Size dependence of the multiple exciton generation rate in CdSe quantum dots

The multiplication rates of hot carriers in CdSe quantum dots are quantified using an atomistic pseudopotential approach and first-order perturbation theory. We consider both the case of an individual carrier (electron or hole) decaying into a trion and the case of an electron-hole pair decaying into a biexciton. The dependence on quantum dot volume of multiplication rate, density of final states, and effective Coulomb interaction are determined. We show that the multiplication rate of a photogenerated electron-hole pair decreases with dot size for a given absolute photon energy. However, if the photon energy is rescaled by the volume-dependent optical gap, then smaller dots exhibit an enhancement in carrier multiplication rate for a given relative photon energy. We find that holes have much higher multiplication rates than electrons of the same excess energy due to the larger density of final states (positive trions). When electron-hole pairs are generated by photon absorption, however, the net carrier multiplication rate is dominated by electrons because they have much higher excess energy on average. We also find, contrary to earlier studies, that the effective Coulomb coupling governing carrier multiplication is energy-dependent.