Mechanisms of copper protrusion in through-silicon-via structures at the nanoscale

Thermal stress-induced copper protrusion is frequently observed in through-silicon-vias (TSVs) based three-dimensional (3D) system integration. In this study, the detailed process of Cu protrusion is reproduced on the atomic scale using a two-mode phase-field-crystal (PFC) model, and the mechanisms of protrusion are identified. To simulate thermal loading, a “penalty term” is added to the governing equation of the PFC model. The application of loading on the TSVs induces copper grain deformation and grain boundary migration at the nanoscale. Furthermore, the simulation results suggest that the Cu protrusion is resulted from diffusional creep, involving both Nabarro-Herring creep and Coble creep. The obtained power index of diffusional creep is around 2.16, suggesting that lattice diffusion contributes more to protrusion than grain boundary diffusion does. The protrusion height in micron-scale TSVs predicted by extrapolating the relationship between the protrusion height and diameter of nanoscale TSVs agrees with the experimental data