Influence of electronic structure and multiexciton spectral density on multiple-exciton generation in semiconductor nanocrystals: Tight-binding calculations

Abstract

Several experimental works have reported that a single high-energy photon could generate multiple excitons in semiconductor nanocrystals and several theories have been proposed to explain these results. Using a tight-binding method, we calculate the electronic structure of InAs, Si, and PbSe nanocrystals and we investigate two models of the multiple exciton generation (MEG). We show that the impact ionization process is efficient at high energy, with lifetimes as small as $10\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$. The behavior of the impact ionization rate versus the energy is basically the same in all materials in spite of large differences in their electronic structure. We present simulations of the MEG showing that, in PbSe and Si nanocrystals, the impact ionization alone cannot explain the efficiencies measured at high energy, even in the limit where there is no relaxation of the excited carriers by electron-phonon scattering. In InAs nanocrystals, the impact ionization process could only explain the lowest yields reported in the literature. We calculate the spectral densities of multiexciton states and we evaluate the possibility of direct and instantaneous photogeneration of multiexcitons. We confirm the importance of the multiexciton spectral densities in the MEG problem because of their rapid variation over several orders of magnitude as a function of the energy. However, we show that the high MEG efficiencies in PbSe and Si nanocrystals, up to seven excitons per photon, would imply a very efficient relaxation in multiexciton states, whereas they are characterized by a negligible density.