Temporal Decay of the Optically Induced Properties of a Small-polaronic Solid

The essential physics of the photoluminescence of a small-polaronic solid (one in which electrons, holes and excitons all find it energetically favorable to self-trap) is described. Emphasis is placed on the dependence of the decay rates associated with the various luminescence bands on excitation energy and temperature. The results are in general accord with observations on chalcogenide glasses. Introduction.An electronic excitation, be it a charge carrier or an exciton, in a material characterized by a short-range electronlattice interaction can exist in one of two distinct types of ~tates.l-~ The excitation can be spread out over a very large number of atomic sites with the displacements of the equilibrium positions of the atoms in its vicinity being small compared with their zero-point amplitudes. This type of excitation is nonpolaronic. Alternatively, the excitation can be localized severely, with a spatial extent less than or comparable to an interatomic separation. In the latter situation, the atoms surrounding this excitation will experience substantial alterations of their equilibrium positions: the excitation is small-polaronic. For an excitation to exist without being small-polaronic it must be able to move between sites sufficiently rapidly so as to preclude the atoms in its vicinity from suffering significant displacements in response to its presence.3 Although the properties of small-polaronic and nonpolaronic excitations are qualitatively distinct from one another, the parameters in many semiconductors and insulators are such that they are near the borderline which determines whether the excitations are polaronic or nonpolaronic. 2 * Since disorder fosters localization, some nonpolaronic excitations in an ordered crystal become polaronic in their disordered counter~art.~ This has been verified in (magnetic and mixed) crystals in which disorder is imposed in a controlled manner. In what follows, it will be presumed that electrons, holes and excitons all find it energetically favorable to self-trap, forming small polarons and self-trapped excitons, respectively. Self-trapping Times.Even if it is energetically favorable for an excitation to self-trap, the time required for an injected excitation to self-trap may be significantly in excess of the minimal time for an atomic displacement, a vibrational period. 6 r The self-trapping time decreases as the coupling of the excitation to the atomic displacements increases.6 Thus, since, by virtue of their chargk, charge carriers typically interact more strongly with the atomic displacements than do excitons, they are associated with shorter self-trapping times than excitons. Furthermore, in that disorder facilitates localizationl. it reduces self-trapping times. Here, anticipating application to the chalcogenide glasses (in which there is evidence of near minimal self-trapping time for holes and no observation of the motion of electrons5), it is assumed that both *Supported by the U. S-; Department of Energy under contract DE-AC0476-DP00789. t A U. S. Department of Energy facility. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814115