Transient Electromagnetic–Thermal Co-Simulation of Microwave/RF Integrated Circuits by the HIE-FDTD Method

In this article, we present an efficient transient electromagnetic–thermal co-simulation solver based on the hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method. This solver is designed to model the multiscale structure and multiphysics field effects of 3-D microwave integrated circuits (ICs). For the first time, we introduce the HIE-FDTD method to solve the heat conduction equation and establish a unified 3-D electromagnetic–thermal co-simulation framework based on the HIE-FDTD algorithm. In addition, this article provides a detailed explanation of the thermal continuity condition, which is rooted in the principle of energy conservation. It addresses the significant variation in thermal conductivity among the different layers of advanced package structures and highlights the potential for substantial errors if the thermal continuity condition is not considered. The stability condition of the proposed method is also given. Numerical results demonstrate that the proposed algorithm achieves the same level of calculation accuracy as the COMSOL software. Thanks to the incorporation of the HIE-FDTD algorithm, our approach significantly enhances computational efficiency compared to the traditional FDTD method and COMSOL software. Furthermore, the proposed algorithm holds the potential for applications in electromagnetic compatibility (EMC) assessments and signal/power integrity (SI/PI) evaluations in radio frequency ICs (RFICs) and advanced packaging.