Positivity preserving discretization of time dependent semiconductor drift-diffusion equations

Authors:
Markus Brunk;Anne KvæRnø
Affiliations:
Department C, Institute of Applied Mathematics and Numerical Analysis, University Wuppertal, 42097 Wuppertal, Germany;Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Venue:
Applied Numerical Mathematics
Year:
2012

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Abstract

Positivity preserving discretization of the semiconductor drift-diffusion equations is considered. The equations are spatially discretized by mixed hybrid finite elements leading to a positive ODE or DAE system with index of at most one. For time discretization a second-order splitting technique based on a combination of explicit exponential integration and implicit one-step methods is proposed. This allows for positivity preservation with larger time steps than the corresponding one-step methods. An algorithm is presented coupling the splitting technique with the Gummel iteration scheme allowing for efficient positivity preserving device simulation. Numerical results for a one-dimensional pn-diode are given, showing that the proposed scheme allows for runtime acceleration.