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

Figure 9 Summary of quantum numbers and important interactions in semiconductornanocrystals. The total electron–hole pair angular momentum (N ) hascontributions due to both the electron ( F e ) and hole (F h ). Each carrier’s angularmomentum (F ) may then be further broken down into a unit-cell component (J ) dueto the atomic basis (‘) and spin (s) of the particle and an envelope functioncomponent (L) due to the particle-in-a-sphere orbital.Although theory clearly predicts the observed avoided crossings, Fig. 11also demonstrates that theory underestimates the repulsion in both avoidedcrossing regions, causing theoretical deviation in the predictions of the1S 1/2 1S e and 2S 1/2 1S e transitions. This discrepancy could be due to the Coulombmixing of the electron–hole pair states, which is ignored by the model(via the strong confinement approximation). If included, this term wouldfurther couple the nS 1/2 1S e transitions such that these states interact morestrongly. In addition, the Coulomb term would cause the 1S 1/2 1S e and2S 1/2 1S e states to avoid one another through their individual repulsion fromthe strongly allowed 1P 3/2 1P e .Despite these discrepancies, however, this theoretical approach isclearly on the right track. Therefore, this model can be used to understandthe physics behind the avoided crossings. As discussed earlier, in the zerothorderpicture of Fig. 8, each valence subband contributes a ladder of holestates. Due to spin-orbit splitting (see Fig. 3) the C-band ladder is offsetCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.