  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.
