Surface electromigration refers to the directed motion of atoms (adatoms) at solid surfaces, grain boundaries and interfaces which is caused by an electric current in the bulk of the material. It is considered a key factor determining the reliability of integrated circuits. As miniaturization progresses and current densities increase, a detailed understanding of failure mechanisms is needed to safely extrapolate from an accelerated testing environment to actual operating conditions. It has been shown that a new type of failure appears when the line width of metallic interconnects becomes comparable to or smaller than the grain size of the film. In this "bamboo" regime grain boundaries no longer provide connected diffusion paths along the conductor line. Instead, failure occurs due to intragranular voids which nucleate at the edges of the line, migrate in the current direction and eventually collapse into a slit which disconnects the conductor. This observation has motivated recent theoretical work on the electromigration-induced motion and shape evolution of voids. Since the conductor lines consist of thin metal films, two-dimensional modeling is appropriate.
The conceptually simplest case consists of an insulating void in an infinitely extended, isotropic, homogeneous two-dimensional conductor. A perfectly circular void then moves at a constant velocity inversely proportional to its radius. The motion proceeds in the direction of the applied current. The momentum transfer from the conduction electrons (the "electron wind") induces mass transport along the inner surface of the void, which therefore translates against the direction of electron flow. The circular solution is found to be linearly stable, however it is destabilized beyond a finite threshold perturbation amplitude which depends on the ratio of the void radius to a characteristic length scale determined by the balance of capillarity and electromigration; larger voids move more slowly and are less stable. The movie below shows the time evolution of a nearly circular void which is initially elongated along the field direction and which becomes unstable in a budding scenario.