Coupled Thermo-Mechanical analysis of 3D ICs Based on an Equivalent Modeling Methodology with Sub-Modeling

The coupled thermo-mechanical field analysis of three-dimensional (3D) stacked integrated circuits (ICs) is evaluated by an efficient and accurate simulation strategy that combines equivalent homogenization modeling methodology and sub-modeling technique. The thermal field is first investigated using the proposed approach, and based on which the structural field is also examined through the calculation of warpage. The utilization of sub-modeling method reveals the local temperature and warpage distributions, which is lost or ignored by the conventional homogenization method. To validate the proposed method, the simulation results of a five-layer stacked integrated circuits are compared against true 3D results of the detailed model, where the maximum deviation for temperature and warpage is as low as 1.62% and 4.89%, respectively, which are greatly improved compared to 8.23% and 7.83% using traditional homogenization method. In addition, the total computation time is reduced by 76.7% in contrast to true 3D finite element analysis (FEa) simulation. Furthermore, the impacts of through-silicon-via (TSV) geometries, underfill and \mu -bump parameters on the temperature and warpage distributions are also studied to guide the design of 3D ICs with high performance and reliability.