Three-dimensional Simulation of Effects of Electro-Thermo-Mechanical Multi-physical Fields on Cu Protrusion and Performance of Micro-bump Joints in TSVs Based High Bandwidth Memory (HBM) Structures

With taking into account the electric load, a simplified 4-hi stack HBM structure model containing through- silicon-vias (TSVs) with a 3×6 distributed matrix in each hierarchical level is built. Distributions of temperature, current density and voltage, as well as the mechanical behavior of TSVs and the micro-bump joints in the HBM model are characterized by finite element simulation. To clarify the roles of various coupled physical fields playing in influencing the performance of TSVs and micro-bump joints, the comprehensive simulations were conducted under the conditions of electro-thermo-mechanical fields, electro-mechanical fields and thermo-mechanical fields, respectively. The simulation results indicate that under the electro-thermo-mechanical fields, not only Joule heating occurs but also the current crowding effect appears at the corners between Cu pads and micro-bump joints, as well as at both ends of TSVs. Notably, the maximum current density under the electro-mechanical fields is larger than that under the electro-thermo-mechanical fields. In addition, the Cu protrusion height at lower ends of TSVs is larger than that at upper ends. For micro-bump joints with the viscoplastic deformation behavior, the strain concentration exhibits a symmetrical distribution along the ZY plane (X=0).