Cavity and dislocation instability due to electric current

Alectric current drives atomic diffusion in aluminum lines. The phenomenon, known as electromigration, has been a persistent problem in integrated circuits, as the current density increases and the linewidth shrinks for every new generation of the technology. As atoms diffuse, cavities nucleate, enlarge and migrate. Evidence has accumulated that an aluminum line often fails when a rounded cavity collapses into a narrow slit across the width of the line. The fatal slits are often found to be transgranular, i.e. each slit cuts across a single grain. We investigate theoretically this instability phenomenon. Because the shape changes in a relatively short time below half the melting temperature of aluminum, atoms are assumed to diffuse only along the cavity surface, under the combined action of the electron wind and surface tension. When subjected to a small electric field, a circular cavity migrates as atoms diffuse from one portion of the cavity surface to another ; the cavity remains circular, so that capillarity does not drive diffusion. However, the cavity buckles above a critical electric field, elongating either along or normal to the electric field. The surface tension now drives the atomic diffusion to restore the circular shape. The instability sets in if the electric field prevails over the surface tension. The general problem is formulated in terms of nonlinear differential equations, and the pre-bifurcation, bifurcation and post-bifurcation solutions are discussed. In addition, we analyse an analogous phenomenon: a prismatic dislocation loop climbs due to core diffusion driven simultaneously by the electron wind and line tension. The climb relocates mass at relatively low temperatures and thereby degrades the aluminum lines.