Abstract

The Abelès method is a classical method for determining the refractive index of dielectric thin films. In this paper we examine the main features of the method in a formal manner, using closed-form equations, and we show that the method is ambiguous in certain yet unreported situations.

© 2006 Optical Society of America

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References

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  1. F. Abelès, "Methods for determining optical parameters of thin films," in Progress in Optics, E. Wolf, ed. (North Holland, 1963), Vol. 2, pp. 249-288.
    [CrossRef]
  2. J. E. Goell and R. D. Standley, "Effect of refractive index gradients on index measurements by the Abelès method," Appl. Opt. 11, 2502-2505 (1972).
    [CrossRef] [PubMed]
  3. I. Awai and J. Ikenoue, "Effect of film transition layers on the Abelès method," Appl. Opt. 23, 1890-1896 (1984).
    [CrossRef] [PubMed]
  4. V. Damian, P. C. Logofǎtu, D. Apostol, F. Garoi, I. Iordache, A. Timcu, O. Ligor, and R. Müller, "Polymer thin film refractive index determination," in Proceedings of IEEE 2004 International Semiconductor Conference (IEEE, 2004), pp. 441-444.
  5. M. V. Klein and T. E. Furtak, Optics (Wiley, 1986).

1984

1972

Abelès, F.

F. Abelès, "Methods for determining optical parameters of thin films," in Progress in Optics, E. Wolf, ed. (North Holland, 1963), Vol. 2, pp. 249-288.
[CrossRef]

Apostol, D.

V. Damian, P. C. Logofǎtu, D. Apostol, F. Garoi, I. Iordache, A. Timcu, O. Ligor, and R. Müller, "Polymer thin film refractive index determination," in Proceedings of IEEE 2004 International Semiconductor Conference (IEEE, 2004), pp. 441-444.

Awai, I.

Damian, V.

V. Damian, P. C. Logofǎtu, D. Apostol, F. Garoi, I. Iordache, A. Timcu, O. Ligor, and R. Müller, "Polymer thin film refractive index determination," in Proceedings of IEEE 2004 International Semiconductor Conference (IEEE, 2004), pp. 441-444.

Furtak, T. E.

M. V. Klein and T. E. Furtak, Optics (Wiley, 1986).

Garoi, F.

V. Damian, P. C. Logofǎtu, D. Apostol, F. Garoi, I. Iordache, A. Timcu, O. Ligor, and R. Müller, "Polymer thin film refractive index determination," in Proceedings of IEEE 2004 International Semiconductor Conference (IEEE, 2004), pp. 441-444.

Goell, J. E.

Ikenoue, J.

Iordache, I.

V. Damian, P. C. Logofǎtu, D. Apostol, F. Garoi, I. Iordache, A. Timcu, O. Ligor, and R. Müller, "Polymer thin film refractive index determination," in Proceedings of IEEE 2004 International Semiconductor Conference (IEEE, 2004), pp. 441-444.

Klein, M. V.

M. V. Klein and T. E. Furtak, Optics (Wiley, 1986).

Ligor, O.

V. Damian, P. C. Logofǎtu, D. Apostol, F. Garoi, I. Iordache, A. Timcu, O. Ligor, and R. Müller, "Polymer thin film refractive index determination," in Proceedings of IEEE 2004 International Semiconductor Conference (IEEE, 2004), pp. 441-444.

Logofatu, P. C.

V. Damian, P. C. Logofǎtu, D. Apostol, F. Garoi, I. Iordache, A. Timcu, O. Ligor, and R. Müller, "Polymer thin film refractive index determination," in Proceedings of IEEE 2004 International Semiconductor Conference (IEEE, 2004), pp. 441-444.

Müller, R.

V. Damian, P. C. Logofǎtu, D. Apostol, F. Garoi, I. Iordache, A. Timcu, O. Ligor, and R. Müller, "Polymer thin film refractive index determination," in Proceedings of IEEE 2004 International Semiconductor Conference (IEEE, 2004), pp. 441-444.

Standley, R. D.

Timcu, A.

V. Damian, P. C. Logofǎtu, D. Apostol, F. Garoi, I. Iordache, A. Timcu, O. Ligor, and R. Müller, "Polymer thin film refractive index determination," in Proceedings of IEEE 2004 International Semiconductor Conference (IEEE, 2004), pp. 441-444.

Appl. Opt.

Other

F. Abelès, "Methods for determining optical parameters of thin films," in Progress in Optics, E. Wolf, ed. (North Holland, 1963), Vol. 2, pp. 249-288.
[CrossRef]

V. Damian, P. C. Logofǎtu, D. Apostol, F. Garoi, I. Iordache, A. Timcu, O. Ligor, and R. Müller, "Polymer thin film refractive index determination," in Proceedings of IEEE 2004 International Semiconductor Conference (IEEE, 2004), pp. 441-444.

M. V. Klein and T. E. Furtak, Optics (Wiley, 1986).

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Figures (4)

Fig. 1
Fig. 1

Reflectance curves corresponding to structure 1 from Table 1. The Brewster angle is β = 58.93 ° . The height of the film was chosen quite large on purpose to illustrate the tangents. One may notice how, for incidence angles higher than β, the film curve switches above the substrate curve and continues to have tangent points.

Fig. 2
Fig. 2

Illustration of the domains where the Abelès method is or is not ambiguous.

Fig. 3
Fig. 3

Experimental application of the Abelès method. We had an intersection that is not a tangent at the Brewster angle β = 54.15 ° , which corresponds to a refractive index for the film of n = 1.38 . The application corresponds to structure 2 in Table 1.

Fig. 4
Fig. 4

Reflectance curves corresponding to structure 3 from Table 1. The Brewster angle is again β = 58.93 ° , because the refractive index of the film is the same, although there is a different substrate. In the conditions of a substrate with a significant absorption coefficient, one cannot distinguish the intersection at the Brewster angle from the spurious solutions.

Tables (1)

Tables Icon

Table 1 Superstrate–Film–Substrate Structures

Equations (16)

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n = tan β .
R p film ( θ ) = R p substrate ( θ ) ,
r p a b = y a y b y a + y b ,
y a = k n a / n a 2 ,
k n a = [ ( n a k 0 ) 2 k t 2 ] 1 / 2 ,
k t = n 0 sin θ ,
r p abc = r p a b + r p b c exp ( i γ ) 1 + r p a b r p b c exp ( i γ ) ,
γ = k n b h .
| r p abc | 2 | r p a c | 2 = 0.
16 sin 2 γ y a y c ( y a 2 y b 2 ) ( y b 2 y c 2 ) = 0.
C m ( θ ) { θ arcsin [ n b 2 ( m π k 0 h ) 2 ] } 2 = 0 ,
cos ( 2 β ) sin ( θ + β ) sin ( θ β ) / sin 4 β = 0.
( n c 2 n b 2 ) [ n b 2 n c 2 sin 2 θ ( n c 2 + n b 2 ) ] / ( n c n b ) 4 = 0 ,
( n b n c ) 2 / ( n b 2 + n c 2 ) < 1.
16 y a y c r ( y a 2 y b 2 ) sin γ [ 2 y b y c i cos γ ( y c r 2 + y c i 2 y b 2 ) sin γ ] ,
γ = tan - 1 [ 2 y b y c i / ( y c r 2 + y c i 2 y b 2 ) ] .

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