Abstract

The optical constants of a thin film on its structure. A technique, based on transmission measurements carried out in vacuo, has been developed to derive the profiles of the refractive index and extinction coefficient. The interpretation of the profiles gives information on the layer structure in vacuo. The technique can be used as a means of monitoring the variations of the optical constants with changes in the deposition parameters. This paper presents the technique, which is based on an envelope method, and gives some experimental results.

© 1985 Optical Society of America

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References

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  1. H. A. Macleod, “Microstructure of Optical Thin Films,” Proc Soc. Photo-Opt. Instrum. Eng. 325, 21 (1982).
  2. C.-C. Lee, “Moisture Adsorption and Optical Instability in Thin Film Coatings,” Ph.D. Dissertation, U of Arizona (1983).
  3. J. P. Borgogno et al., “Inhomogeneity in Films: Limitation of the Accuracy of Optical Monitoring of Thin Films,” Appl. Opt. 2090 (1981).
    [CrossRef] [PubMed]
  4. F. Van Milligen et al., “Development of an Automated Scanning Monochromator for a Balzers 760 Evaporation System,” J. Opt. Soc. Am. A 1, 1258 (1984).
  5. B. Schmitt, Thèse de docteur ingénieur, “Problèmes de réalisation des filtres spectraux multidiélectriques: contrôle simultané de l'indice de réfraction et de l'épaisseur des couches en cours de formation,” Ecole Nationale Supérieure de Physique, Marseille (1983).
  6. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. 9, 1002 (1976).
  7. R. Swanepool. “Determination of the Thickness and Optical Constants of Amorphous Silicon,” J. Phys. E 16, 1214 (1983).
    [CrossRef]
  8. D. P. Arndt et al., “Multiple Determination of the Optical Constants of Thin-Film Coating Materials,” Appl. Opt. 23, 3571 (1984).
    [CrossRef] [PubMed]
  9. R. Jacobsson, “Inhomogeneous and Coevaporated Homogeneous Films for Optical Applications,” Phys. Thin Films 8, 51 (1975).
  10. S. M. Bozic, Digital and Kalman Filtering. An Introduction to Discrete Time Filtering and Optimum Linear Estimation (Edward Arnold, London, 1979).

1984 (2)

F. Van Milligen et al., “Development of an Automated Scanning Monochromator for a Balzers 760 Evaporation System,” J. Opt. Soc. Am. A 1, 1258 (1984).

D. P. Arndt et al., “Multiple Determination of the Optical Constants of Thin-Film Coating Materials,” Appl. Opt. 23, 3571 (1984).
[CrossRef] [PubMed]

1983 (1)

R. Swanepool. “Determination of the Thickness and Optical Constants of Amorphous Silicon,” J. Phys. E 16, 1214 (1983).
[CrossRef]

1982 (1)

H. A. Macleod, “Microstructure of Optical Thin Films,” Proc Soc. Photo-Opt. Instrum. Eng. 325, 21 (1982).

1981 (1)

1976 (1)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. 9, 1002 (1976).

1975 (1)

R. Jacobsson, “Inhomogeneous and Coevaporated Homogeneous Films for Optical Applications,” Phys. Thin Films 8, 51 (1975).

Arndt, D. P.

Borgogno, J. P.

Bozic, S. M.

S. M. Bozic, Digital and Kalman Filtering. An Introduction to Discrete Time Filtering and Optimum Linear Estimation (Edward Arnold, London, 1979).

Fillard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. 9, 1002 (1976).

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. 9, 1002 (1976).

Jacobsson, R.

R. Jacobsson, “Inhomogeneous and Coevaporated Homogeneous Films for Optical Applications,” Phys. Thin Films 8, 51 (1975).

Lee, C.-C.

C.-C. Lee, “Moisture Adsorption and Optical Instability in Thin Film Coatings,” Ph.D. Dissertation, U of Arizona (1983).

Macleod, H. A.

H. A. Macleod, “Microstructure of Optical Thin Films,” Proc Soc. Photo-Opt. Instrum. Eng. 325, 21 (1982).

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. 9, 1002 (1976).

Schmitt, B.

B. Schmitt, Thèse de docteur ingénieur, “Problèmes de réalisation des filtres spectraux multidiélectriques: contrôle simultané de l'indice de réfraction et de l'épaisseur des couches en cours de formation,” Ecole Nationale Supérieure de Physique, Marseille (1983).

Swanepool, R.

R. Swanepool. “Determination of the Thickness and Optical Constants of Amorphous Silicon,” J. Phys. E 16, 1214 (1983).
[CrossRef]

Van Milligen, F.

F. Van Milligen et al., “Development of an Automated Scanning Monochromator for a Balzers 760 Evaporation System,” J. Opt. Soc. Am. A 1, 1258 (1984).

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

F. Van Milligen et al., “Development of an Automated Scanning Monochromator for a Balzers 760 Evaporation System,” J. Opt. Soc. Am. A 1, 1258 (1984).

J. Phys. (1)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. 9, 1002 (1976).

J. Phys. E (1)

R. Swanepool. “Determination of the Thickness and Optical Constants of Amorphous Silicon,” J. Phys. E 16, 1214 (1983).
[CrossRef]

Phys. Thin Films (1)

R. Jacobsson, “Inhomogeneous and Coevaporated Homogeneous Films for Optical Applications,” Phys. Thin Films 8, 51 (1975).

Proc Soc. Photo-Opt. Instrum. Eng. (1)

H. A. Macleod, “Microstructure of Optical Thin Films,” Proc Soc. Photo-Opt. Instrum. Eng. 325, 21 (1982).

Other (3)

C.-C. Lee, “Moisture Adsorption and Optical Instability in Thin Film Coatings,” Ph.D. Dissertation, U of Arizona (1983).

S. M. Bozic, Digital and Kalman Filtering. An Introduction to Discrete Time Filtering and Optimum Linear Estimation (Edward Arnold, London, 1979).

B. Schmitt, Thèse de docteur ingénieur, “Problèmes de réalisation des filtres spectraux multidiélectriques: contrôle simultané de l'indice de réfraction et de l'épaisseur des couches en cours de formation,” Ecole Nationale Supérieure de Physique, Marseille (1983).

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Figures (5)

Fig. 1
Fig. 1

Plot of noisy signal. The extrema are difficult to determine with accuracy.

Fig. 2
Fig. 2

After filtering, the extrema have been extracted from the noise without distorting or attenuating the transmission curve.

Fig. 3
Fig. 3

Profile of refractive index and extinction coefficient for a stable titanium dioxide layer (upper curve represents n, lower curve k).

Fig. 4
Fig. 4

Dispersion of innermost and outermost refractive index for a stable layer of titanium dioxide.

Fig. 5
Fig. 5

Example of result given by the method when applied to an unstable layer. Titanium dioxide layer deposited in an oxygen deficient atmosphere.

Tables (1)

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Table I Results of Simulation Calculations

Equations (14)

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[ ( n in / n out ) 1 / 2 cos δ i sin δ / ( n out n in ) 1 / 2 i ( n in n out ) 1 / 2 sin δ ( n out / n in ) 1 / 2 cos δ ] ,
δ = 2 π ( n ̅ i k ̅ ) d λ ,
[ [ i.e . , n ̅ = 1 d 0 d n ( z ) d z ] ,
[ i.e . , k ̅ = 1 d 0 d k ( z ) d z ] ,
T = 16 n s n 0 n in n out exp ( 2 δ 2 ) C 1 2 + C 2 2 exp ( 4 δ 2 ) + 2 C 1 C 2 exp ( 2 δ 2 ) cos 2 δ 1 ,
C 1 = ( n out + n 0 ) ( n s + n in ) , C 2 = ( n out n 0 ) ( n s n in ) , δ 1 = 2 π n d / λ , δ 2 = 2 π k d / λ .
T max = 16 n 0 n s n in n out exp ( 2 δ 2 ) [ C 1 + C 2 exp ( 2 δ 2 ) ] 2 , T min = 16 n 0 n s n in n out exp ( 2 δ 2 ) [ C 1 C 2 exp ( 2 δ 2 ) ] 2 .
n in = [ N + ( N 2 n 0 2 n s 2 ) 1 / 2 ] 1 / 2 ,
N = n 0 2 + n s 2 2 + 2 n 0 n s ( T max T min T max + T min ) .
n out = 2 n in n s n 0 n in 2 n s 2 ( T max T min T max T min ) + n 0 [ 1 + 4 n in 2 n s 2 ( T max T min T max T min ) 2 ( n in 2 n s 2 ) 2 ] 1 / 2 ,
d = m λ 4 n ̅ , where n ̅ = 1 d 0 d n ( z ) d z ,
k ̅ = λ 4 π d log α ( d ) ,
α ( d ) = C 1 [ 1 ( T max / T min ) 1 / 2 ] C 2 [ 1 + ( T max / T min ) 1 / 2 ] = exp ( 4 π k ̅ d λ ) ,
k ( z ) = λ 4 π 1 α ( z ) d α d z ,

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