On Composite Discontinuous Galerkin Method for simulations of electric properties of semiconductor devices
For researchers simulating electric properties of semiconductor devices, this method handles lower solution regularity at layer interfaces, but the contribution is incremental as it adapts existing SIPG methods to a specific domain.
The paper proposes a Composite Discontinuous Galerkin method for discretizing the van Roosbroeck equations in equilibrium for semiconductor devices, proving well-posedness and uniqueness, and deriving error estimates with numerical simulations.
In this paper, a variant of discretization of the van Roosbroeck equations in the equilibrium state with the Composite Discontinuous Galerkin Method for the rectangular domain is discussed. It is based on Symmetric Interior Penalty Galerkin (SIPG) method. The proposed method accounts for lower regularity of the solution on the interfaces of devices' layers. It is shown that the discrete problem is well-defined and that discrete solution is unique. Error estimates are derived. Finally, numerical simulations are presented.