Interface And Step Localized Phonon Modes Between Two Truncated Thin Films

We have carried out the calculations of vibrational dynamics in the low-dimensional structure with dimensions on the nanometer scale by using the matching formalism. The nanostructure model consists in the surface step produced at a perpendicular interface between two truncated thin films with different thickness. The theoretical approach determines the vibrational field in the direction where the translation symmetry is broken. The calculation concerns in particular the phonon dispersion curves localized on the interface and step edge, and employs the matching procedure in the harmonic approximation. The nearest and next nearest neighbors elastic force constants between the mass sites in the model, as well as a modification of the elastic strain field induced by the presence of the step, are considered. Analytic expressions are obtained for the phonon dispersion relations of the localized surface and edge elastic waves and the bulk phonons near a step. The breakdown of translational symmetry perpendicular to the step edge gives rise to several Raleigh-like branches localized in the neighborhood of step and interface. The effects of varying the elastic force constants at an interface and the strain field parameter near the step are studied. These factors influence the number of localized modes as well as their frequency, intensity and attenuation.