Stresses in Cu Thin Films and Ag/Ni Multilayers - Harvard School of ...

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List of Figures xii 4.18 (a) A schematic showing the width between Ag and Ni (111) planes at the interface. (b) The interface width for Ag/Ni and Ni/Ag interfaces. The mean (111) d-spacing, 0.2197 nm, is indicated by the horizontal line. (d111,Ag = 0.23592 nm, and d111,Ni = 0.20345 nm). .............118 4.19 Schematic showing the method by which SUPREX treats gradients in the out-of-plane d-spacing. ............................119 4.20 High-angle x-ray diffraction peaks for the � = 3.2nm(a) and � = 5.9nm (b) Ag/Ni multilayers. The intensity axis is on a logarithmic scale, and the data taken at E = 8320 eV is offset above the E = 8020 eV data. The circles are the measured intensities, the solid curve is the fit for the strain gradient model, and the dotted curve is the best fit when strain gradients are disallowed. The order of the reflection is indicated above the peak. . . . 119 4.21 Calculated {111} d-spacing profiles for the � = 3.2nm(a) and 5.9nm(b) Ag/Ni multilayers. The results of Jaszczak et al. for their theoretical multilayer are provided in (c) [113]. The vertical dashed lines are the strain-free d-spacings for the bulk phases. ........................120 A.1 Diagram showing the relationship between the sample coordinate system, S, and the laboratory coordinate system, L. .................146 B.1 The focusing circle. ..............................156 D.1 The ratio of ɛ ′ 33 /ɛ′ D.2 11 in the Vook-Witt model. .................172 The biaxial modulus in units of 100 GPa using the Vook-Witt model. ....173 D.3 The maximum resolved shear stress on the (111) slip plane given in GPa using ɛ ′ 11 = 0.704%. .............................174
List of Tables 1.1 Ability of wafer curvature and x-ray techniques to measure different types of stresses. Adapted from Ruud [195]. . ................... 11 1.2 Parameters for ion beam sputter deposition and substrate cleaning. ..... 18 2.1 Measured and calculated values of the Young modulus, E, and the biaxial modulus, Y , for both free-standing and substrate-bonded films on the order of 1 µm thick. . . . .............................. 20 2.2 Parameters for a-SiNx reactive sputter deposition. .............. 26 2.3 Thermomechanical properties of the substrates used for the thermal cycling experiments. .................................. 27 2.4 Calculated values of the biaxial modulus for selected films. The standard deviation is ±22GPa.............................. 35 2.5 Measured values of the biaxial modulus for films of thickness 1 µm or greater. 38 2.6 Comparison of the measured and calculated values of the biaxial modulus for the as-deposited films. ........................... 43 2.7 Comparison of the measured and calculated values of the biaxial modulus for the annealed films. ............................. 44 4.1 The Ag/Ni {111} Interface Energy . . . ................... 96 4.2 {111} Interface Stress Results for FCC Metallic Multilayers . ........ 97 xiii
Page 1 and 2: Stresses in Cu Thin Films and Ag/Ni
Page 3 and 4: Thesis advisor Author Frans Spaepen
Page 5 and 6: Contents v Measuring Both the Biaxi
Page 7 and 8: Contents vii B.2.3 Alignment Errors
Page 9 and 10: List of Figures ix 2.4 (a) Powder d
Page 11: List of Figures xi 4.4 A schematic
Page 15 and 16: Acknowledgments xv Chervinsky, and
Page 17 and 18: Dedicated to my family
Page 19 and 20: Chapter 1: Background 2 films on ri
Page 21 and 22: Chapter 1: Background 4 σ = F/a 0
Page 23 and 24: Chapter 1: Background 6 For more in
Page 25 and 26: Chapter 1: Background 8 T T sinΘ
Page 27 and 28: Chapter 1: Background 10 1.3 Thin F
Page 29 and 30: Chapter 1: Background 12 (a) (b) (c
Page 31 and 32: Chapter 1: Background 14 Prior to t
Page 33 and 34: Chapter 1: Background 16 Figure 1.5
Page 35 and 36: Chapter 1: Background 18 Figure 1.7
Page 37 and 38: Chapter 2: The Elastic Properties o
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Chapter 2: The Elastic Properties o
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Chapter 2: The Elastic Properties o
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Chapter 3: The Plastic Properties o
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Chapter 4 The Ag/Ni {111} Interface
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Chapter 4: The Ag/Ni {111} Interfac
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Bibliography [1] C. W. Allen, H. Sc
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Bibliography 128 [25] W. K. Burton,
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Bibliography 130 [54] M. F. Doerner
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Bibliography 132 [82] P. Gergaud, S
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Bibliography 134 [110] M. S. Jackso
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Bibliography 136 [138] D. R. Lee, Y
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Bibliography 138 [166] M. Murakami
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Bibliography 140 [196] J. A. Ruud,
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Bibliography 142 [224] S. P. Timosh
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Bibliography 144 [249] G. K. White.
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Appendix A: X-Ray Stress Analysis 1
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Appendix B X-Ray Errors In this sec
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Appendix B: X-Ray Errors 154 differ
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Appendix B: X-Ray Errors 156 ψ =
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Appendix B: X-Ray Errors 158 The re
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Appendix B: X-Ray Errors 160 B.3.2
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Appendix C: Alignment Procedure for
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Appendix C: Alignment Procedure for
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Appendix D: Elastic Constants 166 D
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Appendix D: Elastic Constants 168 a
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Appendix D: Elastic Constants 170 n
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Appendix D: Elastic Constants 172 N
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Appendix D: Elastic Constants 174 N
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Appendix E: The Stoney Equation 176
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Appendix E: The Stoney Equation 178
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Appendix F: List of Symbols 180 A a
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