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

semiconductors due to the square root dependence. Furthermore, because theelectron is typically more strongly confined than the hole, the mixing shouldbe more important for the electrons. Therefore, this analysis concludes thateven in wide-gap semiconductors, an eight-band Pidgeon–Brown model maybe necessary to accurately predict the size-dependent structure.B. The Problem Swept Under the RugAlthough the effective mass models can quite successfully reproduce manyaspects of the electronic structure, the reader may be troubled by a problemthat was ‘‘swept under the rug’’ in Section III.c. In our discussion of the sizedependentdata shown in Fig. 7, it was mentioned that the data were plottedrelative to the energy of the first excited state, in part to avoid a difficulty withthe theory. This difficulty is shown more clearly in Fig. 20, where the energy ofthe first excited state (1S 3/2 1S e ) is plotted versus 1/a 2 . Surprisingly, the sametheory that can quantitatively fit the data in Figs. 10 and 11 fails to predict thesize dependence of the lowest transition (Fig. 20). Because the same problemarises in InAs nanocrystals, where a more sophisticated eight-band effectivemass model was used, it is unlikely that this is caused by the inadequacies ofFigure 20 Energy of the first excited state (1S 3/2 1S e ) in CdSe nanocrystals versus1/radius 2 . The curve obtained from the same theory as in Figs. 10 and 11 (solid line)is compared with PLE data (crosses). (Adapted from Ref. 9.)Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.