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Effect of Elastic Anisotropy on Surface Pattern Evolution of Epitaxial Thin Films

Rui Huang's picture

This paper aims to illustrate how anisotropic elastic properties of the crystal substrate affect epitaxial surface evolution and pattern formation. Specifically, for Ge and SiGe films on silicon substrates of various surface orietations, it is shown that the elastic anisotropy plays an important role. However, it must be pointed out that the evolution dynamics of epitaxial surfaces can be much more complicated, due to the combination/competition of various anisotropic properties (e.g., surface energy, surface diffusivity, etc.). Furthermore, for some surface orietations. e.g., Si(111) and Si(113), discrete surface steps play critical roles in the nucleation and growth of epitaxial islands and other surface structures.

As a by-product of this study, we present a general solution for anisotropic elastic half space (3D) subject to arbitrary surface tractions by a Fourier transform method, as summarized in Appendix A of the attached preprint.

This paper has been published as: Y. Pang and R. Huang, Int. J. Solids and Structures 46, 2822-2833 (2009). 

PDF icon Pang2008.pdf700.47 KB


Mike Ciavarella's picture

Rui have you seen also the recent work on JMPS by Barber and Ting?  Maybe you can extend that to films.   Ask Jim.

Three-dimensional anisotropic elasticity - an extended Stroh formalism

Tom Ting and I have recently
developed a method of extending Stroh's anisotropic formalism to
problems in three dimensions. The unproofed paper can be accessed at .

.Regards, Mike  

michele ciavarella

Rui Huang's picture


Thanks. I did take a look at Barbar and Ting's paper. However, I must admit that I do not have a good understanding of the Stroh formalism and found it difficult to follow in some cases. For the problem we had in this study, the method of Fourier transform seems to be straightforward. It may has some similarity with the Stroh formalism, but it is not a simple extension.



Mike Ciavarella's picture

I agree with you the paper by Barber and Ting is extremely sophisticated. 

But maybe they can give you all the mathematica routines you need.

You obviously find his email in the link.





michele ciavarella

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