Residual Stress Characterizations in Silicon-On-Sapphire (SOS)

Residual Stress Characterizations in

Silicon-On-Sapphire (SOS) Thin Film Systems

Mei Liu

A thesis in fulfillment of the requirements for the degree of Doctor of

Philosophy

School of Mechanical and Manufacturing Engineering Faculty of Engineering

June 2013

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School: Mechanical and Manufacturing Engineering Faculty: Engineering

Title: Residual Stress Characterizations In Sllicon-On..Sapphire (SOS) Thin Film Systems

Abstract 350 words maximum: (PLEASE TYPE)

As one of most promising candidates in silicon-on-Insulator (SOl) system, silicon-on-sapphire (SOS) can significantly improve the performance of silicon wafer. The main challenges in producing high quality SOS wafers are lhe excessive residual stresses and defects due to film/substrate mismatches. The present research aims to establish a comprehensive experimental system for characterizing both residual stresses and micro-structural defects, and provide more In-depth understandings of the residual stress mechanism.

In residual stress measurement, the complete stress tensors were reliably obtained by optimized diffraction planes, and a equ1-biaxial stress state was Identified. The thickness-dependent stresses were uncovered by Raman on the chemical etched samples. When the film is less than 700 nm, we observed an obvious stress Increase w1th reduced thickness, manifesltng interface lattice mismatch effects A systematic approach was proposed 1n multilayer stress analySIS by X-Ray diffraction (XRD) techn1ques. The stress was found Independent w1th subsequent depositions, but only determined by the film/substrate mismatch.

To uncover the misfit release mechanism, we examined the micro-structures by Transmission Electron Microscopy (TEM). The results reveal that m1sfit dislocation is most influential to stress release. A finite element analysis incorporating experimental observations proves that residual stresses in thin-film are caused by coupled effects of thermal-lattice mismatches and misfit dislocations, and the discrete distribution of dlslocatiom plays a key role in thickness dependency of stresses.

The ex-situ XRD stress measurement at elevated temperatures reveals the actual stresses accumulation upon cooling, which shows an overall consistency with the theorellcalthermal stresses. At deposition temperature, the compressive stress in thinner film confirms the residuallallice mismatch effect, whereas the tens1le stress observed in thick film evidences the possible stress relief caused by surface modifications. In evaluabng Improvement processes effects on residual stress, we found thatlmplantallon could lead to a stress relief by introducing 1nterface defects. However, annealing aga1n restores the residual stress. A h1gh annealing temperature renders a greater residual stress recovery and the Improved crystalline quality. Whereas annealing at lower temperature gives rise to an amorphous layer of a few atomic planes at interface.

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II Abstract

In microelectronics, the silicon-on-insulator (SOI) system can significantly improve the efficiency and performance of the silicon wafer. Silicon-on-sapphire (SOS) thin film is one of the most promising candidates in the SOI family. A defect-free SOS wafers is desired in the semiconductor industry. However, its production confronts the challenges that the excessive residual stresses and high density of microstructural defects (e.g. twins and dislocations) are inevitable due to thermal and lattice mismatches between dissimilar materials. To overcome these technical barriers, in-depth understandings of the stress generation and relaxation mechanisms are essential, which require accurate characterizations of the residual stresses and microstructures and theoretical modeling.

Although there have been many attempts to investigate the microstructural defects, the existing studies lack comprehensive theoretical analysis and the quantitative relationships between residual stresses and lattice defects. The main reasons are (1) the epitaxial films are of single crystal, which makes stress analysis difficult using conventional XRD or

Raman techniques, and (2) the calculation of the stress relief is complicated because the interface defects are discrete and their interactions are complex.

The aim of the present research is to establish a comprehensive experimental system for characterizing residual stresses and micro-structural defects, so as to provide more in-depth understandings of the residual stress mechanism in the SOS system. To this end, the XRD stress analysis technique was improved to obtain a complete stress tensor for the single crystal. The thickness-dependent stresses were unveiled using a novel Raman technique to simultaneously measure the thickness and the stress. It is found that stress increases when iii the film thickness was reduced, which manifests the effect of interface lattice mismatch.

For the multilayer system, an integrated approach, combining both X-Ray diffraction and wafer curvature, was used to determine the stresses in different layers.

The microstructures, particular the twins and dislocations were examined by Transmission

Electron Microscopy (TEM). A finite element analysis incorporating the realistic dislocation density renders a good agreement with the experimentally measured thickness- dependence of the residuals stress, indicating that the final residual stresses in thin-film are caused by the coupled effects of thermal-lattice mismatches and misfit dislocations, and that the discrete distribution of dislocations plays a key role in thickness dependence of residual stresses.

The XRD stress measurement at elevated temperatures reveals the effects of heat treatment on the residual stresses. The experimental result shows the parallel variation with the theoretical thermal stresses with a thickness-dependent offset. At deposition temperature, a compressive stress is observed in the very thin film, reminiscent of the effects of lattice mismatch and misfit dislocations. However a tensile stress is observed in the thick film, evidencing other stress releasing mechanism at work.

The crystal re-growth, through implantation and annealing, was also investigated. It is found that implantation leads to stress relief by introducing more interface defects.

However, annealing restores the residual stress. The higher annealing temperature renders the greater residual stress recovery and improved crystalline quality. An optimized implantation condition and annealing temperature can give rise to the improved crystal quality and reduced residual stress.

iv Acknowledgements

In the first place, I would like to express my sincerest gratitude to my supervisor, Scientia

Professor Liangchi Zhang, for his supervision, guidance and encouragement. I truly appreciate the research opportunity he gave to me, and his scientist knowledge and intuition have exceptionally inspired my growth as a researcher.

Deepest gratitude is also due to my co-supervisor, Dr. Haihui Ruan, for his unselfish help and patience, without whose assistance, this study would not have been successful. Special thanks are also due to my co-supervisors Dr. Alokesh Pramanik and Dr. Yasser Ali, for their guidance and crucial advice for each research stage.

I gratefully acknowledge our industrial partners Mr. Andrew Brawley, Dr. Petar

Atanackovic, Dr. Steven Duvall and Chris Flynn from Silanna Semiconductor, for providing the XRD facility and samples. Their cooperation and valuable discussion are very much appreciated.

I also would like to thank in particular to Mr. Ali Moridi, for his contribution in finite element simulation and academic discussions.

For the XRD experiment, I would like to thank Mr. Trevor Shearing and Dr. Adam

Sikorski from the University of Sydney, Dr. Yu Wang from The University of New South

Wales (UNSW), Dr David Wexler from University of Wollongong, Dr Koichi Seo from

Phillips Panalytical, thanks for their trainings, discussions and suggestions. Each of them has devoted time to make this thesis a complete work.

The author would also like to convey thanks to Dr. Anne Rich and Dr. Chris Marjo from

Solid State & Elemental Analysis Unit (SSEAU) of UNSW for Raman training, their

v advice in Raman scattering technique was of great value. I would like to thank the staff of

Electron Microscope Unit (EMU) of UNSW: Dr. Chun Kong (Charlie), Dr. Sean Lim and

Dr. Quadir Md Zakaria for their training, assistance and valuable discussions. Thanks are also due to Dr. Demish K. Venkatachalam (ANU Node) and Dr. Fay Hudson (UNSW

Node) from Australian National Nanofabrication Facilities (ANNF), for assisting with implantation and annealing experiments. Many thanks are particularly given to Dr. Warren

McKenzie, for many helpful discussions. Thanks are also due to Mr. Hongtao Cui for assisting with etching experiments.

It is a pleasure to express my gratitude to all of the members in Laboratory for Precision and Nano Processing Technology (LPNPT). I am proud of each of them. I would like to further thank Dr. Fengzai Tang for TEM discussions and Dr. Animesh Basak for assisting with FIB experiments. My heartfelt thanks go to my best friend Dandan, Cui, for her company and encouragements, her true friendship is worth more than my Ph.D. degree.

Last but not the least, to my beloved parents and elder sister and the most importantly, my husband, Xin Zhou, who have evidenced my ups and downs, and shared with me every excitement and sadness; your love, understanding and support over the past four years have made all my success possible.

The continuous financial support from the Australian Research Council is also greatly acknowledged.

vi Table of Content

Originality Statement ...... i

(a) Copyright Statement ...... ii

(b) Authenticity Statement ...... ii

Abstract ...... iii

Acknowledgements ...... v

List of Figures ...... x

List of Tables ...... xv

Nomenclature ...... xvi

Chapter 1 Introduction ...... 1

Chapter 2 Literature Review ...... 8

2.1 Residual Stress mechanisms in Epitaxial Thin Films ...... 8

2.1.1 Lattice Mismatch and Lattice Defect ...... 9

2.1.2 Thermal Mismatch ...... 22

2.1.3 Summary ...... 25

2.2 Residual Stress Measurement ...... 26

2.2.1 X-Ray Diffraction (XRD) ...... 27

2.2.2 Raman Spectroscopy ...... 30

2.2.3 Curvature Method ...... 32

2.2.4 Summary ...... 34

2.3 Silicon on Sapphire (SOS) System ...... 35

2.3.1 Production and Crystallography ...... 36

2.3.2 Micro-structural Defects ...... 40

vii 2.3.3 Residual Stresses ...... 47

2.3.4 Summary ...... 50

2.4 Discussion and Conclusions ...... 51

Chapter 3 Development of New Experimental Methods for Residual Stress Characterizations ...... 53

3.1 Stress Characterization in Epitaxial Thin Film ...... 54

3.1.1 Complete Stress Tensor...... 54

3.1.2 Thickness-Dependent Stress ...... 64

3.2 Stress Characterization of Multi-layered Thin Films ...... 73

3.2.1 Methodologies ...... 75

3.2.2 Results ...... 83

3.3 Summary ...... 89

Chapter 4 Origin and Analysis of the Residual Stresses ...... 92

4.1 Effect of Thermal and Lattice Mismatch ...... 93

4.1.1 Effect of Thermal Mismatch ...... 94

4.1.2 Effect of Lattice Mismatch...... 97

4.1.3 Discussion ...... 98

4.2 Microstructural Defects ...... 101

4.2.1 Microtwins ...... 102

4.2.2 Interface Restructure ...... 108

4.2.3 Threading and Misfit Dislocations ...... 111

4.2.4 Discussion ...... 116

4.3 Modeling ...... 116

4.3.1 Methodology ...... 117

4.3.2 Verification ...... 121

viii 4.4 Conclusions ...... 124

Chapter 5 Effects of Manufacturing Processes on Residual Stresses and Microstructures ...... 127

5.1 Effect of Temperature ...... 128

5.1.1 Measurement ...... 128

5.1.2 Results ...... 133

5.1.3 Discussion ...... 137

5.2 Effect of Implantation and Annealing ...... 143

5.2.1 Experiment ...... 144

5.2.2 Results and Discussion ...... 147

5.3 Conclusions ...... 161

Chapter 6 Conclusions and Future Works ...... 163

6.1 Conclusions ...... 163

6.2 Future Works ...... 166

References ...... 168

List of Publications ...... 181

List of Figures

Figure 1.1 Thesis structure ...... 7

Figure 2.1 Schematic of the growth modes ...... 11

Figure 2.2 Schematic of lattice mismatch accommodation ...... 12

Figure 2.3 Schematic of formation of misfit dislocations...... 13

Figure 2.4 Illustrations of (a) surface undulation and (b) misfit dislocations ...... 14

Figure 2.5 Schematic of (a) partial dislocation at the interface, and (b) repelling of

partial dislocations that produces a ribbon of stacking fault ...... 17

Figure 2.6 Schematic of mismatch stress release mechanism via undulated surface ...... 20

Figure 2.7 Schematic of the stress release via inter-mixing of interface atoms ...... 22

Figure 2.8 Schematic RI%UDJJ¶VODZ ...... 27

Figure 2.9 Schematic of X-ray rocking curve curvature method ...... 33

Figure 2.10 (a) R-plane sapphire and (b) crystallographic orientation of SOS ...... 39

Figure 2.11 Faults distribution in as-grown SOS studied by M.E. Twigg & Richmond

and M.S. Abrahams & Buiocchi ...... 42

Figure 2.12 Schematic of microtwins effects to the stress release ...... 44

Figure 3.1 General procedures for XRD stress tensor determination ...... 55

Figure 3.2 Diffraction peaks from Si powder ...... 56

x Figure 3.3 Coordinate system for XRD experiment ...... 57

Figure 3.4 XRD measuring directions in spherical diagram ...... 59

Figure 3.5 4-FLUFOH;¶3ert MRD diffractometer ...... 60

Figure 3.6 XRD high resolution configuration ...... 61

Figure 3.7 Surface stress uniformity examined by the Raman technique ...... 64

Figure 3.8 An etched SOS thin film ...... 66

Figure 3.9 Schematic of Raman photon stochastic behaviour ...... 68

Figure 3.10 Raman spectra and film thickness determination ...... 70

Figure 3.11 Residual stresses on etched SOS (tf>700 nm) ...... 71

Figure 3.12 Variations of residual stresses with film thickness ...... 72

Figure 3.13 A nonuniform surface of SOS sample etched below 50 nm ...... 73

Figure 3.14 Typical multi-layered thin films and the stress measuring techniques ...... 74

Figure 3.15 Schematic of a general multi-layered system ...... 76

Figure 3.16 XRD medium resolution configuration ...... 79

Figure 3.17 Schematic of multiple-reflections GIXRD technique ...... 79

Figure 3.18 Poly-Si XRD stress analysis (ahkl vs Khkl) ...... 81

Figure 3.19 XRD curvature measurement ...... 82

Figure 3.20 Rocking curves obtained from 6 points on the wafer surface ...... 83

Figure 3.21 Process-dependent bi-axial stresses in epi-Si ...... 85 xi Figure 3.22 Process-dependent stresses in poly-Si (ahkl vs Khkl ) ...... 86

Figure 3.23 Process-dependent radiuses of curvature ...... 88

Figure 4.1 Geometry of an SOS thin film system by FE simulation ...... 95

Figure 4.2 Coordinate systems in the sapphire crystal and in the R-plane ...... 95

Figure 4.3 Thermal mismatch stress contour by FE simulation ...... 96

Figure 4.4 Distributions of thermal mismatch stress ...... 97

Figure 4.5 Lattice mismatch stress contour from FE simulation ...... 98

Figure 4.6 Thermal and lattice mismatch stress variations with ts/tf ...... 100

Figure 4.7 TEM specimen preparations by Focus Ion Beam (FIB) ...... 101

Figure 4.8 Crystallographic relations between silicon and sapphire by FFT analysis .... 103

Figure 4.9 Planar defects distributions in as-grown SOS ...... 105

Figure 4.10 TEM images of twin intersections at interface...... 106

Figure 4.11 High resolution lattice images of twins/stacking faults ...... 107

Figure 4.12 EDS elemental analysis at the SOS wafer with film thickness of 280 nm .... 110

Figure 4.13 Microstructures and distributions of threading dislocations in SOS ...... 112

Figure 4.14 Threading dislocations at the boundary of planar faults ...... 112

Figure 4.15 A bright field HREM image showing mismatch of SOS interface ...... 114

Figure 4.16 Schematic of misfit and threading dislocations ...... 115

Figure 4.17 FE analysis scheme ...... 117 xii Figure 4.18 Schematic of an edge-type dislocation at interface and the FE model...... 119

Figure 4.19 FE simulations of lattice mismatch and dislocation effects ...... 120

Figure 4.20 Comparison of thickness-dependent stresses between experimental results

and FE simulation ...... 121

Figure 4.21 Justification of dislocation distribution effects ...... 124

Figure 5.1 The DHS1100 thermal stage in Phillips MRD ...... 132

2 )LJXUH5.2 En vs sin Ȍplot from high temperature XRD in as-grown SOS ...... 134

)LJXUH5.3 Temperature-dependent lattice constant a0 in as-grown SOS ...... 135

)LJXUH 7HPSHUDWXUH-GHSHQGHQWUHVLGXDOVWUHVVHVIURP;5'H[SHULPHQWV ...... 137

Figure 5.5 Comparisons of temperature-dependent stresses from XRD experiment and

FE calculation for an as grown SOS of 280 QP ......

Figure 5.6 Comparisons of temperature-dependent stresses from XRD experiment and

FE calculation for an as-grown SOS of 5 ȝP ......

Figure 5.7 Surface morphologies examined on the surface of SOS thin ILOPV ......

Figure 5.8 TRIM simulations of collision HYHQWV ......

Figure 5.9 Raman spectrums of implanted SOS VDPSOHV ......

Figure 5.10 Residual Stresses after room-temperature LPSODQWDWLRQV ......

Figure 5.11 Stress variations with annealing temperatures in implanted VDPSOHV ......

Figure 5.12 Comparison of residual stresses between 1-step and 2-step DQQHDOLQJ ......

xiii Figure 5.13 Schematics of microstructures for (a) as-grown, and (b) implanted 626 ......

Figure 5.14 Bright field image of annealed SOS at (a) 600 °C and (b) 1,000 °C ...... 155

Figure 5.15 Mechanism of threading dislocation reduction ...... 156

Figure 5.16 Relation of annealing temperature and film quality by FWHM ...... 157

Figure 5.17 Schematic of atomic structure (a) and (b), high resolution lattice images (c)

and (d), and low magnification bright-field images (e) and (f) for the 600 ºC

and 1,000 ºC annealed samples ...... 158

Figure 5.18 High resolution TEM image of sapphire lattice at the depth of 10 to 20 nm

beneath the interface ...... 160

xiv

List of Tables

Table 2.1 Comparisons of techniques for residual stresses characterization ...... 35

Table 3.1 Measured and calculated strains in 13 [hkl] directions ...... 62

Table 3.2 Strain DQGVWUHVVWHQVRUFRPSRQHQWVİij and ıij (i, j =1, 2, 3) obtained from

XRD expeULPHQWRQQPDQGȝP626 ...... 62

Table 3.3 Nominal and measured film thickness after wet etch ...... 65

Table 3.4 Process-dependent stress in epi-Si (complete stress tensor) ...... 84

Table 3.5 Equi-biaxial stress ı and stress-free lattice parameter a0 in poly-si ...... 86

Table 3.6 Residual stresses in amorphous SiO2 and Si3N4 layers ...... 89

Table 3.7 Summary of residual stresses investigations ...... 89

Table 4.1 Scenario for justification of dislocation distribution effect ...... 123

Table 5.1 Temperature-dependent silicon compliance ...... 135

Table 5.2 Temperature-depended residual stress form XRD measurement ...... 136

Table 5.3 Temperature-dependent residual stresses obtained by FE simulation ...... 138

Table 5.4 The implantation and annealing conditions ...... 145

Nomenclature

İlatt. lattice mismatch strain

İth. thermal mismatch strain

İdisl. dislocation induced strain

H disl. average strain induced by an array of misfit dislocations

g H i growth strain for a layer i

İhkl strain in a certain [h k l] direction

HÖ)< Residuals of strain in [h k l] direction obtained by least square technique

İĭȥ strain in laboratory coordinate

İCɎȥ strain calculated from the strain tensor

İij strain tensor

ı equi-biaxial stress

Vzz out-of-plane stress

Vrr in-plane normal stress

ılatt. lattice mismatch stress

ıth. thermal mismatch stress

xvi L ı i stress caused by the mismatch between the film layer i and substrate

ıij stress tensor (i,j=1,2,3 and i t j)

ıf film stress

ı(z) depth-dependent stress

Wrz interface shear stress

Ȝ wavelength for a characteristic x-ray

Ȝc wavelength of the perturbation exceeds a critical value

ĭ azimuth angle in diffraction

Ȍ inclinational angle in diffraction

Ȥ iso-inclinational offset

Ȧ x-ray rocking curve angle

ȣ 3RVVLRQ¶VUDWLR

Į coefficient of thermal expansion

D mean coefficient of thermal expansion

Eij coefficients for in strain tensor determination

Ȗ Lamé's first parameters

șhkl diffraction peak angle from (h k l) plane

0 ș hkl stress free diffraction peak angle from (h k l) plane

xvii P Lamé's second parameters

Pf unit volume absorptivity of the film

ur radial displacement

ᇞȦ Raman frequency shift

Ȧj frequency of a certain Raman mode under stress

Ȧj0 stress-free frequency of a certain Raman mode

ǻȦi angular difference of rocking curves in x-ray curvature measurement

ȡ substrate coverage on film growth

* eigenvalues for Raman secular equation a lattice constant

a0 stress free lattice constant

a0 (T) temperature-dependent stress free lattice constant

af lattice constant of the film

as lattice constant of the film substrate

ahkl equivalent lattice constant in direction [hkl] b EXUJHU¶VYHFWRU

Bij(n) directional coefficients in x-ray measurement (B11(n), B12(n), B22(n) in plane

stress case) c uniform strain in a multi-layered system xviii Cij elastic stiffness matrix

C11, C12, C14 elastic stiffness in cubic system

CBED convergence beam electron diffraction

CTE coefficient of thermal expansion

CVD chemical vapour deposition d distance to the interface

dhkl lattice spacing for a certain (h k l) plane

0 dhkl stress free spacing for a certain (h k l) plane

Ef Young¶s Modulus of thin film

Es Young¶s Modulus of substrate

Ei Biaxial Modulus of layer i in a multi-layered system

Ehkl elastic constant in [h k l] direction

EDS Energy Dispersive X-ray Spectrometry f lattice mismatch

Fa mismatch force of a bend dislocation

FT restoring force of a bend dislocation

FE finite element

FD number of faults (stacking faults and twins) per cm

xix FIB Focused Ion Beam

FV Frank and Van der Merwe, layer to layer film growth mode

FFT Fast Fourier Transformation

FWHM full width half maximum h k l miller index

hb local of bending axis in multilayer system

hc critical thickness for dislocation formation

Hc critical thickness for the cusps formation

I0 intensity of the incident beam

If Raman peak intensity from film

Is Raman peak intensity from substrate

HREM high resolution transmission electron microscopy

GIXRD grazing incidence x-ray diffraction

Kf scattering probability of absorpted Raman photon for the film

Ks scattering probability of absorpted Raman photon for the substrate

Khkl x-ray stress factor

MBE molecular beam epitaxy

MD misfit dislocations

MEIS medium energy ion scattering xx ns average spacing of dislocations

Nr radial membrane force

Nɽ circumferential membrane force p, q, k phonon deformation potentials in Raman technique

rijpq correlation coefficient for Eij in strain tensor determination

R wafer curvature

Ri wafer curvature of individual layer

Rz surface roughness

RSOS Radius of SOS wafer

RTA rapid thermal annealed

S distance of two points in x-ray curvature measurement

Sij elastic compliance matrix

S11, S12, S14 elastic compliance in cubic system

SOS silicon-on-sapphire

SV Stranski±Krastanov, layer to island film growth mode

SPE solid phase epitaxial c-Si crystalline silicon a-Si amorphous silicon

xxi T deposition temperature

TEM transmission electron microscopy

TRIM transport of ions in matter

T0 room temperature

tf thickness of film

t0 thickness of substrate in multi-layered thin films

ti individual layer thickness in multi-layered thin films

ur radial displacement

VW Volmer±Weber, island growth mode

VOI volume of interest

XRD X-ray diffraction z depth from film surface

xxii Chapter 1. Introduction ______

CHAPTER 1: Introduction

1.1 Motivation

In microelectronics, the silicon-on-insulator (SOI) system is ubiquitous, since it can improve the efficiency of the usage of silicon wafer, reduce the parasitic device capacitance, and thereby improve the performance. As a member of the SOI family, silicon-on-sapphire (SOS) has specific electronic applications because it can reduce noise

[Gentil and Chausse, 1977; Johnson, Chang et al., 1997] and power consumption [Boleky and Meyer, 1972; Fu and Culurciello, 2006] in metal oxide semiconductor transistors.

Because of its high insulation property and low parasitic capacitance, the sapphire substrate provides higher frequency and better linearity and isolation than the bulk silicon, and hence allows its application in highly-demanded areas e.g., the space and military system [Srour, Curtis et al., 1984]. Moreover, the development of ultrathin silicon-on- sapphire (SOS) technology enables greater data storage rates and lower power consumption, leading to smaller size and higher efficiency of telecommunications products.

1 Chapter 1. Introduction ______

For example, the SOS technology has been successfully used as the RF switches in iPhone

[James, 2007].

However, like other semiconductor film systems, the hetero-epitaxial deposition process of

SOS will inevitably introduce defected microstructures and residual stresses caused specifically by the crystal lattice mismatch and differential thermal expansion coefficients

(CTE) [Freund and Suresh, 2003]. The SOS wafer can break and the thin silicon film grown on the wafer can be distorted due to large residual stresses and microstructural defects, such as dislocations. The coupled effects of dislocations and residual stress will cause lower electron Hall mobility [Hughes and Thorsen, 1973], resistivity [Smith, 1954] and interface current leakage problem [Blochl and Stathis, 1999], which can often lead to the degradation of the SOS devices or even unusable wafers thus increase the cost of production, and those are the primary practical challenges associated with this heteroepitaxial system. Furthermore, excessive residual stresses can bring about mechanical failures such as cracking, delamination or buckling at the interface or sub-surface

[Raghavan and Redwing, 2005; Roder, Einfeldt et al., 2006] on the process or at the packaging stage, which leads to an ultimate rejection of the whole process.

In the light of this, a routine, non-destructive and accurate characterization of the residual stress in SOS fabrication processes is essential to ensure the quality and productivity of the

SOS devices.

2 Chapter 1. Introduction ______

1.2 Problem Definition

Semiconductor thin film systems are mostly of a multilayered structure. Thus a tri-axial stress state is expected and depth profiling is desired [Brewer, Peascoe et al., 2003].

Unfortunately, epitaxial films are of single crystal, which make determination of stress tensors difficult by using conventional XRD stress analysis. And for the ultra-thin films of hundreds of nanometres in use, the depth profiling of the stress is hard to resolve by using the conventional Grazing incidence XRD or Raman techniques. In addition, the final product of an electronic devices is generally of multi-layered thin film of various materials for ease of packaging [Egley, Gut et al., 1999] and passivation [Tan, Jong et al., 2009].

The deposition of these layers involves high temperatures and the atomic structure varies across the interfaces. Residual stresses are thus inevitable, which can cause mechanical failure [Itoh, Rhee et al., 1985; Agwai, Guven et al., 2008] if the stress in a single layer exceeds a critical value. An accurate and reliable stress analysis for multilayered thin film systems is essential. However, tR WKH DXWKRU¶V NQRZOHGJH RQO\ WKH DQDO\WLFDO model is available in estimating the stress in a multilayer structure when an amorphous layer is present, which involves a number of assumptions. To cope with all of the abovementioned issues, it is necessary to develop some experimental methods, which are based on traditional techniques such as XRD, Raman, curvatures measurement etc for a more detailed and systematic stress characterisation in the epitaxial materials.

The theoretical predictions of residual stresses have been based on the disparate lattice parameters and coefficients of thermal expansion (CTE), using the theory of elasticity.

Such predictions, however, are only valid for certain film thickness [Frank and Van-der-

Merwe, 1949; People and Bean, 1985], when the lattice mismatch can be entirely accommodated by the elastic strain. Beyond this critical thickness, the residual stresses are

3 Chapter 1. Introduction ______partially relieved by the formation of crystalline defects such as twins [Zhang, Liu et al., ,2007] and dislocations [Matthews and Blakeslee, 1974; Maree, Barbour et al., 1987].

The calculation of the stress relief is however not as simple as previously thought, since the interface defects are discrete and not uniform, and their interactions are complex.

Therefore, the mechanism of how the high level of mismatch strain was released is still disputable and the quantitative relationships between residual stresses and experimentally measured lattice defects have not been established. On the other hand, secondary stress relief could take place upon cooling [Hiramatsu, Detchprohm et al., 1993; Roder, Einfeldt et al., 2006] which makes the theoretical thermal stress prediction more complicated, and the uncertainties of CTEs could also introduce additional errors in stress calculation. For example, the CTEs of sapphire vary from literature to literature [Yim and Paff, 1974;

Reeber, 2000; Ball, 2006].

One of the approaches to improve the residual stress is choosing alternative parameters, such as growth temperature or thickness. Therefore, it is necessary to understand the individual effects of lattice and thermal mismatch to the residual stress. However, it is experimentally infeasible because the results from room temperature stress measurement always involve the superimposing of both effects. Thus, an integrated experimental analysis to decouple the lattice/thermal mismatch stress is another challenge.

To improve the crystalline quality and residual stresses, the improvement processes, i.e. implantation and annealing processes were proposed successfully as a cure for the prevailing defects [Lau, Matteson et al., 1979; Lee, Shichijo et al., 1987]. However, quantitatively, it is still unclear how different parameters such as ion dose density and subsequent annealing temperatures will affect the residual stresses in the SOS material.

4 Chapter 1. Introduction ______

1.3 Objectives and Thesis Structure

This research aims to remove the above technical and theoretical barriers, establish a comprehensive experimental system for residual stresses and micro-structural defect characterizations, and provide more in-depth understandings of the residual stress mechanism in the SOS wafer and general epitaxial thin films. The detailed objectives are:

Technically, to develop a systematic experimental model that enables characterizations of:

(a) the complete residual stress tensor in epitaxial ( single crystalline) thin films,

(b) the thickness dependence of residual stresses in thin film systems,

(c) the residual stresses distributions (e.g. epitaxial, polycrystalline, amorphous materials) in a multilayered thin films system;

And theoretically, to explore the actual residual stress generation and relief mechanism in as-grown SOS by incorporating the experimental results into theoretical thin film stress models. To this end, the following key questions should be answered:

(a) How does the thermal and lattice mismatch affect the residual stresses and residual

stress distributions in SOS?

(b) What is the actual mechanism for accommodating the lattice mismatch and thermal

mismatch stresses in a silicon-on-sapphire system?

(d) How does the residual stress vary with the temperatures?

5 Chapter 1. Introduction ______

(e) What are the effects of implantation and annealing on the residual stresses in an SOS

system?

As shown in Fig. 1.1, this thesis is divided into six chapters.

Chapter 1 : Chapter 3 : General Epitaxial Thin Films introduction Multi-layered Thin full stress tensor Development of Films thickness dependence experimental Chapter 2 : method Literature review verifications Chapter 4 : residual stress Microstructural Finite Element Origins and Chapter 6 : in epitaxial analysis of thin films Defects Modeling Conclusions residual stresses and future dislocations works residual stress measurement Chapter 5 : Implantation and Temperature Effects Effects of SOS system Annealing Effects manufacturing processes

Introduction Main research Conclusions

Figure 1.1 Thesis Structure

After a brief introduction in Chapter 1, Chapter 2 reviews the existing studies on residual stress mechanisms in thin film systems and the stress measurement techniques. A particular attention is paid to SOS system, which is the material used in this thesis research.

Chapter 3 describes the development of measurement techniques for characterizing the complete stress tensor and the thickness-dependent stresses of epitaxial silicon film and the stress distribution in multilayered thin films. To uncover the origin and release mechanism of residual stresses, in Chapter 4, we examine the microstructures by Transmission

Electron Microscopy (TEM) and proposed the finite element models, based on the interface structure observed, for more in-depth understandings of the stress distribution and 6 Chapter 1. Introduction ______release mechanisms. Chapter 5 studies the effects of the manufacturing processes on residual stresses. The temperature-dependent stresses were investigated by high- temperature XRD technique. The effect of re-growth of the film, through implantation and annealing, is also explored. The main conclusions and suggestions for further works are given in Chapter 6.

7 Chapter 2. Literature Review ______

CHAPTER 2: Literature Review

In this chapter, residual stress mechanisms in general hetero-epitaxial thin film systems and techniques for residual stress characterizations are reviewed. Particular focus is put on the existing studies of microstructural defects and residual stresses in the silicon-on- sapphire (SOS) system.

2.1 Residual Stress Mechanism in Epitaxial Thin Films

In a thin film system, residual stresses arise from satisfying the mechanical equilibrium of the film deposited on its substrate. There are two origins of residual stress in a generally thin film system. The first is, intrinsically, deposition-induced crystalline defects such as grain boundaries [Hoffman, 1976], voids [Doerner and Nix, 1988], and impurities

[Thornton, Tabock et al., 1979], etc. The second is, extrinsically, the dissimilar material properties (i.e. lattice parameter and coefficient of thermal expansion) between the film and substrate material [Gartstein, Lach et al., 1998; Kavouras, Komninou et al., 2000;

Roder, Einfeldt et al., 2006] . The superposition of these two mechanisms gives rise to the final residual stress distribution in a thin film system. 8 Chapter 2. Literature Review ______

During the film growth process, the film and substrate must be stretched or compressed to match the lattice parameter of the counterpart. In this case, considerable elastic energy is stored at the vicinity of the interface and lattice mismatch stress results. However, it has been experimentally evidenced that most of this lattice mismatch stress is released by forming interfacial defects such as misfit dislocations [Qian, Skowronski et al., 1997], twins and stacking faults [Petruzzello and Leys, 1988; W.Wegsheider and H.Cerva, 1993], etc. In order to obtain film with good crystalline quality, the films are generally deposited at high temperature (700-1,000ºC), inevitably leading to substantial stress after cooling.

This stress results from the dissimilar Coefficients of Thermal Expansion (CTE) and is termed ³thermal stress´. Thermal stress is generally considered to be the predominant source of residual stress in the literature. This is because the lattice mismatch stress can be fully released by forming lattice defects but the thermal stress can hardly be alleviated.

2.1.1 Lattice Mismatch and Lattice Defects

Lattice misfit stress is attributed to the effect that the dissimilar lattice parameters of the film and the substrate tend to match each other. In the general semiconductor thin films system, the film is always deposited on a stiff substrate (e.g. sapphire), and hence almost all of the misfit effect will be imposed only on the film. If both the film and the substrate are cubic in structure, the elastic strain H latt. imposed in the epitaxial layer is given by

[Freund and Suresh, 2003]:

aa sf H latt. f , (2.1) a f

9 Chapter 2. Literature Review ______

where af and as are the free in-plane lattice parameters of the film and substrate respectively. In most of the cases, the elastic strain H latt. is equivalent to the degree of lattice mismatch f. For an isotropic material, the equi-biaxial residual stress that arises from the misfit is:

E f V latt. ( )H latt. , (2.2) 1X f

where Ef and ȣf are the Young¶s Modulus and PoissRQ¶VUDWLRRIWKHILOP7KHUHIRUHfor a silicon film (ESi =166 GPa and ȣSi = 0.28 [Hull, 1999]), a lattice mismatch f = 5-15 % will produce enormous residual stress of 10-35 GPa, which is much more than the yield strength of silicon (7 GPa). This implies that in a high-misfit epitaxial thin film system, the lattice misfit stress must be released by forming microstructural defects such as dislocation, twins, stacking faults, interfacial new chemical compounds, etc.

Owing to the differences in film/lattice misfit, growth temperature and interface cohesive energy, there could be 3 growth modes of epitaxial film [Venables, Spiller et al., 1984] as illustrated in Fig. 2.1.

Frank and van der Merwe (FV) or layer-by-layer [Frank and Vandermerwe, 1949] growth involves the deposition of one monolayer at a time as shown in Fig. 2.1a, since the cohesive energy between the film and the surface atoms is greater than that of the film atoms and the lattice misfit is small. In contrast, Volmer±Weber (VW) or island growth

[Volmer and Weber, 1926] occurs when the cohesive energy of the atoms within the film is greater than that at the interface and the lattice misfit is significant, as illustrated in Fig.

2.1c. Besides these two extreme cases, the Stranski±Krastanov (SK) [Krastanov, 1938] or layer-island growth involves the growth of the first monolayer and then the growth of 10 Chapter 2. Literature Review ______islands, as illustrated in Fig. 2.1b, which is driven by the excessive strain energy that surpasses the interface cohesive energy, and hence island formation becomes more favourable.

ȡ < 1 ML

1 ML < ȡ < 2 ML

ȡ > 2 ML

(a) FV Growth (b) SK Growth (c) VW Growth

ML-monolayer ȡ - coverage

Figure 2.1 schematic of the growth modes (a) FV (layer-by layer), (b) SK (layer-island), and (c) VW (island growth) (after [Venables, Spiller et al., 1984])

The FV (layer-by-layer) growth mode is uncommon, and is always associated with a small misfit f<1 %, such as the InAs / GaAs (001) system studied by [Trampert, Ploog et al.,

1998]. In the case of a very small misfit, a perfect crystal structural can be obtained. In contrast, SK and VW growth modes occur under a larger lattice mismatch and/or at a high temperature (because the atoms can migrate more easily to form islands). SK and VW modes are more common than the FV mode in producing hetero-epitaxial thin films. And the high density of dislocations or planar defects, observed in the resulting films is induced by the coalescence of islands.

The mechanisms, through which the misfit is accommodated, and the formation of interfacial defects, which release the mismatch stress, are significantly influenced by the growth mode. In the following, misfit dislocations, twinning, and formation of new compound at the interface will be introduced in detail.

11 Chapter 2. Literature Review ______

(a) Misfit Dislocations

The lattice misfit strain (Eq. (1)) can be accommodated by the elastic deformation of film/substrate, especially when their lattice difference is small. In this case, the mismatch is accommodated by tetragonal distortions and no stress relaxation is expected (Fig. 2.2a). As the thickness of a strained film exceeds a certain value (i.e. critical thickness hc), it becomes energetically favourable to have misfit dislocations (MD), relaxing the misfit strain (Fig. 2.2b). The misfit dislocation can be regarded as an extra half-plane of atoms in the substrate or thin film that induces localized deformation.

Since the critical thickness hc is crucial, the theoretical prediction of it has been a focus of a wealth of researches in the past century. The models for critical thickness prediction are generally based on how the film grows.

(a) (b)

Figure 2.2 Schematic of lattice mismatch accommodation (a) fully strained layer with coherent interface (b) semi-coherent interface with misfit dislocations

The earliest work is by Frank and Vandermerwe [1949], who attempted to calculate this critical thickness by minimizing the energy of misfit dislocation array at the interface. A more accurate approach was proposed by Matthews and Blakeslee [1974] and Matthews

[1975], who considered the formation of misfit dislocation: a pre-existing threading

12 Chapter 2. Literature Review ______

GLVORFDWLRQEHQGVRYHUWRJHQHUDWHDOHQJWKRIPLV¿WGLVORFDWLRQLQWKHLQWHUIDFH as shown in

Fig. 2.3a, where h is the film thickness, hc denotes the critical thickness, Fa and FT are the mismatch force and the restoring force, respectively.

Epilayer Epilayer tf > hc FT Fa

Misfit Dislocation Substrate Substrate

(a)

Epilayer Epilayer

Misfit Dislocation Substrate Substrate

(b)

Figure 2.3 Schematic of formation of misfit dislocations via (a) propagation of an existing threading dislocation [Matthews and Blakeslee, 1974]; (b) nucleation of surface half loops and their expansion [Maree, Barbour et al., 1987].

The MB model is applicable in metal films but not in semiconductor films. In the diamond- and zinc-blend structure, the experimentally observed hc was always larger than that estimated in [Kasper and Herzog, 1977; Fiory, Bean et al., 1984]. Later on, Maree et al.

[1987] considered the kinetic barrier in the generation of misfit dislocations in semiconductor films. They argued that in semiconductor films the misfit dislocation results from the expansion of a dislocation half loop from the surface (Fig.2.3b). Based on this consideration, they proposed a theoretical relation between the critical thickness and the strain relaxation. Further works were to increase the accuracy in calculating the dislocation

13 Chapter 2. Literature Review ______core energy modeling [Beltz and Freund, 1994] and to account for the anisotropy effect

[Shintani and Fujita, 1994].

Unlike the FV growth, in layer-island (SV) growth the critical thickness is the transit point from the layer to the island based growth. In this model, besides the film/substrate mismatch the surface energy also plays an important role in determining hc. As shown in

Fig. 2.4a, surface undulations or islanding can result before misfit dislocations form to accommodate the strain energy, however, in the case of a larger mismatch or thicker film, misfit dislocations (Fig. 2.4b) will inevitably form to release the excessive strain energy

[Kukta and Freund, 1997; Schwarz-Selinger, Foo et al., 2002; Li, Liang et al., 2005]͘

Epilayer Epilayer

Misfit Dislocation

Substrate Substrate

(b) (a)

Figure 2.4 Illustration of (a) surface undulation and (b) misfit dislocations in SV growth

In the VW mode, misfit dislocation of the edge type can be formed within the island at the early stage of island growth [Chu, Szafraniak et al., 2004] or at the island corner/boundary where the island meets the substrate [Legoues, Reuter et al., 1994]. These dislocations can glide on the interface. The edge type dislocation was commonly observed in a highly mismatched system. For example in GaSb/GaAs (001) (lattice mismatch f = ±8.2 %), an array of edge dislocations with the average spacing of 57 ± 2 Å along each <110> direction

14 Chapter 2. Literature Review ______was observed by Qian et al. [1997], which nearly fully accommodates the mismatch strain.

Except for the conventional misfit dislocation rows, it is sometimes kinetically favourable for the dislocations to be arranged as misfit dislocation walls (MD walls). This mechanism was proposed by 2YLG¶.2 [1999], who speculated that the MD walls could be formed under non-equilibrium conditions in the process of convergence of islands, and that the misfit stresses in an island were partially released through the sloping of the edge surfaces of the islands, such that the dislocations are of 90° edge type arranged to form the walls.

The theoretical prediction of the critical thickness in island growth was conducted by Luryi and Suhir [1986], who found that hc depended on a critical diameter of the island. For an infinitely small diameter, an infinitely large critical thickness could be achieved, which enables the growth of a dislocation free film with larger thickness.

In epitaxial film, the Burger vectors b of the misfit dislocations is always equal to the smallest translation vector. For example the misfit dislocations in FCC crystals with b= a/2

[110] are orthogonally distributed along the in-plane [011] and the [01 ]1 direction, which could fully accommodate the lattice mismatch [Stowell, 1975]. A misfit dislocation cannot just terminate somewhere in the crystal but generally connects to the threading dislocations at the ends, which extend to the free surface. This high density of the threading dislcoations is the primary technical barrier for thin film applications in the semiconductor industry.

Theoretical predictions of the stress field around a straight edge dislocation have been the subject of many investigations. The earliest model was developed by Peierls and Nabarro

[1947], which was relatively simple but provided a method to bridge the continuum and atomistic theories. Van der Merwe [1950] then formulated a misfit dislocation with a semi- macroscopic approach based on Peierls-Nabarro model and described the equilibrium of an 15 Chapter 2. Literature Review ______interfacial shear force by Fourier analysis procedures. However, this model is complex with tedious mathematical calculations. Later on, researchers tried to modify these models to get more accurate analytical results [Nakahara, 1989; Bonnet, 1996; Yao, Wang et al.,

1999]. Nakahara improved the Van der Merwe model based on a continuous distribution of infinitesimal interface dislocations. Yao and Wang [1999] proposed a simple but exact analytic solution for the MD array and extended the Peierls-Nabarro model by incorporating the atomic simulation into the continuum theory. They unveiled both the core structure and the energy of misfit dislocation in their solution. A more sophisticated approach was suggested by Gutkin and Romanov [1992], who analyzed the stress field around a straight edge dislocation in the interface of two phase hetero-epitaxial plates based on continuum mechanics, directly applicable for the film on substrate system. Their result can be expressed as

f mn d 0 isy mn ) VV ),(),( eyxyx ) V ij sxs ),()( ds ij ij ³ ¦ , (2.3) f m 2,1 ,yxn

where the first term is the stress field around the dislocation being analyzed and the second term is to account for the effect of far field dislocations. Ɏmn(s) are Fourier transforms of

mn the distribution of the far field dislocations and VÖij sx ),( are the stress fields due to far field dislocations. The finite element solution of the stress field around an edge dislocation has verified this analytical solution [Moridi, Ruan et al., In Submission] .

16 Chapter 2. Literature Review ______

(b) Planar Fault

Energetically, a perfect edge dislocation is more favourably dissociated into partial dislocations, forming microtwins or stacking faults. In this case, the Burgers vector is smaller than a full lattice constant [J.P.Hirth and Lothe, 1982]. In the Fcc material, the most common twins were observed in ABC stacking sequence along <111> directions on the dislocations gliding plane {111}, formed by repelling of the partial dislocations as shown in Fig. 2.5. By forming these microtwins, the dislocation energy could be lowered and the sum of the Burgers vectors of the partials shown in Fig.2.5b equals that of the perfect edge dislocation.

Epilayer Epilayer Microtwins

glide plane {111} partial dislocations Substrate Substrate

(a) (b)

Figure 2.5 Schematic of (a) partial dislocation initiated at the interface (b) repelling of partial dislocation produce a ribbon of stacking fault

The mismatch accommodations by microtwins are typically in the layers subjected to tension such as in the super-lattice system of GaP/GaAsP and GaAsP/GaP observed by

Petruzzello and Leys [1988] or Si/Ge super-lattice on (001) Si substrate observed by

Wegsheider and Cerva [1993]. In these studies, the co-existence of twins (or stacking faults) and edge dislocations was always observed when the film is under tensile stress, and both the partial and edge dislocations will contribute to the accommodation of the lattice mismatch strain. On the other hand, in the case of compressive stress, only perfect

17 Chapter 2. Literature Review ______dislocation will form to accommodate the mismatch. These disparate behaviours were ratioanlized by Zhang, Liu et al.[ 2007]. They compared the critical thicknesses of the formation of microtwins and edge dislocations under both compressive and tensile stresses and also took account of the effects of film/substrate elastic constants mismatch. Their results concluded that forming partial dislocations were more favourable in film under tensile stress than compressive stress. When the film is under an increaseing tensile mismatch strain, the transit from perfect dislocation to partial dislocation occurs at the critical lattice mismatch f=3.8%.

It should be noted that although microtwins are quite common in most of the heteroepitaxial films, not all of these twins originate from the mismatch induced deformation.

High density of twins or stacking faults could even exist in a low mismatched system such as epitaxial GaP on (001)Si. In this system, the lattice mismatch f= 0.37 % is too small for the formation of deformation twins. Therefore the twins must generate from the intrinsic growth effects rather than the elastic deformation [Ernst and Pirouz, 1988].

The most plausible explanations for the growth of twins are the accommodation of the translational or rotational misalignments while the islands coalesce [Stowell, 1975 ] or formations of multiple domains during island coalescence [Abrahams, Buiocchi et al.,

1976; Trilhe, Borel et al., 1978]. The thickness of these growth twins is only one or two atomic layers [Hayashi and Kurosawa, 1978] but could be thickened during propagation

[Trilhe, Borel et al., 1978] or meeting with a substrate step [Mendelso.S, 1967].

18 Chapter 2. Literature Review ______

For the SV and VW growth mode, there is another mismatch accommodation mechanism, which is the evolution of the surface morphology. Conceptually, the surface morphologic modification is a consequence of the competition between strain energy and surface energy in hetero-structures. The most comprehensive review of this strain accommodation process was given by Hull and Stach [1999]. In their review, the correlation between strain accommodation and film surface morphological corrugation was analyzed in the GeSi/Si system.

There is a variety surface corrugations, including smooth undulations [Pidduck, Robbins et al., 1992], cusped roughening [Jesson, Pennycook et al., 1993], and island formations

[Snyder, Orr et al., 1991; Tersoff and Legoues, 1994] when relatively larger mismatches exist. In order to achieve the minimum energy, the atoms will diffuse or transport along the film surface. As schematically shown in Fig. 2.6, these mass transports will lead to stress relaxations at the peaks of islands or undulations and a stress concentration at the troughs.

The re-distribution of stress can therefore lower the total elastic energy of the system.

Furthermore, the stress concentrations at the edges or the troughs of the undulations (cusps) could facilitate the formation of misfit dislocations by providing nucleation sites for the half-loops. These half loops under the large residual stresses can expand beyond their critical radius, leaving misfit dislocations to further accommodate mismatch strain. The nucleation of dislocations via this roughened surface was experimentally observed by

Jesson et al. [1993].

19 Chapter 2. Literature Review ______

stress relieved stress relieved

atomic flux atomic flux

high stress concentration

Figure 2.6 Schematic of stress release mechanism via undulated surface

Gao [1994] identified the critical thickness Hc for the formation of cusps, which was achieved by considering an instability with infinite wavelength evolving under plane strain conditions. His result shows that Hc is significantly larger than hc from Matthews¶ model for misfit dislocations, implying that the nucleation of threading dislocations via cusp-formations could be critical in the overall process of strain accommodation.

Based on AFM observations of the growth process of the VPE Si 1-xGex (x=0.20-0.26) alloy layers, Pidduck et al. [1992] summarized 3 critical stages of the surface modification:

(I) isotropic roughing with flat-topped islands during initial growth;

(II) further roughening with increased period (~150 nm) and amplitude (~10 nm),

where regular arrays of undulations along the orthogonal [100] and [010] directions

contributed to pure elastic strain relaxation during pseudomorphic growth;

(III) forming dominant roughs along <110> axes and misfit dislocations to

accommodate mismatch strain.

20 Chapter 2. Literature Review ______

After Stage II, they found that the fluctuations of micro strain along the film surface were associated with film thickness variations, which was observed from the local strain field by transmission electron microscopy (TEM). This confirms that the surface modification indeed contributes to the local stress relaxations. By this means, the total strain energy of the epilayer could be reduced when the wavelength of the undulation exceeds a critical

value Ȝc . Srolovitz [1989] further showed that Oc is inversely proportional to the lattice mismatch strain H latt. .

(d) Formation of interface new compounds

In some thin film systems with high lattice mismatch, the straight prediction of residual stresses based on disparate lattice parameters may be invalid. Even for the lattice mismatch strain up to 10 %-20 %, the residual stress may be insignificant. This is because of the formation of new compound at the interface [Schulz, 1951; Engel, 1952].

This intermediate new structure was theoretically rationalized by Rao and Jacob [1982], which was based on thermodynamic calculations of the chemical reactions in silicon on sapphire (SOS) hetero-epitaxial system. Their results showed that SiO2 and Al6Si2O13 were the most likely products from the interface reactions. These products would form a new interface layer, and mitigate the high lattice mismatch strain. This phenomenon was proved by Ponce [1982] using high resolution TEM (HREM) observations. However, it is still unclear whether and how much these interface new compounds contribute to the stress release.

On the other hand, the inter-mixing of atoms at the interface shown in Fig 2.7 allows the film and substrate to share the strain, and hence lowers the total strain energy of the system.

21 Chapter 2. Literature Review ______

The best example was the Ge/Si (100) system. By medium energy ion scattering (MEIS),

Copel and Reuter et al. [1990] observed that the mismatch strain led to the intermixing of

Ge and Si atoms up to the second and third Ge layer of the initial growth. This intermixing therefore accounts for the observed stress reductions.

Figure 2.7 Schematic of the stress relief via inter-mixing of the interface atoms

2.1.2 Thermal Mismatch

In industrial applications, the films are generally deposited at high temperatures ranging from 700 to 1,000ºC, and this will inevitably produce substantial stresses due to the dissimilar CTE of film and substrate material. For a cooling from deposition temperature T

th. to room temperature T0, the isotropic thermal stress ı is given by:

th E f V D ' TT 0 , (2.4) 1X f

where Ef and Xf are respectively the

1 T 'D 'DdT is the mean differential CTE of film and substrate integrated from 'T ³ T0 deposition temperature to room temperature. When the film is much thinner than the

22 Chapter 2. Literature Review ______

substrate (i.e. tf << ts), the effect of thermal mismatch is merely reflected by the residual stresses in the thin film. It has also been ascertained by analytical studies that the thermal stress is nearly uniform along the film thickness direction if the boundary effect is negligible [Hsueh, 2002].

One problem in predicting the thermal mismatch stress is the uncertainty of the temperature-dependent CTE of the film. All the factors such as film thickness [Wu,

Vanzanten et al., 1995; Fang and Lo, 2000], microstructural defects [Fang and Lo, 2000], and the presence of residual stresses [Wang, Hoffmann et al., 1999] could affect the value of CTE. It is then crucial to determine accurately the value of CTE because a slight change in ƸD can lead to significant error in residual stresses.

The thermal mismatch stress could also be relieved by internal defects or surface undulation during cooling΀Hiramatsu et al., 1993; Simon et al., 2005]. In this context, the prediction of thermal stress becomes more complicated and the straight prediction based on

Eq. (2.4) is unreliable.

One possible mechanism for the release of thermal mismatch stress is via enhancing of the existing microstructural defects. This mechanism was used to explain the thickness- dependent stresses observed in GaN on a sapphire system by [Hiramatsu, Detchprohm et al., 1993]. They demonstrated the consistency between the theoretical calculation of effects of substrate defects and the experimental measurement, and concluded that the stress release had a strong dependence on the film thickness tf : (a) when tf < 4 ȝPthe residual stresses are fully accommodated by the defect microstructures (e.g. misfit dislocations) formed during film growth, whereas thermal mismatch effect could not introduce more stress release; (b) if ȝP < tf ȝP WKH thermal mismatch will have an enhancing

23 Chapter 2. Literature Review ______effects on the existing microstructural defects, and therefore further release the residual stress; (c) when tf > 20 ȝPmore severe defects (i.e. macro-cracks) in the substrate will induce a complete release of thermal mismatch stresses. However, the effects of microstructural defects are difficult to be quantified experimentally, because it requires an accurate measurement of the density of defects and a sophistic model for describing their interaction.

Roder et al. [2006] examined the residual stresses in a-plane GaN film on an r-plane sapphire system with thicknesses ranging from 0 to ȝP7KH\FRUUHODWHGWKHUHVLGXDO stresses with the curvatures in two in-plane directions, and found that the bending curvatures increased with the increased film thicknesses. The curvatures were found larger along the GaN [0001] direction than the [ 11 00] direction, which is consistent with the anisotropy of the residual stresses caused by dissimilar CTE. Hence, they ascribe the relief of thermal stress to the wafer bending, whereas the sub-surface cracks and crystal defects play a minor role.

In addition, surface morphologic modifications during cooling could also contribute to the relief of thermal mismatch stress. In the experimental study done by Simon et al. [2005], stress reduction was observed in epitaxial (Ba0.6Sr0.4)TiO3 when the film thickness was larger than 600 nm. On the surface of these films, obvious undulations were observed, and the amplitudes of the undulations depended on the film thickness. Another important feature they observed was that the planar orientation of the surface roughening showed consistency with the anisotropic stress. They then ascribed this phenomenon as the result of thermal stress relief, which is based on the mechanism proposed by Freund [1992]. In this model, the release of strain energy was achieved by the increase of surface energy via

24 Chapter 2. Literature Review ______high temperature mass transports, which normally happens during film growth or the subsequent cooling process.

2.1.3 Summary

In summary, the lattice mismatch strain/stress accommodations in a hetero-epitaxial thin film system are basically the interplays amongst the strain energy, surface energy, and dislocation energy. Besides, an inherent effect such as the interface bonding energy also plays an important role in stress relief, since it is one of the key factors in determining the growth mode of the epitaxial films.

In a low mismatch system under layer-by-layer (FV) growth, when the film is below a critical thickness hc, the lattice mismatch could be fully accommodated by the elastic deformation; however, this is uncommon because interface misfit dislocations are easily formed when the film thickness increases by even several atomic layers.

In the case of layer-to-island (SV) mode, for example, in the Ge/Si epitaxial system, the epitaxial film is more likely to undergo surface morphological modifications prior to dislocation formation. By this means, the total strain energy could be partially mitigated.

Although it was believed that the morphological modifications only account for a small amount of stress release, the cusp defects at the surface could provide nucleation sites for dislocations, which would indirectly promote further stress relief.

Amongst the abovementioned mechanisms, misfit dislocation of the edge type is the most effective for residual stress release, which is more common in the system with f >5 %. On the other hand, when f <5 %, the formation of partial dislocations (microtwins) is more

25 Chapter 2. Literature Review ______likely. These partial dislocations were more commonly observed in films subjected to tensile stress than compressive stress; however, it should be noted that elastic deformation is not the only source of twin formation. During island coalescence, twins could also be formed to accommodate the islands misorientation, namely growth twins. Thus, identification of the stress relaxation mechanism requires more rational analyses than direct experiment observations.

In addition, in systems with high lattice mismatch (e.g. f=10 %-20 %), chemical reactions could take place, which would modify the interface structures by forming intermediate new compounds, and therefore mitigate lattice mismatch stresses.

The thermal mismatch effect is dominant in the final residual stresses, which is determined by the deposition temperature and the differential CTE of film and substrate. Generally, the residual stress is independent of the film thickness, provided that the film is considerably thinner than the substrate, i.e. tf<

2.2 Residual Stress Measurement

The purpose of this section is to review techniques for characterizing residual stresses in general epitaxial thin films. Amongst different techniques, attention will be paid to X-ray diffraction (XRD), Raman scattering, and substrate curvature measurement.

26 Chapter 2. Literature Review ______

2.2.1 X-Ray Diffraction (XRD)

The XRD technique is the most established technique for analyzing residual stress in crystalline materials. It is based on the well-NQRZQ %UDJJ¶V /DZ [Bragg, 1913] schematically shown in Fig. 2.8.

[hkl]

dhkl ș dhkl sinșhkl

Figure 2.8 6FKHPDWLFVRI%UDJJ¶VODZ

With the Bragg¶s law, the atomic distance dhkl along a certain crystallographic direction

[hkl] could be correlated to the diffraction peak angle șhkl, such that the path difference of two x-rays 2dhklsinșhkl will be equal to an integer number of wavelength, i.e.

2dhkl sinThkl nO (n=1, 2, 3), (2.5) where Ȝ is the wavelength of the characteristic x-rays (e.g. Ȝ=1.540598 Å for copper

radiation). The strains H hkl in the crystallographic [hkl] direction can be obtained by:

dd 0 hkl hkl , (2.6) H hkl 0 d hkl

27 Chapter 2. Literature Review ______

0 where dhkl is the stress-free lattice spacing of the measuring planes (hkl). Solving d hkl and

0 dhkl Eq. (2.5) and substituting them to Eq. (2.6) lead to

S H 2'u cotTT 0 , (2.7) hkl 360 hkl hkl

0 where Thkl denotes the stress-free diffraction angle and 'Thkl are the difference of diffraction peak angle between the stress-free and stressed lattices. From Eq. (2.7), it is

0 obvious that higher diffraction angles Thkl are desirable to minimize the effect of the error in determining șhkl .

The standard procedures and analysis of residual stresses by the XRD technique have been widely studied in polycrystalline materials. Detailed reviews were given by Noyan and

Cohen [1987], Welzel et al. [2005]. In poly crystals, the relationship between the measured strain Hhkl and stress components ı11, ı22, ı33 is given by Dolle, Hauk et al.[1976] and Dolle

[1979]:

X H hkl 11 22 u VVV 33 Ehkl

1X 2 2 2 u[ V 11 cos V 22 sin V 12 sin 2 sin <))) , (2.8) Ehkl 2 V 33 cos V 13 cos V 23 sinsin <))< ]2

where ±Ȟ/Ehkl and (1+Ȟ)/Ehkl are the X-ray elastic constants, which can be determined by the Vook±Witt Grain Interaction Model [Vook and Witt, 1965]; ĭ and Ȍ are respectively the azimuth and inclinational angle in the laboratory coordinate, relative to the x-ray coming direction. With a series of measurement directions determined by ĭ and Ȍ, a

28 Chapter 2. Literature Review ______complete strain tensor can be derived from well-known equations given by [Noyan and

Cohen, 1987] :

22 2 İĭȌ H hkl cos sin 11 sin 2 sin 12 cos sin 2 İȌĭİȌĭİȌĭ 13 , (2.9) sinsin 22 sinsin İȌĭİȌĭ 12 sin 2 İȌ 22 23 33

where İĭȌ is equivalent to H hkl , which is the measured strain along [hkl]; İ11, İ22 , İ33 , etc are the strain tensor components in the sample coordinate. There are three main methods for sovling the residual strains/stresses from the XRD measurement:

(a) Conventional dhkl-sin²Ȍ method: The advantage of this method is that the error

0 associated with stress-free d hkl can be avoided, since the residual stresses are determined by the slope of the dhkl-sin²Ȍ. However, in order to determine a tri-axial stress state, it requires at least 3 sets of ȥ at certain ĭazimuth angles, which is difficult to obtain in mono-crystalline materials.

(b) Least Square method: Compared to the dhkl-sin²Ȍ method, the least square method

[Winholtz and Cohen, 1988; Ward and Hendricks, 1997] is more robust to solve the single crystal tri-axial residual stress measurement issue. In this method, more arbitrary diffraction directions obtained from multiple [hkl] asymmetric diffractions could be utilized, which gives rise to higher accuracy by solving over-determined linear equations.

0 However, the limitation of this method is that d hkl should be pre-determined accurately,

0 otherwise the errors in d hkl could result in the error of hydrostatic components in a stress tensor.

29 Chapter 2. Literature Review ______

Suzuki, Akita et al., 2003; Imafuku, Suzuki et al., 2008] for single crystal stress analysis when a plane-stress condition was satisfied. With this method, stress free lattice constants

0 d hkl can be solved as an intercept of the multiple regression system. However, to determine an accurate tri-axial stress tensor, much more measuring directions (more than twenty directions) are required to avoid the multi-collinearity problem [Weber and Monarchi,

1976; Fernandez, 1997]. Practically, for single crystalline materials, the measuring directions are limited by the inadequate number of crystallographic (hkl) planes that contribute to diffraction. In this context, the least square method is more appropriate if the

0 stress-free d hkl has been reliably obtained.

Measuring depth profiling of residual stresses is difficult. The grazing incidence x-ray diffraction (GIXRD) technique is most commonly employed. However, this technique is only appropriate for polycrystalline materials provided that the film is thick enough so that the whole film thickness could be resolved with the resolution of sub-microns. A more detailed description of this technique can be found in [Stoev and Sakurai, 1999; Bubert and

Jenett, 2002]. For epitaxial thin films, the conventional GIXRD is not applicable for resolving the depth-dependent stresses since only limited incidence angles can lead to diffractions and very low incidence angles (normally < 1°) are infeasible in single crystal materials.

2.2.2 Raman Spectroscopy

Raman spectroscopy is another technique extensively employed for residual stress measurement. It provides a straightforward and fast stress examination in nonmetallic materials. One of the best reviews of Raman stress analysis was done by DeWolf [1996]. 30 Chapter 2. Literature Review ______

The basic principle is that the strain in the crystal affects the Raman phonon frequency, which can be solved from the well-known secular equation [Anastass.E, Pinczuk et al.,

1970; Ganesan, Maradudi.Aa et al., 1970] :

11 qp HHH 3322 * 2kH12 2kH13

2kH12 22 qp HHH 1133 * 2kH 23 0 (2.10)

2kH13 2rH 23 33 qp HHH 2211 *

where p, q and k are the material constants, i.e. phonon deformation potentials, and İij are the strain tensor components, which can be calculated from 3 input of eigenvalues *j. *j are related to the frequency of Raman mode Ȧj under residual stress and the stress-free

2 2 frequency Ȧj0, i.e. *j Ȧj ±Ȧj0 .

Normally, 3 Raman modes are not adequate for solving 6 unknowns of the strain tensor components. Therefore, the model should be simplified by a pre-identified stress state by other techniques such as XRD [Wolf, 2003]. For a simple stress status, e.g. uniaxial or equi-biaxial stress, the Raman scattering technique is more convenient than XRD, owing to the overwhelming advantages of faster spectrum acquisitions and higher spatial resolution

(<ȝP2).

The depth-dependent stresses in the Raman scattering technique are achieved by a confocal mode [Bruneel, Lassegues et al., 2002] in the laser configuration. By this means, a series of resolved focusing volumes is obtained across the film thickness. However, the depth information estimated by this confocal technique is unreliable due to the effects of refraction on the depth resolution and spatial accuracy [Everall, 2000]. Another approach is to employ multiple Raman wavelengths. For example, the excitation lines with wavelengths of 514.5 nm, 488 nm, and 457.9 nm provide different penetration depths of 31 Chapter 2. Literature Review ______

770 nm, 570 nm and 320 nm respectively in silicon [DeWolf, 1996]. Unfortunately, both of the confocal and multi-wavelength techniques are incapable of resolving the stress variation in very thin films of hundreds of nanometres.

2.2.3 Curvature Method

Curvature (or substrate curvature) is the most conventional method for stress measurement in thin film materials. Unlike the XRD and Raman techniques, the main advantage of the curvature method is that the film layer is not necessarily crystalline. This method was first proposed by Stoney [Stoney, 1909]. In his study, the relation of the film stress ıf and the wafer bending curvature R is given by:

2 tE ss V t ff , (2.11) 16 Xs R

where tf and ts are respectively the thicknesses of the film and substrate; Es and ȣs are the

The assumptions are: (a) the residual stress should be uniform across the wafer surface as well as in the direction of film growth, (b) the film should be considerably thinner than the substrate, i.e. tf<

A great number of studies focused on the way to remove these assumptions. Timoshenko

[1925], Rich [1934] and Klein [2000] relaxed the assumption of very thin film thickness, 32 Chapter 2. Literature Review ______and extended the method to thicker films. The uniform stress distribution was then relaxed by Freud and Suresh [2003]. Huang and Rosakis [2005] further H[WHQGHG6WRQH\¶VIRUPXOD to non-uniform temperature distribution in a thin film/ substrate system.

With a high resolution configuration, the wafer curvature can be measured by X-ray rocking [Yua, Lai et al., 2008]. As shown in Fig. 2.9, the radius of curvature R is calculated from the geometrical relationship between distance S on the wafer surface and

WKHDQJXODUGLIIHUHQFHRIURFNLQJFXUYHVǻȦ in X-ray diffractions, i.e., Z RS .

R Ȧ+ǻȦ Ȧ

Figure 2.9 Schematic of X-ray curvature method

Most of the analytical models describing curvature-stress relations are based on classical beam theory and the compatibility of interface strains. The early studies were constrained by no more than two layers because both the number of unknowns and the number of continuity conditions increase with an increasing number of layers. To solve the stress problems in a multi-layered system, Hsueh [2002, 2006] proposed an analytical model based on their previous study in a bi-layer system [Hsueh and Evans, 1985]. In this model, the total strain was decomposed into a uniform strain component and a bending strain component, so as to satisfy the strain continuity condition. The advantage of this solution is that there are always only three unknowns and three boundary conditions regardless of the number of layers in the system. Thus, a closed-form solution with different elastic moduli

33 Chapter 2. Literature Review ______for each layer was formulated. His work indicates that the deposition of the additional layers in a multi-layered system does not affect the residual stress of the existing layers.

However, in hetero-epitaxial thin films, incoherent or semi-coherent interfaces are always formed, associated with high density of the defects such as dislocations and twins, which would make stress analysis by the traditional curvature method erroneous.

2.2.4 Summary

In summary, a proper residual stress characterization needs a description of the full stress tensors and stress distributions either within the individual layer or across multi-layers.

Table 2.1 lists the advantages and capabilities of residual stress characterization techniques.

XRD is superior to other techniques in characterizing a full stress tensor; however, the main challenge is that the diffraction planes in single crystalline (or epitaxial thin films) materials are inadequate, which could induce large errors in strain/stress tensors. In addition, in order to obtain sufficient intensity, the beam size is normally in centimetre squares, such that a localized stress variation cannot be resolved. To determine the tri-axial stress tensor more than ten diffractions from the (hkl) planes are required, which is more time consuming than other techniques such as the Raman and curvature methods.

The Raman scattering technique is capable of measuring localized stress with a high spatial resolution (i.e. ȝP2). However, it should be noted that the stress state (e.g. biaxial or axial) should be pre-determined by another technique such as XRD. Otherwise the stress obtained will be erroneous. If an equi-biaxial or uniaxial stress state is satisfied, the Raman technique could be employed as the standard stress analysis tool, with which the residual stress measurement would be accomplished within several minutes.

34 Chapter 2. Literature Review ______

Table 2.1 Comparisons of residual stress charactering techniques.

Stress Film Spatial Techniques Literatures Assumptions Accuracy Tensor Materials Resolutions

Noyan and uniform stress 1 mm2-1 cm2 Cohen [1987], within XRD tri-axial crystalline ±20 MPa depends on Welzel et al. measuring optics [2005]. area

DeWolf [1996], pre- [Bruneel, axial, non-metal, Raman determined ±30 MPa ȝP2 Lassegues et al., bi-axial crystalline stress state 2002]

tf<

The conventional methods such as XRD and Raman techniques are not able to directly measure stresses in amorphous layers. Although the traditional curvature method is capable of determining the stress in amorphous films, it is only applicable if there is only one film layer. To extend the curvature method to a multi-layered system, the stresses in crystalline layers must be pre-determined by other means.

2.3 Silicon on Sapphire (SOS) System

Silicon-on-sapphire (SOS) thin film systems have specific electronic applications because they can reduce noise and current leakage in metal oxide semiconductor transistors.

However, there are still some issues in producing defect-free SOS wafers. Dislocations, mismatch, micro twins and residual stresses can emerge during the SOS processing and they will reduce the performances of a SOS product. This section is to provide a thorough review of production, defect formation and residual stress characterizations of SOS, which is also the focus of this thesis.

35 Chapter 2. Literature Review ______

2.3.1 Production and Crystallography

(a) Production

The technology for SOS wafer manufacturing was invented in 1963 in North American

Aviation California as reported by Manasevit and Simpson [1964]. Single-crystal deposits of silicon on sapphire crystal were obtained via H2 reduction of SiCl4 at high temperature.

The deposition was on the plane produced by cutting a sapphire rod perpendicular to its fastest growth direction. The quality of the deposited film was found sensitive to the crystal orientation of the substrate.

Since then many methods have been applied for making SOS thin film systems, such as chemical and physical vapour deposition techniques. Weisberg and Miller [1968] used the physical vapour deposition in an oxygen free evaporation system to produce improved crystal. Silicon was sublimed from its solid phase at about 1,390 °C using an electron

ERPEDUGPHQWV\VWHP7KHGHSRVLWLRQUDWHDFKLHYHGZDVWRȝPSHUKRXUWRJHQHUDWHD

ILOPWKLFNQHVVRIWRȝPDWDERXW(-8 Torr. It was found that the use of an ultrahigh vacuum (around 2E-9 Torr) does not significantly improve the results in the oxygen-free system.

The best crystalline quality was obtained in the range of 780 to 1000 °C. Naber and Oneal

[1968] deposited silicon thin films by electron beam evaporation in an ultrahigh vacuum on the (0001) and ( 11 02 ) planes of sapphire substrates. They considered different deposition temperatures (500 to 1,000 °C), different deposition rates (50 to 700 Å/min) and different sapphire surface treatments. They found that mechanically polished substrates had poor reproducibility and crystallinity of silicon films at 800 to 1,000 °C, that single

36 Chapter 2. Literature Review ______crystal and twinned silicon films would form at 700 to 1,000°C on a treated substrate

(silicon etched at 1,300°C), and that fibre textured films would form at low temperatures between 500 to 700°C.

Abrahams et al. [1976] examined the microstructure of chemical vapour deposited (CVD)

SOS wafers to investigate their early growth. The Si layer was grown on the ( 01 21 ) plane at a nominal rate RI ȝPPLQ E\ WKH S\URO\VLV RI VLODQH LQ +2 at 1,000°C. Under a transmission electron microscope, they found micro-twins, stacking faults and misorientation in the Si thin films.

An SOS deposition process is complex and is influenced by many factors. Defects can originate in the vicinity of a silicon-sapphire interface at an early stage of the film growth.

Twins and stacking faults can form while small growth centres having four (110) orientations on ( 11 02 ) sapphire substrates coalesce until they are trapped by the surrounding (100) domains [Abrahams et al., 1976]. Misfit dislocations also exist in SOS wafers [Abrahams et al., 1976]. The formation of the Si layer with small crystallization defects is extremely difficult as the lattice unconformity between the sapphire substrate and

Si thin film is up to 5.7 % and 12.4 % respectively along Si [100] and Si [010] directions.

This mismatch heteroepitaxy remains as a formidable obstacle in the further development of SOS device products.

Recently, some re-growth techniques have been developed to reduce the defects. The first step is to amorpharise a Si thin film by silicon [Inoue and Yoshii, 1980] or oxygen

[Yamamoto, Wilson et al., 1979] ion implantation. Then thermal [Yamamoto, Wilson et al., 1979; Inoue and Yoshii, 1980] or laser [Roulet, Schwob et al., 1979] annealing is used to make the solid phase epitaxially re-growth. The optimum implantation conditions [Inoue

37 Chapter 2. Literature Review ______and Yoshii, 1981] were found to be: (a) the projected range of silicon ions should be around 0.8 times of the Si film thickness, (b) the residual surface crystalline layer should be 0.2 to 0.3 times the deposited Si thickness, and (c) the thermal annealing should be conducted at more than 600 °C in N2 ambient. A higher temperature annealing could lead to more defect reduction [Inoue and Yoshii, 1980] . Two-step growth was also applied to reduce the defects in SOS wafers [Ishida, Tanaka et al., 1988], in which a pre-deposited amorphous thin Si layer was used.

Growing the Si films on sapphire at lower temperatures has been found to be another solution to reduce defects. Si films can be grown at 650 to 800 °C by silicon molecular beam epitaxy (MBE) using an electron gun evaporator. In this case, the Si layer coalesced at a thickness of 500 Å and became smooth at 2000 Å [Bean, 1980]. It has been reported that a better silicon thin film can be grown on sapphire substrates at low temperatures by gas-source silicon MBE using disilane (Si2H6) [Sawada, Ishida et al., 1989], although defects do occur. However, no further research or practical applications have been found about this process.

On the other hand, it has been reported that SOS wafers can also be prepared by a direct wafer bonding method [Imthurn, Garcia et al., 1992], in which a thin silicon wafer is first bonded to a polished sapphire substrate and then is further thinned down to a required

WKLFNQHVV HJ § ȝP E\ PHFKDQLFDO JULQGLQJ DQG FKHPLFDO HWFKLQJ ,W KDV EHHQ claimed that this type of SOS wafer has a better performance compared with the epitaxially grown ones.

In comparison with CVD SOS, the key issues in molecular beam epitaxy (MBE) and bonded SOS are the low throughput and high cost, which is the main constraint in

38 Chapter 2. Literature Review ______industrial applications. In this context, it is of primary importance to improve the crystal quality of conventional CVD SOS, to achieve high quality, high throughput and low cost

SOS wafers. Ultra Thin Si (UTSi®) has been developed by Peregrine Semiconductor to improve the quality of the Si thin film on sapphire. This has accelerated commercialization

RI626GHYLFHV3URFHVVHVIRUȝPDQGȝPWKLFN6LILOPVRQVDSSKLUHKDYHEHHQ developed. The UTSi® technology is very much similar to that of the re-growth method, but the process parameters used in UTSi® to improve the thin film quality have been kept confidential.

(b) Crystallographic orientations and growth mode

As shown schematically in Fig. 2.10a, in a hetero-epitaxial SOS system, a silicon film of

(001) orientation is grown on the sapphire (10 21 ሻplane, with the nominated mismatches f up to 5.7 % along Si [100] and 12.4 % along Si [010] (Fig. 2.10b). In this system, the cohesive energy between silicon atoms is greater than that at the interface. The large lattice mismatch then leads to island growth. 12.4 % 12.4

5.7%

Si[010]||Al2O3[1120]

Al atom

Si atom Si[100]||Al2O3[1101]

(a) (b)

Figure 2.10 (a) R-plane sapphire, (b) crystallographic orientation of silicon and sapphire 39 Chapter 2. Literature Review ______

From a TEM experiment, Hamarthibault and Trilhe [1981] observed the formation of small islands at the initial stage of SOS deposition. These islands were incoherently grown on the sapphire surface, and exhibit characteristics of VW growth. In their study, two orientations were observed after a very short time of deposition, i.e. a majority of {100} domains and some minority {110} oriented domains. Twin pairs were present in the {110} domains, which were lying on the {111} planes and parallel to the [011] and [ 110 ] directions of the

{100} oriented domains. Their investigation also showed that the film consist of square or rectangular islands with {100} orientation, exhibiting a mosaic like structure at the early growth, and becoming more uniform as the film thickness increased. As the growth proceeded, the size of {100} domains increased rapidly, whereas {110} domains remained constant (around 400 Å) [Abrahams, Buiocchi et al., 1976; Hamarthibault and Trilhe,

1981]. After about 1s growth, the hemispherical Si islands were resolved, expanding themselves on the sapphire surface rather than forming new agglomerates. The complete surface coverage film thickness depends on the deposition temperature, varying from 200

Å at 1,000 ºC to 2,000 Å at 1,100 ºC [Cullen, 1978].

2.3.2 Micro-structural Defects

(a) Defect microstructures and distributions

Some early studies used TEM to reveal a high density of defects [Abrahams, Buiocchi et al., 1976; Lihl, Oppolzer et al., 1980; Hamarthibault and Trilhe, 1981; Phillips, Batstone et al., 1987; Aindow, Batstone et al., 1989; Twigg, Richmond et al., 1990; Batstone, 1991] in

SOS, among which micro twins are predominant [Hamarthibault and Trilhe, 1981;

Batstone, 1991]. The microtwins were found lying on the four {111} planes, which exhibit anisotropy in the two subset {111} planes [Abrahams and Buiocchi, 1975; Ham, Abrahams 40 Chapter 2. Literature Review ______et al., 1977; Batstone, 1991]. In these observations, the majority subset twins were found lying on the ( 111 ) plane, whereas the minority subset twins were lying on the ( 111) planes.

This anisotropy of microtwins was induced by the stochastic nature of mis-stacking twins

[Ernst and Pirouz, 1988] or caused by the silicon/sapphire misorientation [Aindow, 1989].

When two twins of SOS intersect with each other, only the majority twins will pass through, and the minority twins will terminate at the intersections. This self-annihilation is a common feature of growth twins.

By employing the Ion-Channelling and Rutherford Backscattering method, Picraux [1972] observed the defects decreased from the interface to the film surface. At the same distance from the interface, the defects LQDȝP film were found more than those LQDȝP film. This experimental result indicates that the defect density is the highest at the interface and decreases, depending on the film thickness, with distance away from the interface. The defect distribution could be explained by the intersections of stacking faults that lead to the suppression of defects [Picraux and Thomas, 1973]. Abrahams and Buiocchi [1975] examined the defects distribution in DȝPSOS by TEM. In their study, a foil plane was prepared at Si (011) and the number of faults (FD) was measured per cm in a Si [011] direction. It was found that the faults decreased with the distance d from the interface. For the two thickness ranges, the FDs were given by:

(i) FD=(3.1x107)/d0.63 d 2400 Å), and

(ii) FD=(1.3x1011)/d1.7 d [4 Å).

Fig. 2.11 compares the defect distribution obtained by Abraham and that from Twigg and

Richmond. The latter quantified the depth profile of the volume fraction of microtwins in a

500 nm SOS [Twigg and Richmond, 1988].

41 Chapter 2. Literature Review ______

7.00E+05 6 Differntial Volume Fraction alsc ..Abrahams _ M.S. Faults/cm by M.E. Twigg 6.00E+05 5 Faults Density by M.S. 5.00E+05 Abrahams 4 4.00E+05 3 3.00E+05

2 2.00E+05

1 1.00E+05

0 0.00E+00 0 100 200 300 400 500

Twins (Differntail Volume Fraction)_M.E.Twigg Distance to the interface (nm)

Figure 2.11 Distribution of faults in as-grown SOS, studied by M.E. Twigg & Richmond [Twigg and Richmond, 1988] and Abrahams & Buiocchi [Abrahams and Buiocchi, 1975]

Since the significant decay of the faults in Abrahams and Buiocchi¶VVWXG\ happened at d<500-600 nm, only the density of faults at d<500 nm were plotted to emphasize the interface effects. In comparison with the observation made by Abraham, the number of twins decreases slower in 7ZLJJ¶V VWXG\. That is possibly because the decrease in the number of twins is balanced by an increase of twinned volume. The results also demonstrate that the greatest volume fraction of twins does not appear at the interface, but at a distance of several hundred angstroms away from the interface. In addition, Yamamoto et a1.[1982] also suggested that with increasing thickness, the types of defect change from twins and stacking faults to dislocations loops, because of the intersection and overgrowth of twins by the matrix.

The anisotropy of microtwins in two subset {111} planes is another noticeable feature in epitaxial silicon film [Abrahams and Buiocchi, 1975; Ham, Abrahams et al., 1977;

Batstone, 1991]. Majority subset twins are frequently observed on ( 111 ), whereas minority 42 Chapter 2. Literature Review ______subset twins are lying on ( 111 ) planes. This twin anisotropy was explained as a consequence of the stochastic nature of mis-stacking twins [Ernst and Pirouz, 1988] or caused by the silicon/sapphire misorientation [Aindow, 1989]. When a twin of the majority subset intersects with the minority twins, it will be more likely to pass through the minority twins, and terminate within the film or penetrate the surface. However, the minority twin will terminate within the film or penetrate the surface. Moreover, the minority twin will terminate by the intersection. This self-annihilation is an important feature generally observed in growth twins, since the deformation twins will pass through each other upon intersections [Cahn, 1954].

(b) Interface structure and mismatch accommodation

The interface structure is the most direct indicator of how the mismatch is accommodated.

The understandings of how the interface is formed in SOS have been the subject of much controversy. The most detailed review of the interface structure of silicon and sapphire was done by Anidow [1990]. In this review, he summarized 3 basic models for interface formation in SOS based on existing transmission electron microscopy observations, namely coherent, semi-coherent and incoherent structures.

In the coherent model, the mismatch is considered to be accommodated by a periodically twinned region. The main reason for the prevalence of this twinning model was the absence of misfit dislocations in the early observations. Instead, high density of twins is the most predominant defect found in SOS [Abrahams, Buiocchi et al., 1976; Hamarthibault and Trilhe, 1981]. The detailed explanation of this model was proposed by Lihl et al.[1980]. They ascribed the stress accommodation to the periodical tensions from the {113} twinned regions as illustrated in Fig. 2.12, such that the compressive stress arising from the 43 Chapter 2. Literature Review ______matrix lattice could be mitigated. This model was further proved by Hutchison et al. [1981], in which the twins were observed to have the {113} orientation and extended from the interface.

Silicon Twin 1 Twin 2

(111) (113) (220) (113) (111)

(0112) (1232) Sapphire

Figure 2.12 Schematic of contributions of microtwins to the stress relief (after Lihl and Oppolzer et al. [1980])

Twigg et al. [1990] further assessed the contribution of the microtwins to strain relief of

SOS by quantifying the differential volume fraction of microtwins based on their previous work [Twigg and Richmond, 1988]. He calculated the strain relief caused by deformation twins [Yasutake, Stephenson et al., 1986] or growth twins [Ernst and Pirouz, 1988], and concluded that the contribution of microtwins to the stress relief was 0.7 % and 0.02 % respectively for those two cases. It was generally consented that the high density twins observed in SOS are growth twins, formed during consolidation or deposition of a crystal.

The formation of a growth twin is therefore to accommodate the small translational or

44 Chapter 2. Literature Review ______rotational misalignments upon island coalescence [Abrahams, Buiocchi et al., 1976]. This mechanism was further proved by Hayashi and Kurosawa [1978] from their HREM image obtained just after the complete substrate coverage. They found that the stacking faults and twins of two atomic layer thickness were the most common, indicating those twins were growth twins induced by island coalescence.

However the later observation indicates that the interface is semi-coherent, since misfit dislocations were observed. They are regarded as the main mechanism for residual stress relief. The experimental observation was first reported by Abrahams et al. [1976]. They examined the CVD SOS at an early growth stage prior to island coalescence using plan view specimens attained dark field imaging technique, and observed orthogonal arrays of misfit dislocations of edge type, which were parallel to the [011] and [ 011 ] directions with the spacing of 36.9±6.0Å. Later on, misfit dislocations were also found by Hamar-

Thibault and Trilhe [1981], with the same BXUJHUV YHFWRUV DV $EUDKDPV¶V UHVXOWV EXW relatively larger spacing of 38 Å.

These edge type dislocations were not detected in the preceding works due to high density planar faults (stacking faults and twins) obscuring the interface contrast in the plan view specimen [Blanc, 1978; Aindow, 1990]. Compared to the plan-view technique, a cross- sectional specimen is more useful to reveal the exact structure, and high resolution transmission electron microscopy (HREM) imaging is necessary for the lattice structure investigations. However, the main disadvantages are that it analyses relatively localized features and more careful interpretation is required since the lattice structure may demonstrate totally different features when the specimens are taken with different orientations. The early HREM images were taken with the specimen on the exact silicon

<110> zone axis. Since the sapphire < 20 12 > is not parallel to the silicon <110> but 45 Chapter 2. Literature Review ______around 4° away from it, in this condition only the fringes of sapphire atoms parallel to the interface were resolved as observed by Ponce and Aranovich [1981]. Phillips et al. [1987] examined the as-grown and RTA (Rapid Thermal Annealed) SOS exactly on the < 20 12 >, and observed occasional and periodic silicon (111) fringe termination at the interface, and interpreted this termination as interface dislocations. Anidow et al. [1989] analysed the interface in a cross-sectional view of a rapid thermal annealed (RTA) sample. Using the weak beam imaging of the interface inclined to the beam direction, he observed misfit dislocations with the line direction of 15° away from [110] towards [010], and ascribed this to the effect of anisotropy of mismatch.

An incoherent model was proposed by Ponce and Aranovich [1981], based on their HREM observation, which demonstrated absence of both misfit dislocations and planar faults such as twins and stacking faults. They claimed that the high mismatch between si/sapphire was accommodated by the chemical bond structure at the interface. It was suggested that the oxygen layer in sapphire acted as a site for (001) silicon nucleation, which occurs with a higher degree of freedom than in aluminosilicate structures, and consequently does not rigidly bind the silicon to the sapphire structure, resulting in the fault-free silicon. Rao and

Jacob [1982] analysed the chemical aspect of the SOS interface using thermodynamic calculations of the chemical reactions. It was found that SiO2 and Al6Si2O13 are the product of reactions between Si and Al2O3 at high temperature. This was believed to be a solid solution and was amorphous in nature, with a thickness of less than one monolayer. This is in good agreement with the previous observations of the interface [Ponce, 1982; Rao and

Jacob, 1982]. Metzger et al. [1999] measured the interface lattice parameter by GIXRD which was assisted with a position sensitive detector, and found that the value of this lattice parameter represents the material Al2SiO5, which was believed to be formed during

46 Chapter 2. Literature Review ______the growth of the Si layer by inter-diffusion and chemical reaction. Those experimental and theoretical studies suggest the existence of this intermediate layer. However, it is more likely that this structure only reflects the feature at the local area since contradictory results

(planar faults and dislocations) were observed in other HREM images. In addition, since the quantitative calculation of its influence on residual stress is quite complicated, it is still under discussion whether and how much this interface complex contributes to residual stress release.

2.3.3 Residual Stresses

The first study of residual stress in SOS was done by Dumin [1965], who analyzed films with different thickness from 2-40 ȝP GHSRVLWHG DW ,100°C using linear beam. The deformation measurement was achieved by a Zeiss light section microscope. The stresses in the deformed silicon films were estimated on the basis of beam bending theory and were of the order 109 to 1010 dyn/cm2. It was found that the deformation of the film was proportional to the silicon film thickness. More accurately the stress was measured by

Englert et al. [1980] using the Raman scattering technique. In their work, a general expression for residual stress in single crystalline silicon was derived, in which the anisotropy in the film was neglected and an equi-axial stress model was assumed in solving the dynamic equations of the cubic lattice. Therefore, the in-plane residual stress is

ı=249xᇞȦ, where ᇞȦ is the observed Raman shift. Using this calculation, the room temperature stress for films of 0.6-0.9 μm thick deposited at 930 °C was ı11=ı22=-700±30

MPa. From those early investigations, it had been shown that the magnitude of residual stresses in as-grown SOS were about 500-1,000 MPa, depending on the different deposition temperatures and the thickness of the films.

47 Chapter 2. Literature Review ______

The biaxial stresses of SOS were first studied by Hughes [1973], who theoretically evaluated the residual stress based on the thermal mismatch. He accounted for the anisotropy of the CTE in sapphire Al2O3 [ 1011 ] and Al2O3 [11 02 ] (corresponding to Si

[010] and Si [100] directions) and obtained the biaxial stresses in the 1,100°C deposited films, which are ı[100]=-890 MPa and ı[010]=-950 MPa. This was consistent with the anisotropy of the electronic properties. Comparable results were obtained from XRD experiments by Vrelland [1986]. He utilized a rocking curve and the multiple wavelengths obtained from different x-ray sources to analyze the strain from {001}, {044} and {333} plane families, so as to determine the principal stresses in the film. For a 400 nm film, the principal stresses in the plane of the silicon were found to be -0.92 r 0.16 GPa in the Si

[100] direction and -0.98±0.17 GPa in the Si [010] direction, which agreed with the estimated thermal stresses developed upon cooling in a coherent Si layer on sapphire from the growth temperature. More detailed investigation was done by Gartstein et al. [1998], who also performed stress analysis in the framework of a biaxial strain model. They used the grazing incidence geometry in a synchrotron XRD and a position sensitive detector, and found that the in-plane strains along Si [100] and Si [010] were -5x10-3 and -6x10-3 respectively, confirming the anisotropy of the residual stress in SOS materials.

In order to investigate the residual stress variations along the film growth direction,

Yamazaki et al. [1984] utilized different excitation wavelengths for Raman stress analysis probing from both the silicon-free surface side and the silicon/sapphire interface of sapphire side. More recently, based on electron microscopy, Akaogi et al. [2006] investigated strain distributions in the vicinity of an improved SOS interface by convergence beam electron diffraction (CBED) which enabled the localized analysis. It was revealed that the lattice parameters of the Si-layer depend on the distance from the

48 Chapter 2. Literature Review ______interface. However, the strain information obtained from the CBED technique is relatively localized, which is more readily affected by microstructural defects. Therefore more care should be paid to the interpretations and analysis.

Post-deposition processes such as implantation and annealing influence residual stresses

[Ohmura, Inoue et al., 1983; Bolotov, Efremov et al., 1992; Dubbelday and Kavanagh,

1998]. The first study was done by Ohmura et al. [1983], who investigated residual stresses in implanted silicon film in an SOS system by a 2-step annealing, first at 600 ºC and then at the temperature ranging from 600 ºC to 900 ºC. They found that the reduced stress after the first 600 °C annealing was not influenced by the second annealing, even though those annealing temperatures were higher than 600 °C. Therefore, they speculated that the stress release was caused by a new interface compound at 600 ºC re-growth, which can sustain the stress at temperatures up to 900 ºC. After this threshold temperature, this new bond will break, resulting in a jump of stresses back to the as-grown level. Bolotov et al. [1992] correlated the stresses and microstructures in the samples with various doping conditions, and suggested that the stress relaxation was induced by formation of vacancy defects at the interface, which decreases the total mechanical energy, and thereby results in stress reduction. At a sufficiently high temperature, the vacancy defects will be annealed out, and the lowered stresses will be restored. Dubbelday and Kavanagh [1998] examined the strains on the samples applying various annealing durations at 700 - 1,000 qC. They found that the in-plane strains oscillated for the annealing time only by 5 to 7 minutes and then approached the theoretical thermal mismatch strains for longer annealing time. He suggested this oscillation is caused by the annealing induced diffusions of Si+ s from sapphire back to silicon, which results in a tensile strain at the early stage. The mechanisms proposed in the above literatures are not convincing because correlations between the

49 Chapter 2. Literature Review ______microstructural changes and residual stress relaxation are never attempted, which requires more investigations.

2.3.4 Summary

In summary, the high mismatch between silicon and sapphire (i.e. f=5.7 % in Si [100] and f=12.4 % in Si [010]) determines its island growth mode and the high density of inherent defects induced by the substantial stress. The mechanism of mismatch accommodation has been subjected to discussions and debates.

The literature reveals that the formation of edge type misfit dislocations is more favourable for mismatch accommodation [Abrahams, Buiocchi et al., 1976; Hamarthibault and Trilhe,

1981; Phillips, Batstone et al., 1987; Aindow, Batstone et al., 1989]. The spacing of the dislocation arrays is close to the theoretical mismatch between film/substrate. However, to verify this mechanism, the residual stress should be quantified and compared with the theoretical modeling of dislocations. The mixture of aluminosilicate was observed by

Ponce, Aranovich [1981] and Rao, Jacob [1982], and was considered as a buffer layer for mismatch mitigation. However, it is more likely that aluminosilicate only reflects the local mixture of different types of atoms, or is the result of misinterpretation of the ambiguous

HREM images. Although microtwins and stacking faults are the predominant defects in the film, it is more suitable to classify them to the growth twin rather than the deformation twin, since the deformation induced partial dislocations mainly occurs in films subject to tension and under a relatively lower mismatch (Sec 2.1.1).

Similar to other thin films, in CVD SOS, the dominant parameters for stresses are the deposition temperature and film thickness, resulting in stresses ranging from 500 MPa to

50 Chapter 2. Literature Review ______

1,000 MPa. Although high density of the micro-structural defects (Sec 2.3.2) implies the residual stresses have been relieved by introducing lattice defects, the relatively larger stress observed in thinner films indicates the interface effect. In this context, more detailed investigations are required for separating the lattice mismatch effect from the total residual stress. The existing studies were based on either an equi-biaxial model, for example in

Raman [Englert, Abstreiter et al., 1980] and curvature techniques [Dumin, 1965], or a biaxial stress model considering only in-plane anisotropy in analytical [Hughes, 1973] and

X-Ray diffraction measurements [T. Vreeland, 1986; Gartstein, Lach et al., 1998].

Practically, the investigation of complete stress tenors is necessary in a detailed stress characterization. This is because the semiconductor materials are always designed with multilayers, which will lead to a tri-axial stress state.

2.4 Discussion and Conclusions

Basically, thermal mismatch stress is dominant in epitaxial thin films, whereas the substantial growth stress due to lattice mismatch has been relieved via misfit dislocation, twins, new compound, or surface morphological modifications. Although the aforementioned defect microstructures have been extensively studied, the quantitative relationships between residual stresses and experimentally measured lattice defects such as dislocation density have not been established. That is because the interface defects are discrete and not uniform, and their interactions are complex, such that the theoretical calculation of stress relief is not as simple as previously thought. In light of this, a more systematic stress analysis in a general epitaxial thin film system requires correlation between the detailed residual stress descriptions (i.e. tri-axial stress tensor and thickness dependence of stresses) and the interface defect structures from microscopic observations.

51 Chapter 2. Literature Review ______

XRD is superior to other techniques in characterizing a full stress tensor, however, the main challenge is the inadequate diffraction planes in single crystalline (or epitaxial thin films) materials. Furthermore, the typical XRD and Raman technique could not be exploited in the multilayer thin films with the amorphous layer involved. The method based on the curvature of the wafer should be extended to a multilayer system.

In the CVD SOS thin films, although there have been attempts of revealing the stress induced defect structures, the actual mismatch relief mechanism is still unclear. Due to difficulties in single crystal stress measurement, the residual stress studies in SOS are fragmentary, and cannot provide sufficient information for a systematic stress analysis.

Therefore, further experimental and theoretical investigations are required.

52 Chapter 3. Experimental Methods for Stress Characterizations

CHAPTER 3: Development of New Experimental

Methods for Residual Stress Characterizations

In high performance integrated circuits and MEMS, a too high residual stress in a thin film system can significantly alter their electronic properties [Hynecek, 1974] and sometimes lead to mechanical failures [Itoh, Rhee et al., 1985]. The residual stresses in a thin film also vary with the film thickness [Kim, Robinson et al., 1996; Bartasyte, Chaix-Pluchery et al., 2008], indicating the effects of interface lattice mismatch and microstructural defect.

Characterization of the residual stresses and their thickness dependence is therefore crucial for improving the reliability of an electronic product. To meet different electrical or optical functionalities, thin films are often of multiple layers [Egley, Gut et al., 1999; Tan, Jong et al., 2009]. The fabrications of these layers are complicated, involving high temperature and the atomic structure variation across the interfaces. Therefore, an understanding of the stress distributions in these multi-layered thin films is particularly important since excessive stress in a single layer will result in ultimate failure of the whole wafer.

53 Chapter 3. Experimental Methods for Stress Characterizations

Unfortunately, epitaxial films are of single crystalline structure whose measuring directions are limited due to insufficient crystallographic orientations that can contribute to

X-ray diffraction. Therefore the characterization of the full stress tensor in single crystal will be difficult and inaccurate if based on the traditional x-ray diffraction (XRD) method.

In addition, probing the thickness dependence requires simultaneous measurement of the thickness and the stress, which has not yet been achieved by any traditional means. In a multi-layered system, the conventional XRD or Raman techniques are not applicable when the system contains an amorphous layer. Although the existing analytical studies [Stoney,

1909; Hsueh, 2002; Hsueh, Lee et al., 2006] could solve the problem of the layer stresses from the overall curvature, this method considers only mismatches of thermal expansion, which is unreliable when the lattice mismatch effect is significant.

Therefore, the aim of this chapter is to develop experimental methods to cope with the aforementioned technical issues. Those methods are based on traditional techniques such as XRD, Raman, curvatures measurement etc, which provide more detail and systematic characterisation of residual stresses in epitaxial thin film materials.

3.1 Stress Characterization in Epitaxial Thin Film

3.1.1 Complete Stress Tensor

(a) Methodology

As illustrated in Fig. 3.1, there are 3 main steps in residual stress tensor analysis by the

XRD technique.

54 Chapter 3. Experimental Methods for Stress Characterizations

Strain Tensor Determination

2șhkl dhkl İ11, İ12, İ13, ı11, ı12, ı13, Diffraction Angle Lattice Spacings İ22, İ23, İ33 ı22, ı23, ı33 i iii

Strain measurement in Stress Tensor individual [hkl] direction Determination

Figure 3.1 General procedures for XRD stress tensor determination

(i) Strain measurement in individual [hkl] direction. 7KH VWUDLQ İhkl in a certain [hkl]

0 hkl dd hkl direction is determined from H hkl 0 , where dhkl is the lattice spacing for d hkl analyzing diffraction planes (hkl), which is calculated from the measured diffraction angles

0 2șhkl EDVHGRQ%UDJJ¶V /DZ [Bragg, 1913], and d hkl is the stress-free lattice spacing. To maximize the accuracy, it is more desirable to utilize the diffraction peaks pertaining to higher Miller index planes. By this means, the resolution in strain measurement could be improved since a larger ǻșhkl can be detected in XRD measurement (see Eq. 2.7). To determine the strain/stress tensor in epitaxial silicon film, the silicon plane families {115},

{404}, {315}, {206}, {335} and {444} were employed. The corresponding diffraction peaks of these plane families are mostly at high angles as indicated in the diffraction pattern of silicon powder (Fig. 3.2).

55 Chapter 3. Experimental Methods for Stress Characterizations

{h k l} ș0 {0 0 4} 69.126 {1 1 5} 94.947

) {4 0 4 } 106.702 {3 1 5} 114.084 counts ( {2 0 6} 127.534 ty ty i {5 3 3} 136.880 {4 4 4} 158.604 ntens i -ray -ray X {4 4 } {4 {5 3 3} {5 {2 0 6} {2 {3 1 {3 5} {4 0 4} {4 {0 0 4} {1 1 {1 5}

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 Silicon diffraction angle 2ș (º)

Figure 3.2 Diffraction peaks from Si powder

(ii) Strain tensor determination. When a sufficient set of H hkl is obtained, the six components İij (i, j=1, 2, 3, and i d j) of strain tensor could be subsequently determined.

For epitaxial silicon film, as illustrated in Fig. 3.3, the three normal strains İ11, İ22, İ33 are predefined to be aligned with crystallographic directions [100], [010] and [001],

respectively. İĭȌ (equvalent to H hkl ) is the normal strain in the measuring direction, which is the normal of a certain (hkl) diffraction plane. The angles ĭ and Ȍ, as defined in Fig.

3.3, are azimuth and inclinational angles relative to silicon [100] and [001] directions respectively.

56 Chapter 3. Experimental Methods for Stress Characterizations

İ33 [001] İĭȌ n (hkl)

Ȍ İ11 [100] ĭ

İ22 [010] Figure 3.3 Coordinate system for XRD experiment

In this coordinate, any arbitrary İĭȌ can be expressed as [Noyan and Cohen, 1987]:

3 İĭȌ hkl ¦ ij ,<) HEH ij d ,1, d jiji 2 2 2 cos sin 11 sin 2 sin 12 cos sin 2 İȌĭİȌĭİȌĭ 13 . (3.1) 2 2 2 sinsin 22 sinsin İȌĭİȌĭ 23 12 sin İȌ 33

where Eij are the coefficients for the strain tensor components Hij, and İĭȌ are obtained directly from the difference between the measured diffraction angles 2Thkl and the stress-

0 free angles 2T hkl .

Therefore, the six strain components can be solved if the number of combinations of ĭ and

Ȍ are larger than or equal to the number of unknowns. If the number of İĭȌ is larger than six, the generalized least square method [Winholtz and Cohen, 1988] can be used to solve the single crystal tri-axial residual stress measurement issue, which could minimize the

statistical counting errors. Suppose that there are n İĭȌ measured from the XRD experiment, the equation set is given by

57 Chapter 3. Experimental Methods for Stress Characterizations

1 1 1 1 1 1 1 ªH I\ º ª 11 12 13 22 23 EEEEEE 33º « » « » H 2 2 2 2 2 2 2 H « I\ » « 11 12 13 22 23 EEEEEE 33» ª 11 º 3 3 3 3 3 3 3 « » «H » « EEEEEE » H « I\ » « 11 12 13 22 23 33» « 12 » 4 4 4 4 4 4 4 « » «H I\ » « 11 12 13 22 23 EEEEEE 33» H13 u « » , (3.2) «H 5 » « 5 5 5 5 5 EEEEEE 5 » H « I\ » « 11 12 13 22 23 33» « 22 » 6 6 6 6 6 6 6 « » «H I\ » « 11 12 13 22 23 EEEEEE 33» H 23 « » « » « » «H » « » « » ¬ 33 ¼ u16 «H n » « EEEEEE nnnnnn » ¬ I\ ¼ nu1 ¬ 1211 13 22 23 33¼ nu6

3 k k or )< ¦ ij ,<) HEH ij , (3.3) d ,1, d jiji

where k runs from 1 to n. In solving the strain tensor, the accuracy can be maximized if (a) the number of combinations of ĭ and Ȍ is maximized, such that the propagation error in a certain [h k l] direction could be minimized in strain tensor calculation; (b) the coefficients

E k for any two different strain components H and H must be sufficiently uncorrelated, ij ij pq that is the correlation:

k k k k n ij pq ij ¦¦¦ EEEE pq r k k k (3.4) ijpq 2 2 k 2 § k · k 2 § k · n ij ¨ EE ij ¸ n E pq ¨¦¦¦¦ E pq ¸ k © k ¹ k © k ¹ is sufficiently smaller than 1. These two considerations are readily achieved in polycrystalline materials. Unfortunately, the epitaxial films are of single crystalline and their measuring directions are limited because of insufficient crystallographic [hkl] orientations pertaining to high diffraction angles as indicated in Fig. 3.2.

In our study, by utilizing both Ȥ and Ȧ offsets in the 90° open Euler Cradle diffractometer, a larger range of ĭ and Ȍ pertaining to thirteen [hkl] directions is attained in epitaxial 58 Chapter 3. Experimental Methods for Stress Characterizations

silicon. The thirteen strain measuring directions are shown in Fig. 3.4. By this means, the accuracy of the strain tensor can be maximized and the aforementioned correlation problem can be avoided.

Figure 3.4 XRD measuring directions in spherical diagram

(iii) Stress tensor determination. As the strain tensor was obtained, the full residual stress field can be built up according to single crystal anisotropic elasticity theory [Zhang, 2001]:

ij CijklHV kl (3.5)

11 In single crystalline silicon, the elastic constants are given by C11= 1.66×10 Pa, C12=

11 11 0.64×10 Pa, C44= 0.796×10 Pa.

(b) Experiments and Results

59 Chapter 3. Experimental Methods for Stress Characterizations

The samples upon investigation were (0 0 1) silicon films of different thicknesses (e.g. 280 nm, 5 μm, etc) grown by CVD at DURXQG & RQ D ȝP WKLFN (10 21 ) sapphire substrate. The X-Ray diffraction measurements were performed on Philips Panalytical

(MRD) diffractometer equipped with 4-circle axes as illustrated in Fig. 3.5.

Figure 3.5 4-FLUFOH;¶3ert MRD diffractometer. Ɏ-rotational axis, Ȥ-inclinational axis, Ȧ - sample tilting axis, and ș-detector axis

Through consecutive scanning around axes (ĭ Ȥ Ȧ), the exact diffraction condition

(diffraction maxima) of the measuring (h k l) planes could be attained, which gives rise to a precise diffraction angle 2șhkl. In addition, the combination of Ȧ and Ȥoffsets provides a larger range of inclinational angles Ȍ, which leads to more accuracy in strain tensor calculations.

To obtain a precise diffraction peak position, the x-ray diffractometer was equipped with a line focused high-resolution setting as shown schematically in Fig.3.6. In this configuration, the high intensity quasi-paralleled beam is collimated by an X-Ray Mirror, and a narrow

60 Chapter 3. Experimental Methods for Stress Characterizations

band of diffraction angle from CuKĮ1 radiation is provided by a four reflection Ge (220)

PRQRFKURPDWRU ZLWK WKH UHVROXWLRQ RI A Parallel Plate Collimator 0.18° was used to control the acceptance angle to the detector, so that the results were made insensitive to the sample displacement.

Figure 3.6 XRD high resolution configurations

Table 3.1 lists the strains obtained from XRD experiment on the epitaxial silicon film (280

nm), where İɎȥ is the experimental measured strain, and HĭȌc is the strain calculated from

the strain tensor by Eq. (3.3). The table shows that the residual HÖ)< = )

0.01 % in each [hkl] direction, indicating that the strain tensor obtained was reliable.

The full stress tensors were evaluated in the typical as-deposited SOS samples with

HSLWD[LDOVLOLFRQILOPRIQPDQGȝPZKLFKZHUHOLVWHGLQ7DEOH,WLVIRXQGWKDW silicon film is basically under an equi-biaxial stress state, i.e. ı11 # ı22, and ı33 = 0. The largest ı33 is of -45 MPa found in the ȝPILOPSRVVLEO\FDXVHGE\WKHVWUHVVJUDGLHQWLQ relatively thicker film. It is however negligible in comparing with ı11 and ı22.

61 Chapter 3. Experimental Methods for Stress Characterizations

Table 3.1 Measured and calculated strains in 13 [hkl] directions. The sample is 280 nm SOS.

İ c [hkl] Ɏ(°) ȥ(°) 2T0 2Thkl Ɏȥ HĭȌ HÖ)< 004 45 0 69.126 68.89 0.303% 0.305% 0.0018% 115 45 15.79 94.947 94.64 0.245% 0.248% 0.0030% 206 0 18.44 127.534 126.99 0.235% 0.237% 0.002% 315 18.44 32.31 114.084 113.90 0.103% 0.104% 0.001% 335 45 40.32 136.880 136.85 0.009% 0.004% -0.005% 404 0 45 106.702 106.76 -0.039% -0.042% -0.003% 444 45 54.736 158.604 159.58 -0.170% -0.168% 0.002% 1 53 168.69 59.53 114.084 114.50 -0.234% -0.225% 0.009% 353 59.04 62.77 136.880 137.64 -0.260% -0.260% 0.000% 3 51 149.04 80.27 114.084 114.79 -0.393% -0.395% -0.002% 2 06 180 18.44 127.534 126.99 0.237% 0.233% -0.004% 3 15 161.56 32.31 114.084 113.90 0.106% 0.110% 0.004% 4 04 180 45 106.702 106.76 -0.038% -0.048% -0.010%

Table 3.2 Strain and stress tensor FRPSRQHQWVİij and ıij (i, j =1, 2, 3) obtained from XRD experiment on 280 nm and ȝP SOS.

İ11 İ22 İ33 İ12 İ13 İ23 İij [%] 280 nm -0.394 -0.410 0.305 0.014 0.003 -0.018

ȝP -0.337 -0.293 0.215 0.010 0.008 -0.005

ıij [MPa] ı11 ı22 ı33 ı12 ı13 ı23

280 nm -723.3 -741.4 -9.96 23.0 4.5 -28.5

ȝP -577.2 -569.5 -45.2 -32.7 -12.3 -7.9

In both of the samples the anisotropy in the Si (001) plane is smaller than that reported in literature [Vreeland, 1986]. The difference is probably due to the insufficient analyzing

62 Chapter 3. Experimental Methods for Stress Characterizations

angles (only {100} and {110} diffractions were used in the 9UHHODQG¶s study), that might cause error in determining the biaxial stresses ı11 and ı22. In addition, the presence of ı33 also leads to error in their bi-axial stress model, giving rise to larger difference in ı11 and

ı22. It should be noted that even though the lattice mismatch strains in the orthogonal lattice directions are very different (i.e. f=5.7 % and 12.4 % respectively along Si [100] and

Si [010]), they must have been well accommodated by the interface defects. This is the reason why our XRD measurement indicated that the stress state is equi-biaxial.

It is also noted that the stress in the 280 nm SOS sample (-730 MPa) is about 150 MPa larger than that observed in 5 ȝPVDPSOHV(-570 MPa). The variation is probably due to the effects of lattice mismatch and interface defect, which is manifested in thinner film.

To examine the uniformity of the in-plane stresses, a Raman experiment was conducted with a backscattering configuration. The applicability of Raman stress measurement is due to the equi-biaxial stress state obtained from the XRD results. The residual stress is calculated by the shift of LO phonon frequency ǻȦ (cm-1), i.e., ı = -249ǻȦ (MPa) [Englert,

Abstreiter et al., 1980] in case of silicon, in which the reference silicon peak position was

-1 Ȧ0 = 520.4 cm . Five points (from 1 to 5 in Fig. 3.7) were measured in the as-grown SOS wafer of 280 nm. From the measured Raman shifts ǻȦ at those points, the residual stress was found nearly uniform, with the average residual stress of -703.84 MPa across the wafer surface, which is the average stress of the five points (ı1 = -706.5 MPa, ı2 = -683.3

MPa, ı3 = -700 MPa, ı4 = -720.7 MPa, ı5 = -708.7 MPa). The Raman result is very close to the XRD measured value -732.4 MPa (the average of the normal stresses V11 and V22 in the wafer plane), which confirms the applicability of both techniques in epitaxial silicon stress analysis.

63 Chapter 3. Experimental Methods for Stress Characterizations

5 2

4 3 [100] [010]

Figure 3.7 Surface stress uniformity examined by the Raman technique. The radius of the SOS wafer Rsos=7.62 cm

3.1.2 Thickness-Dependent Stress

In the above, we have found by XRD that the residual stress increases notably as the film thickness reduces from 5 Pm to 280 nm. This variation indicates the effects of lattice mismatch and interface defect. To fully resolve their effects, a thorough investigation of the stress variation with film thickness is necessary.

Making films of many different thicknesses is costly. Therefore, chemical etching is employed to generate films of different thickness such that a clear picture of thickness dependence can be established. The co-existence of silicon and sapphire peaks in a Raman spectrum allows a simultaneous measurement of film thickness from the peak intensity ratio and the residual stress from the peak shift.

(a) Sample preparations

64 Chapter 3. Experimental Methods for Stress Characterizations

In order to reveal the stress variations, a silicon film of 5 μm was etched to different thicknesses in 80 °C 1:2 KOH etchant with a nominal etching rate of 14 kÅ/min [Williams,

Gupta et al., 2003]. Table 3.3 lists the nominal film thicknesses according to the etching time and the actual film thickness (>700 nm) measured by a reflectometer (Mikropack

NanoCalc 2000 UV-Vis-NIR).

The film thickness is uniform after a short-duration etching, but becomes increasingly non- uniform as the etching time increases. After a 200-second etching, the surface undulates considerably, making the reflectometer inapplicable.

Table 3.3 Nominal and measured film thickness after wet etch

Sample Time(s) Thickness Thickness ID (Nominal) [nm] (Actual) [nm]

S1 0 5000 5000 S2 60 3600 3900 S3 120 2200 2245 S4 160 1300 ~1300±100 S5 180 800 700±100 S6 200 333 N/A

To obtain an accurate thickness value, a significantly etched film was measured from the cross-section of a sample which was obtained by milling a pocket in the material using FIB.

Fig. 3.8a shows the surface of a silicon film after a 200 s etching.

65 Chapter 3. Experimental Methods for Stress Characterizations

Figure 3.8 An etched SOS thin film: (a) the surface of etched SOS (S6); (b) the pocket at Point S6.3 milled by FIB; and (c) film thickness measurement at the cross-sectional view

66 Chapter 3. Experimental Methods for Stress Characterizations

By milling a pocket as shown in Fig. 3.8b, the silicon film was clearly discerned and the thickness could be accurately measured as shown in Fig. 3.8c. It was found that the film thickness varied from 60 nm to 450 nm along the line from Point S6.1 to S6.5. Since TEM cannot be integrated with the residual stress measurement, Raman Spectroscopy was adopted to investigate the thickness-dependent residual stresses here.

(b) Raman thickness-dependent stress measurement

The Raman spectra were used to analyse both the residual stresses and film thickness after etching, which was conducted with a Renishaw Invia spectrometer in the backscattering configuration. A standard setup of 514 nm Argon ion laser and 1800 l/mm grating was utilized to detect the silicon band at around 520.5 cm-1 and the sapphire band at 417 cm-1.

The incident light was focused on the (001) surface of the silicon film using a 20u microscope objective and the scattered light was collected by the same objective. The spot size of the incident beam is about 2 Pm and the penetration depth in Silicon is about 0.77

Pm [DeWolf, 1996], so that a small area of uniform film thickness can be resolved. The spectral resolution is about 1.7 cm-1.

For stress measurement, the shift of a Raman ǻȦ (cm-1) band was used. Since the residual stress in the epitaxial silicon film has been confirmed by the X-Ray diffraction (Sec 3.1.1) to be equi-biaxial, the in-plane normal stresses can well be quantified by ı= -ǻȦ (MPa)

[Englert, et al., 1980]. To determine the peak position, we fit the Raman spectrum with

Gaussians and search for the minima of the second derivative of the fitted function. For thickness measurement, the intensity ratio r of the sapphire to silicon bands was used. This method is applicable when the film is thinner than 800 nm and the sapphire band appears

67 Chapter 3. Experimental Methods for Stress Characterizations

in the spectrum. Within this thickness, the relation between r and film thickness tf can be rationalized by a stochastic model of Raman scattering.

Let us consider the stochastic behaviour of a photon in penetrating into a material as shown schematically in Fig. 3.9.

z=0

-ȝfz e e-ȝfzȝ dz z f z+dz Silicon tf ȝfdz

Sapphire

Figure 3.9 Schematic of Raman photon stochastic behaviour

Pfdz denotes the probability that the photon is absorbed by the film material between the depth z and z+dz, where Pf is the unit volume absorptivity of the film. It is clear that the probability that the photon is not absorbed from the surface to the depth z is simply eP f z .

Therefore, the combined probability for the photon absorbed by the material at the depth

P f z between z and z+dz is e P f dz . Assuming that the absorption of the incident photon scatters a Raman photon of the interested wave length with a constant probability Kf, we can have the following relationship between the measured Raman peak intensity and the film thickness:

t f P f z P t ff ff 0 eIKI P f dz f 0 1 eIK , (3.6) ³0

68 Chapter 3. Experimental Methods for Stress Characterizations

where I0 is the intensity of the incident beam and tf is the thickness of the film. With the same rationale, we can have the relationship between the Raman peak intensity and the substrate thickness as follows:

ts P t ff Ps z ss 0 eeIKI Ps dz , (3.7) ³0

where eP t ff is the fraction of the incident photons that can penetrate through the thin film.

Since the thickness of the substrate is generally very large, it is safe to take ts fo . This gives rise to

eIKI P t ff . (3.8) ss 0

Therefore the relation between the intensity ratio Is/If of substrate/film and the film thickness is

I eK P t ff A s s , (3.9) I 1 eK P t ff e P t ff 1 f f

where KKA fs is a constant to be determined by experiment.

Fig. 3.10a shows the Raman spectra pertaining to the films with known thickness. A thicker film leads to a higher silicon peak and smaller Is/If. Fig. 3.10b shows the intensity ratio r versus the film thickness tf in comparison with the predictions by Eq. (3.9). The excellent fitting indicates that Eq. (3.9) can indeed be used to determine the thickness of the silicon film. For example, for a pristine silicon film of thickness 280 nm, Eq. (3.9) predicts a film thickness of 280.5 nm since the intensity ratio was 0.1359. 69 Chapter 3. Experimental Methods for Stress Characterizations

32000 (a) Sapphire Si 28000 59.0nm (Is/If=1.192) S6.1 24000 111.1nm (Is/If=0.614) S6.2 20000 16000 187.7nm (Is/If=0.214) S6.3 12000

Raman Intensity 289.2nm (Is/If=0.128) S6.4 8000 4000 429.8nm (I /I =0.067) S6.5 0 s f 400 430 460 490 520 550

-1 Raman Shift (cm )

Figure 3.10 Raman spectra and film thickness determination: (a) the Raman spectra of different areas of the sample S6; (b) the film thickness versus sapphire/silicon intensity ratio.

70 Chapter 3. Experimental Methods for Stress Characterizations

However, the method has a limited applicability. According to the fitting parameters shown in Fig. 3.10b, a silicon film of 800 nm can absorb 98 % of the incident laser photons, which is consistent with a penetration depth (770 nm) of 514 nm laser in silicon [DeWolf,

1996].

Therefore, the film thickness to be determined by this method must be smaller than 800 nm.

Two to three Raman spectra were taken from Samples S1 to S5 (tf !ȝP ZLWKDUHODWLYHO\

XQLIRUPWKLFNQHVVDVVKRZQLQ7DEOH7KHPHDVXUHGVWUHVVHVIURPWKH5DPDQVKLIWǻȦ are shown in Fig. 3.11.

-300

-400

-500

-600 - residual MPa) stress ( ı

-700 01.534.56

t f - film thickness ( ȝm )

Figure 3.11 Residual stresses on etched SOS (tf>700 nm)

For Sample S6, the film thickness and residual stress were simultaneously measured from the Raman spectra. Plotting all the stress versus film thickness in Fig. 3.12, it is obvious that the residual stress increases with the reduction of the film thickness. The compressive residual stress in the silicon film is more or less uniform at 600 MPa when the film

71 Chapter 3. Experimental Methods for Stress Characterizations

thickness is larger than 700 nm. Below 700 nm, the stress increases continuously as thickness reduces and becomes larger than 800 MPa at around 100 nm.

-500

-600

-700 2ȝm 500 nm -800 280 nm

-900 etched SOS as-grown SOS

- stresses ( residual MPa ) -1000 ı

-1100 012345 t - film thickness ( ȝm ) f

Figure 3.12 Variations of residual stresses with film thickness on both etched SOS (0 to 5 ȝP DQGDV-deposited SOS (280 nm, 500 nm and 2 μm)

The issue that needs to be clarified is whether the chemically etched thin film has the same residual stresses as those of the as-deposited film. Therefore, we conducted more tests on the as-deposited thin films and the result is shown in Fig. 3.12. It is noted that the residual stresses in the as-deposited film and those in the etched film of the same thickness are very close to each other. This thus justifies that the employment of chemical etching to obtain silicon film of different thickness is rational.

It should be noted that the measurement results scatter significantly when the thickness is below 50 nm. This is mainly caused by the pronounced non-uniformity of film thickness close to the interface, as shown in Fig. 3.13.

72 Chapter 3. Experimental Methods for Stress Characterizations

-780

-760

-740

-720

-700 20 ȝm

40 60 80 100 120 140 160

Figure 3.13 A nonuniform surface of SOS sample etched below 50 nm. The magnification was 20× under Raman microscopy. the white regions are the remaining silicon film, and the black regions are the sapphire substrate uncapped with silicon film.

The film thickness of this region, measured from the Raman intensity ratio, is in the range of ~5 to 50 nm. It is also noted that when the thickness is only of a few nano-metres, the residual stress is neither equal-biaxial nor uniform. This means the stress measured from the Raman spectroscopy has been problematic. On the other hand, the weak Raman signal from such a thin silicon film also makes the identification of the position of silicon peak erroneous. Therefore, only the measurements at a thickness larger than 50 nm are considered reliable.

3.2 Stress Characterization of Multi-layered Thin Films

To meet different electrical or optical functionalities, thin films are often of multiple layers processed at high temperatures. For example, as illustrated in Fig. 3.14, a typical silicon- on-insulator (SOI) system contains 4 layers. The bottom two layers are polycrystalline Si 73 Chapter 3. Experimental Methods for Stress Characterizations

(0.4 μm) for robotic sensing during manufacturing and transferring [Egley, Gut et al.,

1999] and the amorphous Si3N4 layer (0.3 μm) is for protection [Tan, Jong et al., 2009].

The others are functional layers of epitaxial silicon (0.11 μm) and sapphire substrate (600

μm). The fabrications of these layers are complicated, involving high temperatures and the atomic structure varies across the interfaces. Therefore, an understanding of the stress distributions in these multi-layered thin films is particularly important since excessive stress in the single layer will result in an ultimate failure of the whole wafer.

0.11ȝm Epitaxial Si film XRD Least square

600 ȝm XRD Curvature Sapphire Substrate

Multiple Reflection GIXRD 0.4 ȝm Polycrystalline Si 0.3 ȝm Amorphous Si N 3 4 XRD Curvature

Figure 3.14 Typical multi-layered thin films and the stress measuring techniques (the dimensions are not to the scale)

The main challenge in residual stress measurement is the presence of the amorphous layer

(e.g. the Si3N4 film), for which traditional XRD or Raman techniques are not applicable.

Although analytical studies [Stoney, 1909; Hsueh, 2002; Hsueh, Lee et al., 2006΁ of a multi-layer system allow the calculation of in-plane residual stresses of each layer from the overall curvature, this method requires precise mechanical and thermal properties of each layer and only considers the mismatches of thermal expansion. However, in well bonded thin-film systems, the residual stresses are due to not only the disparate thermal properties but also the different atomic structures. Hence, a direct implementation of those equations is unreliable.

74 Chapter 3. Experimental Methods for Stress Characterizations

The aim of this section is to develop an experimental method for stress characterization in a multi-layered thin film system by combining XRD measurement and analytical calculation. The method is based on the rationale that the uncertainties in the analytical calculation of residual stresses, such as the thermal and mechanical properties of different layers and structural mismatches, can be reduced if residual stresses in some crystalline layers can be directly quantified. In doing so, the calculation of residual stress can be more reliable.

3.2.1 Methodologies

(a) Stress-curvature relations in multi-layered thin films

Consider a multi-layer system in Fig. 3.15, the analytical formulation of the relationship between stress and thin film layers is based on a continuity condition [Hsueh, 2002; Hsueh,

Lee et al., 2006].

In Fig. 3.15, z = 0 is the top surface of the substrate. The total in-plane strain at depth z is given by:

hz b H c ,(h-n

where c is the uniform strain, z = hb (hb <0) is the location of the neutral axis and R is the

g radius of curvature. Suppose that the thermodynamic history induces a strain H i in layer i and this strain is partly relaxed due to overall tension/compression and bending. This results in the stress Vi in layer i:

g E HHV iii )( (for i = -n to n), (3.11) 75 Chapter 3. Experimental Methods for Stress Characterizations

Figure 3.15 Schematic of a general multi-layered system

where i = 0 pertains to the substrate (i.e., t0 is the thickness of substrate), i>0 denotes the layers above the substrate, and i <0 stands for the layers below the substrate; E0 and Ei are

g biaxial moduli for the substrate and films respectively; H i is a simplified parameter to represent the effect of the thermal process, including the effects of thermal expansion and atomic structural deformation due to defects and constraints from adjacent layers. In

g [Hsueh, 2002; Hsueh, Lee et al., 2006], H i is only attributed to thermal expansion, which allows direct calculation if the coefficients of thermal expansion and elastic modulus are

g known. However, in reality, H i is unknown.

Based on plate bending theory, the unknown parameters c, tb, R can be solved from three equilibrium conditions which are (a) the equilibrium of the resultant forces due to uniform straining:

n g g - H 000 䌥 - Hii tcEtcE i 0)()( ; (3.12) -ni i 䍴0

76 Chapter 3. Experimental Methods for Stress Characterizations

(b) the equilibrium of the resultant forces due to bending straining:

0 hzE n hi hzE ³ 0 b dz ¦ ³ bi dz 0 ; (3.13) t R ni h R 0 iz0 i1

and (c) the equilibrium of the bending moment with respect to the bending axis at z = hb:

0 n hi V hz )( dz V hz dz 0. (3.14) ³ 0 b ¦ ³ bi t ni h 0 iz0 i1

When the film thickness ti is much smaller than the substrate thickness t0, i.e., if ti << t0,

the second order terms of ti can be neglected and the approximate solutions of c, hb, R are respectively given by:

n g g tE H 000 ¦ tE H iii z ini z 0, c n , (3.15a) 00 ¦ tEtE ii z ini z 0,

n 2 00 2 ¦ htEtE iii 1 t ini z 0, , (3.15b) b § n · 2¨ tEtE ¸ ¨ 00 ¦ ii ¸ © ini z 0, ¹

n 6 tE HH gg 2ht 1 ¦ iii 0 0 i1 z ini z 0, , (3.15c) n R 3 2 2 00 4 ¦ ii 0 i10 33 hhtttEtE i1 z ini z 0,

Since ti << t0, hi-1 §for i > 0 and hi-1 §-t0 for i < 0, Eq. (3.15c) can be further simplified to:

77 Chapter 3. Experimental Methods for Stress Characterizations

n 6 V[ Lt 1 ¦ ii i n 1 ini z 0, (i > 0, [ = 1; i < 0, [ = -1). (3.16) 2 ¦ i i R tE 00 ini z 0, Ri

L gg where i E ii HHV 0 represents the residual stress solely caused by the mismatch between the film layer i (i z 0) and the substrate i = 0. From Eq. (3.16), we can conclude that the overall curvature 1/R is the linear superposition of bending effects from each film layer if the film thickness is sufficiently small, because 1/Ri is evaluated merely from the

L mismatch stress V i between layer i and the substrate. The residual stress Vi in layer i can be obtained by substituting Eqs.(3.10, 15a~c) into Eq.(11). Taking the first order

2 approximation by neglecting ti yields:

2 [i tE 00 2 itE 0 ıi (3.17) 6 Rt ii 3R

If the zero-order approximation is taken, i.e., if t0 is much larger than ti, the above stress- curvature relationship is further simplified to the well-known Stoney Equation:

2 [i tE 00 ı i (3.18) 6 Rt ii

L This leads to ıi ı i, indicating that under zero-order approximation, the stress in the film layer i depends merely on the process-induced mismatch strain between layer i and the substrate. According to Eq. (3.19), if the curvature 1/R and layer stress ıi are reliably obtained, stress ıj in the unknown layer j (-n < j < n, jz 0) is given by:

n V[ Lt 2 ¦ ii i tE 00 z ,0, jini V j (3.19) 6[ Rt jj [ t jj 78 Chapter 3. Experimental Methods for Stress Characterizations

(b) Stress characterizations in polycrystalline layer ( Grazing incidence XRD)

Compared with the epi-Si layer, the X-ray intensity in the polycrystalline silicon (poly-Si) film is considerably lower. Thus the medium resolution was configured as shown in Fig.

3.16, in which the high intensive quasi-paralleled beam is collimated by an X-ray mirror with the presences of both CuKĮ1 and CuKĮ2 wavelengths, giving rise to the average of

CuKĮ = 1.541874 Å.

Figure 3.16 XRD medium resolution configuration

As shown in Fig. 3.17, to obtain sufficient X-Ray intensity, the diffraction angles (șhkl) were measured with a fixed grazing incidence angle (Į=1º). More inclinational angles Ȍ are achieved by multiple asymmetric reflections (Ȍ ș± ĮĮ= 1° in the current case)

[Baczmanski, Braham et al., 2004].

Ȍ1

Ȍ2

Ȍ=ș-Į 2ș1 Į=1 Į=1 2ș2

Figure 3.17 Schematic of multiple-reflections GIXRD technique 79 Chapter 3. Experimental Methods for Stress Characterizations

Assuming that the polycrystalline material is isotropic, the relationship between the measured strain Hhkl and stress components ı11, ı22, ı33 is given by Noyan and Cohen

[1987΁ :

X H hkl 11 22 u VVV 33 E hkl

1X 2 2 2 u[ V 11 cos V 22 sin V 12 sin 2 sin <))) (3.20) E hkl 2 V 33 cos V 13 cos V 23 sinsin <))< ]2

where ±Ȟ/Ehkl and (1+Ȟ)/Ehkl are the X-ray elastic constants. For the case of in-plane equi- biaxial stress state, the above equation reduces to:

§ 12 XX · H ¨ sin 2 <¸V hkl ¨ EE ¸ © hkl hkl ¹ (3.21)

The in-plane equi-biaxial stress state can be verified easily by examining the strains at different azimuth angles (i.e., ĭ= 0º, 45º and 60º). For the present case, the polycrystalline silicon layer is exactly in an equi-biaxial stress state. In Eq. (3.20), the direction-dependent

X-ray elastic constants Ehkl can be determined by the Vook±Witt Grain Interaction Model

-12 [Vook and Witt, 1965]. It is given in Eqs. (3.22) and (3.23) below, where S11 = 7.691u10 ,

-12 -12 S12 = -2.142u10 , and S44 = 12.577u10 are silicon elastic constants:

1 § 1 · 11 2¨ 1211 SSSS 44 ¸ ī (3.22) Ehkl © 2 ¹

hllkkh 222222 ī 222 2 lkh (3.23)

80 Chapter 3. Experimental Methods for Stress Characterizations

The normal strain Hhkl can also be expressed by the lattice deformation as:

hkl aa 0 İhkl (3.24) a 0

where a0 is a stress-free silicon lattice constant, and ahkl are calculated from interplanar

222 spacings dhkl , i.e., hkl hkl lkhda . Substituting Eq. (3.21) into Eq. (3.24) renders the following linear relation:

hkl hklaKa ı a00 (3.25)

2 where hkl hkl 12 sin \ EvEvK hkl is the XRD stress factor in which Ȟ= 0.28 is the

Poisson¶s ratio of the polycrystalline silicon. Fig. 3.18 and Eq. (3.25) then give rise to a compressive equi-biaxial stress of -636.5 MPa and a0 = 5.4234 Å. Note that this a0 value is

0.136 % smaller than that of the bulk silicon (5.4308Å), which can be caused by the fact that the POCl3 GRSDQW DWRPV ORFDWHG LQ WKH VXEVWLWXWLRQDO VLWHV KDG GHÀHFWHG the silicon lattice [Lengsfeld, Nickel et al., 2002].

5.4350

5.4280

5.4210 ǖ

hkl 5.4140 a y = -4309.4x + 5.4234 5.4070

5.4000 -2.00E-06 -1.00E-06 -5.40E-20 1.00E-06 2.00E-06 3.00E-06

-6 Khkl (MPa )

Figure 3.18 Poly-Si XRD stress analysis (ahkl vs Khkl)

81 Chapter 3. Experimental Methods for Stress Characterizations

The curvature 1/R of the thin film system can be determined by X-Ray diffraction if the wafer bends significantly (i.e., R < 200 m) [Yua, Lai et al., 2008]. This can be achieved by the triple-axis analyser, which provides a very high resolution of 0.0033°. As shown in

Fig.3.19, R is calculated from the geometrical relationship between distance S on the wafer surface and the angular difference of rocking curves ǻȦi in X-ray diffractions, i.e.,

Zi RS . The sign convention of the curvature is that it is positive when the top surface is concave and negative when it is convex.

2x2mm Beam

-50,0 -30,0 -10,0 10,0 30,0 50,0 0,0

Figure 3.19 XRD curvature measurements

To minimize the local effects of surface undulations or non-uniformities, it is desirable to have a series of rocking curves examined at different points. For example, as shown in Fig.

3.20, 6 points were sampled along the transverse line on the SOS wafer surface, giving well resolved curvatures acquired from [408] reflections from sapphire substrate. The average radius of curvature, R was calculated from the results of every two of these points.

For the present case R was found to be 80 m, which brings about the residual stress of -

82 Chapter 3. Experimental Methods for Stress Characterizations

794.1 MPa in the back Si3N4 layer ([ h 1 in Eq. (3.19)) with the inputs of thickness information and stresses from crystalline layers.

30,000 50,0 25,000 30,0

20,000 10,0 ǻȦi -10,0 15,000 -30,0 Intensity (cps) 10,000 -50,0

5,000

0 62.45 62.47 62.49 62.51 62.53

Omega ()

Figure 3.20 Rocking curves obtained from 6 points on the wafer surface

3.2.2 Results

To examine the process effects on the residual stresses, 5 samples were taken after the fabrication processes, namely: (a) after epitaxial Si deposition (900 °C) (b) after implantation and annealing (1,000 °C); (c) back poly-Si deposition (600 °C ) and doping

(900 °C); (d) outer layers Si3N4 deposition (800 °C) (e) front etch of SiO2 and Si3N4. In this section, we will present the process-dependent stress variations in individual layers.

(a) Stress variations in epitaxial silicon (epi-Si)

The stress tensors in epi-Si were determined by the XRD method. They are listed in Table

3.4. For each process, it is noted that the in-plane components of the stress tensor are much larger than the others and the silicon films are basically in an equi-biaxial compressive stress state. 83 Chapter 3. Experimental Methods for Stress Characterizations

Table 3.4 Process-dependent stress in epi-Si (complete stress tensor)

Residual Stress VVV Process Descriptions ª º « VVV » « » ±20 MPa

¬« VVV ¼» a. Silicon deposition Epi Si ª º « » ǔ Sapphire ij « » « » ¬ ¼

b. Implantation(25°C), annealing and oxidation

SiO2 Epi Si ª º « » ǔ Sapphire ij « » « » ¬ ¼

c. Polycrystalline silicon deposition and POCl3 Doping

SiO2 Epi Si ª º Sapphire « » ǔ ij « » « » Poly-Si ¬ ¼

d. Nitride deposition

Si3N4 SiO2 Epi Si ª º Sapphire « » ǔ ij « » « » Poly-Si ¬ ¼ Si N 3 4 e. Front Si N and SiO etching (25°C) 3 4 2

Epi Si Sapphire ª º « » ǔ ij « » Poly-Si ¬« ¼» Si N 3 4

84 Chapter 3. Experimental Methods for Stress Characterizations

Fig. 3.21 plots the stress in a biaxial stress model, from which it is easier to examine how the residual stress is affected by the processes. It is notable that the critical process is after the implantation, annealing and oxidation, where the residual stress increases by 100 MPa.

Although these treatments are designed to improve the crystal quality of the epi-Si layer, the residual stress was not improved from annealing. After oxidation, the stresses are kept stable, and not affected by the deposition of other layers.

ıı 11 MPa) ıı 22 MPa) -600.00

-650.00

-700.00 -718.06 -750.00 -734.65 -784.66 -779.63 -786.02 -800.00 -810.72 -807.03 -809.16 -818.40 -834.72 -850.00 Residual Stress(MPa) Residual -900.00

Epi-Si Implantation Poly-Si Si3N4 SiO2 and deposition Annealing, deposition, Deposition Si3N4 Oxidation doping Etching

Figure 3.21 Process-dependent bi-axial stresses in epi-Si

(b) Stresses in polycrystalline silicon (poly-Si)

The residual stresses in the poly-Si film layer after the processes of c, d, and e (Table 3.4) were analyzed by asymmetric-reflection grazing incidence X-ray diffraction (GIXRD), determined by the ahkl vs Khkl plot shown in Fig. 3.22.

85 Chapter 3. Experimental Methods for Stress Characterizations

5.44 finalfinal SiN Si3N and4 and SiO2 SiO etch2 etch

5.433 afterafter SiN Si3N deposition4 deposition

afterafter poly-Si poly-Si depositiondeposition 5.426

(Å) 5.419 hkl a

5.412

5.405 -2.2E-06 -7.0E-07 8.0E-07 2.3E-06 3.8E-06

K (MPa-6) hkl

Figure 3.22 Process-dependent stresses in poly-Si (ahkl vs Khkl )

As shown in Table 3.5, the residual stress is nearly constant at about -648.7 MPa after each process. The stress-free poly-Si lattice parameter was determined from the intercept of the ahkl vs Khkl plot, and was found to be 5.4234 Å on average, which is 0.136 % reduction in comparison to 5.4308Å in bulk silicon, influenced by POCl3 dopant atoms [Lengsfeld,

Nickel et al., 2002].

Table 3.5 Equi-biaxial stress ı and stress-free lattice parameter a0 in poly-Si

XRD Results Process Residual Stress Lattice Constant ı(MPa) ± 30MPa a 0(Å)

After Poly-silicon Deposition -650.05 5.4234

After Nitride Deposition -659.59 5.4241

After Nitride Etching -636.54 5.4248

86 Chapter 3. Experimental Methods for Stress Characterizations

As it was justified in Eq. 3.19, the stresses in amorphous layers can be indirectly

determined by overall curvatures 1/R and the stresses in crystalline layersV i . Fig. 3.23 illustrates R observed after each process using XRD rocking curves. It was found that (a) after epi-silicon deposition, the wafer is convex due to the compressive stress (R=-165 m);

(b) after 1000°C oxidation, the bending is enhanced, with R=-110 m observed because of additional compressive stress in the cap layer SiO2; (c) the deposition of poly-Si minimizes bending by balancing the moment from the back side, resulting in a very small curvature, i.e. R= 664 m, but it is beyond the limit (200 nm) for obtaining a reliable stress; (d) the symmetric stresses from both sides of the Si3N4 layers do not change the bending of the system (Rൎ650 m); (e) after etching of the top layers Si3N4 and SiO2, the system is inversely curved to concave which was measured on the top side, i.e. R=80 m.

The results support well the conclusion drawn from Eq. 3.16, that overall curvature 1/R is the linear superposition of the curvatures 1/Ri from individual layers. It can also conclude that the residual stress of the film layer i depends merely on the process-induced mismatch strain between this layer and the substrate, but not influenced by the deposition of other layers. Therefore, we can determine the stress in amorphous layers SiO2 and Si3N4 from two representative processes (b) and (e), which are respectively -596 MPa and -795.1 MPa

as shown in Table 3.6. Sapphire YouQJ¶VPRGXOXV E s was measured by the IMCE HT650 system on the raw R-sapphire wafer, which was found as 403 GPa in [ 1011 ] direction at room temperature, giving rise to 537.3 GPa for sapphire biaxial modulus (ȣ=0.25).

87 Chapter 3. Experimental Methods for Stress Characterizations

Figure 3.23 Process-dependent radiuses of curvature. The processes are after (a) epi- deposition, (b) implantation, annealing and oxidation, (c) back poly-si deposition, (d) outer

Si3N4 deposition, and (e) front SiO2 and Si3N4

88 Chapter 3. Experimental Methods for Stress Characterizations

Table 3.6 Residual stresses in amorphous SiO2 and Si3N4 layers

Experiment Results Film Thickness Residual (μm) ı5 6WUHVVı i ı ıpoly-si R (MPa) t t t epi-si SiO2 epi-si poly-si (MPa) (MPa) (m)

SiO2 0.275 0.155 N/A -833 N/A 110 -596

Si3N4 0.3 0.11 0.4 -819 -636.5 80 -795.1

3.3 Summary

To summarize, the experimental methods were developed in this chapter, which provide a complete residual stress tensor, thickness dependence and stress distributions in a multi- layered system. The details and experimental findings are summarized in Table 3.7.

Table 3.7 Summary of residual stresses investigations

Investigations 6WUHVVı Techniques Findings

Complete stress ı ı ı XRD 11 12 13 equi-biaxial stress As-grown tensor ı22 ı23 ı33 ( least square ) SOS thickness- Raman, chemical stress increases with (epi-Si ) dependent ı (t ) f etch reduced film thickness stresses stress increased after ı ,ı ı XRD epi-Si 11 12 22 annealing/oxidation at ı ,ı ,ı ( Least Square ) 22 23 33 1,000 °C equi-biaxial multiple-reflection Multi-layer poly-Si -648.7 MPa stress ı GIXRD SOS

Si3N4 plane stress XRD curvature -795.1 MPa

plane SiO XRD curvature -596 MPa 2 stress

89 Chapter 3. Experimental Methods for Stress Characterizations

A complete stress tensor in an epitaxial silicon thin film was obtained by the XRD technique. The accuracy of the XRD method was maximized for the epitaxial silicon film by using thirteen diffraction planes of high Miller indices, and solved by over-determined equations based on the least square method. From the measured stress tensor, the stress in the SOS was found in-plane equi-biaxial and uniformly distributed across the wafer surface.

Raman scattering verified the magnitudes and surface distribution of the XRD results.

The thickness dependence of the residual stress was quantified by a simple but accurate method which is assisted by chemical etching. The new method allows the simultaneous measurement of the film thickness and residual stresses from the Raman spectrum. A clear trend of residual stresses in a submicron scale was achieved and that reveals the pronounced effect of the interface microstructure on residual stresses. It was found that the stress does not vary with thickness when the film is thicker than 700 nm, but increases with the thickness reduction. When the film is as thin as 100 nm, the stress is about 100 ~ 200

MPa larger than that in a thick film (>700 nm). This is because the interface effect is gradually manifested when the film becomes thinner. More detail of this effect will be elaborated in Chapter 4.

In the stress analysis in a multi-layered thin film system, a systematic approach was proposed to characterize the residual stresses in the epitaxial, polycrystalline and amorphous layers by using XRD techniques. The single-point XRD pattern renders the stresses of crystalline layers and the scanning XRD gives the curvature of the whole film.

Based on the newly-developed analytical model, the residual stresses of each layer can all be determined. Similar to the bi-layer system, compressive equi-biaxial stresses were found in individual layers in the stacking SOS.

90 Chapter 3. Experimental Methods for Stress Characterizations

It is interesting to note that the processes such as implantation and annealing cannot improve the residual stress in epitaxial silicon. Instead, these processes will increase the stress value by 100 MPa resulting from high temperature oxidation at 1,000 ºC. More detailed studies are given in Chapter 5, which will correlate the implantation and annealing effects with residual stresses.

91 Chapter 4. Origin and Analysis of the Residual Stresses

CHAPTER 4: Origin and Analysis of the Residual

Stresses

Lattice and thermal mismatches between dissimilar material layers are the two origins of residual stress in hetero-epitaxial thin film systems. Previously, theoretical predictions of residual stresses were based on disparate lattice parameters and the coefficients of thermal expansion (CTE), using the theory of elasticity [Freund and Suresh, 2003]. Such predictions, however, are valid for certain film thickness when the lattice mismatch can be entirely accommodated by elastic strain. Beyond a critical thickness [Frank and Van-der-

Merwe, 1949; People and Bean, 1985], the residual stresses are partially relieved by forming crystalline defects such as twins [Liu, Zhang et al., 2007; Zhang, Liu et al., 2007] and dislocations [Matthews and Blakeslee, 1974; Maree, Barbour et al., 1987]. The calculation of the stress relief is not as simple as previously thought because the interface defects are discrete and not uniform, and their interactions are complex. That is why quantitative relationships between residual stresses and experimentally measured lattice defects have never been established.

92 Chapter 4. Origin and Analysis of the Residual Stresses

A hetero-epitaxial silicon-on-sapphire (SOS) thin film system has a high lattice mismatch strain up to 5.6 % in Si [100] and 13.8 % in Si [010] directions. However, in Chapter 3, the residual stresses, characterised by the x-ray diffraction and Raman methods, were only -

600 to -850 MPa when the film thickness increase from 50 nm to 5 Pm. These experimental results are much smaller than the theoretical predictions (the high lattice mismatch strain in silicon film should lead to a stress in an order of 10 GPa), indicating significant stress relief due to lattice defects. Some early studies using transmission electron microscopy (TEM) showed that there was a high density of lattice defects in the epitaxial silicon film, of which micro twins [Lihl, Oppolzer et al., 1980], misfit dislocations [Abrahams, Buiocchi et al., 1976; Aindow, Batstone et al., 1989], and new interface compounds [Ponce and Aranovich, 1981] were the most popular mechanism to accommodate the mismatch strain. However, it is still unclear to date what is the mechanism to accommodate the mismatch strain in SOS.

The aim of this chapter is to unveil (a) how lattice and thermal mismatches influence the residual stresses, (b) how the mismatch strain is accommodated in SOS, and (c) how to model this accommodation mechanism and predict the thickness-dependent residual stress.

4.1 Effect of Thermal and Lattice Mismatch

The theoretical prediction of residual stresses in a SOS wafer is based on the disparate

CTEs of silicon and sapphire. The lattice mismatch strain is generally not considered

[Hughes, 1973]. However, detailed stress analysis requires the evaluation of both thermal and lattice mismatch effects, as well as the description of the stress distribution. To this end, Finite Element (FE) analysis was performed.

93 Chapter 4. Origin and Analysis of the Residual Stresses

4.1.1 Effects of Thermal Mismatch

A schematic of the three dimensional FE model is shown in Fig. 4.1a. The model shape resembles a silicon-on-sapphire system, which includes all the possible geometrical effects of a silicon wafer [Pramanik and Zhang, 2011]. A volume of interest (VOI) was defined in the centre of the model with the finest mesh as shown in Fig. 4.1b. In order to avoid boundary effects, the radial dimension of the model is 30 times the thickness of the thin film. The VOI contained overall 4,440 elements, and the whole model consisted of 34,628 elements. The finite element model is solved by ANSYS V12.1 with the 10-noded SOLID

98 elements which can cope with both thermal and mechanical responses.

A single crystal sapphire structure is shown in Fig. 4.2, which presents the relation between R-plane stress coordinates and the sapphire crystal coordinate, as well as the orientation relationship between silicon and sapphire. As shown in the figure, ı11 is along the direction of silicon axis [100], ı22 is in the direction of silicon [010] axis, which is parallel to sapphire direction[11 ]02 . The out-of-plane stress ı33 is parallel to silicon [001], which is perpendicular to the sapphire R-plane.

Furthermore, the material layers are assumed to be perfectly bounded to each other. The silicon properties are considered to be orthotropic, whereas the sapphire is regarded as an anisotropic material whose anisotropic elasticity is obtained from the stiffness matrix available in the literature [Goto, Anderson et al., 1989] and is converted from C-plane to

R-plane.

94 Chapter 4. Origin and Analysis of the Residual Stresses

(a) (b) Volume of Interest (VOI)

Crystalline Silicon Interface

Sapphire Substrate

Figure 4.1 Geometry of an SOS thin film system by FE simulation [Moridi, Ruan et al., 2011]: (a) full model (b) VOI c

R-Plane Sapphire

ı33 a3 Si[001]||Al2O3[1102] 32.4

ı11

Si[100]||Al2O3[1101] ı22 Si[010]||Al2O3[1120]

Figure 4.2 Coordinate systems in the sapphire crystal and in the R-plane [Vodenitcharova, Zhang et al., 2007]

95 Chapter 4. Origin and Analysis of the Residual Stresses

The simulation for thermal mismatch was performed without any external force. The bottom of the model was fixed in a z-direction and a node at a bottom corner of the model was fixed in x-, y- and z-axes to eliminate the rigid body motion. The model was cooled down from 900 °C to 25 °C simply by convection from all the surrounding surfaces. The simulation was run for one hundred sub-steps with the film coefficient of convection being

10.45 W/m2°C [Vodenitcharova, Zhang et al., 2007].

The detailed stress contour is shown in Fig. 4.3. The enlarged part is the silicon film from the VOI shown in Fig. 4.1b. It is notable that the compressive stress is nearly uniform at about 600 MPa in the film thickness direction.

= ; < 280 nm

; <

ı33

ı22 ı11

Figure 4.3 Thermal mismatch stress contour by FE simulation. The SOS film thickness is

280 nm, and the stress contour shows the variations in ı22 direction.

Although the CTE differs along the two in-plane directions, the numerical simulation gives rise to approximately a bi-axial stress state. Figs.4.4 (a) and 4.4(b) plot the thermal mismatch stresses distribution respectively for the thinner film of 280 nm and the thicker film of 5 μm. For both of the cases, the resultant thermal mismatch stresses in the Si(001) plane are uniform throughout the thickness of the films, i.e., ı11 and ı22 were -660.9 MPa 96 Chapter 4. Origin and Analysis of the Residual Stresses and -610.8 MPa in the film of 280 nm (Fig. 4.4a), and -646 MPa and -585 MPa in the film

RIȝP )LJE The out-of-plane stresses ı33 in both of the samples were very small compared with the in-plane components, and were negligible. Across the interface, the stresses change from compressive in silicon film to tensile in sapphire substrate. The similar value of the thermal mismatch stresses and stress state in the dissimilar films indicates that the thermal mismatch stress is independent with the film thickness.

Figure 4.4 Distributions of thermal mismatch stresses from FE simulation (a) 280 nm SOS and (b) 5 μm SOS

4.1.2 Effects of Lattice Mismatch

The effect of lattice mismatch was modelled using the same 3D model shown in Fig. 4.1 with a modified CTE to reflect the lattice mismatch strains. The lattice mismatch strains

aa were determined by sf , which are 6.1 % along Si [100] and 14.1 % along Si [010]. a s

97 Chapter 4. Origin and Analysis of the Residual Stresses

The lattice mismatch stresses ı11 and ı22 are plotted in Fig. 4.5, which are -8 GPa and -13

GPa, respectively. In contrast to the thermal mismatch stress, the significant anisotropy of lattice mismatch leads to large difference between ı11 and ı22. Similar to the effect of thermal mismatch, the resultant lattice mismatch stresses are also uniform along the film thickness direction, as shown in Fig. 4.5. This uniformity was also found in the relatively

WKLFNHUILOPȝP.

-7000 ı11 -8000 -9000 = 280 nm

; < -10000 = ; < -11000 -12000 ı33 ı 22 -13000 ı11 ı22 lattice mismatch stresses (MPa) stresses mismatch lattice -14000 0 50 100 150 200 250 300

distance to interface (nm)

Figure 4.5 Lattice mismatch stress contour from FE simulation. The SOS film thickness is

280 nm, and the stress contour shows the variations in ı22 direction.

4.1.3 Discussion

For the anisotropic SOS system under investigation, the above FE analyses lead to two important conclusions: (a) both thermal and lattice mismatch stresses in the film are uniform along the film thickness direction, and (b) both lattice and thermal mismatch effects are thickness independent.

For an isotropic material, the depth independence can be easily derived from the theory of elasticity. Since the film is much thinner than the substrate, it can be assumed that the out- of-plane stress vanishes, i.e., Vzz=0, and that only the in-plane displacements are significant. 98 Chapter 4. Origin and Analysis of the Residual Stresses

For the isotropic case, only the radial displacement ur needs to be considered. The equilibrium along thickness direction

w wWV zz rz 0 , (4.1) w wrz leads to

wW wu rz P r 0 ͘(4.2) wr wz

This shows that the radial displacement ur is independent of z, justifying that the in-plane

wu u normal stress 2 JPJV rr is independent of the depth. Here Ȗ and P are rr wr r

Lamé's first and second parameters, respectively. It can be further proceeded to show that the in-plane stresses are equi-biaxial. The membrane forces should satisfy

wN NN r r T W 0 , (4.3) wr r rz

t t where Nr V rrdz and NT VTTdz are radial and circumferential membrane forces, ³0 ³0 respectively. Since the interface shear stress Wrz=0 [Huang and Rosakis, 2005], the equi- biaxial stress state is then the exact solution of the above equilibrium equation.

The thickness independence can be clearly understood from a dimensional analysis. Since the residual stress in film is merely a function of mismatch strains 'H, elastic modulus Ef,

Es, Poisson ratios vf, vs and thickness tf, ts, the non-dimensional residual stress in the film

Vf can be expressed as

V § E t · f ¨ s s ,,,, 'HXX ¸ , (4.4) ¨ fs ¸ E f © E f t f ¹ 99 Chapter 4. Origin and Analysis of the Residual Stresses

where the subscript f and s pertain to film and substrate, respectively. When ts/tf is very large, the above equation approaches a constant since the stress cannot be infinite. As shown in Fig. 4.6, for the effects of both lattice misfit strain and thermal misfit strain, ts/tf >

30 has ensured thickness independence. For the SOS system we examined, ts/tf t 120.

-100 Thermal Mismatch Sigmaı11 11 5000 (MPa) Latticestresses mismatch -200 Thermal Mismatch Sigmaı22ı22 22 0 Lattice Mismatch Sigmaı11 11 -300 Lattice Mismatch Sigmaı22 22 -5000

-400 -10000 -15000 -500 -20000 -600 -25000 Thermal mismatch stresses (MPa)

-700 -30000 0102030

ts/tf Figure 4.6 Thermal and lattice mismatch stress variations with substrate/film thickness ratio (ts/tf)

However, in Chapter 3, we found that the residual stress in SOS thin film indeed depends on the film thickness. The residual stress increases as the thickness reduces (Fig. 3.12).

Such a thickness effect cannot be explained by merely CTE and lattice mismatches as shown by the above finite element simulations. It should be noted that even though the lattice mismatch strains in the orthogonal lattice directions are very different, the XRD measurement indicated that even for a 280 nm thin silicon film the stress state is still equi- biaxial. It is then apparent that the interface defects, which have been found in many preceding works, must operate to accommodate the lattice mismatch and to remove its effect on residual stress at a large thickness. To reveal the mechanism, it is necessary to use

100 Chapter 4. Origin and Analysis of the Residual Stresses

TEM to uncover the details of the interface defects and the stress accommodation mechanism.

4.2 Microstructural Defects

The samples subjected to TEM observation are as-grown SOS wafers of different epi-Si film thicknesses ranging from 280 nm to ȝP. For TEM investigation, although the plan- view specimen has the advantage of analysing relatively larger areas, it is not applicable for the as-grown SOS thin film because the high density of planar faults will obscure the interface structure and lead to misleading interpretations. Therefore, cross-sectional specimens were prepared.

As shown in Fig. 4.7, the samples were cut along silicon [110] using the Nova 200

Nanolab Focused Ion Beam (FIB) system. In the FIB milling process, the silicon film was protected by Pt deposition on the surface and milled by Ga ion beam at 30 KV and 0.63 nA.

AutoTEM software was used to reduce the thickness to less than 100 nm for a better lattice view. The TEM images were taken in Philips CM-200 with an acceleration voltage of 200

KV. The unit is equipped with a double tilt holder, so that the exact zone axis can be attained which maximizes the quality of the bright field and high resolution lattice images.

(a) (b) Pt protection interface Si [110]

Figure 4.7 TEM specimen preparations by Focus Ion Beam (FIB). The sample was tilted to (a) 53º coincide with ion-beam and (b) 0º coincide with electron-beam 101 Chapter 4. Origin and Analysis of the Residual Stresses

When taking the bright field images for revealing the overview distributions of the defects, the sample was tilted to the Si<110> zone axis for a better highlight of the defects. In order to investigate closely how the interface microstructure is formed to release the lattice mismatch, high resolution TEM (HREM) was utilized which directly uncovers the lattice defects at the Si-A12O3 interface. To reveal the misfit dislocations, the specimen was tilted slightly off the Si <110> zone axis, such that both silicon (11 )1 and sapphire (01 )21 plane fringes were discernible.

4.2.1 Microtwins

The sample was tilted to the Si [110] zone axis as shown in the inset (a) of Fig. 4.8 highlight microtwins as shown in Fig. 4.8. The diffraction pattern for Si [110] was resolved by Fast Fourier Transformation (FFT) analysis. Similarly, the sapphire zone axis, Al2O3

[10 21 ] was identified as shown in inset (b) of Fig. 4.8. These diffraction indices indicate the orientation relationship between silicon and sapphire is Si [110] || sapphire [10 21 ].

Fig. 4.9 is the bright field image taken under low magnification to highlight defect distribution in the film. In order to examine the thickness effect, cross-sections of wafers with film thicknesses of 280 nm, 500 nm, and 5 μm were examined. It is noted that the density of defects is the largest at the interface and diminishes within about 200-300 nm towards the film surface.

102 Chapter 4. Origin and Analysis of the Residual Stresses

FFT

(a) Si [110]

FFT

(b) Sapphire [10 21 ]

Figure 4.8 Crystallographic relations between silicon and sapphire by FFT analysis: the inset (a) shows Si [110] zone axis and (b) Al2O3 [10 21 ] zone axis

103 Chapter 4. Origin and Analysis of the Residual Stresses

The microtwins exhibit pronounced anisotropic characteristics, consistent with previous observations [Abrahams and Buiocchi, 1975; Ham, Abrahams et al., 1977; Batstone, 1991].

Most of them, named the majority twins, lie on the ( 111 ) plane, whereas others, named the minority twins, are on the ( 111 ) planes. This anisotropy is probably due to the stochastic nature of the mis-stacking twinning mechanism proposed by Ernst and Pirouz

[1988]. They explained that the facets of the ( 111 ) planes have a larger area than those of the ( 111) planes, and therefore have a higher probability of fault formation. Another explanation was proposed by Anidow [1989], who ascribed this anisotropy to the misorientation of silicon and sapphire coinciding planes.

It is interesting that the minority twins are more likely terminated within the film due to intersection with the majority twins. In contrast, the majority twins pass through the intersections and self-terminate within the film or at the film surface. The termination of a minority twin is shown in Fig.4.10, which was viewed under a higher magnification of

.[7KHWZLQ¶VRULHQWDWion was analysed by FFT analysis, which was determined to be on the 3( 11) plane. The observed self±termination of growth twins is in sharp contrast to the behaviour of deformation twins [Cahn, 1954]. When two deformation twins intersect, they pass through each other and form secondary twins. Thus, the twinning in SOS is due more likely to intrinsic growth rather than to the deformation induced by the lattice mismatch.

104 Chapter 4. Origin and Analysis of the Residual Stresses

(a)

Majority Silicon Minority twins twins Sapphire

(b)

Silicon

200 nm Sapphire

(c)

Silicon

200 nm Sapphire

Figure 4.9 Planar defects distributions in as-grown SOS of (a) 280 nm (b) 500 nm (c) 5 μm (etched down to 3 μm). The TEM image was taken in Si [110] zone axis

105 Chapter 4. Origin and Analysis of the Residual Stresses

FFT <૜ഥ11> <૚ഥ11>

Majority twins Terminating minority twins

m Silicon

5 nm Sapphire

Figure 4.10 TEM images of twin intersections at interface. The TEM image was taken under 200 K×. The twin orientation was analysed by FFT analysis.

The lattice images of micro-twins are shown in Fig. 4.11. The images were examined by high resolution TEM in the Si [110] zone axis, in which the Si (001) and {111} plane fringes are resolved. The enlarged regions a and b were treated by high resolution filter assisted by DigitalMicrograph software.

As shown in the figures, 1 or 2 atomic planes in the twinning lamella were commonly observed, which are named intrinsic and extrinsic stacking faults, respectively. They are either embedded in the twinning planes as shown in Fig.4.11a or present autonomously as extrinsic stacking faults along Si<110> as shown in Fig.4.11b. Generally, these thinner twins are originated from island coalescence [Hayashi and Kurosawa, 1978]. In this mechanism, islands are formed with small translational or rotational misalignments in the early stages of VW growth and also upon island coalescences.

106 Chapter 4. Origin and Analysis of the Residual Stresses

(a)

1nm 2 nm

(b)

Ex Ex Ex Ex

1nm Si/Sapphire interface

2 nm

Figure 4.11 High resolution lattice images of twins/stacking faults. The enlarged regions are to highlight (a) a multiple stacking faults in twins, (b) a period of extrinsic stacking faults

107 Chapter 4. Origin and Analysis of the Residual Stresses

The formation of microtwins is therefore to accommodate those mis-orientations [Stowell,

1975]. Alternatively, multiple domains (e.g. the co-existence of (100) and (110) domains in silicon films) can also result in microtwins at the islands coalescing boundaries [Abrahams,

Buiocchi et al., 1976; Trilhe, Borel et al., 1978]. It thus leads us to conclude that the most possible cause for twinning in SOS is island coalescences rather than deformation. These growth twins were even observed in the low (0.37 %) mismatch system, e.g. in the GaP film on (001) Si substrate [Ernst and Pirouz, 1988], which further confirms that the formation of twins is not necessarily related to deformation or stress release.

Twinning could, to some extent, release the lattice mismatch stress by geometric effects.

This model was proposed by Lihl et al. [1980]. They found that the {113} twins at interface would result in local tensions since the interplanar spacing of the {113} plane is smaller than the coinciding sapphire planes. By this means, the high compressive stress in silicon could be mitigated (Fig. 2.12). Twigg et al. [1990] argued against this geometric effect on stress relief. Based on the differential volume fraction of twins, they calculated the contribution of twins to stress release under two cases and claimed that the twinning was insignificant, i.e., less than 0.7 % contributes to stress relief.

4.2.2 Interface Restructure

An incoherent interface model was proposed by Ponce and Aranovich [1981], which was based on HREM investigation on the as-grown SOS sample. In their study, the images were taken with the specimen tilted to the exact silicon <110> axis. However, since sapphire <10 21 > is not parallel to silicon <110> but about 4° away from it, observations in this condition can only resolve the fringes parallel to the interface, whereas the misfit dislocations that are orthogonal to the interface are overlooked.

108 Chapter 4. Origin and Analysis of the Residual Stresses

Since the misfit dislocations were absent in their observations, they claimed that the interface was dislocation free, and high mismatch stress was released by forming new interface chemical compounds. In their model, the oxygen from an aluminosilicate (Al-Si-

O) structure would provide a site for (001) silicon, which leads to more freedom than sapphire. By this means, the mismatch between silicon and sapphire could be fully

DFFRPPRGDWHGUHVXOWLQJLQD³IDXOW-IUHH´LQWHUIDFH

However, even if the aluminosilicate mixture induces an incoherent interface, it does not lead to the thickness dependent residual stress as found in Chapter 3. We believe that the aluminosilicate mixture is not the cause of mismatch stress release and thickness dependence. In order to assess the elemental distributions at the silicon/sapphire interface, an Energy Dispersive X-ray Spectrometry (EDS) experiment was performed, which was equipped in the Philips CM200 TEM unit. The sample was an as-grown SOS with silicon film of 280 nm.

Under the magnification of 110 Kx, a complex mixture of the elements Si, O, and Al can be discerned at a region about 10-20 nm away from the Si/sapphire interface, which is shown in Fig. 4.12. These new compounds were probably amorphous SiO2 and Al6Si2O13 based on the thermodynamic calculations of chemical reaction [Rao and Jacob, 1982].

These are the solid solutions from Si and Al2O3 reaction at high temperatures. The presence of an aluminosilicate mixture may lower the interface bonding energy by inter- mixing of atoms [Copel, Reuter et al., 1990]. However its contribution to stress release cannot be quantified.

109 Chapter 4. Origin and Analysis of the Residual Stresses

(a)

Interface new compounds

(b)

Al2O3

MAG: 11000 x HV: 200.0 kV 300 nm

Figure 4.12 EDS elemental analysis at the SOS with film thickness of 280 nm. (a) element distribution (b) cross-section view to highlight the diffusion of elements.

110 Chapter 4. Origin and Analysis of the Residual Stresses

4.2.3 Threading and Misfit Dislocations

(a) Threading dislocations

Fig. 4.13 is the bright field image taken from as-grown 280 nm Si film under the Si<110> zone axis. High density of threading dislocations was observed, as denoted by the arrows.

It seems that the cause of these threading dislocations cannot be explained by the overgrowth of substrate dislocations proposed by Matthews and Blakeslee [1974] (Fig.

2.3), because the observed dislocation density in the substrate is far less than that in the film.

Alternatively, the nucleation of threading dislocations in the present case is more consistent with the model proposed by Maree et al. [1987]. They suggested that the dislocations are easily nucleated at the film surface because the homogeneous nucleation of dislocations inside the crystal requires twice the energy as that of the surface [Hull and

Bacon, 1984]. These dislocations will form half-loops, which can expand, and glide towards the interface along the {111} slip planes, resulting in a network of misfit dislocations. This is the most common dislocation mechanism in semiconductor thin films.

In these materials, the half-loops will be dissociated into two threading segments gliding on the {111} planes, and a misfit segment lying at the interface along the <110> direction.

However, during SOS growth, not all the half-loops could glide to the interface and lead to stress relief. In the early growth stage, a high density of planar faults forms prior to the surface half-loops. These planar faults will block the gliding process of the half-loops

[Aindow, Batstone et al., 1989] because a dislocation can only pass through the twinning

SODQHVLIWKH%XUJHUVYHFWRURIWKLVGLVORFDWLRQOLHVLQWKHWZLQ¶VSODQH

111 Chapter 4. Origin and Analysis of the Residual Stresses

50 nm

Figure 4.13 Microstructures and distributions of threading dislocations in 280 nm SOS. The TEM image was taken with Si<110> zone axis. The arrows indicate the threading dislocations which nucleate from the film surface, and in the process of gliding towards the interface.

100 nm Al2O3

Figure 4.14 Threading dislocations at the boundary of planar faults. The TEM image was taken under Si <110> zone axis. Indicated by white arrows, dislocation lines were observed at the boundary of twinning planes and mostly parallel to the planar faults 112 Chapter 4. Origin and Analysis of the Residual Stresses

The evidences of the above mechanism are shown in Fig. 4.14. The TEM image was taken under Si <110> zone axis, in which the dislocations were found pinned at the boundary of planar faults and it exhibits straight segments surrounding and parallel to the matrix/twining planes.

(b) Misfit Dislocations

Misfit dislocations were not observed in the early works, which is because high density planar faults (stacking faults and twins) will obscure the interface contrast in a plan-view specimen [Blanc, 1978; Aindow, 1990]. This influence was excluded by Abraham et al.

[1976], who prepared a sample at the early stage of growth prior to twin formations. He observed edge dislocation arrays parallel to the [011] and [ 011 ] directions. Later, Anidow et al. [1989] analysed the interface of a rapid thermal annealed (RTA) SOS sample, and observed the misfit dislocations with a line direction of 15° away from [110] towards [010].

The investigations done by Abraham and Anidow prove the existence of misfit dislocations.

However, their analyses were performed either at the early stage of film growth or after further processing (i.e. RTA), which cannot reveal the actual dislocation density in an as- grown SOS sample.

In comparison with plan-view samples, cross-sectional specimens are more powerful to uncover interface microstructures. To reveal the atomic structure at the interface, high resolution bright field images were taken with the specimen tilted slightly off the Si <110> zone axis. By this means, both silicon (111 ) and sapphire ( 01 21 ) plane fringes were discernible as shown in Fig. 4.15.

113 Chapter 4. Origin and Analysis of the Residual Stresses

Figure 4.15 A bright field HREM image showing mismatch of silicon-on-sapphire interface. The TEM image was taken slightly off silicon <110> zone axis, with apparent (11 )1 and sapphire (01 )21 plane fringes visible. The inset is an enlarged view for a single misfit dislocation.

114 Chapter 4. Origin and Analysis of the Residual Stresses

A number of high-resolution images taken at different areas of the sample showed that the dislocated interface structures were similar. The average spacing between the adjacent dislocations was found to be 10.3±0.5 sapphire ( 01 21 ) fringes, which is only slightly larger than the difference of the two lattices. The individual spacing varies from 7 to 17 fringes in our TEM images.

It is worth mentioning that although the misfit dislocations are not uniformly distributed at the interface, residual stress only depends on the average dislocation spacing of a longer range. Local irregularity is however negligible when the film thickness is sufficiently large

(i.e.> 60 nm). The rationale of this will be given in the next section.

Schematically, Fig. 4.16 shows the structure and formation mechanism of the misfit dislocations at the silicon and sapphire interface.

silicon film (111) (110)

(111) fringes Si [001] sapphire substrate [010] [100]

Figure 4.16 Schematic of misfit and threading dislocations

115 Chapter 4. Origin and Analysis of the Residual Stresses

As has been discussed, a threading dislocation is more readily nucleated at the surface forming half-loops, and then expands itself by gliding towards the interface, resulting in a misfit dislocation lying in the orthogonal Si<110> axes. By this means, the high level of lattice mismatch stress could be largely reduced.

4.2.4 Discussions

In summary, our HREM investigation reveals that the misfit dislocation is the dominant mechanism in releasing the mismatch stresses in an SOS system. We observed that the average spacing between adjacent dislocations is in every 10.3±0.5 sapphire ( 01 21 ) fringes. This value is only slightly larger than the theoretical dislocation density induced from lattice mismatches. These misfit dislocations result from half-loop dislocations at the film surface which glide towards the interface and eventually dissociate to a misfit segment lying at the interface.

The microstructures of microtwins imply that the microtwins in SOS are initiated from island growth and coalescences, rather than elastic deformation. It has been proved from literatures that microtwins only contribute less than 0.7 % to the total stress release.

4.3 Modelling

So far, we have identified the lattice mismatch stress release mechanism, and the average misfit dislocation density in an as-grown SOS sample has been quantified. In Chapter 3, we successfully revealed the stress variations with film thickness. Such thickness dependence cannot be explained by any analytical model available, or by the FE simulations based merely on CTE and lattice mismatches. To obtain a complete picture of

116 Chapter 4. Origin and Analysis of the Residual Stresses the effect of interface defect (i.e., misfit dislocations) on stress variations, it is essential to establish a numerical model so as to integrate the micro-structural defects with the macroscopic stress analysis.

4.3.1 Methodology

To integrate all the effects of lattice-thermal mismatches and discrete interfacial dislocations on residual stresses, we proposed a comprehensive finite element (FE) model schematically shown in Fig. 4.17.

Effects of thermal mismatch ſth. =ᇞĮᇞT

FE Simulation Effects of Effects of lattice Coupled Stress dislocations mismatch aa ſdisl. = 1/2 (HREM) ſlatt.= sf a s

Figure 4.17 FE analysis scheme. İth., İlatt.., and İdisl.. respectively denotes thermal, lattice mismatch strains, and edge dislocation induced strain

In this model, the dislocation effects are calculated based on actual misfit dislocation

density along the Si [110] direction (coinciding with Al2O3 [ 01 21 ]) obtained from the

HREM experiment.

In order to find a proper model to describe the misfit dislocation effect on residual stress, let us consider an array of misfit dislocations with an average spacing ns of sapphire

disl. ( 01 21 ) planes. The average strain due to these dislocations is H /1 ns . These

117 Chapter 4. Origin and Analysis of the Residual Stresses dislocations accommodate the lattice mismatch and lead to the vanishing effect of lattice mismatch when the thickness is large. The full accommodation of lattice mismatch

disl. indicates H / aaa ssf , where af and as are lattice constants for film and substrate respectively. Since the interface structure forms at the deposition temperature, we use lattice constants at the corresponding temperature (af =3.857 Å and as=3.507 Å). The calculated dislocation spacing is ns =10.1, which is close to the experimentally measured value of 10.3r0.5. However, if only the average strain H disl. induced by dislocations is considered, there will not be any thickness-dependence. To model these dislocations for a film of only a few hundred nanometres thick, the discreteness of dislocation must not be overlooked.

Continuum mechanics is generally employed to resolve the stress field around a single dislocation [Gutkin and Romanov, 1992]. Accordingly, the finite element (FE) method can be used. The finite element solution of the stress field around an edge dislocation has been verified by an analytical solution [Moridi, Ruan et al., In Press]. For the present problem, it is required to establish a plane-strain finite element model of an array of dislocations at the interface to investigate the stresses in the Si thin film.

The details of the FE model are shown in Fig. 4.18. The element size near the interface was taken to be the same as the substrate lattice constant, such that the dislocations can be

aa sf modelled. The lattice mismatch strain is 10.41 %= , where the lattice constants af a s

=3.857 Å at Si (110), and as = 3.507 Å at sapphire ( 01 21 ).

118 Chapter 4. Origin and Analysis of the Residual Stresses

Figure 4.18 Schematic of an edge-type dislocation at interface and the FE model (x Silicon atoms, R Sapphire atoms).

The effect of the edge dislocations was modelled by the pre-strain corresponding to the introduction of an extra plane of atoms in the substrate as shown in the figure. The edge

dislocations have the Burgers vectors along sapphire, i.e., b=as[ 01 21 ]. Although the Si

(111 ) planes in Fig. 4.15 are the fringes observed in the TEM images, the refined mesh around a dislocation is aligned with the directions of Si [001] and [110] for simplicity, as indicated by the dashed grey line. The local strain corresponding to an edge dislocation is

ɂ=b/2as=1/2, where b is the Burgers vector that is equal to the spacing of the sapphire

( 01 21 ) plane and in the direction parallel to the interface. The introduction of dislocations will cause local compression in the substrate and tension in the film. This is the mechanism that renders the observed thickness-dependence of residual stresses.

The simulation result is shown in Fig. 4.19, in which region A represents an edge dislocation core, whereas B denotes region imposed with lattice mismatch strains.

119 Chapter 4. Origin and Analysis of the Residual Stresses

$16<6 Silicon B A Sapphire

Figure 4.19 FE simulations of lattice mismatch and dislocation effects. Region A represents an edge dislocation core, and B denotes region affected from lattice mismatch.

The stress contours are limited from -3,000 MPa to 3,000 MPa for a better illustration. The results show that the difference of residual stress between region A and B is notable close to the interface and then the deviation becomes negligible when the film thickness becomes larger.

The thermal mismatch stresses were calculated by the 3D FE model as was introduced in

Sec 4.1.1. The model was cooled down from 900°C to 25°C by convection from all surfaces. The in-plane compressive stresses in the thin film obtained from this model were

659 MPa, 609 MPa and 633 MPa in Si [100], [010] and [110] directions, respectively. It has been elaborated that residual stresses due to thermal mismatch are independent of film thickness. This is consistent with the experimental result that the stress is nearly uniform at

550-600 MPa when the thickness is larger than 700 nm (Fig. 3.12).

120 Chapter 4. Origin and Analysis of the Residual Stresses

Due to the linear elasticity assumed in the analysis, the stresses calculated from the thermal mismatch and dislocated lattice structure can be superimposed to compare with the experimental measurements.

4.3.2 Verifications

Fig. 4.20 compares the total residual stresses from the FE analysis with those from the

Raman experiments. The thickness-dependent stresses V z obtained from the FE

t § f P f z · P t ff simulations were averaged using ¨ ezz PVV f dz¸ 1 e to account ©³0 ¹ for the effect of attenuation of the Raman signal.

-500

-600

-700

-800 Raman Results

-900 FEA_ Si [110] ( 10.1 ) FEA_ Si [110] ( 10.3 )

residual stress (MPa) -1000 - FEA_ Si [110] ( 10.5 ) ı

-1100 FEA_ Si [100] ( 17.8 ) FEA_ Si [010] ( 7.3 ) -1200 0 200 400 600 800 1000 1200 1400

tf - film thickness (nm)

Figure 4.20 Comparison of thickness-dependent stresses between experimental results and FE simulation.

121 Chapter 4. Origin and Analysis of the Residual Stresses

When the film thickness is beyond 1,300 nm, the stress levels off at around 550-600 MPa as seen from both the experimental and numerical results. Therefore, Fig. 4.20 shows only the results between 50 nm and 1300 nm to emphasize the effect of the misfit dislocations.

Three stress vs thickness curves were obtained from the FE simulations, corresponding to the dislocation spacings of 10.1, 10.3 and 10.5 of sapphire ( 01 21 ) fringes. As shown in the figure, the denser dislocations (10.1 spacing) lead to smaller compressive stress and also smaller affecting depth. The simulation result based on 10.3 spacing is the closest one to the experimental result, which is identical to the average dislocation spacing measured in the high-resolution TEM images in Fig. 4.15.

Also plotted in Fig. 4.20 are the calculated in-plane normal stresses ı11 and ı22 in Si [100] and Si [010] directions from similar FE simulations. Based on the criteria of minimizing the total strain energy of the system, the dislocation spacings were found to be 17.8 and 7.3 respectively in [100] and [010] directions, which is consistent with the theoretical value calculated based on the lattice difference.

The stress vs thickness curves calculated from three different crystallographic planes agree with the experimental results very well. Both results show that residual stress increases with the reduction of the film thickness. The compressive residual stress in the silicon film is more or less uniform at 600 MPa when the film thickness is larger than 700 nm, which is mainly caused by thermal mismatch effects. Below 700 nm, the stress increases continuously as the thickness reduces and becomes larger than 800 MPa at around 100 nm, manifesting the coupled effects of lattice mismatch and misfit dislocations. In addition, the excellent consistency between experimental and numerical results indicates that the interface misfit dislocation is indeed the mechanism of the thickness-dependence of residual stress.

122 Chapter 4. Origin and Analysis of the Residual Stresses

In order to account for the effect of dislocation distribution, we performed FE simulations with uniformly spaced dislocations (Case 1) and two sets of non-uniform dislocations

(Case 2 and Case 3). For each case, the dislocations spacings in the Si [100] direction are shown in Table 4.1, and the average spacing is around 18 calculated based on the lattice mismatch.

Table 4.1 Scenario for justification of dislocation distribution effect

Average spacing of Case Dislocation spacings dislocations Case 1 18 18, 18, 18, 18, 18, 18

Case 2 18 18, 17, 20, 17, 14, 22

Case 3 18 18, 19, 15, 20, 15, 21

The residual stresses vs film thickness is plotted in Fig. 4.21. It shows that the distribution of dislocations does not have a significant effect on the residual stresses. The resultant total strain energies for the case 1, case 2 and case 3 are respectively 0.0258 J, 0.0284 J and

0.0283 J, which are not influential to the dislocation distribution. It also shows that although the average stress near the interface is slightly affected by the dislocation distribution, the stresses far from the interface (>60 nm) converge to a very similar value to that of the case of uniform distribution. Hence, the FEA simulation results conclude that the dislocation distribution effect is negligible on the total residual stress of the thin film systems.

The excellent consistency between the FE analysis and the experiment confirms that the

FE model captures the main mechanism and can accurately predict residual stresses. It also validates the assertion that discrete interface dislocations are predominant for the

123 Chapter 4. Origin and Analysis of the Residual Stresses thickness-dependence of residual stress in silicon-on-sapphire systems. Although interface dislocations accommodate the lattice mismatch and lead to a vanishing effect on stress when the film thickness becomes sufficiently large, they cannot remove the effect of lattice mismatch at a small thickness due to the discreteness, leading to the observed thickness- dependence.

-80 Case 1 (average 18)

-90 Case 2 (average 18)

Case 3 (average 18) -100

-110

-120 NormalResidual Stresses (MPa) -130 0 60 120 180 240 300

Distance from Interface (nm)

Figure 4.21 Justification of dislocation distribution effects

4.4 Conclusions

This chapter investigates the origins and mismatch accommodations of residual stresses in an SOS system.

Residual stresses induced from thermal and lattice mismatch effects are calculated based on 3D and 2D finite element models. Thermal mismatch stresses are found at -650 MPa and -600 MPa in Si [100] and Si [010] directions, whereas the lattice mismatch effect leads

124 Chapter 4. Origin and Analysis of the Residual Stresses to anisotropic stresses about -8 GPa and -13 GPa respectively along Si [100] and Si [010].

However, neither of these two effects can lead to the depth-dependent or thickness- dependent stresses of the experimental observations.

The comprehensive TEM studies reveal that microtwins and interface elemental modifications are insignificant to the residual stress release, whereas misfit dislocation is influential on stress accommodation. From the HREM image, we have successfully obtained the dislocation density in an as-grown SOS sample.

Based on this experimental observation, a comprehensive finite element analysis incorporating the effect of misfit dislocations at the interface has been successfully carried out. By comparison with the thickness-dependent stresses, some conclusive findings are given:

(1) Basically, residual stresses in a thin-film system are caused by the coupled effects of thermal-lattice mismatches and interface defects (i.e., misfit dislocations).

(2) When the film is thick, the residual stress is equal to the stress caused by the thermal mismatch. The residual stress increases with decreasing film thickness.

(3) An analysis based on merely the average effect of thermal and lattice mismatches cannot uncover the thickness-dependence of the residual stresses in a thin film system. The key factor to consider is the discrete distribution of dislocations at the film-substrate interface. If the thickness of a film is large, the effect of dislocations and the lattice mismatch can be averaged out, which then leaves only the thermal stress as the main cause.

With a small film thickness, however, the interface defect will set in and the effects of lattice mismatch and film thickness will appear.

125 Chapter 4. Origin and Analysis of the Residual Stresses

(4) The misfit dislocation is the predominant mechanism in mitigating lattice mismatch stress and inducing thickness-dependence.

126 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

CHAPTER 5: Effects of Manufacturing Processes on

Residual Stresses and Microstructures

In Chapters 3 and 4, we have proved that interface misfit dislocations were the dominant mechanism for releasing lattice mismatch stresses. After film growth, only a small fraction of the lattice mismatch stresses (0 to -300 MPa) remains in the film. Thinner film has larger residual stress, which is due to the remaining effect of lattice mismatch. As-grown film may undergo a series of post-deposition processes such as cooling, annealing, multilayer deposition, etc. In this case, the CTE mismatch between film and substrate will inevitably lead to more stresses in the thermal cycle. In Chapter 4, we found that the theoretical thermal mismatch stress is about -650 MPa.

However, the main challenge in predicting the stress in a real case involves two main uncertainties: (a) the temperature-dependent CTEs for both silicon and sapphire vary from paper to paper in the literature [Yim and Paff, 1974; Reeber, 2000; Ball, 2006], and (b) de- bonding and stress relaxation could possibly occur upon cooling [Hiramatsu, Detchprohm et al., 1993; Roder, Einfeldt et al., 2006]. Thus, a reliable stress analysis requires experimental examination of the temperature-dependent stresses. To avoid possible

127 Chapter 5. Effects of Processes on Residual Stresses and Microstructures structural modifications at high temperature (~900 °C), the residual stresses were measured reversely at elevated temperatures rather than cooling from the deposition temperature as the real process. This post-mortem stress measurement could provide valuable information to verify and calibrate the theoretical calculations.

Another critical process is film re-growth involving ion implantation and high temperature annealing. It has been evidenced that the crystalline quality of re-grown silicon can be significantly improved [Inoue and Yoshii, 1980; Richmond and Knudson, 1982; W.R.

McKenzie, 2005], and that residual stresses can also be relieved [Ohmura, Inoue et al.,

1983; Bolotov, Efremov et al., 1992; Dubbelday and Kavanagh, 1998]. These studies have shown that the reduction of residual stresses is related to implantation and annealing conditions. However, the mechanism remains elusive.

Therefore, the aim of this chapter is to provide more insights into the process effects on residual stresses. The focus will be on the effects of process parameters such as temperature, implantation and annealing conditions.

5.1 Effect of Temperature

5.1.1 Measurement

In Chapter 3, we employed the least square algorithm in investigating the complete stress tensor in an epitaxial silicon thin film. The accuracy of the residual stress is influenced by the reliability of the stress-free lattice constant a0, which is normally obtained from single crystal silicon. However, a0 varies with temperature, which makes the method used in

Chapter 3 not applicable for analyzing temperature-dependent stress.

128 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

A direct measurement of a0 (T) is infeasible by conventional X-ray diffraction, because thin film is stressed after the deposition and cooling process. In this case, the lattice spacing in a

[hkl] direction will be the superimposition of effects from both stress-free expansion and residual stress induced deformation.

Fortunately, in thin film, the in-plane stresses ı11ı12 and ı22 are much larger than the other stress components (see Section 3.1.1). It is reasonable to assume that the other stress components ı31 ı32 and ı33 vanish. The three in-plane stresses and the stress-free lattice constant can then be simultaneously solved by a multiple regression algorithm [Suzuki,

Akita et al., 2003; Imafuku, Suzuki et al., 2008]. By this means, the thermal expansion and temperature-dependent residual stresses can be resolved.

In XRD analysis of a certain crystallographic direction [hkl], the normal strain İhkl (or İ)< )

0 is expressed by the measured lattice spacing dhkl and stress-free spacing dhkl :

0 hkl dd hkl hkl İİ )< 0 . (5.1) dhkl

0 0 222 For a diamond cubic structure, dhkl can be expressed as hkl 0 / lkhad and Eq.

(5.1) is recast as:

222 hkl alkhd 0 1 H)< . (5.1a)

Invoking the condition that ı13 = ı23 = ı33 = 0 and İ13 = İ23 = 0, the non-zero strain

components obtained from strain-stress relations mn Smnc ijVH ij (i, j, m, and n = 1, 2, and 3) are

129 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

SS VVH 2212111111 , S VH 124412 2 , SS VVH 2211111222 , SS VVH 2212111233 (5.2)

where the conventions SS c , SS c SS c are used. 11 1111 12 1122, 44 2323

The transformation equation of the measured strains in the laboratory coordinate İ)< to the 6 strain tensor components İij (i, j =1, 2, 3) in the crystallographic coordinate system have been given in Eq. (3.1). Substituting Eq. (5.3) into Eq. (3.1), and incorporating Eq.

(5.1a) give rise to the relation between dhkl and stresses ı11, ı12, and ı22:

222 hkl lkhd sin 2 sin 2 <) 1{ >@Sa cos 2 sin 2 S 2 sinsin 2 S 1 sin 2 V <<)<) S V 0 11 12 12 4411 2 12 (S cos 2 sin 2 S 2 sinsin 2 S 1 sin 2 u<<)<) V } >@12 11 12 22 (5.3)

Eq. (5.3) leads to a multiple regression model:

ªE1 º ª 11 )1( 12 )1( BBB 22 )1( º « » «E » BBB « 2 » « 11 )2( 12 )2( 22 )2( »

«E3 » « 11 )3( 12 )3( BBB 22 )3( » « » « » ªV11º E4 11 )4( 12 )4( BBB 22 )4( « « » a « » u V » . (5.4) «E » 0 « BBB » « 12 » 5 « 11 )5( 12 )5( 22 )5( » «V » « » ¬ 22¼ u13 «E6 » « 11 )6( 12 )6( BBB 22 )6( » « » « » « » « » E « BBB » ¬« n ¼» nu1 ¬ 11 n)( 12 n)( 22 n)( ¼ nu3

where

2 2 2 2 2 B11(n)=a0[S11cos ĭsin Ȍ+S12sin ĭsin Ȍ+S12(1-sin Ȍ)],

130 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

2 B12(n)=a0/2(S44 sin2ĭsin Ȍ and

2 2 2 2 2 B22(n)=a0[S12cos ĭsin Ȍ+S11sin ĭsin Ȍ+S12 (1-sin Ȍ)] are the directional coefficients in n measuring directions, which are determined from the silicon elastic compliance matrix and the measuring directions ĭand Ȍ,

E = lkhd 222 n hkl

are the experimental results from multiple asymmetric diffractions.

In a multiple regression model, it is important to use a sufficient number of diffraction directions to minimize the effect of random errors in the individual measuring direction.

These diffraction planes should be arbitrarily selected with higher multiplicity, otherwise the multicollinearity problem [Weber and Monarchi, 1976; Fernandez, 1997] will make the solutions unreliable. In silicon film, we examined 9 representative and arbitrarily diffracted directions of [004], [115], [206], [315], [224], [335], [404], [444], [353], and this yields the most reliable returns of variables ı11, ı12, and ı22. Meanwhile, the temperature-dependent lattice constants a0 can also be solved from the multiple regression model.

CVD SOS wafers with silicon film thickness of 280 nm and 5 μm were examined in the

Philips Panalytical (MRD) diffractometer. The incidence and diffracted optics were configured similar to a room temperature setting (Fig. 3.6). When performing the X-ray diffraction experiment at high temperatures, a domed hot stage (DHS 1100) was used, providing a maximum temperature up to 1,100 ºC.

131 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

As shown in Figs. 5.1a, and 5.1b, the thermal stage consists of: (1) a Graphite Dome that provides high temperature resistance and excellent X-ray transmission; (2) Cooling air supply and control to keep the temperature as required; (3) a tunable cooling ring to direct the cooling air onto the housing and the dome; (4) an aluminum nitride sample holder, with pronounced temperature conductivity that guarantees high temperature uniformity across the sample holder. The heater and the thermocouple are just underneath the sample holder.

(a) (b) 4. AlN sample holder

Figure 5.1 The DHS1100 thermal stage in Phillips MRD (a) the thermal stage covered with Graphite Dome, and (b) the heating unit and sample holder spring

The residual stresses in the two samples were first measured at room temperature 25ºC, and then at 325 ºC, 500 ºC, 700 ºC, 900 ºC with a heating rate of 60 ºC/min. In order to ensure the uniformity and stability of the temperature, the sample was kept at each temperature for 5 minutes before X-ray diffraction measurement.

132 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

5.1.2 Results

2 2 Similar to the dhkl vs sin Ȍmethod, the excellent linear relation between En and sin Ȍ, as shown in Fig. 5.2, implies reliable results from the XRD experiments, where En are the experimental outputs from multiple asymmetric diffractions.

2 In addition, the linear relationship of En and sin Ȍalso implies that the measured stress is independent of azimuth angle ĭ, but only determined by the inclinational angle Ȍ. This is consistent with our previous results from the complete stress tensor, in which the epitaxial silicon film is under an in-plane equi-biaxial stress state, and the in-plane shear stress

2 component is negligible. Similar to the traditional dhkl vs sin Ȍ plot, the negative and positive slopes also indicate the compressive and tensile stresses, respectively.

For the samples of 280 nm and 5 Pm thick, negative slopes (compressive stress) were observed. This is reasonable because the sapphire substrate shrinks more than silicon upon cooling, resulting in a compressive stress in the film. The value of the slope indicates the magnitude of the residual stresses, which are slightly larger in the thinner film of 280 nm.

This disparity is due to the more pronounced impact of lattice mismatch effects in thinner film.

In order to solve for the temperature-dependent stresses, variation of the elastic modulus with the temperature should be considered. As listed in Table 5.1, the temperature- dependent silicon compliances were calculated from the functions given in [Hull, 1999].

By solving for the multiple regression system in Eq. (5.4), we obtained the stress-free lattice constants a0 and the three in-plane stress components ı11, ı12, ı22.

133 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

5.455 004 115 206 315 224 335 404 444 353 5.445 900ºC

700ºC

(Å) 5.435 E 500ºC

5.425 325ºC

(a) 25ºC 5.415 0 0.2 0.4 0.6 0.8

2 sin Ȍ

5.455 444 353 404 315224 335 900ºC 004 115 206 5.445 700ºC

500ºC 5.435 (Å) E 325ºC

5.425

25ºC (b) 5.415 0 0.2 0.4 0.6 0.8

sin2Ȍ

2 )LJXUH5.2 En vs sin Ȍplot from high temperature XRD in as-grown SOS of (a) 280 nm DQG E ȝP

134 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

Table 5.1 Temperature-dependent silicon compliance [Hull, 1999]

Temperature(ºC) 25 325 500 700 900

-12 -1 S11 (ൈ10 Pa ) 7.691 7.937 8.086 8.263 8.449

-12 -1 S12 (ൈ10 Pa ) -2.142 -2.212 -2.254 -2.304 -2.357

-12 -1 S44 (ൈ10 Pa ) 12.58 12.90 13.10 13.33 13.57

In Fig. 5.3, a0 obtained from X-ray diffraction experiments are compared with the stress- free lattice constant of a bulk single crystalline silicon at different temperatures [Hull,

1999]. For both samples, a0 agrees very well with the lattice constants provided in [Hull,

1999] for temperatures lower than 500 qC. When the temperature is higher than 500 qC, the measured a0 slightly deviates from that in bulk material. Thicker film has a larger deviation.

5.455

5.45

5.445 Constant (Å) 5.44 Bulk Silicon 5.435 5 ȝm - Lattice Silicon 0 a 5.43 280 nm

5.425 0 200 400 600 800 1000 Temperature (ºC)

)LJXUH5.3 Temperature-dependent lattice constant a0 in as-grown SOS

135 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

The small discrepancy in a0 may partly be caused by the deviation of the zero position of the diffraction angle 2T at the initial calibration or by the stress gradient. The latter is more striking in the thicker film. The in-plane stresses in the 280 nm and ȝP SOS films are listed in Table 5.2. At each temperature the shear stress in both of the samples is negligible

LQFRPSDULVRQZLWKWKHQRUPDOVWUHVVHVı11 DQGı22.

Table 5.2 Temperature-depended residual stress form XRD measurement. The samples examined are 280 nm and ȝP SOS.

280 nm ȝP

Tempera- ı11 ı22 ı12 ı11 ı22 ı12 ture (ºC) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa)

25 -738.7 -736.6 -28.1 -577.2 -569.5 -32.7

325 -543.5 -518.6 -33.4 -301.3 -333.3 32.2 500 -361.7 -363.6 -8.0 -139.6 -132.9 6.7 700 -186.9 -206.8 -33.7 7.7 6.4 2.2 900 -89.3 -96.9 11.4 93.7 108.1 -6.2

Hence, only normal stresses are plotted in Fig. 5.4, showing notably the temperature- dependence. For both samples, the residual stresses reduce OLQHDUO\ ZLWK WKH LQFUHDVLQJ

WHPSHUDWXUHDQGWKHUHGXFWLRQUDWHVDUHVLPLODU$VLPLODUYDULDWLRQRIUHVLGXDOVWUHVVLQWKH

WZR VDPSOHV LQGLFDWHV WKDW WKH temperature-dependence does not change with WKH ILOP

WKLFNQHVV ,W LV DOVR LQWHUHVWLQJ WR QRWH WKDW DW DERXW & ZKLFK LV WKH GHSRVLWLRQ

WHPSHUDWXUH QHLWKHU VDPSOH LV VWUHVV-IUHH )RU WKH QP 626 VDPSOH D FRPSUHVVLYH

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RIDERXW03D

136 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

200

SOS 5 ȝm -200

-400 SOS 280 nm -600 XRDı11 Sigma 11 Residual Stress (MPa) Stress Residual -800 XRDı22 Sigma22

-1000 0 150 300 450 600 750 900

Temperature (ºC)

)LJXUH7HPSHUDWXUH-GHSHQGHQWUHVLGXDOVWUHVVHVREWDLQHGIURP;5'H[SHULPHQWV7KH VDPSOHVH[DPLQHGDUHDV-JURZQ626VDPSOHVRIPDQGQPWKLFN

'LVFXVVLRQ

Fig. 5.4 exhibits several intriguing phenomena which have never been reported in the literature: (i) in neither the 280 nm nor the 5 Pm films, did the residual stresses vanish at the deposition temperature; and (ii) when the 5 Pm film was heated to the deposition temperature, the residual stress became tensile.

To assist the interpretation of the phenomena, the theoretical thermal mismatch stresses were calculated by the finite element (FE) method. The numerical model and boundary conditions in FE simulation were introduced in Chapter 4. The temperature-dependent elastic modulus was the same as that in XRD stress calculation, and the temperature- dependent CTE of silicon and sapphire was based on the value given in the literatures

[Hull, 1999] and [Reeber, 2000]. The cooling from 900 °C to different temperatures of

137 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

700 °C, 500 °C, 325 °C and 25 °C by convection from all the surrounding surfaces was simulated (convection coefficient 10.45 W/m2°C). The in-plane normal stresses obtained from FE simulation were also very close to each other, as shown in Table 5.3. However, at each temperature, the calculated thermal mismatch stresses do not differ as much as those shown in Fig. 5.4.

Table 5.3 Temperature-dependent residual stresses obtained by FE simulation. The samples examined are as-grown SOS of 280 nm and ȝP

280 nm ȝP

Temperature ı11 ı 22 ı 11 ı 22 (ºC) (MPa) (MPa) (MPa) (MPa) 25 -660.9 -610.8 -672.0 -621.6

325 -450.5 -417.2 -465.2 -431.5

500 -316.5 -292.4 -332.7 -308.5

700 -158.5 -146.1 -178.1 -164.9

900 0 0 0 0

Fig. 5.5 shows a comparison of the XRD and FE simulation results for the thinner film of

280 nm. At room temperature, compressive stress was observed at 737 MPa, which is

~100 MPa larger than the calculated thermal stress (636 MPa). This additional stress indicates the co-existence of both thermal and lattice mismatch effects when the film is sufficiently thin i.e., thinner than 700 nm. This is consistent with the thickness-dependent stress results given in Chapter 3. At the 900 ºC deposition condition, the thermal mismatch should be fully released. Therefore the compressive stress of 93 MPa in 280 nm film is due to the effects of lattice mismatch and misfit dislocations.

138 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

Furthermore, as is indicated in the figure, for all the temperatures examined, the difference between the measured stress and the calculated thermal stress is almost a constant of 80

MPa. This indicates a constant growth stress during thermal cycles. This is because the variation of lattice mismatch strain from deposition temperature (i.e., 5.3 % (along Si [100]) and 12 % (along Si [010]) to the room temperature (5.7 % and 12.4 %) is negligible compared to the significant initial mismatch strain. The constant stress also implies that no further misfit dislocations or stress relaxation occur at the cooling process. This is consistent with the room temperature dislocation density observed in chapter 4 by HREM, which was similar to the theoretical prediction at the deposition temperature.

-100

-200 Average -300 offset -80 MPa

-400 XRD Sigma 11 -500 FEA Sigma 11 Residual Stress (MPa) -600

-700

-800 0 200 400 600 800 1000

Temperature (ºC) Figure 5.5 Comparisons of temperature-dependent stresses from XRD experiment and FE calculation for an as-grown SOS of 280 nm. The trend lines (dashed lines) are fitted with linear function

,Q WKH WKLFNHU ILOP RI ȝP RQ WKH RWKHU KDQG WKH ODWWLFH PLVPDWFK HIIHFW YDQLVKHV DV shown in Chapter 3. Thus, the stress observed from the XRD experiment only reflects the thermal mismatch effect. In this case, the temperature-dependent stresses should be the

139 Chapter 5. Effects of Processes on Residual Stresses and Microstructures same as the FE simulation results. However, as shown in Fig. 5.6, the stress at room temperature was of -573 MPa, which is approximately 70-80 MPa smaller than the calculated thermal stress (647 MPa). As the temperature increases, the measured and calculated stress decreasing rates are similar. The average offset is about 120 MPa, which leads to a tensile stress of about 101 MPa detected at growth temperature (900 ºC).

150

-150 Average Offset 120 MPa -300 XRD Sigma 11

-450 FEA Sigma 22 Residual Stress (MPa)

-600

-750 0 150 300 450 600 750 900

Temperature (ºC)

Figure 5.6 Comparisons of temperature-dependent stresses from XRD experiment and FE calculation for an as-JURZQ626RIȝP

The tensile stresses at the deposition temperature cannot be explained by lattice mismatch since the latter should result in a compressive stress in the silicon film. The measured stress in this case is merely due to the thermal mismatch effect, and thus indicates the relaxation of thermal stress during the cooling process.

The most popular mechanism of thermal stress release is via macro or micro cracks, which was rationalised by the thickness-dependent stresses observed in GaN on a sapphire system

[Hiramatsu, Detchprohm et al., 1993]. In their study, the substrate crack effect was 140 Chapter 5. Effects of Processes on Residual Stresses and Microstructures incorporated in the theoretical stress calculation, which shows good agreement with experimental observations. The relations between the film thickness and the relaxations were then summarized: (1) when the film thickness is smaller than ȝP the relief of thermal stress is not favourable; in a sufficiently thick (> ȝP) film, partial stress relaxation is expected. In this case, the thermal mismatch stresses will be lowered by enhancing the existing microstructural defects. (3) in a film thicker than ȝP Pore severe release occurs. In this condition, the generation of substrate macro-cracks results in a total release of the thermal mismatch stress. However, we have found in an SOS system that the defect density was independent of the film thickness, i.e., the defects were not

HQKDQFHGLQWKHȝP626Therefore, this mechanism cannot explain the stress release in our current case.

On the other hand, the surface morphologic modification could also lead to stress relaxation. Roughened film surfaces were commonly observed in the SV and VW growth model. At the early stage of growth, the film surface is likely to have self-modifications so as to achieve minimum energy in the system. This process normally occurs prior to misfit dislocation nucleation [R. Hull and Stach, 1999]. The stress concentrations at the troughs provide nucleation sites for the half-loops [Jesson, Pennycook et al., 1993]. As the thickness increases, more mass transports are promoted at the high temperature, and therefore magnify the undulations with increased amplitude and wavelength. This was evidenced by surface roughness measurement results as shown in Fig. 5.7. It is noted that the surface undulation becomes greater as the film thickness increases. This indicates that a tensile stress of about 100 MPa in the thicker silicon film (5 ȝm) at the deposition temperature could be the consequence of surface corrugation.

141 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

Figure 5.7 6XUIDFHPRUSKRORJLHVH[DPLQHGRQWKHVXUIDFHRI626WKLQILOPVRI D ȝP E ȝP F QPDQG G QP

142 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

5.2 Effects of Implantation and Annealing

As has been addressed in the former chapters, a high level of compressive stresses of 550-

800 MPa is locked-in the as-grown silicon layer, and it is always accompanied by a high density of planar defects such as twins, stacking faults and dislocations. Those defects are undesirable since they will significantly degrade the electronic properties of devices. To eliminate these defects, the epitaxial re-growth technique [Lau, Matteson et al., 1979] is exploited, which involves processes of ion implantation to induce point defects and amorphous structure and annealing to achieve a solid phase epitaxial (SPE) re-growth. It has been evidenced that the crystalline quality of the re-grown silicon can be significantly improved [Inoue and Yoshii, 1980; Richmond and Knudson, 1982; W.R. McKenzie, 2005], and that the residual stresses can also be relieved [Ohmura, Inoue et al., 1983; Bolotov,

Efremov et al., 1992; Dubbelday and Kavanagh, 1998]. These studies have shown that the reduction of residual stresses is related to implantation and annealing conditions. However, the mechanism remains elusive.

Ohmura et al. [1983] investigated the residual stresses in the silicon film of an SOS system using a 2-step annealing, first at 600 ºC and then at a temperature ranging from 600 to 900

ºC. They found that the annealing temperature at the second step had little effect on stress reduction and therefore speculated that the stress reduction was caused by a new interface formed in the first 600 ºC annealing, which can sustain temperatures up to 900 ºC at the second annealing. Beyond this threshold temperature, this new interface would be destroyed, resulting in a recovery of residual stresses to the as-grown level. Bolotov et al.

[1992] correlated the stresses and microstructures in the samples with the doping conditions and suggested that the stress relaxation was induced by the formation of

143 Chapter 5. Effects of Processes on Residual Stresses and Microstructures vacancies at the interface. If the sample is annealed at a sufficiently high temperature, the vacancies reduce and the residual stresses increase. Dubbelday and Kavanagh [1998] measured the strains in silicon film annealed at 700 - 1,000 qC for different durations. They found that the in-plane strains oscillated for annealing time only by 5 to 7 minutes and then approached the theoretical thermal mismatch strains for longer annealing time. They ascribed the early strain oscillation to the annealing induced diffusions of implanted Si+ from sapphire to silicon, which induces a tensile strain at the early stage of annealing.

This section aims to provide more insight into the effects of the implantation and annealing with a focus on the variation of residual stresses and the microstructure. To quantify the relation between implantation induced defects and stresses, the Si+ implants were doped with different energies and densities. The implanted samples were then annealed at various temperatures to reveal the effects of heat treatment.

5.2.1 Experiment

The samples investigated were the as-grown SOS samples of 280 nm. Those samples (S1 to S6 shown in Table 5.4) were subjected to room temperature Si+ implantation under two implanting energies of 135 KeV and 200 KeV, and three dose densities of 1014, 1015, and

5ൈ1015 ions/cm2. To avoid self-annealing during implantation, the temperature of the sample was kept at 25ºC by active cooling with liquid nitrogen. After implantation, the samples were annealed in a furnace for 1 hour at 600 ºC, 700 ºC, 800 ºC, 900 ºC, and 1,000

ºC, respectively and then cooled in the furnace for half an hour before the final air cooling.

144 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

Table 5.4 The implantation and annealing conditions

Sample Implantation Si+ Dose Density Annealing temperatures ID Energy[Ke] [ion/cm2] [°C]

S1 135 1014 600- 1,000 S2 135 1015 600- 1,000 S3 135 5ൈ1015 600- 1,000 S4 200 1014 600- 1,000 S5 200 1015 600- 1,000 S6 200 5ൈ1015 600- 1,000

The nominal implanting depth and ion ranges were simulated by TRIM (Transport of Ions in Matter) software. This software simulates the random walk of implanting ions, which collide with the lattices during penetration, dissipate their kinetic energy, and finally rest at certain depths.

Fig. 5.8a and 5.8c shows the distribution of collision events with depth. An implanting ion carried more energy, can penetrate deeper, collide with more lattice atoms and have a longer mean-free path. It can be expected from Fig. 5.8c that the implantation with higher energy (200 KeV) has changed the silicon and sapphire interface. Fig. 5.8b and 5.8d, on the other hand, demonstrate the distribution of ions in both silicon film and the sapphire substrate. It is notable that under 200 KeV, the sufficiently high energy results in a large number of ions embedded in the sapphire substrate.

The residual stresses of the implanted and annealed samples were measured at room temperature by Raman Scattering with a Renishaw Invia unit equipped with a backscattering configuration. A standard setup of 514 nm Argon ion laser and 1800 l/mm grating was utilized to detect the silicon band at around 520.5 cm-1. The residual stresses

145 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

ZHUHGHWHUPLQHGE\WKHVKLIWRI5DPDQEDQGǻȦ (cm-1), and the in-plane normal stresses were quantified by ı= -ǻȦ (MPa) [Englert, Abstreiter et al., 1980].

(a) COLLISION EVENTS (b) ION RANGES ) 2 4 135 KeV 135 KeV 7x10 6x104 .6 4 .5 5x10

)/(Atoms/com 4 .4 3 4x10 .3 3x104

Number /(angstrom-Ion) Number .2 2x104 Atoms/cm .1 1x104

0 Å Target Depth 5600 Å 5600 Å 0 Å Target Depth

.4 )/(Atoms/com 3 5x104 .3 4x104 4 .2 3x10 Number /(angstrom-Ion) Number 4 Atoms/cm 2x10 .1 1x104

0 Å Target Depth 5600 Å 0 Å Target Depth 5600 Å

Figure 5.8 TRIM simulations of collision events (a) and (c), and ion ranges (c) and (d) of implanted SOS. (a) and (b) are under the implanting energy of 135 KeV, and (c) and (d) are under 200 KeV

146 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

To study the microstructures, the cross-sectional transmission electron microscopy (TEM) specimens along silicon [110] were prepared by using the Nova 200 Nanolab Focused Ion

Beam (FIB) system, and AutoTEM software was unutilized to reduce the thickness to less than 100 nm for a better lattice view. The bright-field and high resolution lattice images were taken on the silicon <110> zone axis, which was achieved by tilting the TEM specimen by a double tilt holder in a Philips CM-200 TEM.

5.2.2 Results and Discussion

(a) Effects of implantation on residual stresses

Fig.5.9 illustrates the Raman spectra of doped silicon films under different conditions. The occurrence of the broadened peak of the Raman spectra at a small wave number, as shown in Figs. 5.9a and 5.9c indicates the phase transformation from crystalline silicon (c-Si) to amorphous silicon (a-Si). Under both energies, the amorphous fraction increases with increasing Si+ density. With the same dose density, the higher energy (200 KeV) results in more collisions and therefore leads to a more amorphous fraction. Under the extreme conditions 200 KeV and 5ൈ1015 ions/cm2, the collisions produce a fully amorphous silicon layer leaving only a surface layer remaining crystalline. With this structure the silicon film can be annealed to be a single crystal due to crystal re-growth from the surface [Lau,

Matteson et al., 1979]. In other cases with lower energy and dose density, the re-growth may bring about a polycrystalline film.

147 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

9000 9000 (a) 135 KeV (b) 135 KeV 8000 8000 c-Si 7000 a-Si 7000 5E15 6000 6000 5E15 610 5000 5000 E15 E15 4000 4000

3000 E14 3000 E14 Raman Intensity (Counts) (Counts) Intensity Raman 2000 2000 as-grown SOS as-grown SOS 1000 1000 Bulk Si Bulk Si 0 0 80 180 280 380 480 580 460 480 500 520 540

Raman Shift (cm-1) Raman Shift (cm-1)

8000 (c) 7000 200 KeV (d) 200 KeV 7000 c-Si 6000 a-Si 5E15 6000 5E15 610 5000 5000 4000 4000 E15 E15 3000 3000 E14 E14

Raman Intensity (Counts) Intensity Raman 2000 2000 as-grown SOS as-grown SOS 1000 1000 Bulk Si Bulk Si 0 0 80 180 280 380 480 580 460 480 500 520 540 560 Raman Shift ( cm-1) Raman Shift ( cm-1)

Figure 5.9 Raman spectrums of implanted SOS samples. (a) and (c) are under the implanting energy of 135 KeV and 200 KeV. (b) and (d) are the detail of the c-Si band to highlight the residual stress variations with different implantation condition. Si+ dose density are 1014, 1015 and 5ൈ1015 ions/cm2 for the curves E14, E15, 5E15, repsectively.

148 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

Another notable change after implantation is the presence of a new Raman band at around

610 cm-1, and its intensity increases with Si+ density. This new band is discerned as clusters of aluminosilicate [Mozgawa, Handke et al., 2004]. The formation of this new compound is probably caused by the implantation induced rearrangement of Si, Al, and O atoms at the interface. After annealing, this new compound disappears, probably because of the diffusion of Si atoms from sapphire to the silicon film.

Figs. 5.9b and 5.9d are the detail of the c-Si bands in Figs.5.9a and 5.9c, in order to highlight the residual stress variations with different implantation conditions. The stresses are revealed by the Raman peak shift from that of bulk Si. Compared with implantation at

135KeV, the high energy implantation at 200 KeV leads to more obvious stress release from the as-grown SOS. The implanted Si+ ions lead to local expansion, structure amorphization and interface change, which all result in the relief of the compressive residual stress in silicon film.

To quantify the residual stresses, the peak position of the c-Si band was determined by the minima of the second derivative of the Gaussians fitting function of the Raman spectra at around 520.5 cm-1. The variation of residual stress with the ion dose density is plotted in

Fig.5.10.

It is noted that the as-grown compressive stresses (724 MPa) reduce after implantation.

More density and energy leads to more reduction of stress. In the extreme condition with

5u1015 ions/cm2 and under 200 KeV, the residual stress becomes tensile. This tensile stress must be caused by the excessive Si+ implants embedded in sapphire, as indicated by Fig.

5.8d, resulting in expansions of the substrate and therefore tensile stress in the silicon film.

Although implantation induced amorphization of silicon film may also cause expansion

149 Chapter 5. Effects of Processes on Residual Stresses and Microstructures and contribute to the tensile stress of surface crystalline Si, this is a the secondary effect, which will be corroborated by the annealing experiments.

200 5î1015 50

-100 1015 -250

-400 1014 135 KeV Implant -550 Residual Stress (MPa) 200 KeV Implant -700

-850 0123456

15 2 Si+ Dose Density (î10 ions/cm )

Figure 5.10 Residual Stress after 135 KeV and 200 KeV room-temperature implantations

(b) Effects of annealing on residual stresses

Annealing recovers the compressive residual stress in silicon film due to the re-growth of crystal structure. Fig. 5.11 shows residual stress versus annealing temperature, where the continuous and dashed lines illustrate the annealing effects of samples after 200 KeV and

135 KeV implantations respectively. The result shows that a higher annealing temperature renders a greater residual stress recovery. For the samples implanted with smaller dose density (i.e. 1014 and 1015 ions/cm2), the annealing process at a sufficiently high temperature (900 qC) can smear out the implanted defects and recover the residual stresses to the as-grown level. It is noted that the lighter the doping conditions applied, the lower the annealing temperature needed for restoring the residual stress.

150 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

300 200 KeV 150 average offset 150 MPa 135 KeV 0

-150

-300

-450 Residual Stresses (MPa) -600

-750 as-grown SOS

-900 0 200 400 600 800 1000

Annealing temperatures (ºC)

Figure 5.11 Stress variations with annealing temperatures in the implanted samples. The continuous lines are samples under 200 KeV implantation, and the dashed lines are for 135 KeV. Si+ dose density are 1014, 1015 and 5ൈ1015 ions/cm2 for the curves E14, E15, 5E15, repsectively.

For the most heavily implanted sample (200 KeV and 5u1015 ions/cm2), the residual stress is tensile before annealing and remains smaller than that of the as-grown sample even after

1000 qC annealing, as shown in Fig. 5.11. If the tensile stress before annealing is due to the amorphization of the Si layer, it should be effectively removed after annealing and crystal re-growth. However, this is not occurring. In Fig 5.11, a curve of reference residual stress calculated from merely the thermal mismatch strain using finite element analysis (Sec 4.1.1) is also shown. It is surprising to note that the calculated stress variation is parallel to the stress variation of the most heavily implanted sample, which indicates that heating to and annealing at different temperatures cannot remove the tensile stresses induced by the implantation. Therefore, such an implantation induced tensile stress must have its 151 Chapter 5. Effects of Processes on Residual Stresses and Microstructures structural origin in the interface, which will be further elaborated by examining the microstructures of the annealed samples.

The 2-step annealing employed by Ohmura et al. [1983] was also examined. The implanted sample was first annealed at 600 ºC for 1 hour and then annealed at a temperature ranging from 800 ºC to 1,000 ºC. The results are plotted in Fig.5.12. For all those implanted samples, it was found that the variation of stress with the highest annealing temperature is consistent with that obtained from one-step annealing shown in

Fig. 5.12. We thus conclude that the final residual stresses are only dependent on the highest annealing temperatures and are not affected by the 1st annealing at 600 ºC.

100

-100 1-step annealing 2-step annealing -300

-500

Residual Stress (MPa) Stress Residual -700

-900 0 100 200 300 400 500 600 700 800 900 1000

Annealing Temperatures (ºC)

Figure 5.12 Comparison of residual stresses between 1-step annealing and 2-step annealing. The implanted samples are under high energy (200 KeV) implantations. Si+ dose density are 1014, 1015 and 5ൈ1015 ions/cm2 for the curves E14, E15, 5E15, repsectively.

152 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

Implantation and annealing affect not only the residual stress but also the microstructures.

The schematics shown in Figs. 5.13a and 5.13b illustrate how implantation changes the atomic structure.

In Chapter 4, we have observed that the as-grown silicon lattice contains dislocations as shown by red arrows in Fig. 5.13a, planar faults such as twins and stacking faults indicated by black arrows. Those defects were also revealed in the literature studies [Hamarthibault and Trilhe, 1981; Batstone, 1991]. We have also found that misfit dislocations exist at the interface to accommodate the lattice mismatch strain.

(a)

Sapphire

(b) c-Si

a-Si Si

Sapphire

Figure 5.13 Schematics of microstructures for (a) as-grown, and (b) implanted SOS. The red and black arrows indicate threading dislocations and twinning planes, respectively. 153 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

As indicated in Fig. 5.13b, implantation can smear out all these microstructural defects, transform the crystalline structure to an amorphous structure, and bring about a new compound at the interface. These effects have been well characterized by different techniques (see results from TRIM simulation in Fig. 5.8 and Raman spectrum in Fig. 5.9) and evidenced by electron microscopy images [W.R. McKenzie, 2005].

Annealing the implanted material leads to crystal re-growth. The threading dislocations are either the typical structural imprint of growth [Morin, Forticaux et al., 2011; Gerbi, Buzio et al., 2012], or could be the defects inherited from implantation, which can be observed in the TEM images, as shown in Figs. 5.14a and 5.14b (indicated by red arrows). These new dislocations have been reduced remarkably compared with those observed in as-grown samples (Figs. 4.13 and 4.14). The most notable difference between the re-grown and as- grown SOS is the elimination of the high density of threading dislocations in the vicinity of the interface. This is probably caused by a mechanism in SOS re-growth which is different from the initial islands growth mode. During annealing, the re-growth proceeds from film surface to interface, therefore the initial interface effects led by island mis-orientation and coalescences [Stowell, 1975 ] are no longer occurring.

It is also worth mentioning that the annealed film surfaces are more corrugated than those in the as-grown specimen. As indicated by the dashed arrows in Fig. 5.14b, the majority of threading dislocations are nucleated at the place of large curvatures. These curvatures could indicate more stress concentrations (refer to Fig. 2.6 in Chapter 2) and therefore could be the sites for half-loop nucleation. Those half loops would glide towards the interface and result in two threading dislocations and a misfit dislocation segment lying in the interface.

154 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

(a) 600 ºC anneal

50 nm Sapphire

(b) 1000 ºC anneal

Stress concentrations

100 nm Sapphire

Figure 5.14 Bright field image of annealed SOS at (a) 600 °C and (b) 1000 °C. The image was taken in the {111} reflection of Si <110> zone axis. White arrows denote dislocations, and the dashed arrows are to highlight the curvature of the corrugations where stress concentration provides sites for dislocations nucleation.

155 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

A higher temperature annealing leads to less lattice defects. Therefore, the density of the threading dislocation in Fig. 5.14b is much lower than that in Fig. 5.14a. A possible explanation for the better crystal quality after a higher-temperature annealing is that the dislocations would have higher mobility, resulting in more interactions and higher annihilation rate. This explanation was proposed by Anidow [1989] as shown schematically in Fig. 5.15a. He suggested that when the two neighbouring dislocations have the same Burgers vector, the two threads will form attractions during the glide or climbing process, and therefore annihilate each other, resulting in two half loops being shrunk to the surface or the interface due to line tensions. A pair of half loops of this form was observed in the sample after 1,000 °C annealing shown in Fig 5.15b, which justifies the possibility of dislocation reduction based on this mechanism.

(a) (b) 1,000 ºC anneal

attractions

half loops annihilation

interface 20 nm

Figure 5.15 Mechanism of threading dislocation reduction. (a) schematics of the dislocation attraction and annihilations ( reproduced from Anidow (1989) [M.Anidow, 1989.]) (b) TEM observations of a pair of half loof in the sample after 1,000 °C annealing.

The improvement of crystallinity with annealing temperatures could also be quantified by a full width half maximum (FWHM) of Raman band as shown in Fig. 5.16, in which a smaller value in Raman FWHM indicates better crystalline quality in silicon films. It could

156 Chapter 5. Effects of Processes on Residual Stresses and Microstructures also be concluded that implantation with denser Si+ would have more effects on the film microstructures, and therefore lead to more defect reductions via annealing.

5.8

5.6 E14 )

-1 5.4 E15 5.2 5E15 5 4.8 4.6 Raman FWHM(cm 4.4 Bulk Si 4.2 4 0 200 400 600 800 1000

Annealing temperatures (ºC)

Figure 5.16 Relation of annealing temperature and film quality by FWHM. The samples were implanted at 200 KeV with dose density of 1014, 1015, and 5× 1015 ions/cm2.

Figs. 5.17a and 5.17b are schematics of the microstructures of annealed samples at 600 qC and 1,000 qC, respectively. As illustrated in Fig. 5.17a, the re-growth after implantation is from the surface to the interface [Lau et al., 1979], which is different from a deposition process. Therefore the interface may have the memory of the implanted structure after an annealing especially at a lower temperature. After the 600 qC annealing, the interface may remain amorphous. Therefore the residual stress is much smaller than the as-grown value indicated in Fig. 5.10. This amorphous structure was evidenced by the high resolution

TEM image shown in Fig. 5.17c, which was taken on the 600 ºC annealed sample under a heavy implantation condition (200 KeV and 5×1015 ion/cm2).

157 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

(b) (a) c-Si

Si Si a-Si

Sapphire Sapphire

Si Sapphire a-Si 2 nm Sapphire 2 nm (e) 600 ºC anneal (f) 1,000 ºC anneal

Si Si

100 nm Sapphire 100 nm Sapphire Figure 5.17 Schematic of atomic structure (a) and (b), high resolution lattice images (c) and (d), and low magnification bright-field images (e) and (f) for the 600 ºC and 1,000 ºC annealed samples, respectively. The implantation conditions are under 200 KeV and 5×1015 ion/cm2

158 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

On the other hand, the 1,000 qC annealing well restored the interface lattice. This is evidenced by the corresponding high-resolution TEM image illustrated in Fig. 5.17d, where the lattice and misfit dislocation at the interface can be clearly discerned. Similar to it has been observed in as-grown SOS, these edge-type dislocations have a Burger vector of full lattice spacing and will induce local compression in the substrate and tension in the silicon film. The average spacing between the adjacent dislocations was found to be

10.5±0.5 sapphire ( 01 21 ) fringes, which is close to the average spacing of 10.1 fringes calculated from the difference of the film and substrate lattices. This confirms that misfit dislocation is indeed the dominant mechanism for accommodating mismatch stress in both as-grown and re-grown SOS.

However, the implanted Si+ in sapphire cannot effectively be diffused back to silicon film even at an annealing temperature as high as 1,000 qC. These Si+ ions will deflect the sapphire lattice by introducing lattice defects. As shown in Figs 5.17e and 5.17f, the defective zones were observed about 100 nm underneath the interface at sapphire for both samples at 600 qC and 1,000 qC annealing. Those defects were believed to be the products from ion implantation at sufficiently high energy, and the depth of this defective zone is consistent with the ion ranges from TRIM simulation (Fig. 5.8d).

Most importantly, excessive Si+ will result in expansion of sapphire lattice close to the interface. This is clearly reflected by the variation of the residual stress shown in Fig. 5.11.

The expansion of sapphire lattice leads to a tensile stress of 150 MPa in the heavily implanted silicon film. Even after annealing at different temperatures, the expansion of the sapphire lattice remains unchanged, causing the residual stresses to be consistently smaller than those calculated from the thermal mismatch strain at different annealing temperatures.

159 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

Direct evidence of the expansion of sapphire lattice is difficult to obtain. However, a high- resolution TEM image of sapphire lattice close to the interface, as shown in Fig. 5.18, exhibits a pair of edge dislocations. This is clearly evidence of the distorted sapphire lattice, which provides strong support to our deduction.

b=a<0112>

Al2O3[1012]

2 nm Al2O3[0112]

Figure 5.18 High resolution TEM image of sapphire lattice at the depth of 10 to 20 nm beneath the interface. The sample is subjected to the 200 KeV and 5×1015 ions/cm2 implantation and 600 ºC annealing.

In the process described in Chapter 3, we have observed that the compressive stress is about -823 MPa after implantation, annealing and 1,000 ºC thermal oxidation, which was increased by 100 MPa compared with the as-grown SOS (Fig. 3.21). This is due in part to the thermal oxidation temperature of 1,000 ºC, which is higher than deposition temperature

(900 ºC) and causing larger thermal mismatch. As shown in Fig. 5.11, the reference line obtained from finite element (FE) calculation indicates the stresses of -700 MPa and -630

MPa for cooling from 1,000 ºC and 900 ºC respectively.

160 Chapter 5. Effects of Processes on Residual Stresses and Microstructures

Another cause of the increase in the stress is the thickness effect. It is noted that the thickness of silicon film was reduced from 280 nm to 155 nm after oxidation and further to

110 nm after final front etching. As has been elaborated in Chapter 4, the thickness dependence of residual stresses is due to discrete misfit dislocations. These misfit dislocations were also observed in the re-grown sample which underwent annealing at

1000 qC, as shown in Fig. 5.17d. The average spacing of misfit dislocations was found similar to that in as-grown samples. The stress versus thickness shown in Fig. 3.12 indicates that the decrease of film thickness from 280 nm to about 155 nm results in an increase of about 70 MPa in residual stresses.

From the implantation and annealing experiments, we have found that the resultant residual stresses in the existing process could be reduced by introducing excessive implants

(e.g. Si+, O+, etc) in substrates, which is significant in improving electronic property and preventing mechanical failure.

5. 3 Conclusions

This chapter evaluated the effects of manufacturing processes (i.e. temperatures, implantation and annealing conditions) on residual stress in silicon-on-sapphire (SOS).

To investigate the temperature dependence, the residual stresses were examined ex-situ at elevated temperatures. The multiple regression algorithms in X-ray diffraction were found most effective in decoupling the thermal expansion and stress-induced deformation in temperature-dependent stress analyses. In the two samples examined, the thermal stress decreasing rate with increased temperatures shows an overall consistency with the thermal

161 Chapter 5. Effects of Processes on Residual Stresses and Microstructures mismatch stresses calculated by FE analysis, which also indicates that thermal stress is independent of film thickness.

For a thinner film of 280 nm, 100 MPa compressive stresses were detected at the deposition temperature, which is directly indicative of the residual effect from film growth

(i.e., lattice mismatch stress). By this means, the individual effect of lattice/thermal mismatch can be successfully decoupled. On the other hand, a tensile stress of 80 MPa was observed in thick film (5 ȝP , which evidences possible stress relief caused by surface modifications.

Our studies on implantation and annealing effects show that higher implanted energy and dose density give rise to more reductions of residual stress, because of the deeper penetration and more collisions with lattice atoms of ions, respectively. Sufficient implanting energy and dose density to maximize structural amorphization allows the subsequent annealing to render a much better crystal quality and much less defects than the as-grown one.

However, annealing also brings about the recovery of residual stresses. The higher the annealing temperature, the more residual stress is recovered. After a 1,000 qC annealing, most of the implanted samples have the same residual stress as the as-grown, except those resulting from the highest implanting energy. A detailed investigation of the interface structure shows that the ions penetrating into the sapphire cause the expansion of sapphire lattice. Such an expansion is little changed after annealing. Therefore, the residual stress in the silicon film of an SOS system can be effectively reduced after annealing and an ideal crystal quality can be obtained at the same time.

162 Chapter 6. Conclusions and Future Works

CHAPTER 6: Conclusions and Future Works

6.1 Conclusions

In the present research, experimental methods have been developed for characterizing residual stresses.

(a) In X-ray diffraction (XRD) residual stress measurement, an optimized combination of

13 diffraction planes gives rise to the accurate complete stress tensor, which is obtained

by solving over-determined equations based on the least square method.

(b) Using a novel Raman technique, which allows simultaneous measurement of thickness

and residual stress, the thickness-dependent stresses were obtained. The residual

stresses increase with the reduction of thickness.

and curvature method was proposed. The single-point XRD pattern renders the stresses

of crystalline layers and the scanning XRD gives rise to the curvature of the whole

163 Chapter 6. Conclusions and Future Works

wafer. Based on the newly-developed analytical model, the residual stresses in all the

layers, either amorphous or crystalline, are determined.

(d) Temperature dependence of residual stresses was obtained using high-temperature

XRD system. Multiple regression algorithm was employed to resolve the equi-biaxial

stress state.

(e) Based on this experimental observation, a comprehensive finite element analysis

incorporating the coupled effects of thermal-lattice mismatch and misfit dislocations at

the interface was carried out, and successfully explains the experimentally measured

thickness-dependent stresses.

Following the above methodologies, a complete description of residual stresses and stress mechanisms in silicon-on-sapphire (SOS) system were obtained.

(a) Basically, the epitaxial silicon is subjected to equi-biaxial compressive stresses and the

magnitude of stress depends on the film thickness. It is found that the residual stress

does not change when the film is thicker than 700 nm. The stress in this case is mainly

caused by thermal mismatch, which agrees with finite element (FE) simulation. When

the film thickness is smaller than 700 nm, the compressive stress increases with

decreased thickness, and reaches larger than 800 MPa at the thickness of 50 nm. This

thickness dependence of residual stress is caused by the interface structure.

(b) In a multilayered SOS thin film system, the stress was found independent of

subsequent depositions of other layers, but only determined by the thermal and lattice

mismatch between the individual layer and the substrate.

164 Chapter 6. Conclusions and Future Works

image, we have successfully quantified the average spacing of the misfit dislocations.

Based on this observed dislocation density, a finite element analysis incorporating the

effect of interface misfit dislocation proves that the discrete distribution of dislocations

plays a key role in inducing thickness dependency of residual stresses. The consistency

between experimental and numerical results corroborates our theoretical analysis.

(d) The XRD stress measurement at elevated temperatures reveals the effects of

temperature and film thickness on residual stresses. The residual stresses vary in

parallel with the theoretical calculation of thermal mismatch stresses. At the deposition

temperature, the remaining stresses in the film indicate the effect of structural defects.

At the deposition temperature, the compressive stress of about 100 MPa in the 280nm

thin film manifests the presence of the residual lattice mismatch effect. However, the

tensile stress is observed in thicker (5 Pm) film, indicating other stress relief

mechanism, e.g., the surface corrugation.

(e) Post-deposition implantation could lead to relief of the as-grown residual stress by

introducing interface defects. Stress relief was found more remarkable in the more

heavily implanted sample. In the extreme condition, a large number of ions penetrating

into the substrate cause significant expansion of the substrate and tensile stress in

silicon film. However, annealing again restores the residual stress. A high annealing

temperature renders a greater residual stress recovery, improved crystalline quality, and

a clear-cut interface, whereas annealing at lower temperatures gives rise to an

amorphous layer of a few atomic planes at the silicon-sapphire interface of the sample.

This could be due to the incomplete process of re-crystallization.

165 Chapter 6. Conclusions and Future Works

6.2 Future Works

SOS is the prospective material in both the space and telecommunication industries. The current study has provided in-depth understandings of the origins and release of residual stresses in an SOS system. However, process optimisation is beyond the scope of the current project, which will be the focus of future research. Thickness and deposition temperature are the key parameters in determining the final residual stresses. Although thinner films are desirable for improving electronic efficiency, they will be inevitably grown with higher residual stresses than thicker ones. Higher temperatures will lead to better quality of thin films, which is however undesirable because the disparate CTE will unfortunately result in higher residual stresses. Therefore, process improvement should focus on the optimisation of film thickness, deposition temperatures, film quality and residual stresses. The reduction of residual stresses could be achieved with heavy implants such as Si+ or other ions which appears to be a promising area for future study.

Although residual stress in sapphire substrate is insignificant to device electronic properties, a too high tensile stress in sapphire may cause the mechanical failure of the whole wafer. The problem is that sapphire is nearly transparent to conventional x-ray or

Raman beam. The deep penetration (hundreds of microns) of these beams makes it difficult to measure the local stress close to the silicon/sapphire interface. Thus, special methods are required to investigate the stress in sapphire at the interface.

The present research has developed experimental and analytical methods for residual stress characterisations in epitaxial thin film materials. The applications of these methodologies will benefit the semiconductor industry. A wide range of semiconductor thin films should be involved in future studies, such as lattice mismatched epitaxial or super-lattice systems.

166 Chapter 6. Conclusions and Future Works

The accurate measurement and control of residual stresses will lead to desired electronic and optical properties of these materials.

167 References

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180 List of Publications ______

List of Publications

1. M. Liu, H.H. Ruan, L.C. Zhang, Variation of crystal quality and residual stresses in epitaxially grown thin film systems induced by ion implantation and annealing. Journal of Materials Research, 2013, 28(11): p.1413-1419.

2. M. Liu, H.H. Ruan, and L.C. Zhang. Methodologies for measuring residual stress distributions in epitaxial thin films. in 8th International Symposium on Precision Engineering Measurements and Instrumentation. Proceedings of the SPIE, 2013. 8759 87594X-7.

3. M. Liu, H.H. Ruan, L.C. Zhang, and A. Moridi, Effects of misfit dislocation and film- thickness on the residual stresses in epitaxial thin film systems. Journal of Materials Research, 2012, 27(21): p. 2737-2745

4. M. Liu, H.H. Ruan, and L.C. Zhang. Origin of the implantation and annealing effects on the residual stress release in a silicon-on-sapphire system in 7th Australasian Congress on Applied Mechanics. 2012. Adelaide.

5. M. Liu, H.H. Ruan, and L.C. Zhang. A new method for measuring the residual stresses in multi-layered thin film systems. Advanced Materials Research, 2012. 591-593: p. 884- 890

6. M. Liu, H.H. Ruan, and L.C. Zhang. Investigation of Lattice Mismatch Stress in SOS Thin Film Systems by Raman Scattering and XRD Techniques. in Proceedings of AES- $7(0$¶6HYHQWK,QWHUQDWLRQDO&RQIHUHQFHRQ$GYDQFHVDQG7UHQGVLQ(QJLQHHULQJ Materials and their Applications. 2011. Milan, Italy

7. A. Moridi, H.H. Ruan, L.C. Zhang, and M. Liu, A Finite Element Simulation of Residual Stresses Induced by Thermal and Lattice Mismatch in Thin Films in Proceedings of AES-$7(0$¶ 6HYHQWK ,QWHUQDWLRQDO &RQIHUHQFH RQ $GYDQFHV DQG 7UHQGV LQ Engineering Materials and their Applications. 2011. Milan, ITALY

8. A. Pramanik, M. Liu, and L.C. Zhang, Production, Characterization and Application of Silicon-on-sapphire Wafers Key Engineering Materials, 2010. 443: p. 567-572.

9. M. Liu and L.C. Zhang, et al. Determining the Complete Residual Stress Tensors in SOS Hetero-epitaxial Thin Film Systems by the Technique of X-Ray Diffraction Key Engineering Materials, 2010. 443 p. 742-747.

To be submitted

1. M. Liu, H.H. Ruan, and L.C. Zhang, Study of temperature-dependent stresses in silicon- on-sapphire thin films system by XRD technique. To be submitted to Journal of Applied Physics

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