Analysis of Recombination of Excitons Bound to Deep Neutral Donors and Acceptors

On the basis of the plausibility arguments and experimental results of previous workers on shallow-donor and -acceptor levels, the recombination of bound excitons at deep-neutral-donor and -acceptor sites via an Auger process appears to be a likely candidate for a non-radiative or "killer" mechanism in luminescent material. We analytically investigate the effects of this center in a $p$-type semiconductor (the results can be extended in a straightforward manner to $n$-type material) with the goal of uncovering experimentally verifiable properties. The analysis specializes in several specific examples. The first case is that in which the competing nonradiative-recombination mechanism is a shallow exciton bound to an acceptor. For this case the strength of the nonradiative recombination goes through a maximum as a function of temperature, and this effect would be experimentally observed as a minimum in the radiative efficiency of the semiconductor. Such an effect is reported in GaP(Zn, O) in an accompanying paper. Furthermore, on the basis of numerical calculations presented in this paper we consider it unlikely that the silicon acceptor, which has been suggested as a possible nonradiative center in GaP, is a strong recombination site. The second example considered is that of an exciton bound to a neutral donor. Since this situation involves capture of two minority carriers by the donor, the concentrations of the captured electrons are expected to depend nonlinearly on excitation intensity. These effects are easily observed if electrons in either state give rise to a detectable radiative band. In the accompanying paper the intensity variation of the oxygen-donor infrared band in GaP(Zn, O) with excitation level is interpreted in terms of the above model. An approximate time-dependent solution is obtained for the deep-level population which yields an initial fast decay at high-excitation levels. This fast component, which is due to two-electron-recombination processes, has also been observed in the GaP oxygen-donor infrared band.