Analytical thermal model for HEMTs with complex epitaxial structures

Although wide bandgap solid state devices are one of the most promising technologies for high power, high frequency applications, high device temperatures often lead to degraded performance and reliability. Thus, accurately predicting and maintaining device temperature at an acceptable level is a key to realizing the full potential of wide bandgap electronics. In this work, we present a closed-form analytical solution to the steady-state heat equation applicable to compound semiconductor high electronic mobility transistors (HEMTs), such as those based on gallium nitride (GaN). While numerical techniques are widely used to predict device temperature, our analytical solution is more computationally-efficient and can account for complex multi-layer structures, internal heat sources, and a variety of thermal interface conditions. Through a Fourier series-based solution and recursive relations for the Fourier coefficients in adjacent layers, we report manageable expressions for the Fourier coefficients. We also demonstrate that these solutions are two orders of magnitude more efficient than state of the art semi-analytical techniques for complex 3D structures. In addition, we have validated the model with high spatial resolution micro-Raman thermography measurements on GaN device structures.