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 pn-diode are given, showing that the proposed scheme allows for runtime acceleration.