Abstract

The spectral nonlinear phase method and the Fourier amplitude method have been applied to measure the thin-film thickness profile in vertical scanning white-light interferometry (VSWLI). However, both the methods have their disadvantages, and accordingly their applications are limited. In the paper we have investigated the dependence of the sensitivities of both the methods on the thin-film thickness and refractive index, the objective numerical aperture, and the incident light spectral range of VSWLI. The relation of the Fresnel reflection coefficients on the wavelength effect is also discussed. Some important research results reveal that the combination of both Fourier amplitude and nonlinear phase methods may provide a new approach to improve the VSWLI measurement sensitivity for thin-film thickness profile.

© 2012 Optical Society of America

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  1. R. F. M. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria, O. N. Oliveira, M. A. Pereira-da-Silva, and R. M. Faria, “In situ thickness measurements of ultra-thin multilayer polymer films by atomic force microscopy,” Nanotechnology 10, 389–393 (1999).
    [CrossRef]
  2. A. J. Gonzales and E. M. Philofsky, “Applications of scanning electron microscopy to thin film studies on semiconductor devices,” Proc. IEEE 59, 1429–1433 (1971).
    [CrossRef]
  3. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1979).
  4. H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User’s Guide (Wiley, 1999).
  5. S. W. Kim and G. H. Kim, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38, 5968–5973 (1999).
    [CrossRef]
  6. P. Groot and X. C. Lega, “Angle-resolved three-dimensional analysis of surface films by coherence scanning interferometry,” Opt. Lett. 32, 1638–1640 (2007).
    [CrossRef]
  7. D. S. Wan, “Measurement of thin films using Fourier amplitude,” U.S. patent 7,612,891 B2 (3 November 2009).
  8. S. K. Debnath, M. P. Kothiyal, J. Schmit, and P. Hariharan, “Spectrally resolved phase-shifting interferometry of transparent thin films: sensitivity of thickness measurements,” Appl. Opt. 45, 8636–8640 (2006).
    [CrossRef]
  9. Y. S. Kim and S. W. Kim, “Fast, precise, tomographic measurements of thin films,” Appl. Phys. Lett. 91, 091903 (2007).
    [CrossRef]
  10. J. W. You, S. Kim, and D. Kim, “High speed volumetric thickness profile measurement based on full-field wavelength scanning interferometer,” Opt. Express 16, 21022–21031 (2008).
    [CrossRef]
  11. P. Hlubina, D. Ciprian, J. Lunacek, and M. Lesnak, “Thickness of SiO2 thin film on silicon wafer measured by dispersive white light spectral interferometry,” Appl. Phys. B 84, 511–516 (2006).
    [CrossRef]
  12. P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Spectral interferometry and reflectometry used to measure thin films,” Appl. Phys. B 92, 203–207 (2008).
    [CrossRef]
  13. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2005), p. 65.
  14. J. T. Dong, R. S. Lu, Y. Li, and K. Wu, “Automated determination of best focus and minimization of optical path difference in Linnik white light interferometry,” Appl. Opt. 50, 5861–5871 (2011).
    [CrossRef]
  15. P. de Groot, “Method and apparatus for surface topography measurement by spatial frequency analysis of interferograms,” U.S. patent 5,398,113 (14 March 1995).
  16. 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,” Opt. Express 14, 4662–4667 (2006).
    [CrossRef]
  17. S. K. Debnath, S. W. Kim, M. P. Kothiyal, and P. Hariharan, “Spectrally resolved phase-shifting interference microscopy: technique based on optical coherence tomography for profiling a transparent film on a patterned substrate,” Appl. Opt. 49, 6624–6629 (2010).
    [CrossRef]
  18. Y. S. Ghim and S. W. Kim, “Thin-film thickness profile and its refractive index measurements by dispersive white-light interferometry,” Opt. Express 14, 11885–11891 (2006).
    [CrossRef]
  19. P. de Groot and X. C. de Lega, “Signal modeling for low-coherence height-scanning interference microscopy,” Appl. Opt. 43, 4821–4830 (2004).
    [CrossRef]
  20. “Refractive index database,” http://refractiveindex.info/ .

2011 (1)

2010 (1)

2008 (2)

J. W. You, S. Kim, and D. Kim, “High speed volumetric thickness profile measurement based on full-field wavelength scanning interferometer,” Opt. Express 16, 21022–21031 (2008).
[CrossRef]

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Spectral interferometry and reflectometry used to measure thin films,” Appl. Phys. B 92, 203–207 (2008).
[CrossRef]

2007 (2)

Y. S. Kim and S. W. Kim, “Fast, precise, tomographic measurements of thin films,” Appl. Phys. Lett. 91, 091903 (2007).
[CrossRef]

P. Groot and X. C. Lega, “Angle-resolved three-dimensional analysis of surface films by coherence scanning interferometry,” Opt. Lett. 32, 1638–1640 (2007).
[CrossRef]

2006 (4)

2004 (1)

1999 (2)

S. W. Kim and G. H. Kim, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38, 5968–5973 (1999).
[CrossRef]

R. F. M. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria, O. N. Oliveira, M. A. Pereira-da-Silva, and R. M. Faria, “In situ thickness measurements of ultra-thin multilayer polymer films by atomic force microscopy,” Nanotechnology 10, 389–393 (1999).
[CrossRef]

1971 (1)

A. J. Gonzales and E. M. Philofsky, “Applications of scanning electron microscopy to thin film studies on semiconductor devices,” Proc. IEEE 59, 1429–1433 (1971).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1979).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1979).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2005), p. 65.

Chlebus, R.

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Spectral interferometry and reflectometry used to measure thin films,” Appl. Phys. B 92, 203–207 (2008).
[CrossRef]

Ciprian, D.

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Spectral interferometry and reflectometry used to measure thin films,” Appl. Phys. B 92, 203–207 (2008).
[CrossRef]

P. Hlubina, D. Ciprian, J. Lunacek, and M. Lesnak, “Thickness of SiO2 thin film on silicon wafer measured by dispersive white light spectral interferometry,” Appl. Phys. B 84, 511–516 (2006).
[CrossRef]

de Groot, P.

P. de Groot and X. C. de Lega, “Signal modeling for low-coherence height-scanning interference microscopy,” Appl. Opt. 43, 4821–4830 (2004).
[CrossRef]

P. de Groot, “Method and apparatus for surface topography measurement by spatial frequency analysis of interferograms,” U.S. patent 5,398,113 (14 March 1995).

de Lega, X. C.

Debnath, S. K.

Dong, J. T.

Faria, R. M.

R. F. M. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria, O. N. Oliveira, M. A. Pereira-da-Silva, and R. M. Faria, “In situ thickness measurements of ultra-thin multilayer polymer films by atomic force microscopy,” Nanotechnology 10, 389–393 (1999).
[CrossRef]

R. F. M. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria, O. N. Oliveira, M. A. Pereira-da-Silva, and R. M. Faria, “In situ thickness measurements of ultra-thin multilayer polymer films by atomic force microscopy,” Nanotechnology 10, 389–393 (1999).
[CrossRef]

Ghim, Y. S.

Gonzales, A. J.

A. J. Gonzales and E. M. Philofsky, “Applications of scanning electron microscopy to thin film studies on semiconductor devices,” Proc. IEEE 59, 1429–1433 (1971).
[CrossRef]

Groot, P.

Hariharan, P.

Hlubina, P.

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Spectral interferometry and reflectometry used to measure thin films,” Appl. Phys. B 92, 203–207 (2008).
[CrossRef]

P. Hlubina, D. Ciprian, J. Lunacek, and M. Lesnak, “Thickness of SiO2 thin film on silicon wafer measured by dispersive white light spectral interferometry,” Appl. Phys. B 84, 511–516 (2006).
[CrossRef]

Kim, D.

Kim, G. H.

Kim, S.

Kim, S. W.

Kim, Y. S.

Y. S. Kim and S. W. Kim, “Fast, precise, tomographic measurements of thin films,” Appl. Phys. Lett. 91, 091903 (2007).
[CrossRef]

Kothiyal, M. P.

Lega, X. C.

Lesnak, M.

P. Hlubina, D. Ciprian, J. Lunacek, and M. Lesnak, “Thickness of SiO2 thin film on silicon wafer measured by dispersive white light spectral interferometry,” Appl. Phys. B 84, 511–516 (2006).
[CrossRef]

Li, Y.

Lobo, R. F. M.

R. F. M. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria, O. N. Oliveira, M. A. Pereira-da-Silva, and R. M. Faria, “In situ thickness measurements of ultra-thin multilayer polymer films by atomic force microscopy,” Nanotechnology 10, 389–393 (1999).
[CrossRef]

Lu, R. S.

Lunacek, J.

P. Hlubina, D. Ciprian, J. Lunacek, and M. Lesnak, “Thickness of SiO2 thin film on silicon wafer measured by dispersive white light spectral interferometry,” Appl. Phys. B 84, 511–516 (2006).
[CrossRef]

Lunácek, J.

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Spectral interferometry and reflectometry used to measure thin films,” Appl. Phys. B 92, 203–207 (2008).
[CrossRef]

McGahan, W. A.

H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User’s Guide (Wiley, 1999).

Oliveira, O. N.

R. F. M. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria, O. N. Oliveira, M. A. Pereira-da-Silva, and R. M. Faria, “In situ thickness measurements of ultra-thin multilayer polymer films by atomic force microscopy,” Nanotechnology 10, 389–393 (1999).
[CrossRef]

Pereira-da-Silva, M. A.

R. F. M. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria, O. N. Oliveira, M. A. Pereira-da-Silva, and R. M. Faria, “In situ thickness measurements of ultra-thin multilayer polymer films by atomic force microscopy,” Nanotechnology 10, 389–393 (1999).
[CrossRef]

R. F. M. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria, O. N. Oliveira, M. A. Pereira-da-Silva, and R. M. Faria, “In situ thickness measurements of ultra-thin multilayer polymer films by atomic force microscopy,” Nanotechnology 10, 389–393 (1999).
[CrossRef]

Philofsky, E. M.

A. J. Gonzales and E. M. Philofsky, “Applications of scanning electron microscopy to thin film studies on semiconductor devices,” Proc. IEEE 59, 1429–1433 (1971).
[CrossRef]

Raposo, M.

R. F. M. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria, O. N. Oliveira, M. A. Pereira-da-Silva, and R. M. Faria, “In situ thickness measurements of ultra-thin multilayer polymer films by atomic force microscopy,” Nanotechnology 10, 389–393 (1999).
[CrossRef]

Schmit, J.

Tompkins, H. G.

H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User’s Guide (Wiley, 1999).

Wan, D. S.

D. S. Wan, “Measurement of thin films using Fourier amplitude,” U.S. patent 7,612,891 B2 (3 November 2009).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2005), p. 65.

Wu, K.

You, J. W.

Appl. Opt. (5)

Appl. Phys. B (2)

P. Hlubina, D. Ciprian, J. Lunacek, and M. Lesnak, “Thickness of SiO2 thin film on silicon wafer measured by dispersive white light spectral interferometry,” Appl. Phys. B 84, 511–516 (2006).
[CrossRef]

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Spectral interferometry and reflectometry used to measure thin films,” Appl. Phys. B 92, 203–207 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

Y. S. Kim and S. W. Kim, “Fast, precise, tomographic measurements of thin films,” Appl. Phys. Lett. 91, 091903 (2007).
[CrossRef]

Nanotechnology (1)

R. F. M. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria, O. N. Oliveira, M. A. Pereira-da-Silva, and R. M. Faria, “In situ thickness measurements of ultra-thin multilayer polymer films by atomic force microscopy,” Nanotechnology 10, 389–393 (1999).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. IEEE (1)

A. J. Gonzales and E. M. Philofsky, “Applications of scanning electron microscopy to thin film studies on semiconductor devices,” Proc. IEEE 59, 1429–1433 (1971).
[CrossRef]

Other (6)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1979).

H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User’s Guide (Wiley, 1999).

D. S. Wan, “Measurement of thin films using Fourier amplitude,” U.S. patent 7,612,891 B2 (3 November 2009).

“Refractive index database,” http://refractiveindex.info/ .

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2005), p. 65.

P. de Groot, “Method and apparatus for surface topography measurement by spatial frequency analysis of interferograms,” U.S. patent 5,398,113 (14 March 1995).

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Figures (10)

Fig. 1.
Fig. 1.

VSWLI system configuration.

Fig. 2.
Fig. 2.

Definition of sensitivity for (a) nonlinear phase and (b) Fourier amplitude. The solid curve indicates the nonlinear component for the film thickness of 1.0 μm and the dashed curve for the film thickness of 0.3 μm.

Fig. 3.
Fig. 3.

Sensitivity analysis of (a) nonlinear phase and (b) Fourier amplitude as a function of SiO2 film thickness ranging from 1 to 1000 nm. The wavenumber is from 1.43 to 2.0μm1, and the NA of the objective is 0.3.

Fig. 4.
Fig. 4.

Sensitivity analysis of the nonlinear phase and the Fourier amplitude as a function of the refractive index of thin-film layer. The refractive indices of thin films are 1.3, 1.4, 1.5, 1.6, and 1.8. The wavenumber is from 1.43 to 2.0μm1, and the NA of the objective is 0.3.

Fig. 5.
Fig. 5.

Upper: the absolute value of the ratio of the Fresnel reflection coefficient r01 to r12|r01/r12| as a function of the refractive index N1 of the thin film. Lower: the four plots are interference intensity signals corresponding to regions A and D, and points B and C, respectively.

Fig. 6.
Fig. 6.

Sensitivity analysis of (a) the nonlinear phase and (b) the Fourier amplitude as a function of the NA of the objective, which is 0.28, 0.55, 0.70, and 0.90. The refractive indices of the SiO2 film and BK7 substrate are 1.460 and 1.516, respectively. The wavenumber is from 1.43 to 2.0μm1.

Fig. 7.
Fig. 7.

Sensitivity analysis of (a) the nonlinear phase and (b) the Fourier amplitude for the spectral ranges from 1.43 to 2.0μm1 and 1.25 to 2.5μm1. The NA of the objective is 0.3. The refractive indices of the SiO2 film and BK7 substrate are 1.460 and 1.516, respectively.

Fig. 8.
Fig. 8.

(a) Nonlinear phase and (b) Fourier amplitude as a function of the wavenumber. The Fresnel reflection coefficients (i.e., r01 and r12) are independent of the wavenumber for the dashed curve, and dependent on the wavenumber for the solid curve. The refractive indices of the SiO2 film and BK7 substrate are 1.460 and 1.516, respectively, and the SiO2 film thickness is 1 μm. The NA of the objective is 0.3.

Fig. 9.
Fig. 9.

Nonlinear phase function (solid curves) and Fourier amplitude function (dashed curves) versus the wavenumber for film thickness of (a) 101 nm, (b) 148 nm, (c) 202 nm, (d) 254 nm, (e) 302 nm, (f) 352 nm, (g) 403 nm, (h) 454 nm, (i) 504 nm, (j) 555 nm, (k) 605 nm, and (l) 655 nm.

Fig. 10.
Fig. 10.

(a) Nonlinear phase function and (b) the Fourier amplitude function for the propagation angles of the incident beam θ0=16.26°, 33.37°, 44.43°, and 64.16° (NA=0.28, 0.55, 0.70, and 0.90), respectively, when the film thickness is 850 nm.

Equations (20)

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R=r01+r12exp(j2β)1+r01r12exp(j2β),
rij=NicosθiNjcosθjNicosθi+Njcosθj,rij=r01,r12.
β=kdN1cosθ1,
θi=arcsin(N0sinθ0Ni),i=1,2.
R=a+j·b,
R=G·exp(jψ),
ψ=arctan(b/a).
I(z)=γkF(k,d)θcos[2k(hz)cosθ+ψ(k,d,θ)]sinθcosθdθdk,
Φ(k,h,d)=2hk+ψ(k,d).
χ(d)=k[ψmodel(k,d)ψmeasured(k)]2dk.
F(k,d)=S(k)D(k)E(k)G(k,d),
S(k)D(k)E(k)=F(k,0)/G(k,0).
χ(d)=k[Gmodel(k,d)Gmeasured(k)]2dk.
Sψ=max(ψ)min(ψ),
SG=max(G)min(G).
R=r01+r12exp(j2β)1+r01r12exp(j2β)=(r01+r12cos2β)j·r12sin2β(1+r01r12cos2β)j·r01r12sin2β×(1+r01r12cos2β)+j·r01r12sin2β(1+r01r12cos2β)+j·r01r12sin2β=[r01(1+r122)+r12(1+r012)cos2β]+j·[r12(r0121)sin2β]1+2r01r12cos2β+r012r122=a+j·b=G·exp(jψ)
a=r01(1+r122)+r12(1+r012)cos2β1+2r01r12cos2β+r012r122,
b=r12(r0121)sin2β1+2r01r12cos2β+r012r122.
ψ=arctan(ba)=arctan(r12(r0121)sin2βr01(1+r122)+r12(1+r012)cos2β),
G=a2+b2={[r01(1+r122)+r12(1+r012)cos2β]2+[r12(r0121)sin2β]2}1/21+2r01r12cos2β+r012r122,

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