Hybrid Grain-Continuum Model for Thermo-Mechanical Stresses in Polycrystalline Cu 3D IC Vias

We introduce an approach to compute stresses in structures in which grain structures are important. The approach is a hybrid of continuum representations and 3D 'grain-continuum' (GC) models; i.e., models in which grain boundaries are represented and tracked. Stresses due to temperature changes in 3D IC vias are used as to demonstrate our approach. We focus on determining how large the GC region needs to be; that is, how much the computations can be simplified.