  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.
