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Non‐unique solutions in drift diffusion modelling of phototransistors
Author(s) -
Woods S. J.,
Wilson S. P.,
Walker Alison B.
Publication year - 2000
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/(sici)1099-1204(200001/02)13:1<37::aid-jnm380>3.0.co;2-n
Subject(s) - homojunction , photodiode , diffusion , position (finance) , base (topology) , heavy traffic approximation , statistical physics , optoelectronics , physics , doping , materials science , computer science , optics , thermodynamics , mathematics , mathematical analysis , statistics , finance , economics
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 k B T log 2 where k B T 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 In 0·53 Ga 0·47 As homojunction phototransistors, including the influence of the position of the illumination region and base doping. Copyright © 2000 John Wiley & Sons, Ltd.