Abstract

A new null ellipsometer is described that uses photoelastic modulator (PEM). The phase modulation adds a good signal-to-noise ratio, high sensitivity, and linearity near null positions to the traditional high-precision nulling system. The ellipsometric angles Δ and ψ are obtained by azimuth measurement of the analyzer and the polarizer-PEM system, for which the first and second harmonics of modulator frequency cross the zeros. We show that the null system is insensitive to ellipsometer misadjustment and component imperfections and modulator calibration is not needed. In addition, a fast ellipsometer mode for fine changes measurement of ellipsometric angles is proposed.

© 2004 Optical Society of America

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References

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  1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).
  2. I. Ohlídal and D. Franta, “Ellipsometry of thin film systems,” in Progress in Optics , E. Wolf, ed., vol. 41, (North-Holland, Amsterdam, 2000) pp. 181–282.
    [Crossref]
  3. S.-M. F. Nee, “Error analysis of null ellipsometry with depolarization,” Appl. Opt. 38, 5388–5398 (1999).
    [Crossref]
  4. A. B. Winterbottom, in Ellipsometry in the measurement of surfaces and thin films, E. Passaglia, R. R. Stromberg, and J. Kruger, eds., Vol. 256, (National Bureau of Standard Miscellaneous Publication, US Goverment Printing Office, Washington, 1964) p. 97.
  5. H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
    [Crossref]
  6. M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
    [Crossref]
  7. H. Zhu, L. Liu, Y. Wen, Z. Lü, and B. Zhang, “High-precision system for automatic null ellipsometric measurement,” Appl. Opt. 41, 4536–4540 (2002).
    [Crossref] [PubMed]
  8. D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455–456, 3–13 (2004).
    [Crossref]
  9. T. Yamaguchi, “A quick response recording ellipsometer,” Science of Light 16, 64–71 (1967).
  10. D. E. Aspnes and A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975).
    [PubMed]
  11. J. M. M. de Nijs and A. van Silfhout, “Systematic and random errors in rotating-analyzer ellipsometry,” J. Opt. Soc. Am. A 5, 773–781 (1988).
    [Crossref]
  12. J. M. M. de Nijs, A. H. M. Holtslag, A. Hoeksta, and A. van Silfhout, “Calibration method for rotating-analyzer ellipsometers,” J. Opt. Soc. Am. A 5, 1466–1471 (1988).
    [Crossref]
  13. C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
    [Crossref]
  14. T. Mori and D. E. Aspnes, “Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system,” Thin Solid Films 455–456, 33–38 (2004).
    [Crossref]
  15. J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
    [Crossref]
  16. O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
    [Crossref]
  17. C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
    [Crossref]
  18. G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometery: theory,” Appl. Opt.36, 8190–8189 (1997), 42, 3765 (2003).
    [Crossref]
  19. K. Sato, “Measurement of magneto-optical Kerr effect using piezo-birefringent modulator,” Jap. J. Appl. Phys. 20, 2403–2409 (1981).
    [Crossref]
  20. M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
    [Crossref]
  21. G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in a polarization modulation ellipsometry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. of SPIE1166, 231–241 (1990).
  22. B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express 9, 225–235 (2001). URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-5-225.
    [Crossref] [PubMed]
  23. G. P. Nordin and P. C. Deguzman, “Broadband form birefringent quarter-wave plate for the mid-infrared wavelength region,” Opt. Express 5, 163–168 (1999). URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-8-163.
    [Crossref] [PubMed]
  24. T. Yamaguchi and Mizojiri Optical Co., “Four-zone null spectro-ellipsometry using an imperfect phase compensator,” (July 11, 2003). Japanese patent No. 3448652.
  25. R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).
  26. K. Postava, T. Yamaguchi, and R. Kantor, “Matrix description of coherent and incoherent light reflection and transmission by anisotropic multilayer structures,” Appl. Opt. 41, 2521–2531 (2002).
    [Crossref] [PubMed]

2004 (4)

D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455–456, 3–13 (2004).
[Crossref]

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

T. Mori and D. E. Aspnes, “Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system,” Thin Solid Films 455–456, 33–38 (2004).
[Crossref]

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

2003 (1)

M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
[Crossref]

2002 (2)

2001 (1)

1999 (2)

1992 (1)

C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[Crossref]

1989 (1)

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[Crossref]

1988 (2)

1981 (1)

K. Sato, “Measurement of magneto-optical Kerr effect using piezo-birefringent modulator,” Jap. J. Appl. Phys. 20, 2403–2409 (1981).
[Crossref]

1977 (1)

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

1975 (1)

1974 (1)

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
[Crossref]

1967 (1)

T. Yamaguchi, “A quick response recording ellipsometer,” Science of Light 16, 64–71 (1967).

Acher, O.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[Crossref]

An, I.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

Antos, R.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Aspnes, D. E.

T. Mori and D. E. Aspnes, “Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system,” Thin Solid Films 455–456, 33–38 (2004).
[Crossref]

D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455–456, 3–13 (2004).
[Crossref]

D. E. Aspnes and A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975).
[PubMed]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

Badoz, J.

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

Bigan, E.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[Crossref]

Billardon, M.

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

Boulbry, B.

Bousquet, B.

Canit, J.

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

Chao, Y.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Chen, C.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

Chen, S.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Collins, R. W.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

de Nijs, J. M. M.

Deguzman, P. C.

Drévillon, B.

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[Crossref]

Ferreira, G. M.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

Franta, D.

I. Ohlídal and D. Franta, “Ellipsometry of thin film systems,” in Progress in Optics , E. Wolf, ed., vol. 41, (North-Holland, Amsterdam, 2000) pp. 181–282.
[Crossref]

Gerland, J.W.

C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[Crossref]

Guern, Y.

Hoeksta, A.

Holtslag, A. H. M.

Horie, M.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Hotta, Y.

M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
[Crossref]

Jellison, G. E.

G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in a polarization modulation ellipsometry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. of SPIE1166, 231–241 (1990).

G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometery: theory,” Appl. Opt.36, 8190–8189 (1997), 42, 3765 (2003).
[Crossref]

Kantor, R.

Kim, C. C.

C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[Crossref]

Le Jeune, B.

Leou, K.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Lin, T.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Liu, L.

Liu, Y.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Lotrian, J.

Lü, Z.

Mathieu, H. J.

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
[Crossref]

McClure, D. E.

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
[Crossref]

Mistrik, J.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Modine, F. A.

G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in a polarization modulation ellipsometry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. of SPIE1166, 231–241 (1990).

G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometery: theory,” Appl. Opt.36, 8190–8189 (1997), 42, 3765 (2003).
[Crossref]

Mori, T.

T. Mori and D. E. Aspnes, “Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system,” Thin Solid Films 455–456, 33–38 (2004).
[Crossref]

Muller, R. H.

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
[Crossref]

Nee, S.-M. F.

Nordin, G. P.

Ohlidal, I.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Ohlídal, I.

I. Ohlídal and D. Franta, “Ellipsometry of thin film systems,” in Progress in Optics , E. Wolf, ed., vol. 41, (North-Holland, Amsterdam, 2000) pp. 181–282.
[Crossref]

Pistora, J.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Podraza, N. J.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

Postava, K.

K. Postava, T. Yamaguchi, and R. Kantor, “Matrix description of coherent and incoherent light reflection and transmission by anisotropic multilayer structures,” Appl. Opt. 41, 2521–2531 (2002).
[Crossref] [PubMed]

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Raccah, P. M.

C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[Crossref]

Russel, M. F.

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

Sato, K.

K. Sato, “Measurement of magneto-optical Kerr effect using piezo-birefringent modulator,” Jap. J. Appl. Phys. 20, 2403–2409 (1981).
[Crossref]

Sato, M.

M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
[Crossref]

Studna, A. A.

Tsai, F.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

van Silfhout, A.

Visnovsky, S.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

Wang, M.

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Wen, Y.

Winterbottom, A. B.

A. B. Winterbottom, in Ellipsometry in the measurement of surfaces and thin films, E. Passaglia, R. R. Stromberg, and J. Kruger, eds., Vol. 256, (National Bureau of Standard Miscellaneous Publication, US Goverment Printing Office, Washington, 1964) p. 97.

Yamaguchi, T.

K. Postava, T. Yamaguchi, and R. Kantor, “Matrix description of coherent and incoherent light reflection and transmission by anisotropic multilayer structures,” Appl. Opt. 41, 2521–2531 (2002).
[Crossref] [PubMed]

T. Yamaguchi, “A quick response recording ellipsometer,” Science of Light 16, 64–71 (1967).

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

T. Yamaguchi and Mizojiri Optical Co., “Four-zone null spectro-ellipsometry using an imperfect phase compensator,” (July 11, 2003). Japanese patent No. 3448652.

Yamamoto, M.

M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
[Crossref]

Zapien, J. A.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

Zhang, B.

Zhu, H.

Appl. Opt. (4)

J. Opt. Soc. Am. A (2)

J. Optics (Paris) (1)

J. Badoz, M. Billardon, J. Canit, and M. F. Russel, “Sensitive devices to determine the state and degree of polarization of a light beam using a birefringence modulator,” J. Optics (Paris) 8, 373–384 (1977).
[Crossref]

Jap. J. Appl. Phys. (2)

K. Sato, “Measurement of magneto-optical Kerr effect using piezo-birefringent modulator,” Jap. J. Appl. Phys. 20, 2403–2409 (1981).
[Crossref]

M. Wang, Y. Chao, K. Leou, F. Tsai, T. Lin, S. Chen, and Y. Liu, “Calibration of phase modulation amplitude of photoelastic modulator,” Jap. J. Appl. Phys. 43, 827–832 (2004).
[Crossref]

Opt. Express (2)

Rev. Sci. Instrum. (3)

O. Acher, E. Bigan, and B. Drévillon, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[Crossref]

C. C. Kim, P. M. Raccah, and J.W. Gerland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[Crossref]

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798–802 (1974).
[Crossref]

Science of Light (1)

T. Yamaguchi, “A quick response recording ellipsometer,” Science of Light 16, 64–71 (1967).

Thin Solid Films (4)

M. Yamamoto, Y. Hotta, and M. Sato, “A tracking ellipsometer of picometer sensitivity enabling 0.1% sputtering-rate monitoring of EUV nanometer multilayer fabrication,” Thin Solid Films 433, 224–229 (2003).
[Crossref]

D. E. Aspnes, “Expanding horizons: new developments in ellipsometry and polarimetry,” Thin Solid Films 455–456, 3–13 (2004).
[Crossref]

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455–456, 14–23 (2004).
[Crossref]

T. Mori and D. E. Aspnes, “Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system,” Thin Solid Films 455–456, 33–38 (2004).
[Crossref]

Other (7)

G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometery: theory,” Appl. Opt.36, 8190–8189 (1997), 42, 3765 (2003).
[Crossref]

A. B. Winterbottom, in Ellipsometry in the measurement of surfaces and thin films, E. Passaglia, R. R. Stromberg, and J. Kruger, eds., Vol. 256, (National Bureau of Standard Miscellaneous Publication, US Goverment Printing Office, Washington, 1964) p. 97.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

I. Ohlídal and D. Franta, “Ellipsometry of thin film systems,” in Progress in Optics , E. Wolf, ed., vol. 41, (North-Holland, Amsterdam, 2000) pp. 181–282.
[Crossref]

G. E. Jellison and F. A. Modine, “Accurate calibration of a photoelastic modulator in a polarization modulation ellipsometry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. of SPIE1166, 231–241 (1990).

T. Yamaguchi and Mizojiri Optical Co., “Four-zone null spectro-ellipsometry using an imperfect phase compensator,” (July 11, 2003). Japanese patent No. 3448652.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” (submitted for publication).

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Figures (1)

Fig. 1.
Fig. 1.

Schematic description of null PMSCA ellipsometric system consisting of Polarizer-Modulator-Sample-Compensator-Analyzer. Coordinate systems are shown.

Tables (1)

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Table 1. Ideal zone positions for null PMSCA ellipsometer (ϕ=90°). The azimuth of analyzer A is obtained by nulling of the first harmonic signal. The azimuth angle P of the system polarizer-modulator corresponds to the null of the second harmonic.

Equations (15)

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φ = φ 0 + φ A sin ω t ,
[ E x E y ] = E 0 2 [ 1 0 0 0 ] [ cos A sin A sin A cos A ] Analyzer at azimuth A [ cos ( ϕ 2 ) ± sin ( ϕ 2 ) ± sin ( ϕ 2 ) cos ( ϕ 2 ) ] Compensator C = ± 45 ° ×
× [ r ss 0 0 r pp ] Sample [ cos P sin P sin P cos P ] Azimuth of PEM P [ exp ( i φ 2 ) 0 0 exp ( i φ 2 ) ] Modulator ( PEM ) [ 1 1 ] Polarizer 45 ° ,
I = E x E x * + E y E y * = E 0 2 r SS 2 2 ( I 0 + I S sin φ + I C cos φ ) ,
I 0 = [ 1 + cos 2 A cos ϕ + ( 1 cos 2 A cos ϕ ) tan 2 ψ ] 2 ,
I S = tan ψ ( sin 2 A sin Δ ± sin ϕ cos 2 A cos Δ ) ,
I C = sin 2 P [ 1 + cos 2 A cos ϕ ( 1 cos 2 A cos ϕ ) tan 2 ψ ] 2 +
+ cos 2 P tan ψ ( sin 2 A cos Δ sin ϕ cos 2 A cos Δ ) .
sin φ = J 0 ( φ A ) sin φ 0 + 2 J 1 ( φ A ) cos φ 0 sin ω t + 2 J 2 ( φ A ) sin φ 0 cos 2 ω t + ,
cos φ = J 0 ( φ A ) cos φ 0 2 J 1 ( φ A ) sin φ 0 sin ω t + 2 J 2 ( φ A ) cos φ 0 cos 2 ω t + .
tan Δ = sin ϕ tan 2 A = sin ϕ tan [ ± ( 2 A ± π 2 ) ] ,
tan ψ = ± α tan P , tan ψ = ± α tan ( P π 2 ) , for C = + 45 °
tan ψ = ± α ± tan P , tan ψ = ± α ± tan ( P π 2 ) , for C = 45 °
α ± = 1 cos 2 ϕ cos 2 Δ ± cos ϕ sin Δ sin ϕ , α + α = 1 , α ± ( ϕ = 90 ° ) = 1 ,
I S I 0 = ± δ Δ sin 2 ψ 0 , I C I 0 = ± 2 δ ψ .

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