Intraband Auger processes and simple models of the ionization balance in semiconductor quantum-dot lasers

The importance of intraband Auger processes in determining the ionization balance in quantum dots is reported. The numerically inexpensive binary-encounter model for a Coulomb collision between identical particles is found to be a good estimator of the intraband Auger rates out of a quantum dot. Intraband and the conventional interband Auger processes differ in that the former involve only intraband transitions whereas the latter always involve a radiationless interband transition. As such, intraband Auger rates do not involve the evaluation of the very small overlap integral of a conduction band with a valence band Bloch wave function and are thus much larger than interband Auger rates, especially for large-band-gap semiconductors like GaAs. Though intraband Auger processes are not strong enough to establish a quasiequilibrium within the entire conduction band at the room-temperature free-carrier concentrations (${10}^{16}$ ${\mathrm{cm}}^{\mathrm{-}3}$) and bound energy separations (greater than an LO phonon energy) commonly assumed in the quantum-dot literature, they are capable of placing almost as many bound carriers in states near the band edge as would be predicted erroneously by a quasiequilibrium Fermi-Dirac distribution.