MIXED FINITE-ELEMENT APPROACH AND NONLINEAR IMPLICIT SCHEMES FOR DRIFT-DIFFUSION EQUATION SOLUTION OF 2D HETEROJUNCTION SEMICONDUCTOR-DEVICES

We present an abstract mathematical and numerical analysis for Drift-D iffusion equation of heterojunction semiconductor devices with Fermi-D irac statistic. For the approximation, a mixed finite element method i s considered. This can be profitably used in the investigation of the current through the device structure. peculiar feature of this mixed f ormulation is that tile electric displacement D and the current densit ies j(n) and j(p) for electrons and holes, are taken as unknowns, toge ther with the potential phi and quasi-Fermi levels phi(n) and phi(p). This enably D, j(n) and j(p) to be determined directly and accurately. For decoupled system, existence, uniqueness, regularity and stability results of the approximate solution are given. A priori and a posteri ori error estimates are also presented. A nonlinear implicit scheme wi th local time steps is used. This algorithm appears to be efficient an d gives satisfactory results. Numerical results for an heterojunction bipolar transistor, In two dimension, are presented.