Energy states of particles in a quantum sized structure with a complex shaped band diagram - Pashchenko, A.; Gritsunov, O.; Babichenko, O. (ХНУРЕ, 2020)
The subject of research in the article is the energy spectrum of a multilayer quantum sized structure with an energy profile of a complex shape. The goal of this work is to study the interaction of quantum-confined and quasi- continuum energy states of particles under the action of an external stationary electric field applied perpendicular to the planes of quantum confinement. The following tasks were solved in the article: The spectrum of eigenfunctions and eigenvalues of particle energy is determined, both in the area of the quantum confinement and in the area of the quasi-continuum. The definition of the eigenfunctions takes into account the fact that the phase of the eigenfunctions changes due to the motion of particles over the quantum well. The following methods were used to solve the set tasks: quantum mechanical modeling of stationary states in a structure with an energy profile of a complex shape; methods of the theory of small perturbations for describing the interaction of particles in such a structure. The following results were obtained: the basic calculation relations of the mathematical model of the energy states of particles and quasiparticles in quantum-limited and quasi-continuum states were obtained within the framework of the quantum-mechanical approach. The interaction of energy states of particles and quasiparticles in each of the bands between quantum-confined and quasi-continuum states is described depending on the external influence. The theory of small perturbations is applied in the paper to assess the degree of interaction. Conclusions: Analysis of the results of modeling the energy spectrum of a structure with two quantum wells, calculated for an unperturbed state and for the case of external action in the form of a stationary electric field, leads to the following conclusions: in the absence of an external field acting on the considered quantum well structure, electrons and holes located above the separation barrier are characterized by a non-monotonically increasing spectrum of energy states. In this case, the particles are predominantly localized above the quantum wells; the action of a constant external electric field on the structure under consideration leads to the manifestation of the quantum-limited Stark effect both for solitary and for multilayer periodic quantum well structures. In this case, the delocalization of the wave functions and the shift of the corresponding energy levels (the lowest energy levels in the structure under consideration) is expressed as strongly as in multilayer symmetric structures. At the same time, the effect is almost invisible for the higher levels. This is especially pronounced for the energy levels lying above the separation barrier. Thus, it can be expected that an equidistant energy spectrum can be realized at a certain external field strength, which in turn should simplify significantly the attainment of the second harmonic generation mode if the structure under consideration is used in the active region of a semiconductor laser.
Keywords: energy spectrum; quantum limitation; wave function; electron; heavy hole; easy hole; quasi-continuum