A simulation of the base widening effect in a high frequency bipolar transistor using a highly robust finite difference algorithm

This paper presents some simulations of the phenomena of base widening in a high frequency planar n.p.n. transistor. In order to model this structure, a highly robust algorithm for the solution of the equations which can be used to describe the behaviour of semiconductor devices has been developed. The algorithm is based on the simultaneous solution of the Poisson equation and the current continuity equations using a multivariate Newton iterative method. After a geometric averaging formulation for the finite difference approximations is made a highly robust procedure is obtained by considering the jacobian matrix to be local to each point in the finite difference mesh. Such a solution method then appears to be a simple variation of the successive over-relaxation procedure and consequently the computer implementation is extremely straightforward, storage requirements are minimal and processing time short. This method is particularly appropriate to the extremely non-linear condition corresponding to high level injection in a bipolar transistor or strong inversion in a MOS transistor.