Anisotropic dynamics of a vicinal surface under the meandering step instability

TL;DR

This paper models the nonlinear evolution of step meandering on vicinal surfaces, revealing anisotropic effects, coarsening dynamics, and scaling laws relevant to experimental observations.

Contribution

It introduces an asymptotic method to derive a continuous evolution equation capturing anisotropic step flow dynamics.

Findings

Surface dynamics are dominated by anisotropy and elastic relaxation.

Coarsening of undulations follows specific scaling laws.

Characteristic length scales and amplitudes follow deduced exponents.

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.