Abstract

It is possible to measure the thickness of a single layer by the fringes-of-equal-chromatic-order interferometric system with nanometer resolution. This method uses Muller fringes which represent the Fourier transformed autocorrelation (i.e., power spectrum) of the surfaces. We show how this method can be expanded to multilayer structures with a maximum total thickness of some millimeters and a resolution of better than the diameter of an atomic layer. It is possible to evaluate the real multilayer sequence by holographically measuring two power spectra.

© 1990 Optical Society of America

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References

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  1. J.-C. Vienot, J.-P. Goedgebuer, A. Lacourt, “Space and Time Variables in Optics and Holography: Recent Experimental Aspects,” Appl. Opt. 16, 454–461 (1977).
    [CrossRef] [PubMed]
  2. S. Tolansky, An Introduction to Interferometry (Longmans, London, 1966).
  3. N. Aebischer, J.-C. Vienot, “A Dispersive Device Linear in Wave-Numbers: Its Use in Space Time Optics,” Opt. Commun. 22, 103–106 (1977).
    [CrossRef]
  4. J.-C. Vienot, A. Lacuourt, M. Guignard, “Construction of an Interferometric Gauge System for Thickness Measurement in White Light,” Opt. Laser Technol.193–196 (Aug.1978).
  5. G. Hausler, W. Heckel, “Light Sectioning with Large Depth and High Resolution,” Appl. Opt. 27, 5165–5169 (1988).
    [CrossRef] [PubMed]
  6. J. Ishikawa, J. Tsujiuchi, T. Honda, “Accurate Measurement of Flatness by Multiple-Beam Interference,” Kogaku 11, 579 (1982), in Japanese.
  7. N. Wiener, Acta Math. 55, 117 (1930).
    [CrossRef]
  8. A. Y. Khinchine, Math. Ann. 109, 694 (1934).
  9. G. Hausler, J. Hutfiess, M. Maul, H. Weissmann, “Range Sensing Based on Shearing Interferometry,” Appl. Opt. 27, 4638–4644 (1988).
    [CrossRef] [PubMed]
  10. G. Bickel, G. Hausler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975–977 (1985).
    [CrossRef]

1988 (2)

1985 (1)

G. Bickel, G. Hausler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975–977 (1985).
[CrossRef]

1982 (1)

J. Ishikawa, J. Tsujiuchi, T. Honda, “Accurate Measurement of Flatness by Multiple-Beam Interference,” Kogaku 11, 579 (1982), in Japanese.

1978 (1)

J.-C. Vienot, A. Lacuourt, M. Guignard, “Construction of an Interferometric Gauge System for Thickness Measurement in White Light,” Opt. Laser Technol.193–196 (Aug.1978).

1977 (2)

J.-C. Vienot, J.-P. Goedgebuer, A. Lacourt, “Space and Time Variables in Optics and Holography: Recent Experimental Aspects,” Appl. Opt. 16, 454–461 (1977).
[CrossRef] [PubMed]

N. Aebischer, J.-C. Vienot, “A Dispersive Device Linear in Wave-Numbers: Its Use in Space Time Optics,” Opt. Commun. 22, 103–106 (1977).
[CrossRef]

1934 (1)

A. Y. Khinchine, Math. Ann. 109, 694 (1934).

1930 (1)

N. Wiener, Acta Math. 55, 117 (1930).
[CrossRef]

Aebischer, N.

N. Aebischer, J.-C. Vienot, “A Dispersive Device Linear in Wave-Numbers: Its Use in Space Time Optics,” Opt. Commun. 22, 103–106 (1977).
[CrossRef]

Bickel, G.

G. Bickel, G. Hausler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975–977 (1985).
[CrossRef]

Goedgebuer, J.-P.

Guignard, M.

J.-C. Vienot, A. Lacuourt, M. Guignard, “Construction of an Interferometric Gauge System for Thickness Measurement in White Light,” Opt. Laser Technol.193–196 (Aug.1978).

Hausler, G.

Heckel, W.

Honda, T.

J. Ishikawa, J. Tsujiuchi, T. Honda, “Accurate Measurement of Flatness by Multiple-Beam Interference,” Kogaku 11, 579 (1982), in Japanese.

Hutfiess, J.

Ishikawa, J.

J. Ishikawa, J. Tsujiuchi, T. Honda, “Accurate Measurement of Flatness by Multiple-Beam Interference,” Kogaku 11, 579 (1982), in Japanese.

Khinchine, A. Y.

A. Y. Khinchine, Math. Ann. 109, 694 (1934).

Lacourt, A.

Lacuourt, A.

J.-C. Vienot, A. Lacuourt, M. Guignard, “Construction of an Interferometric Gauge System for Thickness Measurement in White Light,” Opt. Laser Technol.193–196 (Aug.1978).

Maul, M.

G. Hausler, J. Hutfiess, M. Maul, H. Weissmann, “Range Sensing Based on Shearing Interferometry,” Appl. Opt. 27, 4638–4644 (1988).
[CrossRef] [PubMed]

G. Bickel, G. Hausler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975–977 (1985).
[CrossRef]

Tolansky, S.

S. Tolansky, An Introduction to Interferometry (Longmans, London, 1966).

Tsujiuchi, J.

J. Ishikawa, J. Tsujiuchi, T. Honda, “Accurate Measurement of Flatness by Multiple-Beam Interference,” Kogaku 11, 579 (1982), in Japanese.

Vienot, J.-C.

J.-C. Vienot, A. Lacuourt, M. Guignard, “Construction of an Interferometric Gauge System for Thickness Measurement in White Light,” Opt. Laser Technol.193–196 (Aug.1978).

J.-C. Vienot, J.-P. Goedgebuer, A. Lacourt, “Space and Time Variables in Optics and Holography: Recent Experimental Aspects,” Appl. Opt. 16, 454–461 (1977).
[CrossRef] [PubMed]

N. Aebischer, J.-C. Vienot, “A Dispersive Device Linear in Wave-Numbers: Its Use in Space Time Optics,” Opt. Commun. 22, 103–106 (1977).
[CrossRef]

Weissmann, H.

Wiener, N.

N. Wiener, Acta Math. 55, 117 (1930).
[CrossRef]

Acta Math. (1)

N. Wiener, Acta Math. 55, 117 (1930).
[CrossRef]

Appl. Opt. (3)

Kogaku (1)

J. Ishikawa, J. Tsujiuchi, T. Honda, “Accurate Measurement of Flatness by Multiple-Beam Interference,” Kogaku 11, 579 (1982), in Japanese.

Math. Ann. (1)

A. Y. Khinchine, Math. Ann. 109, 694 (1934).

Opt. Commun. (1)

N. Aebischer, J.-C. Vienot, “A Dispersive Device Linear in Wave-Numbers: Its Use in Space Time Optics,” Opt. Commun. 22, 103–106 (1977).
[CrossRef]

Opt. Eng. (1)

G. Bickel, G. Hausler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975–977 (1985).
[CrossRef]

Opt. Laser Technol. (1)

J.-C. Vienot, A. Lacuourt, M. Guignard, “Construction of an Interferometric Gauge System for Thickness Measurement in White Light,” Opt. Laser Technol.193–196 (Aug.1978).

Other (1)

S. Tolansky, An Introduction to Interferometry (Longmans, London, 1966).

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Figures (10)

Fig. 1
Fig. 1

Optical system for chromatic analysis of reflected light.

Fig. 2
Fig. 2

Optical data provided by the white light interferometer when a single layer on a thick substrate is measured.

Fig. 3
Fig. 3

Principle of the holographic method for describing the real sequence of layers. The two (different) references (R1 and R2) cause two autocorrelations (AC1 and AC2). The real sequence of the object is calculated by subtracting the autocorrelations (Dif) and searching for the reference pattern (R) to reconstruct the object (Rec). Prerequisite: the distance of the references must not appear as a thickness in the object.

Fig. 4
Fig. 4

Overview of the various methods for calculating the thickness and sequence of a multilayer structure.

Fig. 5
Fig. 5

Axicon for depth expansion with geometrical parameters: F, depth of focus; d, diameter of focus; D, aperture; α′ deflection angle; α, prism angle; I, intensity in a focal plane.

Fig. 6
Fig. 6

White light interferometer. Lower right: Illumination of the multilayer structure. Upper right: Spectral analysis. Upper left: Computing of the sequence and thicknesses. Lower left: Photo of the optical device (height: 120 cm).

Fig. 7
Fig. 7

Spectrum of a 10-μm thick resist on a 500-μm substrate measured with the white light interferometer shown in Fig. 6. Left side: the measured intensities for the two polarizations are shown. Right side: compensation of spectral intensities and sensitivities and the linearization of the spectrum were applied to the same measurement.

Fig. 8
Fig. 8

Attainable resolution for measuring a 10-μm thick resist on a 500-μm substrate. Three independent measurements were made. The standard deviation compared to the total thickness is Δd/d = 10−5.

Fig. 9
Fig. 9

Off-center measurement showing the birefringence of a spin coated 10-μm thick resist. Two independent measurements are shown for both polarizations in the radial (lower) and tangential directions (upper).

Fig. 10
Fig. 10

Tested objectives of the white light interferometer. Left: microscope objective for 2-μm resolution. Center: 1:1 imaging objective for 20-μm resolution. Right: objective with an axicon for depth expansion (resolution 30 μm).

Equations (18)

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A R ( t ) = a 1 ( λ ) A ( t - t 1 ) + a 2 ( λ ) A ( t - t 2 ) + ,
I ( ω ) = FOU { A R ( t ) } 2
= FOU { A R ( t ) } · FOU * { A R ( t ) }
= FOU { A R ( t ) } * A R * ( t ) }
= FOU { A C [ A R ( t ) ] } ,
I 0 ( ω ) : FOU { A ( t ) } 2 ,
f ( t 0 ) = f ( t ) δ ( t - t 0 ) d t ,
I ( ω ) = FOU { - r 1 A ( t - t 1 ) - r 2 A ( t - t 2 ) } 2
= FOU { [ r 1 δ ( t - t 1 ) + r 2 δ ( t - t 2 ) ] * A ( t ) } 2
= FOU { r 1 δ ( t - t 1 ) + r 2 δ ( t - t 2 } 2 · FOU { A ( t ) } 2
= FOU { A C [ r 1 δ ( t - t 1 ) + r 2 δ ( t - t 2 ) ] } I 0 ( ω )
= FOU { ( r 1 2 + r 2 2 ) δ ( t ) + r 1 r 2 δ ( t - ( t 2 - t 1 ) ) + r 1 r 2 δ ( t + ( t 2 - t 1 ) ) ] } I 0 ( ω )
= c { ( r 1 2 + r 2 2 ) + r 1 r 2 cos [ ( t 2 - t 1 ) ω ] } · I 0 ( ω ) .
α = α ( n - 1 )
d = λ / ( 2 α )
= λ / [ 2 α ( n - 1 ) ] .
F = D / [ 2 α ( n - 1 ) ] ,
R < N c / ( 4 n Δ ν ) .

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