A comparison of simple theoretical models for the photoionisation of impurities in semiconductors

Abstract

A comparison of two simple theoretical models, the quantum-defect (QD) model with unit normalisation, and a new billiard-ball model (BB) recently proposed by Ridley (see ibid., vol.13, p.2015, 1980), is effected by relating to a third model which is based upon approximating the true impurity potential to a square-well core and, if the centre is charged, a Coulombic tail. This third model, which requires numerical computation, goes over to the QD or BB models under specific conditions, and so acts as a kind of compromise model. The photoionisation cross section for various depths of level, and for neutral, attractive and repulsive centres, is calculated for each model and conditions for the applicability of the QD and BB models are obtained. It is shown that the QD model predicts spectral dependences well, but underestimates magnitude because of incorrect normalisation. The QD model is expected to be reasonably good for shallow and moderately deep levels, provided the centres are not repulsive, but for very deep levels, and for all levels associated with repulsive centres, the BB model is expected to be more useful.