Steady-State Thermal Modeling of a Power Module: An N-Layer Fourier Approach

The steady-state thermal modeling of a rectangular N-layer structure with an arbitrary number of heat sources on the top surface is obtained by a Fourier series solution. As the structure of power modules can be closely approximated as a rectangular N-layer structure, this model may be used to accurately estimate the temperature field occurring in such modules. Various simplified structures are analyzed to understand the effects of structural approximation on the temperature field. The Fourier-based method developed in this work is compared with the finite-element method simulation, and an excellent matching (approximately 0.27% temperature error) is found in the centers of the semiconductor dies. Experimental temperature measurements taken at the surface of a commercial SiC power module are also presented, demonstrating agreement in the centers of the dies to within 3.5%.