Following the experimental observation that in semiconductor nanocrystals a single high-energy photon can generate multiple electron-hole pairs, several mechanisms have been proposed to explain such process of carrier multiplication (CM). Among them, impact ionization is currently considered as the most prominent mechanism in bulk semiconductors as well as in quantum dots (QDs). However, impact ionization is a multistep process which produces a delayed appearance of multiple excitons, and it cannot explain the instantaneous CM observed in PbSe QDs. In this work we present numerical simulations of the instantaneous mechanism of direct biexciton photogeneration via virtual exciton and biexciton states in PbSe QDs, which takes place only during the pump pulse excitation. The theoretical model is based on a four-band envelope-function calculation of electron and hole states in spherical PbSe QDs and treats Coulomb interaction in the framework of perturbation theory up to the first order. CM efficiency has been numerically evaluated for three different QD samples of various sizes and band structures, considering photon energies up to four times the QD energy gap. The results suggest that the mechanism of direct photogeneration can be only partially responsible for the total experimentally observed CM, which is the sum of instantaneous and delayed contributions. We show that the efficiency of such process strongly depends on the incident photon frequency, being particularly large in spectral regions of weak excitonic absorption. Our simulations also indicate that the virtual exciton channel is much more effective than the virtual biexciton channel and that the presence of a mirror symmetry between valence and conduction bands has only minor impact on the CM efficiency. Even if the contributions of instantaneous and impact generation still have not been experimentally separated, our numerical results are compared with available experimental data, and a detailed discussion of their dependence on the model parameters is presented.

• Received 2 November 2009

DOI:https://doi.org/10.1103/PhysRevB.81.205302