A numerical investigation of grain-boundary grooving was carried out by using a level set method. An idealized polycrystalline interconnect was considered which consisted of grains that were separated by parallel grain boundaries which were aligned normal to the average orientation of the surface. Surface diffusion was the only physical mechanism which was assumed a priori. This diffusion was driven by surface-curvature gradients, while a fixed surface slope and zero atomic flux were assumed to exist at the groove root. This situation was equivalent to an initial boundary value problem for a 2-dimensional equation of Hamilton-Jacobi type. The results which were obtained were in good agreement with Mullins’ analytical small-slope solution of the linearized problem (for an isolated grain boundary) and with solutions for a periodic array of grain boundaries. Upon incorporating an electric field, the problem was changed to one of electromigration.

Numerical Simulation of Grain-Boundary Grooving by Level Set Method. M.Khenner, A.Averbuch, M.Israeli, M.Nathan: Journal of Computational Physics, 2001, 170[2], 764-84