Abstract
The electron-hole exchange interaction in semiconductors is analyzed in the framework of the empirical tight-binding method. It is demonstrated that intra-atomic and interatomic contributions to the long-range exchange interaction enter in an inequivalent way. In particular, for the Γ6×Γ7 exciton in a spherical nanocrystal with a cubic lattice, the dipole-dipole contribution associated only with the intra-atomic (or intra-site) transitions does not lead to singlet-triplet splitting of the exciton level. The interatomic transitions, for example, anion-to-cation transitions between the nearest neighbors in binary semiconductor compounds, determine the so-called monopole-monopole contribution to the exchange splitting of the Γ6×Γ7 exciton, and this contribution does not vanish in a spherical nanocrystal.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. E. Pikus and G. L. Bir, Zh. Éksp. Teor. Fiz. 60, 195 (1971) [Sov. Phys. JETP 33, 108 (1971)]; Zh. Éksp. Teor. Fiz. 62, 324 (1972) [Sov. Phys. JETP 35, 174 (1972)].
G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Nauka, Moscow, 1972; Wiley, New York, 1975).
V. A. Kiselev and A. G. Zhilich, Fiz. Tverd. Tela (Leningrad) 14, 1438 (1972) [Sov. Phys. Solid State 14, 1233 (1972)]; Fiz. Tekh. Poluprovodn. (Leningrad) 8, 641 (1974) [Sov. Phys. Semicond. 8, 411 (1974)].
M. M. Denisov and V. P. Makarov, Phys. Status Solidi B 56, 9 (1973).
F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids (Pergamon, New York, 1975; Nauka, Moscow, 1982).
K. Cho, Phys. Rev. B 10, 4463 (1976).
U. Rössler and H.-R. Trebin, Phys. Rev. B 23, 1961 (1981).
L. C. Andreani, in Confined Electrons and Photons, Ed. by E. Burstein and C. Weisbuch (Plenum, New York, 1995).
S. V. Goupalov, E. L. Ivchenko, and A. V. Kavokin, Superlattices Microstruct. 23, 1205 (1998).
S. V. Goupalov and E. L. Ivchenko, J. Cryst. Growth 184/185, 393 (1998); Acta Phys. Pol. A 94, 341 (1998).
S. V. Goupalov, E. L. Ivchenko, and A. V. Kavokin, Zh. Éksp. Teor. Fiz. 113, 703 (1998) [JETP 86, 388 (1998)].
S. V. Goupalov and E. L. Ivchenko, Fiz. Tverd. Tela (St. Petersburg) 42, 1976 (2000) [Phys. Solid State 42, 2030 (2000)].
T. Takagahara, Phys. Rev. B 47, 4569 (1993); Phys. Rev. B 60, 2638 (1999).
T. Takagahara, J. Lumin. 87–89, 308 (2000); Phys. Rev. B 62, 16840 (2000).
M. Nirmal, D. J. Norris, M. Kuno, et al., Phys. Rev. Lett. 75, 3728 (1995).
D. J. Norris, Al. L. Efros, M. Rosen, and M. G. Bawendi, Phys. Rev. B 53, 16347 (1996).
Al. L. Efros, M. Rosen, M. Kuno, et al., Phys. Rev. B 54, 4843 (1996).
P. Vogl, H. P. Hjalmarson, and J. D. Dow, J. Phys. Chem. Solids 44, 365 (1983).
E. L. Ivchenko, A. Yu. Kaminski, and U. Rössler, Phys. Rev. B 54, 5852 (1996).
T. B. Boykin, Phys. Rev. B 56, 9613 (1997).
E. L. Ivchenko, A. A. Toropov, and P. Voisin, Fiz. Tverd. Tela (St. Petersburg) 40, 1925 (1998) [Phys. Solid State 40, 1748 (1998)].
J.-M. Jancu, R. Scholz, F. Beltram, and F. Bassani, Phys. Rev. B 57, 6493 (1998).
Y.-C. Chang and J. N. Schulman, Phys. Rev. B 31, 2069 (1985).
Y.-C. Chang and D. E. Aspnes, Phys. Rev. B 41, 12002 (1990).
G. D. Sanders and Y.-C. Chang, Phys. Rev. B 45, 9202 (1992).
Z. Xu, Solid State Commun. 76, 1143 (1990).
L. M. Ramaniah and S. V. Nair, Phys. Rev. B 47, 7132 (1993).
L. C. Lew Yan Voon and L. R. Ram-Mohan, Phys. Rev. B 47, 15500 (1993).
M. Graf and P. Vogl, Phys. Rev. B 51, 4940 (1995).
B. Koopmans, P. V. Santos, and M. Cardona, Phys. Status Solidi B 205, 419 (1998).
T. DumitricĂ, J. S. Graves, and R. E. Allen, Phys. Rev. B 58, 15340 (1998).
A. V. Platonov, V. P. Kochereshko, E. L. Ivchenko, et al., Phys. Rev. Lett. 83, 3546 (1999).
A. Franceschetti, L. W. Wang, H. Fu, and A. Zunger, Phys. Rev. B 58, 13367 (1998).
D. R. Yakovlev, E. L. Ivchenko, V. P. Kochereshko, et al., Phys. Rev. B 61, 2421 (2000).
M. Schmidt, M. Grün, S. Petillon, et al., Appl. Phys. Lett. 77, 85 (2000).
Author information
Authors and Affiliations
Additional information
__________
Translated from Fizika Tverdogo Tela, Vol. 43, No. 10, 2001, pp. 1791–1798.
Original Russian Text Copyright © 2001 by Goupalov, Ivchenko.
Rights and permissions
About this article
Cite this article
Goupalov, S.V., Ivchenko, E.L. A tight-binding representation of electron-hole exchange interaction in semiconductors. Phys. Solid State 43, 1867–1875 (2001). https://doi.org/10.1134/1.1410624
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.1410624