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

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Chapter 1: Background 13 Figure 1.4: A schematic of the curvature measurement apparatus at Harvard University. Adapted from Mullin [158]. where Ys is the biaxial modulus of the substrate, ts is the substrate thickness, and tf is the film thickness. This equation assumes tf ≪ ts; in this limit, determination of the film stress does not rely on knowledge of the biaxial modulus of the film. Appendix E provides a derivation of Stoney’s equation. The wafer curvature measurement / annealing apparatus at Harvard University is called ROC and is shown in Figure 1.4. The technical details of how it measures the curvature can be found in Witvrouw’s or Mullin’s thesis [256, 158], but the principle is well known [62]. The 1 inch by 1/4 inch sample rests in a furnace on two sapphire prisms and is abutted on two adjacent sides by steel pins to allow repeatable sample placement. A HeNe laser scans across the long axis of the sample in 1 mm steps, and the reflected beam is collected in a null detector. The position of the reflected spot is recorded as a function of position along the sample, thereby giving the sample curvature.
Chapter 1: Background 14 Prior to thermal cycling, the chamber is evacuated to a pressure of 3 × 10 −4 Pa by a diffusion pump and then backfilled to a slight overpressure of 3 psi with a flowing gas of 95 wt.% He and 5 wt.% H2. 1.4.2 X-Ray Diffraction Measurements As mentioned, strain measurements are often performed by x-ray diffraction, with the strain-free lattice parameter, a0, and the elastic constants known a priori. Although this measurement is straightforward in principle, it still has several problems. First, not every- one agrees on the value of a0. Its value is often determined by performing x-ray diffraction experiments on a strain-free sample, e.g., an annealed powder. Extremely precise tech- niques have been developed to minimize the errors of these measurements [60]. In practice, however, a completely strain-free sample is difficult to produce. Furthermore, the meaning of “strain-free” can be different depending on what the researcher is trying to measure. It may refer to the constrained zero point between an applied tension and compression, or, it may refer to equilibrium lattice parameter. These may differ depending on the thermody- namic state of the material. The determination of elastic constants in polycrystalline materials is also problematic. There exists a substantial body of literature devoted to the proper ways of averaging the single crystal elastic constants for textured and untextured samples [24]. In principle, one can determine a sample’s orientation distribution function (ODF) and use a grain interaction model (e.g., Voigt or Reuss) to determine the stresses from the measured strains. ODF determination is a tedious process, however, and researchers typically either assume the sample has fiber texture or no texture at all. The grain interaction model is also often
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: Chapter 1: Background 12 (a) (b) (c
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
Page 67 and 68: Chapter 3: The Plastic 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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