Abstract

CdSe is used as a prototype to show the implications of valence-band degeneracy for the optical properties of strongly quantum-confined nanocrystals. Absorption spectra and photoluminescence spectra obtained under intermediate and strong pulsed excitation show the presence of new structures. The energy levels for the electron and the hole are calculated with the spherical confinement, the nonparabolicity of the conduction band, and the valence band degeneracy taken into account. The oscillator strengths of the dipole-allowed transitions are also calculated. This model is found to be in good agreement with the experimental observations, which originate mainly from the quantization of the energy spectrum of holes with due account given to valence-band degeneracy.

© 1993 Optical Society of America

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Errata

A. I. Ekimov, F. Hache, M. C. Schanne-Klein, D. Ricard, C. Flytzanis, I. A. Kudryavtsev, T. V. Yazeva, A. V. Rodina, and Al. L. Efros, "Absorption and intensity-dependent photoluminescence measurements on CdSe quantum dots: assignment of the first electronic transitions: erratum," J. Opt. Soc. Am. B 11, 524- 524 (1994)
https://www.osapublishing.org/josab/abstract.cfm?uri=josab-11-3-524

References

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  1. A. I. Ekimov, A. A. Onushchenko, JETP Lett. 34, 345 (1981); JETP Lett. 40, 1137 (1984).
  2. Al. L. Efros, A. L. Efros, Sov. Phys. Semicond. 16, 772 (1982).
  3. L. E. Brus, J. Chem. Phys. 80, 4403 (1984).
    [CrossRef]
  4. R. Rossetti, R. Hull, J. M. Gibson, L. E. Brus, J. Chem. Phys. 82, 552 (1985).
    [CrossRef]
  5. H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
    [CrossRef]
  6. A. I. Ekimov, Al. L. Efros, M. G. Ivanov, A. A. Onushchenko, S. K. Shumilov, Solid State Commun. 69, 565 (1989).
    [CrossRef]
  7. Y. Z. Hu, M. Lindberg, S. W. Koch, Phys. Rev. B 42, 1713 (1990).
    [CrossRef]
  8. J. M. Luttinger, W. Kohn, Phys. Rev. 97, 869 (1955); J. M. Luttinger, Phys. Rev. 102, 1030 (1956); see also N. O. Lipari, A. Baldereschi, Phys. Rev. Lett. 25, 1660 (1971).
    [CrossRef]
  9. A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, Al. L. Efros, Sov. Phys. JETP 88, 891 (1985).
  10. Al. L. Efros, A. V. Rodina, Solid State Commun. 72, 645 (1989).
    [CrossRef]
  11. G. B. Grigoryan, E. M. Kazaryan, Al. L. Efros, T. V. Yazeva, Sov. Phys. Solid State 32, 1031 (1990).
  12. J. B. Xia, Phys. Rev. B 40, 8500 (1989).
    [CrossRef]
  13. A. I. Ekimov, Phys. Scr. T39, 217 (1991).
    [CrossRef]
  14. D. I. Chepic, Al. L. Efros, A. I. Ekimov, M. G. Ivanov, V. A. Kharchenko, I. A. Kudryavtsev, T. V. Yazeva, J. Lumin. 47, 113 (1990).
    [CrossRef]
  15. R. L. Aggarwal, in Semiconductors and Semimetals, R. K. Willardson, A. C. Beer, eds. (Academic, New York, 1972), Vol. 9, p. 151.
    [CrossRef]
  16. V. I. Sheka, D. I. Sheka, Sov. Phys. JETP 24, 975 (1967).
  17. G. B. Grigoryan, A. V. Rodina, Al. L. Efros, Sov. Phys. Solid State 32, 2037 (1990).
  18. C. Hermann, C. Weisbuch, in Optical Orientation, F. Meier, B. P. Zakharchenya, eds. (Elsevier, Amsterdam, 1984), p. 443.
  19. D. W. Hall, N. F. Borrelli, J. Opt. Soc. Am. B 5, 1650 (1988).
    [CrossRef]
  20. N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, M. Lindberg, IEEE J. Quantum Electron. 25, 2516 (1989).
    [CrossRef]
  21. M. G. Bawendi, W. L. Wilson, L. Rothberg, P. J. Carroll, T. M. Jedju, M. L. Steigerwald, L. E. Brus, Phys. Rev. Lett. 65, 1623 (1990).
    [CrossRef] [PubMed]
  22. M. C. Klein, F. Hache, D. Ricard, C. Flytzanis, Phys. Rev. B 42, 11123 (1990).
    [CrossRef]
  23. F. Hache, M. C. Klein, D. Ricard, C. Flytzanis, J. Opt. Soc. Am. B 8, 1802 (1991).
    [CrossRef]
  24. Al. L. Efros, A. I. Ekimov, F. Kozlowski, V. Petrova-Koch, H. Schmidbaur, S. Shumilo, Solid State Commun. 78, 853 (1991).
    [CrossRef]

1991

A. I. Ekimov, Phys. Scr. T39, 217 (1991).
[CrossRef]

Al. L. Efros, A. I. Ekimov, F. Kozlowski, V. Petrova-Koch, H. Schmidbaur, S. Shumilo, Solid State Commun. 78, 853 (1991).
[CrossRef]

F. Hache, M. C. Klein, D. Ricard, C. Flytzanis, J. Opt. Soc. Am. B 8, 1802 (1991).
[CrossRef]

1990

M. G. Bawendi, W. L. Wilson, L. Rothberg, P. J. Carroll, T. M. Jedju, M. L. Steigerwald, L. E. Brus, Phys. Rev. Lett. 65, 1623 (1990).
[CrossRef] [PubMed]

M. C. Klein, F. Hache, D. Ricard, C. Flytzanis, Phys. Rev. B 42, 11123 (1990).
[CrossRef]

D. I. Chepic, Al. L. Efros, A. I. Ekimov, M. G. Ivanov, V. A. Kharchenko, I. A. Kudryavtsev, T. V. Yazeva, J. Lumin. 47, 113 (1990).
[CrossRef]

G. B. Grigoryan, A. V. Rodina, Al. L. Efros, Sov. Phys. Solid State 32, 2037 (1990).

G. B. Grigoryan, E. M. Kazaryan, Al. L. Efros, T. V. Yazeva, Sov. Phys. Solid State 32, 1031 (1990).

Y. Z. Hu, M. Lindberg, S. W. Koch, Phys. Rev. B 42, 1713 (1990).
[CrossRef]

1989

A. I. Ekimov, Al. L. Efros, M. G. Ivanov, A. A. Onushchenko, S. K. Shumilov, Solid State Commun. 69, 565 (1989).
[CrossRef]

J. B. Xia, Phys. Rev. B 40, 8500 (1989).
[CrossRef]

Al. L. Efros, A. V. Rodina, Solid State Commun. 72, 645 (1989).
[CrossRef]

N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, M. Lindberg, IEEE J. Quantum Electron. 25, 2516 (1989).
[CrossRef]

1988

1986

H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
[CrossRef]

1985

R. Rossetti, R. Hull, J. M. Gibson, L. E. Brus, J. Chem. Phys. 82, 552 (1985).
[CrossRef]

A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, Al. L. Efros, Sov. Phys. JETP 88, 891 (1985).

1984

L. E. Brus, J. Chem. Phys. 80, 4403 (1984).
[CrossRef]

1982

Al. L. Efros, A. L. Efros, Sov. Phys. Semicond. 16, 772 (1982).

1981

A. I. Ekimov, A. A. Onushchenko, JETP Lett. 34, 345 (1981); JETP Lett. 40, 1137 (1984).

1967

V. I. Sheka, D. I. Sheka, Sov. Phys. JETP 24, 975 (1967).

1955

J. M. Luttinger, W. Kohn, Phys. Rev. 97, 869 (1955); J. M. Luttinger, Phys. Rev. 102, 1030 (1956); see also N. O. Lipari, A. Baldereschi, Phys. Rev. Lett. 25, 1660 (1971).
[CrossRef]

Aggarwal, R. L.

R. L. Aggarwal, in Semiconductors and Semimetals, R. K. Willardson, A. C. Beer, eds. (Academic, New York, 1972), Vol. 9, p. 151.
[CrossRef]

Antonetti, A.

N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, M. Lindberg, IEEE J. Quantum Electron. 25, 2516 (1989).
[CrossRef]

Baral, S.

H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
[CrossRef]

Bawendi, M. G.

M. G. Bawendi, W. L. Wilson, L. Rothberg, P. J. Carroll, T. M. Jedju, M. L. Steigerwald, L. E. Brus, Phys. Rev. Lett. 65, 1623 (1990).
[CrossRef] [PubMed]

Borrelli, N. F.

Brus, L. E.

M. G. Bawendi, W. L. Wilson, L. Rothberg, P. J. Carroll, T. M. Jedju, M. L. Steigerwald, L. E. Brus, Phys. Rev. Lett. 65, 1623 (1990).
[CrossRef] [PubMed]

R. Rossetti, R. Hull, J. M. Gibson, L. E. Brus, J. Chem. Phys. 82, 552 (1985).
[CrossRef]

L. E. Brus, J. Chem. Phys. 80, 4403 (1984).
[CrossRef]

Carroll, P. J.

M. G. Bawendi, W. L. Wilson, L. Rothberg, P. J. Carroll, T. M. Jedju, M. L. Steigerwald, L. E. Brus, Phys. Rev. Lett. 65, 1623 (1990).
[CrossRef] [PubMed]

Chepic, D. I.

D. I. Chepic, Al. L. Efros, A. I. Ekimov, M. G. Ivanov, V. A. Kharchenko, I. A. Kudryavtsev, T. V. Yazeva, J. Lumin. 47, 113 (1990).
[CrossRef]

Dieman, E.

H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
[CrossRef]

Efros, A. L.

Al. L. Efros, A. L. Efros, Sov. Phys. Semicond. 16, 772 (1982).

Efros, Al. L.

Al. L. Efros, A. I. Ekimov, F. Kozlowski, V. Petrova-Koch, H. Schmidbaur, S. Shumilo, Solid State Commun. 78, 853 (1991).
[CrossRef]

G. B. Grigoryan, E. M. Kazaryan, Al. L. Efros, T. V. Yazeva, Sov. Phys. Solid State 32, 1031 (1990).

D. I. Chepic, Al. L. Efros, A. I. Ekimov, M. G. Ivanov, V. A. Kharchenko, I. A. Kudryavtsev, T. V. Yazeva, J. Lumin. 47, 113 (1990).
[CrossRef]

G. B. Grigoryan, A. V. Rodina, Al. L. Efros, Sov. Phys. Solid State 32, 2037 (1990).

A. I. Ekimov, Al. L. Efros, M. G. Ivanov, A. A. Onushchenko, S. K. Shumilov, Solid State Commun. 69, 565 (1989).
[CrossRef]

Al. L. Efros, A. V. Rodina, Solid State Commun. 72, 645 (1989).
[CrossRef]

A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, Al. L. Efros, Sov. Phys. JETP 88, 891 (1985).

Al. L. Efros, A. L. Efros, Sov. Phys. Semicond. 16, 772 (1982).

Ekimov, A. I.

Al. L. Efros, A. I. Ekimov, F. Kozlowski, V. Petrova-Koch, H. Schmidbaur, S. Shumilo, Solid State Commun. 78, 853 (1991).
[CrossRef]

A. I. Ekimov, Phys. Scr. T39, 217 (1991).
[CrossRef]

D. I. Chepic, Al. L. Efros, A. I. Ekimov, M. G. Ivanov, V. A. Kharchenko, I. A. Kudryavtsev, T. V. Yazeva, J. Lumin. 47, 113 (1990).
[CrossRef]

A. I. Ekimov, Al. L. Efros, M. G. Ivanov, A. A. Onushchenko, S. K. Shumilov, Solid State Commun. 69, 565 (1989).
[CrossRef]

A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, Al. L. Efros, Sov. Phys. JETP 88, 891 (1985).

A. I. Ekimov, A. A. Onushchenko, JETP Lett. 34, 345 (1981); JETP Lett. 40, 1137 (1984).

Fluegel, B.

N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, M. Lindberg, IEEE J. Quantum Electron. 25, 2516 (1989).
[CrossRef]

Flytzanis, C.

F. Hache, M. C. Klein, D. Ricard, C. Flytzanis, J. Opt. Soc. Am. B 8, 1802 (1991).
[CrossRef]

M. C. Klein, F. Hache, D. Ricard, C. Flytzanis, Phys. Rev. B 42, 11123 (1990).
[CrossRef]

Fojtik, A.

H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
[CrossRef]

Gibson, J. M.

R. Rossetti, R. Hull, J. M. Gibson, L. E. Brus, J. Chem. Phys. 82, 552 (1985).
[CrossRef]

Grigoryan, G. B.

G. B. Grigoryan, E. M. Kazaryan, Al. L. Efros, T. V. Yazeva, Sov. Phys. Solid State 32, 1031 (1990).

G. B. Grigoryan, A. V. Rodina, Al. L. Efros, Sov. Phys. Solid State 32, 2037 (1990).

Hache, F.

F. Hache, M. C. Klein, D. Ricard, C. Flytzanis, J. Opt. Soc. Am. B 8, 1802 (1991).
[CrossRef]

M. C. Klein, F. Hache, D. Ricard, C. Flytzanis, Phys. Rev. B 42, 11123 (1990).
[CrossRef]

Hall, D. W.

Henglein, A.

H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
[CrossRef]

Hermann, C.

C. Hermann, C. Weisbuch, in Optical Orientation, F. Meier, B. P. Zakharchenya, eds. (Elsevier, Amsterdam, 1984), p. 443.

Hu, Y. Z.

Y. Z. Hu, M. Lindberg, S. W. Koch, Phys. Rev. B 42, 1713 (1990).
[CrossRef]

Hulin, D.

N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, M. Lindberg, IEEE J. Quantum Electron. 25, 2516 (1989).
[CrossRef]

Hull, R.

R. Rossetti, R. Hull, J. M. Gibson, L. E. Brus, J. Chem. Phys. 82, 552 (1985).
[CrossRef]

Ivanov, M. G.

D. I. Chepic, Al. L. Efros, A. I. Ekimov, M. G. Ivanov, V. A. Kharchenko, I. A. Kudryavtsev, T. V. Yazeva, J. Lumin. 47, 113 (1990).
[CrossRef]

A. I. Ekimov, Al. L. Efros, M. G. Ivanov, A. A. Onushchenko, S. K. Shumilov, Solid State Commun. 69, 565 (1989).
[CrossRef]

Jedju, T. M.

M. G. Bawendi, W. L. Wilson, L. Rothberg, P. J. Carroll, T. M. Jedju, M. L. Steigerwald, L. E. Brus, Phys. Rev. Lett. 65, 1623 (1990).
[CrossRef] [PubMed]

Joffre, M.

N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, M. Lindberg, IEEE J. Quantum Electron. 25, 2516 (1989).
[CrossRef]

Kazaryan, E. M.

G. B. Grigoryan, E. M. Kazaryan, Al. L. Efros, T. V. Yazeva, Sov. Phys. Solid State 32, 1031 (1990).

Kharchenko, V. A.

D. I. Chepic, Al. L. Efros, A. I. Ekimov, M. G. Ivanov, V. A. Kharchenko, I. A. Kudryavtsev, T. V. Yazeva, J. Lumin. 47, 113 (1990).
[CrossRef]

Klein, M. C.

F. Hache, M. C. Klein, D. Ricard, C. Flytzanis, J. Opt. Soc. Am. B 8, 1802 (1991).
[CrossRef]

M. C. Klein, F. Hache, D. Ricard, C. Flytzanis, Phys. Rev. B 42, 11123 (1990).
[CrossRef]

Koch, S. W.

Y. Z. Hu, M. Lindberg, S. W. Koch, Phys. Rev. B 42, 1713 (1990).
[CrossRef]

N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, M. Lindberg, IEEE J. Quantum Electron. 25, 2516 (1989).
[CrossRef]

Koch, U.

H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
[CrossRef]

Kohn, W.

J. M. Luttinger, W. Kohn, Phys. Rev. 97, 869 (1955); J. M. Luttinger, Phys. Rev. 102, 1030 (1956); see also N. O. Lipari, A. Baldereschi, Phys. Rev. Lett. 25, 1660 (1971).
[CrossRef]

Kozlowski, F.

Al. L. Efros, A. I. Ekimov, F. Kozlowski, V. Petrova-Koch, H. Schmidbaur, S. Shumilo, Solid State Commun. 78, 853 (1991).
[CrossRef]

Kudryavtsev, I. A.

D. I. Chepic, Al. L. Efros, A. I. Ekimov, M. G. Ivanov, V. A. Kharchenko, I. A. Kudryavtsev, T. V. Yazeva, J. Lumin. 47, 113 (1990).
[CrossRef]

Kunath, W.

H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
[CrossRef]

Lindberg, M.

Y. Z. Hu, M. Lindberg, S. W. Koch, Phys. Rev. B 42, 1713 (1990).
[CrossRef]

N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, M. Lindberg, IEEE J. Quantum Electron. 25, 2516 (1989).
[CrossRef]

Luttinger, J. M.

J. M. Luttinger, W. Kohn, Phys. Rev. 97, 869 (1955); J. M. Luttinger, Phys. Rev. 102, 1030 (1956); see also N. O. Lipari, A. Baldereschi, Phys. Rev. Lett. 25, 1660 (1971).
[CrossRef]

Migus, A.

N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, M. Lindberg, IEEE J. Quantum Electron. 25, 2516 (1989).
[CrossRef]

Onushchenko, A. A.

A. I. Ekimov, Al. L. Efros, M. G. Ivanov, A. A. Onushchenko, S. K. Shumilov, Solid State Commun. 69, 565 (1989).
[CrossRef]

A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, Al. L. Efros, Sov. Phys. JETP 88, 891 (1985).

A. I. Ekimov, A. A. Onushchenko, JETP Lett. 34, 345 (1981); JETP Lett. 40, 1137 (1984).

Petrova-Koch, V.

Al. L. Efros, A. I. Ekimov, F. Kozlowski, V. Petrova-Koch, H. Schmidbaur, S. Shumilo, Solid State Commun. 78, 853 (1991).
[CrossRef]

Peyghambarian, N.

N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, M. Lindberg, IEEE J. Quantum Electron. 25, 2516 (1989).
[CrossRef]

Plyukhin, A. G.

A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, Al. L. Efros, Sov. Phys. JETP 88, 891 (1985).

Ricard, D.

F. Hache, M. C. Klein, D. Ricard, C. Flytzanis, J. Opt. Soc. Am. B 8, 1802 (1991).
[CrossRef]

M. C. Klein, F. Hache, D. Ricard, C. Flytzanis, Phys. Rev. B 42, 11123 (1990).
[CrossRef]

Rodina, A. V.

G. B. Grigoryan, A. V. Rodina, Al. L. Efros, Sov. Phys. Solid State 32, 2037 (1990).

Al. L. Efros, A. V. Rodina, Solid State Commun. 72, 645 (1989).
[CrossRef]

Rossetti, R.

R. Rossetti, R. Hull, J. M. Gibson, L. E. Brus, J. Chem. Phys. 82, 552 (1985).
[CrossRef]

Rothberg, L.

M. G. Bawendi, W. L. Wilson, L. Rothberg, P. J. Carroll, T. M. Jedju, M. L. Steigerwald, L. E. Brus, Phys. Rev. Lett. 65, 1623 (1990).
[CrossRef] [PubMed]

Schmidbaur, H.

Al. L. Efros, A. I. Ekimov, F. Kozlowski, V. Petrova-Koch, H. Schmidbaur, S. Shumilo, Solid State Commun. 78, 853 (1991).
[CrossRef]

Schmidt, H. M.

H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
[CrossRef]

Sheka, D. I.

V. I. Sheka, D. I. Sheka, Sov. Phys. JETP 24, 975 (1967).

Sheka, V. I.

V. I. Sheka, D. I. Sheka, Sov. Phys. JETP 24, 975 (1967).

Shumilo, S.

Al. L. Efros, A. I. Ekimov, F. Kozlowski, V. Petrova-Koch, H. Schmidbaur, S. Shumilo, Solid State Commun. 78, 853 (1991).
[CrossRef]

Shumilov, S. K.

A. I. Ekimov, Al. L. Efros, M. G. Ivanov, A. A. Onushchenko, S. K. Shumilov, Solid State Commun. 69, 565 (1989).
[CrossRef]

Steigerwald, M. L.

M. G. Bawendi, W. L. Wilson, L. Rothberg, P. J. Carroll, T. M. Jedju, M. L. Steigerwald, L. E. Brus, Phys. Rev. Lett. 65, 1623 (1990).
[CrossRef] [PubMed]

Weisbuch, C.

C. Hermann, C. Weisbuch, in Optical Orientation, F. Meier, B. P. Zakharchenya, eds. (Elsevier, Amsterdam, 1984), p. 443.

Weiss, K.

H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
[CrossRef]

Weller, H.

H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
[CrossRef]

Wilson, W. L.

M. G. Bawendi, W. L. Wilson, L. Rothberg, P. J. Carroll, T. M. Jedju, M. L. Steigerwald, L. E. Brus, Phys. Rev. Lett. 65, 1623 (1990).
[CrossRef] [PubMed]

Xia, J. B.

J. B. Xia, Phys. Rev. B 40, 8500 (1989).
[CrossRef]

Yazeva, T. V.

D. I. Chepic, Al. L. Efros, A. I. Ekimov, M. G. Ivanov, V. A. Kharchenko, I. A. Kudryavtsev, T. V. Yazeva, J. Lumin. 47, 113 (1990).
[CrossRef]

G. B. Grigoryan, E. M. Kazaryan, Al. L. Efros, T. V. Yazeva, Sov. Phys. Solid State 32, 1031 (1990).

Chem. Phys. Lett.

H. Weller, H. M. Schmidt, U. Koch, A. Fojtik, S. Baral, A. Henglein, W. Kunath, K. Weiss, E. Dieman, Chem. Phys. Lett. 124, 557 (1986).
[CrossRef]

IEEE J. Quantum Electron.

N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, M. Lindberg, IEEE J. Quantum Electron. 25, 2516 (1989).
[CrossRef]

J. Chem. Phys.

L. E. Brus, J. Chem. Phys. 80, 4403 (1984).
[CrossRef]

R. Rossetti, R. Hull, J. M. Gibson, L. E. Brus, J. Chem. Phys. 82, 552 (1985).
[CrossRef]

J. Lumin.

D. I. Chepic, Al. L. Efros, A. I. Ekimov, M. G. Ivanov, V. A. Kharchenko, I. A. Kudryavtsev, T. V. Yazeva, J. Lumin. 47, 113 (1990).
[CrossRef]

J. Opt. Soc. Am. B

JETP Lett.

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Absorption spectra (solid curves) and luminescence spectra obtained under weak or intermediate (dashed curves) and strong (short-and-long-dashed curves) excitation at λ = 355 nm for the samples containing CdSe particles with the largest mean radii, 250 Å (top) and 80 Å (bottom). The luminescence intensity is given in arbitrary units.

Fig. 2
Fig. 2

Absorption spectra (solid curves) and luminescence spectra obtained under weak or intermediate (dashed curves) and strong (short-and-long-dashed curve) excitation at λ = 355 nm for the samples containing quantum-confined CdSe particles with mean radii of 38 Å (top), 26 Å (middle), and 21 Å (bottom). In the last case the luminescence was weak and the signal-to-noise ratio was low.

Fig. 3
Fig. 3

Electron and hole energy spectra as calculated in Subsection 3.A, plotted versus the inverse-mean-square radius. The electron energy, which increases upward, is referred to the bottom of the conduction band; the hole energy, increasing downward is referred to the top of the valence band. Only those levels involved in transitions with a significant oscillator strength are shown. The P states of the hole are shown as dashed curves.

Fig. 4
Fig. 4

Comparison between theory and experiment. The absorption spectra shown in Fig. 2 are reproduced with the second-derivative spectra. The calculated positions of the transitions are shown as vertical bars whose height indicates the relative strength (the first or 1S3/1–1Se transition is given the same arbitrary height for all three samples). Only the transitions with a significant oscillator strength are shown. The inset shows the assignment of these transitions.

Equations (18)

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Ψ e , h = μ = - 1 / 2 1 / 2 f c , μ ( r ) u c , μ + μ = - 3 / 2 3 / 2 f 3 / 2 , μ ( r ) u 3 / 2 , μ + μ = - 1 / 2 1 / 2 f s , μ ( r ) u s , μ ,
E + ( E g s / 2 ) + ( 2 Δ / 3 ) E + ( E g s / 2 ) + Δ r ln [ j ( κ s r ) ] r = a = E + E g s / 2 E + E g g / 2 r ln [ K l ( κ g r ) ] r = a E + ( E g g / 2 ) + ( 2 Δ / 3 ) E + ( E g g / 2 ) + Δ ,
K ( z ) = ( π / 2 z ) 1 / 2 K + 1 / 2 ( z ) , κ g 2 = 1 2 V 2 [ ( E g g / 2 ) 2 - E 2 ] E + ( E g g / 2 ) + Δ E + ( E g g / 2 ) + ( 2 Δ / 3 ) , κ s 2 = 1 2 V 2 [ E 2 - ( E g s / 2 ) 2 ] E + ( E g s / 2 ) + Δ E + ( E g s / 2 ) + ( 2 Δ / 3 ) ,
j ( κ s a ) = 0
{ 1 + 2 f + E p 3 [ 2 E + E g / 2 + 1 E + ( E g / 2 ) + Δ ] } p ^ 2 2 m 0 f c ( r ) = ( E - E g 2 ) f c ( r ) ,
1 m e = 1 m 0 [ 1 + 2 f + E p 3 ( 2 E g + 1 E g + Δ ) ] .
f c ( r ) = A k Y m ( θ , ϕ ) j ( α k r / a )
E , k = [ 1 + 2 f + E p 3 ( 2 E , k + E g + 1 E , k + E g + Δ ) ] 2 α , k 2 2 m 0 a 2 .
H ^ = 1 m 0 [ P + Q L M 0 i 1 / 2 L - i 2 M L * P - Q 0 M - i 2 Q i 3 / 2 L M * 0 P - Q - L - i 3 / 2 L * - i 2 Q 0 M * - L * P + Q - i 2 M * - i 1 / 2 L * - i 1 / 2 L * i 2 Q i 3 / 2 L i 2 M P - Δ 0 i 2 M * - i 3 / 2 L * i 2 Q i 1 / 2 L 0 P - Δ ] ,
P = ( γ 1 / 2 ) p ^ 2 ,             Q = γ ( p ^ 2 - 2 p ^ z 2 ) / 2 , L = - i 3 γ p ^ - p ^ z , M = 3 γ p ^ - 2 / 2 ,             p ^ 2 p ^ x 2 + p ^ y 2 ,             p ^ = p ^ x i p ^ y , p ^ x = - i x ,             p ^ y = - i y ,             p ^ z = - i z .
Ψ F M ± ( r h ) = 2 F + 1 [ = F + 1 / 2 , F - 3 / 2 = F + 3 / 2 , F - 1 / 2 ( - 1 ) - 3 / 2 + M R ± ( r h ) × μ = - 3 / 2 3 / 2 ( 3 / 2 F m μ - M ) Y m ( r h / r h ) u 3 / 2 , μ + ( - 1 ) F ± ( 1 / 2 ) - ( 1 / 2 ) + M R s ± ( r h ) × μ = - 1 / 2 1 / 2 ( F ± 1 / 2 1 / 2 F m μ - M ) Y F ± 1 / 2 m ( r h / r h ) u s , μ ] ,
( a b c d e f )
k l , s 2 = m 0 2 ( γ 1 - 2 γ ) ( γ 1 + 4 γ ) ( 2 E ( γ 1 + γ ) - Δ ( γ 1 + 2 γ ) ± { [ 2 E ( γ 1 + γ ) + Δ ( γ 1 + 2 γ ) ] 2 - 4 E ( E - Δ ) ( γ 1 - 2 γ ) ( γ 1 + 4 γ ) } 1 / 2 ) , k h 2 = 2 m 0 E 2 ( γ 1 - 2 γ ) .
( 2 F - 1 ) 2 - ( 1 / k s 2 - 1 / k l 2 ) j F - 1 / 2 ( k l a ) j F + 3 / 2 ( k h a ) j F - 1 / 2 ( k s a ) + 3 ( 2 F + 3 ) [ ( γ 1 + 2 γ ) k l 2 - 2 - k l 2 × j F + 3 / 2 ( k s a ) j F - 1 / 2 ( k l a ) j F - 1 / 2 ( k h a ) - ( γ 1 + 2 γ ) k s 2 - 2 - k s 2 j F + 3 / 2 ( k l a ) j F - 1 / 2 ( k s a ) j F - 1 / 2 ( k h a ) ] = 0 ,
( 2 F + 3 ) 2 + ( 1 / k s 2 - 1 / k l 2 ) j F + 1 / 2 ( k l a ) j F - 3 / 2 ( k h a ) j F + 1 / 2 ( k s a ) - 3 ( 2 F - 1 ) [ ( γ 1 + 2 γ ) k s 2 - 2 + k s 2 × j F + 1 / 2 ( k s a ) j F - 3 / 2 ( k l a ) j F + 1 / 2 ( k h a ) - ( γ 1 + 2 γ ) k l 2 - 2 + k l 2 j F + 1 / 2 ( k l a ) j F - 3 / 2 ( k s a ) j F + 1 / 2 ( k h a ) ] = 0.
j 1 ( k l a ) j 1 ( k s a ) = 0.
K = | Ψ k , , m ( r ) Ψ n , F , M p ( r ) d 3 r | 2 ,
ω = E g + E , k + E ± ( n , F ) - E e h ,

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