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

Matthieu Dufay·Jean-Marc Debierre·Thomas Frisch
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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.

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Matthieu Dufay, Jean-Marc Debierre, Thomas Frisch. 2006-09-22. Electromigration-Induced Step Meandering on Vicinal Surfaces: Nonlinear Evolution Equation. https://doi.org/10.1103/physrevb.75.045413

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