In this paper we analyze evolution of wrinkle patterns of anisotropic crystal films on viscoelastic substrates. The effects of the residual stress state in the film and the anisotropic elastic property are emphasized. Analytical solutions for the initial growth kinetics and the equilibrium states are presented along with numerical simulations based on nonlinear evolution equations. Compared to wrinkling of isotropic elastic films, more ordered wrinkle patterns are predicted, including orthogonal, zigzag, parallel, and checkerboard patterns. Tranistion of the wrinkle patterns under various stress states is elucidated. Some related experimental works are referred to, but quantitative comparisons between the model the experiments await further studies.

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.

Y. Pang and R. Huang, J. Applied Physics 101, 023519 (2007).

Surface instability of epitaxial thin films leads to a variety of surface patterns. Anisotropy in surface and bulk properties has profound effects on the dynamics of pattern formation. In this study, we theoretically predict that, under anisotropic mismatch stresses, a bifurcation of surface pattern occurs in addition to generic symmetry breaking from isotropic systems. Numerical simulations based on a nonlinear evolution equation demonstrate pattern selection at an early stage and nontrivial patterns for long-time evolution.