Hartree–Fock Problem of an Electron-Hole Pair in the Quantum Well GaN

  • L. E. Lokot V.E. Lashkaryov Institute of Semiconductor Physics, Nat. Acad. of Sci. of Ukraine
Keywords: Hartree–Fock approximation, electron-hole pair, wurtzite quantum well, Coulomb effects, lasers


We present microscopic calculations of the absorption spectra for GaN=AlxGa1 xN quantum well systems. Whereas the quantum well structures with the parabolic law of dispersion exhibit the usual bleaching of an exciton resonance without shifting a spectral position, the significant red-shift of an exciton peak is found with increasing the electron-hole gas density for a wurtzite quantum well. The energy of the exciton resonance for a wurtzite quantum well is found. The obtained results can be explained by the influence of the valence band structure on quantum confinement effects. The optical gain spectrum in the Hartree–Fock approximation and the Sommerfeld enhancement are calculated. A red shift of the gain spectrum in the Hartree–Fock approximation with respect to the Hartree gain spectrum is found.


  1. N. Savage, Nature Photonics 1, 83 (2007). https://doi.org/10.1038/nphoton.2006.95

  2. A. Khan, K. Balakrishnan, and T. Katona, Nature Photonics 2, 77 (2008). https://doi.org/10.1038/nphoton.2007.293

  3. H. Kawanishi, M. Senuma, and T. Nukui, Appl. Phys. Lett. 89, 041126 (2006). https://doi.org/10.1063/1.2236792

  4. H. Kawanishi, M. Senuma, M. Yamamoto, E. Niikura, and T. Nukui, Appl. Phys. Lett. 89, 081121 (2006). https://doi.org/10.1063/1.2338543

  5. J. Shakya, K. Knabe, K.H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, Appl. Phys. Lett. 86, 091107 (2005). https://doi.org/10.1063/1.1875751

  6. R.G. Banal, M. Funato, and Y. Kawakami, Phys. Rev. B. 79, 121308(R) (2009).

  7. R.D. Meade, A.M. Rappe, K.D. Brommer, and J.D. Joannopoulos, J. Opt. Soc. Am. B 10, 328 (1993). https://doi.org/10.1364/JOSAB.10.000328

  8. S.H. Park, D. Ahn, and S.L. Chuang, IEEE J. Quantum Electron. 43, 1175 (2007). https://doi.org/10.1109/JQE.2007.905009

  9. M.F. Schubert, J. Xu, J.K. Kim, E.F. Schubert, M.H. Kim, S. Yoon, S.M. Lee, C. Sone, T. Sakong, and Y. Park, Appl. Phys. Lett. 93, 041102 (2008). https://doi.org/10.1063/1.2963029

  10. M.H. Kim, W. Lee, D. Zhu, M.F. Schubert, J.K. Kim, E.F. Schubert, and Y. Park, IEEE J. Sel. Top. Quantum Electron. 15, 1122 (2009). https://doi.org/10.1109/JSTQE.2009.2014395

  11. S.H. Park, D. Ahn, and J.W. Kim, Appl. Phys. Lett. 92, 171115 (2008). https://doi.org/10.1063/1.2920187

  12. A.E. Romanov, T.J. Baker, S. Nakamura, J.S. Speck, and E.J.U. Group, J. Appl. Phys. 100, 023522 (2006). https://doi.org/10.1063/1.2218385

  13. A.A. Yamaguchi, Appl. Phys. Lett. 94, 201104 (2009). https://doi.org/10.1063/1.3139080

  14. H.H. Huang and Y.R.Wu, J. Appl. Phys. 106, 023106 (2009). https://doi.org/10.1063/1.3176964

  15. M. Nido, Jpn. J. Appl. Phys., Part 2 34, L1513 (1995). https://doi.org/10.1143/JJAP.34.L1513

  16. S. Chichibu, T. Azuhata, T. Sota, H. Amano, and I. Akasaki, Appl. Phys. Lett. 70, 2085 (1997). https://doi.org/10.1063/1.118958

  17. D. Fu, R. Zhang, B. Wang, Z. Zhang, B. Liu, Z. Xie, X. Xiu, H. Lu, Y. Zheng, and G. Edwards, J. Appl. Phys. 106, 023714 (2009). https://doi.org/10.1063/1.3174436

  18. P.Y. Dang and Y.R. Wu, J. Appl. Phys. 108, 083108 (2010). https://doi.org/10.1063/1.3498805

  19. S. Fujita, T. Takagi, H. Tanaka, and S. Fujita, Phys. Status Solidi B 241, 599 (2004). https://doi.org/10.1002/pssb.200304153

  20. W.J. Fan, J.B. Xia, P.A. Agus, S.T. Tan, S.F. Yu, and X.W. Sun, J. Appl. Phys. 99, 013702 (2006). https://doi.org/10.1063/1.2150266

  21. S. Sasa, M. Ozaki, K. Koike, M. Yano, and M. Inoue, Appl. Phys. Lett 89, 053502 (2006). https://doi.org/10.1063/1.2261336

  22. K. Koike, I. Nakashima, K. Hashimoto, S. Sasa, M. Inoue, and M. Yano, Appl. Phys. Lett 87, 112106 (2005). https://doi.org/10.1063/1.2045558

  23. S.-H. Park and S.-L. Chuang, J. Appl. Phys. 72, 3103 (1998).

  24. M. Willatzen, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 100 (2001). https://doi.org/10.1109/58.895916

  25. B.A. Auld, Acoustic Fields and Waves in Solids (Wiley, New York, 1973).

  26. L. Duggen and M.Willatzen, Phys. Rev. B 82, 205303 (2010). https://doi.org/10.1103/PhysRevB.82.205303

  27. M. Lindberg and S. W. Koch, Phys. Rev. B. 38, 3342 (1988). https://doi.org/10.1103/PhysRevB.38.3342

  28. W.W. Chow, S.W. Koch, and M. Sargent III, Semiconductor Laser Physics (Springer, New York, 1994). https://doi.org/10.1007/978-3-642-61225-1

  29. W.W. Chow, M. Kira, and S.W. Koch, Phys. Rev. B. 60, 1947 (1999). https://doi.org/10.1103/PhysRevB.60.1947

  30. W.W. Chow and M. Kneissl, J. Appl. Phys. 98, 114502 (2005). https://doi.org/10.1063/1.2128495

  31. G.L. Bir and G.E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, New York, 1974).

  32. R.S. Knox, Theory of Excitons (New York, Academic Press, 1963).

  33. L.O. Lokot, Ukr. J. Phys. 54, 963 (2009).

  34. L.O. Lokot, Ukr. J. Phys. 57, 12 (2012).

  35. M. Gell-Mann and K.A. Brueckner, Phys. Rev. 106, 364 (1956). https://doi.org/10.1103/PhysRev.106.364

  36. C. Kittel, Quantum Theory of Solids (Wiley, New York, 1963).

  37. S. Raimes, Many-Electron Theory (North-Holland, Amsterdam, 1972).

  38. R.D. Mattuck, A Guide to Feynman Diagrams in The Many-Body Problem (McGraw-Hill, New York, 1967).

  39. H. Haug and S. Schmitt-Rink, Prog. Quant. Electr. 9, 3 (1984). https://doi.org/10.1016/0079-6727(84)90026-0
How to Cite
Lokot, L. (2018). Hartree–Fock Problem of an Electron-Hole Pair in the Quantum Well GaN. Ukrainian Journal of Physics, 58(1), 56. https://doi.org/10.15407/ujpe58.01.0056
Solid matter