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.

中文翻译：

---

考虑到多芯片模块的热耦合效应的改进的Cauer热网络

Cauer热网络从理论上使多芯片模块（MCM）的热行为的物理表示成为现实。然而，传统方法假设导热是至关重要的，具有近似一维的导热路径用于计算，并且固定的散热角可弥补近似带来的补偿。这将限制精度，并在估计MCM的结温时引起重大误差。在这项研究中，通过使用横截面将问题更改为二维传热问题，研究了两个相邻芯片区域中的散热角。根据傅立叶定律的计算结果得出的热流，给出了散热角与边界条件的函数表达式，它能够通过调整热行为严重耦合到相邻芯片之间的MCM的有效导热面积来估算结温。有限元法和实验结果验证了所提方法和表达式的准确性，与计算结果吻合良好。