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

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