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

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Chapter 1 Background This thesis deals with the measurement of stresses in thin films and multilayers using two different techniques: wafer curvature and x-ray diffraction. The techniques are com- plementary in that wafer curvature measures the average biaxial stress in the film, while x-ray diffraction measures the strain within the diffracting grains. This strain can be con- verted into a stress if the reference lattice parameter and the elastic constants of the grain are known. In Chapter 2, I will discuss the elastic properties of copper thin films. Our interest is not in the “true” modulus that depends on the curvature of the potential energy function and is usually measured by dynamic methods, but in the macroscopic and static modulus that is sensitive to material defects. We find the modulus of copper films is reduced relative to the dynamic value; it also falls off more quickly than the dynamic value at higher temperatures (≈ 0.4 × the melting temperature). Anelastic mechanisms appear to contribute to the modulus reduction. In the next section, I describe our experiments on the plastic behavior of copper thin 1
Chapter 1: Background 2 films on rigid substrates. While “smaller is stronger” is now an old saw in the thin film mechanics world, why it is so remains an issue of debate. A materials scientist looks at the problem from a dislocation standpoint; a mechanician considers constitutive equations. Strain gradient plasticity (SGP) merges these viewpoints and thus is a mathematically and physically satisfying theory. It is still a theory under development, however, and requires additional experimental support. Although we were unable to verify one of the predictions of SGP in thin films, our experiment can be used as a starting point for future attempts. Finally, we will deal with interface stresses in Ag/Ni multilayers. This field is also tinged with controversy, although not for a lack of good reason. J. W. Gibbs died before formulating the thermodynamics of solid-solid interfaces, and we’ve been struggling ever since. We show that the interface stress of Ag/Ni {111} interfaces is compressive, i.e., the interfaces push out. This is slightly counterintuitive, but the compressive nature results from higher order effects in the interatomic potential. (Our intuition is usually only good to first order). I also show that our method of measuring the interface stress is indeed valid for Ag/Ni; for other multilayers, complications such as intermixing can affect the measurement and should not be ignored. Since we will discuss stresses and strains in thin films, this chapter will review some of the essential mechanics and thin film basics (growth and microstructure). Subsequently, I will describe the wafer curvature and x-ray method of extracting stresses and strains, as well as explain how we grow our films and multilayers. 1.1 Elasticity In what follows, I will only consider “stretch” deformations and no rotations.
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: Dedicated to my family
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
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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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