Ionization balance in semiconductor quantum-dot lasers

Abstract

The commonly assumed quasiequilibrium particle distribution with the same quasi-Fermi-level for all quantum-dot carriers in the same energy (conduction or valence) band is found not to be valid for a wide range of temperatures at the inversion populations and bound energy separations (greater than a LO phonon energy) used in the literature. Bound state occupation factors obtained from the steady state solution of rate equations describing the ionization balance in room-temperature 100-\AA{}-radius GaAs quantum dots whose centers are separated by 400 \AA{} are found to be very different from the quasiequilibrium distribution used in an example from the literature. In such quantum dots, bound state transitions result from collisions between charged particles via the Coulomb interaction, and from interband and intraband radiative processes. The critical free electron concentration above which collisional processes can establish a quasiequilibrium in the conduction band is found to exceed ${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. Our numerical solution is in good agreement with Pitaevskii's model from atomic physics of an electron random walk in energy as modeled by a Fokker-Planck equation. In our simple model, electrons are captured into a bound conduction band state via three-body recombination and phonon emission, and drop into lower energy bound states via a series of collisional deexcitations before combining with a valence band hole. Solution of the rate equations is standard in numerical studies of stimulated emission in atomic plasmas, but our present discussion is, to our knowledge, the first in the literature on semiconductor quantum-dot lasers.