Simulation of bipolar high-voltage devices in the neighborhood of breakdown

This paper investigates numerical techniques for the solution of the system of nonlinear elliptic PDE's that simulates bipolar semiconductor devices under high reverse bias voltage. Bipolar devices are usually modeled as a set of three elliptic PDE's representing the field equation and the electron and hole current continuity equations. However, these equations can be solved effectively in the case of low-voltage devices only, e.g. by use of the the BAMBI program. As shown in this paper, it is possible to simplify the model in case of high-voltage devices. A powerful software toolkit, ELLAPACK, has been used to solve the resulting two-dimensional Poisson equation. ELLAPACK enabled us to easily compare several numerical solution techniques for their efficiency to solve this problem. To analyze the effectiveness of the toolkit as a whole, a comparison was made between ELLAPACK and a special-purpose program written by us.