Excitons in nanocrystals

The excitation energies can be described in the frame of the effective mass approximation when the crystals an not too small. The lowest energy exciton state is split in several sublevels by the electron-hole exchange interaction and by the Crystal field in wurtzite-type semiconductors. We determine the oscillator strength of the transitions. The optical transition to the lowest energy sublevel is forbidden by spin conservation law. The intensity of the transition to the upper sublevel in cubic nanocrystals is proportional to the number of nanocrystals per unit volume in the strong confinement regime and to the volume fraction occupied by the nanocrystals in the weak confinement regime. We show that, in a cubic or a wurtzite-type nanocrystal, all the sublevels are shifted to higher energy by the polarization of the medium and that the intensity of the transition to the lowest energy optically allowed sublevel in a wurtzite-type nanocrystal is very much decreased by the polarization of the medium. The energy relaxation of excited electron-hole pairs is made possible by the coupling to acoustical and optical phonons. We conclude that no "phonon bottleneck" exists in the relaxation. We show that Auger effect is responsible for "photodarkening" of the samples under illumination. It is the source of the random telegraph signal observed in the luminescence of a single nanocrystal. (C) 1998 Elsevier Science B.V. All rights reserved.