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The spectral characteristics of a cascade of broadband quantum cascade detector, functioning in the far IR range, renormalized by the interaction with all modes of interface phonons are studied using the Green’s function method. Partial contributions into the magnitudes of shifts and decays of electron operating states due to their configurational interactions with all states of the cascade in the processes of emission and absorption of phonons are investigated. It is shown that interaction with interface phonons leads to low-energy shift and decay of operating states of the electron, with their magnitudes increasing at bigger temperature. It is shown that when the width of the potential barrier, which is located in the double-well active region, varies both the shifts and decays of high-energy operating states drastically increase.

The quantum theory of renormalized energy spectrum of the system of localized two-level quasiparticle, with degenerated spectrum, interacting with polarization phonons, being the model of multilaye...

Within the unitary transformed Hamiltonian of Frohlich type, using the retarded Green’s function method, the exact renormalized energy spectrum of a quasi-particle strongly interacting with three-mode polarization phonons is obtained at T = 0 K in the model of a system with a limited number of its initial states. The exact analytical expressions for the average number of phonons in the main and all satellite states of the system are obtained. Their dependences on the magnitude of the interaction between quasi-particle and both phonon modes are analyzed.

Based on the generalized method of Feynman–Pines diagram technique, a new method of calculation of the mass operator in the Fourier image of Green’s function is proposed for the system of a three-level localized quasiparticle interacting with polarization phonons at $$T=0\,\hbox {K}$$ . The revealed main class of diagrams gives the opportunity to write the renormalized mass operator in a form of continuous branch chain fraction with typical links. Such presentation allows effective accounting of multi-phonon processes. It is shown that the renormalized energy spectrum contains the complexes of bound-to-phonon states of the quasiparticle. These complexes essentially differ for the resonant and non-resonant systems.

The electron energy spectrum and wave functions in multishell spherical quantum dot, consisting of core and two spherical shells – potential wells separated by thin potential barriers, are obtained in the framework of the effective mass approximation and single band model. The investigations are performed within the matrix method for the nanostructure driven by magnetic field using the complete set of wave functions obtained without the magnetic field. The electron dipole momentum and oscillator strengths of intraband quantum transitions as functions of the magnetic field induction are numerically calculated. In order to increase the sensibility to magnetic field, the geometric parameters of the shells are chosen in such a way that the electron in the ground state is to be located in outer spherical well, but when the magnetic field induction becomes bigger, it moves into the core. It is shown that size of the middle potential well causes the smooth change of the electron location due to the effect of magnetic field, what is displayed on optical properties of nanostructure. The calculations are performed for multishell quantum dot CdSe/ZnS/CdSe/ZnS/CdSe.

Within unitary transformed Hamiltonian of Fr\"ohlich type, using the Green's functions method, exact renormalized energy spectrum of quasiparticle strongly interacting with two-mode polarization phonons is obtained at $T=0$ K in a model of the system with limited number of its initial states. Exact analytical expressions for the average number of phonons in ground state and in all satellite states of the system are presented. Their dependences on a magnitude of interaction between quasiparticle and both phonon modes are analyzed., Comment: 8 pages, 1 figure

The electron - impurity binding energy and photoionization cross-section of hydrogenic impurity are studied in spherical multilayered quantum dot AlxGa1-xAs/GaAs/AlyGa1-yAs driven by external electric field. The problem is solved in the framework of the effective mass approximation and rectangular potential profiles for wells and barriers, using the method of wave function expansion over a complete set of functions obtained as exact solutions of Schrodinger equation in nanostructure without impurity and electric field. The dependence of photoionization cross-section of impurity on electric field intensity is obtained taking into account the excited states of electron. It is shown that the binding energy and photoionization cross-section strongly depend on impurity location, intensity and direction of electric field. If the field is absent, the main contribution into photoionization cross-section is produced by quantum transition of electron from the ground into the first excited state, while if the electric field acts, the main role goes to the transition between ground states of electron with and without impurity. The energy of this transition decreases when electric field intensity increases.

The new method of calculation of a mass operator of Fourier image of Green's function, based at the generalized method of Feynman-Pines diagram technique for the multi-level systems, is proposed for the system of three-level localized quasiparticle interacting with polarization phonons at T=0K. The main class of diagrams, studied in this approach, made it possible to renormalize the mass operator and present it in a form of continuous branch chain fraction with typical chains. It allows effective accounting of multi-phonon processes. It is shown that the complicated complexes of bound-to-multi-phonons states of quasi-particle are observed in the energy spectrum of the system under research.

Using the model of rectangular potential and smooth position-dependent electron effective mass, which is a linear function of coordinate in near-interface regions between wells and barriers of open double-barrier resonant tunneling nano-structure, the solutions of Schrodinger equation are obtained and transmitting coefficient of the structure is analytically calculated. The influence of the sizes of inner and outer near-interface regions on transmitting coefficient of the structure is investigated. The comparative analysis of resonance energies and resonance widths of sub-barrier electron quasi-stationary states as functions of these sizes is performed. It is shown that the relative differences of resonance energies and resonance widths of the same state of electron in the model of linearly-dependent effective mass and simplified abrupt one do not exceed 1% and 5%, respectively, in physically correct interval of the sizes of outer and inner near-interface regions.

The exact solutions of the Schrodinger equation for a double-barrier open semiconductor plane nanostructure are obtained by using two different approaches, within the model of the rectangular potential profile and the continuous position-dependent effective mass of the electron. The transmission coefficient and scattering matrix are calculated for the double-barrier nanostructure. The resonance energies and resonance widths of the electron quasi-stationary states are analyzed as a function of the size of the near-interface region between wells and barriers, where the effective mass linearly depends on the coordinate. It is established that, in both methods, the increasing size affects in a qualitatively similar way the spectral characteristics of the states, shifting the resonance energies into the low- or high-energy region and increasing the resonance widths. It is shown that the relative difference of resonance energies and widths of a certain state, obtained in the model of position-dependent effective mass and in the widespread abrupt model in physically correct range of near-interface sizes, does not exceed 0.5% and 5%, respectively, independently of the other geometrical characteristics of the structure.

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).

Within the model of rectangular potential profile and continuous position-dependent effective mass of electron in the double-barrier open semiconductor plane nano-heterostructure, the exact solutions of Schrodinger equation are obtained. Using them, the transmission coefficient, resonance energies, and widths of sub-barrier quasi-stationary electron states are calculated for the structure with In0.53Ga0.47As wells and In0.52Al0.48As barriers. The transmission coefficient and spectral characteristics of electron states are analyzed as functions of the width of near-interface region where the effective mass linearly depends on coordinate. It is shown that the increasing width of near-interface region between wells and barriers does not change the heights of maxima of transmission coefficient peaks but shifts and broadens them.

The spectrum of two-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 when the energy distance between the both main states varies, the renormalized spectrum of the energies contains two series of levels corresponding to the both main and their excited states which appear due to the interaction with phonons. The quasi-equidistant spectrum is observed in the non-resonance regions of energies while in the resonance regions the anti-crossing effect is seen.

The exact solution of Schrodinger equation for the electron is obtained using the model of δ-like potential barriers and approximation of continuous position-dependent effective mass being linear near interface between the quantum wells and barriers of open double-barrier nano-structure. Within these analytical solutions, the effect of the near-interface size on the transmission coefficient of nano-structure, resonance energies and widths of electron states is studied.

The resonance and non-resonance transmission canals of double-barrier resonant tunneling structure are established for the electron photon system using the exact solution of one-dimensional non-stationary Schrodinger equation expanded into the Fourier range. It is shown that besides the main and satellite, the mixed quasi-stationary states which cause the appearance of speci c transmission canals with the properties strongly dependent on the intensity and frequency of electromagnetic eld, exist in the nanostructure.

The theory of resonance energies and widths of electron quasi-stationary states and electronic conductivity in open cylindrical two-barrier symmetric resonance tunnel structure is developed. The complete Schrodinger equation is solved within the model of effective masses for rectangular potential wells and barriers. Interaction between electrons and electromagnetic field was taken into account using the approximation of the small signal. The calculations of spectral parameters are performed for In0.53Ga0.47As/In0.52Al0.48As resonance tunnel structure. The dependences of conductivity on the energy of mono-energy electrons beam falling at the system and electromagnetic field energy absorbed or emitted by the system are obtained and analyzed. The relation between experimentally measured parameters of conductivity and resonance widths of electron quasi-stationary states in open resonance tunnel structure is established.

The theory of exciton spectrum in the array of hexagon nanotubes is developed within the Bethe method and Green functions taking into account the exciton–phonon interaction. The theory is based at the effective masses model for the excitons’ electron and hole and dielectric continuum model for the interface and confined phonons. For the InAs hexagon nanotubes embedded into InP it is proven that the calculated magnitudes of energies and intensities of quantum transitions correlate to the experimental data.

The exact solutions of Schrodinger equation for the electron in Coulomb field of donor impurity are obtained within the effective masses approximation and dielectric continuum model for the spherical quantum dot CdS/SiO2 and anti-dot ZnS/CdxZn1−xS. The dependences of electron energy spectrum and its probability density on nano-system radius are studied. The numeric calculations and analysis of oscillator strength of intersubband quantum transition from ground into first excited state at the varying radius are performed. It is shown that the oscillator strength for the big quantum dot is close to the respective value for the bulk semiconductor crystal.

Partial summing of infinite range of diagrams for the two-phonon mass operator of polaron described by Fr\"{o}hlich Hamiltonian is performed using the Feynman-Pines diagram technique. Renormalized spectral parameters of ground and first excited (phonon repeat) polaron state are accurately calculated for a weak electron-phonon coupling at $T=0$ K. It is shown that the stronger electron-phonon interaction shifts the energy of both states into low-energy region of the spectra. The ground state stays stationary and the excited one decays at a bigger coupling constant., Comment: 12 pages, 5 figures

The energies of electron and hole Breit–Wigner resonance quasistationary states in opened complicated cylindrical quantum wire are obtained within the effective mass approximation using the S-matrix theory. Numerical calculation is performed on the example of GaAs/AlxGa1−xAs/GaAs system. The S-matrix poles are studied in complex plane of the energies. The quasiparticle lifetimes in quasistationary resonance states as functions of nanosystem geometric sizes and longitudinal quasimomentum are obtained. It is shown that quasiparticle lifetime in resonance state exponentially decreases when quasimomentum increases.

The theoretical investigation of the electron, hole and phonon spectra in the spherical nanoheterosystem CdS/β-HgS/H 2 O is performed within the effective mass approximation in the dielectric continuum model. The Hamiltonian of the exciton-phonon system is established in the representation of second quantization. The energy of the exciton basic state (E ex ) renormalized due to the interaction with phonons is obtained. The existence of a crook in the E ex curve depending on the β-HgS shell thickness is proved and explained. A satisfactory correlation between the theoretical and experimental results is obtained.

The spectrum of an electron confined in a layer with the dielectric constant ϵ, embedded between two media with larger (ϵ> > ϵ) and smaller (ϵ< < ϵ) values of the dielectric constant is calculated. The dependence of the spectrum on the layer thickness and on the ratio between the dielectric constants of the layer and the media is calculated. It is shown that if the crystal thickness increases, the whole spectrum of electrons shifts into the region of negative energies and becomes quasi-hydrogenic there. [Russian Text Ignored].

Electron scattering cross in open spherical quantum dot is calculated within the effective mass approximation and rectangular potential barriers model. It is shown that in nanosystem with the barrier width containing several mono shells, the experimentally measured scattering cross allows to identify well the resonance energies and widths of low energy electron quasistationary spectrum. It is established that for the open quantum dot with weak potential barrier the correct spectral parameters of quasistationary spectrum are the generalized resonance energies and widths.

The electron energy spectrum in a quantum dot (QD) with smooth dependences of the quasiparticle potential energy and the effective mass at the interface between semiconductor media is calculated in the effective mass approximation. It is shown that the electron energy corrections due to the tailing of the interface are nonmonotonous functions of the QD radius, the increasing of which brings to the rapid increasing of shifts, reaching their maxima, and slowly decreasing for the QDs of big sizes. The calculations prove that the relative corrections for the different electron energy levels in a spherical QD are placed closer to each other with increase in the radius. The growth of the parameter of interface tailing leads to the proportional increase in the corrections to electron energy spectra. Numerical calculations are performed for HgS/CdS and GaAs/Al x Ga 1-x As QDs, all dependences being qualitatively similar. Keywords: quantum dot, smooth confinement, interface, electron energy spectrum. Manuscript received 07.02.07; accepted for publication 27.09.07; published online 31.10.07.

The spectra of quasiparticles which are not interacting with phonons are obtained for the model of rectangular wells and the effective mass approximation. The calculation of the quasiparticle spectra renormalized due to the interaction is performed using the Feinman diagram technique for the temperature Green functions. This method opened the ability to investigate the case of weak, middle and tight binding taking into account the interlevel (interband) interaction in the wide range of energies having the phonon repeatings observed in Raman scattering. Due to the spherical symmetry of quantum dot and cylindrical quantum wire in the Raman spectra one cannot see the interface phonon repeatings. There are only the repeatings corresponding to the confined phonons of quantum dot (or quantum wire) and the repeatings due to the phonons of the external medium (in case of semiconductor). The repeatings of the corresponding interface phonons can arise only in the asymmetric states of quasiparticles or in the asymmetric nanosystems

Within the model of rectangular potentials and different effective masses of electrons in different elements of plane two-barrier resonance tunnel structure there is developed a theory of spectral parameters of quasi-stationary states and active conductivity for the case of mono-energetic electronic current interacting with electromagnetic field. It is shown that the two-barrier resonance tunnel structure can be utilized as a separate or active element of quantum cascade laser or detector. For the experimentally studied In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As nano-system it is established that the two-barrier resonance tunnel structure, in detector and laser regimes, optimally operates (with the biggest conductivity at the smallest exciting current) at the quantum transitions between the lowest quasi-stationary states., 11 pages, 4 figures