A theory of energy transfer of the quasi-two-dimensional excitons in GaAs-AlAs quantum-well heterostructures is developed, and the recently observed slow and nonexponential energy relaxation of excitons is explained quantitatively in terms of the one-phonon-assisted transfer of localized excitons among islandlike structures within a quantum well. The nonexponential behavior of energy relaxation is clarified as a general feature to be observed in the low-energy tail of the density of states. The dependence of the energy relaxation rate on the quantum-well thickness is discussed along with the same dependence of the absorption bandwidth. The correlation between the energy relaxation rate and the absorption bandwidth is explained qualitatively on the basis of the scaling property of the rate equation for the exciton distribution function.
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