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Abstract
Using the effective mass model for an electron and the dielectric continuum model, analytical solutions of the self-consistent Schr\"odinger-Poisson system of equations are obtained. Quantum mechanical theory of electronic stationary states, the oscillator strengths of quantum transitions and a method of potential profile calculation is developed for the experimentally constructed three-well resonance-tunneling structure --- a separate cascade of quantum cascade detector. For the proposed method, a comparison with the results of other methods and with the results of the experiment was carried out. A good agreement between the calculated value of the detected energy and its experimental value has been obtained, the difference being no more than $2.5\%$.
Highlights
Quantum cascade lasers (QCL) [1, 2] and detectors (QCD) [3,4,5,6,7,8] created experimentally on the basis of binary and ternary nitride alloys of InN, GaN, AlN, etc., are of considerable practical and theoretical interest
An effective work of nitride QCL and QCD is possible within the range from cryogenic to room temperatures, which is a significant advantage in comparison with the nanodevices created on the basis of arsenide semiconductor compounds of GaAs, InAs, AlAs, which, can work only at cryogenic temperatures
The anisotropy of physical properties of nitride semiconductor materials is caused by strong interatomic bonds and by the fact that their crystal lattice is of the wurtzite type hexagonal structure
Summary
Quantum cascade lasers (QCL) [1, 2] and detectors (QCD) [3,4,5,6,7,8] created experimentally on the basis of binary and ternary nitride alloys of InN, GaN, AlN, etc., are of considerable practical and theoretical interest. The disadvantages of most numerical methods for RTS potential profiles calculation include the linearization of the Schrödinger and Poisson equations at the initial stage of their solution, as well as the neglect of the influence of the boundary conditions for the wave function and the fluxes of its probability. The stationary spectrum of the electron and its wave functions Ψ(z) are determined by solutions of the self-consistent Schrödinger-Poisson system of equations: 2d. The iterative procedure described makes it possible to establish the self-consistent solutions of the Schrödinger and Poisson system of equations, as well as all the components of the effective potential of the RTS for an electron with the required accuracy, which is presented by the obvious relation:.
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