A direct approach to solving the drift-diffusion model equations for use in certain MOSFET devices

The behavior of metal oxide semiconductor field effect transistors (MOSFETs) has frequently been modeled using the drift-diffusion partial differential equations. In this paper, we show how extensions of previously studied techniques may be applied to these equations to obtain both current-voltage relationships and pointwise variation of the potential functions arising in a number of practical cases. While our method makes use of perturbation theory, we are able to avoid the complicated asymptotic matching methods that have been widely adopted by a number of authors for studying such MOSFETs. Our numerical approach can treat the important practical case of variable doping and gives rise to accurate, and numerically stable, solutions of the model equations.