The influence of the surface parameter changes onto the phonon states in ultrathin crystalline films

In this paper, we have analytically investigated how the changes in boundary surface parameters influence the phonon dispersion law in ultrathin films of the simple cubic crystalline structure. Spectra of possible phonon states are analyzed using the method of two-time dependent Green's functions and for the diverse combination of boundary surface parameters, this problem was presented numerically and graphically. It turns out that for certain values and combinations of parameters, displacement of dispersion branches outside of bulk zone occurs, leading to the creation of localized phonon states. This fact is of great importance for the heat removal, electrical conductivity and superconducting properties of ultrathin films.