A finite element analysis of the motion and evolution of voids due to strain and electromigration induced surface diffusion

Microelectronic circuits often fail because cracks and voids cause open circuits in their interconnects. Many of the mechanisms of failure are believed to be associated with diffusion of material along the surfaces, interfaces or grain boundaries in the line; material may also flow through the lattice of the crystal. The diffusion is driven by variations in elastic strain energy and stress in the solid, and by the flow of electric current. To predict the conditions necessary for failure to occur in an interconnect, one must account for the influence of both deformation and electric current flow through the interior of the solid, and also for the effects of mass flow. To this end, we describe a two dimensional finite element method for computing the motion and evolution of voids by surface diffusion in an elastic, electrically conducting solid. Various case studies are presented to demonstrate the accuracy and capabilities of the method, including the evolution of a void towards a circular shape due to diffusion driven by surface energy, the migration and evolution of a void in a conducting strip due to electromigration induced surface diffusion, and the evolution of a void in an elastic solid due to strain energy driven surface diffusion.