ELEKTRONLARNING ENERGIYA SPEKTRINI KRONING VA PENNI USULI YORDAMIDA HISOBLASH

Voxob Rasulov; Baxodir Axmedov; Islomjon Muminov

Physics and technology

No. 3 (2024): FarDU.Ilmiy xabarlar jurnali. Ilova to'plam (Aniq va tabiiy fanlar)

CALCULATION OF THE ENERGY SPECTRUM OF ELECTRONS USING THE KRONIG-PENNEY METHOD

Voxob Rasulov ^▸^▾
Baxodir Axmedov ^▸^▾
Islomjon Muminov ^▸^▾

PDF (Uzbek)

Submitted: August 13, 2024
Published: 2024-09-12

Abstract

In this article, the motion of electrons in crystals in a periodic potential field is analyzed using the Schrödinger equation. The Kronig-Penney method is used to determine the energy spectrum of electrons. According to this method, the atoms in the crystal lattice are represented by rectangular potential wells and barriers. Electrons exist only in allowed energy bands and cannot pass through forbidden bands. Additionally, the relationships between energy bands and forbidden bands are examined.

References

Kittel, C. Introduction to Solid State Physics. 8th ed. Wiley, 2005.
Ashcroft, N.W., Mermin, N.D. Solid State Physics. Harcourt College Publishers, 1976.
Kronig, R. de L., Penney, W.G. Quantum Mechanics of Electrons in Crystal Lattices. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 1931, Vol. 130, pp. 499-513.
Blatt, F.J. Physics of Electronic Conduction in Solids. McGraw-Hill, 1968.
Ziman, J.M. Principles of the Theory of Solids. 2nd ed. Cambridge University Press, 1972.
Rozikov, J., Akhmedov, B., Muminov, I., & Ruziboev, V. (2019). DIMENSIONALLY QUANTIZED SEMICONDUCTOR STRUCTURES. Scientific and Technical Journal of Namangan Institute of Engineering and Technology, 1(6), 58-63.
Rustamovich, R. V., Yavkachovich, R. R., Forrux, K., & Arabboyevich, M. I. (2021). THEORETICAL ANALYSIS OF MULTIPHOTON INTERBAND ABSORPTION OF POLARIZED LIGHT IN CRYSTALS WITH A COMPLEX ZONE (PART 1). European science review, (3-4), 48-51.
Muminov, I. A., & Muminova, M. (2023). QATTIQ JISMLARNING KRISTALL PANJARALARI. Oriental renaissance: Innovative, educational, natural and social sciences, 3(3), 1314-1317.
Arabboyevich, M. I., & Nabijon o‘g, S. U. B. (2022). QATTIQ JISM KRISTALLARINI O’STIRISH NAZARIYASI. Scientific Impulse, 1(3), 696-698.

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[1] Kittel, C. Introduction to Solid State Physics. 8th ed. Wiley, 2005.

[2] Ashcroft, N.W., Mermin, N.D. Solid State Physics. Harcourt College Publishers, 1976.

[3] Kronig, R. de L., Penney, W.G. Quantum Mechanics of Electrons in Crystal Lattices. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 1931, Vol. 130, pp. 499-513.

[4] Blatt, F.J. Physics of Electronic Conduction in Solids. McGraw-Hill, 1968.

[5] Ziman, J.M. Principles of the Theory of Solids. 2nd ed. Cambridge University Press, 1972.

[6] Rozikov, J., Akhmedov, B., Muminov, I., & Ruziboev, V. (2019). DIMENSIONALLY QUANTIZED SEMICONDUCTOR STRUCTURES. Scientific and Technical Journal of Namangan Institute of Engineering and Technology, 1(6), 58-63.

[7] Rustamovich, R. V., Yavkachovich, R. R., Forrux, K., & Arabboyevich, M. I. (2021). THEORETICAL ANALYSIS OF MULTIPHOTON INTERBAND ABSORPTION OF POLARIZED LIGHT IN CRYSTALS WITH A COMPLEX ZONE (PART 1). European science review, (3-4), 48-51.

[8] Muminov, I. A., & Muminova, M. (2023). QATTIQ JISMLARNING KRISTALL PANJARALARI. Oriental renaissance: Innovative, educational, natural and social sciences, 3(3), 1314-1317.

[9] Arabboyevich, M. I., & Nabijon o‘g, S. U. B. (2022). QATTIQ JISM KRISTALLARINI O’STIRISH NAZARIYASI. Scientific Impulse, 1(3), 696-698.