APPEARANCE OF LOCALIZED PHONON STATES
IN THIN BOUNDED CRYSTALLINE STRUCTURES
The thermally or mechanically caused atomic oscillations
around their equilibrium positions in crystal were studied, where the
breaking of translational symmetry is expressed by space limitation along
one crystalographic direction. The phonon dispersion law, which was
evaluated by the method of two-time temperature dependent Green's
functions, is distinctly discrete and finite and posseses the top and
bottom gap. Analyzing the influence of the magnitude of surface parameters
on the energy spectra, the condition for the appearance and existence of the
localized phonon states was found and graphically presented.
The scope of our study in this paper is limited to the analysis of the
phonon behaviour in thin layered structures, i.e. in crystalline films,
which implies the existence of two boundary surfaces perpendicular to a
prefered direction. The existence of the finite structure width along that
direction introduces additional boundary conditions into the analysis of
the phonon behaviour. One of the most important aims is to study if the
minimal frequencies of the phonons in the film are non-vanishing (i.e. does
the phonon energy spectrum possess the gap), as well as to find the
condition for the appearance of the localized phonon states.
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