Improved Cauer thermal network considering thermal coupling effects of multi-chip modules

The Cauer thermal network has made a realistic physical representation of thermal behaviour of a multi-chip module (MCM) theoretically possible. However, the traditional method assumes the heat conduction is critical, with an approximate one-dimensional heat conduction path for calculation and fixed heat spreading angle to make up for the compensation brought by the approximation. It will limit the accuracy and cause a significant error in estimating the junction temperature of MCM. In this study, the heat spreading angle in the area of two adjacent chips is studied by using a cross-section to change the problem to a two-dimensional heat transfer question. Based on the heat flow got from the results of calculation by using Fourier's law, an expression for heat spreading angle as a function of boundary conditions is given, which is capable of estimating the junction temperature by adjusting effective heat conduction area of an MCM whose thermal behaviour is seriously coupled among neighbour chips. The accuracy of the proposed method and expression is validated by both the finite-element method and experimental results and they both show a good agreement with the calculation.