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

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Chapter 2 The Elastic Properties of Cu Thin Films Using a tensile tester especially designed for free-standing films, Huang [106] found that the Young moduli of electron beam evaporated films were about 20% lower than those calculated from the elastic constants found in the literature (such as those from Landolt- Börnstein [12], Simmons and Wang [207], or Huntington [108]). Table 2.1 shows that this “deficit” is well documented and only observed in polycrystalline films. A variety of reasons for this modulus deficit have been hypothesized. They include elastic anisotropy (from preferred orientation), porosity, grain boundary compliance, grain boundary cracking, reversible microplasticity, dislocation anelasticity, and grain boundary sliding [107]. We studied the origin of the modulus deficit by measuring the biaxial modulus of sputtered copper films on substrates using the wafer curvature method. Before discussing how the measurement is made, it is important to first understand the stress- temperature profile. 19
Chapter 2: The Elastic Properties of Cu Thin Films 20 Table 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. Material Emeas E 〈111〉 calc ∗ Ymeas Y 〈111〉 calc ∗ (GPa) (GPa) (GPa) (GPa) Preparation Method Ref. Ag/Cu 87.5 107 - - e-beam [106] Cu 102 130 - - e-beam [106] Cu 104 130 - - e-beam [187] Cu 110 130 - - sputtered [187] Cu 66 130 - - electrodep. [187] Cu 104 130 161 261 sputtered [262] Cu 116 130 - - electrodep. [192] Ag 63 84 - - e-beam [106] Ag - - 50 174 thermal evap. [46] Al 57 72 - - e-beam [106] Al 49 72 - - thermal evap. [97] Al 64 72 - - sputtered [192] Al - - 62 115 thermal evap. [46] W 340 389 - - CVD [192] Si (110) † 166 166 - - etched from bulk [215] ∗ Calculated from the dynamic elastic constants found in Bechmann et al. [12] † Single crystal
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 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: Chapter 1: Background 18 Figure 1.7
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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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