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 diffus ion and electric current in a metal conducting line is developed. The mathe matical model involves moving boundaries governed by a fourth order nonline ar partial differential equation which contains a nonlocal term correspondi ng to the electrical field and a nonlinear term corresponding to the curvat ure. Numerical challenges include efficient computation of the electrical f ield with sufficient accuracy to afford fourth order differentiation along the void boundary and to capture singularities arising in topological chang es. We use the modified immersed interface method with a fixed Cartesian gr id to solve for the electrical field, and the fast local level set method t o update the position of moving voids, Numerical examples are performed to demonstrate the physical mechanisms by which voids interact under electromi gration. (C) 1999 Academic Press.