Optical-transition cross sections involving impurities in semiconductors

Abstract

A formula is derived in a general framework for various optical-transition cross sections involving an impurity bound state (acceptor or donor) and a continuum state belonging to a band (valence or conduction) in semiconductors. A quantum-defect wave function with the correct normalization has been used for the bound state. The results are used to obtain explicitly several improved formulas of interest in the literature. A method is presented and also applied to the case of GaAs to compute the overlap integrals of the cell periodic functions which are needed in our derived formula. Approximate analytical expressions which should be valid with good accuracy for transitions near the band extrema have also been obtained. It has been shown that the formula for photoionization cross section reduces exactly to that for the well-known Lucovsky's $\ensuremath{\delta}$-function model in the appropriate limit. Other limiting cases have been discussed and compared with previous results. Comparison with experiment has been made for the photoionization of manganese impurities in gallium arsenide.