Simulations and theory of electromigration-induced slit formation in unpassivated single-crystal metal lines

We use a phase field method to simulate the time evolution of a perturbation to the edge of a current-carrying, single-crystal metal line. Surface electromigration, surface self-diffusion, and current crowding are all taken into account. We find that if the applied current exceeds a threshold value, the perturbation grows to become a slit-shaped void that spans the wire, and that leads to electrical failure. The slits in our simulations are remarkably similar to the slits observed in experiments. We explain the physical origin of this instability and point out the importance of crystalline anisotropy and mass transport along the edge of the line. In our simulations, we find that the current dependence of the time to failure differs markedly from the behavior observed for wide polycrystalline lines. We find how the resistance diverges as the wire nears failure. Ways to increase the lifetime of single crystal lines are suggested and, furthermore, we point out some interesting similarities between viscous fingers in a Hele-Shaw cell and the slits in these lines.