Efficient Thermal Analysis of Integrated Circuits and Packages With Microchannel Cooling Using Laguerre-Based Layered Finite Element Method

Abstract

In this article, an efficient approach named Laguerre-based layered finite element method (LB-LFEM) is presented for transient thermal analysis of integrated circuits (ICs) and packages with microchannel cooling. A marching-on-in-order scheme based on weighted Laguerre polynomials is employed to deal with the governing equations of conjugate heat transfer, where the time variables are eliminated by the orthogonality of Laguerre basis functions. Then, the layered finite element method is utilized to model complex geometries and reduce the original system matrix to that only involves two-dimensional (2-D) surface unknowns in each layer. Based on the reduced matrix equation, the Laguerre coefficients are solved recursively order by order. The computational efficiency is improved significantly by this means. The validity and high efficiency of LB-LFEM are demonstrated by several examples.