Universality of the Förster’s model for resonant exciton transfer in ensembles of nanocrystals

For nanocrystals in a strong quantum confinement regime, it has been confirmed analytically that resonant exciton transfer proceeds in full accordance with the Förster mechanism. This means that the virtual exciton transitions between the nanocrystals of close sizes are governed only by the dipole–dipole interaction of nanocrystals even in very dense ensembles, while the contributions of all other higher-order multipoles are negligibly small. Based on a simple isotropic model of the envelope function approximation and neglecting the electron–hole interaction inside each nanocrystal, we have computed the rate of the resonant exciton transfer between two nanocrystals. Using the obtained result, we have estimated, for some arbitrarily chosen nanocrystal, the total rate of the exciton non-radiative annihilation caused by the possibility of its resonant virtual transitions into all other nanocrystals of the ensemble. The total rate dependence on the nanocrystal size is determined only by the size distribution function of nanocrystals in the ensemble.