Determination of the temperature dependence of the Fermi energy oscillations in nanostructured semiconductor materials in the presence of a quantizing magnetic field

Determination of the temperature dependence of the Fermi energy oscillations in nanostructured semiconductor materials in the presence of a quantizing magnetic field
U.I. Erkaboev¹

Namangan Institute of Engineering and Technology, Namangan, 160115, Uzbekistan
[e-mail]

ORCID: 0000-0002-6841-8214
G. Gulyamov

Namangan Engineering-Construction Institute,Namangan, 160103, Uzbekistan
[e-mail]

ORCID: 0000-0003-1133-9328
R.G. Rakhimov

Namangan Engineering-Construction Institute, Namangan, 160103, Uzbekistan
Namangan Institute of Engineering and Technology, Namangan, 160115, Uzbekistan
[e-mail]

ORCID: 0000-0003-0850-1398
N.A.Sayidov

Namangan Institute of Engineering and Technology, Namangan, 160115, Uzbekistan
[e-mail]
ORCID: 0000-0002-3402-1059

Abstract

In this article investigated the effects of a quantizing magnetic field and temperature on Fermi energy oscillations in nanoscale semiconductor materials. It is shown that the Fermi energy of a nanoscale semiconductor material in a quantizing magnetic field is quantized. For the first time, a mathematical model was developed for determining the effect of temperature and a quantizing magnetic field on oscillations of the Fermi energy in nanoscale semiconductor structures with a parabolic dispersion law. A mathematical expression is derived for calculating the dependence of the distribution of the Fermi-Dirac function on the magnetic field, on the thickness of the quantum well and on the temperature in low-dimensional semiconductor materials. The possibility of calculating the Fermi energy oscillations in two-dimensional electron gases at high temperatures and weak magnetic fields is shown for the first time. The proposed theory explains the experimental results in two-dimensional semiconductor structures with a parabolic dispersion law.