Abstract

The interband optical transitions near van Hove critical points in semiconductor structures with restricted geometry are studied in the framework of fractional dimensionality in the case of inhomogeneous broadening. The spectral line shapes were derived based on the w function, which is the envelope of the individual homogeneous packets. Similar to the case of homogeneous broadening, the dimensionality, band gaps, and linewidths can be straightforwardly determined by use of fractional differentiation, which converts the line shapes to symmetric profiles. The results show that crystal potential fluctuation plays an important role in the interband optical transitions, and the total linewidth should be accounted for by both phonon processes and crystal strain.

© 1997 Optical Society of America

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References

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  1. See, for example, Spectroscopic Characterization Techniques for Semiconductor Technology III, Proc. SPIE 946, 84 (1988).
  2. M. Cardona, Modulation Spectroscopy (Academic, New York, 1969).
  3. D. E. Aspnes, Surf. Sci., 135, 284 (1983).
    [CrossRef]
  4. For a review, see D. E. Aspnes, in Optical Properties of Solids: New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), p. 799.
  5. S. M. Kelso, D. E. Aspnes, M. A. Pollack, and R. E. Nahory, Phys. Rev. B 26, 6669 (1982).
    [CrossRef]
  6. H. Arwin and D. E. Aspnes, J. Vac. Sci. Technol. A 2, 1316 (1984).
    [CrossRef]
  7. P. Lautenschlager, M. Garriga, S. Logothetidis, and M. Cardona, Phys. Rev. B 35, 9174 (1987).
    [CrossRef]
  8. M. Erman, J. P. Andre, and J. LeBris, J. Appl. Phys. 59, 2019 (1986).
    [CrossRef]
  9. M. Erman, C. Alibert, J. B. Theeten, P. Frijlink, and B. Catte, J. Appl. Phys. 63, 465 (1988).
    [CrossRef]
  10. U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
    [CrossRef]
  11. X.-F. He, Solid State Commun. 75, 111 (1990).
    [CrossRef]
  12. X.-F. He, Phys. Rev. B 42, 11751 (1990).
    [CrossRef]
  13. X.-F. He, R.-R. Jiang, and D. Mo, Phys. Rev. B 41, 5799 (1990).
    [CrossRef]
  14. D. Mo, Y.-Y. Lin, J.-H. Tan, Z.-X. Yu, G.-Z. Zhou, K.-C. Gong, G.-P. Zhang, and X.-F. He, Thin Solid Films 234, 468 (1993).
    [CrossRef]
  15. X.-F. He, in Proceedings of the 22nd International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995), p. 281.
  16. X.-F. He, Phys. Rev. B 43, 2063 (1991).
    [CrossRef]
  17. H. Mathieu, P. Lefebvre, and P. Christol, Phys. Rev. B 46, 4092 (1992).
    [CrossRef]
  18. P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 46, 13603 (1992).
    [CrossRef]
  19. P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 48, 17308 (1993).
    [CrossRef]
  20. P. Christol, P. Lefebvre, and H. Mathieu, J. Appl. Phys. 74, 5626 (1993).
    [CrossRef]
  21. B. O. Seraphin and N. Bottka, Phys. Rev. 145, 628 (1966).
    [CrossRef]
  22. H. Shen, X. C. Shen, F. H. Pollack, and R. N. Sacks, Phys. Rev. B 36, 3487 (1987).
    [CrossRef]
  23. J. W. Carland, H. Adad, M. Viccaro, and P. M. Raccah, Appl. Phys. Lett. 52, 1176 (1988).
    [CrossRef]
  24. P. Lautenschlager, P. B. Allen, and M. Cardona, Phys. Rev. B 33, 5501 (1986).
    [CrossRef]
  25. S. Zollner, S. Gopalan, M. Garriga, J. Humlicek, L. Vina, and M. Cardona, Appl. Phys. Lett. 57, 2838 (1990).
    [CrossRef]
  26. K. B. Oldham and J. Spanier, The Fractional Calculus (Academic, New York, 1974).
  27. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965), p. 297.
  28. See, for example, Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981).

1993 (3)

D. Mo, Y.-Y. Lin, J.-H. Tan, Z.-X. Yu, G.-Z. Zhou, K.-C. Gong, G.-P. Zhang, and X.-F. He, Thin Solid Films 234, 468 (1993).
[CrossRef]

P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 48, 17308 (1993).
[CrossRef]

P. Christol, P. Lefebvre, and H. Mathieu, J. Appl. Phys. 74, 5626 (1993).
[CrossRef]

1992 (3)

H. Mathieu, P. Lefebvre, and P. Christol, Phys. Rev. B 46, 4092 (1992).
[CrossRef]

P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 46, 13603 (1992).
[CrossRef]

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

1991 (1)

X.-F. He, Phys. Rev. B 43, 2063 (1991).
[CrossRef]

1990 (4)

X.-F. He, Solid State Commun. 75, 111 (1990).
[CrossRef]

X.-F. He, Phys. Rev. B 42, 11751 (1990).
[CrossRef]

X.-F. He, R.-R. Jiang, and D. Mo, Phys. Rev. B 41, 5799 (1990).
[CrossRef]

S. Zollner, S. Gopalan, M. Garriga, J. Humlicek, L. Vina, and M. Cardona, Appl. Phys. Lett. 57, 2838 (1990).
[CrossRef]

1988 (3)

J. W. Carland, H. Adad, M. Viccaro, and P. M. Raccah, Appl. Phys. Lett. 52, 1176 (1988).
[CrossRef]

See, for example, Spectroscopic Characterization Techniques for Semiconductor Technology III, Proc. SPIE 946, 84 (1988).

M. Erman, C. Alibert, J. B. Theeten, P. Frijlink, and B. Catte, J. Appl. Phys. 63, 465 (1988).
[CrossRef]

1987 (2)

P. Lautenschlager, M. Garriga, S. Logothetidis, and M. Cardona, Phys. Rev. B 35, 9174 (1987).
[CrossRef]

H. Shen, X. C. Shen, F. H. Pollack, and R. N. Sacks, Phys. Rev. B 36, 3487 (1987).
[CrossRef]

1986 (2)

P. Lautenschlager, P. B. Allen, and M. Cardona, Phys. Rev. B 33, 5501 (1986).
[CrossRef]

M. Erman, J. P. Andre, and J. LeBris, J. Appl. Phys. 59, 2019 (1986).
[CrossRef]

1984 (1)

H. Arwin and D. E. Aspnes, J. Vac. Sci. Technol. A 2, 1316 (1984).
[CrossRef]

1983 (1)

D. E. Aspnes, Surf. Sci., 135, 284 (1983).
[CrossRef]

1982 (1)

S. M. Kelso, D. E. Aspnes, M. A. Pollack, and R. E. Nahory, Phys. Rev. B 26, 6669 (1982).
[CrossRef]

1966 (1)

B. O. Seraphin and N. Bottka, Phys. Rev. 145, 628 (1966).
[CrossRef]

Abstreiter, G.

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

Adad, H.

J. W. Carland, H. Adad, M. Viccaro, and P. M. Raccah, Appl. Phys. Lett. 52, 1176 (1988).
[CrossRef]

Alibert, C.

M. Erman, C. Alibert, J. B. Theeten, P. Frijlink, and B. Catte, J. Appl. Phys. 63, 465 (1988).
[CrossRef]

Allen, P. B.

P. Lautenschlager, P. B. Allen, and M. Cardona, Phys. Rev. B 33, 5501 (1986).
[CrossRef]

Andre, J. P.

M. Erman, J. P. Andre, and J. LeBris, J. Appl. Phys. 59, 2019 (1986).
[CrossRef]

Arwin, H.

H. Arwin and D. E. Aspnes, J. Vac. Sci. Technol. A 2, 1316 (1984).
[CrossRef]

Aspnes, D. E.

H. Arwin and D. E. Aspnes, J. Vac. Sci. Technol. A 2, 1316 (1984).
[CrossRef]

D. E. Aspnes, Surf. Sci., 135, 284 (1983).
[CrossRef]

S. M. Kelso, D. E. Aspnes, M. A. Pollack, and R. E. Nahory, Phys. Rev. B 26, 6669 (1982).
[CrossRef]

Bottka, N.

B. O. Seraphin and N. Bottka, Phys. Rev. 145, 628 (1966).
[CrossRef]

Cardona, M.

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

S. Zollner, S. Gopalan, M. Garriga, J. Humlicek, L. Vina, and M. Cardona, Appl. Phys. Lett. 57, 2838 (1990).
[CrossRef]

P. Lautenschlager, M. Garriga, S. Logothetidis, and M. Cardona, Phys. Rev. B 35, 9174 (1987).
[CrossRef]

P. Lautenschlager, P. B. Allen, and M. Cardona, Phys. Rev. B 33, 5501 (1986).
[CrossRef]

Carland, J. W.

J. W. Carland, H. Adad, M. Viccaro, and P. M. Raccah, Appl. Phys. Lett. 52, 1176 (1988).
[CrossRef]

Catte, B.

M. Erman, C. Alibert, J. B. Theeten, P. Frijlink, and B. Catte, J. Appl. Phys. 63, 465 (1988).
[CrossRef]

Christol, P.

P. Christol, P. Lefebvre, and H. Mathieu, J. Appl. Phys. 74, 5626 (1993).
[CrossRef]

P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 48, 17308 (1993).
[CrossRef]

H. Mathieu, P. Lefebvre, and P. Christol, Phys. Rev. B 46, 4092 (1992).
[CrossRef]

P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 46, 13603 (1992).
[CrossRef]

Eberl, K.

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

Erman, M.

M. Erman, C. Alibert, J. B. Theeten, P. Frijlink, and B. Catte, J. Appl. Phys. 63, 465 (1988).
[CrossRef]

M. Erman, J. P. Andre, and J. LeBris, J. Appl. Phys. 59, 2019 (1986).
[CrossRef]

Frijlink, P.

M. Erman, C. Alibert, J. B. Theeten, P. Frijlink, and B. Catte, J. Appl. Phys. 63, 465 (1988).
[CrossRef]

Garriga, M.

S. Zollner, S. Gopalan, M. Garriga, J. Humlicek, L. Vina, and M. Cardona, Appl. Phys. Lett. 57, 2838 (1990).
[CrossRef]

P. Lautenschlager, M. Garriga, S. Logothetidis, and M. Cardona, Phys. Rev. B 35, 9174 (1987).
[CrossRef]

Gong, K.-C.

D. Mo, Y.-Y. Lin, J.-H. Tan, Z.-X. Yu, G.-Z. Zhou, K.-C. Gong, G.-P. Zhang, and X.-F. He, Thin Solid Films 234, 468 (1993).
[CrossRef]

Gopalan, S.

S. Zollner, S. Gopalan, M. Garriga, J. Humlicek, L. Vina, and M. Cardona, Appl. Phys. Lett. 57, 2838 (1990).
[CrossRef]

He, X.-F.

D. Mo, Y.-Y. Lin, J.-H. Tan, Z.-X. Yu, G.-Z. Zhou, K.-C. Gong, G.-P. Zhang, and X.-F. He, Thin Solid Films 234, 468 (1993).
[CrossRef]

X.-F. He, Phys. Rev. B 43, 2063 (1991).
[CrossRef]

X.-F. He, Solid State Commun. 75, 111 (1990).
[CrossRef]

X.-F. He, Phys. Rev. B 42, 11751 (1990).
[CrossRef]

X.-F. He, R.-R. Jiang, and D. Mo, Phys. Rev. B 41, 5799 (1990).
[CrossRef]

Humlicek, J.

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

S. Zollner, S. Gopalan, M. Garriga, J. Humlicek, L. Vina, and M. Cardona, Appl. Phys. Lett. 57, 2838 (1990).
[CrossRef]

Jiang, R.-R.

X.-F. He, R.-R. Jiang, and D. Mo, Phys. Rev. B 41, 5799 (1990).
[CrossRef]

Kasper, E.

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

Kelso, S. M.

S. M. Kelso, D. E. Aspnes, M. A. Pollack, and R. E. Nahory, Phys. Rev. B 26, 6669 (1982).
[CrossRef]

Kibbel, H.

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

Lautenschlager, P.

P. Lautenschlager, M. Garriga, S. Logothetidis, and M. Cardona, Phys. Rev. B 35, 9174 (1987).
[CrossRef]

P. Lautenschlager, P. B. Allen, and M. Cardona, Phys. Rev. B 33, 5501 (1986).
[CrossRef]

LeBris, J.

M. Erman, J. P. Andre, and J. LeBris, J. Appl. Phys. 59, 2019 (1986).
[CrossRef]

Lefebvre, P.

P. Christol, P. Lefebvre, and H. Mathieu, J. Appl. Phys. 74, 5626 (1993).
[CrossRef]

P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 48, 17308 (1993).
[CrossRef]

H. Mathieu, P. Lefebvre, and P. Christol, Phys. Rev. B 46, 4092 (1992).
[CrossRef]

P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 46, 13603 (1992).
[CrossRef]

Lin, Y.-Y.

D. Mo, Y.-Y. Lin, J.-H. Tan, Z.-X. Yu, G.-Z. Zhou, K.-C. Gong, G.-P. Zhang, and X.-F. He, Thin Solid Films 234, 468 (1993).
[CrossRef]

Logothetidis, S.

P. Lautenschlager, M. Garriga, S. Logothetidis, and M. Cardona, Phys. Rev. B 35, 9174 (1987).
[CrossRef]

Lukes, F.

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

Mathieu, H.

P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 48, 17308 (1993).
[CrossRef]

P. Christol, P. Lefebvre, and H. Mathieu, J. Appl. Phys. 74, 5626 (1993).
[CrossRef]

P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 46, 13603 (1992).
[CrossRef]

H. Mathieu, P. Lefebvre, and P. Christol, Phys. Rev. B 46, 4092 (1992).
[CrossRef]

Mo, D.

D. Mo, Y.-Y. Lin, J.-H. Tan, Z.-X. Yu, G.-Z. Zhou, K.-C. Gong, G.-P. Zhang, and X.-F. He, Thin Solid Films 234, 468 (1993).
[CrossRef]

X.-F. He, R.-R. Jiang, and D. Mo, Phys. Rev. B 41, 5799 (1990).
[CrossRef]

Nahory, R. E.

S. M. Kelso, D. E. Aspnes, M. A. Pollack, and R. E. Nahory, Phys. Rev. B 26, 6669 (1982).
[CrossRef]

Pollack, F. H.

H. Shen, X. C. Shen, F. H. Pollack, and R. N. Sacks, Phys. Rev. B 36, 3487 (1987).
[CrossRef]

Pollack, M. A.

S. M. Kelso, D. E. Aspnes, M. A. Pollack, and R. E. Nahory, Phys. Rev. B 26, 6669 (1982).
[CrossRef]

Presting, H.

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

Raccah, P. M.

J. W. Carland, H. Adad, M. Viccaro, and P. M. Raccah, Appl. Phys. Lett. 52, 1176 (1988).
[CrossRef]

Sacks, R. N.

H. Shen, X. C. Shen, F. H. Pollack, and R. N. Sacks, Phys. Rev. B 36, 3487 (1987).
[CrossRef]

Schmid, U.

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

Seraphin, B. O.

B. O. Seraphin and N. Bottka, Phys. Rev. 145, 628 (1966).
[CrossRef]

Shen, H.

H. Shen, X. C. Shen, F. H. Pollack, and R. N. Sacks, Phys. Rev. B 36, 3487 (1987).
[CrossRef]

Shen, X. C.

H. Shen, X. C. Shen, F. H. Pollack, and R. N. Sacks, Phys. Rev. B 36, 3487 (1987).
[CrossRef]

Tan, J.-H.

D. Mo, Y.-Y. Lin, J.-H. Tan, Z.-X. Yu, G.-Z. Zhou, K.-C. Gong, G.-P. Zhang, and X.-F. He, Thin Solid Films 234, 468 (1993).
[CrossRef]

Theeten, J. B.

M. Erman, C. Alibert, J. B. Theeten, P. Frijlink, and B. Catte, J. Appl. Phys. 63, 465 (1988).
[CrossRef]

Viccaro, M.

J. W. Carland, H. Adad, M. Viccaro, and P. M. Raccah, Appl. Phys. Lett. 52, 1176 (1988).
[CrossRef]

Vina, L.

S. Zollner, S. Gopalan, M. Garriga, J. Humlicek, L. Vina, and M. Cardona, Appl. Phys. Lett. 57, 2838 (1990).
[CrossRef]

Wegscheider, W.

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

Yu, Z.-X.

D. Mo, Y.-Y. Lin, J.-H. Tan, Z.-X. Yu, G.-Z. Zhou, K.-C. Gong, G.-P. Zhang, and X.-F. He, Thin Solid Films 234, 468 (1993).
[CrossRef]

Zhang, G.-P.

D. Mo, Y.-Y. Lin, J.-H. Tan, Z.-X. Yu, G.-Z. Zhou, K.-C. Gong, G.-P. Zhang, and X.-F. He, Thin Solid Films 234, 468 (1993).
[CrossRef]

Zhou, G.-Z.

D. Mo, Y.-Y. Lin, J.-H. Tan, Z.-X. Yu, G.-Z. Zhou, K.-C. Gong, G.-P. Zhang, and X.-F. He, Thin Solid Films 234, 468 (1993).
[CrossRef]

Zollner, S.

S. Zollner, S. Gopalan, M. Garriga, J. Humlicek, L. Vina, and M. Cardona, Appl. Phys. Lett. 57, 2838 (1990).
[CrossRef]

Appl. Phys. Lett. (2)

S. Zollner, S. Gopalan, M. Garriga, J. Humlicek, L. Vina, and M. Cardona, Appl. Phys. Lett. 57, 2838 (1990).
[CrossRef]

J. W. Carland, H. Adad, M. Viccaro, and P. M. Raccah, Appl. Phys. Lett. 52, 1176 (1988).
[CrossRef]

J. Appl. Phys. (3)

P. Christol, P. Lefebvre, and H. Mathieu, J. Appl. Phys. 74, 5626 (1993).
[CrossRef]

M. Erman, J. P. Andre, and J. LeBris, J. Appl. Phys. 59, 2019 (1986).
[CrossRef]

M. Erman, C. Alibert, J. B. Theeten, P. Frijlink, and B. Catte, J. Appl. Phys. 63, 465 (1988).
[CrossRef]

J. Vac. Sci. Technol. A (1)

H. Arwin and D. E. Aspnes, J. Vac. Sci. Technol. A 2, 1316 (1984).
[CrossRef]

Phys. Rev. (1)

B. O. Seraphin and N. Bottka, Phys. Rev. 145, 628 (1966).
[CrossRef]

Phys. Rev. B (11)

H. Shen, X. C. Shen, F. H. Pollack, and R. N. Sacks, Phys. Rev. B 36, 3487 (1987).
[CrossRef]

P. Lautenschlager, M. Garriga, S. Logothetidis, and M. Cardona, Phys. Rev. B 35, 9174 (1987).
[CrossRef]

P. Lautenschlager, P. B. Allen, and M. Cardona, Phys. Rev. B 33, 5501 (1986).
[CrossRef]

S. M. Kelso, D. E. Aspnes, M. A. Pollack, and R. E. Nahory, Phys. Rev. B 26, 6669 (1982).
[CrossRef]

U. Schmid, J. Humlicek, F. Lukes, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider, and G. Abstreiter, Phys. Rev. B 45, 6793 (1992).
[CrossRef]

X.-F. He, Phys. Rev. B 42, 11751 (1990).
[CrossRef]

X.-F. He, R.-R. Jiang, and D. Mo, Phys. Rev. B 41, 5799 (1990).
[CrossRef]

X.-F. He, Phys. Rev. B 43, 2063 (1991).
[CrossRef]

H. Mathieu, P. Lefebvre, and P. Christol, Phys. Rev. B 46, 4092 (1992).
[CrossRef]

P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 46, 13603 (1992).
[CrossRef]

P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 48, 17308 (1993).
[CrossRef]

Proc. SPIE (1)

See, for example, Spectroscopic Characterization Techniques for Semiconductor Technology III, Proc. SPIE 946, 84 (1988).

Solid State Commun. (1)

X.-F. He, Solid State Commun. 75, 111 (1990).
[CrossRef]

Surf. Sci. (1)

D. E. Aspnes, Surf. Sci., 135, 284 (1983).
[CrossRef]

Thin Solid Films (1)

D. Mo, Y.-Y. Lin, J.-H. Tan, Z.-X. Yu, G.-Z. Zhou, K.-C. Gong, G.-P. Zhang, and X.-F. He, Thin Solid Films 234, 468 (1993).
[CrossRef]

Other (6)

X.-F. He, in Proceedings of the 22nd International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995), p. 281.

For a review, see D. E. Aspnes, in Optical Properties of Solids: New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), p. 799.

M. Cardona, Modulation Spectroscopy (Academic, New York, 1969).

K. B. Oldham and J. Spanier, The Fractional Calculus (Academic, New York, 1974).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965), p. 297.

See, for example, Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981).

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Figures (3)

Fig. 1
Fig. 1

Second-derivative spectra of interband optical transitions near a 2.4-dimensional critical point of the minimum type calculated with Eq. (5). Various values of broadening widths used in the calculation are indicated. The crosses correspond to the case of σ=0, i.e., the Lorentzian line shapes.

Fig. 2
Fig. 2

w-function line shapes (dots), compared with the Lorentzian and Gaussian functionals (solid curves).

Fig. 3
Fig. 3

Inhomogeneous linewidth (HWHM) as a function of temperature for different magnitudes of crystal strain. Thermal broadening is given by Eq. (7), where Γ0=30 meV and Θ=300 K.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

(k)(E)=ir-αMα,kE2d-α/2dEg-α/21(Eg-E-iΓ)k+1,
Mα,k=2k!|v|a·p|c|2(e/m)2(mvc/2π)α/22-α/0,
E-2dα/2dEα/2[E2(k)(E)]=irMα,kE21(Eg-E-iΓ)k+1,
g(Eg)=1πσexp-Eg-E¯gσ2,
¯(E)=-g(Eg)(E, Eg)dEg,
¯(k)(E)=ir-α+1Nα,kE2d-α/2dE¯g-α/2w(k)E-E¯g+iΓσ,
w(z)=iπ-exp(-t2)dtz-t,Im z>0.
w(z)=exp(-z2)[1+erf(iz)].
E-2dα/2dEα/2[E2¯(k)(E)]=ir+1Nα,kE2w(k)E-E¯g+iΓσ.
w(z)[1+i2z/π1/2]exp(-z2).
Γ(T)=Γ01+2eΘ/T-1,

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