Electromigration-induced wave propagation on surfaces of voids in metallic thin films: Hopf bifurcation for high grain symmetry

The propagation of stable surface waves induced by surface electromigration on voids in metallic thin films is analyzed by self-consistent numerical simulations of current-driven surface morphological evolution. Emphasis is placed on single-crystalline films characterized by high symmetry of surface diffusional anisotropy, representative of [1 0 0]-oriented grains in fcc metals. The theoretical analysis predicts the onset of stable time-periodic states for the void surface morphological response as either the applied electric field strength, or the void size, or the strength of the diffusional anisotropy is increased over a critical value. These stable states correspond to waves propagating on surfaces of voids that migrate along the metallic film at constant speeds. For parameter values below the critical ones, morphological evolution leads to stable steady states for the void surface morphology. Therefore, the onset of stable surface wave propagation corresponds to a Hopf bifurcation in the current-induced surface morphological response. The examined nonlinear dynamics is very rich, leading to different sequences of morphological transitions and instabilities as different operating conditions and system parameters are varied.