Local Discontinuous Galerkin Methods for Moment Models in Device Simulations: Formulation and One Dimensional Results

We report our preliminary work in applying the local discontinuous Galerkin (LDG) finite element method to solve time dependent and steady state moment models, such as the hydrodynamic (HD) models and the energy transport (ET) models, for semiconductor device simulations, in which both the first derivative convection terms and second derivative diffusion (heat conduction) terms exist and are discretized by the discontinuous Galerkin (DG) method and the LDG method respectively. The potential equation for the electric field is also discretized by the LDG method, thus the numerical tool is based on a unified discontinuous Galerkin methodology for different components and is hence potentially viable for efficient h-p adaptivity and parallel implementation. One dimensional n⁺-n-n⁺ diode is simulated in this paper using the HD and ET models and comparison is made with earlier finite difference Essentially Non-Oscillatory (ENO) simulation results.