Three-dimensional simulation for the reliability and electrical performance of through-silicon vias

The electrical performance and reliability of a through-silicon via is investigated through two-dimensional and three-dimensional simulations. Due to the large differences in material thicknesses present in the structures, a 3D simulation is often not feasible. The thermo-mechanical stress, the electrical parameters including TSV resistance and capacitance, as well as the electromigration-induced stress are investigated. A comparison between the results obtained through 2D and 3D simulations is used to suggest which types of simulations require a 3D modelling approach. It is found that an appropriate analysis of the current density through the structure requires 3D simulation, meaning that electromigration phenomena must be studied with 3D simulation or at least a combination of 2D and 3D analysis. However, a 2D simulation with assumed rotational symmetry is sufficient to estimate the thermo-mechanical stress distribution through the structure as well as the parasitic capacitance and signal loss of the TSV.