A Reduced Order Model based Framework for Efficient Solution of steady state Semiconductor Transport Equations

The semiconductor Boltzmann equation serves as a fundamental kinetic model for describing carrier transport under various physical and geometrical conditions. When uncertain parameters are involved,numerical simulations often require repeated solutions of the equation with different model settings, which lead to high computational cost. To address this issue, this study develops an efficient reduced-order model (ROM) enhanced framework based on an upwind discontinuous Galerkin (DG) discretization for the spatial domain and Hermite polynomial expansions for the velocity space. The proposed method incorporates a parametric training strategy to capture low-rank structures across physical and material parameters within the semiconductor transport model. In the iterative solution process, several types of correction equations are introduced within the synthetic acceleration (SA) step to improve convergence performance. These include the traditional drift–diffusion-type correction suitable for the highly collisional regime and a data-driven ROM-based kinetic correction that remains efficient and accurate in more general parameter settings. Instead of combining them, the framework is designed to flexibly select among multiple correction strategies according to the local physical conditions. In addition, a hybrid acceleration approach inspired by the ROMSAD scheme \cite{peng2024reduced} is implemented to combine the fast convergence behavior of the ROM-based model with the robustness of the diffusion-based correction. In this thesis, we mainly study the DSA (diffusive synthetic acceleration) scheme for the semiconductor Boltzmann model and conduct numerical simulations. The ROMSAD scheme is studied for corresponding parametric problems with numerical simulation as a future work.Numerical experiments on one- or two-dimensional benchmark semiconductor problems demonstrate that the proposed method significantly reduces computational cost while maintaining stable and accurate results across multiscale and parametric regimes. The framework provides a unified and extensible foundation for accelerating kinetic solvers in semiconductor transport modeling.