Accurate deterministic numerical simulation of p-n junctions

It is well known that in order to explain the behavior of devices like p-n junctions or bipolar junction transistors (BJTs), it is necessary to consider the carrier flow both in the conduction band and in the valence band. To do this, different approximations are commonly used to get a numerical solution of the corresponding Boltzmann-Poisson´s system of equations. However, not too much work has focused on a deterministic solution of the Boltzmann equation even when this technique has been proved to yield better results than drift-diffusion or hydrodynamic calculations and also a reduced computational cost compared with Monte Carlo simulations. In this paper some variants of a deterministic simulation of bipolar carrier devices are considered using a FD-WENO scheme (finite differences weighted essentially nonoscillatory). Our goal is the reduction of the computation time while keeping the same precision in our results. To do this we have divided a p-n junction in three different regions. In the neutral regions we solve the transport equation only for the majority carrier and try to approximate the magnitudes related with the other one by an equilibrium assumption. In the space charge region we solve the Boltzmann equation for electrons and holes. The Poisson equation is solved in the entire length of the device. We focus our interest in mechanisms of scattering by means of acoustic phonons in the elastic approximation and optical nonpolar phonons with a single frequency /spl omega/, along with quite simple terms of direct or indirect generation-recombination.