# Morphological stability of electromigration-driven vacancy islands

Source: [Morphological stability of electromigration-driven vacancy islands](<https://www.sota2.com/research/paper/68fa31bc1e209131ce881a52>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T19:03:23.597Z

Authors: Frank Hausser, Philipp Kuhn, Joachim Krug, Axel Voigt

Published: 2007-01-10T16:41:44.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0701208>)

[PDF](<https://arxiv.org/pdf/cond-mat/0701208.pdf>)