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

Full Article  |  PDF Article

References

  • View by:
  • |

  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 Government 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, Jr. and F. A. Modine, �??Two-modulator generalized ellipsometery: theory,�?? Appl. Opt. 36, 8190�??8189 (1997), 42, 3765 (2003).
    [CrossRef]
  19. K. Sato, �??Measurement of magnetooptical 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, Jr. 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 SPIE 1166, 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). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-5-225.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-5-225.</a>
    [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). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-8-163.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-8-163.</a>
    [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]

Appl. Opt. (5)

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 magnetooptical 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]

National Bureau of Standard Misc. Pubs. (1)

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 Government Printing Office, Washington, 1964) p. 97.

Opt. Express (2)

Proc. of SPIE (1)

G. E. Jellison, Jr. 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 SPIE 1166, 231�??241 (1990).

Progress in Optics (1)

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]

Rev. Sci. Instrum. (3)

H. J. Mathieu, D. E. McClure, and R. H. Muller, �??Fast self-compensating ellipsometer,�?? Rev. Sci. Instrum. 45, 798�??802 (1974).
[CrossRef]

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]

Science of Light (1)

T. Yamaguchi, �??A quick response recording ellipsometer,�?? Science of Light 16, 64�??71 (1967).

Thin Solid Films (4)

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. 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]

Other (3)

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

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).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

Tables Icon

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)

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

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 .

Metrics