Numerical Problems in Semiconductor Simulation Using the Hydrodynamical Model: a Second-Order Finite Difference Scheme
Tuesday 29th July 2003
Ballestra, Luca V.; Sacco, Riccardo
In this paper a second-order Total Variation Diminuishing (TVD) finite diffence scheme of upwind type is employed for the numerical approximation of the classical hydrodynamic model for semiconductors proposed byB. and Baccarani-Wordeman. In particular, the high-order hyperbolic fluxes are evaluated by a suitable extrapolation on adjacent cell of the first-order fluxes of Roe, while total variation diminuishing is achieved by limiting th slopes of the discrete Riemann invariants using the so-called Flux Corrected Transport approach. Extensive numerical simulations are performed on a submicron n^+ - n - n^+ ballistic diode. The numerical experiments show that the spurious oscillations arising in the electron current are not completely suppressed by the TVD scheme, and can lead to serious numerical instabilities when the solution of the hydrodynamic model is non-smooth and the computational mesh is coarse. The accuracy of the numerical method is investigated in terms of conservation of the steady electron current. The Obtained results show that the second-order scheme does not behave much better than a corresponding first-order one due to a poor performance of the slope limiters caused by the presence of local extrema of the Riemann invariant associated with the hyperbolic system.