Analysis of current-driven motion of morphologically stable voids in metallic thin films: Steady and time-periodic states

Abstract

We report results of self-consistent numerical simulations of current-induced migration of morphologically stable voids in metallic thin films accounting rigorously for current crowding, surface curvature, and surface diffusional anisotropy effects. In a previous study, we demonstrated that as the morphological stability limit is approached, the migration speed of a morphologically stable steady void deviates substantially from being inversely proportional to the void size. We also derived a scaling relationship for the void migration speed, rescaled properly with a shape factor, as a function of the void size as described by Cho et al. [Appl. Phys. Lett. 85, 2214 (2004)]. In this study, we calculate accurately shape factors for stable steady void morphologies, as well as for stable time-periodic void morphologies with surface waves propagating on the voids. We predict the effects of surface diffusional anisotropy strength on the migration of stable steady voids, as well as the effects of void size on void migration speed for both steady and time-periodic states. The results validate fully our scaling theory for the current-driven migration of morphologically stable voids and establish its universality. This theory provides an enabling tool for better design of interconnects in integrated circuits toward optimal reliability under conditions that render void migration an important source of metallic thin-film failure.