International Journal of Applied Science and Engineering
Published by Chaoyang University of Technology

Ulugbek I. Erkaboev*, Ulugbek M. Negmatov, Rustamjon G. Rakhimov, Jasurbek I. Mirzaev, Nozimjon A. Sayidov

Namangan Institute of Engineering and Technology,Kasansay street 7, 160115 Namangan, Uzbekistan


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In this article we investigated the effects of 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 quantized magnetic field is quantized. The distribution of the Fermi-Dirac function is calculated in low-dimensional semiconductors at weak magnetic fields and high temperatures. The proposed theory explains the experimental results in two-dimensional semiconductor structures with a parabolic dispersion law.

Keywords: Semiconductor, Fermi energy, Quantizing magnetic field, Dispersion law, Two-dimensional semiconductor structure, 2D electron gas.

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  1. Babich, A.V., Pogosov, V.V. 2013. Quantum metal film in the dielectric environment. Physics of the Solid State, 55, 196–204.

  2. Shoenberg, D. 1984. Magnetic Oscillations in Metals (Cambridge Monographs on Physics). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511897870

  3. Dmitriev, I.A., Mirlin A.D., Polyakov D.G., Zudov M.A. 2012. Nonequilibrium phenomena in high Landau levels. Reviews of Modern Physics, 84, 1709–1763.

  4. Dmitriev, I.A., Mirlin, A.D., Polyakov, D.G. 2007. Theory of fractional microwave-induced resistance oscillations. Physical Review Letters, 99, 206805.

  5. Dymnikov, V.D. 2011. Fermi energy of electrons in a thin metallic plate. Physics of the Solid State, 53, 901–907.

  6. Erkaboev, U.I., Gulyamov, G., Mirzaev, J.I., Rakhimov, R.G., Sayidov, N.A. 2021. Calculation of the Fermi-Dirac function distribution in two-dimensional semiconductor materials at high temperatures and weak magnetic fields. Nano, 16, 2150102.

  7. Erkaboev, U.I., Gulyamov, G., Rakhimov, R.G. 2021. A new method for determining the bandgap in semiconductors in presence of external action taking into account lattice vibrations. Indian Journal of Physics. 2021.

  8. Erkaboev, U.I., Gulyamov, U.I., Mirzaev, J.I., Rakhimov, R.G. 2020. Modeling on the temperature dependence of the magnetic susceptibility and electrical conductivity oscillations in narrow-gap semiconductors. International Journal of Modern Physics B, 34, 2050052.

  9. Erkaboev, U.I., Rakhimov, R.G., Sayidov, N.A. 2021. Mathematical modeling determination coefficient of magneto-optical absorption in semiconductors in presence of external pressure and temperature. Modern Physics Letters B, 2021, 2150293.

  10. Gulyamov, G., Abdulazizov, B.T., Baymatov, P.J. 2021. Three-band simulation of the g-factor of an electron in an inas quantum well in strong magnetic fields. Journal of Nanomaterials, 2021, 5542559.

  11. Gulyamov, G., Erkaboev, U.I., Gulyamov, A.G. 2019. Influence of temperature on the oscillations of longitudinal magnetoresistance in semiconductors with a nonparabolic dispersion law. Indian Journal of Physics, 93, 639–645.

  12. Gulyamov, G., Erkaboev, U.I., Rakhimov, R.G., Mirzaev, J.I. 2020. On temperature dependence of longitudinal electrical conductivity oscillations in narrow-gap electronic semiconductors. Journal of Nano- and Electronic Physics, 12, 03012.

  13. Gulyamov, G., Erkaboev, U.I., Sayidov, N.A., Rakhimov, R.G. 2020. The influence of temperature on magnetic quantum effects in semiconductor structures. Journal of Applied Science and Engineering, 23, 453–460.

  14. Kochman, I.V., Mikhailova, M.P., Veinger, A.I., Parfeniev, R.V. 2021. Magnetophone oscillations of magnetoresistance in an InAs / GaSb quantum well with an inverted band spectrum. Semiconductors, 55, 313–318.

  15. Korotun, A.V. 2014. Fermi energy of a metal nanowire with elliptical cross section. Physics of the Solid State, 56, 1245–1248.

  16. Korotun, A.V. 2015. Size oscillations of the work function of a metal film on a dielectric substrate. Physics of the Solid State, 57, 391–394.

  17. Korotun, A.V., Koval, A.A. 2015. On the effect of dielectric environment on oscillations of the Fermi energy of an elliptic metallic nanowire. Physics of the Solid State, 57, 1861–1864.

  18. Kunitsyna, E.V., Andreev, I.A., Konovalov, G.G., Ivanov, E.V., Pivovarova, A.A., Il’inskaya, N.D., Yakovlev, Y.P. 2018. GaSb/GaAlAsSb Heterostructure Photodiodes for the Near-IR Spectral Range. Semiconductors, 52, 1215–1220.

  19. Kurbatsky, V.P., Pogosov, V.V. 2004. Analytical model of oscillating size dependence of energy and force characteristics of subatomic metal films. Physics of the Solid State, 46, 543–551.

  20. Kuz’min, M.V., Loginov, M.V., Mittsev, M.A. 2009. Size dependences in the adsorptive properties of the surface of ytterbium nanofilms deposited on silicon: The CO-Yb-Si(111)7×7 system. Physics of the Solid State, 51, 841–845.

  21. Mikhailova, M.P., Berezovets, V.A., Parfeniev, R.V. et al. 2017. Vertical transport in type-II heterojunctions with InAs/GaSb/AlSb composite quantum wells in a high magnetic field. Semiconductors, 51, 1343–1349.

  22. Yaji, K., Mochizuki, I., Kim, S., Takeichi, Y., Harasawa, A., Ohtsubo, Y., Le Fèvre, P., Bertran, F., Taleb-Ibrahimi, F., Kakizaki, A., Komori, F. 2013. Fermi gas behavior of a one-dimensional metallic band of Pt-induced nanowires on Ge(001). Physical Review B, 87, 241413(R).

  23. Zawadzki, W., Raymond, A., Kubisa, M. 2014. Reservoir model for two-dimensional electron gases in quantizing magnetic fields: A review. Physica Status Solidi (B), 251, 247–262.


Received: 2021-04-27
Revised: 2022-01-28
Accepted: 2022-03-17
Available Online: 2022-05-27

Cite this article:

Erkaboev, U.I., Negmatov, U.M., Rakhimov, R.G., Mirzaev, J.I., Sayidov, N.A., Influence of a quantizing magnetic field on the Fermi energy oscillations in two-dimensional semiconductors. International Journal of Applied Science and Engineering, 19, 2021123.

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