SOLUTION OF THE HYDRODYNAMIC DEVICE MODEL USING HIGH-ORDER NONOSCILLATORY SHOCK CAPTURING ALGORITHMS

Simulation results for the hydrodynamic model are presented here for an n+ - n - n+ diode by use of shock capturing numerical algorithms, applied to the transient model, with subsequent passage to the steady state. The numerical method is first order in time, but of high spatial order in regions of smoothness. Implementation typically requires a few thousand time steps. The algorithms, termed essentially nonoscillatory, have been successfully applied recently to problems in gas dynamics, but are being employed in semiconductor simulation here for the first time. The simulations clearly reveal temporal and spatial velocity overshoot, as well as overshoot relative to an electric field induced by the Poisson equation. Shocks are observed in the transient simulations for certain low temperature parameter regimes.