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

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List of Figures 1.1 Interatomic potentials (a) and their first (b) and second (c) derivatives. Both the Lennard-Jones potential (solid) [140] and a harmonic potential (dashed) are shown. .............................. 4 1.2 (a) A depiction of the vertical force balance between dislocation line tension and the Peach-Koehler force. (b) An illustration of a dislocation bowing between two impenetrable obstacles with separation ℓ. ......... 8 1.3 A schematic showing how the film stress causes substrate curvature. (a) The film and substrate are both shown in their strain-free state. (b) The film is stretched to fit onto the substrate. (c) The film is “glued” onto the substrate. (d) The film/substrate system bends in order to achieve force and moment balance. ............................. 12 1.4 A schematic of the curvature measurement apparatus at Harvard University. Adapted from Mullin [158]. ......................... 13 1.5 A schematic of the four-circle Huber diffractometer at Harvard University. . 16 1.6 A schematic of different scattering geometries. (a) The symmetric θ − 2θ geometry and χ rotation axis, (b) the geometry used for longitudinal diffuse scattering, and (c) the grazing incidence diffraction geometry. . . . 17 1.7 A schematic of the sputtering chamber at Harvard University. ........ 18 2.1 Stress as a function of temperature for a 1.91 µm sputtered Cu film on Si(100). The dotted lines show the hypothetical elastic stress in the film if no relaxation could take place (thermoelastic lines), and the labels (A), (B), and (C) denote elastic thermal cycles as described in the text. The upper thermoelastic line was drawn using the elastic constant data found in Bechmann et al. [12] and assuming mild 〈111〉 texture. . . . ........ 21 2.2 Plan-view TEM micrographs of 0.87 µm thick copper in the as-deposited state (a) and after annealing at 600 ◦ C for 0.5 hrs (b). ............ 29 2.3 A cross-sectional TEM micrograph of 1.90 µm thick copper grown on Ge(111). .................................... 30 viii
List of Figures ix 2.4 (a) Powder diffraction x-ray spectra for sputter-deposited copper films on Ge(111) (dashed), α-Al2O3(0001) (dotted), and Si(100) (solid). (b) (111) fiber texture plot of copper films on Ge(111) (dashed) and Si(100) (solid). . 31 2.5 (a) Powder diffraction spectra, and (b) a (111) fiber texture plot for asdeposited and annealed copper films on Si(100). .............. 32 2.6 Powder diffraction spectra for annealed copper films on Si(100) (solid) and α-Al2O3(0001) (dotted). ........................... 33 2.7 (111) fiber texture plot of as-deposited and annealed 0.50 µm thick copper films. ..................................... 33 2.8 (111) fiber texture plot of an electron beam evaporated copper film. .... 34 2.9 The calculated biaxial modulus for 〈111〉 texture (a) and 〈100〉 texture (b) as a function of the texture pole standard deviation. A Gaussian texture pole is assumed. . . .............................. 35 2.10 Plot showing how the biaxial modulus and CTE can be determined for a set of different substrates. ............................. 37 2.11 Biaxial modulus as a function of the maximum annealing temperature exposed to a 1.88 µm thick copper film on Si(100). .............. 38 2.12 Biaxial modulus as a function of the number of times thermally cycled to 600 ◦ Cfora1.91 µm and 1.93 µm thick copper film. ............ 39 2.13 Stress as a function of temperature for a 1.19 µm thick Cu film on Si(100). The elastic thermal cycles for the measurements of biaxial modulus at five different temperatures are shown for the as-deposited film (a) and the thermally cycled film (b). ............................. 40 2.14 Biaxial modulus as a function of temperature for as-deposited copper films. The error bar denotes two times the standard deviation. The shaded area represents the calculated biaxial moduli after accounting for texture. It is based on a value of 226 ± 22 GPa at room temperature (cf. Table 2.4) and has the temperature dependence found in Simmons and Wang [207]. .... 41 2.15 Biaxial modulus as a function of temperature for a copper film previously annealed at 600 ◦ C. The error bar denotes two times the standard deviation. The shaded area represents the calculated biaxial moduli after accounting for texture. It is based on a value of 256 ± 22 GPa at room temperature (cf. Table 2.4) and has the temperature dependence found in Simmons and Wang [207]. .................................. 42 2.16 Biaxial modulus as a function of temperature for copper films previously thermally cycled to 600 ◦ C for different strain oscillation frequencies. . . . 43 2.17 Depiction of dislocation bowing at high temperatures. Thermal fluctuations help the dislocation to bow past weak obstacles, but the radius of curvature remains below that required for slip. . . ................... 46
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: Contents vii B.2.3 Alignment Errors
Page 11 and 12: List of Figures xi 4.4 A schematic
Page 13 and 14: List of Tables 1.1 Ability of wafer
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 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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