Nanoscale physics

S-matrix and quasi-stationary spectrum of electron in nano-structure with position-dependent effective mass and potential energy
Ju. Seti, М. Ткаch, O. Pytiuk, О. Voitsekhivska
Yuriy Fedkovych Chernivtsi National University, 2, Kotsyubinsky Str., 58012, Chernivtsi, Ukraine,
E-mail: j.seti@chnu.edu.ua

The solutions of Schrodinger equation for an electron in the open resonant tunneling structure are obtained within the model of smooth position-dependent effective mass and potential energy, which linearly depend on coordinate in the near-interface regions between the well and barriers. Using the method of transfer matrix, the analytical calculation of scattering S-matrix is performed. Its poles define the spectral parameters of electron quasi-stationary states [1]. 
The resonance energies and resonance widths of sub-barrier electron states are studied as functions of the sizes of near-interface regions. It is established that their increase causes the high-energy shift of resonance energies of all sub-barrier electron states. Also, the resonance widths of high-energy states increase while that of the low-energy ones – decrease. 
The results obtained in the realistic model of effective mass and potential profile are compared with that of the wide-spread model of abrupt effective mass and potential energy [2] at the interfaces between the wells and barriers of nano-structure. It is shown that in the interval of physically correct sizes of near-interface regions, which do not exceed one lattice constant, the resonance energies in realistic model differ of that in abrupt one not more than at 3 % and the resonance widths – not more than at 18 %, respectively.

1.	Tkach N.V., Seti Yu. A. Evolution and collapse of quasistationary states of an electron in planar symmetric three-barrier resonance-tunneling structures // Low Temp. Phys. – 2009. – 35. ‑ 556.
2.	Harrison P., Valavanis A. Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures, 4th Edition, Wiley, 2016.