Abstract

Construction and performance of a high-speed retardation modulation ellipsometer are described. An ADP four-crystal electrooptic modulator is used for the retardation modulation and a high-speed digitizer for the simultaneous detection of the transmitted light intensity and the modulation voltage. The ellipsometer can acquire the necessary data for determining a data point (Ψ,Δ) in 4 μsec and repeat the data acquisition for fifty data points at intervals of 4 μsec–160 msec. In such conditions, precision represented in terms of an average of root mean squares is 0.05° in Ψ and 0.15° in Δ when a BaK1 standard optical glass is used as a sample at the present stage. An example is given of the application to rapid growth of anodic films on a semiconductor GaAs wafer.

© 1983 Optical Society of America

Full Article  |  PDF Article

Errata

A. Moritani, Y. Okuda, H. Kubo, and J. Nakai, "High-speed retardation modulation ellipsometer: erratum," Appl. Opt. 23, 11-11 (1984)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-23-1-11

References

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  1. R. H. Muller, Surf. Sci. 56, 19 (1976) and references therein.
    [CrossRef]
  2. P. S. Hauge, Surf. Sci. 96, 108 (1980).
    [CrossRef]
  3. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1976).
  4. D. E. Aspnes, Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), p 799.
  5. D. E. Aspnes, A. A. Studna, Appl. Opt. 14, 220 (1975).
    [CrossRef] [PubMed]
  6. D. E. Aspnes, J. Opt. Soc. Am. 64, 639 (1974).
    [CrossRef]
  7. S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
    [CrossRef]
  8. J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci instrum. 44, 793 (1973).
    [CrossRef]
  9. V. M. Bermudez, V. H. Ritz, Appl. Opt. 17, 542 (1978).
    [CrossRef] [PubMed]
  10. H. Takasaki, Appl. Opt. 5, 759 (1966).
    [CrossRef] [PubMed]
  11. T. Yamaguchi, H. Hasunuma, Sci. Light 16, 64 (1967).
  12. T. Kasai, Rev. Sci. Instrum. 47, 1044 (1976).
    [CrossRef]
  13. H. J. Mathieu, D. E. McClure, R. H. Muller, Rev. Sci. Instrum., 45, 798 (1974).
    [CrossRef]
  14. A. Moritani, J. Nakai, Appl. Opt. 21, 3231 (1982).
    [CrossRef] [PubMed]
  15. A. Moritani, Y. Okuda, J. Nakai, Appl. Opt. 22, 1329 (1983).
    [CrossRef] [PubMed]
  16. Model GLG 2073, NEC, Tokyo, Japan.
  17. Model 36V, Mizojiri Optical Co., Ltd., Tokyo, Japan.
  18. Model 22, Coherent Associates, Danbury, Conn.
  19. W. L. Wolfe, in Handbook of Optics, W. G. Driscoll, Ed. (McGraw Hill, New York, 1978) p. 7–1.
  20. G. E. Francois, F. M. Librecht, Appl. Opt. 11, 472 (1972).
    [CrossRef] [PubMed]
  21. Model R550, Hamamatsu TV Co., Ltd., Hamamatsu, Japan.
  22. See Catalog for Hamamatsu TV Photomultiplier Tubes (Hamamatsu TV, Hamamatsu, Japan, 1980).
  23. Model 1435, Teledyne-Philbrick, Dedham, Mass.
  24. Instruction Manual for Digital Memory DM- 703 (Iwatsu Electric Co., Tokyo, Japan, 1978).
  25. A. Moritani, J. Nakai, Trans. Inst. Electr. Commun. Eng. Jpn. J66C, 129 (1983).
  26. Real parts of these imperfection parameters and x4 in Eq. (31) of Ref. 15 have been found negligible in the present optical system. See Ref. 15.
  27. P. G. Hoel, Introduction to Mathematical Statistics (Wiley, New York, 1966).
  28. This best fit has led to the expression of Eq. (1) in which the real parts of x1 and x3, and x4 have been disregarded in the present optical system (see Ref. 26). Therefore, the best fit actually yields the imaginary part of x3 in this case.
  29. P. S. Hauge, Surf. Sci. 96, 108 (1980).
    [CrossRef]
  30. P. S. Hauge, F. H. Dill, IBM J. Res. Develop. 17, 472 (1973).
    [CrossRef]
  31. D. E. Aspnes, Appl. Opt. 14, 1131 (1975).
    [CrossRef] [PubMed]
  32. T. Hoshino, A. Moritani, J. Nakai, Oyo Buturi 52, 443 (1983).
  33. H. Hasegawa, H. L. Hartnagel, J. Electrochem. Soc. 123, 713 (1976).
    [CrossRef]
  34. J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
    [CrossRef]
  35. A. Gat, IEEE Electron Device Lett. EDL-2, 85 (1981).
    [CrossRef]
  36. R. T. Fulks, C. J. Russo, P. R. Hanley, T. I. Kamins, Appl. Phys. Lett. 39, 604 (1981).
    [CrossRef]
  37. For example, model DM-902, Iwatsu Electric Co., Tokyo, Japan, operates at the writing speed U = 0.04 μsec/word with the memory capacity W = 6 kwords/channel in the external mode. See the Iwatsu Catalog for Electronic Measuring Instruments (1981). For another example, model 7612D, Tektronix, Inc. (Beaverton, Ore.), has the best available sampling rate of 5 nsec at 8 bits with W = 2 kwords/channel.See N. A. Robin, B. Ramirez, Electron. Des. 28, No. 3, 50 (1980).
  38. Note added in proof: Drevillon et al. have reported a fast polarization modulated ellipsometer using a piezobirefringent element in their recent publication;Rev. Sci. Instrum. 53, 969 (1982). It has capability of the shortest time measurement of about 20 μsec per data point with their digital detection system.

1983

A. Moritani, J. Nakai, Trans. Inst. Electr. Commun. Eng. Jpn. J66C, 129 (1983).

T. Hoshino, A. Moritani, J. Nakai, Oyo Buturi 52, 443 (1983).

A. Moritani, Y. Okuda, J. Nakai, Appl. Opt. 22, 1329 (1983).
[CrossRef] [PubMed]

1982

A. Moritani, J. Nakai, Appl. Opt. 21, 3231 (1982).
[CrossRef] [PubMed]

Note added in proof: Drevillon et al. have reported a fast polarization modulated ellipsometer using a piezobirefringent element in their recent publication;Rev. Sci. Instrum. 53, 969 (1982). It has capability of the shortest time measurement of about 20 μsec per data point with their digital detection system.

1981

A. Gat, IEEE Electron Device Lett. EDL-2, 85 (1981).
[CrossRef]

R. T. Fulks, C. J. Russo, P. R. Hanley, T. I. Kamins, Appl. Phys. Lett. 39, 604 (1981).
[CrossRef]

1980

For example, model DM-902, Iwatsu Electric Co., Tokyo, Japan, operates at the writing speed U = 0.04 μsec/word with the memory capacity W = 6 kwords/channel in the external mode. See the Iwatsu Catalog for Electronic Measuring Instruments (1981). For another example, model 7612D, Tektronix, Inc. (Beaverton, Ore.), has the best available sampling rate of 5 nsec at 8 bits with W = 2 kwords/channel.See N. A. Robin, B. Ramirez, Electron. Des. 28, No. 3, 50 (1980).

P. S. Hauge, Surf. Sci. 96, 108 (1980).
[CrossRef]

P. S. Hauge, Surf. Sci. 96, 108 (1980).
[CrossRef]

1978

J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
[CrossRef]

V. M. Bermudez, V. H. Ritz, Appl. Opt. 17, 542 (1978).
[CrossRef] [PubMed]

1976

R. H. Muller, Surf. Sci. 56, 19 (1976) and references therein.
[CrossRef]

T. Kasai, Rev. Sci. Instrum. 47, 1044 (1976).
[CrossRef]

H. Hasegawa, H. L. Hartnagel, J. Electrochem. Soc. 123, 713 (1976).
[CrossRef]

1975

1974

D. E. Aspnes, J. Opt. Soc. Am. 64, 639 (1974).
[CrossRef]

H. J. Mathieu, D. E. McClure, R. H. Muller, Rev. Sci. Instrum., 45, 798 (1974).
[CrossRef]

1973

P. S. Hauge, F. H. Dill, IBM J. Res. Develop. 17, 472 (1973).
[CrossRef]

S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
[CrossRef]

J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci instrum. 44, 793 (1973).
[CrossRef]

1972

1967

T. Yamaguchi, H. Hasunuma, Sci. Light 16, 64 (1967).

1966

Aspnes, D. E.

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1976).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1976).

Bermudez, V. M.

Brown, W. L.

J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
[CrossRef]

Burge, D. K.

S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
[CrossRef]

Callender, A. B.

J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci instrum. 44, 793 (1973).
[CrossRef]

Dill, F. H.

P. S. Hauge, F. H. Dill, IBM J. Res. Develop. 17, 472 (1973).
[CrossRef]

Francois, G. E.

Fulks, R. T.

R. T. Fulks, C. J. Russo, P. R. Hanley, T. I. Kamins, Appl. Phys. Lett. 39, 604 (1981).
[CrossRef]

Gat, A.

A. Gat, IEEE Electron Device Lett. EDL-2, 85 (1981).
[CrossRef]

Hanley, P. R.

R. T. Fulks, C. J. Russo, P. R. Hanley, T. I. Kamins, Appl. Phys. Lett. 39, 604 (1981).
[CrossRef]

Hartnagel, H. L.

H. Hasegawa, H. L. Hartnagel, J. Electrochem. Soc. 123, 713 (1976).
[CrossRef]

Hasegawa, H.

H. Hasegawa, H. L. Hartnagel, J. Electrochem. Soc. 123, 713 (1976).
[CrossRef]

Hasunuma, H.

T. Yamaguchi, H. Hasunuma, Sci. Light 16, 64 (1967).

Hauge, P. S.

P. S. Hauge, Surf. Sci. 96, 108 (1980).
[CrossRef]

P. S. Hauge, Surf. Sci. 96, 108 (1980).
[CrossRef]

P. S. Hauge, F. H. Dill, IBM J. Res. Develop. 17, 472 (1973).
[CrossRef]

Hoel, P. G.

P. G. Hoel, Introduction to Mathematical Statistics (Wiley, New York, 1966).

Hoshino, T.

T. Hoshino, A. Moritani, J. Nakai, Oyo Buturi 52, 443 (1983).

Jasperson, S. N.

S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
[CrossRef]

Kamins, T. I.

R. T. Fulks, C. J. Russo, P. R. Hanley, T. I. Kamins, Appl. Phys. Lett. 39, 604 (1981).
[CrossRef]

Kasai, T.

T. Kasai, Rev. Sci. Instrum. 47, 1044 (1976).
[CrossRef]

Leamy, H. J.

J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
[CrossRef]

Librecht, F. M.

Mathieu, H. J.

H. J. Mathieu, D. E. McClure, R. H. Muller, Rev. Sci. Instrum., 45, 798 (1974).
[CrossRef]

McClure, D. E.

H. J. Mathieu, D. E. McClure, R. H. Muller, Rev. Sci. Instrum., 45, 798 (1974).
[CrossRef]

Moritani, A.

A. Moritani, Y. Okuda, J. Nakai, Appl. Opt. 22, 1329 (1983).
[CrossRef] [PubMed]

T. Hoshino, A. Moritani, J. Nakai, Oyo Buturi 52, 443 (1983).

A. Moritani, J. Nakai, Trans. Inst. Electr. Commun. Eng. Jpn. J66C, 129 (1983).

A. Moritani, J. Nakai, Appl. Opt. 21, 3231 (1982).
[CrossRef] [PubMed]

Muller, R. H.

R. H. Muller, Surf. Sci. 56, 19 (1976) and references therein.
[CrossRef]

H. J. Mathieu, D. E. McClure, R. H. Muller, Rev. Sci. Instrum., 45, 798 (1974).
[CrossRef]

Nakai, J.

A. Moritani, Y. Okuda, J. Nakai, Appl. Opt. 22, 1329 (1983).
[CrossRef] [PubMed]

A. Moritani, J. Nakai, Trans. Inst. Electr. Commun. Eng. Jpn. J66C, 129 (1983).

T. Hoshino, A. Moritani, J. Nakai, Oyo Buturi 52, 443 (1983).

A. Moritani, J. Nakai, Appl. Opt. 21, 3231 (1982).
[CrossRef] [PubMed]

O'Handley, R. C.

S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
[CrossRef]

Okuda, Y.

Poate, J. M.

J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
[CrossRef]

Ramirez, B.

For example, model DM-902, Iwatsu Electric Co., Tokyo, Japan, operates at the writing speed U = 0.04 μsec/word with the memory capacity W = 6 kwords/channel in the external mode. See the Iwatsu Catalog for Electronic Measuring Instruments (1981). For another example, model 7612D, Tektronix, Inc. (Beaverton, Ore.), has the best available sampling rate of 5 nsec at 8 bits with W = 2 kwords/channel.See N. A. Robin, B. Ramirez, Electron. Des. 28, No. 3, 50 (1980).

Ritz, V. H.

Robin, N. A.

For example, model DM-902, Iwatsu Electric Co., Tokyo, Japan, operates at the writing speed U = 0.04 μsec/word with the memory capacity W = 6 kwords/channel in the external mode. See the Iwatsu Catalog for Electronic Measuring Instruments (1981). For another example, model 7612D, Tektronix, Inc. (Beaverton, Ore.), has the best available sampling rate of 5 nsec at 8 bits with W = 2 kwords/channel.See N. A. Robin, B. Ramirez, Electron. Des. 28, No. 3, 50 (1980).

Rodgers, J. W.

J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
[CrossRef]

Rousseau, D.

J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
[CrossRef]

Rozgonyi, G. A.

J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
[CrossRef]

Russo, C. J.

R. T. Fulks, C. J. Russo, P. R. Hanley, T. I. Kamins, Appl. Phys. Lett. 39, 604 (1981).
[CrossRef]

Schnatterly, S. E.

J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci instrum. 44, 793 (1973).
[CrossRef]

Shelnutt, J. A.

J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
[CrossRef]

Sheng, T. T.

J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
[CrossRef]

Studna, A. A.

Takasaki, H.

Treu, J. I.

J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci instrum. 44, 793 (1973).
[CrossRef]

Williams, J. S.

J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
[CrossRef]

Wolfe, W. L.

W. L. Wolfe, in Handbook of Optics, W. G. Driscoll, Ed. (McGraw Hill, New York, 1978) p. 7–1.

Yamaguchi, T.

T. Yamaguchi, H. Hasunuma, Sci. Light 16, 64 (1967).

Appl. Opt.

Appl. Phys. Lett.

J. S. Williams, W. L. Brown, H. J. Leamy, J. M. Poate, J. W. Rodgers, D. Rousseau, G. A. Rozgonyi, J. A. Shelnutt, T. T. Sheng, Appl. Phys. Lett. 33, 542 (1978).
[CrossRef]

R. T. Fulks, C. J. Russo, P. R. Hanley, T. I. Kamins, Appl. Phys. Lett. 39, 604 (1981).
[CrossRef]

Electron. Des.

For example, model DM-902, Iwatsu Electric Co., Tokyo, Japan, operates at the writing speed U = 0.04 μsec/word with the memory capacity W = 6 kwords/channel in the external mode. See the Iwatsu Catalog for Electronic Measuring Instruments (1981). For another example, model 7612D, Tektronix, Inc. (Beaverton, Ore.), has the best available sampling rate of 5 nsec at 8 bits with W = 2 kwords/channel.See N. A. Robin, B. Ramirez, Electron. Des. 28, No. 3, 50 (1980).

IBM J. Res. Develop.

P. S. Hauge, F. H. Dill, IBM J. Res. Develop. 17, 472 (1973).
[CrossRef]

IEEE Electron Device Lett.

A. Gat, IEEE Electron Device Lett. EDL-2, 85 (1981).
[CrossRef]

J. Electrochem. Soc.

H. Hasegawa, H. L. Hartnagel, J. Electrochem. Soc. 123, 713 (1976).
[CrossRef]

J. Opt. Soc. Am.

Oyo Buturi

T. Hoshino, A. Moritani, J. Nakai, Oyo Buturi 52, 443 (1983).

Rev. Sci instrum.

J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci instrum. 44, 793 (1973).
[CrossRef]

Rev. Sci. Instrum.

Note added in proof: Drevillon et al. have reported a fast polarization modulated ellipsometer using a piezobirefringent element in their recent publication;Rev. Sci. Instrum. 53, 969 (1982). It has capability of the shortest time measurement of about 20 μsec per data point with their digital detection system.

T. Kasai, Rev. Sci. Instrum. 47, 1044 (1976).
[CrossRef]

H. J. Mathieu, D. E. McClure, R. H. Muller, Rev. Sci. Instrum., 45, 798 (1974).
[CrossRef]

Sci. Light

T. Yamaguchi, H. Hasunuma, Sci. Light 16, 64 (1967).

Surf. Sci.

P. S. Hauge, Surf. Sci. 96, 108 (1980).
[CrossRef]

S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
[CrossRef]

R. H. Muller, Surf. Sci. 56, 19 (1976) and references therein.
[CrossRef]

P. S. Hauge, Surf. Sci. 96, 108 (1980).
[CrossRef]

Trans. Inst. Electr. Commun. Eng. Jpn.

A. Moritani, J. Nakai, Trans. Inst. Electr. Commun. Eng. Jpn. J66C, 129 (1983).

Other

Real parts of these imperfection parameters and x4 in Eq. (31) of Ref. 15 have been found negligible in the present optical system. See Ref. 15.

P. G. Hoel, Introduction to Mathematical Statistics (Wiley, New York, 1966).

This best fit has led to the expression of Eq. (1) in which the real parts of x1 and x3, and x4 have been disregarded in the present optical system (see Ref. 26). Therefore, the best fit actually yields the imaginary part of x3 in this case.

Model GLG 2073, NEC, Tokyo, Japan.

Model 36V, Mizojiri Optical Co., Ltd., Tokyo, Japan.

Model 22, Coherent Associates, Danbury, Conn.

W. L. Wolfe, in Handbook of Optics, W. G. Driscoll, Ed. (McGraw Hill, New York, 1978) p. 7–1.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1976).

D. E. Aspnes, Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), p 799.

Model R550, Hamamatsu TV Co., Ltd., Hamamatsu, Japan.

See Catalog for Hamamatsu TV Photomultiplier Tubes (Hamamatsu TV, Hamamatsu, Japan, 1980).

Model 1435, Teledyne-Philbrick, Dedham, Mass.

Instruction Manual for Digital Memory DM- 703 (Iwatsu Electric Co., Tokyo, Japan, 1978).

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Figures (10)

Fig. 1
Fig. 1

Photograph of the electrooptic modulator (EOM) for retardation modulation mounted on an optical arm followed by the analyzer and the photomultiplier. Modulation voltage is fed through the black wire and dc bias through the white one, separately. The EOM is 23 cm long.

Fig. 2
Fig. 2

Block diagram of the ellipsometer system. EOM and PM are the abbreviations for electrooptic modulator and photomultiplier, respectively. Light intensity I and modulation voltage V are simultaneously read by the two-channel digitizer. The sampling controller feeds external trigger pulses to the digitizer to control the number of sampling points and intervals of sampling. The triangular voltage is applied by the function generator through the EOM power amplifier to modulate the retardation with the EOM.

Fig. 3
Fig. 3

Modulation voltage waveform and timing of sampling. (a) The modulation voltage with amplitude Vm applied to the EOM. (b) Sampling pulses fed to the external trigger-in of the digitizer produced by the sampling controller. In a cycle period T, sampling pulses N are generated to acquire the necessary data for determining a data point (Ψ,Δ). The data acquisition is repeated at intervals Ti. (c) The trigger that the function generator feeds by which the start of sampling pulses for each data-acquisition cycle and that of modulation voltage are controlled.

Fig. 4
Fig. 4

Block diagram of the sampling controller circuit. The trigger shown in Fig. 3(c) is fed to the external pulse-in. The start trigger with which an experimental run starts is fed through the start pulse-in. See the text.

Fig. 5
Fig. 5

Transmitted light intensity vs modulation voltage in a single optical cycle: (a) was measured for calibration with P = 0°, and (b) for the high-speed measurement with P ≈ Ψ of a GaAs sample. The measurement was made with N = 50, U = 0.2 μsec/word and hence T = 10 μsec. The operating supply voltage to the photomultiplier in (a) is different from that in (b). The solid curves are the best-fitted ones obtained with Eq. (8).

Fig. 6
Fig. 6

Ψ and Δ of a BaK1 optical glass vs time measured at 3-min intervals except those of 6 min indicated by arrows for the purpose of checking the long-term stability of the absolute values. The measurement conditions are described in the text.

Fig. 7
Fig. 7

Scatter in data (Ψ,Δ) defined by Eq. (12) in the high-speed measurement as the function of a number of sampling points N in a single optical cycle with T kept constant at 40 μsec. The BaK1 glass is used as the sample.

Fig. 8
Fig. 8

Scatter in data (Ψ,Δ) defined by Eq. (12) measured as a function of the data-acquisition time T with N kept constant at 40. The BaK1 glass is used as the sample.

Fig. 9
Fig. 9

Scatter in data (Ψ,Δ) defined by Eq. (12) measured as a function of the polarizer azimuth P. Theoretical minimum of δΨ and δΔ should be at P = Ψ (= 26.1° for ϕ = 75°) of the BaK1 sample.

Fig. 10
Fig. 10

Variation of (Ψ,Δ) vs time in the anodization process in GaAs. Constant current anodization with 100-mA/cm2 current density was performed to grow anodic film ∼970 Å thick at a growth rate of 0.6 Å/msec. The ellipsometric measurement was made with T = 4 μsec, N = 40, Ti= 32 msec, P = 20°, and ϕ = 60°.

Tables (1)

Tables Icon

Table I Forty Actual Data Points (ψ,Δ) of a Si Real Surface Measured In an Experimental Run and Important Parameters Used and Derived from the Data

Equations (16)

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

T p 11 = 1 , T p 12 = x 3 x 2 exp [ i ( δ 1 2 δ ) ] x 1 exp [ i ( δ 1 δ 2 4 δ ) ] , T p 21 = x 1 * + x 2 exp [ i ( δ 2 + 2 δ ) ] x 3 * exp [ i ( δ 1 δ 2 4 δ ) ] , T p 22 = exp [ i ( δ 1 δ 2 4 δ ) ] .
δ 1 = δ 01 + δ 02 , δ 2 = δ 03 + δ 04 .
I = I 0 ( 1 + a 1 cos 4 δ + a 2 sin 4 δ + a 3 cos 2 δ + a 4 sin 2 δ ) ,
4 δ = EV + G ,
G = A p ( δ 1 δ 2 ) , a 1 = cos 2 Ψ e , a 2 = sin 2 Ψ e sin Δ e + 2 i x 3 sin 2 Ψ e cos Δ e ,
a 3 = 2 x 2 sin 2 Ψ e cos Δ e cos 1 2 ( δ 1 + δ 2 ) , a 4 = 2 x 2 sin 2 Ψ e cos Δ e sin 1 2 ( δ 1 + δ 2 ) .
tan Ψ = tan P tan Ψ e , Δ = Δ e
I = I 0 ( 1 + a 1 cos EV + a 2 sin EV + a 3 cos 1 2 EV + a 4 sin 1 2 EV ) ,
a 1 = a 1 cos G + a 2 sin G , a 2 = a 1 sin G + a 2 cos G , a 3 = a 3 cos G 2 + a 4 sin G 2 , a 4 = a 3 sin G 2 + a 4 cos G 2 .
G = tan 1 ( a 2 a 1 ) .
a 1 = a 1 cos G a 2 sin G , a 2 = a 1 sin G + a 2 cos G ;
δ Ψ = j = 1 m i = 1 l ( Ψ aj Ψ ij ) 2 l m ,
a 1 = 0.121
a 2 = 0.431
a 3 = 0.009
a 4 = 0.044

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