Eur. Phys. J. Plus (2018) 133: 90
https://doi.org/10.1140/epjp/i2018-11921-4

Regular Article

Quasi-stationary states of an electron with linearly dependent effective mass in an open nanostructure within transmission coefficient and S-matrix methods

Yuriy Fedkovych Chernivtsi National University, 2 Kotsyubinsky Str., 58012, Chernivtsi, Ukraine

^* e-mail: j.seti@chnu.edu.ua

Received: 2 January 2018
Accepted: 8 February 2018
Published online: 5 March 2018

Abstract

The exact solutions of the Schrödinger 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.