Localization of Excitons in Weakly Disordered Systems

Abstract

We will concentrate on one particular disordered semiconducting system, the “quantum well”. This is a semiconductor sandwich in which the central layer has a smaller bandgap than the outer layers, so that electrons are confined within it. When the latter is ~ 100 A thick the electron states are quantized normal to the layer, and only the lowest state is occupied at low temperatures and low electron densities. Excitons in quantum wells form a model system for the study of the localization of neutral particles by a two-dimensional random potential. Wannier excitons (neutral particles, analogous to positronium, in which an electron is bound to a hole by the Coulomb interaction) can be created optically in the well, with an energy defined by the exciting photon. If the layer were perfectly uniform, the excitons would move freely within it, and their wave functions would be two-dimensional Bloch wave. However, fluctuations in layer width produce a random potential, which can localize excitons of sufficiently low energy. The wave function of a localized particle, unlike a Bloch wave, fall off exponentially with distance. Localization greatly reduces the rate of loss of phase coherence after excitation by an optical pulse. This rate has been measured in the frequency domain by resonant Rayleigh scattering [1], and in the time domain by the photon echo technique [2]. Other methods, such as hole-burning and transient gratings, have also been used [3].