Abstract

The optical properties of very-thin chromium films and their suitability for use in precision, scanning, reflection interferometry have been studied. The thickness range was from 0–36 nm. The reflectances and transmittances were measured with an absolute reflectometer. The phase change F = 2β1 + ϕ1ϕ1′ of the film was measured by scanning interferometry, where ϕ1 and ϕ1′ are the phase changes at reflection from the air/film and silica substrate/film interfaces, respectively, and β1 is the phase change on transmission through the film. F influences the form and symmetry of the reflection interference fringes. The phase changes ϕ1 and ϕ1′ have also been measured directly. For films 6–10 nm thick (air/film reflectance 20–40%), and with a highly reflecting second surface, the reflection fringes are transmission-like fringes (F → 2n π) of high contrast and good symmetry. Fringes of optimum contrast (visibility nearly unity) and symmetry are obtained for films with air/film reflectances of 20–30%, which was obtained with thicknesses from 6–8 nm. Accurate settings on these fringes can be made to the order of 0.001 fringe in a scanning-interferometer system. The results indicate that the films have continuous structures, with optical properties insensitive to wavelength, and with the phase properties very different from metal films such as silver.

© 1974 Optical Society of America

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References

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1971 (2)

1970 (1)

F. Spiegelhalter, R. Bünnagel, and J. Moser, Optik 311, 533 (1970).

1967 (1)

1966 (1)

1965 (3)

I. N. Shkliarevskii, N. A. Nosulenko, and A. N. Ryazanov, Opt. Spektrosk. 18, 102 (1965) [Opt. Spectrosc. 18, 51 (1965)].

N. Barakat and F. G. Abouzakakhm, Opt. Acta 12, 321 (1965).
[CrossRef]

W. K. Clothier, Metrologia 1, 18 (1965).

1964 (4)

1963 (3)

C. Mc and D. Hargraves, Nature 197, 890 (1963).

A. R. Cownie, J. Opt. Soc. Am. 53, 425 (1963).
[CrossRef]

E. F. Idczak, Opt. Spektrosk. 15, 107 (1963) [Opt. Spectrosc. 15, 54 (1962)].

1961 (1)

C. F. Bruce and R. M. Hill, Aust. J. Sci. Res. 14, 64 (1961).

1960 (1)

P. E. Ciddor, Opt. Acta 7, 4 (1960).

1959 (1)

1958 (2)

R. M. Hill and C. Weaver, Trans. Faraday Soc. 54, 1140 (1958).
[CrossRef]

R. M. Hill and C. Weaver, Trans. Faraday Soc. 54, 1464 (1958).
[CrossRef]

1956 (1)

I. N. Shkliarevskii, Zh. Tekh. Fiz. 26, 333 (1956) [Sov. Phys.-Tech. Phys. 1, 327 (1956)].

1951 (2)

C. F. Bruce, Aust. J. Sci. Res. 4, 117 (1951).

J. Holden, J. Opt. Soc. Am. 41, 504 (1951).
[CrossRef]

1950 (2)

1949 (1)

J. Holden, Proc. Phys. Soc. (Lond.) 62, 405 (1949).
[CrossRef]

1937 (1)

H. Wolter, Z. Phys. 105, 269 (1937).
[CrossRef]

1906 (1)

M. Hamy, J. Phys. Rad. 5, 789 (1906).

Abouzakakhm, F. G.

N. Barakat and F. G. Abouzakakhm, Opt. Acta 12, 321 (1965).
[CrossRef]

Barakat, N.

N. Barakat and F. G. Abouzakakhm, Opt. Acta 12, 321 (1965).
[CrossRef]

Bennett, Jean M.

Blevin, W. R.

Bolger, B.

B. Bolger, Opt. Commun. 4, 313 (1971).
[CrossRef]

Bruce, C. F.

C. F. Bruce, Appl. Opt. 10, 880 (1971).
[CrossRef] [PubMed]

C. F. Bruce and R. M. Hill, Aust. J. Sci. Res. 14, 64 (1961).

C. F. Bruce, Aust. J. Sci. Res. 4, 117 (1951).

Bünnagel, R.

F. Spiegelhalter, R. Bünnagel, and J. Moser, Optik 311, 533 (1970).

Ciddor, P. E.

P. E. Ciddor, Opt. Acta 7, 4 (1960).

Clothier, W. K.

W. K. Clothier, Metrologia 1, 18 (1965).

Cownie, A. R.

Dufour, C.

C. Dufour, J. Phys. Rad. 11, 327 (1950).
[CrossRef]

Hamy, M.

M. Hamy, J. Phys. Rad. 5, 789 (1906).

Hargraves, D.

C. Mc and D. Hargraves, Nature 197, 890 (1963).

Henderson, G.

Hill, R. M.

C. F. Bruce and R. M. Hill, Aust. J. Sci. Res. 14, 64 (1961).

C. Weaver, R. M. Hill, and J. E. S. MacLeod, J. Opt. Soc. Am. 49, 992 (1959).
[CrossRef]

R. M. Hill and C. Weaver, Trans. Faraday Soc. 54, 1140 (1958).
[CrossRef]

R. M. Hill and C. Weaver, Trans. Faraday Soc. 54, 1464 (1958).
[CrossRef]

Hoffman, D. M.

D. M. Hoffman and J. Riseman, in Vacuum Symposium Transactions, edited by C. Robert Meissner (Pergamon, New York, 1959), p. 218.

Holden, J.

J. Holden, J. Opt. Soc. Am. 41, 504 (1951).
[CrossRef]

J. Holden, Proc. Phys. Soc. (Lond.) 62, 405 (1949).
[CrossRef]

Idczak, E. F.

E. F. Idczak, Opt. Spektrosk. 17, 923 (1964) [Opt. Spectrosc. 17, 501 (1964)].

E. F. Idczak, Opt. Spektrosk. 15, 107 (1963) [Opt. Spectrosc. 15, 54 (1962)].

Lee, P. H.

MacLeod, J. E. S.

Mc, C.

C. Mc and D. Hargraves, Nature 197, 890 (1963).

Moser, J.

F. Spiegelhalter, R. Bünnagel, and J. Moser, Optik 311, 533 (1970).

Nosulenko, N. A.

I. N. Shkliarevskii, N. A. Nosulenko, and A. N. Ryazanov, Opt. Spektrosk. 18, 102 (1965) [Opt. Spectrosc. 18, 51 (1965)].

Pastor, J.

Riseman, J.

D. M. Hoffman and J. Riseman, in Vacuum Symposium Transactions, edited by C. Robert Meissner (Pergamon, New York, 1959), p. 218.

Ryazanov, A. N.

I. N. Shkliarevskii, N. A. Nosulenko, and A. N. Ryazanov, Opt. Spektrosk. 18, 102 (1965) [Opt. Spectrosc. 18, 51 (1965)].

Scott, G. D.

Scow, K. B.

K. B. Scow and R. E. Thun, in Vacuum Symposium Transactions, edited by G. H. Bancroft (Pergamon, New York, 1962), p. 151.

Sennett, R. S.

Shaw, J. E.

Shkliarevskii, I. N.

I. N. Shkliarevskii, N. A. Nosulenko, and A. N. Ryazanov, Opt. Spektrosk. 18, 102 (1965) [Opt. Spectrosc. 18, 51 (1965)].

I. N. Shkliarevskii, Zh. Tekh. Fiz. 26, 333 (1956) [Sov. Phys.-Tech. Phys. 1, 327 (1956)].

Smith, F. D.

F. D. Smith, Thesis, (Inst. of Optics, Univ. of Rochester, Rochester, N. Y., 1951).

Spiegelhalter, F.

F. Spiegelhalter, R. Bünnagel, and J. Moser, Optik 311, 533 (1970).

Thun, R. E.

K. B. Scow and R. E. Thun, in Vacuum Symposium Transactions, edited by G. H. Bancroft (Pergamon, New York, 1962), p. 151.

Tolansky, S.

S. Tolansky, Multiple Beam Interferometry (Clarendon, Oxford, 1948), p. 147.

Weaver, C.

Wolter, H.

H. Wolter, Z. Phys. 105, 269 (1937).
[CrossRef]

Appl. Opt. (1)

Aust. J. Sci. Res. (2)

C. F. Bruce, Aust. J. Sci. Res. 4, 117 (1951).

C. F. Bruce and R. M. Hill, Aust. J. Sci. Res. 14, 64 (1961).

J. Opt. Soc. Am. (9)

J. Phys. Rad. (2)

M. Hamy, J. Phys. Rad. 5, 789 (1906).

C. Dufour, J. Phys. Rad. 11, 327 (1950).
[CrossRef]

Metrologia (1)

W. K. Clothier, Metrologia 1, 18 (1965).

Nature (1)

C. Mc and D. Hargraves, Nature 197, 890 (1963).

Opt. Acta (2)

P. E. Ciddor, Opt. Acta 7, 4 (1960).

N. Barakat and F. G. Abouzakakhm, Opt. Acta 12, 321 (1965).
[CrossRef]

Opt. Commun. (1)

B. Bolger, Opt. Commun. 4, 313 (1971).
[CrossRef]

Opt. Spektrosk. (3)

E. F. Idczak, Opt. Spektrosk. 15, 107 (1963) [Opt. Spectrosc. 15, 54 (1962)].

E. F. Idczak, Opt. Spektrosk. 17, 923 (1964) [Opt. Spectrosc. 17, 501 (1964)].

I. N. Shkliarevskii, N. A. Nosulenko, and A. N. Ryazanov, Opt. Spektrosk. 18, 102 (1965) [Opt. Spectrosc. 18, 51 (1965)].

Optik (1)

F. Spiegelhalter, R. Bünnagel, and J. Moser, Optik 311, 533 (1970).

Proc. Phys. Soc. (Lond.) (1)

J. Holden, Proc. Phys. Soc. (Lond.) 62, 405 (1949).
[CrossRef]

Trans. Faraday Soc. (2)

R. M. Hill and C. Weaver, Trans. Faraday Soc. 54, 1140 (1958).
[CrossRef]

R. M. Hill and C. Weaver, Trans. Faraday Soc. 54, 1464 (1958).
[CrossRef]

Z. Phys. (1)

H. Wolter, Z. Phys. 105, 269 (1937).
[CrossRef]

Zh. Tekh. Fiz. (1)

I. N. Shkliarevskii, Zh. Tekh. Fiz. 26, 333 (1956) [Sov. Phys.-Tech. Phys. 1, 327 (1956)].

Other (4)

F. D. Smith, Thesis, (Inst. of Optics, Univ. of Rochester, Rochester, N. Y., 1951).

S. Tolansky, Multiple Beam Interferometry (Clarendon, Oxford, 1948), p. 147.

D. M. Hoffman and J. Riseman, in Vacuum Symposium Transactions, edited by C. Robert Meissner (Pergamon, New York, 1959), p. 218.

K. B. Scow and R. E. Thun, in Vacuum Symposium Transactions, edited by G. H. Bancroft (Pergamon, New York, 1962), p. 151.

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Figures (13)

Fig. 1
Fig. 1

Arrangement of interferometer for determining the phase changes F and ϕ1.

Fig. 2
Fig. 2

Arrangement of interferometer for determining the phase change ϕ1′.

Fig. 3
Fig. 3

Vector-analysis diagram.

Fig. 4
Fig. 4

Relation between film thickness and air/film reflectance.

Fig. 5
Fig. 5

Relation between Raf, Rsf, T, and A and the Wolter factor.

Fig. 6
Fig. 6

Experimental arrangement of interferometer system.

Fig. 7
Fig. 7

Measured values of F, ϕ1, and ϕ1′ as a function of air/ film reflectance. ● F values from scan measurements; × F values from profile measurements.

Fig. 8
Fig. 8

Photograph of fringes for film of thickness varying from 0 to 6 nm. Upper portion (C): coated region; lower portion (D): uncoated region.

Fig. 9
Fig. 9

Fizeau-fringe profiles for chromium film. Raf = 7.1%; t = 2.9 nm; back reflector 70% reflectance; plate separation <0.1 mm; λ = 0.63 μm; — R profile; - - - - T profile. Order increasing left to right; 0X: dark-current level; 0Y: intensity scale.

Fig. 10
Fig. 10

Fizeau-fringe profiles for chromium film. Raf = 22.5%; t = 6.0 nm; back reflector 70% reflectance; plate separation <0.1 mm; λ = 0.63 μm; — R profile; - - - - T profile; ● calculated R profile. Order increasing left to right; 0X: dark-current level; 0Y: intensity scale.

Fig. 11
Fig. 11

Fizeau-fringe profiles for chromium film. Raf = 44.3%; t = 14.9 nm; back reflector 70% reflectance; plate separation <0.1 mm; λ = 0.63 μm; — R profile; - - - - T profile. Order increasing left to right; 0X: dark-current level; 0Y: intensity scale.

Fig. 12
Fig. 12

Fizeau-fringe profiles for chromium film. Raf = 52.9%; t = 35.5 nm; back reflector 70% reflectance; plate separation <0.1 mm; λ = 0.63 μm; — R profile; - - - - T profile. Order increasing left to right; 0X: dark-current level; 0Y: intensity scale.

Fig. 13
Fig. 13

Reflection Fabry–Perot fringe profile for chromium film. Raf = 20.2%; t = 6.2 nm; back reflector 70% reflectance; plate separation 10 mm; λ = 0.63 μm. Order increasing left to right; 0X: dark-current level; 0Y: intensity scale.

Equations (21)

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A R exp ( i ϕ R ) = r 1 exp ( i ϕ 1 ) + r 2 t 1 2 exp [ i ( δ a + ϕ 2 + 2 β 1 ) ] 1 - r 1 r 2 exp [ i ( δ a + ϕ 1 + ϕ 2 ) ] .
I R = A R 2 = r 1 2 + B Δ r 2 2 t 1 4 + 2 B Δ r 1 r 2 t 1 2 [ cos ( Δ + F ) - r 1 r 2 cos F ] ,
m sin Δ + n cos Δ = p ,
m = t 1 2 r 2 2 r 1 + r 1 cos F - r 1 2 r 2 2 r 1 cos F , n = r 1 sin F + r 1 2 r 2 2 r 1 sin F ,
p = 2 r 1 r 2 r 1 sin F .
Δ = 2 n π + θ 1             for maxima ,
Δ = ( 2 n + 1 ) π - θ 2             for minima ,
θ 1 = sin - 1 [ m p / ( m 2 + n 2 ) + n ( m 2 + n 2 + p 2 ) 1 2 / ( m 2 + n 2 ) ]
θ 2 = sin - 1 [ m p / ( m 2 + n 2 ) - n ( m 2 + n 2 + p 2 ) 1 2 / ( m 2 + n 2 ) ] .
OM = a + p exp [ i ( Δ + π ) ]
OP = r exp [ i ( F - π ) ] + k ,
O A = a = k / ( 1 - r 1 2 r 2 2 ) ,             O K = k = t 1 2 / r 1 ,
F = - F = α + sin - 1 [ t 1 2 r 2 sin α r 1 r 1 ( 1 - r 2 ) ] ,
F = ϕ 1 + ϕ 1 - 2 β 1 , α = θ 1 + 2 tan - 1 ( r sin θ 1 / ( 1 - r cos θ 1 ) ) ,
r = r 1 r 2 .
I T = t 1 2 t 2 2 / ( 1 - 2 r 1 r 2 cos ( δ a + ϕ 1 + ϕ 2 ) + r 1 2 r 2 2 )
I T = t 0 2 t 2 2 / ( 1 - 2 r 0 r 2 cos ( δ a + π + ϕ 2 ) + r 0 2 r 2 2 ) ,
Δ ϕ = ( δ a - δ a ) + π - ϕ 1 .
ϕ 1 = π + K - Δ ϕ ,
ϕ 1 = - Δ ϕ .
R af = R af - T 2 R s 1 - R s ( 2 - R sf )             and             R sf = R sf - R s 1 - R s ( 2 - R sf ) .