Competition between noise and determinism in step flow growth

Abstract

The continuum equations of Burton, Cabrera, and Frank are extended to include thermal fluctuations and used to derive a nonlinear stochastic equation describing the meandering of an isolated step on a crystal face grown from a vapor. Meandering is found to result from a unique competition between thermal noise, which dominates close to equilibrium, and deterministic noise (spatiotemporal chaos), which becomes increasingly dominant beyond the morphological instability point. Numerical and analytical results characterizing the step roughness as a function of the supersaturation and the noise strength, ${\mathit{k}}_{\mathit{B}}$T/γ${\mathit{x}}_{\mathit{s}}$, are presented.