Twin-aware Monte Carlo simulation of microstructural evolution in copper through-silicon vias (TSVs) based on EBSD-initiated microstructures

Abstract

Annealing is a critical step in the fabrication of through-silicon vias (TSVs). As TSVs continue scaling down, the microstructure evolution of copper during annealing plays an increasingly significant role in determining the overall performance of the device. This is primarily because thermo-mechanical processes during fabrication largely determine TSV reliability, and at reduced scales, copper's anisotropic mechanical properties amplify the role of microstructure in this response. In this study, we investigate the annealing behavior of two types of high-aspect ratio, small-dimension TSVs: one filled with conventionally electroplated copper (Normal TSV) and the other with nanotwinned copper (Nanotwin TSV). For both types, we employ Monte Carlo simulations to model grain growth based on pre-annealing electron backscatter diffraction data. Two approaches are compared: a conventional method that treats all twin boundaries as random high-angle grain boundaries and a modified method that incorporates their effects by correcting their grain boundary energy. In the case of Normal TSVs, the conventional method produces grain size evolution consistent with von Neumann's law, with twin boundary's total length decreasing significantly and the misorientation angle distribution developing multiple peaks. The microstructure gradually evolves into a characteristic bamboo-like morphology, where large grains align along the TSV axis. The modified method shows that, during annealing, the total length of twin boundaries within both types of TSVs initially increases and then stabilizes. The grain growth rate is significantly lower than that predicted by the conventional method, and it predicts a persistent 60° peak in the misorientation angle distribution. In both cases, the bamboo-like structure is attributed to the combination of nearly isotropic grain growth and the high aspect ratio of the TSV geometry. Additionally, stable twin boundaries may act as pinning sites, impeding grain-boundary motion and altering growth behavior. These findings suggest that long-term annealing of small-scale TSVs naturally leads to bamboo-like grain structures, and that the presence of twins introduces deviations from classical grain growth theory—deviations that are more accurately captured when twin boundaries are explicitly considered in simulations.