The original Shockley-Read-Hall recombination statistics is extended to include recombination of localized excitations. The recombination is treated as a bimolecular process rather than a monomolecular recombination of excitons. The emphasis is placed on an interplay between two distinct channels of radiative recombination (shallow localized states vs extended states) mediated by trapping of photogenerated charge carriers by non-radiative centers. Results of a numerical solution for a given set of parameters are complemented by an approximate analytical expression for the thermal quenching of the photoluminescence intensity in non-degenerate semiconductors derived in the limit of low pump intensities. The merit of a popular double-exponential empirical function for fitting the thermal quenching of the photoluminescence intensity is critically examined.
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