Auger and radiative transition rates for acceptor bound excitons in direct-gap semiconductors

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Abstract
We present calculations of the Auger and radiative recombination rates for acceptor bound excitons in the HgCdTe alloy system and in GaAs. The transition rates are computed as a function of band gap in the HgCdTe alloy and as a function of the acceptor binding energy. The Auger rate is found to increase and the radiative rate to decrease with increasing acceptor binding energy. The radiative recombination rate is found to increase with increasing band gap. The Auger rate decreases with increasing band gap except when the band gap first exceeds the spin-orbit splitting in the valence band and for band gaps less than about 0.2 eV where the density of final hole states and the electron-hole overlap becomes small. We find that Auger recombination is dominant for hydrogenic acceptors in HgCdTe for materials with a band gap less than about 0.35 eV and radiative recombination is dominant for larger gap materials. For deeper acceptors, this crossover occurs at larger band gaps. For GaAs, we find that radiative recombination dominates for all reasonably shallow acceptors.