[P2-73] Phase-field Approach to Thermo-mechanical Behavior of Through-silicon Vias
Three-dimensional stacking of silicon chips via Through-silicon vias (TSVs) is an innovative technique for electronic devices due to the drastically shortened electrical path which leads to the faster operation. When TSVs are exposed to high temperature, the higher coefficient of thermal expansion (CTE) of Cu generate the out-of-plane extrusion of Cu from TSV, so-called Cu pumping, which may damage the above lying silicon chip. Furthermore, the thermal expansion is irreversible because the Cu grains are coarsened during the annealing. The comprehensive understanding of Cu pumping mechanism according to the geometry of TSV and annealing conditions is indispensably required to ensure the reliability of electronic devices. A finite element analysis has been used to predict the Cu pumping. However, the finite element method does not incorporate the grain coarsening mechanisms that reduce the elastic energy generated by the thermal expansion. Here, we propose a phase field model that is modified to consider the thermal expansion of Cu polycrystalline during annealing process. The phase field model is the most suitable method to model the evolution of microstructures, since it has benefits for incorporating multiple mechanisms simultaneously. In this study, the significant mechanisms of Cu pumping, including grain boundary migration, thermal expansion, and interfacial characteristics, are considered into the free energy functional of the phase field model