Positivity preserving discretization of time dependent semiconductor drift-diffusion equations

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 pit-diode are given, showing that the proposed scheme allows for runtime acceleration. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.