On reproducing the copper extrusion of through-silicon-vias from the atomic scale

Three-dimensional system integration with through-silicon-vias (TSVs) is regarded as a promising solution to the 'More-than-Moore' challenge to improve the performance of micro- and nano-electronic devices. However, the copper extrusion of TSVs during the back-end-of-the-line (BEOL) process and under service conditions poses serious reliability concerns. Substantial experimental and simulation work have been carried out to clarify the origins of copper extrusion, which as yet remain unclear. This study uses a two-mode phase field crystal (PFC) model to reproduce the process of the copper extrusion from the atomic scale. A 'penalty term' is added to the governing equations of the PFC model to simulate the application of a compressive strain to the TSV samples. The application of strain reveals the process of emission and annihilation, and the climb and slip motions of dislocations. In general, the irreversible plastic extrusion is a cumulative effect of the motion of dislocations and the migration of the grain boundaries. The simulation results also suggest that the applied strain rate and the grain structure of the polycrystalline TSVs are important factors controlling the process of copper extrusion.