Energy transfer between semiconductor nanocrystals: Validity of Forster's theory

We theoretically study the energy transfer between semiconductor nanocrystals and we calculate the rate of this process in the case of direct-gap (InAs) and indirect-gap (Si) semiconductors. The calculations are based on the tight-binding method that enables us to determine the transfer rate, including electronic structure effects, dielectric screening, and multipolar Coulomb interactions using a microscopic approach. In the case of direct-gap semiconductor nanocrystals, we show that the energy transfer arises only from dipole-dipole interactions in agreement with experimental observations. We obtain that the transfer rate is well described by Forster's theory, and we provide an analytical expression in which the Forster rate is determined not only by the spectral overlap between the emission and absorption spectra of the nanocrystals but also by a factor that simulates the dielectric effects on the Coulomb interactions. In the case of Si nanocrystals, the situation is different because dipolar transitions are weak due to the indirect gap of Si. For this reason, we show that multipolar terms dominate when the distance between the nanocrystals is small and surface effects play an important role in the screening. We predict that the energy transfer between Si nanocrystals by a no-phonon process is possible only when the dots are almost in close contact.