Exciton thermodynamics in coupled quantum wells (Invited Paper)

Abstract

In a single quantum well with no applied electric field, the typical exciton lifetime is subnanosecond. Excitons do not have time to reach thermodynamic quasi-equilibrium before recombining. Quasi-equilibrium requires both an average exciton kinetic energy of kT and thermalized occupation of the inhomogeneously broadened exciton density of states. In a coupled double quantum well under an electric field, lifetimes of the `indirect' excitons (i.e., electrons and holes mostly confined in different wells) are substantially longer, typically in the range 10 to 100 nsec. We have measured cw and time-resolved photoluminescence and photoluminescence excitation spectra as a function of temperature from a symmetric coupled double quantum well. The double wells consisted of 50 angstrom GaAs wells separated by a 40 angstrom Al0.3Ga0.7As barrier, and an electric field of 30 kV/cm was applied across the wells. The indirect exciton lifetime was measured to be 40 nsec for temperatures between 2 K and 30 K. Direct analysis of the data (discussed in detail in Refs. 3 and 4 shows that: (1) Below 6 K, the excitons are metastably trapped in spatial domains which are local energy minima; thermodynamic quasi-equilibrium is not achieved within the exciton lifetime. (2) Raising the temperature above 6 K increases the exciton kinetic energy and allows the excitons to be thermally activated out of these local minima; thermodynamic quasi-equilibrium is achieved. (3) The quasi-equilibrium occupation of the exciton density of states is very well approximated by a Fermi-Dirac distribution. This last observation is particularly noteworthy, in that excitons are bosons and there have been predictions of Bose-Einstein condensation in this system. Because of the electric dipole of the indirect excitons in coupled wells, there is a repulsion between the excitons. This repulsion is strong enough to cause the excitons to avoid each other, but sufficiently short ranged to be neglected for spatially separated excitons. Since the different energies in the inhomogeneously broadened density of states correspond to spatially different positions in the well, this exciton-exciton interaction can be modelled using non-interacting thermodynamic statistics but using a Fermi-Dirac distribution to approximately account for the repulsion.