Theoretical analysis of current-driven interactions between voids in metallic thin films

Abstract

We analyze the electromigration-induced interactions between voids in metallic thin films using self-consistent numerical simulations of current-driven void morphological evolution. We focus on the interactions between two voids that, if isolated, they would be morphologically stable and migrate at constant speed along the metallic thin film. It is demonstrated that, under certain electromigration conditions, two such different-sized voids migrating in the same direction along a metallic thin film can lead to stable time-periodic states characterized by wave propagation on a void’s surface or cause failure prior to or following their coalescence. Moreover, various complex phenomena are revealed, including void breakup into two morphologically stable voids following the coalescence of the original two voids and voids attempting to pass each other. In numerous cases, it is noteworthy that the void-void interactions examined arise due to a larger void migrating faster than an originally leading smaller one in a finite-width conducting film with anisotropic material properties, contrary to the conventional notion that smaller voids migrate faster than larger ones for electromigration-driven void motion. These results set the stage toward a fundamental understanding of the current-driven dynamics of populations of interacting voids in metallic interconnect lines. Finally, our analysis predicts that void breakup preceded by void coalescence can cause an abrupt increase in the electrical resistance of an interconnect line, in qualitative agreement with observations from accelerated electromigration testing experiments.