ТЕОРЕТИЧЕСКОЕ ИССЛЕДОВАНИЕ ВЛИЯНИЯ КВАНТОВОГО ОГРАНИЧЕНИЯ НА ЭНЕРГЕТИЧЕСКИЙ СПЕКТР ПОЛУПРОВОДНИКОВЫХ СФЕРИЧЕСКИХ КВАНТОВЫХ ТОЧЕК С ИСПОЛЬЗОВАНИЕМ ЧАСТИЦЫ В МОДЕЛИ ЛОВУШКИ

Authors

  • К.А. Корабоев

    Tashkent State Technical University named after Islam Karimov image/svg+xml

  • У.К. Сапаев

    Tashkent State Technical University named after Islam Karimov image/svg+xml

Keywords: Schrödinger equation, quantum dot, semiconductor, quantum particle in trap, electron and holes

Abstract

Using the particle model is studied in the trap, the effect of quantum limitation on the energy spectrum of spherical quantum dots CdSe, GaP, and GaAs. The energy levels of the free electrons in the conduction band and the holes in the valence band at the quantum dots have been shown to be discrete. It has also been shown that the energy between the two levels depends on the measurement of the quantum dots and increases with decreasing the size of the quantum dots. Our results show that as the radius of the limit point increases, the energy decreases, but never the zero mark.

References

1. Schaller and R. D., Klimov V. I. ―High Efficiency Carrier Multiplication in PbSe Nanocrystals: Implications for Solar Energy Conversion,‖ Physical Review Letters, Vol. 92, No. 18, 2004, Article ID 186601. doi:10.1103/PhysRevLett.92.186601

2. Wang С., Shim М. and Guyot-Sionnest Р. ―Electrochromic Nanocrystal Quantum Dots,‖ Science, Vol. 291, No. 5512, 2001, -Р. 2390. 2392. doi:10.1126/science.291.5512.2390

3. Martyniuk Р. and Rogalski А. ―Quantum-Dot Infrared Photodetectors: Status and Outlook,‖ Progress in Quantum Electronics, Vol. 32, No. 3-4, 2008, -Р. 89-120. doi:10.1016/j.pquantelec.2008.07.001

4. Lagatsky А.А., Leburn C.G., C. T. A. Brown, W. Sibbett, S. A. Zolotovskaya and E. U. Rafailov, ―Ultrashort-Pulse Lasers Pas- sively Mode Locked by Quantum-Dot-Based Saturable Absorbers,‖ Progress in Quantum Electronics, Vol. 34, N. 1, 2010, pp. 1- 45. doi:10.1016/j.pquantelec.2009.11.001

5. Sinclair J. and Dagotto Dr., ―An Introduction to Quantum Dots: Confinement, Synthesis, Artificial Atoms and Applications,‖ Solid State II Lecture Notes, University of Tennessee, Knoxville, 2009.

6. Michler Р. ―Single Quantum Dots: Fundamentals, Applications and New Concept, Physics and Astronomy Classification Scheme (PACS),‖ Springer-Verlag, Berlin, 2003.

7. Brus L.E., ―Electron-Electron and Electron-Hole Interactions in Small Semiconductor Crystallites: The Size Dependence of the Lowest Excited Electronic State,‖ Journal of Chemical Physics, Vol. 80, No. 9, 1984, p. 4403. doi:10.1063/1.447218

8. Kayanuma Y., ―Quantum-Size Effects of Interacting Electrons and Holes in Semiconductor Microcrystals with Spherical Shape,‖ Physical Review B, Vol. 38, No. 14, 1988, pp. 9797-9805. doi:10.1103/PhysRevB.38.9797

9. Kippeny T., Swafford L. A. and Rosnethal S. A. ―Semiconductor Nanocrystals: A Powerful Visual Aid for Introducing the Parti- cle in a Box,‖ Journal of Chemical Education, Vol. 79, No. 9, 2002, pp. 1094-1100. doi:10.1021/ed079p1094

10. Brus L.E. ―A Simple Model for the Ionization Potential, Electron Affinity and Aqueous Redox Potentials of Small Semiconduc- tor Crystallites,‖ Journal of Chemical Physics, Vol. 79, No. 11, 1983, pp. 5566-5571. doi:10.1063/1.445676

11. Harbold J. M. ―The Electronic and Optical Properties of Colloidal Lead Selenide Semiconductor Nanocrysta,‖ Ph.D. Disserta- tion, Cornell University, New York: 2005.