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

Coulomb interaction that is absent in the tunneling data [6]. Agreement isgood for the larger nanocrystal radii, with increasing deviation for smallernanocrystals. The deviation occurs because the TEM sizing curve provides alower limit to the nanocrystal radius due to its insensitivity to the (possiblyamorphous) surface layer. On the other hand, the size extracted from theSTM topographic images is overestimated because of the tip–nanocrystalconvolution effect [74]. These differences should be more pronounced in thesmall size regime, as is indeed observed.Next, in Fig. 11b, we compare the size dependence of the higher stronglyallowed optical transitions, with the level spacings measured by tunnelingspectroscopy. We plot excited level spacings versus the observed bandgap forboth PLE and tunneling spectra, thus eliminating the problem of QD sizeestimation discussed earlier. The two lower datasets (II) in Fig. 11b comparethe difference between the first strong excited optical transition and the bandgapfrom PLE (E 3 E 1 in Figs. 5 and 7), with the separation D VB = 2 VB 1 VBin the tunneling data (open and full squares, respectively). The excellentcorrelation observed enables us to assign this first excited transition in thePLE to a 2 VB 1S e excitation, as shown schematically in the inset of Fig. 11a.Strong optical transitions are allowed only between electron and hole stateswith the same envelope function symmetry. Employing this optical selectionrule, we thus infer that the envelope function for state 2 VB should have scharacter and this state can be directly identified as the 2S 3/2 valence-bandlevel.Another important comparison is depicted by the higher pair of curvesin Fig. 11b (set III). The second strong excited optical transition relative to thebandgap (E 5 E 1 in Fig. 7) is plotted along with the spacing D CB = 1P e 1S efrom the tunneling spectra. Again, excellent correlation is observed, whichallows us to assign this peak in the PLE to the 1 VB 1P e transition (Fig. 11a,inset). The topmost VB level, 1 VB , should thus have some p character for thistransition to be allowed. From this and considering that the bandgap opticaltransition 1 VB 1S e is also allowed, we conclude that 1 VB has mixed s and pcharacter. Pseudopotential calculations of the level structure in InAs QDsshow mixed s and p characteritics for the topmost VB state, whereas theeffective-mass-based calculations predict that the 1S 3/2 and the 1P 3/2 states arenearly degenerate.D. Theoretical DescriptionsThe theoretical treatments for both optical and tunneling experiments onQDs first require the calculation of the level structure. Various approacheshave been developed to treat this problem, including effective-mass-basedmodels, with various degrees of band-mixing effects [47,49,76], and a moreCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.