Theory of lifetime of exciton incoherently created below its resonance frequency by inelastic scattering

TL;DR

This paper proposes a model for the lifetime of excitons created below their resonance frequency via inelastic scattering, emphasizing the role of coherence volume in the transient exciton state before polariton formation.

Contribution

It introduces a new expression for the P-emission lifetime based on the coherence volume of excitons, providing a different perspective from the immediate polariton creation assumption.

Findings

The exciton remains as a transient state far below resonance energy.

The P-emission lifetime depends on the coherence volume of excitons.

Time-resolved measurements can test the proposed model.

Abstract

When an exciton in semiconductor is scattered and its energy is decreased far below the resonance energy of the bare exciton state, it has been considered that an exciton-polariton is created immediately by the scattering process, because there is no exciton level at that energy. However, according to the recent time-resolved measurements of P emission originating from inelastic exciton-exciton scattering, it looks rather natural to consider that the exciton-polariton is created in a finite time scale which is restricted by a coherence volume of the exciton after the scattering. In this interpretation, the exciton remains in this time scale far below its resonance energy as a transient state in a series of processes. We propose an expression of the P-emission lifetime depending on the coherence volume of the scattered excitons through the conversion process from them to the polaritons. The coherence volume of the scattered excitons appears in the calculation of the inelastic scattering process on the assumption of a finite coherence volume of the bottleneck excitons.Time-resolved optical-gain measurements could be a way for investigating the validity of our interpretation.