An unfitted finite element method for the numerical approximation of void electromigration

Microelectronic circuits usually contain small voids or cracks, and if those defects are large enough to sever the line, they cause an open circuit. We present a numerical method for investigating the migration of voids in the presence of both surface diffusion and electric loading. Our mathematical model involves a bulk-interface coupled system, with a moving interface governed by a fourth-order geometric evolution equation and a bulk where the electric potential is computed. Thanks to a novel approximation of the interface, equidistribution of its vertices is guaranteed, and no remeshing is necessary. In addition, the used curvature approximation means that our method is unconditionally stable for the evolution by surface diffusion only. Various examples are performed to demonstrate the accuracy of the method.