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

Abstract

We report on a systematic numerical study of carrier multiplication (CM) processes in spherically symmetric nanocrystalline 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 and the effective mass based electronic structure model for the lead chalcogenide semiconductors. The analysis of CM pathways predicted by the interband exciton scattering model shows complete lack of their interference during the biexciton photogeneration. This allows us to interpret this process as a single impact ionization event and to explain a major contribution of the multiple impact ionization events during the phonon-assited population decay 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 nanocrystals 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 nanocrystals for the photovoltaic applications. Comparison to published experimental data 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 impact ionization rate in the latter materials. However, the fast phonon-assisted population decay in PbS nanocrystals can lead to experimentally observed reduction in QE as compared to PbSe nanocrystals.