Abstract

We propose an algorithm for correcting deposition termination levels that allows elimination of the cumulative effect of errors in previously deposited layers. For the application of this algorithm at least one monitoring signal extremum should be registered during a layer deposition. We also derive a theoretical relation for the estimation of errors in layer refractive indices based on the results of on-line monitoring measurements. At least two monitoring signal extrema are required for its application.

© 2007 Optical Society of America

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References

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  1. H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).
  2. H. Macleod, "Monitoring of optical coatings," Appl. Opt. 20, 82-89 (1981).
    [CrossRef] [PubMed]
  3. R. R. Willey, "Optical thickness monitoring sensitivity improvement using graphical methods," Appl. Opt. 26, 729-737 (1987).
    [CrossRef] [PubMed]
  4. B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. I. Theoretical description," Appl. Opt. 31, 3821-3835 (1992).
    [CrossRef] [PubMed]
  5. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, "Statistical approach to choosing a strategy of monochromatic monitoring of optical coating production," Appl. Opt. 45, 7863 (2006).
    [CrossRef] [PubMed]
  6. P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
    [CrossRef]
  7. H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 19, 1-28 (1972).
    [CrossRef]
  8. H. Macleod and D. Richmond, "The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 21, 429-443 (1974).
    [CrossRef]
  9. H. Macleod and E. Pelletier, "Error compensation mechanisms in some thin-film monitoring systems," Opt. Acta 24, 907-930 (1977).
    [CrossRef]
  10. A. V. Tikhonravov and M. K. Trubetskov, "Automated design and sensitivity analysis of wavelength-division multiplexing filters," Appl. Opt. 41, 3176-3182 (2002).
    [CrossRef] [PubMed]
  11. F. Zhao, "Monitoring of periodic multilayers by the level method," Appl. Opt. 24, 3339-3342 (1985).
    [CrossRef] [PubMed]
  12. R. Willey, "Variation of band-edge position with errors in the monitoring of layer termination level for long- and short-wave pass filters," Appl. Opt. 38, 5447-5451 (1999).
    [CrossRef]
  13. C. J. van der Laan, "Optical monitoring of nonquarterwave stacks," Appl. Opt. 25, 757-760 (1989).
  14. J. A. Dobrowolski and A. Waldorf, "Manufacture of all-dielectric filters with layers of arbitrary thickness and refractive index," J. Opt. Soc. Am. 60, 725 (1970).
  15. C. Holm, "Optical thin film production with continuous reoptimization of layer thicknesses," Appl. Opt. 18, 1978-1982 (1978).
    [CrossRef]
  16. C.-C. Lee, K. Wu, C.-C. Kuo, and S.-H. Chen, "Improvement of the optical coating process by cutting layers with sensitive monitoring wavelengths," Opt. Express 13, 4854-4861 (2005).
    [CrossRef] [PubMed]
  17. B. Chun, C. K. Hwangbo, and J. S. Kim, "Optical monitoring of nonquarterwave layers of dielectric multilayer filters using optical admittance," Opt. Express 14, 2473-2480 (2006).
    [CrossRef] [PubMed]
  18. S. Furman and A. V. Tikhonravov, "Basics of optics of multilayer systems," (http://www.optilayer.com, 1992).
  19. A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).
  20. A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

2006 (2)

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, "Statistical approach to choosing a strategy of monochromatic monitoring of optical coating production," Appl. Opt. 45, 7863 (2006).
[CrossRef] [PubMed]

B. Chun, C. K. Hwangbo, and J. S. Kim, "Optical monitoring of nonquarterwave layers of dielectric multilayer filters using optical admittance," Opt. Express 14, 2473-2480 (2006).
[CrossRef] [PubMed]

2005 (2)

C.-C. Lee, K. Wu, C.-C. Kuo, and S.-H. Chen, "Improvement of the optical coating process by cutting layers with sensitive monitoring wavelengths," Opt. Express 13, 4854-4861 (2005).
[CrossRef] [PubMed]

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

2002 (1)

1999 (1)

1992 (1)

1989 (1)

C. J. van der Laan, "Optical monitoring of nonquarterwave stacks," Appl. Opt. 25, 757-760 (1989).

1987 (1)

1985 (1)

1981 (1)

1978 (1)

1977 (1)

H. Macleod and E. Pelletier, "Error compensation mechanisms in some thin-film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

1974 (1)

H. Macleod and D. Richmond, "The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 21, 429-443 (1974).
[CrossRef]

1972 (2)

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 19, 1-28 (1972).
[CrossRef]

1970 (1)

J. A. Dobrowolski and A. Waldorf, "Manufacture of all-dielectric filters with layers of arbitrary thickness and refractive index," J. Opt. Soc. Am. 60, 725 (1970).

Amotchkina, T. V.

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, "Statistical approach to choosing a strategy of monochromatic monitoring of optical coating production," Appl. Opt. 45, 7863 (2006).
[CrossRef] [PubMed]

Boos, M.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Bousquet, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Chen, S.-H.

Chun, B.

Dobrowolski, J. A.

B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. I. Theoretical description," Appl. Opt. 31, 3821-3835 (1992).
[CrossRef] [PubMed]

J. A. Dobrowolski and A. Waldorf, "Manufacture of all-dielectric filters with layers of arbitrary thickness and refractive index," J. Opt. Soc. Am. 60, 725 (1970).

Fornier, A.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Furman, S.

S. Furman and A. V. Tikhonravov, "Basics of optics of multilayer systems," (http://www.optilayer.com, 1992).

Goetzelmann, R.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

Hagedorn, H.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Holm, C.

Hwangbo, C. K.

Kim, J. S.

Klug, W.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Kowalczyk, R.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Kuo, C.-C.

Lee, C.-C.

Macleod, H.

H. Macleod, "Monitoring of optical coatings," Appl. Opt. 20, 82-89 (1981).
[CrossRef] [PubMed]

H. Macleod and E. Pelletier, "Error compensation mechanisms in some thin-film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

H. Macleod and D. Richmond, "The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 21, 429-443 (1974).
[CrossRef]

Macleod, H. A.

H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 19, 1-28 (1972).
[CrossRef]

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).

Pelletier, E.

H. Macleod and E. Pelletier, "Error compensation mechanisms in some thin-film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Richmond, D.

H. Macleod and D. Richmond, "The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 21, 429-443 (1974).
[CrossRef]

Roche, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Schmitt, C.

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Sullivan, B. T.

Tikhonravov, A. V.

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, "Statistical approach to choosing a strategy of monochromatic monitoring of optical coating production," Appl. Opt. 45, 7863 (2006).
[CrossRef] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, "Automated design and sensitivity analysis of wavelength-division multiplexing filters," Appl. Opt. 41, 3176-3182 (2002).
[CrossRef] [PubMed]

S. Furman and A. V. Tikhonravov, "Basics of optics of multilayer systems," (http://www.optilayer.com, 1992).

Trubetskov, M. K.

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, "Statistical approach to choosing a strategy of monochromatic monitoring of optical coating production," Appl. Opt. 45, 7863 (2006).
[CrossRef] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, "Automated design and sensitivity analysis of wavelength-division multiplexing filters," Appl. Opt. 41, 3176-3182 (2002).
[CrossRef] [PubMed]

van der Laan, C. J.

C. J. van der Laan, "Optical monitoring of nonquarterwave stacks," Appl. Opt. 25, 757-760 (1989).

Waldorf, A.

J. A. Dobrowolski and A. Waldorf, "Manufacture of all-dielectric filters with layers of arbitrary thickness and refractive index," J. Opt. Soc. Am. 60, 725 (1970).

Willey, R.

Willey, R. R.

Wu, K.

Zhao, F.

Zoeller, A.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Appl. Opt. (9)

J. Opt. Soc. Am. (1)

J. A. Dobrowolski and A. Waldorf, "Manufacture of all-dielectric filters with layers of arbitrary thickness and refractive index," J. Opt. Soc. Am. 60, 725 (1970).

Opt. Acta (3)

H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 19, 1-28 (1972).
[CrossRef]

H. Macleod and D. Richmond, "The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 21, 429-443 (1974).
[CrossRef]

H. Macleod and E. Pelletier, "Error compensation mechanisms in some thin-film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

Opt. Express (2)

Proc. SPIE (1)

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

Thin Solid Films (1)

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Other (3)

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual Technical Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

S. Furman and A. V. Tikhonravov, "Basics of optics of multilayer systems," (http://www.optilayer.com, 1992).

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).

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Figures (3)

Fig. 1
Fig. 1

Admittance diagram of an arbitrary coating layer: ζ and ρ are the center and radius of the admittance circle, A ^ is the initial admittance value at the start of a layer deposition, and the thick arc of the circle designates the admittance diagram between the start of a layer deposition and the first reflectance extremum (see the text for details).

Fig. 2
Fig. 2

Variation of the admittance diagram in the case of errors in previously deposited layers: solid circle corresponds to the admittance diagram in the absence of errors and dashed circle corresponds to the admittance diagram in the presence of errors ( ζ ˜ and ρ ˜ are the new circle center coordinates and radius).

Fig. 3
Fig. 3

Schematic illustrating the determination of the initial admittance value A i n : solid curve—isoreflectance circle with the center ζ i n and radius ρ i n corresponding to the reflectance level R i n at the start of a layer deposition; dashed curve—the admittance diagram of the monitored layer; A e —the admittance value corresponding to the first reflectance extremum registered during the layer deposition.

Equations (33)

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φ = 2 π λ n d .
A ( φ ) = i n sin φ + A ^ cos φ cos φ + ( i / n ) A ^ sin φ .
ζ = | A ^ | 2 + n 2 2 Re A ^ , ρ = | A ^ 2 n 2 | 2 Re A ^ .
r ( φ ) = n a A ( φ ) n a + A ( φ ) ,
R ( φ ) = | n a A ( φ ) n a + A ( φ ) | 2 .
h t = h in + ( m 1 ) λ 4 + h fin ,
h i n + h f i n = h ˜ i n + h ˜ fin ,
R i n = | n a A i n n a + A i n | 2 .
ζ i n = n a 1 + R i n 1 R i n , ρ i n = 2 n a R i n 1 R i n .
A e = n a 1 + r e 1 r e .
r e = ± R e ,
A e = i n sin φ ˜ + A i n cos φ ˜ cos φ ˜ + ( i / n ) A i n sin φ ˜ ,
φ ˜ = 2 π λ h ˜ i n .
A i n = i n sin φ ˜ + A e cos φ ˜ cos φ ˜ ( i / n ) A e sin φ ˜ .
ξ = tan φ ˜ .
A i n = i n ξ + A e 1 ( i / n ) A e ξ .
R i n = ( n a A e ) 2 + ξ 2 ( n n a A e / n ) 2 ( n a + A e ) 2 + ξ 2 ( n + n a A e / n ) 2 .
ξ = [ ( n a A e ) 2 R i n ( n a + A e ) 2 R i n ( n + n a A e / n ) 2 ( n n a A e / n ) 2 ] 1 / 2 .
h ˜ i n = λ 2 π arctan ξ .
A term = i n sin φ fin + A f cos φ fin cos φ fin + ( i / n ) A f sin φ fin ,
φ fin = 2 π λ h ˜ fin .
R term = | n a A term n a + A term | 2 .
ζ 2 ρ 2 = n 2 .
( ζ ρ ) δ ( ζ + ρ ) + ( ζ + ρ ) δ ( ζ ρ ) = 2 n δ n .
δ ( ζ + ρ ) ζ + ρ + δ ( ζ ρ ) ζ ρ = 2 δ n n .
δ A e 1 A e 1 + δ A e 2 A e 2 = 2 δ n n .
R e = ( n a A e n a + A e ) 2 .
δ R e = 4 n a n a A e ( n a + A e ) 3 δ A e .
1 R e = 4 n a A e ( n a + A e ) 2 .
n a A e n a + A e = r e .
δ R e = r e ( 1 R e ) δ A e A e .
δ n n = 1 2 [ δ R e 1 r e 1 ( 1 R e 1 ) + δ R e 2 r e 2 ( 1 R e 2 ) ] .
δ R e 1 r e 1 ( 1 R e 1 ) = δ R e 2 r e 2 ( 1 R e 2 ) .

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