  The multiplication rates of hot carriers in CdSe quantum dots are quantified
using an atomistic pseudopotential approach and first order perturbation
theory. Both excited holes and electrons are considered, and electron-hole
Coulomb interactions are accounted for. We find that holes have much higher
multiplication rates than electrons with 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 photogenerated electrons, because they have on average much higher
excess energy. We also find, contrary to earlier studies, that the effective
Coulomb coupling governing carrier multiplication is energy dependent. We show
that smaller dots result in a decrease in the carrier multiplication rate for a
given absolute photon energy. However, if the photon energy is scaled by the
volume dependent optical gap, then smaller dots exhibit an enhancement in
carrier multiplication for a given relative energy.
