  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.
