Abstract

To resolve observed absorption anomalies in the visible region in very thin films on evaporated metals a model is proposed which assumes that: (1) absorption can be separated into <i>x</i>, <i>y</i>, and <i>z</i> components and each of the components decreases exponentially with distance from the film-metal interface and that (2) the absorption at a point in the film is given by the sum of products involving the relative electric-field components and the respective absorption coefficients in the coordinate directions. A procedure is presented for calculation of the relative electric field components for a given film, substrate, wavelength, and angle of incidence. The relative tangential electric field has a dominant influence on the absorption, particularly for very thin films. This conclusion is based on the observed correlation between the slopes of the measured absorption and the calculated tangential field. The substrate has an important influence. This is evident in differences in measured absorption and calculated fields comparing Au and Cr substrates.

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  1. S. A. Francis and A. H. Ellison, J. Opt. Soc. Am. 49, 131 (1959).
  2. F. P. Mertens, P. Theroux, and R. C. Plumb, J. Opt. Soc. Am. 53, 788 (1963).
  3. F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. 67A, 363 (1963).
  4. F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds. (Natl. Bur. Std. Miscl. Publ., No. 256, Washington, D. C., 1964), p. 61.
  5. N. M. Bashara and C. T. Doty, J. Appl. Phys. 35, 3498 (1964).
  6. F. Rouard and F. Bousquet, in Progress in Optics, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1965), IV, p. 147.
  7. L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954); L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 363 (1954).
  8. A. C. Hall, J. Opt. Soc. Am. 55, 911 (1965).
  9. Contamination films of water on Cr and Au are discussed by McCrackin et al.3
  10. The variation may be partly due to a change of substrate properties caused by a difference of structure.
  11. D. W. Peterson and N. M. Bashara, J. Opt. Soc. Am. 55, 845 (1965).
  12. The approximate equation for the thickness used is derived assuming that higher-order terms of the ratio (d0) can be neglected. This assumption holds best for film thickness <50 Å.
  13. V. V. Andreeva, Corrosion 20, 35t. (1964).
  14. L. S. Bartell and D. Churchill, J. Phys. Chem. 65, 2242 (1961).
  15. O. Wiener, Ann. Physik 40, 203 (1890).
  16. See the discussion by Hayfield and White17 on this point, p. 161.
  17. P. C. S. Hayfield and G. W. T. White, in Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds. (Natl. Bur. Std. Miscl. Publ., No. 256, Washington, D. C., 1964), p. 157.
  18. We are uncertain of the homogeneity of a 22-Å film of polybutadiene.
  19. The changes of film absorption for the film on Au between 4900 and 5300 Å are not dealt with by our model nor is the rapid increase of absorption for films on both substrates as measurements extend into the ultraviolet. The changes of absorption between 4900 and 5300 Å are probably related to the large change of the optical properties of Au, Fig. 1. In contrast, the properties of Cr are considerably different, Fig. 2.
  20. Compare Figs. 1 and 2 with Fig. 12.
  21. The initial part of this section follows a presentation by Hayfield and White.17 Fry's22 analysis of the field in a film sandwiched between air and a metal base was used by Francis and Ellison. Strachan23 has also studied this general problem.
  22. T. C. Fry, J. Opt. Soc. Am. 22, 307 (1932).
  23. C. Strachan, Proc. Cambridge Phil. Soc. 29, 116 (1933).
  24. The absorption and phase lag which occur in the traversals of the film are not shown explicitly in Fig. 15 but are included in the analysis.

Andreeva, V. V.

V. V. Andreeva, Corrosion 20, 35t. (1964).

Bartell, L. S.

L. S. Bartell and D. Churchill, J. Phys. Chem. 65, 2242 (1961).

Bashara, N. M.

N. M. Bashara and C. T. Doty, J. Appl. Phys. 35, 3498 (1964).

D. W. Peterson and N. M. Bashara, J. Opt. Soc. Am. 55, 845 (1965).

Bousquet, F.

F. Rouard and F. Bousquet, in Progress in Optics, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1965), IV, p. 147.

Churchill, D.

L. S. Bartell and D. Churchill, J. Phys. Chem. 65, 2242 (1961).

Colson, J. P.

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds. (Natl. Bur. Std. Miscl. Publ., No. 256, Washington, D. C., 1964), p. 61.

Doty, C. T.

N. M. Bashara and C. T. Doty, J. Appl. Phys. 35, 3498 (1964).

Ellison, A. H.

S. A. Francis and A. H. Ellison, J. Opt. Soc. Am. 49, 131 (1959).

Francis, S. A.

S. A. Francis and A. H. Ellison, J. Opt. Soc. Am. 49, 131 (1959).

Fry, T. C.

T. C. Fry, J. Opt. Soc. Am. 22, 307 (1932).

Hall, A. C.

A. C. Hall, J. Opt. Soc. Am. 55, 911 (1965).

Hayfield, P. C. S.

P. C. S. Hayfield and G. W. T. White, in Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds. (Natl. Bur. Std. Miscl. Publ., No. 256, Washington, D. C., 1964), p. 157.

McCrackin, F. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. 67A, 363 (1963).

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds. (Natl. Bur. Std. Miscl. Publ., No. 256, Washington, D. C., 1964), p. 61.

Mertens, F. P.

F. P. Mertens, P. Theroux, and R. C. Plumb, J. Opt. Soc. Am. 53, 788 (1963).

Passaglia, E.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. 67A, 363 (1963).

Peterson, D. W.

D. W. Peterson and N. M. Bashara, J. Opt. Soc. Am. 55, 845 (1965).

Plumb, R. C.

F. P. Mertens, P. Theroux, and R. C. Plumb, J. Opt. Soc. Am. 53, 788 (1963).

Rouard, F.

F. Rouard and F. Bousquet, in Progress in Optics, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1965), IV, p. 147.

Schulz, L. G.

L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954); L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 363 (1954).

Steinberg, H. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. 67A, 363 (1963).

Strachan, C.

C. Strachan, Proc. Cambridge Phil. Soc. 29, 116 (1933).

Stromberg, R. R.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. 67A, 363 (1963).

Theroux, P.

F. P. Mertens, P. Theroux, and R. C. Plumb, J. Opt. Soc. Am. 53, 788 (1963).

White, G. W. T.

P. C. S. Hayfield and G. W. T. White, in Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds. (Natl. Bur. Std. Miscl. Publ., No. 256, Washington, D. C., 1964), p. 157.

Wiener, O.

O. Wiener, Ann. Physik 40, 203 (1890).

Other (24)

S. A. Francis and A. H. Ellison, J. Opt. Soc. Am. 49, 131 (1959).

F. P. Mertens, P. Theroux, and R. C. Plumb, J. Opt. Soc. Am. 53, 788 (1963).

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. 67A, 363 (1963).

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds. (Natl. Bur. Std. Miscl. Publ., No. 256, Washington, D. C., 1964), p. 61.

N. M. Bashara and C. T. Doty, J. Appl. Phys. 35, 3498 (1964).

F. Rouard and F. Bousquet, in Progress in Optics, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1965), IV, p. 147.

L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954); L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 363 (1954).

A. C. Hall, J. Opt. Soc. Am. 55, 911 (1965).

Contamination films of water on Cr and Au are discussed by McCrackin et al.3

The variation may be partly due to a change of substrate properties caused by a difference of structure.

D. W. Peterson and N. M. Bashara, J. Opt. Soc. Am. 55, 845 (1965).

The approximate equation for the thickness used is derived assuming that higher-order terms of the ratio (d0) can be neglected. This assumption holds best for film thickness <50 Å.

V. V. Andreeva, Corrosion 20, 35t. (1964).

L. S. Bartell and D. Churchill, J. Phys. Chem. 65, 2242 (1961).

O. Wiener, Ann. Physik 40, 203 (1890).

See the discussion by Hayfield and White17 on this point, p. 161.

P. C. S. Hayfield and G. W. T. White, in Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds. (Natl. Bur. Std. Miscl. Publ., No. 256, Washington, D. C., 1964), p. 157.

We are uncertain of the homogeneity of a 22-Å film of polybutadiene.

The changes of film absorption for the film on Au between 4900 and 5300 Å are not dealt with by our model nor is the rapid increase of absorption for films on both substrates as measurements extend into the ultraviolet. The changes of absorption between 4900 and 5300 Å are probably related to the large change of the optical properties of Au, Fig. 1. In contrast, the properties of Cr are considerably different, Fig. 2.

Compare Figs. 1 and 2 with Fig. 12.

The initial part of this section follows a presentation by Hayfield and White.17 Fry's22 analysis of the field in a film sandwiched between air and a metal base was used by Francis and Ellison. Strachan23 has also studied this general problem.

T. C. Fry, J. Opt. Soc. Am. 22, 307 (1932).

C. Strachan, Proc. Cambridge Phil. Soc. 29, 116 (1933).

The absorption and phase lag which occur in the traversals of the film are not shown explicitly in Fig. 15 but are included in the analysis.

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