Intraband optical transitions in the complex valence band of spherical nanocrystals based on semiconductors with Td and Oh symmetries have been studied. The energy spectrum of the holes is calculated, using k·p perturbation theory. Analytical expressions are obtained for the hole–photon-interaction matrix elements. It is shown that the size dependence of these matrix elements is determined by the states that participate in the transitions. The selection rules obtained here permit transitions between a large number of states with various symmetries that are forbidden in the conduction zone. The radiative lifetime of the states in the valence band are computed as a function of the radius of the nanocrystal, and it is shown that it can vary in a wide range from 10−12 to 10−3 s.
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