An HDG Method for Time-dependent Drift-Diffusion Model of Semiconductor Devices
This work provides a rigorous numerical analysis for a nonlinear coupled system relevant to semiconductor simulation, but the method is an incremental extension of existing HDG techniques.
The paper proposes a hybridizable discontinuous Galerkin method for the time-dependent drift-diffusion model of semiconductor devices, achieving optimal convergence rates for the electric potential, electron concentration, and their gradients, as confirmed by numerical experiments.
We propose a hybridizable discontinuous Galerkin (HDG) finite element method to approximate the solution of the time dependent drift-diffusion problem. This system involves a nonlinear convection diffusion equation for the electron concentration $u$ coupled to a linear Poisson problem for the the electric potential $ϕ$. The non-linearity in this system is the product of the $\nabla ϕ$ with $u$. An improper choice of a numerical scheme can reduce the convergence rate. To obtain optimal HDG error estimates for $ϕ$, $u$ and their gradients, we utilize two different HDG schemes to discretize the nonlinear convection diffusion equation and the Poisson equation. We prove optimal order error estimates for the semidiscrete problem. We also present numerical experiments to support our theoretical results.