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

TL;DR

This paper investigates how a constant electrical field causes step meandering on vicinal surfaces like Si(111), deriving a nonlinear evolution equation to describe the long-term coarsening behavior of the instability.

Contribution

It extends previous linear stability analysis to a nonlinear regime, deriving an amplitude equation for step dynamics under electrical fields.

Findings

Nonlinear regime exhibits long-time coarsening dynamics.

Amplitude equation captures large meandering amplitudes.

Both small and large attachment lengths show similar coarsening behavior.

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.