A Finite Element Framework for Solving the Density-Gradient Model

This paper presents a positive-preserving, stable finite element scheme for the density-gradient (DG) model. An ef-ficient Newton-Krylov solver is designed to address the nonlinear coupled discrete system. Simulation results for gate-all-around (GAA) devices demonstrate the robustness and effectiveness of the proposed scheme. Notably, the simulation time using our method is only half that of the Sentaurus Device, highlighting its superior computational efficiency.