Analysis and Simulation of Two { Dimensional Dopant Diffusion in Silicon Wilhelm

The production of modern microchips requires a large number of fabrication steps. One important step is the creation of semiconducting areas, where charged dopants are implanted into a semiconducting material and under the in uence of high temperatures the dopants penetrate into the layer. This redistribution of dopants and point defects can be described in terms of pair di usion mechanisms. The resulting reaction{drift{di usion equations include systems of nonlinear parabolic, ordinary and elliptic di erential equations. We state a new existence result of strong solutions in Sobolev spaces. Moreover we present an adaptive algorithm for the numerical simulation of the doping process which is based on an error controlled mesh design in the course of time integration. The adaptation of the mesh is automatically done up to a prescribed tolerance.