Abstract

We present a white-light spectral interferometric technique for measuring the absolute spectral optical path difference (OPD) between the beams in a slightly dispersive Michelson interferometer with a thin-film structure as a mirror. We record two spectral interferograms to obtain the spectral interference signal and retrieve from it the spectral phase, which includes the effect of a cube beam splitter and the phase change on reflection from the thin-film structure. Knowing the effective thickness and dispersion of the beam splitter made of BK7 optical glass, we use a simple procedure to determine both the absolute spectral phase difference and OPD. The spectral OPD is measured for a uniform SiO2 thin film on a silicon wafer and is fitted to the theoretical spectral OPD to obtain the thin-film thickness. The theoretical spectral OPD is determined provided that the optical constants of the thin-film structure are known. We measure also the nonlinear-like spectral phase and fit it to the theoretical values in order to obtain the thin-film thickness.

© 2006 Optical Society of America

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  1. U. Schnell, E. Zimmermann, and R . Dändliker, "Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry," Pure Appl. Opt. 4, 643-651 (1995).
    [CrossRef]
  2. U. Schnell, R. Dändliker, and S. Gray, "Dispersive white-light interferometry for absolute distance measurement with dielectric multilayer systems on the target," Opt. Lett. 21, 528-530 (1996).
    [CrossRef] [PubMed]
  3. J. Schwider and L. Zhou, "Dispersive interferometric profilometer," Opt. Lett. 19, 995-997 (1994).
    [CrossRef] [PubMed]
  4. A.F. Zuluaga and A.F. Richards-Kortum, "Spatially resolved spectral interferometry for determination of subsurface structure," Opt. Lett. 24, 519-521 (1999).
    [CrossRef]
  5. S.-W. Kim and G.-H. Kim, "Thickness-profile measurement of transparent thin-film layer by white-light scanning interferometry," Appl. Opt. 38, 5968-5973 (1999).
    [CrossRef]
  6. C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381-390 (1994).
    [CrossRef]
  7. V.N. Kumar and D.N. Rao, "Using interference in the frequency domain for precise determination of the thickness and refractive indices of normal dispersive materials," J. Opt. Soc. Am. B 12, 1559-1563 (1995).
    [CrossRef]
  8. P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica," Opt. Commun. 193, 1-7 (2001).
    [CrossRef]
  9. P. Hlubina, "Dispersive spectral-domain two-beam interference analysed by a fibre-optic spectrometer," J. Mod. Opt. 51, 537-547 (2004).
  10. P. Pavlíček and G. Häusler, "White-light interferometer with dispersion: an accurate fiber-optic sensor for the measurement," Appl. Opt. 442978-2983 (2005).
    [CrossRef] [PubMed]
  11. I. Gurov, P. Hlubina, V. Chugunov, "Evaluation of spectral modulated interferograms using a Fourier transform and the iterative phase-locked loop method," Meas. Sci. Technol. 14, 122-130 (2003).
    [CrossRef]
  12. I. Gurov, E. Ermolaeva, A. Zakharov, "Analysis of low-coherence interference fringes by the Kalman filtering method," J. Opt. Soc. Am. A 21, 242-251 (2004).
    [CrossRef]
  13. A. Pförtnerand J. Schwider, "Dispersion error in white-light Linnik interferometers and its applications for evaluation procedures," Appl. Opt. 40, 6223-6228 (2001).
    [CrossRef]
  14. P. Hlubina, "White-light spectral interferometry to measure the effective thickness of optical elements of known dispersion," Acta Phys. Slov. 55, 387-393 (2005).
  15. R. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  16. J. D. Plummer, M. D. Deal, and P. B. Griffin, Silicon VLSI Technology Fundamentals, Practice and Modeling (Prentice Hall, Upper Saddle River, 2000).
  17. P. Hlubina, I. Gurov, and V. Chugunov, "White-light spectral interferometric technique to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer," J. Mod. Opt. 50, 2067-2074 (2003).
  18. Schott Computer Glass Catalog 1.0. (Schott Glasswerke, Mainz, 1992).
  19. K. Postava and T. Yamaguchi, "Optical functions of low-k materials for interlayer dielectrics," J. Appl. Phys. 89, 2189-2193 (2001).
    [CrossRef]
  20. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, 1995).
  21. Optimalization Toolbox for Use with MATLAB (MathWorks, Mass., 2000).
  22. P. Hlubina, "Spectral reflectrometry and white-light interferometry used to measure thin films," Proc. of SPIE 5457, 756-764 (2004).
    [CrossRef]
  23. S.K. Debnath, M.P. Kothiyal, J. Schmit, and P. Hariharan, "Spectrally resolved white-light phase-shifting interference microscopy for thickness-profile measurements of transparent thin film layers on patterned substrates," oe  14, 4662-4667 (2006).

2005 (2)

P. Pavlíček and G. Häusler, "White-light interferometer with dispersion: an accurate fiber-optic sensor for the measurement," Appl. Opt. 442978-2983 (2005).
[CrossRef] [PubMed]

P. Hlubina, "White-light spectral interferometry to measure the effective thickness of optical elements of known dispersion," Acta Phys. Slov. 55, 387-393 (2005).

2004 (3)

P. Hlubina, "Spectral reflectrometry and white-light interferometry used to measure thin films," Proc. of SPIE 5457, 756-764 (2004).
[CrossRef]

I. Gurov, E. Ermolaeva, A. Zakharov, "Analysis of low-coherence interference fringes by the Kalman filtering method," J. Opt. Soc. Am. A 21, 242-251 (2004).
[CrossRef]

P. Hlubina, "Dispersive spectral-domain two-beam interference analysed by a fibre-optic spectrometer," J. Mod. Opt. 51, 537-547 (2004).

2003 (2)

I. Gurov, P. Hlubina, V. Chugunov, "Evaluation of spectral modulated interferograms using a Fourier transform and the iterative phase-locked loop method," Meas. Sci. Technol. 14, 122-130 (2003).
[CrossRef]

P. Hlubina, I. Gurov, and V. Chugunov, "White-light spectral interferometric technique to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer," J. Mod. Opt. 50, 2067-2074 (2003).

2001 (3)

K. Postava and T. Yamaguchi, "Optical functions of low-k materials for interlayer dielectrics," J. Appl. Phys. 89, 2189-2193 (2001).
[CrossRef]

A. Pförtnerand J. Schwider, "Dispersion error in white-light Linnik interferometers and its applications for evaluation procedures," Appl. Opt. 40, 6223-6228 (2001).
[CrossRef]

P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica," Opt. Commun. 193, 1-7 (2001).
[CrossRef]

1999 (2)

1996 (1)

1995 (2)

U. Schnell, E. Zimmermann, and R . Dändliker, "Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry," Pure Appl. Opt. 4, 643-651 (1995).
[CrossRef]

V.N. Kumar and D.N. Rao, "Using interference in the frequency domain for precise determination of the thickness and refractive indices of normal dispersive materials," J. Opt. Soc. Am. B 12, 1559-1563 (1995).
[CrossRef]

1994 (2)

J. Schwider and L. Zhou, "Dispersive interferometric profilometer," Opt. Lett. 19, 995-997 (1994).
[CrossRef] [PubMed]

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381-390 (1994).
[CrossRef]

Calatroni, J.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381-390 (1994).
[CrossRef]

Chugunov, V.

I. Gurov, P. Hlubina, V. Chugunov, "Evaluation of spectral modulated interferograms using a Fourier transform and the iterative phase-locked loop method," Meas. Sci. Technol. 14, 122-130 (2003).
[CrossRef]

P. Hlubina, I. Gurov, and V. Chugunov, "White-light spectral interferometric technique to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer," J. Mod. Opt. 50, 2067-2074 (2003).

Dändliker, R

U. Schnell, E. Zimmermann, and R . Dändliker, "Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry," Pure Appl. Opt. 4, 643-651 (1995).
[CrossRef]

Dändliker, R.

Ermolaeva, E.

Escalona, R.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381-390 (1994).
[CrossRef]

Gray, S.

Gurov, I.

I. Gurov, E. Ermolaeva, A. Zakharov, "Analysis of low-coherence interference fringes by the Kalman filtering method," J. Opt. Soc. Am. A 21, 242-251 (2004).
[CrossRef]

I. Gurov, P. Hlubina, V. Chugunov, "Evaluation of spectral modulated interferograms using a Fourier transform and the iterative phase-locked loop method," Meas. Sci. Technol. 14, 122-130 (2003).
[CrossRef]

P. Hlubina, I. Gurov, and V. Chugunov, "White-light spectral interferometric technique to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer," J. Mod. Opt. 50, 2067-2074 (2003).

Häusler, G.

Hlubina, P.

P. Hlubina, "White-light spectral interferometry to measure the effective thickness of optical elements of known dispersion," Acta Phys. Slov. 55, 387-393 (2005).

P. Hlubina, "Dispersive spectral-domain two-beam interference analysed by a fibre-optic spectrometer," J. Mod. Opt. 51, 537-547 (2004).

P. Hlubina, "Spectral reflectrometry and white-light interferometry used to measure thin films," Proc. of SPIE 5457, 756-764 (2004).
[CrossRef]

I. Gurov, P. Hlubina, V. Chugunov, "Evaluation of spectral modulated interferograms using a Fourier transform and the iterative phase-locked loop method," Meas. Sci. Technol. 14, 122-130 (2003).
[CrossRef]

P. Hlubina, I. Gurov, and V. Chugunov, "White-light spectral interferometric technique to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer," J. Mod. Opt. 50, 2067-2074 (2003).

P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica," Opt. Commun. 193, 1-7 (2001).
[CrossRef]

Jourdain, P.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381-390 (1994).
[CrossRef]

Kim, G.-H.

Kim, S.-W.

Kumar, V.N.

Pavlícek, P.

Pförtner, A.

Postava, K.

K. Postava and T. Yamaguchi, "Optical functions of low-k materials for interlayer dielectrics," J. Appl. Phys. 89, 2189-2193 (2001).
[CrossRef]

Rao, D.N.

Richards-Kortum, A.F.

Sáinz, C.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381-390 (1994).
[CrossRef]

Schnell, U.

U. Schnell, R. Dändliker, and S. Gray, "Dispersive white-light interferometry for absolute distance measurement with dielectric multilayer systems on the target," Opt. Lett. 21, 528-530 (1996).
[CrossRef] [PubMed]

U. Schnell, E. Zimmermann, and R . Dändliker, "Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry," Pure Appl. Opt. 4, 643-651 (1995).
[CrossRef]

Schwider, J.

Yamaguchi, T.

K. Postava and T. Yamaguchi, "Optical functions of low-k materials for interlayer dielectrics," J. Appl. Phys. 89, 2189-2193 (2001).
[CrossRef]

Zakharov, A.

Zhou, L.

Zimmermann, E.

U. Schnell, E. Zimmermann, and R . Dändliker, "Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry," Pure Appl. Opt. 4, 643-651 (1995).
[CrossRef]

Zuluaga, A.F.

Acta Phys. Slov. (1)

P. Hlubina, "White-light spectral interferometry to measure the effective thickness of optical elements of known dispersion," Acta Phys. Slov. 55, 387-393 (2005).

Appl. Opt. (3)

J. Appl. Phys. (1)

K. Postava and T. Yamaguchi, "Optical functions of low-k materials for interlayer dielectrics," J. Appl. Phys. 89, 2189-2193 (2001).
[CrossRef]

J. Mod. Opt. (2)

P. Hlubina, "Dispersive spectral-domain two-beam interference analysed by a fibre-optic spectrometer," J. Mod. Opt. 51, 537-547 (2004).

P. Hlubina, I. Gurov, and V. Chugunov, "White-light spectral interferometric technique to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer," J. Mod. Opt. 50, 2067-2074 (2003).

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Meas. Sci. Technol. (1)

I. Gurov, P. Hlubina, V. Chugunov, "Evaluation of spectral modulated interferograms using a Fourier transform and the iterative phase-locked loop method," Meas. Sci. Technol. 14, 122-130 (2003).
[CrossRef]

Opt. Commun. (2)

P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica," Opt. Commun. 193, 1-7 (2001).
[CrossRef]

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381-390 (1994).
[CrossRef]

Opt. Lett. (3)

Proc. of SPIE (1)

P. Hlubina, "Spectral reflectrometry and white-light interferometry used to measure thin films," Proc. of SPIE 5457, 756-764 (2004).
[CrossRef]

Pure Appl. Opt. (1)

U. Schnell, E. Zimmermann, and R . Dändliker, "Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry," Pure Appl. Opt. 4, 643-651 (1995).
[CrossRef]

Other (6)

Schott Computer Glass Catalog 1.0. (Schott Glasswerke, Mainz, 1992).

R. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

J. D. Plummer, M. D. Deal, and P. B. Griffin, Silicon VLSI Technology Fundamentals, Practice and Modeling (Prentice Hall, Upper Saddle River, 2000).

S.K. Debnath, M.P. Kothiyal, J. Schmit, and P. Hariharan, "Spectrally resolved white-light phase-shifting interference microscopy for thickness-profile measurements of transparent thin film layers on patterned substrates," oe  14, 4662-4667 (2006).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, 1995).

Optimalization Toolbox for Use with MATLAB (MathWorks, Mass., 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup comprising a slightly dispersive Michelson interferometer with a thin-film structure and a low-resolution spectrometer.

Fig. 2.
Fig. 2.

(a) Spectra recorded for two suitable OPDs; (b) The spectral interference signal corresponding to the spectra in (a).

Fig. 3.
Fig. 3.

(a) Comparison of the measured spectral interference signal with the theoretical one (red curve) that uses the retrieved spectral phase; (b) The absolute OPD as a function of the refractive index of BK7 glass. Red line is linear fit.

Fig. 4.
Fig. 4.

The absolute OPD as a function of wavelength together with the corresponding fit (red curve); (b) The nonlinear-line phase as a function of wavelength together with the corresponding fit (red curve).

Equations (11)

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I ( λ ) = I ( 0 ) ( λ ) { 1 + V ( λ ) exp { ( π 2 / 2 ) [ Δ g ( λ ) Δ λ R / λ 2 ] 2 } cos [ ( 2 π / λ ) Δ ( λ ) ] } ,
Δ ( λ ) = 2 L + 2 n ( λ ) t ef λ δ r ( λ ) / ( 2 π ) ,
N ( λ ) = n ( λ ) λ d n ( λ ) .
ʌ ( λ ) = λ 2 / Δ g ( λ ) .
S ( λ ) = I ( λ ) / I ( 0 ) ( λ ) 1 .
S ( λ ) = V ( λ ) exp { ( π 2 / 2 ) [ Δ g ( λ ) Δ λ R / λ 2 ] 2 cos [ ( 2 π / λ ) Δ ( λ ) ] } .
δ r ( λ ) = 2 n 1 ( λ ) d + ϕ nl ( λ ) ,
S ( λ ) = a ( λ ) cos [ Φ ( λ ) ] ,
Δ ( λ ) = [ Φ ( λ ) / ( 2 π ) + m ] λ
δ ( λ ) = ( 2 π / λ ) [ 2 L 0 + 2 n ( λ ) t ef Δ ( λ ) ] .
χ 2 ( L , d ) = i = 1 N [ Δ e ( λ i ) Δ ( λ i ; L , d ) ] 2

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