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

Figure 10 Theoretically predicted pair states (solid lines) assigned to features (a),(b), and (d) in Fig. 7. The experimental data is shown for comparison (circles).(Adapted from Ref. 9.)0.42 eV below the A- and B-band ladders. This leads to possible resonancesbetween hole levels from the A and B bands with C-band levels. Because thelevels are spreading out with decreasing dot size, resonance conditions aresatisfied only in certain special sizes. Figure 12 demonstrates the tworesonances responsible for the observed avoided crossings. For simplicity,we treat the A and B bands together. In Fig. 12a (12b), the 2D (1D) level fromthe A and B bands is resonant with the 1S level from the C band. The sizedependence of these levels is depicted in Fig. 12c. Due to both valence bandmixing and S-D mixing, these resonant conditions lead to the observedavoided crossings. Although this description is based on the simple particlein-a-spheremodel of Fig. 8, the explanation has been shown to be consistentwith a more detailed analysis [9].D. Beyond the Spherical ApproximationThe above success in describing the size dependence of the data wasachieved within the spherical approximation (Sect. II.F). In this case, thebands are assumed to be spherically isotropic [i.e., warping terms in Eq.(21) are ignored]. Furthermore, the CdSe nanocrystals are assumed to havea spherical shape and a cubic crystal lattice (i.e., zinc blende). With theseCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.