Nanoscale physics

Properties of transmission coefficient of multicascade element in quantum cascade detector
Seti Ju., Vereshko E., Voitsekhivska O., Tkach M., Markin O.
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

Within the model of rectangular potentials and position-dependent effective mass, the electron wave functions are obtained by solving of the Schrödinger equation. On their basis, the transmission coefficient is analytically calculated for a multicascade open nanostructure being a model of a typical quantum cascade detector [1] operating in far infrared range.
The transmission coefficient as function of a number of the same cascades consisting of a single-well active region and a double-well extractor is studied. It is shown that in a single-cascade structure in the dependences of the transmission coefficient on energy the four quasi-Lorentz peaks are observed, which, as it is well known [2], correspond to the quasi-stationary states of the electron. The positions of the maxima of these peaks define the magnitudes of the resonant energies of quasi-stationary states while the widths at half of their heights determine the resonant widths. It is established that if the number of cascades becomes bigger, quasi-Lorentz curves are deformed and transformed into complicated complexes of peaks, the number of maxima in which does not exceed the number of cascades.
Numerical calculations of the probabilities |𝛹(𝑧,𝐸)|2 reveal the areas of electron most probable location in different quasi-stationary states. In particular, it is found that in the states of the first and fourth complexes the electron is mostly localized in the active regions of the structure cascades and in the states of the third and second complexes - in the first and second wells of the extractors, respectively. It is shown that the high tunnel transmission of potential barriers causes a weak localization of the electron in the active region of the first cascade and the second potential well of the extractor of the last cascade of the structure.

1.	Zhou X., Li N., Lu W. Progress in quantum well and quantum cascade infrared photodetectors in SITP // Chin. Phys. B. – 2019. – 28. – 027801.
2.	Tkach N.V., Seti Yu.A. Evolution and collapse of quasistationary states of an electron in planar symmetric three-barrier resonance-tunneling structures // Low Temperature Physics. – 2009. – 35. – 556.