The vibrational spectra of CdSe/CdS superlattices (SLs) with different layer thicknesses are calculated from first principles within the density functional theory. It is shown that, along with folded acoustic and confined optical modes, a number of confined acoustic modes appear in SLs. In structures with a minimum thickness of one of the layers, microscopic interface modes similar to local and gap modes in crystals appear. An analysis of projections of the eigenvectors of vibrational modes in SLs onto the orthonormal basis of normal modes in binary compounds enables to establish the details of formation of these vibrational modes and, in particular, to determine the degree of intermixing of acoustic and optical modes. A comparison of the frequencies of vibrational modes in CdSe/CdS SLs and CdSe/CdS nanoplatelets enables to separate the influence of size quantization and surface relaxation on the vibrational frequencies in the nanoplatelets. Keywords: phonon spectra, semiconductor superlattices, cadmium selenide, cadmium sulfide, nanostructures.

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