Nonlinear wavelength selection in surface faceting under electromigration

Abstract

We report on the control of the faceting of crystal surfaces by means of surface electromigration. When electromigration reinforces the faceting instability, we find perpetual coarsening with a wavelength increasing as $t^{1/2}$. For strongly stabilizing electromigration, the surface is stable. For weakly stabilizing electromigration, a cellular pattern is obtained, with a nonlinearly selected wavelength. The selection mechanism is not caused by an instability of steady-states, as suggested by previous works in the literature. Instead, the dynamics is found to exhibit coarsening {\it before} reaching a continuous family of stable non-equilibrium steady-states.

5 pages, 4 figures, submitted

References in corpus (6)

• Dynamics of Phase Separation of Crystal Surfaces
• A quantitative theory of current-induced step bunching on Si(111)
• When does coarsening occur in the dynamics of one-dimensional fronts ?
• Complex shape evolution of electromigration-driven single-layer islands
• Vicinal silicon surfaces: from step density wave to faceting
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Cited by in corpus (3)

• Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologies
• 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