A numerical study of electro-migration voiding by evolving level set functions on a fixed Cartesian grid

A numerical method for studying migration of voids driven by surface diffusion and electric current in a metal conducting line is developed. The mathematical model involves moving boundaries governed by a fourth order nonlinear partial differential equation which contains a nonlocal term corresponding to the electrical field and a nonlinear term corresponding to the curvature. Numerical challenges include efficient computation of the electrical field with sufficient accuracy to afford fourth order differentiation along the void boundary and to capture singularities arising in topological changes. We use the modified immersed interface method with a fixed Cartesian grid to solve for the electrical field, and the fast local level set method to update the position of moving voids, Numerical examples are performed to demonstrate the physical mechanisms by which voids interact under electromigration. (C) 1999 Academic Press.