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

Authors

  • L. E. Lokot V.E. Lashkaryov Institute of Semiconductor Physics, Nat. Acad. of Sci. of Ukraine

DOI:

https://doi.org/10.15407/ujpe58.01.0056

Keywords:

Hartree–Fock approximation, electron-hole pair, wurtzite quantum well, Coulomb effects, lasers

Abstract

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.

References

<ol>
<li> N. Savage, Nature Photonics 1, 83 (2007).&nbsp;<a href="https://doi.org/10.1038/nphoton.2006.95">https://doi.org/10.1038/nphoton.2006.95</a></li>
<li> A. Khan, K. Balakrishnan, and T. Katona, Nature Photonics 2, 77 (2008).&nbsp;<a href="https://doi.org/10.1038/nphoton.2007.293">https://doi.org/10.1038/nphoton.2007.293</a></li>
<li> H. Kawanishi, M. Senuma, and T. Nukui, Appl. Phys. Lett. 89, 041126 (2006).&nbsp;<a href="https://doi.org/10.1063/1.2236792">https://doi.org/10.1063/1.2236792</a></li>
<li> H. Kawanishi, M. Senuma, M. Yamamoto, E. Niikura, and T. Nukui, Appl. Phys. Lett. 89, 081121 (2006).&nbsp;<a href="https://doi.org/10.1063/1.2338543">https://doi.org/10.1063/1.2338543</a></li>
<li> J. Shakya, K. Knabe, K.H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, Appl. Phys. Lett. 86, 091107 (2005).&nbsp;<a href="https://doi.org/10.1063/1.1875751">https://doi.org/10.1063/1.1875751</a></li>
<li> R.G. Banal, M. Funato, and Y. Kawakami, Phys. Rev. B. 79, 121308(R) (2009).</li>
<li> R.D. Meade, A.M. Rappe, K.D. Brommer, and J.D. Joannopoulos, J. Opt. Soc. Am. B 10, 328 (1993).&nbsp;<a href="https://doi.org/10.1364/JOSAB.10.000328">https://doi.org/10.1364/JOSAB.10.000328</a></li>
<li> S.H. Park, D. Ahn, and S.L. Chuang, IEEE J. Quantum Electron. 43, 1175 (2007).&nbsp;<a href="https://doi.org/10.1109/JQE.2007.905009">https://doi.org/10.1109/JQE.2007.905009</a></li>
<li> 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).&nbsp;<a href="https://doi.org/10.1063/1.2963029">https://doi.org/10.1063/1.2963029</a></li>
<li> 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).&nbsp;<a href="https://doi.org/10.1109/JSTQE.2009.2014395">https://doi.org/10.1109/JSTQE.2009.2014395</a></li>
<li> S.H. Park, D. Ahn, and J.W. Kim, Appl. Phys. Lett. 92, 171115 (2008).&nbsp;<a href="https://doi.org/10.1063/1.2920187">https://doi.org/10.1063/1.2920187</a></li>
<li> A.E. Romanov, T.J. Baker, S. Nakamura, J.S. Speck, and E.J.U. Group, J. Appl. Phys. 100, 023522 (2006).&nbsp;<a href="https://doi.org/10.1063/1.2218385">https://doi.org/10.1063/1.2218385</a></li>
<li> A.A. Yamaguchi, Appl. Phys. Lett. 94, 201104 (2009).&nbsp;<a href="https://doi.org/10.1063/1.3139080">https://doi.org/10.1063/1.3139080</a></li>
<li> H.H. Huang and Y.R.Wu, J. Appl. Phys. 106, 023106 (2009).&nbsp;<a href="https://doi.org/10.1063/1.3176964">https://doi.org/10.1063/1.3176964</a></li>
<li> M. Nido, Jpn. J. Appl. Phys., Part 2 34, L1513 (1995).&nbsp;<a href="https://doi.org/10.1143/JJAP.34.L1513">https://doi.org/10.1143/JJAP.34.L1513</a></li>
<li> S. Chichibu, T. Azuhata, T. Sota, H. Amano, and I. Akasaki, Appl. Phys. Lett. 70, 2085 (1997).&nbsp;<a href="https://doi.org/10.1063/1.118958">https://doi.org/10.1063/1.118958</a></li>
<li> 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).&nbsp;<a href="https://doi.org/10.1063/1.3174436">https://doi.org/10.1063/1.3174436</a></li>
<li> P.Y. Dang and Y.R. Wu, J. Appl. Phys. 108, 083108 (2010).&nbsp;<a href="https://doi.org/10.1063/1.3498805">https://doi.org/10.1063/1.3498805</a></li>
<li> S. Fujita, T. Takagi, H. Tanaka, and S. Fujita, Phys. Status Solidi B 241, 599 (2004).&nbsp;<a href="https://doi.org/10.1002/pssb.200304153">https://doi.org/10.1002/pssb.200304153</a></li>
<li> 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).&nbsp;<a href="https://doi.org/10.1063/1.2150266">https://doi.org/10.1063/1.2150266</a></li>
<li> S. Sasa, M. Ozaki, K. Koike, M. Yano, and M. Inoue, Appl. Phys. Lett 89, 053502 (2006).&nbsp;<a href="https://doi.org/10.1063/1.2261336">https://doi.org/10.1063/1.2261336</a></li>
<li> K. Koike, I. Nakashima, K. Hashimoto, S. Sasa, M. Inoue, and M. Yano, Appl. Phys. Lett 87, 112106 (2005).&nbsp;<a href="https://doi.org/10.1063/1.2045558">https://doi.org/10.1063/1.2045558</a></li>
<li> S.-H. Park and S.-L. Chuang, J. Appl. Phys. 72, 3103 (1998).</li>
<li> M. Willatzen, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 100 (2001).&nbsp;<a href="https://doi.org/10.1109/58.895916">https://doi.org/10.1109/58.895916</a></li>
<li> B.A. Auld, Acoustic Fields and Waves in Solids (Wiley, New York, 1973).</li>
<li> L. Duggen and M.Willatzen, Phys. Rev. B 82, 205303 (2010).&nbsp;<a href="https://doi.org/10.1103/PhysRevB.82.205303">https://doi.org/10.1103/PhysRevB.82.205303</a></li>
<li> M. Lindberg and S. W. Koch, Phys. Rev. B. 38, 3342 (1988).&nbsp;<a href="https://doi.org/10.1103/PhysRevB.38.3342">https://doi.org/10.1103/PhysRevB.38.3342</a></li>
<li> W.W. Chow, S.W. Koch, and M. Sargent III, Semiconductor Laser Physics (Springer, New York, 1994).&nbsp;<a href="https://doi.org/10.1007/978-3-642-61225-1">https://doi.org/10.1007/978-3-642-61225-1</a></li>
<li> W.W. Chow, M. Kira, and S.W. Koch, Phys. Rev. B. 60, 1947 (1999).&nbsp;<a href="https://doi.org/10.1103/PhysRevB.60.1947">https://doi.org/10.1103/PhysRevB.60.1947</a></li>
<li> W.W. Chow and M. Kneissl, J. Appl. Phys. 98, 114502 (2005).&nbsp;<a href="https://doi.org/10.1063/1.2128495">https://doi.org/10.1063/1.2128495</a></li>
<li> G.L. Bir and G.E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, New York, 1974).</li>
<li> R.S. Knox, Theory of Excitons (New York, Academic Press, 1963).</li>
<li> L.O. Lokot, Ukr. J. Phys. 54, 963 (2009).</li>
<li> L.O. Lokot, Ukr. J. Phys. 57, 12 (2012).</li>
<li> M. Gell-Mann and K.A. Brueckner, Phys. Rev. 106, 364 (1956).&nbsp;<a href="https://doi.org/10.1103/PhysRev.106.364">https://doi.org/10.1103/PhysRev.106.364</a></li>
<li> C. Kittel, Quantum Theory of Solids (Wiley, New York, 1963).</li>
<li> S. Raimes, Many-Electron Theory (North-Holland, Amsterdam, 1972).</li>
<li> R.D. Mattuck, A Guide to Feynman Diagrams in The Many-Body Problem (McGraw-Hill, New York, 1967).</li>
<li> H. Haug and S. Schmitt-Rink, Prog. Quant. Electr. 9, 3 (1984).&nbsp;<a href="https://doi.org/10.1016/0079-6727(84)90026-0">https://doi.org/10.1016/0079-6727(84)90026-0</a>
</ol>

Published

2018-10-05

How to Cite

Lokot, L. E. (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

Issue

Section

Solid matter