Microstructure simulation of grain growth in Cu through silicon vias using phase-field modeling

Abstract

A computationally-efficient 3D phase-field model for simulating grain growth in through silicon vias (TSVs) is presented. The model is capable of simulating grain growth in the cylindrical shape of a TSV. The results generated from the phase-field simulations are used in a finite element model with anisotropic elastic and isotropic plastic effects to investigate the large statistical distribution of Cu pumping (i.e. the irreversible thermal expansion of TSV) experimentally seen. The model thus allows to correlate the macroscopic plastic deformation with the grain size and grain orientations.