Nonlinear wavelength selection in surface faceting under electromigration

TL;DR

This paper investigates how surface electromigration influences crystal surface faceting, revealing nonlinear wavelength selection mechanisms and different surface behaviors depending on electromigration strength.

Contribution

It demonstrates that nonlinear wavelength selection occurs through coarsening dynamics rather than steady-state instabilities, challenging previous theories.

Findings

Perpetual coarsening with wavelength ~ t^{1/2} under reinforcing electromigration

Surface stability when electromigration strongly stabilizes the surface

Cellular pattern formation with nonlinearly selected wavelength under weak stabilization

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.