Abstract

It is demonstrated that the interference oscillations in the intensity of light reflected from a substrate during deposition of a semitransparent film allows one to determine the optical constants of the film by graphical techniques. The method assumes that the optical constants of the substrate are known, and that the optical constants of the film are not a function of film thickness. This technique is applicable in any wavelength region, although surface irregularities, which are more important at short wavelengths, will generally lead to an overestimate of k. A discussion of probable errors is presented. Because the method is dependent on multiple reflections through the deposited film it is useful only for small k, or, more precisely, 2πk/n < 1.

© 1971 Optical Society of America

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References

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  1. O. S. Heavens, Optical Properties of Tin Solid Films (Academic, New York, 1955).
  2. D. Male, C. R. Acad. Sci. (Paris) 230, 1349 (1950).
  3. S. P. F. Humphery-Owens, Proc. Phys. Soc. (London), 77, 949 (1961).
    [CrossRef]
  4. R. Tousey, J. Opt. Soc. Amer. 29, 235 (1939).
    [CrossRef]
  5. W. R. Hunter, J. Opt. Soc. Amer. 55, 1197 (1965).
    [CrossRef]
  6. D. M. Roessler, Brit. J. Appl. Phys. 16, 1119, 1359 (1965); Brit. J. Appl. Phys. 17, 1313 (1966).
    [CrossRef]
  7. H. W. Verleur, J. Opt. Soc. Amer. 58, 1356 (1968).
    [CrossRef]
  8. At normal incidence one may use Eq. 4 (115a) of Ref. 1.
  9. K. Rabinovitch, L. R. Canfield, R. P. Madden, Appl. Opt. 4, 1005 (1965); D. L. Steinmetz, W. G. Phillips, M. Wirick, F. F. Forbes, Appl. Opt. 6, 1001 (1967); V. G. Horton, E. T. Arakawa, R. N. Hamm, M. W. Williams, Appl. Opt. 8, 667 (1969).
    [CrossRef] [PubMed]
  10. We follow the notation of Ref. 1, Chap. 4.
  11. We use the term isoreflectance curve in the same sense as Hunter (Ref. 5). This term refers to a curve in the k1, n1 plane that corresponds to a constant reflectivity. In our case we are referring to a constant value of Rmax or Rmin.
  12. L. R. Canfield, G. Hass, W. R. Hunter, J. Phys. Chem. 25, 124 (1964).
  13. D. Beaglehole, Proc. Phys. Soc. (London) 85, 1007 (1965).
    [CrossRef]
  14. R. G. Johnston, L. R. Canfield, R. P. Madden, Appl. Opt. 6, 719 (1967).
    [CrossRef] [PubMed]
  15. We have observed well-structured deposition curves on a flat substrate using an f/11.4 monochromator.
  16. S. R. Scharber, S. E. Webber, “The Optical Constants of Simple Molecular Crystals. I. Results for CO and O2,” “ … II. Results for Kr and Xe,” to be published in J. Chem. Phys.

1968 (1)

H. W. Verleur, J. Opt. Soc. Amer. 58, 1356 (1968).
[CrossRef]

1967 (1)

1965 (4)

D. Beaglehole, Proc. Phys. Soc. (London) 85, 1007 (1965).
[CrossRef]

K. Rabinovitch, L. R. Canfield, R. P. Madden, Appl. Opt. 4, 1005 (1965); D. L. Steinmetz, W. G. Phillips, M. Wirick, F. F. Forbes, Appl. Opt. 6, 1001 (1967); V. G. Horton, E. T. Arakawa, R. N. Hamm, M. W. Williams, Appl. Opt. 8, 667 (1969).
[CrossRef] [PubMed]

W. R. Hunter, J. Opt. Soc. Amer. 55, 1197 (1965).
[CrossRef]

D. M. Roessler, Brit. J. Appl. Phys. 16, 1119, 1359 (1965); Brit. J. Appl. Phys. 17, 1313 (1966).
[CrossRef]

1964 (1)

L. R. Canfield, G. Hass, W. R. Hunter, J. Phys. Chem. 25, 124 (1964).

1961 (1)

S. P. F. Humphery-Owens, Proc. Phys. Soc. (London), 77, 949 (1961).
[CrossRef]

1950 (1)

D. Male, C. R. Acad. Sci. (Paris) 230, 1349 (1950).

1939 (1)

R. Tousey, J. Opt. Soc. Amer. 29, 235 (1939).
[CrossRef]

Beaglehole, D.

D. Beaglehole, Proc. Phys. Soc. (London) 85, 1007 (1965).
[CrossRef]

Canfield, L. R.

Hass, G.

L. R. Canfield, G. Hass, W. R. Hunter, J. Phys. Chem. 25, 124 (1964).

Heavens, O. S.

O. S. Heavens, Optical Properties of Tin Solid Films (Academic, New York, 1955).

Humphery-Owens, S. P. F.

S. P. F. Humphery-Owens, Proc. Phys. Soc. (London), 77, 949 (1961).
[CrossRef]

Hunter, W. R.

W. R. Hunter, J. Opt. Soc. Amer. 55, 1197 (1965).
[CrossRef]

L. R. Canfield, G. Hass, W. R. Hunter, J. Phys. Chem. 25, 124 (1964).

Johnston, R. G.

Madden, R. P.

Male, D.

D. Male, C. R. Acad. Sci. (Paris) 230, 1349 (1950).

Rabinovitch, K.

Roessler, D. M.

D. M. Roessler, Brit. J. Appl. Phys. 16, 1119, 1359 (1965); Brit. J. Appl. Phys. 17, 1313 (1966).
[CrossRef]

Scharber, S. R.

S. R. Scharber, S. E. Webber, “The Optical Constants of Simple Molecular Crystals. I. Results for CO and O2,” “ … II. Results for Kr and Xe,” to be published in J. Chem. Phys.

Tousey, R.

R. Tousey, J. Opt. Soc. Amer. 29, 235 (1939).
[CrossRef]

Verleur, H. W.

H. W. Verleur, J. Opt. Soc. Amer. 58, 1356 (1968).
[CrossRef]

Webber, S. E.

S. R. Scharber, S. E. Webber, “The Optical Constants of Simple Molecular Crystals. I. Results for CO and O2,” “ … II. Results for Kr and Xe,” to be published in J. Chem. Phys.

Appl. Opt. (2)

Brit. J. Appl. Phys. (1)

D. M. Roessler, Brit. J. Appl. Phys. 16, 1119, 1359 (1965); Brit. J. Appl. Phys. 17, 1313 (1966).
[CrossRef]

C. R. Acad. Sci. (Paris) (1)

D. Male, C. R. Acad. Sci. (Paris) 230, 1349 (1950).

J. Opt. Soc. Amer. (3)

R. Tousey, J. Opt. Soc. Amer. 29, 235 (1939).
[CrossRef]

W. R. Hunter, J. Opt. Soc. Amer. 55, 1197 (1965).
[CrossRef]

H. W. Verleur, J. Opt. Soc. Amer. 58, 1356 (1968).
[CrossRef]

J. Phys. Chem. (1)

L. R. Canfield, G. Hass, W. R. Hunter, J. Phys. Chem. 25, 124 (1964).

Proc. Phys. Soc. (London) (2)

D. Beaglehole, Proc. Phys. Soc. (London) 85, 1007 (1965).
[CrossRef]

S. P. F. Humphery-Owens, Proc. Phys. Soc. (London), 77, 949 (1961).
[CrossRef]

Other (6)

At normal incidence one may use Eq. 4 (115a) of Ref. 1.

We follow the notation of Ref. 1, Chap. 4.

We use the term isoreflectance curve in the same sense as Hunter (Ref. 5). This term refers to a curve in the k1, n1 plane that corresponds to a constant reflectivity. In our case we are referring to a constant value of Rmax or Rmin.

We have observed well-structured deposition curves on a flat substrate using an f/11.4 monochromator.

S. R. Scharber, S. E. Webber, “The Optical Constants of Simple Molecular Crystals. I. Results for CO and O2,” “ … II. Results for Kr and Xe,” to be published in J. Chem. Phys.

O. S. Heavens, Optical Properties of Tin Solid Films (Academic, New York, 1955).

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Figures (5)

Fig. 1
Fig. 1

A comparison of the experimental deposition curve of CO on a Au-coated substrate (bottom curve) and the theoretical deposition curve using the optical constants derived from the experiment (λ = 1544 Å, substrate at 20 K, n2 = 1.447, k2 = 1.108, n1 = 1.448, k1 = 0.039). The theoretical curve has been scaled to agree with the raw experimental data for zero film thickness.

Fig. 2
Fig. 2

Isoreflectaince curve of Rmin(---) and Rmax (—) in the n1, k1, plane for CO (for λ = 1544 Å, Au-coated substrate with n2 = 1.447, k2 = 1.108).

Fig. 3
Fig. 3

Graphical solution for n1,k1 at 1544 Å for CO on Au-coated substrate. The number on each line is the corresponding value of Rmin (---) or Rmax (—).

Fig. 4
Fig. 4

Schematic representation of experimental arrangement for observation of deposition curves: S = substrate whose radius of curvature matches the divergence of the beam from the monochromator (M), P = photomultiplier, and D = furnace or gas delivery tube.

Fig. 5
Fig. 5

Comparison of theoretical deposition curve for ideal film (—) and rough film model discussed in text (---). The parameters are the same as Fig. 1, and γ = 0.1.

Equations (4)

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R = r 1 + r 2 e - i 2 δ 1 1 + r 1 r 5 e - i 2 δ 1 ,
δ 1 = ( 2 π n ˜ 1 d 1 / λ ) cos θ 1
( d 1 - d 1 ) 2 1 2 d 1 = γ
P ( d 1 , d 1 ) = 1 γ d 1 2 π exp [ - ( d 1 - d 1 ) 2 2 γ d 1 ] ,

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