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The spectrum of three-level localized quasi-particle renormalized due to the interaction with polarization phonons is studied within the Feynman-pines diagram technique at cryogenic temperature. It is shown that in such system, besides the renormalized three main states, the complexes of bound states exist. Their properties are essentially different depending on the energetic distance between the starting levels, which are in resonance with the phonon energy or not.

The theory of phonon spectra in the three-layer anisotropic wurtzite-based nano-heretostructures with binary- and ternary compounds is developed using the dielectric continuum Loudon's model. The energy spectra of confined, interface, halfspace, and propagating phonons are obtained and analyzed. The ranges where the certain phonon modes exist are established depending on the concentration of Al in ternary compound AlGaN of three-layered nano-heterostructure (AlN/GaN/AlN/AlGaN/AlN).