Stability of a circular void in a passivated, current-carrying metal film

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Abstract
We perform a linear stability analysis of a preexisting circular void in a passivated current-carrying metal thin film. We introduce small perturbations to the shape of a circular void and study the time evolution of these perturbations in two cases. In the first case, we take only current crowding and surface electromigration into account and find that the void relaxes to a nontrivial steady state in which there are slitlike projections from an otherwise circular void. The relaxation time needed to approach this steady state is also calculated. We then include the effect of surface self-diffusion in our analysis and find that the steady state is a circular void drifting with constant speed. Our calculations indicate that a circular void whose radius is small compared to the line width is stable with respect to small perturbations of its shape in the presence of current crowding, surface electromigration, and surface self-diffusion.