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We present a theoretical analysis of the band-edge exciton structure in nanometer-size crystallites of direct semiconductors with a cubic lattice structure or a hexagonal lattice structure which can be described within the framework of a quasicubic model. The lowest energy exciton, eightfold degenerate in spherically symmetric dots, is split into five levels by the crystal shape asymmetry, the intrinsic crystal field (in hexagonal lattice structures), and the electron-hole exchange interaction. Transition oscillator strengths and the size dependence of the splittings have been calculated. Two of the five states, including the ground state, are optically passive (dark excitons). The oscillator strengths of the other three levels (bright excitons) depend strongly on crystal size, shape, and energy band parameters. The relative ordering of the energy levels is also heavily influenced by these parameters. The distance between the first optically active state and the optically forbidden ground exciton state increases with decreasing size, leading to an increase of the Stokes shift in the luminescence. Our results are in good agreement with the size dependence of Stokes shifts obtained in fluorescence line narrowing and photoluminescence experiments in CdSe nanocrystals. Mixing of the dark and bright excitons in an external magnetic field allows the direct optical recombination of the dark exciton ground state. The observed shortening of the luminescence decay time in CdSe nanoncrystals in a magnetic field is also in excellent agreement with the theory, giving further support to the validity of our model. 1996 The American Physical Society.
Éfros et al. (Thu,) studied this question.