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

the volume fraction (filling factor) of semiconductor material in the sample(s=4pn NQD R 3 /3):s ASE ¼ 4pR33nnr g cð11ÞIn the case for which the gain decay is dominated by the intrinsic two-pairAuger recombination (decay time s 2 ), ASE can only be observed if s ASE < s 2 .The Auger data discussed in the previous subsection indicate that s 2 scaleswith dot size as R 3 (s 2 cbR 3 , where bc5 ps/nm 3 ) which allows one to derivethe following critial condition for the development of ASE:n >4pnð12Þ3cbr gFrom this condition one can see that one approach to overcoming fast Augerrecombination is by using samples with high NQD densities. For r 0 = 10 –17cm 2 (a lower estimate for the gain cross section; Ref. 59) and n = 2 (an upperestimate for the refractive index), Eq. (12) indicates that minimal fillingfactors required for achieving the ASE regime are of the order of 0.005(0.5%). The densities in excess of the critical value can be achieved in matrixfree,close-packed films [59], glass [3], and sol-gel titania [11] matrices, andconcentrated solutions [60].The highest dot densities are provided by close-packed NQD films(NQD solids). For example, films made of 1.3-nm CdSe NQDs capped withTOPO have filling factors as high as f20% (1.1-nm length of a cappingmolecule is assumed) for which the condition given by Eq. (12) is easilysatisfied. Solid-state films of close-packed CdSe NQDs were used in Ref. 59to demonstrate ASE with a color that is controlled by NQD sizes. These filmswere fabricated by drop casting from hexane/octane solutions using eitherTOPO-capped or ZnS-overcoated dots. Transmission electron microscopy(TEM) indicated random close-packing of dots in the samples (Fig. 23a). Thefilms’ emission color was tunable over an entire visible range by changing thedot size (Fig. 23a).The effect of light amplification that leads to the development of a sharpASE band above a certain pump threshold is illustrated in Fig. 23b. Thisfigure shows pump-dependent emission spectra recorded for a CdSe NQDfilm fabricated from TOPO-capped CdSe NQDs with R = 2.1 nm. Thespectra were taken using a frequency-doubled output of an amplified Tisapphirelaser as a pump (the photon energy was 3.1 eV, the pulse durationwas 100 fs); the ASE was detected at the edge of the film, which acted as anoptical waveguide. At pump levels of f1.5 e–h per dot, a sharp ASE peakdevelops on the low-energy side of the spontaneous emission band. The pumpCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.