A new Control Volume Finite Element Method for the stable and accurate solution of the driftadiffusion equations on general unstructured grids

We present a new Control Volume Finite Element Method with multi-dimensional ScharfetteraGummel upwinding (CVFEM-SG) for the driftadiffusion equations. The method combines a conservative formulation of the carrier density continuity equations with an edge element lifting of the one-dimensional Schar...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2013-02, Vol.254, p.126-145
Main Authors: Bochev, Pavel, Peterson, Kara, Gao, Xujiao
Format: Article
Language:English
Subjects:
Computer simulation
Drift
Finite element method
Mathematical analysis
Mathematical models
MOSFETs
Robustness
Scalars
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Summary:We present a new Control Volume Finite Element Method with multi-dimensional ScharfetteraGummel upwinding (CVFEM-SG) for the driftadiffusion equations. The method combines a conservative formulation of the carrier density continuity equations with an edge element lifting of the one-dimensional ScharfetteraGummel edge currents into curl-conforming elemental currents. These elemental currents combine the upwind effect from all element edges and enable accurate computation of the flux on arbitrary surfaces inside the elements. In so doing, we obtain a formulation that is stable and accurate on general unstructured finite element grids. This approach sets our formulation apart from other methods, which require the control volumes to be topologically dual to the primal grid. Numerical studies of the CVFEM-SG for a suite of scalar advectionadiffusion test problems confirm the accuracy and the robustness of the new formulation. Simulations of a PN diode and an n-channel MOSFET device demonstrate the performance of the method for the fully coupled driftadiffusion system.
ISSN:0045-7825