Abstract

A method is given for the measurement of the optical thickness of nonabsorbing dielectric films when it is inconvenient to apply an overlay film to measure the thickness by Fizeau fringe shift. The method is based on fringe-step displacements which have been observed in CdS films evaporated over reflecting metal films. The fringe-step structure is accounted for by a Fresnel reflection coefficient analysis of double-layer multiple reflection within the dielectric film and an air film, formed between the dielectric and a half-silvered mirror.

© 1966 Optical Society of America

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References

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  1. S. Tolansky, Multiple Beam Interferometry of Surfaces and Films (Clarendon Press, Oxford, 1948).
  2. A. C. S. van Heel and A. Walther, Opt. Acta 5, 47 (1958).
    [Crossref]
  3. F. Reizman, J. Appl. Phys. 36, 3804 (1965).
    [Crossref]
  4. S. Tolansky, Ref. 1, p. 146.
  5. O. S. Heavens, Optical Properties of Thin Solid Films (Butter-worths Scientific Publications, London, 1955).
  6. Joan Gottesman and W. F. C. Ferguson, J. Opt. Soc. Am. 44, 368 (1954).
    [Crossref]
  7. J. F. Hall and W. F. C. Ferguson, J. Opt. Soc. Am. 45, 714 (1955).
    [Crossref]

1965 (1)

F. Reizman, J. Appl. Phys. 36, 3804 (1965).
[Crossref]

1958 (1)

A. C. S. van Heel and A. Walther, Opt. Acta 5, 47 (1958).
[Crossref]

1955 (1)

1954 (1)

Ferguson, W. F. C.

Gottesman, Joan

Hall, J. F.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butter-worths Scientific Publications, London, 1955).

Reizman, F.

F. Reizman, J. Appl. Phys. 36, 3804 (1965).
[Crossref]

Tolansky, S.

S. Tolansky, Ref. 1, p. 146.

S. Tolansky, Multiple Beam Interferometry of Surfaces and Films (Clarendon Press, Oxford, 1948).

van Heel, A. C. S.

A. C. S. van Heel and A. Walther, Opt. Acta 5, 47 (1958).
[Crossref]

Walther, A.

A. C. S. van Heel and A. Walther, Opt. Acta 5, 47 (1958).
[Crossref]

J. Appl. Phys. (1)

F. Reizman, J. Appl. Phys. 36, 3804 (1965).
[Crossref]

J. Opt. Soc. Am. (2)

Opt. Acta (1)

A. C. S. van Heel and A. Walther, Opt. Acta 5, 47 (1958).
[Crossref]

Other (3)

S. Tolansky, Multiple Beam Interferometry of Surfaces and Films (Clarendon Press, Oxford, 1948).

S. Tolansky, Ref. 1, p. 146.

O. S. Heavens, Optical Properties of Thin Solid Films (Butter-worths Scientific Publications, London, 1955).

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Figures (10)

F. 1
F. 1

Optical arrangement for interference observation of CdS film thickness profile.

F. 2
F. 2

Fringe-step displacements due to air–CdS interference of light (5890 Å).

F. 3
F. 3

(a) Optical system for double-layer interference. (b) Coalescence of optical system into equivalent reduced configuration.

F. 4
F. 4

Double-layer interference condition with n2=1.0, n3=2.45, θ34=0°.

F. 5
F. 5

Change of total gap vs change in film thickness with n2 = 1.0, n3 = 2.45, λ = 5890 Å (solid curve θ34 = 0°; dashed curve θ34 = 78.9°).

F. 6
F. 6

Fringe-shift thickness determination (total gap thickness increases towards bottom of figure).

F. 7
F. 7

CdS film thickness profile. (a) Double-layer fringes, (b) Fizeau fringes.

F. 8
F. 8

Fizeau fringes for contoured CdS film (λ = 5890 Å).

F. 9
F. 9

Fringe steps for various wavelengths (scale 0.001 units = 34 μ).

F. 10
F. 10

Transmittance through 6800-Å CdS film.

Equations (17)

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r j k = ( n j n k ) / ( n j + n k ) .
r a c = r a b + r b c ( t a b t b a r a b r b a ) e 2 i δ b 1 r b a r b c e 2 i δ b .
δ b = ( 2 π / λ ) n b t b
r a c = r a b + r b c e 2 i δ b 1 + r a b r b c e 2 i δ b
r a b = r b a
t a b t b a r a b r b a = 1
r 24 = r 23 + r 34 e 2 i δ 3 1 + r 23 r 34 e 2 i δ 3 .
δ 3 = ( 2 π / λ ) n 3 t 3 .
r 04 = r 02 + ( t 02 t 20 r 02 r 20 ) r 24 e 2 i δ 2 1 r 20 r 24 e 2 i δ 2 ,
δ 2 = ( 2 π / λ ) n 2 t 2 .
2 δ 2 + arg r 24 = constant .
Δ ( 2 δ 2 ) = Δ arg r 24 .
r 34 = exp ( i θ 34 ) ,
Δ ( 2 δ 2 ) = Δ tan 1 { ( 1 r 23 2 ) sin ( 2 δ 3 + θ 34 ) 2 r 23 ( 1 + r 23 2 ) cos ( 2 δ 3 + θ 34 ) } .
t 2 = 8.18 ( 2 δ 2 ) ,
t 3 = 3.34 ( 2 δ 3 ) ,
Δ ( t 2 + t 3 ) = ( D ( x ) / d ) λ / 2 .