Phonon localization in two-dimensional self-supported films

Phonon localization in thin self-supported films is investigated. The localization in the sense of Anderson depends critically on inelastic phonon processes; defects and roughness at the film boundaries are assumed to result in resonant phonon scattering by two-level systems. We define a phonon localization length ξ from the elastic diffusion determined by two-dimensional isotope scattering and by partially specular reflection from boundaries. The localization frequency edge ${\mathrm{\omega }}_0$ is shown to depend essentially on the conditions of the film surfaces.