Carrier statistics in quantum-dot lasers

Abstract

The description of quantum dot ensembles using solely average carrier populations is insucient. Bookkeeping of the probability of all micro-states and soluiton of the master equations for the transitions between them allows proper modeling of the phonon bottleneck and laser properties. We predict that single exciton shows gain and calculate the dependence of threshold current density of the type of capture process. The gain-current relation in quantum dot lasers is linear. 1. Quantum dots represent a unique electronic system which was recently successfully implemented for novel semiconductor lasers [1n4]. The charge carriers populate discrete electronic levels and (at least at suciently low temperature) all dots in an ensemble are laterally decoupled from each other. Therefore an event in a quantum dot, e. g. a recombination process, does not depend on the average carrier density (involving all other dots) but only on the particular population of the present dot with electrons and holes [5]. The ensemble has to be averaged over the probability distribution of the dierent micro-states. Dierent probability distributions of micro-states can have the same average carrier population but show dierent properties like recombination current. In order to illustrate this point with a simple example, we compare two QD ensembles with the same average carrier population: in ensemble I all electrons are in dierent dots than the holes: no radiative recombination takes place. In ensemble II electrons and holes populate the dots by pairs, leading to radiative recombination. We further discuss modeling of the phonon bottleneck eect. 2. Since the epitaxially created self-ordered QDs [6,7] are in the strong confi nement regime, it is adequate to model electronic levels in the single particle picture, i. e. electrons and holes populate single particle levels. Ground state luminescence is said to originate from the radiative recombination of an electron and a hole in their respective single particle ground states (exciton). The lifetime of the exciton shall be denoted be X. The Coulomb correlation shall not fundamentally alter that picture. One eect is the shift of recombination energy of the biexciton (two electrons and two holes in their spin-degenerate ground states) with respect to that of the exction. For InAs/GaAs quantum dots this shift is expected to be small (< 2m eV )[ 8 ] ;f or IInVI compounds this shift will be larger. The radiative lifetime XX of the biexciton in the strong confi nement limit is XX = X= 2 (as if two independent exciton decay);