Grain Based Modeling of Stress Induced Copper Migration for 3D-IC Interwafer Vias

We discuss our grain-continuum approach to modeling stress-driven grain boundary migration in polycrystalline Cu films, assuming that migration is due to differences in strain energies. We focus on thermally induced stresses and compute those using comsol multiphysics. To account for grain structure in polycrystalline films, the anisotropic elastic constants of single crystal Cu are used for each grain, after aligning them with each grain´s orientation. Local grain boundary velocities are calculated based on the differences in strain energy across grain boundaries. The computed velocities are then used to update the level sets that represent the grain boundaries using the PLENTE software. Simple and more complicated grain structures are studied as part of a larger effort to understand the effects of thermally induced stresses in 3D-IC inter-wafer vias