Non-unique solutions in drift diffusion modelling of phototransistors

Abstract

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 is well known that the DD equations can yield non‐unique solutions for pn structures which contain three or more junctions and two terminals with applied biases greater than kBT log 2 where kBT is the thermal energy at a temperature T, but DD models of phototransistors under illumination have been 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 weakness 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 position of the illumination region and base doping. Copyright © 2000 John Wiley & Sons, Ltd.

Modeling Sources of Nonlinearity in a Simple p-i-n Photodetector

“…The basic variables in the drift-diffusion equations, (1), are the potential (or electric field), the electron concentration, and the hole concentration. Therefore, it is more convenient to rewrite (18) in terms of the carrier concentration instead of the quasi-Fermi levels:…”