Abstract

A new technique for determining the IR optical constants of materials that can be formed into thin films is presented. At a given wavelength the thickness of the film t, the index of refraction n, and the extinction coefficient k combine to produce interference effects in the film, which in turn control reflectance from the film. When reflectance is plotted vs thickness the resultant curve is a unique function of n and k. Values of n and k are determined by curve fitting. The technique is illustrated using thin films of muscovite mica, and values of n and k are reported for wave numbers from 1200 to 400 cm−1, which include the reststrahlen region of mica.

© 1983 Optical Society of America

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References

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  1. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955), Sect. 4.
  2. See, for example, M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford U. P., London, 1954), pp. 116–128.
  3. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).
  4. A. Hjortsberg, C. G. Granquist, Appl. Opt. 19, 1694 (1980).
    [CrossRef] [PubMed]
  5. A. Hjortsberg, Appl. Opt. 20, 1254 (1981).
    [CrossRef] [PubMed]
  6. P.-O. Nilsson, Appl. Opt. 7, 435 (1968).
    [CrossRef] [PubMed]
  7. W. Driscoll, Ed., Handbook of Optics (McGraw-Hill, New York, 1978), p. 10–108.
  8. W. Vedder, Am. Mineral. 49, 736 (1964).

1981

1980

1968

1964

W. Vedder, Am. Mineral. 49, 736 (1964).

Born, M.

See, for example, M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford U. P., London, 1954), pp. 116–128.

Granquist, C. G.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955), Sect. 4.

Hjortsberg, A.

Huang, K.

See, for example, M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford U. P., London, 1954), pp. 116–128.

Nilsson, P.-O.

Vedder, W.

W. Vedder, Am. Mineral. 49, 736 (1964).

Am. Mineral.

W. Vedder, Am. Mineral. 49, 736 (1964).

Appl. Opt.

Other

W. Driscoll, Ed., Handbook of Optics (McGraw-Hill, New York, 1978), p. 10–108.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955), Sect. 4.

See, for example, M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford U. P., London, 1954), pp. 116–128.

D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

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Figures (7)

Fig. 1
Fig. 1

Computer generated thin film reflectance R and transmittance T for an open film and reflectance from a film with an opaque aluminum substrate Rm plotted vs film thickness t for the wavelength and index of refraction indicated. Note the Fabry-Perot interference fringes with increasing film thickness.

Fig. 2
Fig. 2

Computer generated thin film reflectance R and transmittance T for an open film and reflectance from a film with an opaque aluminum substrate Rm plotted vs film thickness t for the wavelength and index of refraction shown. For this relatively high value of k absorption has become complete before Fabry-Perot interference fringes can be formed.

Fig. 3
Fig. 3

Computer generated reflectance R plotted in (n,k) space for the case in which reflectance no longer changes with increasing thickness.

Fig. 4
Fig. 4

Tracings of reflectance spectra from the (001) plane of muscovite mica for unpolarized light at near normal incidence. Reflectance from sample films with an opaque aluminum substrate Rm and from an open film R are shown for selected film thicknesses t.

Fig. 5
Fig. 5

Tracing of a transmission spectrum for unpolarized light incident normally on the (001) plane of a sample of muscovite mica 0.29 μm thick.

Fig. 6
Fig. 6

Computer generated thin film reflectance from an open film R and an aluminum backed film Rm plotted vs film thickness t with n = 2.49 and k = 1.90 chosen to best fit the indicated experimental data points.

Fig. 7
Fig. 7

Computer generated and smoothed plot of n, k, and nk for muscovite mica from the data of Table I.

Tables (2)

Tables Icon

Table I Real Part n and Imaginary Part k of the Index of Refraction of Muscovite Mica for Unpolarized Light at Near Normal Incidence on the (001) Plane, from 1200 to 400 cm−1, as Determined by the Present Work

Tables Icon

Table II Comparison of Maxima in the Product nk from Fig. 7, Transmission Minima from Fig. 5, and Absorption Peaks Reported by Vedder in Ref. 8 for Muscovite Mica Using Unpolarized Light Incident Normally on the (001) Plane

Equations (3)

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r 1 = n ˆ 0 n ˆ 1 n ˆ 0 + n ˆ 1 = 1 n ˆ 1 1 + n ˆ 1 .
δ = 2 π λ 0 n ˆ 1 t = 2 π λ 0 ( n 1 i k 1 ) t ,
r = n ˆ 1 n ˆ 2 n ˆ 1 + n ˆ 2 ,

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