Abstract

A method to determine the thickness of a nonabsorbing thin film on an absorbing substrate is presented. A linear relation between the thin-film thickness and the tangent wavelength of the reflectance spectrum for a specific interference order is revealed, which permits the calculation of the thickness provided that the wavelength-dependent optical parameters of the thin film and the substrate are known. The thickness can be calculated precisely from the reflectance spectrum by using one extreme only, as is demonstrated theoretically for SiO2 thin film on a Si substrate. The application of this method is demonstrated experimentally for the same thin-film structure but with different Si substrates. The results are compared with those given by the algebraic fitting method, and very good agreement is confirmed.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  9. P. Hlubina, J. Lu?á?ek, D. Ciprian, and R. Chlebus, “Spectral interferometry and reflectometry used to measure thin films,” Appl. Phys. B 92, 203-207 (2008).
    [CrossRef]
  10. P. Hlubina, D. Ciprian, J. Lu?á?ek, and M. Les?ák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678-7685(2006).
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  14. Optimization Toolbox for Use with MATLAB, (MathWorks, 2000).

2008 (1)

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

2007 (1)

2006 (1)

P. Hlubina, D. Ciprian, J. Lu?á?ek, and M. Les?ák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678-7685(2006).

2001 (1)

I. Ohlidal, D. Franta, M. Ohlidal, and K. Navratil, “Determination of thicknesses and spectral dependences of refractive indices of non-absorbing and weakly absorbing thin films using the wavelengths related to extrema in spectral reflectances,” Vacuum 61, 285-289 (2001).
[CrossRef]

2000 (2)

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

Optimization Toolbox for Use with MATLAB, (MathWorks, 2000).

1999 (1)

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

1996 (1)

G. E. Jellison, Jr., “The calculation of thin film parameters from spectroscopic ellipsometry data,” Thin Solid Films 290-291, 40-45 (1996).
[CrossRef]

1995 (2)

1991 (1)

O. Stenzel, V. Hopfe, and P. Klobes, “Determination of optical parameters for amorphous thin film materials on semitransparent substrates from transmittance and reflectance measurements,” J. Phys. D 24, 2088-2094 (1991).
[CrossRef]

1990 (1)

1986 (1)

C. K. Carniglia, “Effects of dispersion on the determination of optical constants of thin films,” Proc. SPIE 652, 158-165 (1986).

1977 (1)

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

Amaratunga, G. A. J.

and, R.

Azzam, R. A.

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

Bashara, N. M.

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

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Carniglia, C. K.

C. K. Carniglia, “Effects of dispersion on the determination of optical constants of thin films,” Proc. SPIE 652, 158-165 (1986).

Chlebus, R.

P. Hlubina, J. Lu?á?ek, 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. Lu?á?ek, 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. Lu?á?ek, and M. Les?ák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678-7685(2006).

Deal, M. D.

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

Express, Opt.

P. Hlubina, D. Ciprian, J. Lu?á?ek, and M. Les?ák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678-7685(2006).

Franta, D.

I. Ohlidal, D. Franta, M. Ohlidal, and K. Navratil, “Determination of thicknesses and spectral dependences of refractive indices of non-absorbing and weakly absorbing thin films using the wavelengths related to extrema in spectral reflectances,” Vacuum 61, 285-289 (2001).
[CrossRef]

Griffin, P. B.

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

Hlubina, P.

P. Hlubina, J. Lu?á?ek, 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. Lu?á?ek, and M. Les?ák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678-7685(2006).

Hopfe, V.

O. Stenzel, V. Hopfe, and P. Klobes, “Determination of optical parameters for amorphous thin film materials on semitransparent substrates from transmittance and reflectance measurements,” J. Phys. D 24, 2088-2094 (1991).
[CrossRef]

Humphrey, S.

Jellison, G. E.

G. E. Jellison, Jr., “The calculation of thin film parameters from spectroscopic ellipsometry data,” Thin Solid Films 290-291, 40-45 (1996).
[CrossRef]

Klobes, P.

O. Stenzel, V. Hopfe, and P. Klobes, “Determination of optical parameters for amorphous thin film materials on semitransparent substrates from transmittance and reflectance measurements,” J. Phys. D 24, 2088-2094 (1991).
[CrossRef]

Lesnák, M.

P. Hlubina, D. Ciprian, J. Lu?á?ek, and M. Les?ák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678-7685(2006).

Lunácek, J.

P. Hlubina, J. Lu?á?ek, 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. Lu?á?ek, and M. Les?ák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678-7685(2006).

Merklein, T. M.

Navratil, K.

I. Ohlidal, D. Franta, M. Ohlidal, and K. Navratil, “Determination of thicknesses and spectral dependences of refractive indices of non-absorbing and weakly absorbing thin films using the wavelengths related to extrema in spectral reflectances,” Vacuum 61, 285-289 (2001).
[CrossRef]

Ohlidal, I.

I. Ohlidal, D. Franta, M. Ohlidal, and K. Navratil, “Determination of thicknesses and spectral dependences of refractive indices of non-absorbing and weakly absorbing thin films using the wavelengths related to extrema in spectral reflectances,” Vacuum 61, 285-289 (2001).
[CrossRef]

Ohlidal, M.

I. Ohlidal, D. Franta, M. Ohlidal, and K. Navratil, “Determination of thicknesses and spectral dependences of refractive indices of non-absorbing and weakly absorbing thin films using the wavelengths related to extrema in spectral reflectances,” Vacuum 61, 285-289 (2001).
[CrossRef]

Palik, E. D.

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

Plummer, J. D.

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

Stenzel, O.

O. Stenzel, V. Hopfe, and P. Klobes, “Determination of optical parameters for amorphous thin film materials on semitransparent substrates from transmittance and reflectance measurements,” J. Phys. D 24, 2088-2094 (1991).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Appl. Opt. (3)

Appl. Phys. B (1)

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

J. Phys. D (1)

O. Stenzel, V. Hopfe, and P. Klobes, “Determination of optical parameters for amorphous thin film materials on semitransparent substrates from transmittance and reflectance measurements,” J. Phys. D 24, 2088-2094 (1991).
[CrossRef]

Proc. SPIE (1)

C. K. Carniglia, “Effects of dispersion on the determination of optical constants of thin films,” Proc. SPIE 652, 158-165 (1986).

Thin Solid Films (1)

G. E. Jellison, Jr., “The calculation of thin film parameters from spectroscopic ellipsometry data,” Thin Solid Films 290-291, 40-45 (1996).
[CrossRef]

Vacuum (1)

I. Ohlidal, D. Franta, M. Ohlidal, and K. Navratil, “Determination of thicknesses and spectral dependences of refractive indices of non-absorbing and weakly absorbing thin films using the wavelengths related to extrema in spectral reflectances,” Vacuum 61, 285-289 (2001).
[CrossRef]

Other (6)

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

P. Hlubina, D. Ciprian, J. Lu?á?ek, and M. Les?ák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678-7685(2006).

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

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

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

Optimization Toolbox for Use with MATLAB, (MathWorks, 2000).

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Figures (3)

Fig. 1
Fig. 1

Theoretical reflectance spectrum calculated by using Eq. (1) for four different thin-film thicknesses with the outer envelopes calculated by using Eqs. (7, 8).

Fig. 2
Fig. 2

Linear dependence between the thin-film thickness d tan and the tangent wavelength λ tan , m for three interference orders m = 3 , 4 , 5 .

Fig. 3
Fig. 3

Experimental reflectance spectra for samples 2 and 7 with only one suitable minimum with interference order m = 3 .

Tables (2)

Tables Icon

Table 1 Calculated Thicknesses d tan of the Si O 2 Thin Films with Corresponding Parameters A and B of Eq. (11) for Theoretical Thickness d = 450 nm

Tables Icon

Table 2 Thicknesses d fit and d tan of the Si O 2 Thin Films with Corresponding Correlation Coefficients C fit for Seven Different Types of Si Substrate with Dopant Concentration N D

Equations (12)

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R ( λ ) = R 1 ( λ ) + R 2 ( λ ) + 2 [ R 1 ( λ ) R 2 ( λ ) ] 1 / 2 cos [ 2 β ( λ ) + ϕ ( λ ) ] 1 + R 1 ( λ ) R 2 ( λ ) + 2 [ R 1 ( λ ) R 2 ( λ ) ] 1 / 2 cos [ 2 β ( λ ) + ϕ ( λ ) ] ,
R 1 ( λ ) = [ 1 n 1 ( λ ) ] 2 [ 1 + n 1 ( λ ) ] 2 ,
R 2 ( λ ) = [ n 1 ( λ ) n 2 ( λ ) ] 2 + κ 2 2 ( λ ) [ n 1 ( λ ) + n 2 ( λ ) ] 2 + κ 2 2 ( λ ) .
β ( λ ) = 2 π λ n 1 ( λ ) d ,
tan φ ( λ ) = 2 n 1 ( λ ) κ 2 ( λ ) n 1 2 ( λ ) n 2 2 ( λ ) κ 2 2 ( λ ) .
cos [ 2 β ( λ ) + ϕ ( λ ) ] = ± 1.
R + ( λ ) = [ R 1 1 / 2 ( λ ) + R 2 1 / 2 ( λ ) 1 + R 1 1 / 2 ( λ ) R 2 1 / 2 ( λ ) ] 2 ,
R ( λ ) = [ R 1 1 / 2 ( λ ) R 2 1 / 2 ( λ ) 1 R 1 1 / 2 ( λ ) R 2 1 / 2 ( λ ) ] 2 .
4 π λ tan , m n 1 ( λ ) d + tan 1 [ 2 n 1 ( λ ) κ 2 ( λ ) n 1 2 ( λ ) n 2 2 ( λ ) κ 2 2 ( λ ) ] = m π ,
d = λ tan , m 4 π n 1 ( λ ) ( m π tan 1 [ 2 n 1 ( λ ) κ 2 ( λ ) n 1 2 ( λ ) n 2 2 ( λ ) κ 2 2 ( λ ) ] ) .
d tan = A + B λ tan , m ,
R = I mea I bkg I ref I bkg R ref ,

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