Phonon spectra in quantum wires

Green's function method, adjusted to bound crystalline structures, was applied to obtain the phonon dispersion law in quantum wires. The condition of the existence of small mechanical atom movements defining phonon spectra can be found by solving the secular equation. This problem was presented graphically for different boundary parameters. The presence of boundaries, as well as the change of boundary parameters, leads to the appearance of new properties of the layered structure. The most important feature is that, beside the allowed energy zones (which are continuous as in the bulk structure), zones of forbidden states appear. Different values of the boundary parameters lead to the appearance of lower and upper energy gaps, or dispersion branches spreading out of the bulk energy zone. The spectra of phonons in corresponding unbound structures were correlated to those in bound structures