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Numerical analysis of carrier multiplication mechanisms in nanocrystal and bulk forms of PbSe and PbS

We report on systematic numerical study of carrier multiplication (CM) processes in spherically symmetric nanocrystal (NC) and bulk forms of PbSe and PbS representing the test bed for understanding basic aspects of CM dynamics. The adopted numerical method integrates our previously developed Interband Exciton Scattering Model (IESM) and the effective mass based electronic structure model for the lead chalocogenide semiconductors. The analysis of the IESM predicted CM pathways shows complete lack of the pathway interference during the biexciton photogeneration. This allows us to interpret the biexciton photogeneration as a single impact ionization (II) event and to explain major contribution of the multiple II events during the phonon-induced population relaxation into the total quantum efficiency (QE). We investigate the role of quantum confinement on QE, and find that the reduction in the biexciton density of states (DOS) overruns weak enhancement of the Coulomb interactions leading to lower QE values in NCs as compared to the bulk on the absolute photon energy scale. However, represented on the photon energy scale normalized by corresponding band gap energies the trend in QE is opposite demonstrating the advantage of NCs for photovoltaic applications. Comparison to experiment allows us to interpret the observed features and to validate the applicability range of our model. Modeling of QE as a function of pulse duration shows weak dependence for the gaussian pulses. Finally, comparison of the key quantities determining QE in PbSe and PbS demonstrates the enhancement of II rate in the latter materials. However, the fast phonon-induced carrier relaxation processes in PbS can lead to the experimentally observed reduction in QE in NCs as compared to PbSe NCs.