Morphological stability of electromigration-driven vacancy islands

TL;DR

This paper investigates the stability and shape evolution of vacancy islands under electromigration, revealing stable circular shapes under certain conditions and fingering instabilities leading to pinch-off, with analytical and numerical insights.

Contribution

It demonstrates the linear stability of circular vacancy islands under electromigration and explores non-circular shapes when attachment kinetics are finite, advancing understanding of shape dynamics.

Findings

Circular islands are linearly stable at high driving forces.

Fingering instability leads to pinch-off of the island.

Non-circular stationary shapes are analytically approximated.

Abstract

The electromigration-induced shape evolution of two-dimensional vacancy islands on a crystal surface is studied using a continuum approach. We consider the regime where mass transport is restricted to terrace diffusion in the interior of the island. In the limit of fast attachment/detachment kinetics a circle translating at constant velocity is a stationary solution of the problem. In contrast to earlier work [O. Pierre-Louis and T.L. Einstein, Phys. Rev. B 62, 13697 (2000)] we show that the circular solution remains linearly stable for arbitrarily large driving forces. The numerical solution of the full nonlinear problem nevertheless reveals a fingering instability at the trailing end of the island, which develops from finite amplitude perturbations and eventually leads to pinch-off. Relaxing the condition of instantaneous attachment/detachment kinetics, we obtain non-circular elongated stationary shapes in an analytic approximation which compares favorably to the full numerical solution.