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

independently, Eq. (13) is commonly rewritten in terms of the single-particlestates:P ¼ hCe !e pˆCh i 2ð14ÞBecause the envelope functions are slowly varying in terms of ! r, the operatorpˆ acts only on the unit cell portion (u nk ) of the wave function. Equation (14)is simplified toP ¼ huc !e pˆue i 2 h fe j f h i 2ð15ÞIn the particle-in-a-sphere model, this yieldsP ¼ huc !e pˆuv i 2 y ne ;n hy Le ;L hð16Þdue to the orthonormality of the envelope functions. Therefore, simpleselection rules (Dn = 0 and DL = 0) are obtained.D. A More Realistic Band StructureIn the above model, the bulk conduction and valence bands are approximatedby simple parabolic bands (Fig. 1). However, the real band structureof II–VI and III–V semiconductors is typically more complicated.For example, whereas the conduction band in CdSe is fairly well describedwithin the effective mass approximation, the valence band is not. The valenceband arises from Se 4p atomic orbitals and is sixfold degenerate atk = 0, including spin. (In contrast, the conduction band arises from Cd 5sorbitals and is only twofold degenerate at k = 0.) This sixfold degeneracyleads to a valence-band substructure that modifies the results of the particle-in-a-spheremodel [26].To incorporate this structure in the most straightforward way, CdSe isoften approximated as having an ideal diamondlike band structure, asillustrated in Fig. 3a. Although the bands are still assumed to be parabolic,due to strong spin-orbit coupling (D = 0.42 eV in CdSe [27]) the valence banddegeneracy at k = 0 is split into p 3/2 and p 1/2 subbands, where the subscriptrefers to the angular momentum J = l+s (l = 1,s = 1/2), with l the orbitaland s the spin contribution to the angular momentum. Away from k = 0, thep 3/2 band is further split into J m = F3/2 and J m = F1/2 subbands, where J mis the projection of J. These three subbands are referred to as the heavy-hole(hh), light-hole (lh), and split-off-hole (so) subbands, as shown in Fig. 3a.Alternatively, they are sometimes referred to as the A, B, and C subbands,respectively.Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.