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

formation of a long-lived dark exciton. Particularly strong confirmation ofour model is found in the magnetic field dependence of the dark-exciton decaytime [2], magnetic circular dichroism of CdSe NCs, and the polarization of theCdSe NC PL in a strong magnetic field.The chapter is organized as follows. In Section II, we calculate theenergy structure of the band-edge exciton and obtain selection rules andtransition oscillator strengths. In Section III, the effect of an externalmagnetic field on the fine-level structure and transition oscillator strengthsis discussed. The polarization properties of the NC PL, Stokes shift of theresonant PL, field-induced shortening of the dark-exciton lifetime, magneticcircular dichroism, and PL polarization in strong magnetic fields are consideredwithin the developed theoretical model in Section IV. The results aresummarized and discussed in Section V.II.FINE STRUCTURE OF THE BAND-EDGE EXCITONIN CdSe NANOCRYSTALSA. Band-Edge Quantum-Size LevelsIn semiconductor crystals that are smaller than the bulk exciton Bohr radius,the energy spectrum and the wave functions of electron–hole pairs can beapproximated using the independent quantization of the electron and holemotions (the so-called strong confinement regime [4]). The electron and holequantum confinement energies and their wave functions are found in theframework of the multiband effective mass approximation [5]. The formalprocedure for deriving this method demands that the external potential besufficiently smooth. In the case of nanosize semiconductor crystals, thisrequirement leads to the condition 2a >> a 0 , where a is the crystals radiusand a 0 is the lattice constant. In addition, the effective mass approximationholds only if the typical energies of electrons and holes are close to the bottomof the conduction band and to the top of the valence band, respectively. Inpractice, this means that the quantization energy must be much smaller thanthe energy distance to the next higher (lower)-energy extremum in the conduction(valence) band.In the framework of the effective mass approximation, for sphericallysymmetric NCs having a cubic lattice structure, the first electron quantumsizelevel, 1S e , is doubly degenerate with respect to the spin projection. Thefirst hole quantum-size level, 1S 3/2 , is fourfold degenerate with respect to theprojection (M) of the total angular momentum, K, (M = 3/2, 1/2, 1/2, and3/2) [6,7]. The energies and wave functions of these quantum-size levels canCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.