Bulletin of the Korean Chemical Society

Korean Chemical Society (대한화학회)
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On the Size of Quantum Dots with Bound Hydrogenic Impurity States

  • Sun, Ho-Sung (Department of Chemistry, Sungkyunkwan University)
  • Published : 2009.02.20
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Abstract

Some particular bound state energies of an electron, under Coulomb potential field, confined in a two-dimensional circle and a three-dimensional sphere are analytically derived. The derivation shows that the electron cannot be bound in a negative energy state when the circle (or sphere) is smaller than a certain critical size. The critical size dependency on the strength of Coulomb potential and the angular momentum of the electron is also analytically derived. This system mimics quantum dots. Therefore the derivation provides new information on a minimum critical size of quantum dots with hydrogenic impurity.

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References

  1. Goff, S. L.; Stébé, B. J. Phys. B 1992, 25, 5261 https://doi.org/10.1088/0953-4075/25/24/007
  2. Jacak, L.; Hawrylak, P.; Wójs, A. Quantum Dots; Springer: Berlin, 1997
  3. Bimberg, D.; Grundmann, M.; Ledentsov, N. N. Quantum Dot Heterostructures; Wiley: New York, 1998
  4. Chuu, D. S.; Hsiao, C. M.; Mei, W. N. Phys. Rev. B 1992, 46, 3898 https://doi.org/10.1103/PhysRevB.46.3898
  5. Zrenner, A. J. Chem. Phys. 2000, 112, 7790 https://doi.org/10.1063/1.481384
  6. Keren, K.; Stern, A.; Sivan, U. Eur. Phys. J. B 2000, 18, 311 https://doi.org/10.1007/s100510070063
  7. Yoffe, A. D. Adv. Phys. 2001, 50, 1
  8. Varshni, Y. P. Superlatt. Microstruc. 2001, 29, 233 https://doi.org/10.1006/spmi.2000.0963
  9. Reimann, S. M.; Manninen, M. Rev. Mod. Phys. 2002, 74, 1283 https://doi.org/10.1103/RevModPhys.74.1283
  10. Yi, H. S.; Lee, H. R.; Sohn, K. S. Phys. Rev. A 1994, 49, 3277 https://doi.org/10.1103/PhysRevA.49.3277
  11. Mal'shukov, A. G.; Brataas, A.; Chao, K. A. Phys. Rev. B 1995, 51, 7669 https://doi.org/10.1103/PhysRevB.51.7669
  12. Blaschke, J.; Brack, M. Phys. Rev. A 1997, 56, 182 https://doi.org/10.1103/PhysRevA.56.182
  13. Maksym, P. A. Physica B 1998, 249, 233 https://doi.org/10.1016/S0921-4526(98)00105-7
  14. Klama, S.; Rossler, U. J. Phys.: Condens. Matt. 1998, 10, 3411 https://doi.org/10.1088/0953-8984/10/15/016
  15. Hirose, K.; Wingreen, N. S. Phys. Rev. B 1999, 59, 4604 https://doi.org/10.1103/PhysRevB.59.4604
  16. Pino, R. Eur. Phys. J. B 2000, 13, 723 https://doi.org/10.1007/s100510050091
  17. Adamowski, J.; Sobkowicz, M.; Szafran, B.; Bednarek, S. Phys. Rev. B 2000, 62, 4234 https://doi.org/10.1103/PhysRevB.62.4234
  18. Varshni, Y. P. Superlatt. Microstruc. 2001, 30, 253 https://doi.org/10.1006/spmi.2001.1012
  19. Sinha, A.; Roychoudhury, R.; Varshni, Y. P. Physica B 2003, 325, 214 https://doi.org/10.1016/S0921-4526(02)01527-2
  20. Xu, T.; Cao, Z.; Ou, Y.; Shen, Q. Phys. Lett. A 2005, 341, 308 https://doi.org/10.1016/j.physleta.2005.04.091
  21. Main, J. Phys. Rep. 1999, 316, 233 https://doi.org/10.1016/S0370-1573(98)00131-8
  22. Friedrich, H.; Trost, J. Phys. Rep. 2004, 397, 359 https://doi.org/10.1016/j.physrep.2004.04.001
  23. Louk, J. D.; Galbraith, H. W. Rev. Mod. Phys. 1976, 48, 69 https://doi.org/10.1103/RevModPhys.48.69
  24. Abramowitz, M.; Stegun, I. A. Handbook of Mathematical Functions; Wiley: New York, 1972
  25. Cooper, F.; Khare, A.; Sukhatme, U. P. Phys. Rep. 1995, 251, 267 https://doi.org/10.1016/0370-1573(94)00080-M
  26. Sun, H. Phys. Lett. A 2005, 338, 309 https://doi.org/10.1016/j.physleta.2005.02.054
  27. Sun, H. Bull. Korean Chem. Soc. 2006, 27, 515 https://doi.org/10.5012/bkcs.2006.27.4.515
  28. Sun, H. Bull. Korean Chem. Soc. 2007, 28, 408 https://doi.org/10.5012/bkcs.2007.28.3.408
  29. Sun, H. Bull. Korean Chem. Soc. 2008, 29, 85 https://doi.org/10.5012/bkcs.2008.29.1.085