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Electronic color charts for dielectric films on silicon

Justin Henrie, Spencer Kellis, Stephen M. Schultz, and Aaron Hawkins

Open Access Open Access

Abstract

This paper presents the calculation of the perceived color of dielectric films on silicon. A procedure is shown for computing the perceived color for an arbitrary light source, light incident angle, and film thickness. The calculated color is converted into RGB parameters that can be displayed on a color monitor, resulting in the generation of electronic color charts for dielectric films. This paper shows generated electronic color charts for both silicon dioxide and silicon nitride films on silicon.

©2004 Optical Society of America

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References

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  • Author
  • Publication
  1. W.A. Pliskin and E.E. Conrad, “Nondestructive Determination of Thickness and Refractive Index of Transparent Films,” IBM Journal, p. 48, January 1964.
  2. T. Huen, “Reflectance of thinly oxidized silicon at normal incidence,” Appl. Opt. 18, 1927–1932, 1979.
    [Crossref] [PubMed]
  3. B. Dawes, “Metal Halide and Fluorescent Lamp Spectra,” http://www.colorpro.com/info/data/lamps.html.
  4. E. Hecht and A Zajac, Optics (Addison-Wesley, 1975).
  5. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
  6. J. Walker, “Colour rendering of spectra,” (1996), http://www.fourmilab.ch/documents/specrend/
  7. D. Post, “Colorimetric measurement, calibration, and characterization of self-luminous displays,” in Color in Electronic Displays, (Plenum Press, 1992).
  8. B Lindbloom “XYZ to RGB,” http://www.brucelindbloom.com.
  9. C. A. Poynton, A Technical Introduction to Digital Video, (John Wiley and Sons, New York, 1996).
  10. M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet-sRGB,” (1996). http://www.w3.org/Graphics/Color/sRGB.
  11. “BYU Cleanroom-Electronic Color Charts,” http://www.ee.byu.edu/cleanroom/color_chart.phtml.

1979 (1)

Anderson, M.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet-sRGB,” (1996). http://www.w3.org/Graphics/Color/sRGB.

Chandrasekar, S.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet-sRGB,” (1996). http://www.w3.org/Graphics/Color/sRGB.

Conrad, E.E.

W.A. Pliskin and E.E. Conrad, “Nondestructive Determination of Thickness and Refractive Index of Transparent Films,” IBM Journal, p. 48, January 1964.

Dawes, B.

B. Dawes, “Metal Halide and Fluorescent Lamp Spectra,” http://www.colorpro.com/info/data/lamps.html.

Hecht, E.

E. Hecht and A Zajac, Optics (Addison-Wesley, 1975).

Huen, T.

Lindbloom, B

B Lindbloom “XYZ to RGB,” http://www.brucelindbloom.com.

Motta, R.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet-sRGB,” (1996). http://www.w3.org/Graphics/Color/sRGB.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

Pliskin, W.A.

W.A. Pliskin and E.E. Conrad, “Nondestructive Determination of Thickness and Refractive Index of Transparent Films,” IBM Journal, p. 48, January 1964.

Post, D.

D. Post, “Colorimetric measurement, calibration, and characterization of self-luminous displays,” in Color in Electronic Displays, (Plenum Press, 1992).

Poynton, C. A.

C. A. Poynton, A Technical Introduction to Digital Video, (John Wiley and Sons, New York, 1996).

Stokes, M.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet-sRGB,” (1996). http://www.w3.org/Graphics/Color/sRGB.

Walker, J.

J. Walker, “Colour rendering of spectra,” (1996), http://www.fourmilab.ch/documents/specrend/

Zajac, A

E. Hecht and A Zajac, Optics (Addison-Wesley, 1975).

Appl. Opt. (1)

Other (10)

B. Dawes, “Metal Halide and Fluorescent Lamp Spectra,” http://www.colorpro.com/info/data/lamps.html.

E. Hecht and A Zajac, Optics (Addison-Wesley, 1975).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

J. Walker, “Colour rendering of spectra,” (1996), http://www.fourmilab.ch/documents/specrend/

D. Post, “Colorimetric measurement, calibration, and characterization of self-luminous displays,” in Color in Electronic Displays, (Plenum Press, 1992).

B Lindbloom “XYZ to RGB,” http://www.brucelindbloom.com.

C. A. Poynton, A Technical Introduction to Digital Video, (John Wiley and Sons, New York, 1996).

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet-sRGB,” (1996). http://www.w3.org/Graphics/Color/sRGB.

“BYU Cleanroom-Electronic Color Charts,” http://www.ee.byu.edu/cleanroom/color_chart.phtml.

W.A. Pliskin and E.E. Conrad, “Nondestructive Determination of Thickness and Refractive Index of Transparent Films,” IBM Journal, p. 48, January 1964.

Supplementary Material (2)

Media 1: MOV (457 KB)     
Media 2: MOV (510 KB)     

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Figures (9)
Fig. 1.
Fig. 1. Standard fluorescent light wavelength spectrum normalized by total power.

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Fig. 2.
Fig. 2. Dielectric film.

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Fig. 3.
Fig. 3. Material parameters for silicon dioxide, silicon nitride, and silicon.

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Fig. 4.
Fig. 4. CIE color-matching functions (CIE 1931 2 degree observer).

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Fig. 5.
Fig. 5. Reflectance R(λ), normalized spectrum Pi(λ), and corresponding reflected spectrum Pr(λ) for silicon dioxide films of thickness d=200nm, and d=300nm.

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Fig. 6.
Fig. 6. Apparent color of a SiO2 film on silicon as a function of thickness.

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Fig. 7.
Fig. 7. Apparent color of a Si3N4 film on silicon as a function of thickness.

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Fig. 8.
Fig. 8. (457 KB) Quicktime movie showing the color of a silicon dioxide (SiO2) film as a function of film thickness.

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Fig. 9.
Fig. 9. (511 KB) Quicktime movie showing the color of a silicon nitride (Si3N4) film as a function of film thickness.

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Tables (1)

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Table 1. color parameters for two SiO2 films.

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Equations (12)

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R ( λ ) = ∣ Y f ( Y c − Y s ) cos ϕ + i ( Y c Y s − Y f 2 ) sin ϕ Y f ( Y c + Y s ) cos ϕ + i ( Y c Y s + Y f 2 ) sin ϕ ∣ 2 .
Y m = η o n m cos θ m ,
Y m = η o n m ⁄ cos θ m ,
ϕ = k o n f h cos θ f ,
X = ∫ 0 ∞ R ( λ ) P o P i ( λ ) X λ ( λ ) d λ ,
Y = ∫ 0 ∞ R ( λ ) P o P i ( λ ) Y λ ( λ ) d λ ,
Z = ∫ 0 ∞ R ( λ ) P o P i ( λ ) Z λ ( λ ) d λ ,
[ R G B ] = [ X Y Z ] [ M ] − 1
[ M ] = [ S r X r S r Y r S r Z r S g X g S g Y g S g Z g S b X b S b Y b S b Z b ] ,
[ S r S g S b ] = [ X W Y W Z W ] [ X g Y r Z r X g Y g Z g X b Y b Z b ] .
[ R G B ] = 1 P o [ X Y Z ] [ 23.42 − 9.83 1.16 − 11.11 19.02 − 4.24 − 3.60 0.42 21.96 ] − 1 .
ℓ = { 12.92 ℓ ℓ ≤ 0.00313 1.055 ℓ 1 ⁄ 2.4 − 0.055 ℓ ≥ 0.00313 ,

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