Transient Thermomechanical Coupling Analysis of Power Device Encapsulation Using an FDTD-Based Explicit Time-Stepping Framework

To address critical thermomechanical coupling challenges affecting power device reliability during encapsulation processes, this paper develops a transient thermomechanical coupled numerical model based on the Finite-Difference Time-Domain (FDTD) method. By extending the explicit time-stepping strategy of FDTD, the heat conduction equation and solid mechanics equations are discretized and solved within a unified computational framework. This approach eliminates the need for generating and inverting large stiffness matrices inherent to implicit algorithms, thereby significantly reducing computational complexity. The thermal field is discretized using the Fourier law with a Yee grid-centered difference scheme, and a real-time thermal expansion strain tensor correction mechanism is introduced to accurately capture material nonlinearities and continuously update displacements and stresses in the structural field. Based on the proposed numerical model, we simulated the actual reflow welding process and validate results against COMSOL simulations and experimental data. The three-dimensional deformation distribution of the encapsulation shells under thermal cycling loading was revealed, and a quantitative mapping relationship between material parameters, temperature fields, and stress fields has been established. These results provide a critical theoretical foundation for optimizing encapsulation structures and controlling power device performance parameters.