A Higher-Order Stabilized Hybridized Discontinuous Galerkin Method for Simulating Semiconductor Devices

The simulation of carrier transport in power electronic devices imposes stringent requirements on numerical stability, confining the previous methods to low-order schemes. To address this issue, a stabilized higher-order hybridized discontinuous Galerkin method (S-HDG) is proposed, where we decouple the exponentially varying carrier density from the differential operator and project it onto a lower-dimensional equation. Based on the numerical jumps as indicator, an adaptive artificial diffusion term is introduced to dynamically control oscillatory errors and over diffusion during the iterations for solving nonlinear equations. We validate the proposed method to abrupt junction models, demonstrating its high-order accuracy and robustness against severe mesh skewness and curvature. Furthermore, we apply the method to lateral double-diffused MOSFET (LDMOS), a class of typical power electronic devices, achieving good agreement with the industrial-standard FVSG solver in simulating electrical parameters. Notably, our method can offer higher-order convergence and better compatibility with unstructured meshes.