  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.
