Abstract

A new ellipsometric method for the complete unambiguous optical characterization of double layers consisting of two strongly absorbing thin films placed on a nonabsorbing substrate is described in this paper. The method utilizes simultaneous interpretation of ellipsometric parameters measured for light reflected and transmitted by the ambient side and the substrate side of the two samples of the double layer investigated. These samples must have different thicknesses of both strongly absorbing films (at least the thickness of one of the two films). The method was successfully employed for analyzing the double layers formed by gold and chromium films at a wavelength of 632.8 nm.

© 1990 Optical Society of America

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  1. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k, and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002–1004 (1976).
    [CrossRef]
  2. S. G. Tomlin, “Determination of the Optical Constants of Thin Absorbing Films,” Thin Solid Films 13, 265–268 (1972).
    [CrossRef]
  3. S. E. Weber, S. R. Scharber, “Method for Determining the Optical Constants of Semitransparent Films,” Appl. Opt. 10, 338–341 (1971).
    [CrossRef]
  4. P. Joensen, J. C. Irwin, J. F. Cochran, A. E. Curzon, “Transmission Method for Determining the Optical Constants of Metals,” J. Opt. Soc. Am. 63, 1556–1562 (1973).
    [CrossRef]
  5. Y. Demner, J. Shamir, “Weakly Absorbing Layers: Interferometric Determination of Their Optical Parameters,” Appl. Opt. 17, 3738–3745 (1978).
    [CrossRef] [PubMed]
  6. A. Hjortsberg, “Accurate Determination of Optical Constants of Absorbing Materials: Measurements of Transmittance and Reflectance of Thin Films on Partially Metallized Substrates,” Thin Solid Films 69, L15–L17 (1980).
    [CrossRef]
  7. P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  8. R. Carey, B. W. J. Thomas, D. N. Newman, “The Optical Properties of Thin Cobalt Films by a Self-Consistent Photometric Techniques,” Thin Solid Films 66, 139–149 (1980).
    [CrossRef]
  9. J. E. Nestell, R. W. Christy, “Derivation of Optical Constants of Metals from Thin-Film Measurements at Oblique Incidence,” Appl. Opt. 11, 643–651 (1972).
    [CrossRef] [PubMed]
  10. J. I. Cisneros et al., “A Method for the Determination of the Complex Refractive Index of Non-Metallic Thin Films Using Photometric Measurements at Normal Incidence,” Thin Solid Films 100, 155–167 (1983).
    [CrossRef]
  11. L. Vriens, W. Rippens, “Optical Constants of Absorbing Thin Solid Films on a Substrate,” Appl. Opt. 22, 4105–4110 (1983).
    [CrossRef] [PubMed]
  12. R. C. McPhedran, L. C. Botten, D. R. McKenzie, R. P. Netterfield, “Unambiguous Determination of Optical Constants of Absorbing Films by Reflectance and Transmittance Measurements,” Appl. Opt. 23, 1197–1205 (1984).
    [CrossRef] [PubMed]
  13. T. C. Paulick, “Inversion of Normal-Incidence (R, T) Measurements to Obtain n + ik for Thin Films,” Appl. Opt. 25, 562–564 (1986).
    [CrossRef] [PubMed]
  14. I. Ohlidal, K. Navratil, “Simple Method of Spectroscopic Reflectometry for the Complete Optical Analysis of Weakly Absorbing Thin Films: Application to Silicon Films,” Thin Solid Films 156, 181–189 (1988).
    [CrossRef]
  15. I. Ohlidal, K. Navratil, “Optical Analysis of Inhomogeneous Weakly Absorbing Thin Films by Spectroscopic Reflectometry: Application to Carbon Films,” Thin Solid Films 162, 101–109 (1988).
    [CrossRef]
  16. I. Ohlidal, F. Lukes, “Optical Analysis of Thin Gold Films by Combined Reflection and Transmission Ellipsometry,” Thin Solid Films 85, 181–190 (1981).
    [CrossRef]
  17. R. M. A. Azzam, “Simple and Direct Determination of Complex Refractive Index and Thickness of Unsupported or Embedded Thin Films by Combined Reflection and Transmission Ellipsometry at 45° Angle of Incidence,” J. Opt. Soc. Am. 73, 1080–1082 (1983).
    [CrossRef]
  18. D. P. Arndt et al., “Multiple Determination of the Optical Constants of Thin-Film Coating Materials,” Appl. Opt. 23, 3571–3596 (1984).
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  19. D. E. Aspnes, H. G. Craighead, “Multiple Determination of the Optical Constants of Thin-Film Coating Materials: a Rh Sequel,” Appl. Opt. 25, 1299–1310 (1986).
    [CrossRef] [PubMed]
  20. I. Ohlidal, F. Lukes, “Optical Analysis of Absorbing Double Layers by Combined Reflection and Transmission Ellipsometry,” Thin Solid Films 115, 269–282 (1984).
    [CrossRef]
  21. J. Humlicek, “Sensitivity Extrema in Multiple-Angle Ellipsometry,” J. Opt. Soc. Am. A 2, 713–722 (1985).
    [CrossRef]
  22. D. H. Loescher, R. J. Detry, M. J. Clauser, “Least-Squares Analysis of the Film-Substrate Problem in Ellipsometry,” J. Opt. Soc. Am. 61, 1230–1235 (1971).
    [CrossRef]
  23. F. Lukes, “Ellipsometry of Silicon with Natural Surface Film at 632.8 nm,” Phys. Status Solidi A 94, 223–230 (1986).
    [CrossRef]
  24. H. E. Bennett, J. M. Bennett, “Precision Measurements in Thin Film Optics,” Phys. Thin Films 4, 1–96 (1967).
  25. H. K. Pulker, Coatings on Glass (Elsevier, Amsterdam, 1984).

1988 (2)

I. Ohlidal, K. Navratil, “Simple Method of Spectroscopic Reflectometry for the Complete Optical Analysis of Weakly Absorbing Thin Films: Application to Silicon Films,” Thin Solid Films 156, 181–189 (1988).
[CrossRef]

I. Ohlidal, K. Navratil, “Optical Analysis of Inhomogeneous Weakly Absorbing Thin Films by Spectroscopic Reflectometry: Application to Carbon Films,” Thin Solid Films 162, 101–109 (1988).
[CrossRef]

1986 (3)

1985 (1)

1984 (3)

1983 (3)

1981 (1)

I. Ohlidal, F. Lukes, “Optical Analysis of Thin Gold Films by Combined Reflection and Transmission Ellipsometry,” Thin Solid Films 85, 181–190 (1981).
[CrossRef]

1980 (2)

R. Carey, B. W. J. Thomas, D. N. Newman, “The Optical Properties of Thin Cobalt Films by a Self-Consistent Photometric Techniques,” Thin Solid Films 66, 139–149 (1980).
[CrossRef]

A. Hjortsberg, “Accurate Determination of Optical Constants of Absorbing Materials: Measurements of Transmittance and Reflectance of Thin Films on Partially Metallized Substrates,” Thin Solid Films 69, L15–L17 (1980).
[CrossRef]

1978 (1)

1976 (1)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k, and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

1973 (1)

1972 (3)

S. G. Tomlin, “Determination of the Optical Constants of Thin Absorbing Films,” Thin Solid Films 13, 265–268 (1972).
[CrossRef]

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

J. E. Nestell, R. W. Christy, “Derivation of Optical Constants of Metals from Thin-Film Measurements at Oblique Incidence,” Appl. Opt. 11, 643–651 (1972).
[CrossRef] [PubMed]

1971 (2)

1967 (1)

H. E. Bennett, J. M. Bennett, “Precision Measurements in Thin Film Optics,” Phys. Thin Films 4, 1–96 (1967).

Arndt, D. P.

Aspnes, D. E.

Azzam, R. M. A.

Bennett, H. E.

H. E. Bennett, J. M. Bennett, “Precision Measurements in Thin Film Optics,” Phys. Thin Films 4, 1–96 (1967).

Bennett, J. M.

H. E. Bennett, J. M. Bennett, “Precision Measurements in Thin Film Optics,” Phys. Thin Films 4, 1–96 (1967).

Botten, L. C.

Carey, R.

R. Carey, B. W. J. Thomas, D. N. Newman, “The Optical Properties of Thin Cobalt Films by a Self-Consistent Photometric Techniques,” Thin Solid Films 66, 139–149 (1980).
[CrossRef]

Christy, R. W.

Cisneros, J. I.

J. I. Cisneros et al., “A Method for the Determination of the Complex Refractive Index of Non-Metallic Thin Films Using Photometric Measurements at Normal Incidence,” Thin Solid Films 100, 155–167 (1983).
[CrossRef]

Clauser, M. J.

Cochran, J. F.

Craighead, H. G.

Curzon, A. E.

Demner, Y.

Detry, R. J.

Fillard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k, and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k, and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Hjortsberg, A.

A. Hjortsberg, “Accurate Determination of Optical Constants of Absorbing Materials: Measurements of Transmittance and Reflectance of Thin Films on Partially Metallized Substrates,” Thin Solid Films 69, L15–L17 (1980).
[CrossRef]

Humlicek, J.

Irwin, J. C.

Joensen, P.

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Loescher, D. H.

Lukes, F.

F. Lukes, “Ellipsometry of Silicon with Natural Surface Film at 632.8 nm,” Phys. Status Solidi A 94, 223–230 (1986).
[CrossRef]

I. Ohlidal, F. Lukes, “Optical Analysis of Absorbing Double Layers by Combined Reflection and Transmission Ellipsometry,” Thin Solid Films 115, 269–282 (1984).
[CrossRef]

I. Ohlidal, F. Lukes, “Optical Analysis of Thin Gold Films by Combined Reflection and Transmission Ellipsometry,” Thin Solid Films 85, 181–190 (1981).
[CrossRef]

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k, and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

McKenzie, D. R.

McPhedran, R. C.

Navratil, K.

I. Ohlidal, K. Navratil, “Simple Method of Spectroscopic Reflectometry for the Complete Optical Analysis of Weakly Absorbing Thin Films: Application to Silicon Films,” Thin Solid Films 156, 181–189 (1988).
[CrossRef]

I. Ohlidal, K. Navratil, “Optical Analysis of Inhomogeneous Weakly Absorbing Thin Films by Spectroscopic Reflectometry: Application to Carbon Films,” Thin Solid Films 162, 101–109 (1988).
[CrossRef]

Nestell, J. E.

Netterfield, R. P.

Newman, D. N.

R. Carey, B. W. J. Thomas, D. N. Newman, “The Optical Properties of Thin Cobalt Films by a Self-Consistent Photometric Techniques,” Thin Solid Films 66, 139–149 (1980).
[CrossRef]

Ohlidal, I.

I. Ohlidal, K. Navratil, “Simple Method of Spectroscopic Reflectometry for the Complete Optical Analysis of Weakly Absorbing Thin Films: Application to Silicon Films,” Thin Solid Films 156, 181–189 (1988).
[CrossRef]

I. Ohlidal, K. Navratil, “Optical Analysis of Inhomogeneous Weakly Absorbing Thin Films by Spectroscopic Reflectometry: Application to Carbon Films,” Thin Solid Films 162, 101–109 (1988).
[CrossRef]

I. Ohlidal, F. Lukes, “Optical Analysis of Absorbing Double Layers by Combined Reflection and Transmission Ellipsometry,” Thin Solid Films 115, 269–282 (1984).
[CrossRef]

I. Ohlidal, F. Lukes, “Optical Analysis of Thin Gold Films by Combined Reflection and Transmission Ellipsometry,” Thin Solid Films 85, 181–190 (1981).
[CrossRef]

Paulick, T. C.

Pulker, H. K.

H. K. Pulker, Coatings on Glass (Elsevier, Amsterdam, 1984).

Rippens, W.

Scharber, S. R.

Shamir, J.

Thomas, B. W. J.

R. Carey, B. W. J. Thomas, D. N. Newman, “The Optical Properties of Thin Cobalt Films by a Self-Consistent Photometric Techniques,” Thin Solid Films 66, 139–149 (1980).
[CrossRef]

Tomlin, S. G.

S. G. Tomlin, “Determination of the Optical Constants of Thin Absorbing Films,” Thin Solid Films 13, 265–268 (1972).
[CrossRef]

Vriens, L.

Weber, S. E.

Appl. Opt. (8)

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

J. Phys. E (1)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n, k, and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Phys. Rev. B (1)

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Phys. Status Solidi A (1)

F. Lukes, “Ellipsometry of Silicon with Natural Surface Film at 632.8 nm,” Phys. Status Solidi A 94, 223–230 (1986).
[CrossRef]

Phys. Thin Films (1)

H. E. Bennett, J. M. Bennett, “Precision Measurements in Thin Film Optics,” Phys. Thin Films 4, 1–96 (1967).

Thin Solid Films (8)

S. G. Tomlin, “Determination of the Optical Constants of Thin Absorbing Films,” Thin Solid Films 13, 265–268 (1972).
[CrossRef]

A. Hjortsberg, “Accurate Determination of Optical Constants of Absorbing Materials: Measurements of Transmittance and Reflectance of Thin Films on Partially Metallized Substrates,” Thin Solid Films 69, L15–L17 (1980).
[CrossRef]

R. Carey, B. W. J. Thomas, D. N. Newman, “The Optical Properties of Thin Cobalt Films by a Self-Consistent Photometric Techniques,” Thin Solid Films 66, 139–149 (1980).
[CrossRef]

J. I. Cisneros et al., “A Method for the Determination of the Complex Refractive Index of Non-Metallic Thin Films Using Photometric Measurements at Normal Incidence,” Thin Solid Films 100, 155–167 (1983).
[CrossRef]

I. Ohlidal, K. Navratil, “Simple Method of Spectroscopic Reflectometry for the Complete Optical Analysis of Weakly Absorbing Thin Films: Application to Silicon Films,” Thin Solid Films 156, 181–189 (1988).
[CrossRef]

I. Ohlidal, K. Navratil, “Optical Analysis of Inhomogeneous Weakly Absorbing Thin Films by Spectroscopic Reflectometry: Application to Carbon Films,” Thin Solid Films 162, 101–109 (1988).
[CrossRef]

I. Ohlidal, F. Lukes, “Optical Analysis of Thin Gold Films by Combined Reflection and Transmission Ellipsometry,” Thin Solid Films 85, 181–190 (1981).
[CrossRef]

I. Ohlidal, F. Lukes, “Optical Analysis of Absorbing Double Layers by Combined Reflection and Transmission Ellipsometry,” Thin Solid Films 115, 269–282 (1984).
[CrossRef]

Other (1)

H. K. Pulker, Coatings on Glass (Elsevier, Amsterdam, 1984).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of methods of determining the ellipsometric parameters characterizing a system formed by a nonabsorbing substrate and an absorbing double layer: I, double layer; II, substrate; D, detector.

Fig. 2
Fig. 2

Schematic diagram of the samples of the Au/Cr double layer on the nonabsorbing substrate: I, a glass substrate; II, Cr film; III, Au film with thickness d1; IV, Au film with thickness d 1 (the other symbols are explained in the text).

Fig. 3
Fig. 3

Angular dependence of the ellipsometric parameters ψRE, ΔRE, ψTE, and ΔTE for sample 1 (for details see text). Theoretical (—,- - - - -) and experimental (+, ○) values of the ellipsometric parameters are shown.

Fig. 4
Fig. 4

Angular dependence of the ellipsometric parameters ψRE, ΔRE, ψTE, and ΔTE for sample 2 (for details see text). Theoretical (—, - - - - -) and experimental (+, ○) values of the ellipsometric parameters are shown.

Fig. 5
Fig. 5

Angular dependence of the ellipsometric parameters ψRI (+, —) and ΔRI (○, - - - - -); theoretical (—, - - - - -) and experimental (+, ○) values of the ellipsometric parameters are shown; 1, sample 1 and 2, sample 2.

Tables (2)

Tables Icon

Table I Values of the Optical Parameters for the Chosen Samples of the Au/Cr Double Layers and Values of Their Standard Deviations

Tables Icon

Table II Values of the Optical Parameters for the Chosen Samples of the Au/Cr Double Layers and Values for Their Standard Deviations

Equations (13)

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R ^ j = r ^ 1 j + r ¯ ^ 2 j exp ( i x ^ 1 ) 1 + r ¯ ^ 1 j r ¯ ^ 2 j exp ( i x ^ 1 ) ,
r ¯ ^ 2 j = r ^ 2 j + r ^ 3 j exp ( i x ^ 2 ) 1 + r ^ 2 j r ^ 3 j exp ( i x ^ 2 ) ,             j = p , s ,
x ^ l = 4 π λ n ^ l d l cos φ ^ l ,             l = 1 , 2 ,
r ^ q p = n ^ q cos φ ^ q - 1 - n ^ q - 1 cos φ ^ q n ^ q cos φ ^ q - 1 + n ^ q - 1 cos φ ^ q , r ^ q s = n ^ q - 1 cos φ ^ q - 1 - n ^ q cos φ ^ q n ^ q - 1 cos φ ^ q - 1 + n ^ q cos φ ^ q , q = 1 , 2 , 3 ,             n ^ 0 n 0 ,             n ^ 3 = n ,             φ ^ 0 φ 0 ,             φ ^ 3 = φ ,
cos φ ^ l = 1 n ^ l ( n ^ l 2 - n 0 2 sin 2 φ 0 ) 1 / 2 , cos φ = 1 n ( n 2 - n 0 2 sin 2 φ 0 ) 1 / 2 , n ^ 1 n 1 + i k 1 ,             n ^ 2 n 2 + i k 2 .
x ^ 1 = 4 π λ n ^ 2 d 2 cos φ ^ 2 ,             x ^ 2 = 4 π λ n ^ 1 d 1 cos φ ^ 1 ,             r ^ 1 p = - r ^ 3 p , r ^ 1 s = - r ^ 3 s ,             r ^ 2 p = - r ^ 2 p ,             r ^ 2 s = - r ^ 2 s ,             r ^ 3 p = - r ^ 1 p , r ^ 3 s = - r ^ 1 s ,
cos φ ^ l = 1 n ^ 1 ( n ^ l 2 - n 2 sin 2 φ ) 1 / 2 , cos φ 0 = 1 n 0 ( n 0 2 - n 2 sin 2 φ ) 1 / 2 ,
T ^ j = t ^ 1 j t ¯ ^ 2 j exp ( i x ^ 1 / 2 ) 1 + r ^ 1 j r ¯ ^ 2 j exp ( i x ^ 1 ) ,
t ¯ ^ 2 j = t ^ 2 j t ^ 3 j exp ( i x ^ 2 / 2 ) 1 + r ^ 2 j r ^ 3 j exp ( i x ^ 2 ) ,
t ^ q p = 2 n ^ q - 1 cos φ ^ q - 1 n ^ q cos φ ^ q - 1 + n ^ q - 1 cos φ ^ q , t ^ q s = 2 n ^ q - 1 cos φ ^ q - 1 n ^ q - 1 cos φ ^ q - 1 + n ^ q cos φ ^ q .
tan ψ R E exp ( i Δ R E ) = R ^ p R ^ s ,             tan ψ T E exp ( i Δ T E ) = T ^ p T ^ s , tan ψ R I exp ( i Δ R I ) = R ^ p R ^ s ,
Q = z = 1 K b = 1 N ( F z b δ z b ) 2
F z b = ψ z R E ( φ o i ) - ψ z R E ( φ o i ) ,             b = i , F z b = Δ z R E ( φ o i ) - Δ z R E ( φ o i ) ,             b = N 1 + i , F z b = ψ z R I ( φ i ) - ψ z R I ( φ i ) ,             b = 2 N 1 + i , F z b = Δ z R I ( φ i ) - Δ z R I ( φ i ) ,             b = 3 N 1 + i , F z b = ψ z T E ( φ o i ) - ψ z T E ( φ o i ) ,             b = 4 N 1 + i , F z b = Δ z T E ( φ o i ) - Δ z T E ( φ o i ) ,             b = 5 N 1 + i ;

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