Electromigration-Induced Step Meandering on Vicinal Surfaces: Nonlinear Evolution Equation

Abstract

We study the effect of a constant electrical field applied on vicinal surfaces such as the Si$(111)$ surface. An electrical field parallel to the steps induces a meandering instability with a nonzero phase shift. Using the Burton-Cabrera-Frank model, we extend the linear stability analysis performed by Liu, Weeks and Kandel (Phys. Rev. Lett. {\bf 81}, p.2743, 1998) to the nonlinear regime for which the meandering amplitude is large. We derive an amplitude equation for the step dynamics using a highly nonlinear expansion method. We investigate numerically two limiting regimes (small and large attachment lengths) which both reveal long-time coarsening dynamics.

submitted to Phys. Rev. B

References in corpus (1)

• Effect of step stiffness and diffusion anisotropy on the meandering of a growing vicinal surface

Cited by in corpus (5)

• On the role of step-flow advection during electromigration-induced step bunching
• Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologies
• Anti-Coarsening and Complex Dynamics of Step Bunches on Vicinal Surfaces during Sublimation
• Electromigration-guided composition patterns in thin alloy films: a computational study
• Electromigration-driven Evolution of the Surface Morphology and Composition for a Bi-Component Solid Film