, Volume 52, Issue 14, pp 1791–1794 | Cite as

Classification of Energy States of the Exciton in Square Quantum Well

  • P. A. BelovEmail author


The energy states of the exciton in a single square GaAs-based quantum well are obtained from a numerical solution of the three-dimensional Schrödinger equation for the envelope of the exciton wave function. This equation is based on the exciton effective energy operator with a spherical approximation of the Luttinger Hamiltonian. The calculated states are classified based on the types of one-dimensional functions for the factorized form of the wave function. The upper limit for the energies of the exciton states in a quantum well is confirmed by the complex scaling method.



The work is supported by RFBR (grants nos. 16-02-00245, 18-32-00568). The calculations were carried out using the facilities of the SPbU Resource Center “Computational Center of SPbU”.


  1. 1.
    Zh. I. Alferov, Semiconductors 32, 1 (1998).ADSCrossRefGoogle Scholar
  2. 2.
    L. V. Butov, A. Imamoglu, A. V. Mintsev, et al., Phys. Rev. B 59, 1625 (1999).ADSCrossRefGoogle Scholar
  3. 3.
    E. L. Ivchenko, Optical Spectroscopy of Semiconductor Nanostructures (Alpha Science, Harrow, 2005).Google Scholar
  4. 4.
    S. V. Poltavtsev and B. V. Stroganov, Phys. Solid State 52, 1899 (2010).ADSCrossRefGoogle Scholar
  5. 5.
    S. V. Poltavtsev, Yu. P. Efimov, Yu. K. Dolgikh, et al., Solid State Commun. 199, 47 (2014).ADSCrossRefGoogle Scholar
  6. 6.
    A. V. Trifonov, S. N. Korotan, A. S. Kurdyubov, et al., Phys. Rev. B 91, 115307 (2015).ADSCrossRefGoogle Scholar
  7. 7.
    D. B. T. Thoai, R. Zimmermann, M. Grundmann, and D. Bimberg, Phys. Rev. B 42, 5906(R) (1990).Google Scholar
  8. 8.
    B. Gerlach, J. Wüsthoff, M. O. Dzero, and M. A. Smondyrev, Phys. Rev. B 58, 10568 (1998).ADSCrossRefGoogle Scholar
  9. 9.
    K. Sivalertporn, L. Mouchliadis, A. L. Ivanov, et al., Phys. Rev. B 85, 045207 (2012).ADSCrossRefGoogle Scholar
  10. 10.
    E. S. Khramtsov, P. A. Belov, P. S. Grigoryev, et al., J. Appl. Phys. 119, 184301 (2016).ADSCrossRefGoogle Scholar
  11. 11.
    P. A. Belov and E. S. Khramtsov, J. Phys.: Conf. Ser. 816, 012018 (2017).Google Scholar
  12. 12.
    P. A. Belov, Semiconductors 52, 551 (2018).ADSCrossRefGoogle Scholar
  13. 13.
    A. A. Samarskii, The Theory of Difference Schemes (Nauka, Moscow, 1989) [in Russian].Google Scholar
  14. 14.
    N. Moiseyev, Phys. Rep. 302, 212 (1998).ADSCrossRefGoogle Scholar
  15. 15.
    C. W. McCurdy and F. Martin, J. Phys. B: At. Mol. Opt. Phys. 37, 917 (2004).ADSCrossRefGoogle Scholar
  16. 16.
    P. A. Belov, V. A. Gradusov, M. V. Volkov, et al., Few-Body Syst. 58, 114 (2017).ADSCrossRefGoogle Scholar
  17. 17.
    J. M. Luttinger, Phys. Rev. 102, 1030 (1956).ADSCrossRefGoogle Scholar
  18. 18.
    P. A. Belov, E. R. Nugumanov, and S. L. Yakovlev, J. Phys.: Conf. Ser. 929, 012035 (2017).Google Scholar
  19. 19.
    I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).ADSCrossRefGoogle Scholar
  20. 20.
    Y. Chen, N. Maharjan, Z. Liu, et al., J. Appl. Phys. 121, 103101 (2017).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Department of Computational Physics, St. Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations