Abstract

A simple method for measuring refractive index and thickness of nearly transparent films from Fizeau interferograms is described. The method requires no polarizing optics, variation of wavelength or angle of incidence, or precise light intensity comparisons. Commercially available Fizeau surface relief measuring instruments can be used without modification, the only necessary change being a partial, rather than complete, metallization of the sample surface. Analysis of the contributions of different sources of error to the over-all error in the refractive-index measurement indicates that the measurement is quite insensitive to weak absorption in the dielectric film and to finite absorption in the metal layer. For typical values of index and thickness, the thickness error is about 0.005 wavelengths, and the refractive-index error is of the order 0.01.

© 1978 Optical Society of America

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References

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  1. D. W. Peterson, N. M. Bashara, J. Opt. Soc. Am. 55, 845 (1965).
    [Crossref]
  2. A. B. Buckman, N. H. Hong, D. Wilson, J. Opt. Soc. Am. 65, 914 (1975).
    [Crossref]
  3. H. Yokota, M. Nishibori, K. Kinosita, Surf. Sci. 16, 275 (1969).
    [Crossref]
  4. V. Daneu, A. Sanchez, Appl. Opt. 13, 122 (1974).
    [Crossref] [PubMed]
  5. N. J. Harrick, Appl. Opt. 10, 2344 (1971).
    [Crossref] [PubMed]
  6. J. M. White, P. F. Heidrich, Appl. Opt. 15, 151 (1976).
    [Crossref] [PubMed]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), pp. 286ff.
  8. The interferograms used in these experiments were produced by an Angstrometer purchased from Sloan Technology, Inc., and operated without modification.

1976 (1)

1975 (1)

1974 (1)

1971 (1)

1969 (1)

H. Yokota, M. Nishibori, K. Kinosita, Surf. Sci. 16, 275 (1969).
[Crossref]

1965 (1)

Bashara, N. M.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), pp. 286ff.

Buckman, A. B.

Daneu, V.

Harrick, N. J.

Heidrich, P. F.

Hong, N. H.

Kinosita, K.

H. Yokota, M. Nishibori, K. Kinosita, Surf. Sci. 16, 275 (1969).
[Crossref]

Nishibori, M.

H. Yokota, M. Nishibori, K. Kinosita, Surf. Sci. 16, 275 (1969).
[Crossref]

Peterson, D. W.

Sanchez, A.

White, J. M.

Wilson, D.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), pp. 286ff.

Yokota, H.

H. Yokota, M. Nishibori, K. Kinosita, Surf. Sci. 16, 275 (1969).
[Crossref]

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

Surf. Sci. (1)

H. Yokota, M. Nishibori, K. Kinosita, Surf. Sci. 16, 275 (1969).
[Crossref]

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), pp. 286ff.

The interferograms used in these experiments were produced by an Angstrometer purchased from Sloan Technology, Inc., and operated without modification.

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Figures (5)

Fig. 1
Fig. 1

Sample configurations for Fizeau interferometry of thin films: (a) metal overcoating film edge; (b) bare film. Shaded regions are metal.

Fig. 2
Fig. 2

D′ vs D for a wide range of n, with k = 0 and km = ∞.

Fig. 3
Fig. 3

(a) Cross section of mask for making groove in evaporated dielectric film; (b) resulting film thickness profile.

Fig. 4
Fig. 4

Schematic of sample for one-step measurement of n and d by Fizeau interferometry. The field of view is centered at the junction of regions 2 and 6. Shaded regions are metal.

Fig. 5
Fig. 5

Typical interferogram taken by this method. The regions are numbered to coincide with those of Fig. 4.

Tables (1)

Tables Icon

Table I Relative Contributions to Measurement Error in n

Equations (15)

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d = ( x / Λ ) ( λ / 2 ) ,
Δ ϕ a = R 1 R 2 = 4 π D ,
r m = ( n m n ) i ( k m k ) ( n m + n ) i ( k m + k ) ,
ζ ( n ) = tan 1 [ 2 n k m / ( k m 2 n 2 ) ] ,
R f = r ˜ 1 + ( 1 δ ) exp { i [ 4 π n D + ξ ( n ) ] } 1 + r ˜ 1 ( 1 δ ) exp { i [ 4 π n D + ξ ( n ) ] } ,
r ˜ 1 = n 1 n + 1 exp [ i ( 2 k n 2 1 ) ] r 1 exp ( i α ) ;
δ = 1 | r m | exp ( 4 π D k ) .
R f = tan 1 { ( r 1 2 1 ) sin [ 4 π n D + ξ ( n ) ] ( 1 + r 1 2 ) cos [ 4 π n D + ζ ( n ) ] + 2 r 1 } ,
Δ ϕ b = R f + 4 π D + ζ ( 1 ) .
D = Δ ϕ b / 4 π .
R f = tan 1 [ ( r 1 2 1 ) sin θ ( 1 + r 1 2 ) cos θ + 2 r 1 ] 2 M π .
( 2 M 1 ) π θ ( 2 M + 1 ) π .
D = D + 1 4 π [ ζ ( 1 ) + tan 1 × { ( r 1 2 1 ) sin [ 4 π n D + ζ ( n ) ] ( 1 + r 1 2 ) cos [ 4 π n D + ζ ( n ) + 2 r 1 ] } M π ] .
E q 2 = ( D q δ q ) 2 .
E tot = [ q ( E q 2 ) ] 1 / 2 .

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