Thermal-WLP: A Transient Thermal Simulation Method Based on Weighted Laguerre Polynomials for 3-D ICs

Thermal issue becomes a key challenge in 3-D integrated circuits (3-D ICs) due to their highly integrated and compact design. To give a fast and accurate prediction of the transient temperature field, a new unconditional stable scheme for heat conduction equation is proposed in this paper. This method, thermal-weighted Laguerre polynomials (WLP), uses WLPs as basis functions and Galerkin's method as a testing procedure, to eliminate the time variables of the temperature field. Thus, a marching-on-in-order scheme can be obtained, which is more efficient on computation than those marching-on-in-time schemes of conventional numerical methods, especially for 3-D ICs with complex structures. Two examples of the transient thermal problems in 3-D ICs are presented, and the numerical results show the accuracy and efficiency of the proposed method.