Exciton scattering model of carrier multiplication in semiconductor nanocrystals

Abstract

The effect of carrier multiplication (CM) in semiconductor nanocrystals is systematically treated by employing an exciton scattering approach. Using projection operators, we reduce the Coulomb coupled multi-exciton dynamics to scattering dynamics in the space spanning both single- and bi-exciton states. We derive a closed set of equations determining the scattering matrix elements. This allows us to interpret CM dynamics as a series of odd-order interband scattering events. Using the time-dependent density matrix formalism, we provide a rigorous description of the CM dynamics induced by a finite-time pump pulse. Within this approach, both processes of single- and bi-exciton photogeneration and the consequent population relaxation are treated on the same footing. This approach provides a framework for numerical calculations and for comparisons of the quantum efficiencies associated with each process. For applications, the limit of weak interband Coulomb coupling is considered. Finally, we demonstrate that three previously used theoretical models can be recovered as limiting cases of our exciton scattering model.

20 pages, 8 figures, Revised version, Accepted for publication in the Journal of Chemical Physics

References in corpus (3)

• Carrier multiplication yields in PbS and PbSe nanocrystals measured by transient photoluminescence
• Carrier multiplication yields in CdSe and CdTe nanocrystals by transient photoluminescence
• Distribution of carrier multiplication rates in CdSe and InAs nanocrystals

Cited by in corpus (8)

• Numerical Study of Carrier Multiplication Pathways in Nanocrystalline and Bulk Form of PbSe
• Numerical analysis of carrier multiplication mechanisms in nanocrystal and bulk forms of PbSe and PbS
• Multiple Exciton Generation in Nanostructures for Advanced Photovoltaic Cells
• Coulomb matrix elements for the impact ionization process in nanocrystals: the envelope function approach
• Probing Interband Coulomb Interactions in Semiconductor Nanocrystals with 2D Double-Quantum Coherence Spectroscopy
• Ab Initio Modeling of Phonon-Assisted Relaxation of Electrons and Excitons in Semiconductor Nanocrystals for Multiexciton Generation
• Inter-band Coulomb coupling in narrow gap semiconductor nanocrystals: $\mathbf{k}\cdot \mathbf{p}$ theory
• Dynamics of dissipative multiple exciton generation in nanocrystals