Phase field model of surface electromigration in single crystal metal thinfilms

A phase field model is developed for numerically studying the time evolutio n of insulating voids in a current-carrying single crystal metal thin film. In our model, we include the effects of surface electromigration, surface self-diffusion and current crowding in the fully nonlinear regime. A contin uously varying scalar order parameter is used to describe the metal and voi d "phases" within the wire in this phase field formulation. The time evolut ion of the metal-void interface is given by two partial differential equati ons: one embodying the conserved dynamics of the order parameter and the ot her a modified Laplace's equation for the electrical potential. We also car ry out detailed asymptotic analysis to verify that our phase field formulat ion faithfully represents the surface electromigration problem. (C) 1999 El sevier Science B.V. All rights reserved.