Exciton luminescence from fluctuation-induced tails in the density of states of disordered solid solutions

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Abstract
The shape of the luminescence spectra of excitons localized by composition fluctuations in a disordered solid solution, is calculated by a theoretical model that takes into account two different aspects of the electron-phonon interaction: 1) the lifetimes of localized states are limited because of transitions (tunneling) between states of the tail with emission of phonons. This implies that only a relatively small fraction of the states in the tail-those which have no access to such transitions-are populated long enough to emit radiation; 2) the luminescence spectra from these long-lived radiating states is also caused by the simultaneous emission of phonons. It is shown that both these aspects are important in explaining the observed shift in the maximum of the luminescence band relative to the maximum of the exciton absorption line. The shape of the short-wavelength edge of the luminescence band is determined primarily by the dependence of the number of clusters of minimum size on the localization energy, in particular its rapid decrease in the neighborhood of the mobility edge, whereas the spectrum of recombination with emission of phonons determines the shape of the long-wavelength tail of the primary emission band. The calculated shape of the emission spectrum is compared with spectra obtained experimentally for luminescence from the solid solution CdS(1−c)Sec. It turns out that a satisfactory description of the experimental spectra of CdS(1−c)Sec over a wide range of compositions requires two models of the localized exciton: localization of the exciton as a whole (model I) or localization of the hole with the electron bound to it by the Coulomb interaction (model II).