Abstract

An experimental technique is described for determining the optical constants n and k of a metal by shining monochromatic light through thin films of the material and measuring the transmittance and phase change on transmission for samples of various thicknesses. The technique has the advantage, when compared to reflection techniques, that the results obtained are characteristic of the bulk material and are insensitive to surface conditions. Measurements were performed on vacuum-deposited gold films with thicknesses in the range from approximately 170 to 1800 Å, using lasers at wavelengths of 4880, 5145, and 6328 Å. In an attempt to evaluate the technique, the results obtained for the optical constants of gold are compared with those obtained by previous workers using different methods of measurement. In particular, the values obtained here are in agreement, within experimental error, with the recent work of Johnson and Christy.

© 1973 Optical Society of America

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References

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  1. O. S. Heavens, in Physics of Thin Films, Vol. 2, edited by G. Hass and R. Thun (Academic, New York, 1964), p. 193ff.
  2. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).
  3. F. Abeles, in Physics of Thin Films, Vol. 6, edited by G. Hass and R. Thun (Academic, New York, 1971), p. 151ff.
    [Crossref]
  4. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [Crossref]
  5. G. P. Pells and M. Shiga, J. Phys. C 2, 1835 (1969).
    [Crossref]
  6. L. G. Schulz, Adv. Phys. 6, 102 (1957).
    [Crossref]
  7. F. Goos, Z. Phys. 100, 95 (1936).
    [Crossref]
  8. F. Goos, Z. Phys. 106, 606 (1937).
    [Crossref]
  9. C. F. E. Simons, Physica (Utr.) 10, 141 (1943).
    [Crossref]
  10. R. Fleischmann, Z. Phys. 129, 275 (1951); R. Fleischmann and H. Schopper, Z. Phys. 129, 285 (1951); Z. Phys. 131, 225 (1952); R. Fleischmann and A. Lohmann, Z. Phys. 137, 362 (1954).
    [Crossref]
  11. Conditions corresponding to the anomalous skin effect in pure metals are therefore excluded from consideration. See, for example, Sec. VII 2 of Ref. 3.
  12. Cominco 69 grade gold. Cominco Ltd., 630 Dorchester Blvd. W., Montreal 2, Que., Canada.
  13. M.-L. Theye, Phys. Rev. B 2, 357 (1954).
  14. The Sloan Instrument Corp., P.O. Box 4206, Santa Barbara, Calif.
  15. M. Francon, Optical Interferometry (Academic, New York, 1966).
  16. The photomultipliers were type IP28 with an S-5 response.
  17. L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954).
    [Crossref]
  18. L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 362 (1954).
    [Crossref]
  19. G. P. Pells and M. Shiga (private communication). The values of n and k shown in Figs. 4 and 5 are the data from which Pells and Shiga calculated the curves of 2nk/λ at 293 K presented in Ref. 5. The authors are very grateful to Dr. G. Pells for making these data available to us.
  20. O. Hunderi, Appl. Opt. 11, 1572 (1972).
    [Crossref] [PubMed]
  21. P. Croce, G. Devant, M. G. Sere, and M. F. Verhaeghe, Surf. Sci. 22, 173 (1970).
    [Crossref]
  22. R. L. Mozzi and O. J. Guentert, Rev. Sci. Instrum. 35, 75 (1964).
    [Crossref]
  23. P. J. Haysman and A. P. Lenham, J. Opt. Soc. Am. 62, 333 (1972).
    [Crossref]

1972 (3)

1970 (1)

P. Croce, G. Devant, M. G. Sere, and M. F. Verhaeghe, Surf. Sci. 22, 173 (1970).
[Crossref]

1969 (1)

G. P. Pells and M. Shiga, J. Phys. C 2, 1835 (1969).
[Crossref]

1964 (1)

R. L. Mozzi and O. J. Guentert, Rev. Sci. Instrum. 35, 75 (1964).
[Crossref]

1957 (1)

L. G. Schulz, Adv. Phys. 6, 102 (1957).
[Crossref]

1954 (3)

1951 (1)

R. Fleischmann, Z. Phys. 129, 275 (1951); R. Fleischmann and H. Schopper, Z. Phys. 129, 285 (1951); Z. Phys. 131, 225 (1952); R. Fleischmann and A. Lohmann, Z. Phys. 137, 362 (1954).
[Crossref]

1943 (1)

C. F. E. Simons, Physica (Utr.) 10, 141 (1943).
[Crossref]

1937 (1)

F. Goos, Z. Phys. 106, 606 (1937).
[Crossref]

1936 (1)

F. Goos, Z. Phys. 100, 95 (1936).
[Crossref]

Abeles, F.

F. Abeles, in Physics of Thin Films, Vol. 6, edited by G. Hass and R. Thun (Academic, New York, 1971), p. 151ff.
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Croce, P.

P. Croce, G. Devant, M. G. Sere, and M. F. Verhaeghe, Surf. Sci. 22, 173 (1970).
[Crossref]

Devant, G.

P. Croce, G. Devant, M. G. Sere, and M. F. Verhaeghe, Surf. Sci. 22, 173 (1970).
[Crossref]

Fleischmann, R.

R. Fleischmann, Z. Phys. 129, 275 (1951); R. Fleischmann and H. Schopper, Z. Phys. 129, 285 (1951); Z. Phys. 131, 225 (1952); R. Fleischmann and A. Lohmann, Z. Phys. 137, 362 (1954).
[Crossref]

Francon, M.

M. Francon, Optical Interferometry (Academic, New York, 1966).

Goos, F.

F. Goos, Z. Phys. 106, 606 (1937).
[Crossref]

F. Goos, Z. Phys. 100, 95 (1936).
[Crossref]

Guentert, O. J.

R. L. Mozzi and O. J. Guentert, Rev. Sci. Instrum. 35, 75 (1964).
[Crossref]

Haysman, P. J.

Heavens, O. S.

O. S. Heavens, in Physics of Thin Films, Vol. 2, edited by G. Hass and R. Thun (Academic, New York, 1964), p. 193ff.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

Hunderi, O.

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Lenham, A. P.

Mozzi, R. L.

R. L. Mozzi and O. J. Guentert, Rev. Sci. Instrum. 35, 75 (1964).
[Crossref]

Pells, G. P.

G. P. Pells and M. Shiga, J. Phys. C 2, 1835 (1969).
[Crossref]

G. P. Pells and M. Shiga (private communication). The values of n and k shown in Figs. 4 and 5 are the data from which Pells and Shiga calculated the curves of 2nk/λ at 293 K presented in Ref. 5. The authors are very grateful to Dr. G. Pells for making these data available to us.

Schulz, L. G.

Sere, M. G.

P. Croce, G. Devant, M. G. Sere, and M. F. Verhaeghe, Surf. Sci. 22, 173 (1970).
[Crossref]

Shiga, M.

G. P. Pells and M. Shiga, J. Phys. C 2, 1835 (1969).
[Crossref]

G. P. Pells and M. Shiga (private communication). The values of n and k shown in Figs. 4 and 5 are the data from which Pells and Shiga calculated the curves of 2nk/λ at 293 K presented in Ref. 5. The authors are very grateful to Dr. G. Pells for making these data available to us.

Simons, C. F. E.

C. F. E. Simons, Physica (Utr.) 10, 141 (1943).
[Crossref]

Tangherlini, F. R.

Theye, M.-L.

M.-L. Theye, Phys. Rev. B 2, 357 (1954).

Verhaeghe, M. F.

P. Croce, G. Devant, M. G. Sere, and M. F. Verhaeghe, Surf. Sci. 22, 173 (1970).
[Crossref]

Adv. Phys. (1)

L. G. Schulz, Adv. Phys. 6, 102 (1957).
[Crossref]

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

J. Phys. C (1)

G. P. Pells and M. Shiga, J. Phys. C 2, 1835 (1969).
[Crossref]

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

M.-L. Theye, Phys. Rev. B 2, 357 (1954).

Physica (Utr.) (1)

C. F. E. Simons, Physica (Utr.) 10, 141 (1943).
[Crossref]

Rev. Sci. Instrum. (1)

R. L. Mozzi and O. J. Guentert, Rev. Sci. Instrum. 35, 75 (1964).
[Crossref]

Surf. Sci. (1)

P. Croce, G. Devant, M. G. Sere, and M. F. Verhaeghe, Surf. Sci. 22, 173 (1970).
[Crossref]

Z. Phys. (3)

F. Goos, Z. Phys. 100, 95 (1936).
[Crossref]

F. Goos, Z. Phys. 106, 606 (1937).
[Crossref]

R. Fleischmann, Z. Phys. 129, 275 (1951); R. Fleischmann and H. Schopper, Z. Phys. 129, 285 (1951); Z. Phys. 131, 225 (1952); R. Fleischmann and A. Lohmann, Z. Phys. 137, 362 (1954).
[Crossref]

Other (9)

Conditions corresponding to the anomalous skin effect in pure metals are therefore excluded from consideration. See, for example, Sec. VII 2 of Ref. 3.

Cominco 69 grade gold. Cominco Ltd., 630 Dorchester Blvd. W., Montreal 2, Que., Canada.

O. S. Heavens, in Physics of Thin Films, Vol. 2, edited by G. Hass and R. Thun (Academic, New York, 1964), p. 193ff.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

F. Abeles, in Physics of Thin Films, Vol. 6, edited by G. Hass and R. Thun (Academic, New York, 1971), p. 151ff.
[Crossref]

The Sloan Instrument Corp., P.O. Box 4206, Santa Barbara, Calif.

M. Francon, Optical Interferometry (Academic, New York, 1966).

The photomultipliers were type IP28 with an S-5 response.

G. P. Pells and M. Shiga (private communication). The values of n and k shown in Figs. 4 and 5 are the data from which Pells and Shiga calculated the curves of 2nk/λ at 293 K presented in Ref. 5. The authors are very grateful to Dr. G. Pells for making these data available to us.

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the experimental arrangement.

Fig. 2
Fig. 2

Block diagram of electronic apparatus.

Fig. 3
Fig. 3

Representative chart-recorder output during a phase measurement.

Fig. 4
Fig. 4

Plot of k vs λ for gold. Two sets of results were obtained in this work: The values designated by ● were obtained in the thick-film limit and are considered to be the actual values of n and k; the values designated by the open circles ○ were obtained by use of the general expressions (1) and (2) and are subject to surface conditions. The values obtained by Schulz (Ref. 17) (Δ), Pells and Shiga (Ref. 19) (×), and Johnson and Christy (Ref. 4) (■) have been included for comparison purposes.

Fig. 5
Fig. 5

Plot of n vs λ for gold. Two sets of results were obtained in this work. The values designated by ● were obtained in the thick-film limit and are considered to be the actual values of n and k; the values designated by the open circles ○ were obtained by use of the general expressions (1) and (2) and are subject to surface conditions. The values obtained by Schulz and Tangherlini (Ref. 18) (Δ), Pells and Shiga (Ref. 19) (×), and Johnson and Christy (Ref. 4) (■) have been included for comparison purposes.

Tables (3)

Tables Icon

Table I Measured optical densities (O.D.) and phase shifts (ϕ) vs thickness for gold films.

Tables Icon

Table II Experimental results for the optical constants of gold, determined in the thick-film limit. These values are independent of surface conditions and are to be considered the “correct” or actual values of n and k.

Tables Icon

Table III n and k for gold, determined from the general theory. (These values are influenced by surface effects; the “correct” values of n and k are listed in Table II.)

Equations (14)

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t = 4 n 0 ( n i k ) C + i D ,
C = [ ( n 0 + n ) ( n + n s ) k 2 ] e K cos N + k ( n 0 + 2 n + n s ) e K sin N + [ ( n 0 n ) ( n n s ) + k 2 ] e K cos N k ( n 0 2 n + n s ) e K sin N , D = [ ( n 0 + n ) ( n + n s ) k 2 ] e K sin N k ( n 0 + 2 n + n s ) × e K cos N [ ( n 0 n ) ( n n s ) + k 2 ] × e K sin N k ( n 0 2 n + n s ) e K cos N ,
K = 2 π k d λ , N = 2 π n d λ .
T = n s n 0 | t | 2 = 16 n 0 n s ( n 2 + k 2 ) C 2 + D 2 ,
α = arctan ( n D + k C k D n C ) .
exp ( 4 π k d λ ) 0.01.
T = A exp { 4 π k d λ } ,
α = χ 1 + χ 2 2 π n d λ ,
S = R 1 cos ω t + A ( 1 + cos 2 π f t ) cos ( ω t + ϕ ) ,
e S 2 av = 1 2 R 1 2 + 1 4 3 A 2 + R 1 A cos ϕ + 1 4 A 2 cos 4 π f t + ( A 2 + R 1 A cos ϕ ) cos 2 π f t .
O . D . = log 10 1 / T ,
ϕ = 2 π d λ + α ,
( O . D . ) d = 4 π k λ log 10 e
ϕ d = 2 π λ ( 1 n )