Radiative decay of the bound exciton in direct-gap semiconductors: The correlation effect

We present a theory of the radiative decay of excitons bound to neutral donors and acceptors in direct-gap semiconductors within the spherical-effective-mass approximation. The calculation is carried out using a three-particle wave function which incorporates Pauli exchange and important interparticle correlation effects over the entire range of electron- to hole-mass ratios. Thus donor-and acceptor-bound excitons are treated within the same framework. Radiative lifetimes are studied and are found to be particularly sensitive to the interparticle distance between electron and hole for all mass ratios of physical interest. Calculations are carried out for the radiative decay rates of bound excitons in a number of materials and comparison is made with the measured radiative lifetimes of both donor- and acceptor-bound excitons in GaAs, InP, and CdS.