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

where n i (i=1, 2 . . . , N ) is the concentration of dots in the sample that containi e–h pairs and s i is the lifetime of the i-pair NQD state. If one neglectsrecombination during the pump pulse, these equations have a straightforwardsolution for time-dependent NQD average populations: hN ðtÞi ¼ P Ni¼1 A sie ti ,where A i are the coefficients determined by initial carrier densities. In thecase for which absorption saturation at the pump wavelength is small, theinitial conditions for Eq. (9) can be calculated using the Poisson distribution:hNi m 0n m ðt ¼ 0Þ ¼ n NQD e hN i 0 ; m ¼ 1; 2; . . . ; N ð10Þm!where n NQD is the concentration of NQDs in a sample.Quantized steps during Auger decay in strongly confined CdSe NQDswere experimently resolved in Ref. 16 using a femtosecond TA experiment. Inthis work, dynamics of NQD populations, hN(t)i, were derived from timeresolved1S bleaching signals. Figure 20a displays these dynamics measuredfor a 1.7-nm sample at carrier injection levels, hNi 0 , from 0.2 to 3.2. In Ref. 16,a simple subtractive procedure was used to extract single exponential dynamicsthat are characteristic of the decay of different multiple-pair NQD statesfrom the measured hN(t)i time transients. This procedure is based on the factthat at long times after photoexcitation, the decay is governed by singlyexcitedNQDs independent of the initial carrier density. This observationallows one to normalize time transients taken at different pump levels tomatch their long-time-delay ‘‘tails,’’ as shown in Fig. 20a. By subtracting thelow-pump-intensity trace (hNi 0 1, it was possible to derive the dynamics, DN(t), due torelaxation of multiple-pair states with N z 2. For initial carrier densities 1