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

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

2006-09-22

arxiv.org/abs/cond-mat/0609573v1

Physics

Condensed Matter

Materials Science

submitted to Phys. Rev. B

Scientific paper

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.

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