A High-Efficiency Design Method of TSV Array for Thermal Management of 3-D Integrated System

In this article, a high-efficient design method of through silicon via (TSV) array for thermal management of 3-dimensional (3-D) integrated system is developed based on the equivalent thermal conductivity (ETC) model and the particle swarm optimization algorithm. Due to the anisotropy of TSV, the ETC model along the vertical direction is established, and the finite element method (FEM) is utilized to validate the accuracy of the ETC model. The relative error of the peak temperature between FEM and ETC model is less than 1.27%, and the average computational time of ETC model is greatly decreased from 261 to 13.3 s. In addition, the TSV array for heat management of 3-D integrated system is investigated and designed by the developed method. According to the designed scheme, the peak and average temperatures of the FEM based on $6\times 6$ TSV array are 314.60 and 303.84 K, which will agree with the desired indexes (315 and 310 K). The temperature differences of top and bottom surfaces are all less than 4.3 K, which implies that the thermal distribution of the 3-D integrated system is homogeneous. Therefore, the developed design method can efficiently design TSV array to achieve relatively low and uniform thermal distribution, and it can be applied in the 3-D integrated heat management system.