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

Transient absorption data obtained for NQDs of different sizes (Fig.21a) indicate that the s 2 time constant rapidly decreases with decreasing NQDsize following a cubic size dependence (s 2 ~ R 3 ) (see data shown by solidcircles in Fig. 21b). The two-pair lifetime shortens from 363 ps to only 6 ps asthe dot radius is decreased from 4.1 to 1.2 nm. Interestingly, the timeconstants measured for the three- and four-pair decay (open squares andsolid triangles in Fig. 21b, respectively) follow the same cubic size dependenceas that of the two-pair state such that the time-constant ratios predicted by thebulk-semiconductor model hold for all NQD sizes. Simple bulk-materialreasoning would suggest that the enhancement in the Auger decay in smallerparticles is caused by an effective increase in carrier concentrations resultingfrom the increased spatial confinement. This reasoning would predict the R 6scaling for Auger times [s N ~ (N/V 0 ) 2 ~ R 6 ]. However, the experimentallymeasured size dependence is R 3 , indicating that in 3D-confined systems, theAuger ‘‘constant’’ depends on the particle size. For CdSe NQDs, C A scalesapproximately as R 3 and decreases from f710 –29 to f210 –30 cm 6 /s as thedot radius is reduced from 4.1 to 1.2 nm (Fig. 22). For all NQD sizes, the C Avalues calculated by using lifetimes of two-, three-, and four-e–h pair statesare close to each other (compare data shown by circles, squares, and trianglesin Fig. 22), indicating that the cubic density dependence of the Auger ratesholds for all sizes between 1 and 4 nm.Because of their strong size dependence, Auger effects, which play aminor role in relatively large epitaxial dots, become significant in stronglyconfined colloidal nanoparticles. For moderately well-passivated dots, nonradiativeAuger relaxation of doubly-excited dots (NQD biexcitons) is moreefficient than the surface trapping that imposes an intrinsic limit on thelifetime of the optical gain in strongly confined NQDs. The dominance ofthe Auger effect in NQDs also implies that even relatively poorly passivatedsamples could behave as well as the best samples with respect to gain andstimulated emission because as long as trapping rates are lower than Augerrates, the two-e–h-pair lifetime is determined by the intrinsic Auger decay.Very short optical-gain lifetimes imply that the regimes of light amplificationand lasing in NQDs are easiest to achieve using a pulsed excitationwith a pulse duration (s p ) that is shorter than the Auger decay time ofbiexcitons (s 2 ). When s p