Calculation of the zero-temperature Auger recombination rate in the quaternary semiconductor alloy GaAlAsSb

Abstract

For a certain composition (close to GaSb), GaAlAsSb has a band gap (0.8 eV) equal to the spin-orbit splitting at the top of the valence band, and Auger recombination involving the spin-split-off band can proceed with zero threshold energy. An analytic expression for the zero-temperature recombination rate due to this process has been derived assuming a large heavy hole mass. The recombination rate is found to depend on the injected carrier density to the power 7/3 in contrast to the cubic dependence for the non-degenerate case. The room-temperature lifetime against this Auger recombination at electron and hole densities of 10²⁴ m^-3 typically found at lasing thresholds is estimated to be 3*10^-10 s, and order of magnitude smaller than the lifetime against spontaneous emission. This shows that efficient lasing is not possible with this alloy.