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

Figure 3 (a) Valence-band structure at k = 0 for diamondlike semiconductors.Due to spin-orbit coupling (D), the valence band is split into two bands ( J = 3/2 andJ = 1/2) at k = 0. Away from k = 0, the J = 3/2 band is further split into the J m =F3/2 heavy-hole (hh or A) and the J m = F1/2 light-hole (lh or B) subbands. TheJ=1/2 band is referred to as the split-off (so or C) band. (b) The valence bandstructure for wurtzite CdSe near k = 0. Due to the crystal field of the hexagonallattice the A and B bands are split by D cf (25 meV) at k = 0.For many semiconductors, the diamondlike band structure is a goodapproximation. In the particular case of CdSe, two additional complicationsarise. First, Fig. 3a ignores the crystal field splitting which occurs in materialswith a wurtzite (or hexagonal) lattice. This lattice, with its unique c axis, has acrystal field which lifts the degeneracy of the A and B bands at k = 0, as shownin Fig. 3b. This A–B splitting is small in bulk CdSe (D cf = 25 meV [27]) and isoften neglected in quantum-dot calculations. However, we discuss below howthis term can cause additional splittings in the nanocrystal optical transitions.The second complication is that, unlike the diamond structure, thehexagonal CdSe lattice does not have inversion symmetry. In detailedcalculations, this lack of inversion symmetry leads to linear terms in k whichfurther split the A and B subbands in Fig. 3b away from k = 0 [28]. Becausethese linear terms are extremely small, they are generally neglected and areignored in the following.E. The k p MethodBecause of the complexity in the band structure, the particle-in-a-spheremodel [Eq. (11)] is insufficient for accurate nanocrystal calculations. Instead,Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.