On the Choice of Coordinates for Semiconductor Simulation.

The semiconductor simulation problem is defined by a set of three coupled nonlinear elliptic partial differential equations. These equations are usually solved either by a coupled or by a decoupling algorithm. Because the solution of semiconductor simulation problems varies over many orders of magnitude, the numerical solution of this nonlinear problem easily gives rise to scaling and conditioning problems in either case. In this report it is shown that important properties of the numerical solution depend on the method of discretization and on three systems of coordinates The system of coordinates which is used for discretization, the system of coordinates in which we linearize and possibly a third systems of coordinates employed for the solution of the linear systems of equations. For the solution to the original partial differential equations charge is conserved and certain maximum principles are valid. In order to preserve these properties for the discretized solution special care has to be taken with respect to the discretization procedure and the choice of coordinates. It is shown that the choice of solution algorithm and the desire to preserve charge and to obtain acceptable numerical properties restrict the possible discretization procedures and sets of coordinates. Author.