Fermi-Dirac distribution of excitons in coupled quantum wells

Abstract

Time-resolved and cw photoluminescence of excitons in coupled quantum wells with an applied electric field is modeled using a Fermi-Dirac distribution. This distribution can result from inhomogeneous broadening due to interface roughness and the strong, short-range electric dipole repulsion between excitons. The model quantitatively explains the striking temperature dependence of the luminescence linewidth and peak position previously interpreted as a phase transition to an ordered state [T. Fukuzawa, E. E. Mendez, and J. M. Hong, Phys. Rev. Lett. 64, 3066 (1990)]. At very low temperatures (;S6 K), the excitons are in a metastable distribution.PACS numbers: 73.20.Dx, 78.47.+p, 78.55.Cr, 78.65.Fa An exciton in a bulk semiconductor or a quantum structure is an electron and a hole which pair up because of their mutual Coulomb attraction. Because both electron and hole are fermions, the exciton is bosonlike. Recently, several experiments have been interpreted in terms of a possible condensation of excitons, in bulk CU2O (Refs. 1 and 2) and in coupled quantum wells. 3 In a symmetric coupled quantum well with an electric field applied along the growth direction, the electrons and holes separate. This separation reduces the overlap between their respective wave functions, and greatly increases the exciton radiative lifetime. 4 ' 5 Because of the longer lifetime, it has been suggested that there would be sufficient time for the excitons to come to a condensed, ordered phase. 6 The recent observation 3 of a sharply narrower linewidth of excitons in a coupled quantum well as the temperature was decreased from 12 to 6 K was interpreted as possible evidence for this condensation.On the other hand, the quantum-well structures grown by modern epitaxial techniques do not result in microscopically smooth heterointerfaces. 7,s It has been known for some time that this roughness leads to an inhomogeneous broadening of the excitonic absorption. 9 Here we show that the excitonic occupation of this inhomogeneous line can be modeled with a Fermi-Dirac distribution. (Using a Fermi-Dirac distribution does not imply that the excitons are fermions. For example, the equilibrium occupation of a set of impurity states follows a Fermi-Dirac distribution if each impurity can trap only a single particle.) Since isolated excitons have boson characteristics, the Fermi-Dirac distribution apparently results from a strong repulsion of the excitons. The repulsion must be large enough that two excitons do not occupy the same spatial position, yet short ranged enough to be neglected for spatially separated excitons. Excitons in coupled quantum wells in an electric field have an electric dipole along the growth direction, and we will show that the repulsion between the dipoles can satisfy these conditions. The p-i-n diode sample used here consists of ten undoped double-quantum-well units separated by 200 A of Alo.3Gao.7As. Each unit consists of two 50-A-wide GaAs quantum wells separated by a 40-A-thick Alo.3Gao.7As barrier. The layers were grown on a...

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