Transient temperature distribution in a multilayer semiconductor device with dynamic thermal load and non-uniform thermal contact resistance between layers

Abstract

The thermal management challenge in microelectronic chips is exacerbated by their multilayer architecture and manufacturing processes that introduce non-uniform thermal contact resistance between adjacent layers. Most of the past work on development of thermal models to predict temperature distribution in microelectronic chips either does not account for such thermal contact resistance at all, or simply assumes it to be spatially uniform. This work presents an exact analytical solution for the transient temperature distribution in a multilayer chip with non-uniform thermal contact resistance between layers as well as dynamic, non-uniform heat generation. The problem is solved by first carrying out a Laplace transformation and then implementing a series solution, the coefficients of which are determined by solving a set of algebraic equations derived from the non-uniform thermal contact resistances between adjacent layers. While the problem is solved for a general M-layered chip, the solution for the practical case of a two-layer chip is also provided. Results indicate that the temperature distribution and its evolution over time is determined by the nature of the non-linear thermal contact resistance, and its overlap with the dynamic heat loads imposed on the chip. The impact of these and other relevant parameters is examined in detail. Results presented here improve the fundamental understanding of thermal transport modeling in multilayer semiconductor chips, with possible applications in other multilayer engineering systems as well.