Strain energy driven and curvature driven grain boundary migration in 3D-IC Cu vias

We use grain-focused models to study grain boundary (GB) migration (GBM) in polycrystalline Cu vias that interconnect MLM layers in 3D ICs. Curvature-driven GB velocities are calculated by PLENTE [1-3] using the local mean curvature of the GBs, as described in Ref. 2. We use Comsol Multiphysics [4] to calculate GB velocities due to thermally induced strain energy jumps across GBs [5]. The thermo-mechanical calculations needed for this are made using model structures that combine continuum models and grain-continuum (GC) models (see [1-3, 5]); we call these 'hybrid' grain-continuum (HGC) models. Curvature driven GB dominates in this work; however, there are uncertainties in the absolute stress values used and how the relative magnitudes of these phenomena will change as the structure evolves.