Using the transfer matrix method within the effective mass approximation and rectangular potentials model, the accurate analytical expression for the scattering S-matrix in an open multi-cascade resonant tunnel nanostructure was obtained. It made possible to develop the theory of spectral characteristics of quasi-stationary electron states in a multi-cascade element of a quantum cascade detector. Using the example of a nanostructure with GaAs wells and AlGaAs barriers, the peculiarities of the dependences of resonance energies and resonance widths of electron states on the number of cascades were investigated. It was established that in the N-cascade structure, the resonance bands are observed in spectrum, each of which is formed by the energies of N quasi-stationary states. If the number of cascades increases in the interval of small values, the widths of the energy bands become bigger and almost do not change at N≥20.
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).
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