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

e easily found in the parabolic approximation. The electrons energy levelsand wave functions respectively are:E 1S ¼ t2 p 22m e a 2rffiffiffi2w a ðrÞ ¼ nðrÞ j Sai ¼asinðpr=aÞrY 00 ðVÞ j Saiwhere m e is the electron effective mass, a is the NC radius, Y lm (V) are sphericalharmonic functions, jSai are the Bloch functions of the conduction band, anda = z (#) is the projection of the electron spin, s z = + ( ) 1/2. The energiesand wave functions of holes in the fourfold degenerate valence band can bewritten respectively asE 3=2 ðbÞ ¼ t2 u 2 ðbÞ2m hh a 2w M ðrÞ ¼ 2 XXR l ðrÞð 1Þ M 3=2l ¼ 0;2mþl ¼ M3=2 l 3=2Yl m M lm ðVÞu lwhere b = m lh /m hh is the ratio of the light- to heavy-hole effective masses, u(b)is the first root of the equation [8–12]pffiffiffi pffiffiffij 0 ðuÞj 2 b u þ j 2 ðuÞj 0 b u ¼ 0ð4Þwhere j n (x) are spherical Bessel functions, ð i k l m n pÞ are Wigner 3j-symbols,and u l (l = F1/2, F3/2) are the Bloch functions of the fourfold degeneratevalence band G 8 [13]:u 3=2 ¼ p 1 ffiffi2ðX þ iYÞz; u 3=2 ¼ p i ffiffi2ðX iYÞ #ð1Þð2Þð3Þu 1=2 ¼ p i ffiffi6½ðX þ iYÞ # 2ZzŠð5Þu 1=2 ¼ p 1 ffiffi6½ðX iYÞz þ 2Z #ŠThe radial functions R l (r) are [8,10–12]R 2 ðrÞ ¼A ja 3=2 2 ður=aÞ þ j 0ðuÞpj 0 ðuffiffiffipj 2 u ffiffiffi b r=ab ÞR 0 ðrÞ ¼Aa 3=2j 0 ður=aÞj 0 ðuÞpj 0 uffiffiffip j 0 u ffiffiffi !b r=abð6ÞCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.