Exciton scattering model of carrier multiplication in semiconductor nanocrystals

TL;DR

This paper introduces an exciton scattering model for carrier multiplication in semiconductor nanocrystals, providing a unified quantum-mechanical framework that captures multi-exciton dynamics and compares well with existing models.

Contribution

The paper develops a comprehensive exciton scattering approach that unifies different models and offers a rigorous quantum description of carrier multiplication in nanocrystals.

Findings

Derives a set of equations for scattering matrix elements.

Provides a framework for numerical calculations of quantum efficiencies.

Shows that previous models are limiting cases of the new approach.

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.