Non-unique solutions in drift diffusion modelling of phototransistors

We report non-unique solutions for the potential in a Drift Diffusion (DD) model of a two terminal phototransistor. These solutions are present under bias without illumination, and persist until high illumination levels, It i s well known that the DD equations can yield non-unique solutions for pn st ructures which contain three or more junctions and two terminals with appli ed biases greater than k(B)T log 2 where k(B)T is the thermal energy at a t emperature T, but DD models of phototransistors under illumination have bee n less well studied. The implicit belief is that one needs to artificially impose a potential in the base of the phototransistor in order to obtain a unique solution. We show here that this is only necessary because of a weak ness in the numerical methods used to solve the equations, and describe two methods which circumvent this for which we show that this problem does not occur. These methods are used to investigate the operation of GaAs and In0 .53Ga0.47As homojunction phototransistors, including the influence of the p osition of the illumination region and base doping. Copyright (C) 2000 John Wiley & Sons, Ltd.