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, n, k, and d are simultaneously determined by the measured values of ψ, Δ, and the transmittance of p-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.

© 1972 Optical Society of America

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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).
    [Crossref]
  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).
    [Crossref]
  5. R. S. Sennett and G. D. Scott, J. Opt. Soc. Am. 40, 203 (1950).
    [Crossref]
  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).
    [Crossref]
  8. S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 62 (1971).
    [Crossref]
  9. R. Philip and J. Trompette, J. Phys. Radium 18, 92 (1957).
    [Crossref]
  10. J. Trompette, Ann. Phys. (Paris) 5, 915 (1960); N. Emeric and A. Emeric, Thin Solid Films 1, 13 (1967).
    [Crossref]
  11. P. Rouard and P. Bousquet, in Progress in Optics IV, edited by E. Wolf (North-Holland, Amsterdam, 1965), p. 145.
    [Crossref]
  12. W. G. Oldham, Surface Sci. 16, 97 (1969).
    [Crossref]
  13. S. Yoshida, T. Yamaguchi, and A. Kinbara, J. Opt. Soc. Am. 61, 463 (1971).
    [Crossref]
  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).
    [Crossref] [PubMed]
  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 f(the depolarizing factor) = 13 (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]∊-∊a=q(∊i-∊a)/[1+(f+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.
    [Crossref]
  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).
    [Crossref]
  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).
    [Crossref]
  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).
    [Crossref] [PubMed]
  19. H. G. Jerrard, Surface Sci. 16, 67 (1969).
    [Crossref]

1971 (2)

1970 (1)

1969 (4)

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

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

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).
[Crossref]

1967 (1)

1966 (1)

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 f(the depolarizing factor) = 13 (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]∊-∊a=q(∊i-∊a)/[1+(f+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.
[Crossref]

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).
[Crossref]

1960 (1)

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

1957 (1)

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

1951 (1)

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

1950 (2)

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).
[Crossref]

Archer, R. J.

Bousquet, P.

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

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).
[Crossref] [PubMed]

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).
[Crossref]

Dixon, L. C. W.

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

Doremus, R. H.

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 f(the depolarizing factor) = 13 (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]∊-∊a=q(∊i-∊a)/[1+(f+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.
[Crossref]

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).
[Crossref]

Jerrard, H. G.

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

Kinbara, A.

Kuwahara, G.

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

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).
[Crossref]

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).
[Crossref]

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).
[Crossref] [PubMed]

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).
[Crossref]

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).
[Crossref]

Philip, R.

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

Rouard, P.

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

Scott, G. D.

Sennett, R. S.

Shank, C. V.

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).
[Crossref]

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).
[Crossref]

Trompette, J.

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

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

Ward, L.

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

Yamaguchi, T.

Yoshida, S.

Ann. Phys. (Paris) (1)

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

Brit. J. Appl. Phys. (1)

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

Compt. Rend. (1)

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

J. Appl. Phys. (1)

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 f(the depolarizing factor) = 13 (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]∊-∊a=q(∊i-∊a)/[1+(f+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.
[Crossref]

J. Opt. Soc. Am. (5)

J. Phys. Radium (1)

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

J. Phys. Soc. Japan (1)

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

J. Res. Natl. Bur. Std. (U. S.) (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).
[Crossref]

Japan J. Appl. Phys. (1)

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

Surface Sci. (2)

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

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

Z. Physik (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).
[Crossref]

Other (3)

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

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).
[Crossref] [PubMed]

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

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Figures (4)

Fig. 1
Fig. 1

Experimental results of effective isotropic parameters kiso2niso2, 2nisokiso, and qiso as functions of dw for silver films deposited at two substrate temperatures; open circle: room temperature, closed circle: 85°C, together with the deviations calculated from the errors of optical measurements. Convergence ranges of anisotropic parameters k||2n||2, 2n||k||, and q of the films deposited at 85°C are hatched. The results from the optical constants of Philip and Trompette (Ref. 9) (crosses) and from the packing factor of Malé (Ref. 1) (open triangle) at room temperature are also shown.

Fig. 2
Fig. 2

The convergence range of anisotropic parameters for the film of 40 Å thick deposited at 85°C. The solid symbols or crosses in correspond to the convergent or divergent values, respectively, in the computation of || and q. The convergent values of || and q are indicated by open symbols of the same form, some of which are connected to by thin broken lines to make the correspondence clear.

Fig. 3
Fig. 3

Variations of iso, ||, and with γ ¯ and σ calculated from the RE model for dw = 60 Å, q = 0.3. The values of qiso are written in parentheses.

Fig. 4
Fig. 4

Variations of observed iso with dw for films deposited at two substrate temperatures, open circles: room temperature, closed circles: 85°C, together with deviations calculated from the errors of the optical measurements. a, b, and c show the deviations that arise from δTp, δψ, and δΔ, respectively. The values of dw and qiso are written along the curves. Convergence ranges of || for films deposited at 85°C are hatched.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

P = ( P 1 , P 2 , P 3 ) ,             Q = ( Q 1 , Q 2 , Q 3 ) ,
P ( new ) = P ( old ) - S d S / d P ( old ) .
P 1 = n iso ,             P 2 = k iso ,             P 3 = d iso .
Q 1 + i Q 2 = tan ψ e i Δ ( = R ˜ p / R ˜ s ) ,             Q 3 = T p ,
P 1 = n ,             P 2 = k ,             P 3 = d ,
- a = q g ( γ ) α ( γ ) , d γ / ( 1 - A , ) ,
A , = d w g ( γ ) α ( γ ) , ( A k , , ) d γ ,
I = 1 8 [ R p 2 cos 2 ϕ + 2 R p R s sin ϕ cos ϕ sin ( 2 θ - Δ ) + R s 2 sin 2 ϕ ] ,
δ ψ = [ 8 I n / ( R p 2 + R s 2 ) ] 1 2 , δ Δ = [ 16 I n / ( R p 2 + R s 2 ) ] 1 2 / sin 2 ψ .
(-a)/(+2a)=q(i-a)/(i+2a)
-a=q(i-a)/[1+(f+β)(i-a)/a].