Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

hole state. Although state filling explains the saturation of the 1S transition(dashed-dotted line), it fails to describe the pump dependence of the TAsignals within the gain band (dashed line). Experimental data clearly indicatea threshold in the development of Da, which is not predicated by state-fillingreasoning.The thresholdlike behavior of the TA signal within the gain band canbe explained in terms of Coulomb multipartilce interactions [50] that leadto a shift of the emission band of multiexcitons (specifically, biexcitons)with respect to that of a single exciton [51,52]. The radiative decay of abiexction produces both a photon and an exciton. The energy of the photonresulting from this decay is determined by the expression tx bx ¼ 2E i x dE 2E f x , where Ei x is the energy of the excitons comprising the biexcion, dE 2 is theexciton–exciton interaction energy (if two excitons attract to each other, thisenergy can be treated as a biexciton binding energy), and E f xis the energy ofthe exciton that is left as a product of the biexciton recombination. Thebiexciton decay can, in principle, produce several emission lines withpositions that are determined by the energy of the exciton in the final state,E f x (Fig. 18). In the case of the biexciton formed by two ground-state excitons(E 0 x ), the shift of the biexciton emission line with respect to the single-excitonline ( tx x ) is given by the expression dE bx = dE 2 +(E f x Ex 0 ). This expressionindicates that a significant red shift of the biexciton emission band can arisefrom both confinement-enhanced two-e–h-pair interactions [47,53] and/orthe existence of decay channels that produce an excited-state exciton ratherthan a ground-state exciton [54]. Figure 18 schematically shows two possiblebiexciton decay channels resulting in emission lines at tx bx,0 and tx bx,1 thatcorrespond to two different final exciton states (these states are associatedwith ‘‘emitting’’ and ‘‘absorbing’’ band-edge transitions). The red shift of thetx bx,0 band with respect to the single-exciton emission spectrum is due to theexciton–exciton interaction energy (dE 2 ), whereas the red shift of the tx bx,2band is due to both dE 2 and the energy difference between ground-state andexcited-state exciton.Because biexcitons dominate optical gain (and hence stimulated emission),the ‘‘biexciton’’ red shift is at least one of the reasons for large shiftsbetween the ASE peak and the center of the spontaneous PL observedexperimentally (Fig. 16). However, other factors, such as interference fromthe strong 1S absorption, can also contribute to the ASE red shift observed inexperimental spectra.Multiparticle effects can be phenomenologically incorporated into thestate-filling model by introducing biexciton shifts into both the absorptionline of NQDs occupied with a single e–h pair and the emission line of NQDsthat contain multiple e–h pairs [47]. The latter assumption presumes thatmultiexcitons contribute to gain primarily via a biexciton state that is formedCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.