Calculation of the Energy Spectrum of Quantum Particle in Double Potential Pit

A. S. Lazarenko, K. M. Tikhovod, S. S. Kovachov, I. T. Bohdanov, Y. O. Sychikova

Berdyansk State Pedagogical University, 4 Shmidt Str., UA-71100 Berdyansk, Ukraine

Received: 12.06.2022; final version - 11.07.2022. Download: PDF

The problem of quantum particle in infinitely deep potential pit with an internal potential barrier of finite height is solved. The solution is performed in a simple algorithmic approach, which allows you to use the result in the study of semiconductor nanostructures. The real heterostructure corresponding to this model should look like thin layer of wideband semiconductor placed between two slightly thicker layers of narrowband semiconductor. To ensure the ‘infinite depth’ of the potential pit, layers of conductor must be applied to the outer side surfaces of the triple semiconductor heterostructure and negative electric potential must be applied. Another option for the practical implementation of the model can be done by placing two electrons in one potential pit. In this case, the pit is a local space, at the boundary of which negative electric potential is applied. The internal potential barrier arises due to the Coulomb interaction of electrons. An example of such a structure is a nanopore on the surface, or in the volume of a metal sample.

Key words: quantum particle, potential pit, heterostructure, potential barrier.

URL: https://mfint.imp.kiev.ua/en/abstract/v44/i08/0963.html

DOI: https://doi.org/10.15407/mfint.44.08.0963

PACS: 71.15.-m, 71.20.Nr, 71.30.+h, 73.20.-r, 73.43.-f

Citation: A. S. Lazarenko, K. M. Tikhovod, S. S. Kovachov, I. T. Bohdanov, and Y. O. Sychikova, Calculation of the Energy Spectrum of Quantum Particle in Double Potential Pit, Metallofiz. Noveishie Tekhnol., 44, No. 8: 963—974 (2022)


REFERENCES
  1. S. H. Lee, S. W. Lee, T. Oh, S. H. Petrosko, C. A. Mirkin, and J. W. Jang, Nano Lett., 18, Iss. 1: 109 (2018). Crossref
  2. Y. Suchikova, S. Vambol, V. Vambol, and N. Mozaffari, J. Achievements in Materials and Manufacturing Engineering, 92, Iss. 1-2: 19 (2019). Crossref
  3. Y. Lee, B. Gupta, H. H. Tan, C. Jagadish, J. Oh, and S. Karuturi, STAR Protocols, 3, Iss. 1: 101015 (2022). Crossref
  4. Y. Lee, I. Yang, H. H. Tan, C. Jagadish, and S. K. Karuturi, ACS Appl. Mater. Interfaces, 12, Iss. 32: 36380 (2020). Crossref
  5. Q. Li, L. Xu, K. W. Luo, L. L. Wang, and X. F. Li, Mater. Chem. Phys., 216: 64 (2018). Crossref
  6. M. Zhou, S. Wang, P. Yang, Z. Luo, R. Yuan, A. M. Asiri, and X. Wang, Chemistry-A European J., 24, Iss. 69: 18529 (2018). Crossref
  7. T. P. Weiss, B. Bissig, T. Feurer, R. Carron, S. Buecheler, and A. N. Tiwari, Scientific Reports, 9: 5389 (2019). Crossref
  8. I. Vladimirov, M. Kellermeier, T. Geßner, Z. Molla, S. Grigorian, U. Pietsch, and R. T. Weitz, Nano Lett., 18, Iss. 1: 9 (2018). Crossref
  9. Y. B. Lyanda-Geller, Solid State Communications, 352: 114815 (2022). Crossref
  10. B. Aragie, M. Bekele, and G. Pellicane, Pramana, 96: 59 (2022). Crossref
  11. K. S. Thygesen, 2D Mater., 4: 022004 (2017). Crossref
  12. R. S. Mong, D. J. Clarke, J. Alicea, N. H. Lindner, P. Fendley, C. Nayak, and M. P. Fisher, Phys. Rev. X, 4: 011036 (2014). Crossref
  13. Y. Suchikova, A. Lazarenko, S. Kovachov, Z. Karipbaev, and A. I. Popov, Proc. 16th Int. Conf. Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (Feb. 22-26, 2022), p. 410. Crossref
  14. A. Usseinov, Z. Koishybayeva, A. Platonenko, V. Pankratov, Y. Suchikova, A. Akilbekov, M. Zdorovets, J. Purans, and A. I. Popov, Materials, 14, Iss. 23: 7384 (2021). Crossref
  15. Y. Suchikova, Handbook of Nanoelectrochemistry: Electrochemical Synthesis Methods, Properties, and Characterization Techniques (Eds. Mahmood Aliofkhazraei and Abdel Salam Hamdy Makhlouf) (Springer Cham: 2016), p. 283 (2016). Crossref
  16. Y. A. Suchikova, V. V. Kidalov, and G. A. Sukach, J. Nano- Electron. Phys., 1, No. 4: 111 (2009).
  17. Z. T. Karipbayev, K. Kumarbekov, I. Manika, Y. Suchikova, and A. I. Popov, phys. status solidi (b), (2022). Crossref
  18. Y. O. Suchikova, S. S. Kovachov, G. O. Shishkin, V. V. Bondarenko, and I. T. Bogdanov, Archives of Materials Science and Engineering, 107, No. 2: 72 (2021). Crossref
  19. Y. Bai, M. Hao, S. Ding, P. Chen, and L. Wang, Adv. Mater., 34, Iss. 4: 2105958 (2022). Crossref
  20. R. Zheng, J. Ueda, K. Shinozaki, and S. Tanabe, Chem. Mater., 34, Iss. 4: 1599 (2022). Crossref
  21. J. A. Suchikova, V. V. Kidalov, and G. A. Sukach, ECS Transactions, 25, No. 24: 59 (2009). Crossref
  22. K. J. Kim, Surface and Interface Analysis, 54, Iss. 4: 405 (2022). Crossref
  23. D. E. Tsurikov, Appl. Phys. A, 128: 3 (2022). Crossref
  24. U. Rogulis, G. Krieke, A. Antuzevics, A. Fedotovs, D. Berzins, A. I. Popov, and V. Pankratov, Opt. Mater., 129: 112545 (2022). Crossref
  25. H. Klym, I. Karbovnyk, A. Luchechko, Y. Kostiv, V. Pankratova, and A. I. Po-pov, Crystals, 11, Iss. 12: 1515 (2021). Crossref
  26. O. I. Aksimentyeva, V. P. Savchyn, V. P. Dyakonov, S. Piechota, Y. Y. Horbenko, I. Y. Opainych, and H. Szymczak, Molecular Crystals and Liquid Crystals, 590, Iss. 1: 35 (2014). Crossref
  27. C. Yi and E. Crosson, Quantum Information, 8: 37 (2022). Crossref
  28. C. H. T. Santos and V. Pereira, Digital Signal Processing, 120: 103229 (2022). Crossref
  29. B. Tariq and X. Hu, Quantum Information, 8: 53 (2022). Crossref
  30. P. Garbaczewski, V. A. Stephanovich, and G. Engel, New J. Phys., 24: 033052 (2022). Crossref
  31. D. L. Aronstein and C. R. Stroud, American J. Phys., 68: 943 (2000). Crossref