An atomistic study of copper extrusion in through-silicon-via using phase field crystal models

Three-dimensional system integration using Cu through-silicon-via (TSV) technology enables vertical interconnection of stacked dies. However, the large statistical distribution of plastic Cu extrusion, also known as Cu pumping, presents a serious reliability concern. Traditional finite element method (FEM) based thermo-mechanical modeling that neglects microstructure has been extensively attempted in order to identify the root cause of the extrusion, which yet remains unknown. This study utilizes recently developed phase field crystal (PFC) models, which resolve systems on atomic length scales and diffusive timescales, to capture the creation, destruction, and interaction of defects in polycrystalline Cu TSV structures and thereby elucidate the atomistic mechanisms of the Cu extrusion. The governing kinetic equation of the PFC model is first solved using FEM to generate Cu grains with an atomic resolution in TSVs by referring to experimental EBSD images. A shearing term is then added to the governing equation to simulate TSV deformation under shear strain. The solidification process at the atomistic scale is simulated to prepare polycrystalline TSV samples. Rotation and coalescence of grains with low mis-orientations are observed in solidification. The application of shear strain to the polycrystalline TSVs reveals the movement of defects at the atomistic scale. The defects diffuse through grain boundaries and aggregate at the edges of TSVs, where the defects become immobile. The process of rotation and coalescence of grains is found to be accelerated under the shear strain. The simulation results also suggest that the geometry of the TSVs is an important factor controlling the behavior of defect diffusion and microstructures in TSVs, and thus the mechanical behavior of TSVs.