Abstract

The possibilities of obtaining the optical constants of very thin films from ellipsometric measurements are analyzed with the help of the approximate Drude formulas. The influence of ellipsometric errors on the determination of the optical constants of thin films is examined. It is shown that the accuracy is extremely small when the dielectric constant ˜ of the thin film is equal to the refractive index of the substrate n˜s=˜s.

© 1982 Optical Society of America

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References

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  1. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 4.
  2. F. Abelès, Thin Solid Films 34, 291 (1976).
    [CrossRef]
  3. D. E. Aspnes, in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), Chap. 15, p. 186.
  4. R. M. A. Azzam, Surf. Sci. 96, 67 (1980).
    [CrossRef]
  5. F. Abelès, in Advanced Optical Techniques, A. C. S. van Heel, Ed. (North-Holland, Amsterdam, 1967), p. 145.

1980 (1)

R. M. A. Azzam, Surf. Sci. 96, 67 (1980).
[CrossRef]

1976 (1)

F. Abelès, Thin Solid Films 34, 291 (1976).
[CrossRef]

Abelès, F.

F. Abelès, Thin Solid Films 34, 291 (1976).
[CrossRef]

F. Abelès, in Advanced Optical Techniques, A. C. S. van Heel, Ed. (North-Holland, Amsterdam, 1967), p. 145.

Aspnes, D. E.

D. E. Aspnes, in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), Chap. 15, p. 186.

Azzam, R. M. A.

R. M. A. Azzam, Surf. Sci. 96, 67 (1980).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 4.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 4.

Surf. Sci. (1)

R. M. A. Azzam, Surf. Sci. 96, 67 (1980).
[CrossRef]

Thin Solid Films (1)

F. Abelès, Thin Solid Films 34, 291 (1976).
[CrossRef]

Other (3)

D. E. Aspnes, in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), Chap. 15, p. 186.

F. Abelès, in Advanced Optical Techniques, A. C. S. van Heel, Ed. (North-Holland, Amsterdam, 1967), p. 145.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 4.

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Figures (8)

Fig. 1
Fig. 1

Isoprecision curves (i.e., curves with a constant value of C = |∂/∂α|−1) in the 1-2 plane for a substrate s = −10 and an angle of incidence φ = 60°. The values of C are indicated for each curve.

Fig. 2
Fig. 2

Isoprecision curves in the α1-α2 plane [α1 = −(δΔ/2η), α2 = (δψ/η sin2 ψ ¯)] for the same numerical example as in Fig. 1. The values of C are also indicated for each curve. (a) + solutions (corresponding to the region labeled +1 in Fig. 1). (b) solutions (region labeled − in Fig. 1).

Fig. 3
Fig. 3

Isoprecision curves (C = constant) in the 1-2 plane for a chromium substrate (s = 2.6 + i12.3) and for an angle of incidence φ = 60°.

Fig. 4
Fig. 4

Isoprecision curves in the α1-α2 plane for the same numerical example as in Fig. 3. (a) + solutions (corresponding to the regions labeled +1 and +2 in Fig. 3). The discontinuous lines correspond to the physical solution (2 > 0) and the dotted lines to 2 < 0. (b) solutions (corresponding to the region labeled − in Fig. 3).

Fig. 5
Fig. 5

Isoprecision curves (C = constant) in the 1-2 plane for a glass substrate (s = 2.25) and an angle of incidence φ = 70°.

Fig. 6
Fig. 6

Isoprecision curves in the α1-α2 plane corresponding to the and + solutions labeled − and +2 in Fig. 5, respectively.

Fig. 7
Fig. 7

Values of the dielectric constant of a 5 nm thick film on a Ag substrate (s = −10 + i0.13, λ = 550 nm) giving values of −2.1° ± 0.1° for δψ (vertical shading) and of 5.7° ± 0.25° for δΔ (horizontal shading). The values δψ = −2.1° and δΔ = 5.7° correspond to a thin film with = s = 0.02 + i 3.15 (●).

Fig. 8
Fig. 8

Same calculations as in Fig. 7 but with −1.9° ± 0.1° for δψ and 4.9° ± 0.25° for δΔ. The values δψ = −1.9° and δΔ = 4.9° correspond to a thin film with = 1.3 + i1.8 (×).

Equations (8)

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tan ψ exp ( i Δ ) = | r p r s | exp [ i ( Δ p - Δ s ) ] ,
δ Δ = 2 η 0 cos φ S 2 × Re { ( - s ) ( - 0 ) s ( s - 0 ) [ S 2 ( 0 + s ) - 0 s ] } ,
δ ψ = - η 0 cos φ S 2 sin 2 ψ ¯ × Im { ( - s ) ( - 0 ) s ( s - 0 ) [ S 2 ( 0 + s ) - 0 s ] } .
α = α 1 + i α 2 = m [ + 0 s - ( 0 + s ) ] ,
α 1 = - δ Δ 2 η ,             α 2 = δ ψ η sin 2 ψ ¯ , m = - 0 cos φ S 2 s [ S 2 ( 0 + s ) - 0 s ] ( s - 0 ) .
= - b ( 1 ± 1 - 0 s b 2 )
δ = α α .
α = 1 2 m ( - 1 ± 1 1 - 0 s b 2 ) .

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