Abstract

Second-harmonic generation and linear photomodulation are combined to study free-charge trapping mechanisms at ZnSe–GaAs(001) heterointerfaces. The variation of second-harmonic intensity as a function of charged-trap density at the buried junction is analyzed quantitatively and used with time-dependent measurements to determine interfacial charge-trap lifetimes.

© 1993 Optical Society of America

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References

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  1. E. Y. Wang, W. A. Albers, C. E. Bliel, in II–VI Semiconducting Compounds, D. G. Thomas, ed. (Benjamin, New York, 1967), p. 136.
  2. H. Shen, P. Parayanthal, F. H. Pollak, M. Tomkiewicz, T. J. Drummond, J. N. Schulman, Appl. Phys. Lett. 48, 653 (1986).
    [CrossRef]
  3. M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 296; T. Zhang, Z. Xu, W. Lin, G. K. Wong, J. B. Ketterson, X. Wang, R. P. H. Chang, S. Liu, M. M. Kappes, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Washington, D.C., 1992), p. 262.
  4. M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 69, 3579 (1992).
    [CrossRef] [PubMed]
  5. See, for example, H. H. K. Tom, T. F. Heinz, Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983); T. F. Heinz, M. M. T. Loy, W. A. Thompson, Phys. Rev. Lett. 54, 63 (1985); H. W. K. Tom, G. D. Aumiller, Phys. Rev. B 33, 8818 (1986), and references therein.
    [CrossRef] [PubMed]
  6. J. F. McGilp, Y. Yeh, Solid State Commun. 59, 91 (1986).
    [CrossRef]
  7. T. F. Heinz, F. J. Himpsel, E. Palange, E. Burstein, Phys. Rev. Lett. 63, 644 (1989).
    [CrossRef] [PubMed]
  8. M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 68, 3761 (1992).
    [CrossRef] [PubMed]
  9. L. Kassel, H. Abad, J. W. Garland, P. M. Raccah, J. E. Potts, M. A. Haase, H. Cheng, Appl. Phys. Lett. 56, 42 (1990).
    [CrossRef]
  10. K. Yokoyama, K. Hess, Phys. Rev. B 33, 5595 (1986).
    [CrossRef]
  11. We have calculated that the density of carriers generated by two-photon absorption of the fundamental dye laser light is at least 4 orders of magnitude smaller than the density of the carriers generated by the photomodulating lamp light.
  12. Our theoretical modeling was based on the integration of the one-dimensional Schrödinger equation for quantum-well potential. It showed that there existed six resonance states.
  13. B. V. Zhuk, I. A. Zhukov, A. A. Zlenko, Solid-State Electron. 29, 247 (1986).
    [CrossRef]
  14. The other elements of the second-order susceptibility tensor and the higher-order bulk contribution were measured to be negligible. For more detail, see M. S. Yaganeh, “Nonlinear optical spectroscopy of solid–solid interfaces,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1992).
  15. S. Wang, Solid State Electronics (McGraw-Hill, New York, 1963).
  16. N. V. Joshi, Phys. Rev. B 27, 6272 (1983).
    [CrossRef]
  17. R. Shankar, Principles of Quantum Mechanics (Plenum, New York, 1985), p. 186.
  18. See, for example, M. C. Tamargo, J. L. de Miguel, D. M. Hwang, H. H. Farrell, J. Vac. Sci. Technol. B 6, 784 (1988), and references therein.
    [CrossRef]
  19. M. S. Yeganeh, J. Qi, J. P. Culver, A. G. Yodh, M. C. Tamargo, Phys. Rev. B 46, 1603 (1992).
    [CrossRef]

1992

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 69, 3579 (1992).
[CrossRef] [PubMed]

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 68, 3761 (1992).
[CrossRef] [PubMed]

M. S. Yeganeh, J. Qi, J. P. Culver, A. G. Yodh, M. C. Tamargo, Phys. Rev. B 46, 1603 (1992).
[CrossRef]

1990

L. Kassel, H. Abad, J. W. Garland, P. M. Raccah, J. E. Potts, M. A. Haase, H. Cheng, Appl. Phys. Lett. 56, 42 (1990).
[CrossRef]

1989

T. F. Heinz, F. J. Himpsel, E. Palange, E. Burstein, Phys. Rev. Lett. 63, 644 (1989).
[CrossRef] [PubMed]

1988

See, for example, M. C. Tamargo, J. L. de Miguel, D. M. Hwang, H. H. Farrell, J. Vac. Sci. Technol. B 6, 784 (1988), and references therein.
[CrossRef]

1986

K. Yokoyama, K. Hess, Phys. Rev. B 33, 5595 (1986).
[CrossRef]

B. V. Zhuk, I. A. Zhukov, A. A. Zlenko, Solid-State Electron. 29, 247 (1986).
[CrossRef]

H. Shen, P. Parayanthal, F. H. Pollak, M. Tomkiewicz, T. J. Drummond, J. N. Schulman, Appl. Phys. Lett. 48, 653 (1986).
[CrossRef]

J. F. McGilp, Y. Yeh, Solid State Commun. 59, 91 (1986).
[CrossRef]

1983

See, for example, H. H. K. Tom, T. F. Heinz, Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983); T. F. Heinz, M. M. T. Loy, W. A. Thompson, Phys. Rev. Lett. 54, 63 (1985); H. W. K. Tom, G. D. Aumiller, Phys. Rev. B 33, 8818 (1986), and references therein.
[CrossRef] [PubMed]

N. V. Joshi, Phys. Rev. B 27, 6272 (1983).
[CrossRef]

Abad, H.

L. Kassel, H. Abad, J. W. Garland, P. M. Raccah, J. E. Potts, M. A. Haase, H. Cheng, Appl. Phys. Lett. 56, 42 (1990).
[CrossRef]

Albers, W. A.

E. Y. Wang, W. A. Albers, C. E. Bliel, in II–VI Semiconducting Compounds, D. G. Thomas, ed. (Benjamin, New York, 1967), p. 136.

Bliel, C. E.

E. Y. Wang, W. A. Albers, C. E. Bliel, in II–VI Semiconducting Compounds, D. G. Thomas, ed. (Benjamin, New York, 1967), p. 136.

Burstein, E.

T. F. Heinz, F. J. Himpsel, E. Palange, E. Burstein, Phys. Rev. Lett. 63, 644 (1989).
[CrossRef] [PubMed]

Cheng, H.

L. Kassel, H. Abad, J. W. Garland, P. M. Raccah, J. E. Potts, M. A. Haase, H. Cheng, Appl. Phys. Lett. 56, 42 (1990).
[CrossRef]

Culver, J. P.

M. S. Yeganeh, J. Qi, J. P. Culver, A. G. Yodh, M. C. Tamargo, Phys. Rev. B 46, 1603 (1992).
[CrossRef]

de Miguel, J. L.

See, for example, M. C. Tamargo, J. L. de Miguel, D. M. Hwang, H. H. Farrell, J. Vac. Sci. Technol. B 6, 784 (1988), and references therein.
[CrossRef]

Drummond, T. J.

H. Shen, P. Parayanthal, F. H. Pollak, M. Tomkiewicz, T. J. Drummond, J. N. Schulman, Appl. Phys. Lett. 48, 653 (1986).
[CrossRef]

Farrell, H. H.

See, for example, M. C. Tamargo, J. L. de Miguel, D. M. Hwang, H. H. Farrell, J. Vac. Sci. Technol. B 6, 784 (1988), and references therein.
[CrossRef]

Garland, J. W.

L. Kassel, H. Abad, J. W. Garland, P. M. Raccah, J. E. Potts, M. A. Haase, H. Cheng, Appl. Phys. Lett. 56, 42 (1990).
[CrossRef]

Haase, M. A.

L. Kassel, H. Abad, J. W. Garland, P. M. Raccah, J. E. Potts, M. A. Haase, H. Cheng, Appl. Phys. Lett. 56, 42 (1990).
[CrossRef]

Heinz, T. F.

T. F. Heinz, F. J. Himpsel, E. Palange, E. Burstein, Phys. Rev. Lett. 63, 644 (1989).
[CrossRef] [PubMed]

See, for example, H. H. K. Tom, T. F. Heinz, Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983); T. F. Heinz, M. M. T. Loy, W. A. Thompson, Phys. Rev. Lett. 54, 63 (1985); H. W. K. Tom, G. D. Aumiller, Phys. Rev. B 33, 8818 (1986), and references therein.
[CrossRef] [PubMed]

Hess, K.

K. Yokoyama, K. Hess, Phys. Rev. B 33, 5595 (1986).
[CrossRef]

Himpsel, F. J.

T. F. Heinz, F. J. Himpsel, E. Palange, E. Burstein, Phys. Rev. Lett. 63, 644 (1989).
[CrossRef] [PubMed]

Hwang, D. M.

See, for example, M. C. Tamargo, J. L. de Miguel, D. M. Hwang, H. H. Farrell, J. Vac. Sci. Technol. B 6, 784 (1988), and references therein.
[CrossRef]

Joshi, N. V.

N. V. Joshi, Phys. Rev. B 27, 6272 (1983).
[CrossRef]

Kassel, L.

L. Kassel, H. Abad, J. W. Garland, P. M. Raccah, J. E. Potts, M. A. Haase, H. Cheng, Appl. Phys. Lett. 56, 42 (1990).
[CrossRef]

McGilp, J. F.

J. F. McGilp, Y. Yeh, Solid State Commun. 59, 91 (1986).
[CrossRef]

Palange, E.

T. F. Heinz, F. J. Himpsel, E. Palange, E. Burstein, Phys. Rev. Lett. 63, 644 (1989).
[CrossRef] [PubMed]

Parayanthal, P.

H. Shen, P. Parayanthal, F. H. Pollak, M. Tomkiewicz, T. J. Drummond, J. N. Schulman, Appl. Phys. Lett. 48, 653 (1986).
[CrossRef]

Pollak, F. H.

H. Shen, P. Parayanthal, F. H. Pollak, M. Tomkiewicz, T. J. Drummond, J. N. Schulman, Appl. Phys. Lett. 48, 653 (1986).
[CrossRef]

Potts, J. E.

L. Kassel, H. Abad, J. W. Garland, P. M. Raccah, J. E. Potts, M. A. Haase, H. Cheng, Appl. Phys. Lett. 56, 42 (1990).
[CrossRef]

Qi, J.

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 68, 3761 (1992).
[CrossRef] [PubMed]

M. S. Yeganeh, J. Qi, J. P. Culver, A. G. Yodh, M. C. Tamargo, Phys. Rev. B 46, 1603 (1992).
[CrossRef]

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 69, 3579 (1992).
[CrossRef] [PubMed]

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 296; T. Zhang, Z. Xu, W. Lin, G. K. Wong, J. B. Ketterson, X. Wang, R. P. H. Chang, S. Liu, M. M. Kappes, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Washington, D.C., 1992), p. 262.

Raccah, P. M.

L. Kassel, H. Abad, J. W. Garland, P. M. Raccah, J. E. Potts, M. A. Haase, H. Cheng, Appl. Phys. Lett. 56, 42 (1990).
[CrossRef]

Schulman, J. N.

H. Shen, P. Parayanthal, F. H. Pollak, M. Tomkiewicz, T. J. Drummond, J. N. Schulman, Appl. Phys. Lett. 48, 653 (1986).
[CrossRef]

Shankar, R.

R. Shankar, Principles of Quantum Mechanics (Plenum, New York, 1985), p. 186.

Shen, H.

H. Shen, P. Parayanthal, F. H. Pollak, M. Tomkiewicz, T. J. Drummond, J. N. Schulman, Appl. Phys. Lett. 48, 653 (1986).
[CrossRef]

Shen, Y. R.

See, for example, H. H. K. Tom, T. F. Heinz, Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983); T. F. Heinz, M. M. T. Loy, W. A. Thompson, Phys. Rev. Lett. 54, 63 (1985); H. W. K. Tom, G. D. Aumiller, Phys. Rev. B 33, 8818 (1986), and references therein.
[CrossRef] [PubMed]

Tamargo, M. C.

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 69, 3579 (1992).
[CrossRef] [PubMed]

M. S. Yeganeh, J. Qi, J. P. Culver, A. G. Yodh, M. C. Tamargo, Phys. Rev. B 46, 1603 (1992).
[CrossRef]

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 68, 3761 (1992).
[CrossRef] [PubMed]

See, for example, M. C. Tamargo, J. L. de Miguel, D. M. Hwang, H. H. Farrell, J. Vac. Sci. Technol. B 6, 784 (1988), and references therein.
[CrossRef]

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 296; T. Zhang, Z. Xu, W. Lin, G. K. Wong, J. B. Ketterson, X. Wang, R. P. H. Chang, S. Liu, M. M. Kappes, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Washington, D.C., 1992), p. 262.

Tom, H. H. K.

See, for example, H. H. K. Tom, T. F. Heinz, Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983); T. F. Heinz, M. M. T. Loy, W. A. Thompson, Phys. Rev. Lett. 54, 63 (1985); H. W. K. Tom, G. D. Aumiller, Phys. Rev. B 33, 8818 (1986), and references therein.
[CrossRef] [PubMed]

Tomkiewicz, M.

H. Shen, P. Parayanthal, F. H. Pollak, M. Tomkiewicz, T. J. Drummond, J. N. Schulman, Appl. Phys. Lett. 48, 653 (1986).
[CrossRef]

Wang, E. Y.

E. Y. Wang, W. A. Albers, C. E. Bliel, in II–VI Semiconducting Compounds, D. G. Thomas, ed. (Benjamin, New York, 1967), p. 136.

Wang, S.

S. Wang, Solid State Electronics (McGraw-Hill, New York, 1963).

Yaganeh, M. S.

The other elements of the second-order susceptibility tensor and the higher-order bulk contribution were measured to be negligible. For more detail, see M. S. Yaganeh, “Nonlinear optical spectroscopy of solid–solid interfaces,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1992).

Yeganeh, M. S.

M. S. Yeganeh, J. Qi, J. P. Culver, A. G. Yodh, M. C. Tamargo, Phys. Rev. B 46, 1603 (1992).
[CrossRef]

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 68, 3761 (1992).
[CrossRef] [PubMed]

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 69, 3579 (1992).
[CrossRef] [PubMed]

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 296; T. Zhang, Z. Xu, W. Lin, G. K. Wong, J. B. Ketterson, X. Wang, R. P. H. Chang, S. Liu, M. M. Kappes, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Washington, D.C., 1992), p. 262.

Yeh, Y.

J. F. McGilp, Y. Yeh, Solid State Commun. 59, 91 (1986).
[CrossRef]

Yodh, A. G.

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 68, 3761 (1992).
[CrossRef] [PubMed]

M. S. Yeganeh, J. Qi, J. P. Culver, A. G. Yodh, M. C. Tamargo, Phys. Rev. B 46, 1603 (1992).
[CrossRef]

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 69, 3579 (1992).
[CrossRef] [PubMed]

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 296; T. Zhang, Z. Xu, W. Lin, G. K. Wong, J. B. Ketterson, X. Wang, R. P. H. Chang, S. Liu, M. M. Kappes, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Washington, D.C., 1992), p. 262.

Yokoyama, K.

K. Yokoyama, K. Hess, Phys. Rev. B 33, 5595 (1986).
[CrossRef]

Zhuk, B. V.

B. V. Zhuk, I. A. Zhukov, A. A. Zlenko, Solid-State Electron. 29, 247 (1986).
[CrossRef]

Zhukov, I. A.

B. V. Zhuk, I. A. Zhukov, A. A. Zlenko, Solid-State Electron. 29, 247 (1986).
[CrossRef]

Zlenko, A. A.

B. V. Zhuk, I. A. Zhukov, A. A. Zlenko, Solid-State Electron. 29, 247 (1986).
[CrossRef]

Appl. Phys. Lett.

H. Shen, P. Parayanthal, F. H. Pollak, M. Tomkiewicz, T. J. Drummond, J. N. Schulman, Appl. Phys. Lett. 48, 653 (1986).
[CrossRef]

L. Kassel, H. Abad, J. W. Garland, P. M. Raccah, J. E. Potts, M. A. Haase, H. Cheng, Appl. Phys. Lett. 56, 42 (1990).
[CrossRef]

J. Vac. Sci. Technol. B

See, for example, M. C. Tamargo, J. L. de Miguel, D. M. Hwang, H. H. Farrell, J. Vac. Sci. Technol. B 6, 784 (1988), and references therein.
[CrossRef]

Phys. Rev. B

M. S. Yeganeh, J. Qi, J. P. Culver, A. G. Yodh, M. C. Tamargo, Phys. Rev. B 46, 1603 (1992).
[CrossRef]

N. V. Joshi, Phys. Rev. B 27, 6272 (1983).
[CrossRef]

K. Yokoyama, K. Hess, Phys. Rev. B 33, 5595 (1986).
[CrossRef]

Phys. Rev. Lett.

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 69, 3579 (1992).
[CrossRef] [PubMed]

See, for example, H. H. K. Tom, T. F. Heinz, Y. R. Shen, Phys. Rev. Lett. 51, 1983 (1983); T. F. Heinz, M. M. T. Loy, W. A. Thompson, Phys. Rev. Lett. 54, 63 (1985); H. W. K. Tom, G. D. Aumiller, Phys. Rev. B 33, 8818 (1986), and references therein.
[CrossRef] [PubMed]

T. F. Heinz, F. J. Himpsel, E. Palange, E. Burstein, Phys. Rev. Lett. 63, 644 (1989).
[CrossRef] [PubMed]

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, Phys. Rev. Lett. 68, 3761 (1992).
[CrossRef] [PubMed]

Solid State Commun.

J. F. McGilp, Y. Yeh, Solid State Commun. 59, 91 (1986).
[CrossRef]

Solid-State Electron.

B. V. Zhuk, I. A. Zhukov, A. A. Zlenko, Solid-State Electron. 29, 247 (1986).
[CrossRef]

Other

The other elements of the second-order susceptibility tensor and the higher-order bulk contribution were measured to be negligible. For more detail, see M. S. Yaganeh, “Nonlinear optical spectroscopy of solid–solid interfaces,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1992).

S. Wang, Solid State Electronics (McGraw-Hill, New York, 1963).

R. Shankar, Principles of Quantum Mechanics (Plenum, New York, 1985), p. 186.

M. S. Yeganeh, J. Qi, A. G. Yodh, M. C. Tamargo, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 296; T. Zhang, Z. Xu, W. Lin, G. K. Wong, J. B. Ketterson, X. Wang, R. P. H. Chang, S. Liu, M. M. Kappes, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Washington, D.C., 1992), p. 262.

We have calculated that the density of carriers generated by two-photon absorption of the fundamental dye laser light is at least 4 orders of magnitude smaller than the density of the carriers generated by the photomodulating lamp light.

Our theoretical modeling was based on the integration of the one-dimensional Schrödinger equation for quantum-well potential. It showed that there existed six resonance states.

E. Y. Wang, W. A. Albers, C. E. Bliel, in II–VI Semiconducting Compounds, D. G. Thomas, ed. (Benjamin, New York, 1967), p. 136.

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Figures (8)

Fig. 1
Fig. 1

Energy band profile as a function of depth for the ZnSe–GaAs(001) system. This band profile was determined by solving the Poisson equation for a Gaussian charge distribution. The thickness of the ZnSe overlayer is 21.5 nm.

Fig. 2
Fig. 2

Schematic of the PSHG experiment. The sample was illuminated at normal incidence by light from a tungsten-lamp monochromator while the SHG experiment was in progress: PMT, photomultiplier tube; P, polarizer; SF, spectral filter; M, monochromator; ωp, angular frequency of photomodulating beam.

Fig. 3
Fig. 3

(a) Variation of the conduction band profile with photomodulation. The variation was calculated on the basis of the creation of positive interface charge. The band bending increases (decreases) on the GaAs (ZnSe) side of the junction. The solid (broken) curve represents the band profile in the absence (presence) of the photomodulation light source. (b) Variation of quantum-well wave-function amplitude with photomodulation. The same variation for the valence band wave function is shown in the inset. The amplitude of the wave function within the well and the depletion region decreases. The solid (broken) curve represents the wave function in the absence (presence) of the photomodulation light source.

Fig. 4
Fig. 4

Variation of the resonance interface SHG peak intensity at 2.72 eV as a function of lamp photon energy. The intensity transmitted into the sample was kept constant at 10 μW/cm2.

Fig. 5
Fig. 5

Normalized second-harmonic intensity at lamp photon energies of 2.4 eV (*) and 3.0 eV (⋄) as a function of time. The sample was illuminated by the photoexcitation beam for at least 2 min, then the photoexcitation shutter was closed (at t = 0) and data acquisition began.

Fig. 6
Fig. 6

Normalized second-harmonic intensity as a function of time. A photoexcitation beam with intensity 5.3 μW/cm2 illuminated the sample at t = 0.

Fig. 7
Fig. 7

The inverse of charging time (τh) as a function of the intensity. The solid line is the best fit to the data.

Fig. 8
Fig. 8

The steady-state normalized second-harmonic intensity as a function of lamp intensity. The dotted curve is the best fit when all the available data are used, and the solid curve is the best fit when only the low intensity portion of the data is used.

Equations (21)

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

p t t = k 1 h p ( N h p t ) k 2 h n p t r h p t .
p = α 1 h I l + p 0 ,
n = α 2 h I l + n 0 .
p t ( t ) = A h exp ( t / τ h ) + k 1 h α 1 h N h τ d h I l 1 + I l / I c h ,
I c h = 1 ( k 1 h α 1 h + k 2 h α 2 h ) τ d h ,
τ d h = 1 k 2 h n 0 + r h ,
τ h = τ d h 1 + I l / I c h .
A h = k 1 h α 1 h N h τ d h I l 1 + I l / I c h .
p t ( t ) = p t 0 exp ( t / τ d h ) .
H h ( 1 ) = 2 π e q h p t ( z d ) ,
| w = | w 0 + w w | H h ( 1 ) | w 0 E w w 0 | w .
χ z z z χ z z z , 0 = 1 + w 2 π e q h p t E w o w × ( υ | z | w w | z | w 0 υ | z | w 0 + w 0 | z | w w | z | e w 0 | z | e ) 1 + M h p t ,
M h w 2 π e q h E w o w ( υ | z | w w | z | w 0 υ | z | w 0 + w 0 | z | w w | z | e w 0 | z | e ) .
I ( 2 ω ) I 0 ( 2 ω ) = [ 1 + C 1 h + C 2 h exp ( t / τ h ) ] 2 .
C 1 h = M h k 1 h α 1 h N h τ d h I l 1 + I l / I c h ,
C 2 h = M h A h ,
n t t = k 1 e n ( N e n t ) k 2 e p n t r e n t .
δ n t = A e exp ( t / τ e ) + k 1 e ( k 2 e p 0 + r e ) α 2 e N e τ d e 2 I l 1 + I l / I c e ,
τ e = τ d e 1 + I l / I c e ,
I c e = 1 α 2 e k 1 e τ d e ,
τ d e = 1 ( k 1 e n 0 + k 2 e p 0 + r e ) .

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