Electromigration-Induced Step Meandering on Vicinal Surfaces: Nonlinear Evolution Equation
Matthieu Dufay, Jean-Marc Debierre, Thomas Frisch
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. 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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