Anisotropic dynamics of a vicinal surface under the meandering step instability

Abstract

We investigate the nonlinear evolution of the Bales-Zangwill instability, responsible for the meandering of atomic steps on a growing vicinal surface. We develop an asymptotic method to derive, in the continuous limit, an evolution equation for the two-dimensional step flow. The dynamics of the crystal surface is greatly influenced by the anisotropy inherent to its geometry, and is characterized by the coarsening of undulations along the step direction and by the elastic relaxation in the mean slope direction. We demonstrate, using similarity arguments, that the coalescence of meanders and the step flow follow simple scaling laws, and deduce the exponents of the characteristic length scales and height amplitude. The relevance of these results to experiments is discussed.

10 pages, 7 figures; submitted to Phys. Rev. B

References in corpus (9)

• Four Lectures on the Physics of Crystal Growth
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Cited by in corpus (3)

• Double step structure and meandering due to the many body interaction at GaN(0001) surface in N-rich conditions
• Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models
• Strong anisotropy in two-dimensional surfaces with generic scale invariance: Non-linear effects