The Drift Diffusion Equations

The drift diffusion equations are the most widely used model to describe semiconductor devices today. The bulk of the literature on mathematical models for device simulation is concerned with this nonlinear system of partial differential equations and numerical software for its solution is commonplace at practically every research facility in the field. From an engineering point of view, the interest in the drift diffusion model is to replace as much laboratory testing as possible by numerical simulation in order to minimize costs. To this end, it is important that computations can be performed in a reasonable amount of time. This implies that the involved mathematical models cannot be too complicated, such as, for instance, the higher dimensional transport equations described in Chapter 1. For the current state of technology the drift diffusion equations seem to represent a reasonable compromise between computational efficiency and an accurate description of the underlying device physics. Therefore transport equations are used mainly to compute data for the model parameters in the drift diffusion equations in the engineering environment. It should be pointed out, however, that, with the increased miniaturization of semiconductor devices, one comes closer and closer to the limits of validity of the drift diffusion equations, even in an industrial environment.