Electromigration-driven motion of morphologically stable voids in metallic thin films: Universal scaling of migration speed with void size

Abstract

The dependence on void size of the migration speed of morphologically stable voids that translate along metallic thin films due to surface electromigration is analyzed in finite-width films through self-consistent numerical simulations taking surface diffusional anisotropy into account. It is shown that, as the morphological stability limit is approached, the void migration speed deviates substantially from being inversely proportional to the void size. A nonlinear “shape function” that includes both current crowding and diffusional anisotropy effects is derived and incorporated into the well-known theoretical result that is valid for infinite-conductor domains and isotropic surface diffusivity. Rescaling the void migration velocity with the corresponding, numerically evaluated shape function results in a universally valid relationship for the migration speed as a function of void size. This result is important in understanding electromigration-induced void dynamics in metallic interconnect lines.