PHONON SCATTERING VIA AN ATOMIC WELL IN FREE STANDING THIN SOLID FILMS

Abstract

A theoretical model is presented for the study of the scattering of phonons at an extended inhomogeneous boundary separating thin solid monatomic films. The model system consists of two solid films with otherwise stress-free surfaces on either side of an atomic well boundary. The coherent reflection and transmission scattering cross sections for phonons incident from the interior of the thin films on the inhomogeneous atomic well boundary are calculated in accordance with the Landauer–Büttiker coherent scattering description, using the matching method with nearest and next-nearest neighbor elastic force constants. This is done specifically for two different cases of elastic interactions on the boundary to investigate the consequences of their softening and hardening for the coherently scattered spectra. The numerical results yield an understanding for the effects on coherent phonon conductance due to phonon incidence and to the elastic nature of the boundary. The coherent reflection and transmission scattering cross sections show characteristic spectral features that are invariant with the change of the boundary force constants, depending solely on the cutoff frequencies for the propagating phonons and on incidence angle. They also show the Fano resonances that result from the interactions of propagating phonons with the localized vibrational Rayleigh-like modes on the boundary, depending on the boundary elastic force constants. The evolution of the system average conductance per phonon mode with incidence illustrates an interesting effect. An experimental observable this average conductance remains constant at half a phonon in intensity over significant frequency intervals. The effect is remarkable inasmuch as it permits in principle the possibility of a constant intensity phonon source.