Solving the Drift Diffusion Equations

The Drift Diffusion equations constitute the simplest and most commonly used model for simulating semicon-ductor devices. This paper contains a comparitive study of the performance and stability of several algorithms that solve these coupled equations without decoupling them. The considered techniques include Successive Over-Relaxation schemes, Nonlinear Conjugate Gradients, and Damped Inexact Newton methods using various linear solvers such as GMRES and Multigrid. Numerical simulation of semiconductor devices is of course of considerable technological importance; in addition, it also presents a very interesting and chal-lenging problem from the perspective of numerical par-tial differential equation solution algorithms. The extreme electric field and temperature sensitivity of electron and hole distribution functions in the semi-conductor bands, which makes semiconductors useful for electronic devices, causes instabilities in the partia