Abstract

We present a theoretical approach enabling one to perform a preproduction investigation of the effect of accumulation of thickness errors in the course of optical coating production using broadband optical monitoring. On the basis of this approach we investigate and compare thickness errors that may be associated with such factors as random and systematic errors in measurement data, instabilities of deposition rates, and inaccuracies of on-line algorithms predicting termination instants for layer depositions.

© 2006 Optical Society of America

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  1. B. Vidal, A. Fornier, and E. Pelletier, "Optical monitoring of nonquarterwave multilayer filters," Appl. Opt. 17, 1038-1047 (1978).
  2. B. Vidal, A. Fornier, and E. Pelletier, "Wideband optical monitoring of nonquarterwave multilayer filters," Appl. Opt. 18, 3851-3856 (1979).
  3. B. Vidal and E. Pelletier, "Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors," Appl. Opt. 18, 3857-3862 (1979).
  4. H. Macleod, "Monitoring of optical coatings," Appl. Opt. 20, 82-89 (1981).
  5. X.-Q. Hu, Y.-M. Chen, and J.-F. Tang, "Apparatus for wideband monitoring of optical coatings and its uses," Appl. Opt. 28, 2886-2888 (1989).
  6. C. Clark and H. A. Macleod, "Errors and tolerances in optical coatings," in 40th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 1997), pp. 274-279.
  7. L. Li and Y. Yen, "Wideband monitoring and measuring system for optical coatings," Appl. Opt. 28, 2890-2894 (1989).
  8. B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. I. Theoretical description," Appl. Opt. 31, 3821-3835 (1992).
  9. B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. II. Experimental results--sputtering system," Appl. Opt. 32, 2351-2360 (1993).
  10. B. Sullivan, G. Clarke, T. Akiyama, N. Osborne, M. Ranger, J. A. Dobrowolski, L. Howe, A. Matsumoto, Y. Song, and K. Kikuchi, "High-rate automated deposition system for the manufacture of complex multilayer coatings," Appl. Opt. 39, 157-167 (2000).
  11. A. V. Tikhonravov and M. K. Trubetskov, "Online characterization and reoptimization of optical coatings," Proc. SPIE 5250, 406-413 (2003).
    [CrossRef]
  12. D. Ristau, T. Gross, and M. Lappschies, "Optical broadband monitoring of conventional and ion process," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE1.
  13. M. Lappschies, B. Goertz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion beam sputtering," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE4.
  14. S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In-situ broadband monitoring and characterization of optical coatings," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.
  15. S. Dligatch, "Real time process control and monitoring in multilayer filter deposition," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE5.
  16. A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
    [CrossRef]
  17. B. V. Gnedenko, Theory of Probability (Gordon & Breach Science, 1997).
  18. A. V. Tikhonravov, "Virtual deposition plant," Proc. SPIE 5870, 108-120 (2005).
  19. A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, "Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films," Appl. Opt. 41, 2555-2560 (2002).

2005 (2)

2003 (1)

A. V. Tikhonravov and M. K. Trubetskov, "Online characterization and reoptimization of optical coatings," Proc. SPIE 5250, 406-413 (2003).
[CrossRef]

2002 (1)

2000 (1)

1993 (1)

1992 (1)

1989 (2)

L. Li and Y. Yen, "Wideband monitoring and measuring system for optical coatings," Appl. Opt. 28, 2890-2894 (1989).

X.-Q. Hu, Y.-M. Chen, and J.-F. Tang, "Apparatus for wideband monitoring of optical coatings and its uses," Appl. Opt. 28, 2886-2888 (1989).

1981 (1)

1979 (2)

1978 (1)

Akiyama, T.

Amotchkina, T. V.

Chen, Y.-M.

Clark, C.

C. Clark and H. A. Macleod, "Errors and tolerances in optical coatings," in 40th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 1997), pp. 274-279.

Clarke, G.

Dligatch, S.

S. Dligatch, "Real time process control and monitoring in multilayer filter deposition," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE5.

Dobrowolski, J. A.

Duparré, A.

Fornier, A.

Gabler, D.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In-situ broadband monitoring and characterization of optical coatings," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

Gnedenko, B. V.

B. V. Gnedenko, Theory of Probability (Gordon & Breach Science, 1997).

Goertz, B.

M. Lappschies, B. Goertz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion beam sputtering," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE4.

Gross, T.

D. Ristau, T. Gross, and M. Lappschies, "Optical broadband monitoring of conventional and ion process," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE1.

Günster, S.

Howe, L.

Hu, X.-Q.

Kaiser, N.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In-situ broadband monitoring and characterization of optical coatings," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

Kikuchi, K.

Kokarev, M. A.

Lappschies, M.

D. Ristau, T. Gross, and M. Lappschies, "Optical broadband monitoring of conventional and ion process," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE1.

M. Lappschies, B. Goertz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion beam sputtering," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE4.

Leitel, R.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In-situ broadband monitoring and characterization of optical coatings," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

Li, L.

L. Li and Y. Yen, "Wideband monitoring and measuring system for optical coatings," Appl. Opt. 28, 2890-2894 (1989).

Macleod, H.

Macleod, H. A.

C. Clark and H. A. Macleod, "Errors and tolerances in optical coatings," in 40th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 1997), pp. 274-279.

Matsumoto, A.

Osborne, N.

Pelletier, E.

Quesnel, E.

Ranger, M.

Ristau, D.

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, "Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films," Appl. Opt. 41, 2555-2560 (2002).

D. Ristau, T. Gross, and M. Lappschies, "Optical broadband monitoring of conventional and ion process," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE1.

M. Lappschies, B. Goertz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion beam sputtering," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE4.

Song, Y.

Stenzel, O.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In-situ broadband monitoring and characterization of optical coatings," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

Sullivan, B.

Sullivan, B. T.

Tang, J.-F.

Tikhonravov, A. V.

Trubetskov, M. K.

Vidal, B.

Wilbrandt, S.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In-situ broadband monitoring and characterization of optical coatings," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

Yen, Y.

L. Li and Y. Yen, "Wideband monitoring and measuring system for optical coatings," Appl. Opt. 28, 2890-2894 (1989).

Appl. Opt. (11)

B. Vidal, A. Fornier, and E. Pelletier, "Optical monitoring of nonquarterwave multilayer filters," Appl. Opt. 17, 1038-1047 (1978).

B. Vidal, A. Fornier, and E. Pelletier, "Wideband optical monitoring of nonquarterwave multilayer filters," Appl. Opt. 18, 3851-3856 (1979).

B. Vidal and E. Pelletier, "Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors," Appl. Opt. 18, 3857-3862 (1979).

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

X.-Q. Hu, Y.-M. Chen, and J.-F. Tang, "Apparatus for wideband monitoring of optical coatings and its uses," Appl. Opt. 28, 2886-2888 (1989).

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

B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. II. Experimental results--sputtering system," Appl. Opt. 32, 2351-2360 (1993).

B. Sullivan, G. Clarke, T. Akiyama, N. Osborne, M. Ranger, J. A. Dobrowolski, L. Howe, A. Matsumoto, Y. Song, and K. Kikuchi, "High-rate automated deposition system for the manufacture of complex multilayer coatings," Appl. Opt. 39, 157-167 (2000).

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, "Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films," Appl. Opt. 41, 2555-2560 (2002).

A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
[CrossRef]

L. Li and Y. Yen, "Wideband monitoring and measuring system for optical coatings," Appl. Opt. 28, 2890-2894 (1989).

Proc. SPIE (2)

A. V. Tikhonravov and M. K. Trubetskov, "Online characterization and reoptimization of optical coatings," Proc. SPIE 5250, 406-413 (2003).
[CrossRef]

A. V. Tikhonravov, "Virtual deposition plant," Proc. SPIE 5870, 108-120 (2005).

Other (6)

C. Clark and H. A. Macleod, "Errors and tolerances in optical coatings," in 40th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 1997), pp. 274-279.

D. Ristau, T. Gross, and M. Lappschies, "Optical broadband monitoring of conventional and ion process," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE1.

M. Lappschies, B. Goertz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion beam sputtering," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE4.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In-situ broadband monitoring and characterization of optical coatings," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

S. Dligatch, "Real time process control and monitoring in multilayer filter deposition," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE5.

B. V. Gnedenko, Theory of Probability (Gordon & Breach Science, 1997).

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Figures (8)

Fig. 1
Fig. 1

Theoretical transmittance of the 38-layer bandpass filter.

Fig. 2
Fig. 2

Theoretical transmittance of the 42-layer hot mirror.

Fig. 3
Fig. 3

Standard deviations of errors in layer thicknesses of the 38-layer bandpass filter caused by random measurement errors with σ meas = 0.2 % .

Fig. 4
Fig. 4

Standard deviations of errors in layer thicknesses of the 42-layer hot mirror caused by random measurement errors with σ meas = 0.2 % .

Fig. 5
Fig. 5

Standard deviations of errors in layer thicknesses of the 38-layer bandpass filter caused by direct thickness errors with the level σ d = 0.2   nm (see text for details).

Fig. 6
Fig. 6

Standard deviations of errors in layer thicknesses of the 42-layer hot mirror caused by direct thickness errors with the level σ d = 0.2   nm (see text for details).

Fig. 7
Fig. 7

Errors in layer thicknesses of the 38-layer bandpass filter caused by systematic deviations of transmittance data for 0.2 % during depositions of all coating layers: gray bars, additional errors specified by Eq. (29); black bars, total errors calculated using Eq. (15).

Fig. 8
Fig. 8

Errors in layer thicknesses of the 42-layer hot mirror caused by systematic deviations of transmittance data for 0.2 % during depositions of all coating layers: gray bars, additional errors specified by Eq. (29); black bars, total errors calculated using Eq. (15).

Tables (1)

Tables Icon

Table 1 Construction Parameters of the Theoretical Designs Considered in the Text a

Equations (29)

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d i a = d i t + δ d i .
d j ( t ) = d j t + δ d j ( t ) .
T meas j ( t ; λ k ) = T j ( d 1 a , . . . , d j - 1 a , d j ( t ) ; λ k ) + δ T meas j ( t , λ k ) .
F = λ k [ T j ( d 1     t ,     ,   d j 1 t , d j     e ( t ) , λ k ) T meas j ( t , λ k ) ] 2 .
d j e ( t ) = d j t + δ d j e ( t ) ,
T j ( d 1 t ,     ,   d j 1 t , d j e ( t ) , λ k ) = T j ( d 1 t ,     ,   d j t , λ k ) + T j d j δ d j e ( t ) .
T meas j ( t , λ k ) = T j ( d 1 t ,     ,   d j t , λ k ) + i = 1 j 1 T j d i δ d i + T j d j δ d j ( t ) + δ T meas ( λ k ) .
F = { λ k } [ T j d j δ d j + i = 1 j 1 T j d i δ d i + δ T meas ( λ k ) ] 2 .
δ d j = δ d j ( t ) δd j e ( t ) .
δ d j = d j ( t ) d j e ( t ) ,
F = a ( δ d j ) 2 2 b δ d j + c ,
a = { λ k } ( T j d j ) 2 ,
b = - i = 1 j 1 [ { λ k } ( T j d j T j d i ) ] δ d i { λ k } T j d j δ T meas ( λ k ) .
δ d j = b / a .
δ d j = i = 1 j 1 α j i δ d i + β j ,
α j i = { λ k } ( T j d j T j d i ) / { λ k } ( T j d j ) 2 .
β j = { λ k } T j d j δ T meas ( λ k ) / { λ k } ( T j d j ) 2 .
σ ( β j ) = σ meas / [ { λ k } ( T j d j ) 2 ] 1 / 2 .
δ d 1 = β 1 ,
δ d j = i = 1 j μ j i β i .
μ j i = k = i j 1 α j k μ k i , for   i = 1 ,  .  .  .   ,   j 1 ; μ j     j = 1 .
σ j = [ i = 1 j ( μ j i ) 2 σ 2 ( β i ) ] 1 / 2 .
σ ( β j ) = σ meas / | T j d j |
r ( t ) = r mean + δ r ( t ) ,
Δ d = 0 τ δ r ( t ) d t + Δ r mean τ + r mean Δ τ ,
δ d j = i = 1 j 1 α j i δ d i + Δ d j ,
σ j = [ i = 1 j ( μ j     i ) 2 ] 1 / 2 σ d .
δ T meas ( λ k ) = Δ T .
β j = Δ T j ( { λ k } T j d j ) / { λ k } ( T j d j ) 2 ,

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