Abstract

Optical properties of vacuum-deposited silver films have been investigated by ellipsometry. A method of calculating optical parameters has been developed and applied to this investigation. On the assumption that the film is optically isotropic, <i>n</i>, <i>k</i>, and <i>d</i> are simultaneously determined by the measured values of ψ, Δ, and the transmittance of <i>p</i>-polarized light. For very thin films, those isotropic parameters show an anomalous behavior, and for thinner films, the computation for determining them does not converge. The computation converges only when the optical anisotropy of the film is taken into account, and the convergent range of the anisotropic parameters is determined. The convergence range includes the anisotropic parameters predicted by the theory for the optical properties of an aggregated silver film. An anomalous increase of the isotropic parameters with decrease of thickness, for thinner films, arises from regarding the anisotropic film as isotropic.

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  1. D. Malé, Compt. Rend. 230B, 1349 (1950).
  2. K. Ishiguro and G. Kuwahara, J. Phys. Soc. Japan 6, 71 (1951).
  3. L. Ward, A. Nag, and L. C. W. Dixon, Brit. J. Appl. Phys. 2, 301 (1969).
  4. T. Yamaguchi, S. Yoshida, and A. Kinbara, Japan J. Appl. Phys. 8, 559 (1969).
  5. R. S. Sennett and G. D. Scott, J. Opt. Soc. Am. 40, 203 (1950).
  6. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955), p. 176.
  7. E. David, Z. Physik 114, 389 (1939); H. Schopper, Z. Physik 130, 565 (1951); S. Yamaguchi, J. Phys. Soc. Japan 15, 1577 (1960); G. Rasigni and P. Rouard, J. Opt. Soc. Am. 53, 604 (1963) G. Henderson and C. Weaver, J. Opt. Soc. Am. 56, 1551 (1966); A. Carlan, Ann. Phys. (Paris) 4, 5 (1969); A. Donnadieu, Thin Solid Films 6, 249 (1970).
  8. S. Yoshida, T. Yamaguchi, and A. Kinhara, J. Opt. Soc. Am. 61, 62 (1971).
  9. R. Philip and J. Trompette, J. Phys. Radium 18, 92 (1957).
  10. J. Trompette, Ann. Phys. (Paris) 5, 915 (1960); N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).
  11. P. Rouard and P. Bousquet, in Progress in Optics IV, edited by E. Wolf (North-Holland, Amsterdam, 1965), p. 145.
  12. W. G. Oldham, Surface Sci. 16, 97 (1969).
  13. S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).
  14. F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, edited by E. Passaglia, R. R. Stromberg, and J. Kruger, Natl. Bur. Std. (U. S.) Misc. Publ. 256 (U. S. Government Printing Office, Washington, D. C., 1964); J. M. Bennett and M. J. Booty, Appl. Opt. 5, 41 (1966); P. O. Nilsson, Appl. Opt. 7, 435 (1968); J. Shewchun and E. C. Rowe, J. Appl. Phys. 41, 4128 (1970).
  15. Optical properties of aggregated metal films have also been explained in terms of Maxwell-Garnett (MG) theory, which is based on the three-dimensional (3D) distribution of spherical particles [cf. R. H. Doremus, J. Appl. Phys. 37, 2775 (1966)]. The MG equation (∊ - ∊a) / (∊ + 2∊a) = q (∊ i - ∊ a) / (∊i + 2∊a) is identical with the equation for the case ƒ (the depolarizing factor) = ⅓ (i.e., spherical shape) and β (the interaction term) =-q/3 in the equation of RE model having a single value of the axial ratio [Eq. (9) in Ref. 6]. ∊ - ∊i = q(∊i - ∊ a) / [1 + (ƒ + β) (∊i - ∊a) / ∊a]. In the 2D system, β has different values of opposite sign for electric fields parallel and perpendicular to the substrate, which causes the anisotropic property, whereas in the 3D system, β has the unique value -q/3.
  16. F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. (U. S.) 67A, 363 (1963); F. Lukes, Surface Sci. 16, 74 (1969).
  17. F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970); R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 61, 773 (1971).
  18. R. J. Archer and C. V. Shank, J. Opt. Soc. Am. 57, 191 (1967); D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 57, 466 (1967); W. G. Oldham, J. Opt. Soc. Am. 57, 617 (1967); P. H. Smith, Surface Sci. 16, 34 (1969).
  19. H. G. Jerrard, Surface Sci. 16, 67 (1969).

1971 (2)

S. Yoshida, T. Yamaguchi, and A. Kinhara, J. Opt. Soc. Am. 61, 62 (1971).

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).

1970 (1)

F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970); R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 61, 773 (1971).

1969 (4)

H. G. Jerrard, Surface Sci. 16, 67 (1969).

W. G. Oldham, Surface Sci. 16, 97 (1969).

L. Ward, A. Nag, and L. C. W. Dixon, Brit. J. Appl. Phys. 2, 301 (1969).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Japan J. Appl. Phys. 8, 559 (1969).

1967 (1)

R. J. Archer and C. V. Shank, J. Opt. Soc. Am. 57, 191 (1967); D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 57, 466 (1967); W. G. Oldham, J. Opt. Soc. Am. 57, 617 (1967); P. H. Smith, Surface Sci. 16, 34 (1969).

1964 (1)

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, edited by E. Passaglia, R. R. Stromberg, and J. Kruger, Natl. Bur. Std. (U. S.) Misc. Publ. 256 (U. S. Government Printing Office, Washington, D. C., 1964); J. M. Bennett and M. J. Booty, Appl. Opt. 5, 41 (1966); P. O. Nilsson, Appl. Opt. 7, 435 (1968); J. Shewchun and E. C. Rowe, J. Appl. Phys. 41, 4128 (1970).

1963 (1)

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. (U. S.) 67A, 363 (1963); F. Lukes, Surface Sci. 16, 74 (1969).

1960 (1)

J. Trompette, Ann. Phys. (Paris) 5, 915 (1960); N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).

1957 (1)

R. Philip and J. Trompette, J. Phys. Radium 18, 92 (1957).

1951 (1)

K. Ishiguro and G. Kuwahara, J. Phys. Soc. Japan 6, 71 (1951).

1950 (2)

D. Malé, Compt. Rend. 230B, 1349 (1950).

R. S. Sennett and G. D. Scott, J. Opt. Soc. Am. 40, 203 (1950).

1939 (1)

E. David, Z. Physik 114, 389 (1939); H. Schopper, Z. Physik 130, 565 (1951); S. Yamaguchi, J. Phys. Soc. Japan 15, 1577 (1960); G. Rasigni and P. Rouard, J. Opt. Soc. Am. 53, 604 (1963) G. Henderson and C. Weaver, J. Opt. Soc. Am. 56, 1551 (1966); A. Carlan, Ann. Phys. (Paris) 4, 5 (1969); A. Donnadieu, Thin Solid Films 6, 249 (1970).

Archer, R. J.

R. J. Archer and C. V. Shank, J. Opt. Soc. Am. 57, 191 (1967); D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 57, 466 (1967); W. G. Oldham, J. Opt. Soc. Am. 57, 617 (1967); P. H. Smith, Surface Sci. 16, 34 (1969).

Bousquet, P.

P. Rouard and P. Bousquet, in Progress in Optics IV, edited by E. Wolf (North-Holland, Amsterdam, 1965), p. 145.

Colson, J. P.

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, edited by E. Passaglia, R. R. Stromberg, and J. Kruger, Natl. Bur. Std. (U. S.) Misc. Publ. 256 (U. S. Government Printing Office, Washington, D. C., 1964); J. M. Bennett and M. J. Booty, Appl. Opt. 5, 41 (1966); P. O. Nilsson, Appl. Opt. 7, 435 (1968); J. Shewchun and E. C. Rowe, J. Appl. Phys. 41, 4128 (1970).

David, E.

E. David, Z. Physik 114, 389 (1939); H. Schopper, Z. Physik 130, 565 (1951); S. Yamaguchi, J. Phys. Soc. Japan 15, 1577 (1960); G. Rasigni and P. Rouard, J. Opt. Soc. Am. 53, 604 (1963) G. Henderson and C. Weaver, J. Opt. Soc. Am. 56, 1551 (1966); A. Carlan, Ann. Phys. (Paris) 4, 5 (1969); A. Donnadieu, Thin Solid Films 6, 249 (1970).

Dixon, L. C. W.

L. Ward, A. Nag, and L. C. W. Dixon, Brit. J. Appl. Phys. 2, 301 (1969).

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955), p. 176.

Ishiguro, K.

K. Ishiguro and G. Kuwahara, J. Phys. Soc. Japan 6, 71 (1951).

Jerrard, H. G.

H. G. Jerrard, Surface Sci. 16, 67 (1969).

Kinbara, A.

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Japan J. Appl. Phys. 8, 559 (1969).

Kinhara, A.

S. Yoshida, T. Yamaguchi, and A. Kinhara, J. Opt. Soc. Am. 61, 62 (1971).

Kuwahara, G.

K. Ishiguro and G. Kuwahara, J. Phys. Soc. Japan 6, 71 (1951).

Malé, D.

D. Malé, Compt. Rend. 230B, 1349 (1950).

McCrackin, F. L.

F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970); R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 61, 773 (1971).

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, edited by E. Passaglia, R. R. Stromberg, and J. Kruger, Natl. Bur. Std. (U. S.) Misc. Publ. 256 (U. S. Government Printing Office, Washington, D. C., 1964); J. M. Bennett and M. J. Booty, Appl. Opt. 5, 41 (1966); P. O. Nilsson, Appl. Opt. 7, 435 (1968); J. Shewchun and E. C. Rowe, J. Appl. Phys. 41, 4128 (1970).

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. (U. S.) 67A, 363 (1963); F. Lukes, Surface Sci. 16, 74 (1969).

Nag, A.

L. Ward, A. Nag, and L. C. W. Dixon, Brit. J. Appl. Phys. 2, 301 (1969).

Oldham, W. G.

W. G. Oldham, Surface Sci. 16, 97 (1969).

Passaglia, E.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. (U. S.) 67A, 363 (1963); F. Lukes, Surface Sci. 16, 74 (1969).

Philip, R.

R. Philip and J. Trompette, J. Phys. Radium 18, 92 (1957).

Rouard, P.

P. Rouard and P. Bousquet, in Progress in Optics IV, edited by E. Wolf (North-Holland, Amsterdam, 1965), p. 145.

Scott, G. D.

R. S. Sennett and G. D. Scott, J. Opt. Soc. Am. 40, 203 (1950).

Sennett, R. S.

R. S. Sennett and G. D. Scott, J. Opt. Soc. Am. 40, 203 (1950).

Shank, C. V.

R. J. Archer and C. V. Shank, J. Opt. Soc. Am. 57, 191 (1967); D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 57, 466 (1967); W. G. Oldham, J. Opt. Soc. Am. 57, 617 (1967); P. H. Smith, Surface Sci. 16, 34 (1969).

Steinberg, H. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. (U. S.) 67A, 363 (1963); F. Lukes, Surface Sci. 16, 74 (1969).

Stromberg, R. R.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. (U. S.) 67A, 363 (1963); F. Lukes, Surface Sci. 16, 74 (1969).

Trompette, J.

J. Trompette, Ann. Phys. (Paris) 5, 915 (1960); N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).

R. Philip and J. Trompette, J. Phys. Radium 18, 92 (1957).

Ward, L.

L. Ward, A. Nag, and L. C. W. Dixon, Brit. J. Appl. Phys. 2, 301 (1969).

Yamaguchi, T.

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).

S. Yoshida, T. Yamaguchi, and A. Kinhara, J. Opt. Soc. Am. 61, 62 (1971).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Japan J. Appl. Phys. 8, 559 (1969).

Yoshida, S.

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).

S. Yoshida, T. Yamaguchi, and A. Kinhara, J. Opt. Soc. Am. 61, 62 (1971).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Japan J. Appl. Phys. 8, 559 (1969).

Other (19)

D. Malé, Compt. Rend. 230B, 1349 (1950).

K. Ishiguro and G. Kuwahara, J. Phys. Soc. Japan 6, 71 (1951).

L. Ward, A. Nag, and L. C. W. Dixon, Brit. J. Appl. Phys. 2, 301 (1969).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Japan J. Appl. Phys. 8, 559 (1969).

R. S. Sennett and G. D. Scott, J. Opt. Soc. Am. 40, 203 (1950).

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955), p. 176.

E. David, Z. Physik 114, 389 (1939); H. Schopper, Z. Physik 130, 565 (1951); S. Yamaguchi, J. Phys. Soc. Japan 15, 1577 (1960); G. Rasigni and P. Rouard, J. Opt. Soc. Am. 53, 604 (1963) G. Henderson and C. Weaver, J. Opt. Soc. Am. 56, 1551 (1966); A. Carlan, Ann. Phys. (Paris) 4, 5 (1969); A. Donnadieu, Thin Solid Films 6, 249 (1970).

S. Yoshida, T. Yamaguchi, and A. Kinhara, J. Opt. Soc. Am. 61, 62 (1971).

R. Philip and J. Trompette, J. Phys. Radium 18, 92 (1957).

J. Trompette, Ann. Phys. (Paris) 5, 915 (1960); N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).

P. Rouard and P. Bousquet, in Progress in Optics IV, edited by E. Wolf (North-Holland, Amsterdam, 1965), p. 145.

W. G. Oldham, Surface Sci. 16, 97 (1969).

S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurement of Surfaces and Thin Films, edited by E. Passaglia, R. R. Stromberg, and J. Kruger, Natl. Bur. Std. (U. S.) Misc. Publ. 256 (U. S. Government Printing Office, Washington, D. C., 1964); J. M. Bennett and M. J. Booty, Appl. Opt. 5, 41 (1966); P. O. Nilsson, Appl. Opt. 7, 435 (1968); J. Shewchun and E. C. Rowe, J. Appl. Phys. 41, 4128 (1970).

Optical properties of aggregated metal films have also been explained in terms of Maxwell-Garnett (MG) theory, which is based on the three-dimensional (3D) distribution of spherical particles [cf. R. H. Doremus, J. Appl. Phys. 37, 2775 (1966)]. The MG equation (∊ - ∊a) / (∊ + 2∊a) = q (∊ i - ∊ a) / (∊i + 2∊a) is identical with the equation for the case ƒ (the depolarizing factor) = ⅓ (i.e., spherical shape) and β (the interaction term) =-q/3 in the equation of RE model having a single value of the axial ratio [Eq. (9) in Ref. 6]. ∊ - ∊i = q(∊i - ∊ a) / [1 + (ƒ + β) (∊i - ∊a) / ∊a]. In the 2D system, β has different values of opposite sign for electric fields parallel and perpendicular to the substrate, which causes the anisotropic property, whereas in the 3D system, β has the unique value -q/3.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl. Bur. Std. (U. S.) 67A, 363 (1963); F. Lukes, Surface Sci. 16, 74 (1969).

F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970); R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 61, 773 (1971).

R. J. Archer and C. V. Shank, J. Opt. Soc. Am. 57, 191 (1967); D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 57, 466 (1967); W. G. Oldham, J. Opt. Soc. Am. 57, 617 (1967); P. H. Smith, Surface Sci. 16, 34 (1969).

H. G. Jerrard, Surface Sci. 16, 67 (1969).

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