Numerical simulation of grain-boundary grooving by level set method

A numerical investigation of grain-boundary grooving by means of a level se t method is carried out. An idealized polycrystalline interconnect which co nsists of grains separated by parallel grain boundaries aligned normal to t he average orientation of the surface is considered. Initially. the surface diffusion is the only physical mechanism assumed. The surface diffusion is driven by surface-curvature gradients. while a tired surface slope and zer o atomic flux are assumed at the groove root. The corresponding mathematica l system is an initial boundary value problem For a two-dimensional equatio n of Hamilton-Jacobi type. The results obtained are in good agreement with both Mullins analytical "small-slope" solution of the linearized problem (W . W. Mullins. 1957. J. Appl. Phys. 28. 333) (for the case of an isolated gr ain boundary) and with the solution for a periodic array of grain boundarie s (S. A. Hackney, 1988. Scripta Metall. 22. 1731). Incorporation of an elec tric field changes the problem to one of electromigration. Preliminary resu lts of electromigration drift velocity simulations in copper lines art: pre sented and discussed. (C) 2001 Academic Press.