The Validity of the Drift-Diffusion Equation in Small Semiconductor Devices

Abstract

The classic-diffusion equation has for years been the standard equation used to model semiconductor devices. For silicon devices with size scales of one to two microns, previous studies have found it necessary to use a field-dependent mobility. Several recent GaAs devices have again raised the question of the validity of the drift-diffusion equation for modeling small semiconductor devices. We have developed the following guidelines for the applicability of the drift-diffusion equation. When few electrons transfer into the upper valley, the drift-diffusion equation works well for modeling large-scale GaAs devices operated at room and liquid-nitrogen temperatures. Using the drift-diffusion equation for very small, cold devices, however, leads to physically impossible results. We discuss a different approach to the derivation of the drift-diffusion equation and suggest methods to extend or replace it. Finally, we show that the drift-diffusion equation can be used to model many small, room temperature GaAs devices, without the use of a field-dependent mobility, provided the applied voltage does not drive electrons into the upper valley.