Morphological stability of electromigration-driven vacancy islands

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 noncircular elongated stationary shapes in an analytic approximation that compares favorably to the full numerical solution.