Nanoscale physics

Properties of electron states in open multi-cascade nanostructure: S-matrix, transmission coefficient and probability function methods
Seti Ju., Vereshko E., Voitsekhivska O., Tkach M.
Department of Theoretical Physics and Computer Simulation, Yuriy Fedkovych Chernivtsi National University, 2, Kotsyubinsky Str., 58012, Chernivtsi, Ukraine
E-mail: vereshko.yevheniia@chnu.edu.ua
The problem of quasiparticles states in low-dimensional structures, for a long time, has been purely fundamental. It became practically important only after the creation of first devices based on nanostructures (quantum well infrared photodetectors, quantum cascade detectors, quantum cascade lasers, etc.). This has significantly intensified theoretical research in the field of nanostructure physics. In the majority of papers, due to the complexity of analytical and numerical calculations, structures with a small number of nano layers were studied, while complicated multi-cascade nanostructures were not observed. Therefore, the properties of the basic elements of nano devices containing dozens of cascades are still not completely studied.
The aim of the proposed paper is to study the spectral characteristics of an electron in a multi-cascade open nanostructure [1]. The models of effective mass and rectangular potentials based on the solutions of Schrödinger equation in three different approaches (transmission coefficient (D), scattering matrix (S) and probability distribution function (W)) are used for the calculation of the resonant energies and widths of electron quasi-stationary states. The analysis of the spectral characteristics as functions of the number of cascades show that in the simplest single-cascade nanostructure the resonant energies and widths of the electron states in all three approaches coincide with an accuracy not less than 0.1%. If the number of cascades increases, it leads to the formation of bands. The number of resonant energies in the band is equal to the number of cascades in the S-matrix approach, while in D- and W-approaches – it is smaller. Also, it is established that in the S-approach the sum of resonant widths of electron states in each band is independent of the number of cascades and coincides with the width of the corresponding quasi-stationary state in single-cascade structure, while in D- and W-approaches the sum of widths in the bands only decreases.

1.	Tkach M.V., Seti J.O., Voitsekhivska O.M. Quasiparticles in Nanoheterostructures: Quantum Dots, Wires and Layers. // Books-XXI, Chernivtsi.-2015