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

passive, as was shown in Ref. 12. The separation between the ground stateand the lower optically active F = F1 state initially increases with decreasingsize as 1/a 3 but tends to 3D/4 for very small sizes. In oblate crystals (Fig. 2b),the order of the exciton levels is the same as in spherical ones. However,the splitting does not saturate, because in these crystals, D increases withdecreasing NC size.In prolate NCs, D becomes negative with decreasing size and thischanges the order of the exciton levels at some value of the radius (Fig. 2c);in small NCs, the optically passive (as we show below) F = 0 state becomesthe ground exciton state. The crossing occurs when D goes through 0. In NCsof this size, the shape asymmetry exactly compensates the asymmetry due tothe hexagonal lattice structure [16]. The electronic structure of exciton levelshave ‘‘spherical’’ symmetry although the NCs do not have spherical shape. Asa result there is one fivefold degenerate exciton with total angular momentum2 (which is reflected in the crossing of the 0 L , F1 L , and F2 levels) and onethreefold degenerate exciton state with total angular momentum 1 (reflectedin the crossing of the 0 U and F1 U levels).In Fig. 2d, the band-edge exciton fine structure is shown for the case forwhich the ellipticity varies with size.* This size-dependent ellipticity was experimentallyobserved in CdSe NCs using small-angle x-ray scattering(SAXS) and transmission electron microscopy (TEM) studies [19]. The levelstructure calculated for this case closely resembles that obtained for sphericalcrytals.The size dependence of the band-edge exciton splitting in CdTe NCswith cubic lattice structure calculated for particles of different shapes is shownin Fig. 3. The calculation was done using the parameters b = 0.086 andtx ST = 0.04 meV. One can see that in the spherical NCs, the electron–holeexchangeinteraction splits the eightfold degenerate band-edge exciton into afivefold degenerate exciton with total angular momentum 2 and a threefolddegenerate exciton with total angular momentum 1 (Fig. 3a). The NC shapeasymmetry lifts the degeneracy of these states and completely determines therelative order of the exciton states (see Figs. 3b and 3c for comparison).C. Selection Rules and Transition Oscillator StrengthsTo describe the fine structure of the absorption and PL spectra, we calculatetransition oscillator strengths for the lowest five exciton states. The mixing* In accordance with SAXS and TEM measurements, the ellipticity was approximatedby the polynomial l(a) = 0.101 0.034a + 3.507 10 3 a 2 1.177 10 4 a 3 + 1.863 10 6 a 4 1.418 10 8 a 5 + 4.196 10 11 a 6 .Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.