An HDG Method for the Time-dependent Drift–Diffusion Model of Semiconductor Devices

  • Gang Chen
  • Peter MonkEmail author
  • Yangwen Zhang


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 electric potential \(\phi \). The non-linearity in this system is the product of the \(\nabla \phi \) with u. An improper choice of a numerical scheme can reduce the convergence rate. To obtain optimal HDG error estimates for \(\phi \), 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.


Hybridizable discontinuous Galerkin method Drift–diffusion Error analysis Optimal convergence rate 



G. Chen is supported by National natural science Foundation of China (NSFC) under Grant Number 11801063 and China Postdoctoral Science Foundation under Grant Number 2018M633339. The research of P. B. Monk and Y. Zhang is partially supported by the US National Science Foundation (NSF) under Grant Number DMS-1619904.


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Authors and Affiliations

  1. 1.College of MathematicsSichuan UniversityChengduChina
  2. 2.Department of Mathematical SciencesUniversity of DelawareNewarkUSA

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