The donor-acceptor radiative and Auger transitions have been investigated theoretically for the simple model of a direct semiconductor with parabolic bands and a random distribution of hydrogenic impurities. Both effects have been estimated as a function of donor-acceptor separation R, and expressions for the rates (when summed over all R) have also been obtained. The results have been evaluated for GaAs at 80 K and for CdS at 1.6 K to facilitate comparison with experiment. The radiative calculations agree with the experimental results both as regards the numerical value in the limit R → 0 and also as regards the R-dependence. For the usual concentrations the radiative transitions are found to dominate in these materials. The Auger effect is likely to be a serious competitor only for electron collisions when n > 1020 cm-3.
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Landsberg et al. (1973) studied this question.
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