Abstract

An original (to the best of our knowledge) method to achieve azimuthal alignments of all polarizing components in ellipsometry is presented. It is an accurate nulling method, and it is easy to implement and can be used with any isotropic reflecting layer. It also allows one to check the eventual presence of surface anisotropy. The ferrofluid modulator used in this setup is briefly described. Measurements made for three reflecting surfaces (fused silica, silicon, and germanium) are presented.

© 1994 Optical Society of America

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References

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  1. M. J. Dignam, M. Moskovits, “Azimuthal misalignment and anisotropy as sources of error in ellipsometry,” Appl. Opt. 9, 1868–1873 (1970).
    [PubMed]
  2. D. E. Aspnes, A. A. Studna, “Geometrically exact ellipsometer alignment,” Appl. Opt. 10, 1024–1030 (1971).
    [CrossRef] [PubMed]
  3. J. R. Adams, N. M. Bashara, “In process ellipsometer azimuth angle calibration,” Appl. Opt. 15, 3179–3184 (1976).
    [CrossRef] [PubMed]
  4. V. M. Bermudez, V. H. Ritz, “Wavelength-scanning polarization-modulation ellipsometry: some practical consideration,” Appl. Opt. 17, 542–552 (1978).
    [CrossRef] [PubMed]
  5. F. A. Modine, G. E. Jellison, G. R. Gruzalski, “Errors in ellipsometry measurements made with a photoelastic modulator,” J. Opt. Soc. Am. 73, 892–900 (1983).
    [CrossRef]
  6. R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
    [CrossRef]
  7. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 5, pp. 364–411.
  8. A. C. Hall, “Experimental determination of the optical constants of metals,” J. Opt. Soc. Am. 55, 911–915 (1965).
  9. E. P. Mertens, R. C. Plumb, “Determining optical constants of metals by reflection of elliptically polarized light,” J. Opt. Soc. Am. 54, 106–107 (1964).
    [CrossRef]
  10. F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67Sect. A, 363–368 (1963).
  11. J. Monin, “Contribution à l’étude des propriétés optiques et photo-électriques des métaux alcalins,” thèse d’etat (Paris-VI University, Paris, 1972).
  12. R. J. Archer, Manual on Ellipsometry (Gaertner Scientific, Chicago, 1968).
  13. R. M. A. Azzam, N. M. Bashara, “Calibration of ellipsometer divided circles,” J. Opt. Soc. Am. 61, 1118–1121 (1971).
    [CrossRef]
  14. J. Monin, O. Brevet-Philibert, V. Cabuil, L. Delaunay, “Polarization modulator using ferrofluid material,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1319, 601 (1990).
  15. R. Massart, “Preparation of aqueous magnetic liquids in alkaline and acidic media,” IEEE Trans. Magn. M-17, 1247–1248 (1981).
    [CrossRef]

1990 (1)

R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
[CrossRef]

1983 (1)

1981 (1)

R. Massart, “Preparation of aqueous magnetic liquids in alkaline and acidic media,” IEEE Trans. Magn. M-17, 1247–1248 (1981).
[CrossRef]

1978 (1)

1976 (1)

1971 (2)

1970 (1)

1965 (1)

1964 (1)

E. P. Mertens, R. C. Plumb, “Determining optical constants of metals by reflection of elliptically polarized light,” J. Opt. Soc. Am. 54, 106–107 (1964).
[CrossRef]

1963 (1)

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67Sect. A, 363–368 (1963).

Adams, J. R.

Archer, R. J.

R. J. Archer, Manual on Ellipsometry (Gaertner Scientific, Chicago, 1968).

Aspnes, D. E.

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, “Calibration of ellipsometer divided circles,” J. Opt. Soc. Am. 61, 1118–1121 (1971).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 5, pp. 364–411.

Bashara, N. M.

Bermudez, V. M.

Brevet-Philibert, O.

J. Monin, O. Brevet-Philibert, V. Cabuil, L. Delaunay, “Polarization modulator using ferrofluid material,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1319, 601 (1990).

Cabuil, V.

J. Monin, O. Brevet-Philibert, V. Cabuil, L. Delaunay, “Polarization modulator using ferrofluid material,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1319, 601 (1990).

Collins, R. W.

R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
[CrossRef]

Delaunay, L.

J. Monin, O. Brevet-Philibert, V. Cabuil, L. Delaunay, “Polarization modulator using ferrofluid material,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1319, 601 (1990).

Dignam, M. J.

Gruzalski, G. R.

Hall, A. C.

Jellison, G. E.

Massart, R.

R. Massart, “Preparation of aqueous magnetic liquids in alkaline and acidic media,” IEEE Trans. Magn. M-17, 1247–1248 (1981).
[CrossRef]

McCrackin, F. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67Sect. A, 363–368 (1963).

Mertens, E. P.

E. P. Mertens, R. C. Plumb, “Determining optical constants of metals by reflection of elliptically polarized light,” J. Opt. Soc. Am. 54, 106–107 (1964).
[CrossRef]

Modine, F. A.

Monin, J.

J. Monin, “Contribution à l’étude des propriétés optiques et photo-électriques des métaux alcalins,” thèse d’etat (Paris-VI University, Paris, 1972).

J. Monin, O. Brevet-Philibert, V. Cabuil, L. Delaunay, “Polarization modulator using ferrofluid material,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1319, 601 (1990).

Moskovits, M.

Passaglia, E.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67Sect. A, 363–368 (1963).

Plumb, R. C.

E. P. Mertens, R. C. Plumb, “Determining optical constants of metals by reflection of elliptically polarized light,” J. Opt. Soc. Am. 54, 106–107 (1964).
[CrossRef]

Ritz, V. H.

Steinberg, H. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67Sect. A, 363–368 (1963).

Stromberg, R. R.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67Sect. A, 363–368 (1963).

Studna, A. A.

Appl. Opt. (4)

IEEE Trans. Magn. (1)

R. Massart, “Preparation of aqueous magnetic liquids in alkaline and acidic media,” IEEE Trans. Magn. M-17, 1247–1248 (1981).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Res. Natl. Bur. Stand. (1)

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67Sect. A, 363–368 (1963).

Rev. Sci. Instrum. (1)

R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
[CrossRef]

Other (4)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 5, pp. 364–411.

J. Monin, “Contribution à l’étude des propriétés optiques et photo-électriques des métaux alcalins,” thèse d’etat (Paris-VI University, Paris, 1972).

R. J. Archer, Manual on Ellipsometry (Gaertner Scientific, Chicago, 1968).

J. Monin, O. Brevet-Philibert, V. Cabuil, L. Delaunay, “Polarization modulator using ferrofluid material,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1319, 601 (1990).

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Figures (4)

Fig. 1
Fig. 1

Arrangement for azimuthal polarizer alignment.

Fig. 2
Fig. 2

Arrangement for azimuthal analyzer alignment.

Fig. 3
Fig. 3

Ferrofluid modulator device with the following attractive points: small amount of ferrofluid material with no residual polarization, no stray magnetic field radiation, and high sensitivity, especially in the IR spectral range.

Fig. 4
Fig. 4

Alignment for three high-quality reflecting surfaces.

Equations (16)

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r p r s = tan ψ exp ( j Δ ) ,
tan 2 ψ = R p R s             ( R s = r s 2 , R p = r p 2 ) .
α ( t ) = α M cos ω t .
θ = θ 0 + α M cos ω t .
I = a 2 + b 2 = K I 0 R s ( tan 2 ψ cos 2 θ + sin 2 θ ) ( K is constant ) .
I = ½ K I 0 { ( R s + R p ) - ( R s - R p ) × [ cos 2 θ 0 cos ( 2 α M cos ω t ) - sin 2 θ 0 sin ( 2 α M cos ω t ) ] } .
cos ( 2 α M cos ω t ) = J 0 ( 2 α M ) + 2 k = 1 ( - 1 ) k J 2 k ( 2 α M ) × cos ( 2 k ω t ) ,
sin ( 2 α M cos ω t ) = 2 k = 0 ( - 1 ) k J 2 k + 1 ( 2 α M ) sin [ ( 2 k + 1 ) ω t ] ,
cos ( 2 α M cos ω t ) J 0 ( 2 α M ) - 2 J 2 ( 2 α M ) cos 2 ω t ,
sin ( 2 α M cos ω t ) 2 J 1 ( 2 α M ) cos ω t ,
I = a 2 + b 2 = ½ K I 0 [ R s + R p ) - ( R s - R p ) cos 2 θ 0 J 0 ( 2 α M ) ] + K I 0 ( R s - R p ) × sin 2 θ 0 J 1 ( 2 α M ) cos ω t + K I 0 ( R s - R p ) × cos 2 θ 0 J 2 ( 2 α M ) cos 2 ω t + .
I ω = K I 0 ( R s - R P ) sin 2 θ 0 J 1 ( 2 α M ) .
Δ I ω Δ θ 0 = 2 K I 0 ( R s - R p ) J 1 ( 2 α M ) 2 K I 0 ( R s - R p ) α M .
I ( 0 ) = ½ K I 0 [ ( R s + R p ) - ( R s - R p ) J 0 ( 2 α M ) ] K I 0 R p ,
I ( 0 ) = 1 / 2 K I 0 [ ( R s + R p ) + ( R s - R p ) J 0 ( 2 α M ) K I 0 R s ,
I ω = K I 0 R s J 1 ( 2 α M ) sin 2 β             ( K = const . ) .

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