Abstract

Optical monitoring of periodic thin-film stacks by the termination of each layer at the same constant photometric level has certain advantages. One of these principal advantages is the error compensation effect in the vicinity of the monitoring wavelength. In this study, we examine, by simulation, the effect of an error in the knowledge of the absolute value of the photometric termination level on the probable stability in the manufacture of the edge position of a blocked band. The results include equations that allow the determination of the appropriate values of parameters associated with the optimum termination levels to minimize the effects of such errors.

© 1999 Optical Society of America

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References

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  1. W. P. Thoeni, “Deposition of optical coatings: process control and automation,” Thin Solid Films 88, 385–397 (1982).
    [CrossRef]
  2. H. A. Macleod, E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta 24, 907–930 (1977).
    [CrossRef]
  3. F. Zhao, “Monitoring of periodic multilayer by the level method,” Appl. Opt. 24, 3339–3342 (1985).
    [CrossRef]
  4. R. R. Willey, “Monitoring and control of thin film growth,” in Practical Design and Production of Optical Thin Films (Marcel Dekker, New York, 1996).
  5. R. R. Willey, “Optical thickness monitoring sensitivity improvement using graphical methods,” Appl. Opt. 26, 729–737 (1987).
    [CrossRef] [PubMed]
  6. J. H. Apfel, “Graphics in optical coating design,” Appl. Opt. 11, 1303–1312 (1972).
    [CrossRef] [PubMed]
  7. S. R. Schmidt, R. G. Launsby, “Box-Behnken designs,” in Understanding Industrial Designed Experiments (Air Academy Press, Colorado Springs, Colo., 1994), Sect. 3.8.
  8. doe kiss, version 97 for Windows, Air Academy Associates (and Digital Computations, Inc.), 1155 Kelly Johnson Blvd., Colorado Springs, Colo. 80920 (1997).
  9. FilmStar Design, FTG Software Associates, P.O. Box 579, Princeton, N.J. 08542 (1998).

1987

1985

1982

W. P. Thoeni, “Deposition of optical coatings: process control and automation,” Thin Solid Films 88, 385–397 (1982).
[CrossRef]

1977

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

1972

Apfel, J. H.

Launsby, R. G.

S. R. Schmidt, R. G. Launsby, “Box-Behnken designs,” in Understanding Industrial Designed Experiments (Air Academy Press, Colorado Springs, Colo., 1994), Sect. 3.8.

Macleod, H. A.

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

Pelletier, E.

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

Schmidt, S. R.

S. R. Schmidt, R. G. Launsby, “Box-Behnken designs,” in Understanding Industrial Designed Experiments (Air Academy Press, Colorado Springs, Colo., 1994), Sect. 3.8.

Thoeni, W. P.

W. P. Thoeni, “Deposition of optical coatings: process control and automation,” Thin Solid Films 88, 385–397 (1982).
[CrossRef]

Willey, R. R.

R. R. Willey, “Optical thickness monitoring sensitivity improvement using graphical methods,” Appl. Opt. 26, 729–737 (1987).
[CrossRef] [PubMed]

R. R. Willey, “Monitoring and control of thin film growth,” in Practical Design and Production of Optical Thin Films (Marcel Dekker, New York, 1996).

Zhao, F.

Appl. Opt.

Opt. Acta

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

Thin Solid Films

W. P. Thoeni, “Deposition of optical coatings: process control and automation,” Thin Solid Films 88, 385–397 (1982).
[CrossRef]

Other

R. R. Willey, “Monitoring and control of thin film growth,” in Practical Design and Production of Optical Thin Films (Marcel Dekker, New York, 1996).

S. R. Schmidt, R. G. Launsby, “Box-Behnken designs,” in Understanding Industrial Designed Experiments (Air Academy Press, Colorado Springs, Colo., 1994), Sect. 3.8.

doe kiss, version 97 for Windows, Air Academy Associates (and Digital Computations, Inc.), 1155 Kelly Johnson Blvd., Colorado Springs, Colo. 80920 (1997).

FilmStar Design, FTG Software Associates, P.O. Box 579, Princeton, N.J. 08542 (1998).

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Figures (9)

Fig. 1
Fig. 1

Spectral transmittance of a SWP filter (0.5L 1H 0.5L)10 quarter-wave optical thicknesses at 1000 nm used for simulations of this research. H is index 2.2 and L is index 1.46.

Fig. 2
Fig. 2

Simulated monitoring trace in which each of the periodic layers are terminated when the photometric level reaches 53%. This is monitored at 878.6 nm on an effective index of 0.2593.

Fig. 3
Fig. 3

Locus on a reflectance amplitude versus reflectance phase or circle diagram of the monitoring trace represented in Fig. 2 to achieve the desired result of Fig. 1.

Fig. 4
Fig. 4

View of Δλ, the difference between edge and monitoring wavelength, as a function of termination level K and high index H. Note the preferred area in the lower right where the rate of change with both K and H approach zero.

Fig. 5
Fig. 5

Overhead or contour view of Δλ as in Fig. 4 with a line drawn along the region of zero change of Δλ with termination level.

Fig. 6
Fig. 6

Comparison of the edge position of the termination of each layer at 16% R with terminations having a photometric calibration error of 1% and thereby a termination level of 15%. This is an amplified view of the same coating as in Fig. 1 and was monitored at 808 nm.

Fig. 7
Fig. 7

Comparison of the edge position of the termination of each layer from the design of Fig. 1 at 53% R with terminations having a photometric calibration error of 1% and thereby a termination level of 52%. The monitoring wavelength is 878 nm.

Fig. 8
Fig. 8

Simulated monitoring trace (for comparison with Fig. 2) where each of the periodic layers are terminated when the photometric level reaches 16%. This is monitored at 808 nm on an effective index of 0.7826.

Fig. 9
Fig. 9

Locus on a circle diagram of the monitoring trace represented in Fig. 8.

Equations (19)

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NF=-0.07882+0.01522H+0.2088L.
NF=-0.624-0.00086K+0.113H+1.07L- 0.00184KH-0.01625KL-0.00021K2.
λmon=1112.4-337.9H+180L+51.202H2.
λmon=1207.8+1.189K-449.7H+180L+2.109KH-0.0564K2+51.202H2.
Δλ=-109.03-1.00065K+112.5H-2.11KH+ 0.0538K2.
Δλ/ΔK=-1.00065-2.11H+0.1076K.
K=9.294+19.61H.
K=-14.818+29.62H.
%RT=-0.575+1.288K+26.43H-20.48L-0.111KH+0.283KL-0.0074K2-2.505H2,
%RB=12.64+1.122K-2.603H-8.25L-0.565KL-0.00822K2.
NF=-2.175+0.1789H+0.241L,  at 53% termination level,
NF=-0.425-0.0159K+0.852H+0.241L-0.0127KH-0.000343K2,
λmon=1327.03+161.43H+361.8L  (at 53% termination level),
λmon=669+4.137K+637.1H-361.8L-8.975KH+0.1562K2,
Δλ=-597.37+4.49K+441.1H-8.975KH+0.1513K2,
Δλ/ΔK=+4.49-8.975H+0.3026K,
K=-14.818+29.62H
%RT=-5.34+1.233K-6.044H+13L+0.075KH-0.00491K2,
%RB=19.61+0.679K-23.57H-0.592KH+0.0158K2+8.026H2.

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