A numerical investigation was made of grain-boundary grooving by using the level set method. Such grooving was a key element of electromigration drift in polycrystalline interconnects. An idealized polycrystalline interconnect was considered here which consisted of grains that were separated by parallel grain boundaries which were aligned normal to the average orientation of the interconnect surface. Surface and grain-boundary diffusion were the only diffusion mechanisms which were assumed to operate. The diffusion was driven by surface curvature gradients and by an externally applied electric field. The corresponding mathematical system was an initial boundary-value problem for a 2-dimensional Hamilton-Jacobi type of equation. In order to solve the electrostatic problem at a given time step, a full model was used which was based upon the solution of the Laplace equation for the electric potential. The resultant set of linear algebraic equations was solved by using a multi-grid iterative procedure. The details of transient slit and ridge formation processes were compared with theoretical predictions of steady-state grooving.

Level Set Modelling of Transient Electromigration Grooving. M.Khenner, A.Averbuch, M.Israeli, M.Nathan, E.Glickmnn: Computational Materials Science, 2001, 20[2], 235-50