Abstract

This article introduces a simple metrology set-up based on white light interference. The aim is to determine the thickness of thin transparent films by their reflection color under white illumination. Therefore, one digital color image of a large field of view is taken in nontelecentric geometry. To obtain reflected light at all angles of view without having to move the camera the substrate has to be sufficiently rough. Additionally, interference occurs at the thin transparent film covering the substrate surface from which a two-dimensional lateral thickness distribution can be calculated. This method has been used as industrial inline process control for a CdS semiconductor layer on top of a rough Cu(In,Ga)(Se,S)2 thin film solar absorber and yielded 74 nm film thickness with only a 1 nm standard deviation. Options to further reduce the standard deviation with different illuminants and other cameras are proposed.

© 2017 Optical Society of America

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References

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  1. A. Michel-Lévy, Les minéraux des roches. 1°. Application des méthodes minéralogiques et chimiques a leur étude microscopique (Librairie Polytechnique Baudry et cie, 1888).
  2. B. E. Sorensen, “A revised Michel–Lévy interference colour chart based on first-principles calculations,” Eur. J. Mineral. 25, 5–10 (2013).
    [Crossref]
  3. P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
    [Crossref]
  4. U. P. Kumar, W. Haifeng, N. Krishna Mohan, and M. P. Kothiyal, “White light interferometry for surface profiling with a colour CCD,” Opt. Lasers Eng. 50, 1084–1088 (2012).
    [Crossref]
  5. N. J. Elton and J. C. C. Day, “A reflectometer for the combined measurement of refractive index, microroughness, macroroughness and gloss of low-extinction surfaces,” Meas. Sci. Technol. 20, 025309 (2009).
    [Crossref]
  6. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).
  7. N. J. Elton, “A two-scale roughness model for the gloss of coated paper,” J. Opt. A 10, 085002 (2008).
    [Crossref]
  8. N. J. Elton, “Optical measurement of microroughness of pigment coatings on rough substrates,” Meas. Sci. Technol. 20, 025303 (2009).
    [Crossref]
  9. K. Orgassa, U. Rau, Q. Nguyen, H. W. Schock, and J. H. Werner, “Role of the CdS buffer layer as an active optical element in Cu(In, Ga)Se2 thin-film solar cells,” Prog. Photovoltaics Res. Appl. 10, 457–463 (2002).
    [Crossref]
  10. C. S. McCamy, H. Marcus, and J. G. Davidson, “A color-rendition chart,” J. Appl. Photogr. Eng. 2, 95–99 (1976).
  11. V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

2013 (1)

B. E. Sorensen, “A revised Michel–Lévy interference colour chart based on first-principles calculations,” Eur. J. Mineral. 25, 5–10 (2013).
[Crossref]

2012 (1)

U. P. Kumar, W. Haifeng, N. Krishna Mohan, and M. P. Kothiyal, “White light interferometry for surface profiling with a colour CCD,” Opt. Lasers Eng. 50, 1084–1088 (2012).
[Crossref]

2009 (2)

N. J. Elton and J. C. C. Day, “A reflectometer for the combined measurement of refractive index, microroughness, macroroughness and gloss of low-extinction surfaces,” Meas. Sci. Technol. 20, 025309 (2009).
[Crossref]

N. J. Elton, “Optical measurement of microroughness of pigment coatings on rough substrates,” Meas. Sci. Technol. 20, 025303 (2009).
[Crossref]

2008 (1)

N. J. Elton, “A two-scale roughness model for the gloss of coated paper,” J. Opt. A 10, 085002 (2008).
[Crossref]

2002 (1)

K. Orgassa, U. Rau, Q. Nguyen, H. W. Schock, and J. H. Werner, “Role of the CdS buffer layer as an active optical element in Cu(In, Ga)Se2 thin-film solar cells,” Prog. Photovoltaics Res. Appl. 10, 457–463 (2002).
[Crossref]

1995 (1)

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[Crossref]

1976 (1)

C. S. McCamy, H. Marcus, and J. G. Davidson, “A color-rendition chart,” J. Appl. Photogr. Eng. 2, 95–99 (1976).

Batereau-Neumann, G.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Beckmann, P.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

Davidson, J. G.

C. S. McCamy, H. Marcus, and J. G. Davidson, “A color-rendition chart,” J. Appl. Photogr. Eng. 2, 95–99 (1976).

Day, J. C. C.

N. J. Elton and J. C. C. Day, “A reflectometer for the combined measurement of refractive index, microroughness, macroroughness and gloss of low-extinction surfaces,” Meas. Sci. Technol. 20, 025309 (2009).
[Crossref]

de Groot, P.

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[Crossref]

Deck, L.

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[Crossref]

Elton, N. J.

N. J. Elton and J. C. C. Day, “A reflectometer for the combined measurement of refractive index, microroughness, macroroughness and gloss of low-extinction surfaces,” Meas. Sci. Technol. 20, 025309 (2009).
[Crossref]

N. J. Elton, “Optical measurement of microroughness of pigment coatings on rough substrates,” Meas. Sci. Technol. 20, 025303 (2009).
[Crossref]

N. J. Elton, “A two-scale roughness model for the gloss of coated paper,” J. Opt. A 10, 085002 (2008).
[Crossref]

Eschrich, H.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Feichtinger, J.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Hahn, T.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Haifeng, W.

U. P. Kumar, W. Haifeng, N. Krishna Mohan, and M. P. Kothiyal, “White light interferometry for surface profiling with a colour CCD,” Opt. Lasers Eng. 50, 1084–1088 (2012).
[Crossref]

Hergert, F.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Jasenek, A.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Kothiyal, M. P.

U. P. Kumar, W. Haifeng, N. Krishna Mohan, and M. P. Kothiyal, “White light interferometry for surface profiling with a colour CCD,” Opt. Lasers Eng. 50, 1084–1088 (2012).
[Crossref]

Kötschau, I.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Krishna Mohan, N.

U. P. Kumar, W. Haifeng, N. Krishna Mohan, and M. P. Kothiyal, “White light interferometry for surface profiling with a colour CCD,” Opt. Lasers Eng. 50, 1084–1088 (2012).
[Crossref]

Kumar, U. P.

U. P. Kumar, W. Haifeng, N. Krishna Mohan, and M. P. Kothiyal, “White light interferometry for surface profiling with a colour CCD,” Opt. Lasers Eng. 50, 1084–1088 (2012).
[Crossref]

Maier, M.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Marcus, H.

C. S. McCamy, H. Marcus, and J. G. Davidson, “A color-rendition chart,” J. Appl. Photogr. Eng. 2, 95–99 (1976).

McCamy, C. S.

C. S. McCamy, H. Marcus, and J. G. Davidson, “A color-rendition chart,” J. Appl. Photogr. Eng. 2, 95–99 (1976).

Michel-Lévy, A.

A. Michel-Lévy, Les minéraux des roches. 1°. Application des méthodes minéralogiques et chimiques a leur étude microscopique (Librairie Polytechnique Baudry et cie, 1888).

Nguyen, Q.

K. Orgassa, U. Rau, Q. Nguyen, H. W. Schock, and J. H. Werner, “Role of the CdS buffer layer as an active optical element in Cu(In, Ga)Se2 thin-film solar cells,” Prog. Photovoltaics Res. Appl. 10, 457–463 (2002).
[Crossref]

Novak, E.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Orgassa, K.

K. Orgassa, U. Rau, Q. Nguyen, H. W. Schock, and J. H. Werner, “Role of the CdS buffer layer as an active optical element in Cu(In, Ga)Se2 thin-film solar cells,” Prog. Photovoltaics Res. Appl. 10, 457–463 (2002).
[Crossref]

Probst, V.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Rau, U.

K. Orgassa, U. Rau, Q. Nguyen, H. W. Schock, and J. H. Werner, “Role of the CdS buffer layer as an active optical element in Cu(In, Ga)Se2 thin-film solar cells,” Prog. Photovoltaics Res. Appl. 10, 457–463 (2002).
[Crossref]

Schock, H. W.

K. Orgassa, U. Rau, Q. Nguyen, H. W. Schock, and J. H. Werner, “Role of the CdS buffer layer as an active optical element in Cu(In, Ga)Se2 thin-film solar cells,” Prog. Photovoltaics Res. Appl. 10, 457–463 (2002).
[Crossref]

Sorensen, B. E.

B. E. Sorensen, “A revised Michel–Lévy interference colour chart based on first-principles calculations,” Eur. J. Mineral. 25, 5–10 (2013).
[Crossref]

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

Thyen, R.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Walther, B.

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

Werner, J. H.

K. Orgassa, U. Rau, Q. Nguyen, H. W. Schock, and J. H. Werner, “Role of the CdS buffer layer as an active optical element in Cu(In, Ga)Se2 thin-film solar cells,” Prog. Photovoltaics Res. Appl. 10, 457–463 (2002).
[Crossref]

Eur. J. Mineral. (1)

B. E. Sorensen, “A revised Michel–Lévy interference colour chart based on first-principles calculations,” Eur. J. Mineral. 25, 5–10 (2013).
[Crossref]

J. Appl. Photogr. Eng. (1)

C. S. McCamy, H. Marcus, and J. G. Davidson, “A color-rendition chart,” J. Appl. Photogr. Eng. 2, 95–99 (1976).

J. Mod. Opt. (1)

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[Crossref]

J. Opt. A (1)

N. J. Elton, “A two-scale roughness model for the gloss of coated paper,” J. Opt. A 10, 085002 (2008).
[Crossref]

Meas. Sci. Technol. (2)

N. J. Elton, “Optical measurement of microroughness of pigment coatings on rough substrates,” Meas. Sci. Technol. 20, 025303 (2009).
[Crossref]

N. J. Elton and J. C. C. Day, “A reflectometer for the combined measurement of refractive index, microroughness, macroroughness and gloss of low-extinction surfaces,” Meas. Sci. Technol. 20, 025309 (2009).
[Crossref]

Opt. Lasers Eng. (1)

U. P. Kumar, W. Haifeng, N. Krishna Mohan, and M. P. Kothiyal, “White light interferometry for surface profiling with a colour CCD,” Opt. Lasers Eng. 50, 1084–1088 (2012).
[Crossref]

Prog. Photovoltaics Res. Appl. (1)

K. Orgassa, U. Rau, Q. Nguyen, H. W. Schock, and J. H. Werner, “Role of the CdS buffer layer as an active optical element in Cu(In, Ga)Se2 thin-film solar cells,” Prog. Photovoltaics Res. Appl. 10, 457–463 (2002).
[Crossref]

Other (3)

V. Probst, A. Jasenek, I. Kötschau, E. Novak, H. Eschrich, F. Hergert, T. Hahn, R. Thyen, J. Feichtinger, G. Batereau-Neumann, M. Maier, and B. Walther, “Novel absorber mass production technology for high-efficiency CIS-modules,” in Proceedings of 28th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC), Paris, France, 2014, pp. 2109–2113.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

A. Michel-Lévy, Les minéraux des roches. 1°. Application des méthodes minéralogiques et chimiques a leur étude microscopique (Librairie Polytechnique Baudry et cie, 1888).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Optical paths of light beams in a thin film causing interference. (b) The arrangement of light source, sample, and camera. The camera detects only that fraction of light which is reflected from correctly inclined surface facets (macroroughness) plus scattered light due to microroughness and diffuse scattering.

Fig. 2.
Fig. 2.

Reflection from a pure microrough surface (a) and from a surface with superimposed macro- and microroughness (b). In the latter case the specular spikes and diffuse lobes are tilted as determined by the inclination of the facets on the macrorough surface. The spike intensities and the shape of the lobes depend on microroughness σr and wavelength λ. Pictures redrawn after Ref. [8].

Fig. 3.
Fig. 3.

Exemplification of a typical set-up as depicted in Fig. 1(b) demonstrating how an incident polychromatic spectrum can reach the camera nearly unaltered after reflection at a macro- and microrough surface: (a) a beam of white light incident at θ=60° is reflected at an inclined facet (macroroughness) into the camera. Due to microroughness σr>0 the intensity of the specular reflection (straight arrow) is reduced, more in the blue than in the red spectral range. The remaining intensity is diffusely scattered into the lobe, whose intensity is mainly confined within the apex angle δ and indicated by the two dashed arrows. This light is (mostly) not in the acceptance angle of the camera. However, other facets (not drawn) close by, which are inclined in the range of θ/2±δ/2 can reflect scattered light from the lobe into the camera. (b) Now a normal distribution F(θf) for the inclination angle θf of the facets is assumed and θf=θ/2=30° is selected as the corresponding value for the case depicted above. Then, F(θf) can be well approximated by a linear slope (dotted line) in the range θ/2±δ/2=30°±10°. For this simplification, the intensities for <θf and >θf sum up to the same result as if F(θf) were a constant. Therefore, a microrough substrate can reflect the illuminating spectrum (almost) unmodified, if the macroroughness distribution F(θf) is (nearly) point symmetric about the inclination angles θf for all relevant of incidence angles θ [cf. Fig. 1(b)].

Fig. 4.
Fig. 4.

Capability tested on 25 measurements. Average and σ(d) are highlighted.

Fig. 5.
Fig. 5.

Estimated reflectance of two CdS layers calculated according to Eq. (1), typical spectral absorption curves of the color channels R, G, B (right axis) and a representative emission spectrum of a white LED (arbitrary units). Note that the reflection of the 74 and the 76 nm layer differ most at 480 nm, where it amounts to 0.8%. Due to the illumination spectrum (LED) and the quantum efficiencies of the three color channels, the largest intensity change occurs in the green channel.

Equations (5)

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

ln(I/I0)=(4πσr/λcosθ)2.
I/I0=[rt2+rb2(1rt2)2+2rtrb(1rt2)cos(4πnd/λ)],
rt=(nn0)/(n+n0)    and    rb=(nSn)/(nS+n).
(I/I0)/d=2  rtrb(1rt2)sin(4πnd/λ)·4πn/λ.
IR,G,B=LED(λ)·QER,G,B(λ)·I(d,λ)dλ,

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