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

Within the state-filling model corrected for multiparticle interactions,the thresholdlike behavior in the development of optical gain is a directconsequence of a nonzero biexciton shift which ‘‘generates’’ a new ‘‘emitting’’transition at a spectral energy that is spectrally offset with respect to the singleexciton‘‘emitting’’ transition. Another important consequence of biexcitoninteractions is their effect on the magnitude of the optical gain. In the statefillingmodel, the maximum of the optical gain, corresponding to a completepopulation inversion, is limited by the magnitude of the ground-state absorption[ g max (tx) = a 0 (tx)]. In the case of multiparicle interactions, the gainamplitude can, in principle, exceed this level, which is due to a red shift ofmultiparticle transitions into the region of the reduced ground-state absorption.Gain with a magnitude that is greater than the ground-state absorptionis observed for both NQD solutions (Fig. 12b) and solid-state samples (Fig.17), providing an addition piece of evidence that Coulomb interactions playam important role in optical-gain properties of NQDs.B. Multiparticle Auger Recombination and Optical GainDynamicsAn important mechanism for nonradativie carrier losses in NQDs is multiparticleAuger recombination. The Auger recombination is a process in whichthe e–h recombination energy is not emitted as a photon but is transferredto a third particle (an electron or a hole) that is reexcited to a higher energystate within the dot or outside it (the latter effect is known as Auger ionization).The Auger recombination has a relatively low efficiency in bulksemiconductors, for which significant thermal energies are required toactivate the effect [55,56]. However, Auger decay is greatly enhanced inquantum-confined systems, in which the relaxation in momentum conservationremoves the activation barrier [57,58].In well-passivated dots, Auger recombination dominates the multiparticledecay dynamics. Furthermore, because the Auger recombination has thesame activation threshold as optical gain (hNi>1), it is unavoidable in theregime of optical amplification. The effect of Auger recombination on gaindynamics is clearly seen in Fig. 19, which shows TA time transients recordedin the region on the gain band for dots of 2.5-nm radius before (open circles)and after (solid squares and open diamonds) the gain threshold. Before thethreshold (hNi 0 = 0.5), the bleaching signal shows a slow decay that is incontrast to the fast signal relaxation observed above the threshold (hNi 0 =2.3 and 8) (i.e., at pump powers for which muliparticle Auger decay becomesactive).In bulk semiconductors, Auger decay is characterized by a cubic carrierdecay rate C A n 3 eh , where C A is the Auger constant and n eh is the carrier density.In this case, one can also introduce an instant time constant, s A = (C A n 2 eh ) 1 ,Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.