensional materials, heralded by graphene, has rekindled the interest on h-BN [196, 197]. Earlier research involved exfoliated h-BN, since the boron and nitrogen atoms form a 2D honeycomb structure with strong covalent bonds in the plane and weak bonds between different planes [192]. Exfoliation maintains the pristine structure of the material, but thickness control and integration with nanoelectronics are challenging. While studies on exfoliated materials are impactful for fundamental insights, integration and application driven research has focused more on large area growth [198, 199] such as chemical vapor deposition (CVD). This comes with its own cost, which is relative loss in crystallinity through the introduction of defects and grain boundaries due to the substrates and the deposition process. Since nanoscale materials are more sensitive to defects, there is a strong need for accurate characterization of large area 2D materials.

In this work, we investigate thermal conductivity of chemical vapor deposited h-BN films. This is motivated by the tremendous potential of thermal management in next generation nanoelectronics, arising from its very high thermal conductivity and low electrical conductivity. The concept of in-plane heat spreader comes from the observation that the thermal conductivity is only 2 Wm-1K-1 along the c-axis of the h-BN compared to the basal plane value of 390 Wm-1K-1.

Theoretical studies on 2D h-BN indicate reasonable agreement with the bulk values [193]. Unfortunately, very little is known about thermal transport in less than perfect materials systems, such as CVD h-BN. The only experimental studies available in the literature are either pristine exfoliated [200] layers or nanotube materials [201]. These studies show very high thermal conductivity, close to the bulk basal plane value for few atomic layer systems. This is intriguing because typically surface and interface scattering of phonons decrease thermal conductivity as films get thinner, giving rise to the size effect on thermal conductivity. For h-BN, this effect is mitigated probably because of the atomically smooth surface that is expected to be free of dangling bonds as well as its h-BN’s high-energy surface optical phonon modes reducing phonon scattering from the dielectric. These observations hint that even after the less than perfect crystallinity found in large area h-BN layers, the material will still result in high thermal conductivity. Unfortunately, no experimental or theoretical study is available in the literature to validate or refute this hypothesis.

Thermal characterization of ultra-thin films is challenging because of the precise needs for (i) spatial (or temporal for transient techniques) temperature measurement (ii) heat loss through the boundary conditions (substrates and interfaces) and the surrounding medium (iii) length-scale induced variation in other properties such as the specific heat or physics that must be accounted for the metrology models. For example, the transient 3 technique [153] is not feasible for 2D materials from unrealistic frequency control needed to circumvent the thermal penetration problem. The in-plane [160-162] 3technique is not possible with h-BN because insulating specimens must be integrated with heaters, and the influence of the metallic heaters with finite thickness [163] may not be favorable, especially for <100 nm thick specimens. Thermo-reflectance techniques use ultrafast laser pulses to limit the thermal penetration depth to tens of nanometers, thereby allowing accurate measurement on nanoscale thin films on a substrate [164]. However, it measures the thermal diffusivity of the specimen. To obtain thermal conductivity from TDTR, one needs to know the volumetric heat capacity of the specimen. Unfortunately, this value is not known for many thin film or nanoscale materials and assumptions must be made that limit the accuracy of the technique. Furthermore, the experimental setup (laser and optical equipment) and the analysis required to include the interfacial thermal resistance make the TDTR technique non-trivial [166, 167]. Steady state techniques appear to be more suitable class for ultra-thin films because of the simplicity in thermal transport modeling. Nevertheless, the challenges in heating and temperature sensing persist. The very high thermal conductivity of h-BN makes spatial temperature profile measurement difficult the same way as diamond like carbon films. Accounting for the heat losses is another critical issue since removal of the substrate and surrounding medium (freestanding specimens in

less than 10-6 Torr pressure) is not trivial. The low thermal conductivity of air may seem to mitigate the heat loss concern to the surrounding, however the literature has consistently shown that the heat loss coefficient can be up to two orders of magnitude larger at the nanoscale.

3.3.2 Experimental Setup

To study thermal conductivity of CVD grown h-BN films, we employ both steady state and transient techniques that use freestanding specimens transferred on a micro-electro-mechanical heater and non-contact infrared thermometry. The micro-heater is fabricated out of heavily doped silicon-on-insulator wafers with 20 microns thick device layer and complete removal of the buried oxide and the handle silicon layer. Hexagonal boron nitride is grown on Cu foils via a catalytic thermal CVD method utilizing a single ammonia borane (NH3BH3) precursor [198]. For many growth runs, the Cu foils were encapsulated in a Cu enclosure to increase the gas-phase Cu overpressure during the pre-growth anneal and growth processes, which we find to lead to a reduction in the amount of copper loss from the sample surface and an improvement in the starting grain size similar to graphene [202]. The as-grown h-BN films are subsequently detached from the Cu substrate and transferred to arbitrary substrates for characterization or device integration. The transfer process is similar to the previously reported techniques for transfer of CVD grown graphene from Cu [203].

Figure 3.14a shows the characterization device with schematic rendering of the h-BN specimen after the transfer process. Figure 3.14b shows the infrared thermography of the heater and the suspended specimen using a liquid nitrogen-cooled Indium-Antimonide infrared detector. The focal plane array type detector measures the radiance from target objects to calculate the temperature with 0.1 °C resolution. Post processing of the image or video data allows us to perform line (or temporal) scans of the temperature profile. In this study, a 15x objective was used, which provides pixel-to-pixel resolution of 1.66 microns.

3.3.3 Mathematical model for thermal conductivity measurement

The temperature profile in Figure 3.14b clearly shows one dimensional heat flow, perpendicular to the heater lines. Figure 3.14c shows the outline of a rectangular specimen of length L (the distance between two heater lines) and unit width along with the temperature boundary condition of T = Th at x = 0 and x = L. Figure 3.14d shows the energy balance for a small segment of this length. We can write the energy balance equation for a small element of length ∆x located near the specimen edge[185].

푑푇 푑푇 푘퐴 | − 푘퐴 | = ℎ푃∆푥(푇 − 푇∞) (36) 푑푥 푥 푑푥 푥+∆푥

Here, k is thermal conductivity, A and P are cross-sectional area and perimeter, h is convective heat transfer coefficient and T is the ambient temperature. Even though the temperature is not very high, we account for the radiation loss by determining an effective radiation heat transfer coefficient

(hr) and adding it to the convective heat transfer coefficient. For small temperature difference between an object and the ambient (Tobj  Tamb), the following linearization can be performed,

4 4 3 (푇표푏푗 − 푇푎푚푏) ≈ 4푇푎푚푏(푇표푏푗 − 푇푎푚푏) (37)

The total heat transfer coefficient then is obtained as the sum of convective (hc) and radiative (hr) components,

3 ℎ = 휀휎4푇푎푚푏 + ℎ푐 (38)

Where  is the emissivity (0.8 for h-BN from experimental measurement) and  is the Stefan- Boltzmann constant (5.670373×10−8 W m−2 K−4). The general solution of equation 36 is given in terms of the variable  = (T-T∞) and can be written as,

푚푥 −푚푥 휃 = 퐶1푒 + 퐶2푒 ; 푚 = √ℎ푃⁄푘퐴 (39)

The constants C1 and C2 are obtained from the boundary conditions, which are the temperatures at the two edges, T1 and T2. The solution is given by,

푇−푇 [푇 −푇 ⁄푇 −푇 ] sinh 푚퐿+sinh 푚(퐿−푥) ∞ = 2 ∞ 1 ∞ (40) 푇1−푇∞ sinh 푚퐿

Recognizing that both ends of the specimen in this study have the same temperature as the heater

(T1 = T2 = Th), we can calculate the temperature profile and compare that with the experimentally obtained temperature profile. The only unknown parameter is the convective heat transfer coefficient, hc, which can be obtained by equating heat transfer rate at the specimen surface by conduction with that due to convection. This is given by,

휕 −푘 퐴 (푇 − 푇 | = ℎ 퐴(푇 − 푇 ) (41) 푎푖푟 휕푦 푠) 푦=0 푐 푠 ∞

Where, y is the perpendicular direction to the specimen length (y = 0 denotes specimen surface) and Ts is the specimen temperature. The advantage of infrared thermometry is that the thermal boundary layer can be visualized and quantified simultaneously. This allows us to fit the temperature at the thermal boundary layer as,

−푠푦 푇 = 푇∞ + (푇푠 − 푇∞) ∗ 푒 (42)

So that the convective heat transfer coefficient is given by hc = kair*s.

3.3.4 Result and discussion

Figure 3.15a shows how the parameter s is obtained from the measured thermal boundary

-1 -1 profile. Taking kair to be 0.024 Wm K , the convective heat transfer coefficient is measured to be 3475 Wm-2K-1. This value is very high compared to the bulk, but matches well with the microscale values literature and can exactly reproduce thermal profile of silicon as a calibration material with

known thermal conductivity [204]. The correction for the radiation losses is then added to this value and subsequently used in equation (40) to calculate the predicted temperature distribution in the h- BN specimens. Figure 3.15b shows the experimental data juxtaposed with the model data for both 10 nm and 20 nm thick films. The best fit is obtained for thermal conductivity of about k = 100 Wm-1K-1 for both the film thicknesses. To demonstrate the resolution of this one-parameter data fitting technique, model predictions for k = 110 Wm-1K-1 are also shown in Figure 3.15b, which clearly suggests that the measurement error of this steady state technique is less than 10%.

A powerful feature of the infrared microscopy is the ability to provide temporal information as well with a few microseconds resolution. This allows transient thermal characterization, albeit the measurand is thermal diffusivity, and not conductivity. In other words, one needs accurate values of the density () and specific heat (c) to measure the thermal conductivity. The one dimensional transient heat transfer is given by,

푘 휕2푇 ℎ푝 휕푇 − (푇 − 푇 ) = (43) 휌푐 휕푥2 휌푐퐴 ∞ 휕푡

Figure 3.16 shows the steady state spatial as well as the temporal (cooling rate) temperature profile. If we consider the steady state spatial temperature profile, the right hand side of equation

(43) to be zero, and we would expect the ln(T-T) to be a linear function of the specimen length variable x. Figure 3.16a shows this validity of the data for both the 10 nm and 20 nm thicknesses. At the same time, if we turn the heater off and measure the time dependence of the specimen

temperature, the parameter ln(T-T) is expected to a linear function of time as well. Once again, Figure 3.16b shows this validity of the data for both the thicknesses. The slopes of these two plots would then contain information on the thermal diffusivity,  as given by,

푏휌푐 훼 = (44) 푎2

Where, a (= 63500) and b (= 0.1729) are the slopes of Figure 3.16a and 3.16b respectively for the 20 nm thick specimen. For h-BN, the density and specific heat values are 2100 Kg m-3 and 700 J Kg-1 K-1 respectively [205]. These values yield thermal conductivity of 93 and 97 Wm-1K-1 for the 20 nm and 10 nm specimens respectively. Therefore, the transient analysis results fall within the 10% of the steady state analysis (100 Wm-1K-1), which is within the steady state measurement resolution.

Figure 3.16. Combination of (a) spatial and (b) temporal temperature profile allows measurement of the thermal diffusivity

Even though the thermal conductivity obtained in this study is about 100 times higher than the conventional oxide dielectric, it is also much lower than the only other experimental study in the literature on h-BN films, where about 360 Wm-1K-1 was measured for an 11 atomic layer specimen [200]. The authors measured 250 Wm-1K-1 for a 5 atomic layer to suggest that increase in thermal conductivity due to reduction in interlayer phonon scattering [193] as the number of layers decreases may not hold good. It is also suggested that presence of surface contaminants [206, 207] (in our case a polymeric residue of specimen transfer process) can lead to suppression of thermal conductivity. However, the similar values of the thermal conductivity measured in two different thickness suggests that such effect could be pronounced for thinner specimens only. Also,

such low-frequency phonon scattering is important only at lower temperatures. For the temperature involved in this study, Umklapp scattering should dominate. A unique feature of this study is that it involves specimens grown with a large area, continuous and uniform synthesis process that yields microstructure that is very different from the exfoliated structures mentioned above. Figure 3.17 shows a high-resolution TEM image of an h-BN film transferred to SiO2 (Figure 3.17a), which clearly shows that the hBN transitions to a turbostratic structure after the first few layers of growth. Additionally, while the hBN maintains its hexagonal structure at the atomic scale (Figure 3.17b), the domain size decreases with increasing film thickness to the point where a nanocrystalline structure dominates (Figure 3.17c). We propose that these structural evolutions with thickness cause drastic phonon scattering compared to that at the surface. Because the average crystallite size is quite similar for the two thicknesses studied, the thermal conductivity values are also similar and undistinguishable for the experimental resolution.

3.3.5 Conclusion

In conclusion, we performed both steady state and transient analysis on large area CVD grown h-BN thin films to measure thermal conductivity about 100 Wm-1K-1. No apparent difference was observed between 10 nm and 20 nm thick specimens. The measured value is lower than the measurements on exfoliated h-BN or nanotubes in the literature, but still 100 times larger than conventional oxide dielectrics, which is ascribed to the turbostratic structure of the specimen and not due to surface contaminants of film thickness. Since CVD growth is more pertinent to real life implementation of h-BN in 2D electronics, this study highlights the role of microstructural defects on thermal transport that can be useful in future applications.

CHAPTER 4

EFFECT OF MECHANICAL STRAIN ON THERMAL CONDUCTIVITY OF THIN FILM

Content of this chapter are based on the following journal articles:  Alam, M. T., Manoharan, M. P., Haque, M. A., Muratore, C. and Voevodin, A., Influence of Strain on Thermal Conductivity of Silicon Nitride Thin Films, Journal of Micromechanics and Microengineering, Vol. 22, Issue 4, 045001, 2012. Author of this dissertation designed the experiment, performed the thin film and device preparation, experimentation, data analysis and manuscript writing. Mohan Manoharan assisted in experiment design, device preparation, measurement and corresponding manuscript writing. Aman Haque took part in experiment design, data analysis and manuscript writing. Chris Muratore and Andrey Voevodin helped in the manuscript preparation.

 Alam, M. T., Pulavarthy, R. A., Muratore, C. and Haque, M. A., Mechanical Strain Dependence of Thermal Transport in Amorphous Silicon Thin Films", Nanoscale and Microscale Thermophysical Engineering, 19:1, 1-16, 2015. Author of this dissertation designed the experiment, performed the thin film and device preparation, experimentation, data analysis and manuscript writing. Raghu Pulavarthy assisted in measurement, data analysis and corresponding manuscript writing. Aman Haque took part in experiment design, data analysis and manuscript writing. Chris Muratore helped in the manuscript preparation.

4.1 Influence of Strain on Thermal Conductivity of Silicon Nitride Thin Films

A micro-electro-mechanical systems based experimental technique to measure thermal conductivity of freestanding ultra-thin films of amorphous silicon nitride (Si3N4) as a function of mechanical strain is presented here. Using a combination of infrared thermal micrographs and multi-physics simulation, thermal conductivity of 50 nm thick silicon nitride films is measured and

observed that it decrease from 2.7 W/m-K at zero strain to 0.34 W/m-K at about 2.4% tensile strain. It is propose that such strong strain-thermal conductivity coupling is due to strain effects on fracton- phonon interaction that decrease the dominant hopping mode conduction in the amorphous silicon nitride specimens.

4.1.1 Introduction

Multi-domain (electrical, mechanical and thermal, to name a few) coupling is an essential feature of micro and nanoscale devices and systems [208]. The same is true for other applications in micro-electronics [209, 210], opto-electronics [211, 212], flexible-electronics [213, 214] and energy conversion [215, 216]. These devices are commonly fabricated out of thin film materials, which experience mechanical strain during deposition as well as device operation. Mechanical reliability of thin films is therefore as important as their transport (electrical and thermal) properties. While electro-mechanical coupling is commonly exploited in microelectronic and other small scale systems, the thermal domain must also be considered in these applications, whether due to intentional design or unintentional coupling (for example excessive heat generation in chips devices [217]). Thermo-mechanical coupling in thin films is typically studied in terms of temperature effects on mechanical properties [218-220] and not from a thermal transport perspective. The fundamental question whether mechanical strain can influence thermal transport is therefore the core theme for this study.

Here, low pressure chemical vapor deposited silicon nitride (LPCVD Si3N4) thin film is investigated. Silicon nitride is prevalently for isolation, passivation, etch masking as well as structural and optical layers for various micro-electronic, optoelectronic and micro-electro- mechanical systems (MEMS) [221-224]. It also experiences very large residual strain during deposition and exerts similar strains to other thin film materials attached to it, which makes it a suitable candidate for the present study. In fact, the large elastic strain has led researchers to propose silicon nitride substrates to tune the electron mobility in microelectronic devices [225, 226]. Further motivation for this study comes from the observation that the role of mechanical deformation on thermal conductivity has been computationally explored by only a few researchers [37-39, 227, 228] and experimental efforts are appearing in the literature only very recently [148, 229, 230].

A brief review of the state of the art in thermal conductivity of silicon nitride is given below. Mastrangelo et al. [231] measured thermal conductivity of microns thick silicon nitride films to be around 3.2W/m-K. Zhang & Grigoropuolos [232] observed anomalous thickness

dependence and suggested that microstructural defects may strongly influence thermal conductivity. Jain & Goodson [177] measured in-plane thermal conductivity of 1.5 micron thick specimens to be about 5 W/m-K. At the nanoscale, Sultan et al. [233] 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 [234] observed stronger temperature effects thermal conductivity varying from 0.07 to 4 W/m-K at a temperature range of 3 -300 K. The cross-plane thermal conductivity measured by Lee & Cahill [159] and Shin et al. [235] for less than 100 nm thickness were in the range of 0.4-0.7 W/m-K, showing very strong pseudo-size effects which were ascribed to the interfacial thermal resistance. Stojanovich et al. [236] measured thermal conductivity of 180 nm thick freestanding specimens to be about 2.1 W/m-K. Bai et al. [237] measured thermal conductivity of stoichiometric silicon nitride to be about 1.2-2.0 W/m-K for thicknesses 37 to 200 nm thick films. It is very important to note that none of the above studies measure thermal conductivity as a function of mechanical strain. Even though the specimens are typically freestanding, the mechanical boundary conditions result in about 0.2-0.3% residual strain depending on the silicon: nitrogen ratio.

4.1.2 Device design and fabrication

Silicon nitride is a very brittle material with unusually large tensile residual stress, which makes its thermo-physical characterization challenging. Common approaches are to synthesize low stress, silicon rich (SiNx, x = 1-1.1) nitride or to study the specimen on a rigid substrate. Because the interfacial thermal resistance is challenging to measure and plays a significant role in nanoscale experiments, studies on freestanding specimens are desirable. Characterization and control of the amount of stress or strain in ultra-thin specimens is also challenging. To obtain specimens with different values of strain, one needs to vary the deposition parameters from wafer to wafer, which is cumbersome and changes the composition and microstructure of the specimen. This issue is addressed with the concept of ‘self-actuation’ by exploiting the tensile residual stress in silicon nitride. Here, both actuator and the specimen are designed in the same film plane but cross-sectional area of the actuator portion is increased compared to the specimen. This is shown in Figure 4.1a, where three actuator strips are patterned in series with the specimen. Before release from the substrate, both actuator and specimen experience the same tensile strain (residual strain after deposition). However, removal of the substrate also removes the uniform strain level and force distribution in the freestanding actuator and specimen is re-organized according to their respective cross-sectional areas. Because of its larger cross-sectional area, the three actuator strips (with length

La and cross sectional area Aa) will apply a tensile force on the specimen (with length Ls and cross

sectional area As). The amount of this force and associated strain can be controlled by the actuator design utilizing the force equilibrium condition,

퐹 = 푘푎훿푎 = 푘푠훿푠 (1)

Where, k is stiffness,  is net displacement and the subscripts a and s denote the actuator and specimen respectively. The equilibrium equation thus can be written as a function of the length (L), cross-sectional area (A) and Young’s modulus (E) of the actuator and specimen,

퐸푎퐴푎 퐸푠퐴푠 푛 훿푎 = 훿푠 (2) 퐿푎 퐿푠 where n is the number of actuator strips. Larger value of n implies higher value of stress and strain on the specimen. However, experimental results deviate more than 25% from the model for n > 5 because of the compliance of the outer actuator strips compared to the inner ones. It is notable that the total displacement in the fabricated structure, , is the sum of the actuator and specimen displacement (훿푎 + 훿푠 = 훿). This displacement can be measured by fracturing the specimen after the experiment and then measuring the gap between the fractured surfaces. Therefore, irrespective of the overestimation (if at all) of the model, the resolution of strain measurement is governed by the scanning electron microscope magnification. Using the force equilibrium equation, the specimen displacement can be related with the total displacement as follows,

퐸푠퐴푠퐿푎 훿푠 [1 + ] = 훿 (3) 푛퐸푎퐴푎퐿푠

The strain in the specimen, s, is then given by,

훿푠 훿푛퐸푎퐴푎 휀푠 = = (4) 퐿푠 (푛퐸푎퐴푎퐿푠+퐸푠퐴푠퐿푎)

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

훿푛퐴푎 휀푠 = (5) (푛퐴푎퐿푠+퐴푠퐿푎)

The device fabrication process is schematically described in Figure 4.2. The process starts with deposition of 50 nm thick freestanding LPCVD Si3N4 using ammonia and dichlorosilane at 820 ºC (Figure 4.2a). The residual stress in the deposited film is about 1.2 GPa. The device design showed in Figure 4.1a is then patterned on the nitride layer using lithography, after which the exposed nitride is etched with reactive ion etching using CF4/O2 plasma. This is shown in Figure 4.2b. Using front side alignment, a negative lithography is performed to pattern a line perpendicular to the silicon nitride line and 175 nm thick aluminum film is evaporated to complete the lift-off process. Figure 4.2c shows the aluminum and nitride lines patterned on the silicon wafer, which are still attached to the substrate. The next step is to release the two lines using isotropic XeF2 etching. Figure 4.2d shows the freestanding nitride specimen and the aluminum heater line schematically, for which a scanning electron micrograph is shown in Figure 4.1b.

Figure 4.2. Fabrication processing for the device integrating the actuator, specimen and heater for thermal conductivity characterization.

4.1.3 Experimental Procedure and Analysis

To measure thermal conductivity of the freestanding nitride specimens, DC current through the aluminum heaters is passed. Since the heater line is also freestanding, the 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 milli-amps 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 4.1b 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. Calculation of the thermal conductivity requires the heat flux in the specimen, which can be approximated from the power supply to the heater or more accurately by performing finite element simulation [236]. Commercially available software COMSOL Multiphysics™ is used to carry out the finite element solution of the described problem. Among the various application modes, electro-thermal application mode is used for the 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 (though the air to the etched substrate below the specimen) were included in the model. Tables 4.1

and 4.2 describe primary input parameters for the model. The physical properties are taken for bulk scale since silicon nitride is an amorphous material and aluminum film is too thick to show any size effect.

Table 4.1. Multi-physics modules and input parameters.

Application mode Properties Silicon nitride Aluminum Resistivity (Ω-m) 1.72e12 3.75e-8 Conductive media Temperature coefficient 0.0038 0.003 DC mode of resistance (1/K) Reference temp (k) 300 300 Thermal conductivity Varied to match 237 (W/m-K) measured temperature Heat transfer mode profile Density (kg/m3) 3100 2700

Heat capacity, Cp (J/kg K) 700 904 Young’s modulus (Pa) 250e9 70e9 Poisson’s ratio 0.23 0.35 Solid mechanics Thermal expansion 2.3e-6 23.1e-6 mode coefficient (1/K) Density (kg/m3) 3100 2700

Table 4.2. Geometry parameters for the aluminum and silicon nitride structures.

Material Length (micron) Width (micron) Thickness (micron) Aluminum 35 3 0.175 Silicon nitride 100 5 0.050

Figure 4.3 shows the finite element model, where the four boundaries are numbered for the ease of identification. The conductive media DC mode solves the following equation,

퐞 −∇ ∙ (σ∇푉 − 퐉 ) = 푄푗 (6)

Where,  is the electrical conductivity, V is the potential, Je is the external current density vector and Qj is the current source. This mode assumes that the model has symmetry and the electric potential varies only in the X and Y direction and is constant in Z (film thickness) direction.

Figure 4.3. Multi-physics simulation model for the device showing temperature profile at zero strain. Infrared microscopy shows the large drop in thermal conductivity at 2.4% strain (inset).

For Joule heating, the electrical conductivity is temperature dependent and maintains the following relationship,

1 휎 = (7) 휌표(1+훼(푇−푇표))

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 4.4. All other boundaries of aluminum and silicon nitride are chosen to be electrically insulated (n∙J=0).

The heat transfer mode solves the following governing equation:

∇ ∙ (−푘∇푇) = 푄 + 푞푠푇 (8)

Where, k is the thermal conductivity, ∇T is the temperature difference, 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, heat flux boundary condition is applied through the following equation,

−퐧 ∙ 퐪 = 푞표 + ℎ(푇0 − 푇) (9)

where, n is the outward normal vector, 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. In this study To is taken to be 300 K. Because the experiments were conducted at lower temperatures, radiation was neglected. At the same time, heat loss through air (in this case, from the bottom surface of the nitride specimen to the device floor) is known to be dominant in the literature [135], which was incorporated through an ‘effective convective heat transfer coefficient’. A sensitivity

2 analysis of the multiphysics model yielded the value of hair = 500 W/m K for the etch depth of about 15 microns in the present study, for which the temperature profiles in the specimen and the heater were in very close agreement for all input current values. A simple scaling analysis may

2 suggest higher values (hair = 1666 W/m K), but is unable to reproduce the actual temperature profile in the specimen.

The solid mechanics mode employs the governing equation,

휎 = 퐸휀 (10)

Where, σ is the stress, E is the Young’s modulus and ε is the net strain. The net strain includes applied elastic strain, thermal strain and initial strain. Boundaries 1-4 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 experimental temperature profile along the aluminum heater line is compared with that obtained from simulation for different values of input current. Figure 4.4 shows the excellent agreement between the actual and simulated heater temperature profile. It also shows the heat flux value from the simulation. Since the governing equations of the finite element model do not have any strain-thermal conductivity coupling, first the temperature profile along the specimen length for various levels of mechanical strain is measured. To extract the thermal conductivity of the specimen for each strain values, the heat flow is simulated for the calculated

heat flux values for various trial values of thermal conductivity until the simulated temperature profile closely matched that obtained from thermal microscopy. Figure 4.5 shows this procedure for two different values of strain.

Figure 4.4. Comparison of the experimental and simulation results on the heater temperature profile as a function of input current.

Specimen temperature,

Figure 4.5. Comparison of experimental and simulation results on the temperature profile of the silicon nitride specimens with fitted values of thermal conductivity.

4.1.4 Result and discussion

Figure 4.6 shows the experimental results for room temperature thermal conductivity of 50 nm thick freestanding amorphous silicon nitride as a function of mechanical strain up to 2.4%. The fracture strain of silicon nitride can be as high as 3% [238, 239]. Also shown (in letter form) are the data taken from the literature for comparable specimen thicknesses. The literature data is shown at about 0.3% strain because even though the specimens are freestanding, their clamped edge boundary conditions do not relieve the residual strain. These studies involve SiNx (also known as low stress or hydrogen rich silicon nitride) with x varying from 1 to 1.1, for which the residual strain reported is about 0.2-0.3% [240]. When interpolated between 0 and 0.6% strain, present results are in excellent agreement with the literature except two instances (studies D and E). These two studies involved specimens on substrate, for which thermal conductivity is expected to show a pseudo size effect unless corrected for thermal contact resistance. This is because such cross-plane measurements involve nanoscale length of heat flow path (L = specimen thickness) and two interfacial thermal resistances (th) [241],

1 1 퐴휌 = + 푡ℎ (11) 휅(푇,퐿) 휅(푇,퐿→∞) 퐿

Where, A is the cross-section of the specimen. Lee and Cahill [159] explained their observed size effect with the above argument, while Bai et al. [237] corrected their data after developing a technique to measure the interfacial thermal resistance.

Figure 4.6. Thermal conductivity of 50 nm thick Si3N4 films as a function of mechanical strain. The letters (A-E) corresponding to 0.3% strain represent data from the literature. The symbol () denote cross-plane thermal conductivity data.

Two concerns related to the experimental technique deserve further scrutiny. The first one 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 current

-12 2 -8 experiments in equation 11. For heater-specimen interfacial area A = 25x10 m , th = 2~3x10 m2-K/W [159, 237] 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 a 125 nm thick aluminum film on silicon oxide, such strain effects have been shown to be pronounced [148], 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,

(−휈휎 +휎 ) 휀 = 휀 = 푥 푦 + 휀 (12) 퐴푙 푦 퐸 푟푒푠푖푑푢푎푙

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 specimens of this study and is bi-axial and tensile in nature. The actuation method applies uniaxial tension in the nitride specimens with stress (x) about 6 GPa for about 2.4% strain (the fracture stress of silicon nitride varies from 8-10 GPa). For these values, the net strain in the aluminum heater considering the Poisson effect is -0.5%. In other words, there is no appreciable strain developed in the aluminum heater for the actuated nitride specimens. This is also verified by measurements of electrical resistance of the aluminum heater before and after the release from substrate, which did not show any appreciable change in the resistance due to the loading of the heater line. 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 [148].

To explain the observed influence of strain on thermal conductivity, it is noted that commonly cited size effects for low dimensional materials [38, 242] and hetero-structures [243, 244] cannot be used because of the amorphous microstructure of the specimens. The phonon mean free path of amorphous materials is on the same order of the structural disorder [245], rendering thermal conductivity size independent. 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. In other words, heat transfer in amorphous solids is a random walk of energy between localized oscillators of varying sizes and frequencies. The Cahill [246] model for thermal conductivity of amorphous materials integrates the specific heat (C), phonon velocity (v) and the mean free path (l) over the entire range of frequencies,

1 ∞ 푑퐶 휅 = ∫ 푣(휔)푙(휔)푑휔 (13) 푑푖푓푓 3 0 푑휔

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 [247]. While fractons alone in a harmonic system cannot transfer heat, it has been shown in the literature that anharmonicity induces interaction between phonons and fractons that allows transfer of energy from a localized excitation to other. Such fraction-phonon interaction resembles spatial overlapping of the localized vibrational modes [248]. Without such overlap, amorphous materials would exhibit zero thermal conductivity. At the same time, the overlap must be minimal because amorphous materials are known to exhibit very low thermal conductivity. Therefore, it is proposed that overlap is extremely

marginal and sensitive to tensile deformation. This is supported by current experimental observation of about one order of magnitude reduction in thermal conductivity at about 2.4% strain. On the other hand, compressive deformation would only increase such overlap, which will eliminate the influence of strain, unless the stress is so large that the elastic constants are changed. Interestingly, this conjecture is supported by both theory and recent experiments [230].

While the influence of strain on thermal conductivity is not a size effect, it is suggested that thermal conductivity depends on the vibrational density of states, which in turn depends on atomic bond energy, distance etc. parameters. Unlike crystalline materials, where all the modes are nonlocalized (diffusive), amorphous materials show the spectra of both localized (fraction) and diffusive (phonon) modes [249]. Therefore, the thermal conductivity cam be expressed as,

휅(푇) = 휅푑푖푓푓(푇) + 휅ℎ표푝(푇) (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, depend on the lack of long-range order and atomic bond energy. Crystalline or polycrystalline materials exemplify diffusion dominated thermal transport, for which very large strain (~10% [38]) or stress (~ 20 GPa [250]) 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, which is very close to the cut-off (below which localization effect is too strong to transport heat) value of 72 meV [251]. It is hypothesize 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, it is expected that the peak frequency to be higher than amorphous silicon because the Si-N bond energy (78.32 kcal/mol) is much higher than Si-Si bond (53.31 kcal/mol) [252]. 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. Currently, atomistic simulations are in progress to verify this hypothesis.

4.1.5 Conclusion

In this study, the concept of tuning thermal conductivity of nanoscale solids using externally applied mechanical strain is investigated. An experimental technique developed to apply

controllable strain on freestanding amorphous silicon nitride specimens and measure their thermal conductivity. The technique demonstrated on 50 nm thick specimens at up to 2.4% strain. It is commonly held that amorphous solids already show minimum values of thermal conductivity strain at zero strain and hence are expected to show the weakest strain-transport coupling. To the contrary, observed experimental results show very strong influence of thermal conductivity, which decreased from 2.7 to 0.34 W/m-K under 2.4% strain. It is proposed that thermal conductivity in amorphous solids is a strong function of vibration localization, which increases with tensile strain; whereas, crystalline solids do not show such strong coupling because of their non-localized vibrational modes.

4.2 Mechanical Strain Dependence of Thermal Transport in Amorphous Silicon Thin Films

Recent computational studies predict mechanical strain–induced changes in thermal transport, which is yet to be validated by experimental data. In this article, we present experimental evidence of an increase in thermal conductivity of nominally 200-nm-thick freestanding amorphous silicon thin films under externally applied tensile loading. Using a combination of nanomechanical testing and infrared microscopy, we show that 2.5% tensile strain can increase thermal conductivity from 1 to 2.4 W/m-K. We propose that such an increase in thermal conductivity might be due to strain-induced changes in microstructure and/or carrier density. Microstructural and optical reflectivity characterization through Raman and infrared spectroscopy are presented to investigate this hypothesis.

4.2.1 Introduction

Amorphous silicon (a-Si) is a high impact technological material with major applications in liquid crystal displays, flexible electronics, image sensing and photovoltaic conversion [253] . It enjoys all the major processing related expertise and semiconducting properties related to its crystalline counterpart to enable the new technology for large-area or ‘macro electronics’ at lower costs and benign processing conditions. A major difference is the globally disordered atomic structure arising from the low temperature growth so that the silicon atoms do not have the mobility to assume the lowest-energy (crystalline) configurations. Hybridization of the 3s2 and 3p2 levels results in four valence electrons in degenerate 3sp3 levels with tetrahedral symmetry. The Si-Si bond forms because electron energy in bonding state is lower and the anti-bonding state is empty. Therefore, there is no periodicity, only short-range order exists. The major defect in a-Si is the dangling bond. Since all carriers are trapped by the disorder, a-Si shows electron mobility and thermal conductivity about two orders of magnitude lower that its crystalline counterpart [254- 256]. Even though the presence of hydrogen minimizes the dangling bonds, external stimuli such as light, heat and mechanical strain strongly influence electron transport properties. This serves as the foundation of this study where we argue that if external stimuli, such as light, heat or strain, can influence band gap or electron mobility, they can also influence thermal transport.

Thermal transport in a-Si thin films has received considerable attention in the last few decades, with the advent of the material as a low cost solution to technological problems typical to solar cells [257, 258], displays [259], sensors and thermoelectric applications [260, 261]. Due to its

disordered nature, thermal transport in amorphous material is challenging to study theoretically and still not described fully. In addition, experimental measurement of thermal properties is regarded as a difficult task because a-Si is available only in thin film form. So far, a number of experimental [254, 256, 262-265] and theoretical [266-271] studies reported thermal conductivity of amorphous film, which is significantly low compared to its crystalline counterpart. Zink et al. [262] used electron beam evaporation technique to deposit the a-Si film and measured thermal conductivity by membrane based micro-calorimeters at 5-300K temperature. Room temperature thermal conductivity is reported as 2.2 and 1.5 W/m-K for 130 nm and 277nm thick films respectively. Moon et al. [256] measured thermal conductivity by optical transmission technique which yield a value of 2.2 W/m-K for 200nm thick low pressure chemical vapor deposition (LPCVD) films. It also reports that thermal conductivity reduces to 1.5 W/m-K as thickness reduces to 97 and 53 nm. Yang et al. [265] reported room temperature thermal conductivity value as 2 W/m-K for 200nm thick films. Molecular dynamics and theoretical models also predicted a room temperature thermal conductivity value between 1-2 W/m-K for a-Si thin film [267-270]. In general, these data conform well to the entire class of amorphous materials – for which the thermal conductivity is roughly about 1 W/m-K.

In this study, we investigate role of mechanical strain on thermal conductivity of sputter deposited 200nm thick freestanding (to eliminate any substrate effects) a-Si thin films. Mechanical strain can be used favorably to improve material properties for the thin film applications. It has been found in 1990’s that that strained silicon in metal-oxide-semiconductor field-effect transistors [272] exhibited a tremendous increase in electron mobility. However, there is not a single study in the literature exploring the effect of strain on thermal properties, which motivated us to investigate thermo-mechanical coupling in a-Si thin films. This is probably because classical physics does not predict any strain-thermal conductivity coupling, particularly for structurally disordered materials. However, amorphous silicon is more para-crystalline (local cubic ordering at the 10 to 20 angstrom length scale) than amorphous [273], which lends to the concept that external strain energy can result in microstructural changes, which may also influence other intrinsic properties. Although temperature effect on the mechanical properties is studied rigorously for thin films [218, 274], theoretical and experimental studies on thermal transport and strain coupling are appearing only recently. It is important to note that only in cases of ultra-thin crystalline materials, existing studies predict weak influence inform of decrease in thermal conductivity under tensile strain [37, 275, 276]. In this study, we present a steady state and direct thermal conductivity measurement technique based on temperature mapping of the sample under an Infrared Microscope. We

successfully applied a similar technique in our earlier work to estimate thermal conductivity of low dielectric constant oxide [277] and heat transfer coefficient of air in the vicinity of thin films [204].

4.2.2 Experimental Setup

The experimental setup consists of (i) freestanding a-Si thin films clamped at both ends on a micro-tensile testing device, (ii) a 2 mm × 2 mm resistance heater element mounted on the testing device at one end of the specimen to setup a spatial temperature gradient and (iii) an infra-red microscope to quantify the specimen temperature profile as well as the thermal boundary layer around it. Characterization of the thermal boundary layer allows us to accurately measure the heat loss to the ambient. Therefore, the only unknown parameter in an energy balance model of one- dimensional heat transfer remains to be the thermal conductivity of the specimen. This allows us to fit the experimental spatial temperature profile with an energy balance model to extract the thermal conductivity. Details of these components are given below.

Figure 4.7a shows the micro tensile testing device, which has the footprint 10 mm × 6 mm × 0.5 mm. The device is nanofabricated using a process sequence such that at the end of fabrication processing, freestanding specimens are automatically integrated with the device. This eliminates the task of manual specimen gripping or aligning with the test structure. The operation of the device is described schematically in Figure 4.7b, where the specimen is suspended between a fixed end and a moving end with supporting guide beam structures. The guide beams and the u-springs provide structural integrity between fixed and movable end of the micro device and to eliminate any displacement misalignment. Thus applied displacement is aligned to the specimen axis with lithographic resolution [278]. Scanning electron microscope (SEM) image of two freestanding a- Si thin films is shown in Figure 4.7(c). Actuation of the testing device is provided by a piezoelectric stack with a maximum driving voltage of 150V and maximum displacement of 17 micron. One end of the piezoelectric actuator is connected to a big metal block for stability and other side is connected to a 90° metal angle, as shown in the Figure 4.7(a, d). Then fixed end of the micro device is attached to the top surface of the metal block while the movable end is attached to the metal angle. Displacement of the piezoelectric actuator with applied voltage is calibrated by measuring distances from SEM images.

Device fabrication process starts with a silicon wafer, coated with thermally grown 1 micron thick silicon dioxide layer. Boron doped amorphous silicon is sputtered on the oxide coated side of the wafer at room temperature and 5x10-7 Torr pressure. The specimen is patterned on the amorphous silicon by photolithography and SF6 gas based dry etching of silicon. The tensile specimens are 110 microns long, 5 microns wide and 200 nm thick. In the next step, backside of the wafer is patterned with a 10 micron thick photoresist. From the backside of the wafer, bulk silicon is etched anisotropically by deep reactive ion etching (DRIE) which will provide the tensile testing structure for the thin film. Finally, freestanding sample is obtained by the removal of underneath oxide with vapor hydrofluoric (HF) acid etch. A step-by-step fabrication process is schematically shown in Figure 4.8.

Figure 4.8. Fabrication processing steps for freestanding amorphous silicon on a silicon wafer.

4.2.3 Thermal Conductivity Measurement

We used a technique based on temperature mapping of the specimen under an Infrared (IR) Microscope (Infrascope II from Quantum Focus) to estimate the thermal conductivity of the specimen as well as natural convection heat transfer coefficient of air. The spatial and temperature resolutions of this infrared microscope are 2 microns and 0.1 degree K respectively. Commercially available resistance temperature detector (RTD) is used as a heating element for this study. A typical experiment starts with the placement RTD heater on the device to the vicinity of freestanding specimen by using a micro manipulator, schematically shown in Figure 4.9a. As current is passed through the RTD, it heats up the fixed end of the device as well as one end of the specimen. Due to the low thermal conductivity of amorphous silicon, a temperature gradient can be found in the freestanding part of the specimen. Figure 4.9b shows an IR micrograph of the temperature distribution micrograph of specimen for input current of 70 mA to the RTD. For any small segment of the specimen, the heat lost through convection can balance the incoming heat flux through conduction. This is schematically shown in Figure 4.9c. The IR microscope data is very sensitive to the flatness of the specimen. Hence, any slack in the specimen can be detected through a flat temperature profile. This can be corrected by actuation of the piezo to bring the specimen in taut condition before beginning the experiment.

A mathematical model for thermal conductivity measurement of the specimen can be found from the heat transfer model of a simple rectangular fin-type structure [141]. The energy conservation principle is applied to a specimen element of length ∆x and width w. For a surface area of S and cross sectional area A, heat incoming to the control volume by conduction is balanced by heat leaving in the form of conduction, convection and radiation. This is schematically shown in Figure 4.9(c) and can be expressed as,

푑푇 푑푇 4 4 −퐾퐴 | + 퐾퐴 | − ℎ ∗ 푑푆 ∗ (푇 − 푇∞) − 휀 ∗ 휎 ∗ 푑푆 ∗ (푇 − 푇∞ ) = 0 (15) 푑푥 푥 푑푥 푥+∆푥

Here, K is the thermal conductivity of the specimen, T is the ambient temperature, h is convection heat transfer coefficient, ε is emissivity and σ is Stefan – Boltzmann constant.

For small temperature differences, radiation loss can be linearized and equation (15) can be approximated as,

푑푇 푑푇 3 −퐾퐴 | + 퐾퐴 | − (ℎ + 휀 ∗ 휎 ∗ 4푇∞ ) ∗ 푑푆 ∗ (푇 − 푇∞) = 0 (16) 푑푥 푥 푑푥 푥+∆푥

The general solution of equation 16 is given in terms of the variable 휃 = (푇 − 푇∞) and can be written as

푚푥 −푚푥 휃 = 퐶1푒 + 퐶2푒 (17)

The constants C1 and C2 can be found from boundary conditions, which are the temperatures at the two edges T1 and T2. The solution is given by

푇−푇 [(푇 −푇 )⁄(푇 −푇 )] sinh 푚퐿+sinh 푚(퐿−푥) ∞ = 2 ∞ 1 ∞ (18) 푇1−푇∞ sinh 푚퐿

푃 Where, 푚2 = (ℎ + 휀 ∗ 휎 ∗ 4푇 3) ∗ and 휃 = (푇 − 푇 ). This model is particularly suitable for ∞ 퐾퐴 ∞ the present experimental configuration from IR images.

Next, using the IR microscopy data, the temperature along the specimen length, T(x), and the boundary condition temperatures, T1 and T2,can be accurately measured as shown by the representative temperature profile in Figure 4.9(d). Equation 18 therefore allows us to predict the spatial temperature profile of the specimen and then compare that to the experimentally measured T(x). However, to obtain the modeled T(x), accurate measurement of natural convective heat transfer coefficient is required. This can be accomplished easily from the measurement of temperature distribution of air around a heated surface [204]. Same IR micrograph can be used, except a line scale is made perpendicular to the specimen. This gives the profile of the thermal boundary layer around the specimen. Detail mathematical model for calculating natural convective heat transfer coefficient can be found in our previous work [204].

Exponential distribution of temperature in space can be given by

푇−푇 ln ∞ = 푠 ∗ 푦 (19) 푇푤−푇∞

Where, s is a constant determined from the plot of logarithm of temperature difference ratio against distance (y) from the specimen surface at temperature Tw. Then local natural convective heat

transfer coefficient of air (h) can found from the product of thermal conductivity of air, kair and s [279].

ℎ = 푘푎푖푟 ∗ 푠 (20)

The obtained convective heat transfer coefficient can be used in Equation (20) to model the spatial temperature profile of the specimens.

4.2.4 Experimental result and analysis

The first step in this study was to calibrate the experimental technique with 200 nm thick freestanding thermally grown silicon oxide specimens, for which thermal conductivity of about 1.2 W/m-K is very well established in the literature [191]. To obtain the thermal conductivity of these specimens, we evaluated the value of constant s and h first (by Equations 19 and 20), as discussed in the previous section. Figure 4.10(a) shows how the value of constant s is determined from slope of the straight-line fit of the data. For our experiments, the local natural convection heat transfer coefficient (h) was measured to be about 115 W/m2K from Equation 20, assuming thermal conductivity of air to be 0.024 W/m-K. This value was measured for each of the specimens studied and was found to be within 5% variation only. Equation 18 can be used to model the temperature profile along the specimen. Since the convective heat transfer coefficient is accurately characterized, only the thermal conductivity remains to be the unknown parameter in the model. In other words, the experimentally obtained spatial temperature distribution in the specimen (in the a- a′ direction) can be compared with model predictions for various trial values of thermal conductivity to obtain the best fit. Figure 4.10(b) shows such best fit for thermal oxide (calibration) specimens, yielding thermal conductivity of 1.2 W/m-K for calibration purpose. Figure 4.10(b) also shows representative experimental results for amorphous silicon specimen under no externally applied strain. The thermal conductivity was found to be about 1.0 W/m-K, which is consistent with the previously reported minimum thermal conductivity for amorphous thin films [280].

After the completion of thermal conductivity measurement at zero strain, the amorphous silicon specimens are loaded in tension by applying voltage in the piezoelectric actuator with an increment of 5V. Figure 4.11a shows the strain resolution possible through the calibration data for the piezo actuator. Temperature distribution in the specimen at different strain values are the recorded until the sample is fractured. The specimen fracture was inherently brittle in nature with no apparent sign of plastic deformation. Figures 4.11(b-d) show the experimental data and model predictions for various levels of mechanical strain. Due to the experimental challenges, it was not possible to keep the hot end temperature of all the specimens exactly the same. Nevertheless, the difference in the temperature is accounted for in the model. In addition, the thermal conductivity of the specimens does not show temperature dependence at these small temperature deviations, which is obvious from the remarkable agreement between the experimental and model (temperature independent thermal conductivity) data.

Figure 4.11. (a). Calibration data for the actuator. Model prediction and experimental values of specimen temperature profile for (b) 1.09%, (c) 1.81% and (d) 2.45% strain in the specimen.

We carried out the experiment for 3 different samples from same fabrication batch and the results are summarized in the Figure 4.12. It shows an increasing trend of thermal conductivity with applied mechanical strain. Thermal conductivity does not change initially and start to increase after about 0.7% strain and gradually increase to 2.5 W/m-K for 2.5% applied strain. For calibration, we also performed similar experiment on thermal oxide, which is known to exhibit no such strain dependence. This data is also shown in Figure 4.12. In literature, we could not find such experimental study on amorphous silicon to compare our result. However, few experimental [276, 281] and molecular dynamic [39, 228, 244, 275, 282-284] studies are available for other thin film material and nano structures. In our previous work on amorphous Si3N4 thin film [276], we observed a decrease in thermal conductivity with applied tensile strain. Gan et al. [281] used a highly doped single crystal silicon atomic force microscope tip to measure both strain and thermal conductivity. They observed an increase in thermal conductivity with compressive strain. Li et al. [275] conducted a comprehensive equilibrium molecular dynamics (EMD) study on bulk material

and various nano structures including silicon thin film. Thermal conductivity of 2-4nm silicon thin films are found to decreasing continuously as loading changes from compressive to tensile strain. It has been found that tensile strain lowers both group velocities of the acoustic phonons and specific heat, which in turn, reduces the thermal conductivity.

Figure 4.12. Thermal conductivity of a-Si specimens as a function of externally applied mechanical strain.

4.2.5 Experimental uncertainty analysis

The mathematical model of thermal conductivity is influenced by the temperature (T), heat transfer coefficient (h), and distances (x and y) along and across the specimen that are evaluated using the experimental measurements. To ascertain the sensitivity of thermal conductivity to these measurands, we observe the following expressions:

Δℎ Δ푥 2∆푇 1 푇−푇∞ = + 푇−푇∞ [1 − ] (21) ℎ 푥 ln( ) (푇−푇∞) 푇푤−푇∞ 푇푤−푇∞

∆푇 [ 푇−푇 −푚∆푥 tanh(푚(퐿−푥))] ( ∞ ) ∆푚 = 푇푤−푇∞ (22) [(퐿−푥) tanh(푚(퐿−푥))+tanh(푚퐿)]

∆푘 2∆푚 ∆ℎ = + (23) 푘 푚 ℎ

It should be noted that the spatial resolution of the temperature measurement is dependent on the output of the IR microscope, which is a pixel-by-pixel temperature map. The specimen length and width were measured with an SEM, with <5% error. Because the specimen material is brittle, there is no appreciable change in cross-sectional area. Completely elastic (such as Poisson’s ratio) effects may induce only a minor change in the perimeter and cross-sectional area, because the tensile strain itself is very small. The corresponding uncertainty in the thermal conductivity is observed to vary between 9.5 and 11.5 % according to the chosen length uncertainty. Figure 4.13a shows the dependence on relative error in length at a specimen temperature of 50° C. It is verified that it is not highly sensitive to the temperature of the sample specimen. Figure 4.13b shows the dependence of thermal conductivity on temperature uncertainty, though the resolution of the microscope can be taken as an approximate value for estimation. The uncertainty in thermal conductivity is found to lie in the range of 7.5–11.5% for temperature error ΔT/T in the range of 0.05–0.1.

Figure 4.13. (a) Uncertainty in the thermal conductivity with (a) relative error in length at T = 50° C and (b) temperature measurement

4.2.6 Discussion

The experimental results summarized in Figure 4.12 cannot be explained by classical theories of thermal transport. The phonon mean free path of amorphous materials is on the same order of the structural disorder [245], rendering thermal conductivity size independent. Heat transfer in amorphous solids is a random walk of energy between localized oscillators of varying sizes and frequencies. The Cahill [246] model for diffusive transport integrates the specific heat, phonon velocity and the mean free path over the entire range of frequencies. Another perspective

is hopping mode transport through highly localized vibrational modes (fractons) [247]. It is also proposed that anharmonicity induces interaction between phonons and fractons that allows transfer of energy from a localized excitation to other. These concepts have been upheld in the a-Si literature for decades until new insights emerged on the major role of minute fraction of propagating waves. Very recent theory and experiments show that only a very small population of phonons with mean free path on the order of a micron and wavelength much longer than the expected thermal wavelengths carry up to 50% of the heat in amorphous materials (silicon [270] and silicon nitride [285]) Si-N at room temperature. Mechanical strain is known to influence the phonon density states in materials [244, 286] but tensile strain is expected to reduce and not increase the thermal conductivity. This suggests that a straightforward relationship between strain and phonon density of states is not able to explain the experimental results. While a comprehensive experiment- modeling research is needed to gain insight in this anomalous phenomenon, we propose two possible mechanisms.

In the strain induced microstructural change hypothesis, the increase of thermal conductivity is ascribed to stress assisted grain growth or phase transformation, which is shown to be feasible in the literature [287]. A moderate to change in thermal conductivity can take place if the grain size is increased [288]. Therefore, a jump from 1 to 2.5 W/m-K as observed in this study is feasible if the amorphous structure can be slightly modified to even nanocrystalline domain. We observed similar phase transformation [289] earlier, and this proposition is bolstered by the recent finding that amorphous silicon is truly para-crystalline (short or medium range order only) with structures containing local cubic ordering at the 10 to 20 angstrom length scale [273]. This findings helps explain the anomalously high value (6 W/m-K) of thermal conductivity even without any application of mechanical strain [265]. Interestingly, the magnitude, temperature, and frequency dependence of the paracrystalline a-Si may resemble the behavior of crystalline semiconductor alloys, even though Raman spectra do not show any distinguishable features compared to the amorphous ones [290]. Certain polymers also show such short or medium range crystallinity, which can be moderated with the externally applied mechanical strain. This has been shown to increase thermal conductivity, albeit at very high strain [229]. To explore any such strain induced change in crystallinity; we performed the same tensile testing under a confocal Raman spectroscope with 488nm wavelength excitation laser. Intensity of film at 1.1% strain is compared with zero strain data in Figure 4.14. From the spectrum for zero strain we can identify four regions, four corresponding phonon bands: transverse optical (TO) with a peak around 460 cm-1, longitudinal optical (LO) around 370 cm-1, longitudina1 acoustic (LA) with a peak around 290 cm-1 and

transverse acoustic (TA) with a peak around 150 cm-1. For 1.1% strained sample, intensity of the peaks decreases by a small amount and peak positions are found to shift to the higher frequencies. Such change in peak intensity can be attributed to the change in structural disorder of the amorphous matrix of the film [291, 292]. In the literature, it has been found that tensile strain in ultrathin films can cause amorphous to nano-crystalline transformation at room temperature [290]. Similar stress assisted grain growth at room temperature is reported for nickel and platinum thin films as well [122, 293]. Tensile strain in our amorphous silicon film might cause some structural change of the film, which is responsible for thermal conductivity increase. The Raman peak shift is, as shown in the inset of Figure 4.14, not very large, but at the same time, a very large change in crystallinity is not necessary for a thermal conductivity increase from 1 to 2.5 W/m-K.

Figure 4.14. Raman spectroscopy of the a-Si specimens at two levels of mechanical strain. The inset shows zoomed view of the shifts in Raman peaks.

The second hypothesis is strain induced carrier density changes that is based in increased density of conduction electrons as a result of mechanical strain. Typically, vibrational transport dominates electronic transport in semiconductors and doping does not increase thermal conductivity because the impurities only enhance the phonon scattering [294]. However, the

premise of our hypothesis is that number of conduction electrons can be increased through strain, which reduces the electronic band. Such change does not involve any change in the internal structure of the material; hence, we suggest that the increased conduction electron density, unlike conventional doping, can increase the thermal conductivity. The strain induced band gap change is enhanced at the nanoscale, which further bolsters the proposition. Shiri et al. [295] showed that for silicon nanowire band gap can be lowered as much as 100meV with 1% tensile strain. Such strain induced band gap shrinkage is also observed in other semiconducting material such as, germanium thin film and carbon nanotube [296-298]. The only drawback to our hypothesis is the conventional wisdom that the abundant dangling defects trap the carriers to reduce their mobility. This argument can be countered by the observation that the slope of the conduction band tail is influenced by the mechanical strain [299], which is a reason electron mobility is seen to increase under tensile strain. A thermal analogy of this phenomenon is therefore expected to find an increase in thermal conductivity with mechanical strain as well, which we directly show in this study. To further support our hypothesis, we perform another set of experiments on the effects of strain on optical reflectance of the a-Si thin films. The rationale is that the optical reflectance directly depends on the free electron [300-302]. Therefore, any increase in reflectivity with externally applied strain indirectly but strongly supports our hypothesis.

Figure 4.15. Reflectivity on an a-Si specimen at various levels of tensile strains.

Figure 4.15a shows the strain dependence of optical reflectivity of amorphous silicon specimens, measured by a Fourier transform infrared microscope. The initial lower values could be due to any residual compressive stress in the thin-film specimens. Application of the external strain makes the specimens taut and an increasing trend in optical reflectivity is observed. The reflectivity values show a decrease at the end, suggesting that the specimens were fractured. The strain– reflectivity trend appears to support our hypothesis that mechanical strain increases the free carrier density without introducing dopant or impurity structures, which in turn results in increased electronic conduction of heat or the thermal conductivity of the solid. However, it must be noted that electronic thermal conductivity is overshadowed by phonon transport in unstrained specimens; hence, the contribution of strain-induced free electrons may not be the critical factor in explaining the observed strain dependence of thermal conductivity.

4.2.6 Conclusion

Contrary to the conventional wisdom that amorphous materials do not exhibit size or strain effects on thermal transport, we present experimental evidence of increase in thermal conductivity in a-Si from 1 to 2.5 W/m-K under tensile strain. The experiments were performed on 200 nm thick freestanding specimens integrated with nanofabricated tensile testing devices that were operated under an IR-based thermal microscope to measure the spatial temperature profile of the specimens as well as the surrounding thermal boundary layer. An energy balance model was used to calculate the thermal conductivity values. Since tensile strain induced phonon spectra shifts suggest decrease in thermal conductivity, classical physics is unable to explain the observed phenomena. We propose two hypotheses and supporting experiments to address this shortcoming of the literature. The first hypothesis suggests that the increase in thermal conductivity is due to the increase in short or medium range crystallinity in a-Si under tensile strain, which is supported by our supporting Raman spectroscopy. The second hypothesis suggests that the increase in thermal conductivity is due to strain-induced increase in free electron density. Contrary to the literature, we propose that electronic conduction can increase thermal conductivity because the straining process does not increase the impurity structures normally seen for doping. Our supporting experiments on the optical reflectivity (proportional to free electrons) clearly show increase in reflectivity as function of tensile strain. These results indicate that either or both of the proposed mechanisms may be relevant to the anomalous observation of increase in thermal conductivity of a-Si under externally applied mechanical strain.

CHAPTER 5

DOMAIN ENGINEERING OF PHYSICAL VAPOR DEPOSITED TWO- DIMENSIONAL MATERIALS

This chapter has been previously published in modified form in Applied Physics Letters (Alam, M. T., Wang, B., Raghu, A. P., Haque, M. A., Muratore, C., Glavin, N. , Roy, A. K.and Voevodin, A., Domain engineering of two-dimensional materials, Applied Physics Letters, Vol. 105, 213110, 2014) Experiment design: M T Alam, Baoming Wang, Raghu Pulavarthy and Aman Haque Thin film preparation: Chris Muratore, N. Glavin, A. Roy and A Voevodin Device fabrication and sample integration: M T Alam, Baoming Wang and Raghu Pulavarthy Experiment and measurement: M T Alam and Baoming Wang Data Analysis and Manuscript preparation: M T Alam, Baoming Wang, Raghu Pulavarthy, Chris Muratore and Aman Haque

Physical vapor deposited two-dimensional (2D) materials span larger areas compared to exfoliated flakes, but suffer from very small grain or domain sizes. In this work, we fabricate freestanding molybdenum disulfide (MoS2) and amorphous boron nitride (BN) specimens to expose both surfaces. We performed in situ heating in a transmission electron microscope (TEM) to observe the domain restructuring in real time. The freestanding MoS2 specimens showed up to 100x increase in domain size, while the amorphous BN transformed in to polycrystalline hexagonal BN (h-BN) at temperatures around 600 C much lower than the 850-1000 C range cited in the literature.

5.1 Introduction

The rise of graphene[4] has galvanized the research on low dimensional materials that, to date, has extended to semiconducting transition metal di-chalcogenides (MoS2 or WS2), and insulating h-BN. This special class of materials consist of atomic layers with strong in-plane covalent bonding that are stacked together, with each layer bound by weak van der Waals bonding. The technological expertise from graphene has translated to other materials in 2D form and their

intriguing layer/thickness dependence of thermo-physical properties as well as novel phenomena such as spin, valley or strain-tronics have led to the current resurgence of interest. For example the indirect bandgap of bulk MoS2 (1.29 eV) shifts to direct type for a monolayer at 1.8eV [303]. This gives rise to unprecedented interaction with light[304] that can be exploited in opto-electronic devices. Monolayers of MoS2 in transistors show on/off ratios many orders of magnitude larger than the best graphene transistors at room temperature, with comparable mobility [305] and are aggressively pursued for electronic and optoelectronic devices [306, 307]. A perfect foil for the semi-metal graphene is h-BN, also known as the white graphene, where atomically thick layers comprised of equal parts boron and nitrogen atoms form a 2D honeycomb structure iso-structural to graphite yet exhibiting very wide band gap of 5.9 eV nearing an insulator and a very high in- plane thermal conductivity [200] around 390 Wm-1K-1. Their low energy atomically smooth surfaces are free of dangling bonds as well as surface optical phonon modes, reducing phonon scattering from the dielectric. While these individual 2D materials are potentially interesting on their own, the exciting prospect of their stacking into heterostructures (or van der Waals’ solids [196]) that currently propels 2D materials research. These are complex ‘on-demand designer materials’ with controlled stacks of individual molecular or atomic layers building novel 3D materials with interesting structural, electronic, optical, mechanical and other properties [308-310].

The most influential microstructural parameter for 2D materials physics is the grain or domain boundaries, which reflect degree of laterally coherent atomic ordering within the material. Mechanical exfoliation of bulk crystals allows maintenance of a high degree of atomic-scale order in the transition from bulk to 2D when compared to vapor phase synthesis, but only over areas below 100 m2. As a result, exfoliated crystals make excellent specimens for fundamental research but are impractical for scaling up technological applications. Therefore, alternate techniques for large area growth using processes amenable to microelectronics, such as chemical or physical vapor deposition; have seen a major thrust in the literature. In this time, none of the large area synthesis processes has been able to produce exfoliation-grade results, primarily due to the domain boundaries. Chemical vapor deposition (CVD) of MoS2, for example, results in triangular domains with size scale of few tens of microns. The growth of these domains is sensitive to the precursor gas concentration and chamber pressure, while the nucleation rate dependence on extrinsic process parameters is yet to be understood and controlled. High surface energy features [311], such as scratches, edges, as well as special precursor treatment [312] have been used to increase the nucleation site density. As a result, even though the individual triangles are highly crystalline, they physically overlap upon extended growth and form domain boundaries [313]. The presence of these

overlaps critically influences the overall microstructure, which is obvious from the remarkable difference seen in the Raman spectra as a function of the number of monolayers [314]. The physical overlap of these crystallites increases nonlinearly with the number of layers; therefore, even though the individual domains can be large, the effective domain sizes are much smaller. Physical vapor deposition (PVD) does not suffer from the isolated nucleation sites as CVD for continuous coverage, but in this case, the crystallites are smaller. Hence, the domain sizes are even smaller although the films demonstrate continuous coverage. Other large area synthesis processes, such as solution based dip-coating and thermolysis [315] are also limited by such domain boundaries.

In this work, we first highlight that atomic ordering of CVD, PVD or solution based process is typically localized in individual domains or crystallites. Over larger areas, these isolated regions of highly ordered atoms are interrupted by domain boundaries, which generally degrades the properties of 2D materials [311, 312, 316, 317]. Low temperature (200-300 C) annealing is routinely done in the literature to eliminate surface contaminations or to improve the electrode contacts, for bulk and thin film materials but there is very little evidence of increased domain size of 2D materials, via post-process annealing. However, it was shown recently that a combination of localized and global heating results in in-situ annealing of high angle grain boundaries in chemical vapor deposited graphene [318]. While high temperature annealing is expected to induce such recrystallization of the grain boundaries, the required temperatures are too high for MoS2 [315] and

o BN [319]. MoS2 for example has been extensively used as high temperature (>700 C) solid lubricant (in vacuum), while h-BN, which is less sensitive to the composition of the ambient environment, does not show substantial phase transformation (amorphous to crystalline) or grain size increase unless the temperature and pressure are very high (>1000 °C and 7.7 GPa) [320, 321]. Evidence in the literature for microstructural changes in h-BN thin films involve special catalysts [322] or lattice matched substrates [323], such as ruthenium, with temperature exceeding 850 °C in either cases. In air, annealing of MoS2 results in layer thinning [324], but most often complete oxidation at temperatures as low as 330 oC [325] Sulfur desorption is sometimes observed at high temperatures under high vacuum [326]. Grain sizes of MoS2 films do not increase beyond 10 nm [327] even after annealing at 750 C based on x-ray diffraction peaks peak sharpening methods of the structure analysis. However, we also note that 2D materials are expected to be extremely sensitive to external stimuli, particularly because of the predominance of surface atoms, which are also expected to have a higher mobility. In this study, we expose both surfaces of the specimens by releasing them from the substrate. Our hypothesis is that doubling the number of highly mobile surface atoms (not to mention high-energy features such as surface steps and ledges) will reduce

the activation energy of atomic migration for domain reconstructions driven by a reduction of domain boundary energy. To test this hypothesis, we selected thicker (40 layer) MoS2 and (10 layer) amorphous BN specimens. Thicker specimens are more robust for the pick-and-place technique for transferring films to devices used here, and facilitate characterization for definitive evidence of structural effects. Moreover, it is anticipated that the recrystallization temperature increases with the specimen length-scale and hence thicker specimens pose a rigorous test of the proposed hypothesis. In this study, we adopt an in-situ TEM approach that is known to be effective in detecting precise changes in crystallinity through both imaging and electron diffraction modes [328].

5.2 Sample preparation and experimental setup

To examine the effects of heating of freestanding films, nanocrystalline MoS2 (domain size around 5 nm) and amorphous BN films were integrated into a micro-electro-mechanical system (MEMS) fitted with micro-heaters for in situ heating inside TEM. PVD techniques were used for growth of both materials on silicon substrates coated with 200 nm thick spin on glass. Briefly, the sputtering process involves generation of a magnetically confined, cold, low-pressure argon plasma adjacent to a pure MoS2 disk. The disk also serves as the plasma cathode, driving positively charged argon ions into the disk, and liberating atoms from its surface. Those atoms condense on the substrate surface, where their kinetic energy and the substrate temperature dictate the resulting film microstructure. Asymmetric, bipolar voltage pulses were applied to the sputtering magnetron to control microstructure for surface plane (002) orientation [329]. BN films were deposited by pulsed laser deposition, where a focused laser beam pulse causes both ionized and neutral components from a BN target to accelerate to the desired substrate surface as a plasma plume in a nitrogen gas background. The deposition characteristics are controlled by laser wavelength, power, pulse rate, pulse duration, target-to-substrate working distance and relative orientation, background gas type and pressure, and substrate temperature. Previously, we have deposited few-layer MoS2 and BN (mono to few-layers) on oxidized silicon substrates at temperatures as low as 350 C and have performed complete characterization of the specimens [330, 331]. A 10 nm titanium layer was deposited in the same PVD growth chamber to protect the BN and MoS2 specimen layers without breaking the vacuum. This is shown in Figure 5.1a, with inset elaborating the protective sandwich structure. In the next step, photolithography and reactive ion etching were used to pattern 10 micron wide and 100 micron long rectangular specimens that are released from the substrate. This step is shown in Figure 5.1b. These sandwich (oxide-specimen-titanium) structures were then mechanically cleaved at the supporting ends and then manipulated on the MEMS device. Figure

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5.1c shows this step with the cleaved specimen and the nanomanipulator needle in a focused ion beam (FIB) chamber.

Once the specimen is aligned with the MEMS device, it was secured with carbon deposition at the ends using a focused ion beam. The effective gage length of the specimen was about 10 microns. The MEMS device was then exposed to hydrofluoric acid vapor to remove the protective layers of spin on glass (SiO2) and titanium without damaging the specimens. These two steps are shown in Figures 5.1d and 1e respectively. Energy filtered chemical element mapping confirmed

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removal of all traces of the Ti layer. No carbon was present either, suggesting that the specimen transfer technique is much cleaner than the conventional practice involving poly(methyl methacrylate) [332]. Figure 5.1f shows an infrared image of the heaters integrated with the test chip. A finite element model was developed to calculate the temperature profile for heating at ambient conditions. The excellent agreement between the measurement and calculation is obvious from the overlap of these two lines. Next, the convective mode heat transfer was turned off in the model to estimate the temperature profile inside the TEM chamber.

5.3 Result and discussion

Figure 5.2 shows the experimental results on the MoS2 specimen. In as-deposited form, the microstructure was turbo-stratic as evident from the diffused rings in the electron diffraction pattern, Figure 5.2b. High resolution TEM indicated average domain size around 3-5 nm. The

Raman spectra, Figure 5.2c, clearly showed the signature peaks for stoichiometric MoS2, but with reduced intensity indicative of phonon scattering over 5-10 nm domains.

After annealing for 30 minutes at 600 C minutes, significant domain restructuring was observed as the average domain size increased to approximately 100 nm. Figure 5.2d shows a high- resolution TEM image where the lattice spacing of 0.61 nm clearly indicates crystalline phases of

MoS2, and the electron diffraction pattern shows spotty rings indicating grain growth. The effect of such low temperature and short time annealing is evident in Figure 5.2f, where the Raman spectra of the annealed sample is compared with the as-deposited as well as a bulk single crystal of MoS2. The comparison with the bulk crystal is very promising and currently electrical measurements on the domain-engineered specimens are underway.

While turbo-stratic to nanocrystalline phase transformation at relatively lower temperature in MoS2 is remarkable, it is not energetically forbidden as seen in literature for carbonaceous materials albeit at higher temperatures [333]. A rather challenging and long lasting problem lies in amorphous specimens that typically require impractical magnitudes of temperature and pressure [334]. Figure 5.3 shows the experimental results with in-situ TEM annealing of the amorphous BN films at 600 °C for 30 minutes. The as-deposited amorphous boron nitride transformed into crystallites with average domain size of 100 nm. Indexing of the resulting electron diffraction pattern reveals a match with that for hexagonal structure of boron nitride as shown in Figure 5.3d. The transformed structure was stable after the temperature was lowered to ambient.

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Figure 5.2. Experimental results on MoS2 (a) bright field TEM, (b) electron diffraction and (c) Raman spectroscopy of the as-deposited specimen while supported on the substrate measured with 10 mW excitation laser power. After in-situ TEM annealing at 600 C, (d) bright field TEM and (e) electron diffraction shows significant grain/domain growth, (f) comparison of the as- deposited and annealed Raman spectra with that for a single crystal MoS2. The power was reduced to 1 mW to avoid damage to the freestanding specimens, thus the intensity of the as-deposited film is significantly reduced.

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To explain the observed phenomenon of grain growth in MoS2 and the amorphous to nanocrystalline phase transformation in BN at only 600 C, we note the dominant role of surface diffusion. In general, surface is the fastest pathway for atomic migration, which can be orders of magnitude higher than bulk and grain boundary diffusion[335]. Since the specimens in this study were freestanding, both surfaces provide a reduced activation energy for diffusion compared to specimens on substrates where the grain boundaries are essentially pinned or constrained by the substrate and even extremely high temperature is not effective in their migration towards grain growth. An extension of the present study under progress is quantification of the activation energy for grain or domain boundaries by measuring the grain sizes as function of temperature and time, carrying out the experiments for various thicknesses. The implications of our finding are two-fold: i) provides an avenue for a large area synthesis of 2D materials by PVD methods with post- annealing and; ii) experimental guidance to the concept of domain size engineering while using free surfaces to significantly reduce temperature requirements for structure restructuring activation.

5.4 Conclusion

Successful implementation of domain engineering may allow us to grow these materials on any desired substrates and yet maintain acceptable crystallinity through post processing, relaxing the substrate constraint. However, domain size and grain-boundary defect engineering is mostly theoretical concept because studies on grain boundaries in 2D materials is still at its infancy [317]. By maximizing domain size and minimizing boundary defect concentrations, it may be possible to achieve pristine-like performance in large area 2D materials, which is a dominant technological barrier for integration of this class of materials in diverse applications.

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CHAPTER 6

MECHANICAL STRESS FIELD ASSISTED CHARGE DE-TRAPPING IN CARBON DOPED OXIDES

This chapter has been previously published in modified form in Microelectronics Reliability (Alam, M.T., Maletto, K. E., King, S., and Haque, M. A., Mechanical stress field assisted charge de- trapping in carbon doped oxides, Microelectronics Reliability, Vol. 55, Issue 5, pp 846-851, 2015) Experiment design: M T Alam and Aman Haque Thin film preparation: Sean King Sample and device fabrication: M T Alam Experiment and measurement: M T Alam and Kyle Maletto Data Analysis and Manuscript preparation: M T Alam, Sean King and Aman Haque

Leakage current and dielectric breakdown effects are conventionally studied under electrical fields alone, with little regard for mechanical stresses. In this letter, we demonstrate that mechanical stress can influence the reliability of dielectrics even at lower field strengths. We applied tensile stress (up to 8 MPa) to a 33% porous, 504 nm thick carbon doped oxide thin film and measured the leakage current at constant electrical fields (up to 2.5 MV/cm). The observed increase in leakage current at relatively low electric fields suggests that mechanical stress assists in trap/defect mediated conduction by reducing the energy barrier potential to de-trap charges in the dielectric.

6.1 Introduction

Reliability of dielectric films has always been crucial for the semiconductor industry, particularly in the context of metal-oxide-semiconductor field effect transistor (MOSFET) technology in integrated circuits (IC). Typically, the conduction current in insulators (i.e. leakage) at normal values of applied electric field is very small, but it can be noticeably increased with the electrical field strength to induce catastrophic failure (breakdown) or gradual degradation known as time dependent dielectric breakdown (TDDB) at lower than the breakdown field strength [336]. The leakage current, thus, must be lower than a certain level to meet the specific reliability criteria under normal operation of the gate, capacitor or tunneling dielectrics in applications such as

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MOSFETs, dynamic random access memories and Flash memories [337]. The physics of leakage current in relation with electrical field, moisture, temperature, bonding and microstructure is therefore a very active fundamental research area.

In addition to electrical stress, ICs experience thermal and mechanical stresses [338]. The current state of the art for investigating the reliability of ICs as a function of stress is to study the stress dependencies in their individual domains, such as electrical, mechanical or thermal. For instance, electrical leakage currents and dielectric breakdown failure studies have been predominantly correlated to the electrical field strength. However, electrical, thermal, and mechanical stress fields may all interact to influence the reliability of ICs in a non-linear or additive manner. For example, thermal stresses arising from growth or deposition conditions are well known to generate mechanical stresses in multilayered systems such through mismatches in the thermal expansions coefficients of the constituent materials [339, 340]. Although perhaps less pronounced, thermal and mechanical stresses may influence electrical leakage currents or breakdown strengths in dielectrics through increased bond strain or breakage. Similarly, electrical stress may manifest in thermal and mechanical properties through electrical polarization inducing changes in bond strain and/or defect generation. However, there have been relatively few efforts reported in the literature to investigate the role of mechanical or thermal stress fields on electrical properties and vice versa. This is perhaps due to the brittle nature of most dielectrics and the experimental challenge of applying a significant mechanical strain without inducing catastrophic mechanical fracture.

One early attempt by Jeffery et al. [341] to investigate dielectric mechanical-electrical stress interactions attempted to overcome the inherent fragility of brittle materials in tension by looking at compressive contact stresses introduced by nanoindentation on a 2.2 nm thick native oxide. However, the mechanics of nanoindentation are yet to be validated for specimens of this thickness. Yang and Saraswat [340] studied the role of physical stress on constant current gate injection at the oxide-semiconductor interface to find that the breakdown mechanism is very closely related to the Si–Si bond formation from the breakage of Si–O–Si bond. Wu et al. used a conductive atomic force microscope tip to apply an electrical field on a 3 nm thick silicon dioxide specimen while bending the silicon substrate to apply mechanical stress [342]. The authors reported around 10% decrease in dielectric breakdown strength and even more pronounced effects on time dependent failure. Intriguingly, the breakdown strength decreased with both applied tension and compression stresses. The opposite trend under tension and compression was reported by Yang et al. [343] who studied non-porous SiOC dielectric films under mechanical stress. They did not

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observe any appreciable influence of the mechanical stress at lower electrical field strengths. In addition, the mechanical stresses were indirectly reported in form of substrate curvatures. At electrical field strengths exceeding 4 MV/cm, the authors observed a 2.5% increase in leakage current under tensile stress (decrease under compressive stress). Based on a detailed analysis of the current-voltage traces, they concluded that the conduction mechanism is dominated by Poole- Frenkel (PF) emission and mechanical stress changes the energy barrier of the dielectric material. While limited, these studies highlight the need for further investigation on the fundamental mechanisms of mechanical stress mediated electrical conduction in insulators.

In this regard, we have chosen to investigate the influence of mechanical stress on the leakage current and breakdown strength of dielectric materials utilized in IC metal interconnect structures. Leakage currents and dielectric breakdown are an important reliability concern for interconnects in ICs where ultra large-scale integration has resulted in higher device/interconnect density and thereby increases in operating electric fields and resistance-capacitance (RC) delays. An early solution to the capacitance problem was to replace silicon dioxide as the insulating interlayer (ILD) dielectric with materials having lower dielectric constants (i.e. low-k) to reduce the capacitance between metal lines [344]. Typically, the dielectric constant is reduced by decreasing dipole strength (using materials with chemical bonds of lower polarizability than Si-O), but the practical limit to this approach has required the industry to adopt a second approach of reducing the number of dipoles through incorporating open porosity [149]. Unfortunately, such manipulation of bond structure can negatively influence the thermal, mechanical, electrical properties of low-k materials as well [345]. In fact, it is well known that low-k materials have remarkably low stiffness and structural stability [346, 347] and similarly degraded thermal properties [348]. Therefore, an intuitive foundation for this study is that the chemical-mechanical restructuring processes imposed on low-k dielectrics to achieve low permittivity and density will also make their electrical properties inherently more sensitive to mechanical stress. Thus, low-k dielectric materials should represent an ideal material for investigating the influence of mechanical and thermal stress on dielectric properties and electrical reliability. In this study, we specifically investigate the influence of mechanical stress on the electrical leakage and breakdown strength of a porous a-SiOC:H, k = 2.3 dielectric under consideration for advanced (< 10 nm) Cu interconnect technologies.

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6.2 Experimental setup

A four point bending technique was employed to apply both tensile and compressive stresses in a metal-(low-k) insulator-semiconductor (MIS) specimen. The experimental setup was similar to Wu et al. [342], but with small modifications to be described later. The low-k SiOC:H thin films were deposited on 300 mm diameter 750 micron thick Si (100) wafers using industry standard high volume manufacturing PECVD tools with alkoxysilane or organosilane precursors diluted in helium and various oxidizing gases (O2, CO2 etc.) at 250-400C. Films with high porosity were obtained by controlling the amount of a second phase organic pore builder (i.e. porogen) incorporated in the film during deposition and removed post deposition using either an electron beam or UV cure. Table 6.1 below summarizes some of the key material properties for the specific low-k film employed in this study including thickness, dielectric constant, mass density, porosity, Young’s modulus and hardness.

Table 6.1: Material properties for the low-k dielectric films investigated in this study.

Film type Thickness Dielectric Mass Porosity Young’s Hardness Constant, Density Modulus (2 nm) (2%) (0.5 GPa) “k” (0.5 GPa) (0.1 (0.1) g/cm3)

SiOC:H 504.2 2.3 1.1 33 4.7 0.7

To make the electrical measurements while performing the four point bending tests, a physical shadow mask was used to evaporate 10 nm titanium and 150 nm thick gold contact pads on the dielectric film with diameters ranging 1-3 mm. Similar blanket contact metal deposition was performed on the silicon side. Electrical connection was made to these contacts through micro- solders. In a typical test, the electrical leakage current is measured as the mechanical stress is systematically varied, while keeping the electrical stressing at a constant value. This step is then repeated for various values of the applied voltage. The experimental design for this study was based on two critical considerations. Firstly, the electrical field strength needs to be smaller than that obtained by a voltage-ramped breakdown test. This allows us to attribute the bond straining or breaking to mechanical stressing and not the electrical field. Secondly, both the mechanical and electrical field strengths need to be small while the mechanical stressing rate should be as high as possible. This is because it is known that leakage current increases with time for a constant voltage

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in carbon doped oxide (CDO) [349], and minimization of such time dependence is helpful in isolating the effects of mechanical stress from other possible parameters. To obtain the ideal experimental parameters, we performed a conventional voltage-ramped breakdown test without any mechanical stressing. The voltage range was set to 0-210V with a ramp rate of 20V/min. The electrical stressing and measurements were carried out with a Kiethley 2400 source-meter and a KUSB 488B adapter. As voltage was ramped, measurements were carried out at every 0.5 sec and the breakdown criteria for all the tests was defined as an abrupt 3x or larger increase in leakage current during the test. Figure 6.1(a) shows typical leakage currents as a function of applied electrical voltage, while Figure 6.1(b) shows the breakdown values were around 3.5±0.5 MV/cm. This value is consistent with the experiments performed on other carbon doped thin films with 33% porosity.

Figure 6.1. (a) Measured leakage current as a function of applied electrical field (b) Dielectric breakdown field strength for samples without any mechanical stress.

Once the breakdown voltages were obtained, we performed the mechanical stress controlled experiments. For mechanical loading, individual specimens were mounted in the four point bending fixture for tensile loading, as shown in Figure 6.2 (b-d). The top crosshead of the mechanical loading was programmed to bend the specimen with a rate of 0.1mm/min. Tensile loading in the specimen was achieved by placing the sample side in a downward direction (Figure 6.2e). Mechanical load was applied in a test piece until the load reached 2 Newtons and then a dwelling period of 5 seconds was allowed for the leakage current measurement, then the load was increased for another 2 Newtons and the process was continued until the load reached 30 Newtons. The entire process required about 2-3 minutes. In the 4 point bending fixture, the distance between inner most cylindrical supports (Li) was 10 mm and the distance between the two outer cylinders

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(L) was 20 mm. The amount of stress on the 750 nm thick silicon substrate was found from the beam bending formula [350].

3퐹퐿 휎 = (1) 4푏푑2

Where, F is applied load, L is distance between the outermost support, b is the width of the sample and d is the thickness of the sample. From strain compatibility condition, the dielectric film specimen has the same strain as silicon at the interface. We therefore convert the silicon stress at the interface to strain, and multiply this value with the measured Young’s modulus of the dielectric film. For the single crystal silicon substrate, Young’s modulus is considered as 170 GPa [42]. In our experiments, the stress on the silicon substrate for 30 Newtons load was calculated from equation (1) as 267 MPa and the stress on the 33% porous SiOC:H thin film was calculated to be 7.3 MPa.

Figure 6.2. (a) sample with two electrodes, (b) Four-point bending fixture in a universal testing machine, (c-d) schematic diagram of sample, (e) schematic diagram of tensile loading

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6.3 Experimental results and discussion

Since the objective of this study was to observe the effect of mechanical stress on leakage current, we intentionally kept the applied electrical field at 0.6 MV/cm, 1.0 MV/cm, 2.0 MV/cm and 2.4 MV/cm, which were lower than the breakdown voltage of the film (3.5±0.5 MV/cm). Unlike a typical voltage ramped experiment, we kept the electrical field constant and then continuously increased mechanical stress while measuring the leakage current. The representative sets of results in Figure 6.3 show the influence of tensile loading (expressed as the stress in the semiconductor substrate) on leakage current of SiOC:H samples. At the lowest electrical field (0.6 MV/cm), the leakage current increased by 22% for a tensile stress increase of 267 MPa (7.3 MPa in the specimen). However, for higher electrical fields of 1.0, 2.0 and 2.6 MV/cm the effect was even more pronounced; maximum leakage current increase was about 36%, 40% and 70% respectively. These results indicate that mechanical stress can be detrimental to the dielectric reliability at even lower electrical field strengths, which is a key finding of the present study.

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To understand the origin of the leakage current, we focus on the conduction mechanisms in dielectrics, which can be dominated by the interface or the bulk of dielectric itself. The interface limited conduction mechanisms are Schottky emission (SE), Fowler-Nordheim (FN) tunneling, direct tunneling, and thermionic-field emission. Bulk-limited mechanisms include Poole-Frenkel (PF) emission, hopping conduction, ohmic conduction, space-charge-limited conduction and grain- boundary-limited conduction. Further details on these mechanisms are reviewed in [337], which also highlights the role of defects (broken or dangling bonds, interstitials). Defects in dielectric materials are well known to trap charges through potential wells and contribute to electrical leakage where the role of the electric field is to excite the trapped electrons out of the well and into the conduction band of the dielectric material [343, 351]. Leakage currents, dielectric breakdown and TDDB in low-k dielectrics are all routinely attributed to the presence of defect and trap states and the creation of additional traps/defects during electrical stressing [352]. Porous low-k materials are also known to possess a broad distribution of defect states originating from oxygen vacancy defects (created during UV curing) and carbon residues from incomplete porogen removal [353]. Such carbon-rich microstructure may result in higher leakage currents, lower breakdown voltages, and shorter TDDB lifetimes [354]. For CDOs, the dominant mechanisms are known to be SE, where an energy barrier exists between the metal Fermi level and oxide conduction band, and the electron from the electrode can be emitted over the barrier to the oxide by thermal emission when an electric field is applied [355]. In a recent electron paramagnetic resonance (EPR) study, Pomorski et al. [356] has shown that for a-SiOC:H SE dominates at moderate electric fields (> 2.5 MV/cm), but at lower fields, leakage occurs through carbon dangling bond defect populations via other mechanisms such as variable range hopping (VRH). Similar conduction mechanism studies have been carried out for SiOC:H [351] and silicon dioxide [355] thin films as well. Another dominant mechanism for CDOs is the PF mechanism, where the excitation emits electrons from defects or traps into the conduction band of the dielectric. Studies by Vilmay et al. [352] and Yang et al. [343] suggest that PF conduction is the most dominant type in the low-k SiOC:H thin film at high electric fields (> 3.5 MV/cm).

Recognizing from the discussion above that no single conduction mechanism might be held responsible for the entire range of electrical field strength, we analyzed the voltage ramped data shown in Figure 6.1 for the SE, FN, PF, hopping and space charge mechanisms by fitting the data with their governing equations compiled in [337]. For SE and PF, these are

−푞(휑 −√푞퐸/4휋휀 ) 퐽 = 퐴∗푇2푒푥푝 [ 퐵 푑 ] (2) 푘푇

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−푞(휑 −√푞퐸/휋휀 ) 퐽 ∼ 퐸 푒푥푝 [ 퐵 푑 ] (3) 푘푇

where, J denotes the current density, A* is the Richardson constant, T is absolute temperature, q is the electronic charge, ϕB is the potential barrier at the metal/dielectric interface, E is applied electric field, εd is the dielectric constant and k is the Boltzmann constant. Figure 6.4a below shows the plot of ln (J) versus E1/2, which represents the Schottky emission. In the plot, two linear regions can be identified and from the slopes of the linear fit, the effective dielectric constants were obtained as 3.05 (from 1.4 to 2.7 MV/cm) and 0.99 (from 2.7 MV/cm to breakdown field). As the measured dielectric constant for this material is 2.31, only the region from 1.4 to 2.7 MV/cm yields the closest match. Hence, SE is the dominant mechanism in this electric field range. To explore the conduction mechanism in the region beyond 2.7 MV/cm, we plotted ln (J/E) vs E1/2 for PF mechanism. Figure 6.4b shows such plot with two linear regions. We calculated the effective dielectric constants as 19.93 (from 1.4 to 2.7 MV/cm) and 4.88 (beyond 2.7 MV/cm) from the corresponding slopes, which confirm that PF is a match for only electrical fields beyond 2.7 MV/cm.

Figure 6.3 suggests that the role of mechanical stress field is to accelerate the electrical breakdown process. The extent of such acceleration is obvious in Figures 6.4c and 6.4d, where the conventional voltage ramped test leads to very quick breakdown that results in fewer data points that could be recorded. To investigate the possibility of other leakage mechanisms, we also plotted the current density-electrical field data in a log-log fashion to investigate the suitability of space charge conduction. Typical space charge limited conduction has three characteristic region (linear regime J~E; square regime, J~E2 after a transition voltage; and a jump at the trap filled limited voltage after which the J~E2 continues [337]), which was not the case for our data. The conduction is also not Ohmic because the current–voltage trace did not show linear relationship (Figure 6.3 has logarithmic y-axis) with either mechanical or electrical stress. This leaves hopping conduction mechanism, which is known to be in effect for lower values of electrical field strength, where both SE and PF are absent [351]. Here, the charge essentially hops from one trap to other. Thus, the analysis in Figure 6.4 suggests that SE is the dominant conduction mechanism for our electrical- mechanical stress measurements performed at 2.0 and 2.4 MV/cm, while VRH is more likely for electrical-mechanical stress measurements performed at 0.6 and 1.0 MV/cm.

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Since tensile strain can decrease the inter-defect spacing through the Poisson’s effect, this may influence the leakage current which is perpendicular to the direction of the applied mechanical stress. To model the observed role of mechanical stress on leakage current, we note that the stress can have two ways to influence the breakdown, (i) the strain energy supplied in mechanical form can lower the trap barrier energy and (ii) the strain energy can create new defects. In both cases, the leakage current is expected to increase in tension. In principle, these two mechanisms can work simultaneously, making the separation of their effects difficult. For the first case, it is possible to approximate the equivalent electrical field for a given applied mechanical strain energy. For a solid with relative dielectric constant d under electrical field E, the equivalent tensile stress t is relationship is given by [357],

1 1 휎 = 0.171599(휀 − 1)2 휀 퐸2 + 휀 퐸2 (4) 푡 푑 2 0 2 0

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Where 0 is the permittivity of free space. Based on this analysis, an externally applied stress of 7.3 MPa is an electrical field equivalent of about 3 MV/cm. However, this is only the upper bound because a portion of this strain energy is released by generation of new defects, which requires significant amount of energy [358]. The rest of the energy is used to lower the trap barrier height, which are given for SE [359] by,

푞퐸 Δ휙 푆퐸 = √ (5) 4휋휀푑

Where, d is the dielectric constant for the dielectric. Equations (2) and (3) suggest that the lowering of the barrier height for PF ( PF) is twice as strong as the SE mechanism. Unfortunately, it is not possible to quantify the part of the total strain energy dedicated towards new trap generation unless the interfacial (for SE) and bulk (for PF) trap density is measured as function of the applied stress. The quantitative modeling is further complicated by the possibility that pre-existing or precursor defects, and not the newly created ones) may dominate the conduction and breakdown mechanisms.

In a recent study, Veksler and Bersuker [360] modeled electron trapping/detrapping processes using multi-phonon assisted electron transport to show that pre-existing defects can satisfactorily follow experimental observations on stress time dependency of the threshold voltage, leakage current, charge pumping current, and low frequency noise. Their findings suggest that a comparatively small density of new defects is generated at the interfacial region and generation of new dielectric defects becomes a dominant process at longer stress times, most likely immediately prior to and during the dielectric breakdown phase. While this may sound intriguing, this is one of the foundations of fracture mechanics. Here pre-existing defects (internal surfaces) act as localized mechanical stress amplifier that increases the surface area of these defects. It is also a foundational assumption that since generating a new surface (new defect) is more energetically expensive, fracture mechanics is primarily about growth of ‘existing’ flaws [361] and less on new defects generation. Therefore, the entirety of the externally supplied strain energy is not necessarily used in lowering the trap barrier height. This might be the reason we did not observe dielectric breakdown at applied field of 2.4 MV/cm and a mechanical equivalent of 3 MV/cm, even though the same specimen fails at around 3.5 MV/cm. In other words, the externally applied mechanical stress may not significantly alter the effective trap density.

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To validate the pre-dominance of the pre-existing defects, a simple experiment could be the mechanical unloading test. If the leakage current decreases upon decrease of the mechanical stress, one can deduce that no or very little new defects were created since removal of the mechanical strain energy should restore the original potential barrier for the de-trapping. To investigate this, we performed another set of experiments in which the mechanical load was first increased and then decreased at the same rate of loading, while measuring the leakage current for both loading and unloading process. For small values of electrical field (0.6 and 1.0 MV/cm), unloading of mechanical stress was observed to decrease the leakage current back to the original value with zero mechanical load. However, the unloading stress vs. leakage current curve showed very small hysteresis, which could originate from time dependence of trapping and de-trapping (upon mechanical unloading). This is shown in Figure 6.5, which supports our hypothesis that tensile stress lowers the energy barrier in the dielectric material and its removal restores the energy barrier to its initial condition. For larger field strength (2.4 MV/cm), no decrease in leakage current was observed after the mechanical unloading, which suggests that the permanent effects of mechanical stress on the defects or traps were beyond repair or redistribution, and the leakage current was more influenced by the relatively large electrical field than the mechanical stress field.

6.4 Conclusion

While the current art in dielectric reliability studies is to investigate breakdown phenomenon under electrical fields only, we propose that the influence of mechanical stresses should not be ignored. The existence of mechanical stress in the highly dissimilar multilayers in

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ICs can make these devices susceptible to electrical fields that may be too small to be of any reliability concern under normal circumstances. Motivated by the lack of studies on mechanical- electrical compounded field effect, we experimentally investigated the role of mechanical stress in both tension and compression on the electrical leakage current in low-k SiOC:H thin films at low to moderate electrical field strengths. Our experimental results demonstrate about 22% increase of leakage current at only 0.6 MV/cm field and 7.3 MPa, which can be attributed to de-trapping of the charge after mechanical stress reduces the potential barrier. For moderate to higher electrical fields, the influence of mechanical stress can be greater (70% increase in leakage current at 2.4 MV/cm compares to 22% increase at 0.6 MV/cm), which may be due to the compounded effect of electrical and mechanical stressing. While the highlighted contribution of this study is the experimental evidence that the role of mechanical stress can be particularly detrimental for reliability at lower electrical field strengths, temperature field may also play a significant role. The miniaturization trend in ICs exponentially increases the heat dissipation density, rendering the highly localized temperature field an essential future extension of this study.

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Md Tarekul Alam 317 Leonhard Building, Pennsylvania State University, University Park, PA 16802 E-mail: [email protected], [email protected]

EDUCATION

2009 - Present Doctor of Philosophy (expected June, 2015), CGPA: 3.87 / 4.00, Mechanical Engineering (MNE), Pennsylvania State University, University Park, PA. 2004 - 2007 Master of Science in Mechanical Engineering, CGPA 3.83 / 4.00, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh. 2000 - 2004 Bachelor of Science in Mechanical Engineering, CGPA 3.96 / 4.00, Ranked 1st among 140 students, Bangladesh University of Engineering and Technology.

AWARDS & HONORS

 “Alumni Association Dissertation Award”, awarded by Graduate School, Penn State University, 2014.  “MEMS Division Award” in ASME-wide Micro-Nano Forum competition, International Mechanical Engineering Congress and Exposition (IMECE), Houston, 2012.  “Innovation award” in ASME-wide Micro-Nano Forum competition, International Mechanical Engineering Congress and Exposition (IMECE), Vancouver, 2010.  “Dr. V.G. Desa Gold Medal” for obtaining university wide highest CGPA in B. Sc. Mechanical Engineering, Bangladesh University of Engineering and Technology (BUET), 2004.

KEY PUBLICATIONS

1. Alam, M.T., Maletto, K. E., King, S., and Haque, M. A., Mechanical stress field assisted charge de-trapping in carbon doped oxides, Microelectronics Reliability, Vol. 55, Issue 5, pp 846-851, 2015. 2. Alam, M. T., Wang,B., Raghu,A. P., Haque,M.A., Muratore, C., Glavin, N. , Roy, A. K.and Voevodin, A., Domain engineering of two-dimensional materials, Applied Physics Letters, Vol. 105, 213110, 2014. 3. Alam, M. T., Bresnehan, M, Robinson, J. A. and Haque, M. A., Thermal Conductivity of Ultra- thin Chemical Vapor Deposited Hexagonal Boron Nitride Films, Applied Physics Letters, Vol. 104, 013113, 2014. 4. Alam, M. T., Raghu, A. P., Haque, M. A., Muratore, C. and Voevodin, A., Size and Temperature Dependence of Solid to Air Heat Transfer, International Journal of Thermal Sciences, Vol. 73, pp 1-7, 2013. 5. Alam, M. T., Manoharan, M. P., Haque, M. A., Muratore, C. and Voevodin, A., Influence of Strain on Thermal Conductivity of Silicon Nitride Thin Films, Journal of Micromechanics and Microengineering, Vol. 22, Issue 4, 045001, 2012. 6. Kumar, S., Alam, M. T., Haque, M. A., Fatigue Insensitivity of Nanoscale Freestanding Aluminum Films, Journal of Microelectromechanical Systems, Vol. 20 Issue 1, pp. 53–58, 2011.

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