Evidence for quantum statistics of the exciton-biexciton system in a GaAs/AlAs type-II superlattice

Abstract

We have investigated the decay processes of the photoluminescence from excitons and biexcitons in a $(\mathrm{GaAs}{)}_{12}/(\mathrm{AlAs}{)}_{12}$ type-II superlattice, where electrons and holes are confined in the X-valley potential of the AlAs layer and in the \ensuremath{\Gamma}-valley potential of the GaAs layer, respectively. The long lifetime of the type-II exciton, e.g., $\ensuremath{\sim}2\ensuremath{\mu}\mathrm{s}$ at a bath temperature of 5 K, enables us to obtain the precise information of the exciton-biexciton density relation estimated from the line-shape analysis of time-resolved photoluminescence spectra. In a relatively low-exciton-density region (a time region later than $\ensuremath{\sim}1\ensuremath{\mu}\mathrm{s}),$ the biexciton density obeys a well-known square law. At an exciton density around $1\ifmmode\times\else\texttimes\fi{}{10}^{10}{\mathrm{cm}}^{\ensuremath{-}2},$ the biexciton density suddenly increases with a thresholdlike nature. This behavior can be understood from Bose-Einstein statistics of the exciton-biexciton system. We have examined the quantum-statistics characteristics of the exciton-biexciton system at various excitation powers and bath temperatures. It is found that the quantum-statistics regime is realized at the bath temperature up to 8 K under a low excitation power of the order of 100 ${\mathrm{m}\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ and that it continues in a long time range of the order of submicroseconds.