Stable and robust finite element methods for the convective hydrodynamic model of semiconductor devices are developed and implemented on distributed memory parallel computers. Specifically, a stable and accurate space-time and Galerkin/least-squares finite element formulation is developed for the hydrodynamic transport equations for the conservation laws. In addition, Galerkin finite element methods are employed for the Poisson and lattice thermal diffusion equations. The inclusion of the lattice thermal diffusion equation in the numerical solution of the convective hydrodynamic model is presented for the first time. Numerical results for a bipolar transistor are included to illustrate the effectiveness of the numerical methods. Numerical simulations of semiconductor devices using the convective hydrodynamic model require a significant amount of computations. A single-program-multiple-data (SPMD) programming model is proposed for the implementation of the hydrodynamic model on distributed memory parallel computers. Employing the SPMD programming model, a serial program developed on a workstation can be converted into a parallel program with minimal changes. The parallel program has been ported to a wide range of distributed memory parallel computers including the iPSC/860 hypercube, the Touchstone Delta machine, and the IBM SP-1. Parallel performance results are reported for a bipolar transistor, silicon MESFET and diodes. The results indicate that the parallel hydrodynamic device simulator exhibits excellent speedups and scalability on distributed memory parallel computers with minimum communication overhead.
['N. R. Aluru', 'Robert W. Dutton']
Simulation of the hydrodynamic device model on distributed memory parallel computers