Abstract

The significance of the degree of polarization on reflection from the sample in photometric ellipsometry is examined. The degree of polarization was calculated from the four Stokes parameters that were measured by photometric ellipsometry in the IR region, including an additional retarder in the experimental setup. Examples are given for the polarization-degree spectra in the IR region for film-covered surfaces and polished surfaces as well as for the excitation of surface polaritons and the Berreman effect [ Phys. Rev. 130, 2193 ( 1963)]. In some cases the polarization effects can be explained by an averaging process of the ellipsometric phase over the investigated region.

© 1992 Optical Society of America

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References

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  1. D. E. Aspnes, “The accurate determination of optical properties by ellipsometry,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 88–112.
  2. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  3. A. Röeler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349–355 (1981).
    [CrossRef]
  4. A. Röeler, “Spectroscopic IR-ellipsometry by means of FTS,” Sci. Instrum. 2, 57–72 (1987).
  5. R. T. Graf, J. L. Koenig, H. Ishida, “Fourier transform infrared ellipsometry of thin polymer films,” Anal. Chem. 58, 64–68 (1986).
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), pp. 544–555.
  7. A. Röeler, W. Molgedey, “Improvement in accuracy of spectroscopic IR-ellipsometry by the use of IR-retarders,” Infrared Phys. 24, 1–5 (1984).
    [CrossRef]
  8. A. Röeler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990), pp. 34–35, 73–76, and 103–111.
  9. L. Schrottke, “Einfluss des transparenten Substrates auf die ellipsometrischen Grössen von Schichtsystemen,” in 3 Interferenzschicht-Kolloquium, Potsdamer Forschungen Reihe B53, 130–136 (1988).
  10. A. Röseler, “Spectroscopic infrared ellipsometry with the Fourier transform spectroscopy, preprint 85-4 (Zentral Institute für” Optik und Spektroskopie, Berlin, 1985), pp. 24–45.
  11. A. Röseler, “Die Berechnung der Polarisationseigenschaften eines Fourierspektrometers mit Mueller-Matrizen,” Optik (Stuttgart) 60, 237–246 (1982); “Die Anwendung der Mueller-Matrix auf die spektroskopische Infrarot-Ellipsometrie,” Optik (Stuttgart) 61, 177–186 (1982).
  12. A. Otto, “Spectroscopy of surface polaritons by attenuated total reflection,” in Optical Properties of Solids—New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 679–726.
  13. A. Röseler, M. Golz, U. Trutschel, M. Abraham, “Prism-less excitation of surface plasmons in the infrared spectral region by ATR,” Opt. Commun. 70, 8–11 (1989).
    [CrossRef]
  14. A. A. Maradudin, “Surface waves,” in Advances in Solid State Physics, J. Treusch, ed. (Vieweg, Braunschweig, 1981), pp. 5–116.
  15. A. Röseler, “Measurement of surface polaritons by spectroscopic infrared ellipsometry,” Phys. Status Solidi A 107, K69–K73 (1988).
    [CrossRef]
  16. F. Abeles, “Methods for determining optical parameters of thin films,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. II, pp. 251–288.
  17. A. Röseler, “Ellipsometrie einer spektral selektiv absorbierenden Schicht auf einem Metallsubstrat (Berreman-Effekt, Oberflächenwellen und Resonanzabsorption),” in 3 Interferenzschicht-Kolloquium, Potsdamer Forschungen Reihe B53, 81–100 (1988).
  18. D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev. 130, 2193–2198 (1963).
    [CrossRef]

1989 (1)

A. Röseler, M. Golz, U. Trutschel, M. Abraham, “Prism-less excitation of surface plasmons in the infrared spectral region by ATR,” Opt. Commun. 70, 8–11 (1989).
[CrossRef]

1988 (1)

A. Röseler, “Measurement of surface polaritons by spectroscopic infrared ellipsometry,” Phys. Status Solidi A 107, K69–K73 (1988).
[CrossRef]

1987 (1)

A. Röeler, “Spectroscopic IR-ellipsometry by means of FTS,” Sci. Instrum. 2, 57–72 (1987).

1986 (1)

R. T. Graf, J. L. Koenig, H. Ishida, “Fourier transform infrared ellipsometry of thin polymer films,” Anal. Chem. 58, 64–68 (1986).
[CrossRef]

1984 (1)

A. Röeler, W. Molgedey, “Improvement in accuracy of spectroscopic IR-ellipsometry by the use of IR-retarders,” Infrared Phys. 24, 1–5 (1984).
[CrossRef]

1982 (1)

A. Röseler, “Die Berechnung der Polarisationseigenschaften eines Fourierspektrometers mit Mueller-Matrizen,” Optik (Stuttgart) 60, 237–246 (1982); “Die Anwendung der Mueller-Matrix auf die spektroskopische Infrarot-Ellipsometrie,” Optik (Stuttgart) 61, 177–186 (1982).

1981 (1)

A. Röeler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349–355 (1981).
[CrossRef]

1963 (1)

D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev. 130, 2193–2198 (1963).
[CrossRef]

Abeles, F.

F. Abeles, “Methods for determining optical parameters of thin films,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. II, pp. 251–288.

Abraham, M.

A. Röseler, M. Golz, U. Trutschel, M. Abraham, “Prism-less excitation of surface plasmons in the infrared spectral region by ATR,” Opt. Commun. 70, 8–11 (1989).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, “The accurate determination of optical properties by ellipsometry,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 88–112.

Azzam, R. M. A.

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

Bashara, N. M.

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

Berreman, D. W.

D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev. 130, 2193–2198 (1963).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), pp. 544–555.

Golz, M.

A. Röseler, M. Golz, U. Trutschel, M. Abraham, “Prism-less excitation of surface plasmons in the infrared spectral region by ATR,” Opt. Commun. 70, 8–11 (1989).
[CrossRef]

Graf, R. T.

R. T. Graf, J. L. Koenig, H. Ishida, “Fourier transform infrared ellipsometry of thin polymer films,” Anal. Chem. 58, 64–68 (1986).
[CrossRef]

Ishida, H.

R. T. Graf, J. L. Koenig, H. Ishida, “Fourier transform infrared ellipsometry of thin polymer films,” Anal. Chem. 58, 64–68 (1986).
[CrossRef]

Koenig, J. L.

R. T. Graf, J. L. Koenig, H. Ishida, “Fourier transform infrared ellipsometry of thin polymer films,” Anal. Chem. 58, 64–68 (1986).
[CrossRef]

Maradudin, A. A.

A. A. Maradudin, “Surface waves,” in Advances in Solid State Physics, J. Treusch, ed. (Vieweg, Braunschweig, 1981), pp. 5–116.

Molgedey, W.

A. Röeler, W. Molgedey, “Improvement in accuracy of spectroscopic IR-ellipsometry by the use of IR-retarders,” Infrared Phys. 24, 1–5 (1984).
[CrossRef]

Otto, A.

A. Otto, “Spectroscopy of surface polaritons by attenuated total reflection,” in Optical Properties of Solids—New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 679–726.

Röeler, A.

A. Röeler, “Spectroscopic IR-ellipsometry by means of FTS,” Sci. Instrum. 2, 57–72 (1987).

A. Röeler, W. Molgedey, “Improvement in accuracy of spectroscopic IR-ellipsometry by the use of IR-retarders,” Infrared Phys. 24, 1–5 (1984).
[CrossRef]

A. Röeler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349–355 (1981).
[CrossRef]

A. Röeler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990), pp. 34–35, 73–76, and 103–111.

Röseler, A.

A. Röseler, M. Golz, U. Trutschel, M. Abraham, “Prism-less excitation of surface plasmons in the infrared spectral region by ATR,” Opt. Commun. 70, 8–11 (1989).
[CrossRef]

A. Röseler, “Measurement of surface polaritons by spectroscopic infrared ellipsometry,” Phys. Status Solidi A 107, K69–K73 (1988).
[CrossRef]

A. Röseler, “Die Berechnung der Polarisationseigenschaften eines Fourierspektrometers mit Mueller-Matrizen,” Optik (Stuttgart) 60, 237–246 (1982); “Die Anwendung der Mueller-Matrix auf die spektroskopische Infrarot-Ellipsometrie,” Optik (Stuttgart) 61, 177–186 (1982).

A. Röseler, “Ellipsometrie einer spektral selektiv absorbierenden Schicht auf einem Metallsubstrat (Berreman-Effekt, Oberflächenwellen und Resonanzabsorption),” in 3 Interferenzschicht-Kolloquium, Potsdamer Forschungen Reihe B53, 81–100 (1988).

A. Röseler, “Spectroscopic infrared ellipsometry with the Fourier transform spectroscopy, preprint 85-4 (Zentral Institute für” Optik und Spektroskopie, Berlin, 1985), pp. 24–45.

Schrottke, L.

L. Schrottke, “Einfluss des transparenten Substrates auf die ellipsometrischen Grössen von Schichtsystemen,” in 3 Interferenzschicht-Kolloquium, Potsdamer Forschungen Reihe B53, 130–136 (1988).

Trutschel, U.

A. Röseler, M. Golz, U. Trutschel, M. Abraham, “Prism-less excitation of surface plasmons in the infrared spectral region by ATR,” Opt. Commun. 70, 8–11 (1989).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), pp. 544–555.

Anal. Chem. (1)

R. T. Graf, J. L. Koenig, H. Ishida, “Fourier transform infrared ellipsometry of thin polymer films,” Anal. Chem. 58, 64–68 (1986).
[CrossRef]

Infrared Phys. (2)

A. Röeler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349–355 (1981).
[CrossRef]

A. Röeler, W. Molgedey, “Improvement in accuracy of spectroscopic IR-ellipsometry by the use of IR-retarders,” Infrared Phys. 24, 1–5 (1984).
[CrossRef]

Opt. Commun. (1)

A. Röseler, M. Golz, U. Trutschel, M. Abraham, “Prism-less excitation of surface plasmons in the infrared spectral region by ATR,” Opt. Commun. 70, 8–11 (1989).
[CrossRef]

Optik (Stuttgart) (1)

A. Röseler, “Die Berechnung der Polarisationseigenschaften eines Fourierspektrometers mit Mueller-Matrizen,” Optik (Stuttgart) 60, 237–246 (1982); “Die Anwendung der Mueller-Matrix auf die spektroskopische Infrarot-Ellipsometrie,” Optik (Stuttgart) 61, 177–186 (1982).

Phys. Rev. (1)

D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev. 130, 2193–2198 (1963).
[CrossRef]

Phys. Status Solidi A (1)

A. Röseler, “Measurement of surface polaritons by spectroscopic infrared ellipsometry,” Phys. Status Solidi A 107, K69–K73 (1988).
[CrossRef]

Sci. Instrum. (1)

A. Röeler, “Spectroscopic IR-ellipsometry by means of FTS,” Sci. Instrum. 2, 57–72 (1987).

Other (10)

D. E. Aspnes, “The accurate determination of optical properties by ellipsometry,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 88–112.

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

A. Röeler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990), pp. 34–35, 73–76, and 103–111.

L. Schrottke, “Einfluss des transparenten Substrates auf die ellipsometrischen Grössen von Schichtsystemen,” in 3 Interferenzschicht-Kolloquium, Potsdamer Forschungen Reihe B53, 130–136 (1988).

A. Röseler, “Spectroscopic infrared ellipsometry with the Fourier transform spectroscopy, preprint 85-4 (Zentral Institute für” Optik und Spektroskopie, Berlin, 1985), pp. 24–45.

F. Abeles, “Methods for determining optical parameters of thin films,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. II, pp. 251–288.

A. Röseler, “Ellipsometrie einer spektral selektiv absorbierenden Schicht auf einem Metallsubstrat (Berreman-Effekt, Oberflächenwellen und Resonanzabsorption),” in 3 Interferenzschicht-Kolloquium, Potsdamer Forschungen Reihe B53, 81–100 (1988).

A. A. Maradudin, “Surface waves,” in Advances in Solid State Physics, J. Treusch, ed. (Vieweg, Braunschweig, 1981), pp. 5–116.

A. Otto, “Spectroscopy of surface polaritons by attenuated total reflection,” in Optical Properties of Solids—New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 679–726.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), pp. 544–555.

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Figures (10)

Fig. 1
Fig. 1

Principle of the combination of a Fourier-transform spectrometer with a photometric ellipsometer.

Fig. 2
Fig. 2

Multiple reflections in an optically thick substrate.

Fig. 3
Fig. 3

Ellipsometric parameters and the degree of phase polarization PPh of a SiO2 film (thickness d = 2.8 μm) on an Al substrate at the angle of incidence φ0 = 82°.

Fig. 4
Fig. 4

Same film as in Fig. 3, measured in the visible region for different areas and at the angles of incidence (a) φ0 = 72° and (b) φ0 = 81°.

Fig. 5
Fig. 5

Excitation of SP’s at the SiO2–Al boundary at σ = 1318 cm−1 and the Brewster mode (′ max) at σ = 992 cm−1. This figure is a detail of Fig. 3.

Fig. 6
Fig. 6

Excitation of SP’s on the SiO2 surface in the Otto configuration with the air gap d = 4.5 μm and a KBr prism alt the angle φ0 = 43.3°. PPh shows the characteristic decrease at the excitation position.

Fig. 7
Fig. 7

Ellipsometric parameters and PPh showing the Berreman effect, measured with a SiO2 film (d = 70 nm) on aluminum for the angle of incidence φ0 = 82°.

Fig. 8
Fig. 8

Decrease of PPh in the range of the reststrahlen bands of (a) polished quartz glass and (b) BK7 glass (n and k are included for comparison). (c) Theoretical PPh spectrum of quartz glass.

Fig. 9
Fig. 9

PPh spectrum of PbF2 on a Si substrate. The decrease of PPh is caused by reflections from the rough back side of the substrate.

Fig. 10
Fig. 10

PPh spectra of a PbTe film on a glass (BK7) and a KBr substrate.

Equations (24)

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ρ = tan ψ exp ( i Δ ) = r x / r y ,             r = r exp ( i δ ) , tan ψ = r x / r y ,             Δ = δ x - δ y ,
I ( α 1 ) = ½ ( s 0 + s 1 cos 2 α 1 + s 2 sin 2 α 1 ) .
I ( α 1 ) = ( s 0 / 2 ) [ 1 - cos 2 ψ cos 2 α 1 + sin 2 ψ cos ( Δ + δ ) sin 2 α 1 ] ,
cos 2 ψ = s 1 s 0 ,             sin 2 ψ cos ( Δ + δ ) = s 2 s 0 , tan ψ = tan ψ / tan α 2 ,
s ˜ 2 ( Δ + δ ) = s ˜ 0 sin 2 ψ cos ( Δ + δ ) ,
s ˜ i = s i ( Δ + δ ) for δ ,             i = 0 , 1 , 2 , 3.
s 3 = sin 2 ψ sin Δ = s 2 cos δ / s 0 - s ˜ 2 ( Δ + δ ) / s ˜ 0 sin δ .
P = s 0 P s 0 = ( s 1 2 + s 2 2 + s 3 2 ) 1 / 2 s 0 ,
P = [ cos 2 2 ψ + sin 2 2 ψ ( cos 2 Δ + sin 2 Δ ) ] 1 / 2 .
P Ph = ( cos Δ ¯ 2 + sin Δ ¯ 2 ) 1 / 2 = ( s 2 2 + s 3 2 s 0 2 - s 1 2 ) 1 / 2 .
P = cos 2 ψ = | I ( ) - I ( 90° ) I ( ) + I ( 90° ) |             for P Ph = 0.
s 2 = s 0 ( ψ 2 - ψ 1 ) ( Δ 2 - Δ 1 ) ψ 1 ψ 2 Δ 1 Δ 2 sin 2 ψ cos Δ d Δ d ψ , s 2 = s 0 [ sin 2 ψ ¯ sinc ( ψ 2 - ψ 1 ) ] ( cos Δ ¯ sinc ) = s 0 sin 2 ψ ¯ cos Δ ¯ , Δ ¯ = Δ 2 + Δ 1 2 ,             ψ ¯ = ψ 2 + ψ 1 2 ,             = Δ 2 - Δ 1 2 ,
cos Δ ¯ = cos Δ ¯ sinc ,             sinc = sinc , sin 2 ψ ¯ = sin 2 ψ ¯ sinc ( ψ 2 - ψ 1 ) .
s 3 = s 0 sin 2 ψ ¯ sin Δ ¯ sinc = s 0 sin 2 ψ ¯ sin Δ ¯ , s 1 = - s 0 cos 2 ψ ¯ sinc ( ψ 2 - ψ 1 ) = s 0 cos 2 ψ ¯ .
tan 2 ψ = sin 2 ψ ¯ cos 2 ψ ¯ = 1 P Ph ( s 2 2 + s 3 2 s 1 2 ) 1 / 2 , P = sinc ( ψ 2 - ψ 1 ) × { cos 2 2 ψ ¯ + sin 2 2 ψ ¯ [ ( cos Δ ¯ 2 ) + ( sin Δ ¯ ) 2 ] } 1 / 2 .
P Ph = [ ( cos Δ ¯ ) 2 + ( sin Δ ¯ ) 2 ] 1 / 2 = sinc 1.
cos Δ = cos Δ ¯ = cos Δ ¯ sinc , sin Δ = sin Δ ¯ = sin Δ ¯ sinc .
tan Δ Pol = tan Δ ¯ , R = [ ( cos Δ ¯ ) 2 + ( sin Δ ¯ ) 2 ] 1 / 2 = sinc , R = P Rh ,
s 0 = E x E x * + E y E y * = ( r x r x * cos 2 α + r y r y * sin 2 α ) I 0 , E x = r x cos α E 0 ,             E y = r y sin α E 0 ,             I 0 = E 0 E 0 * , s 1 = E x E x * - E y E y * = ( r x r x * cos 2 α - r y r y * sin 2 α ) I 0 , s 1 s 0 = - cos 2 ψ = tan 2 ψ - 1 tan 2 ψ + 1 = R x - R y R x + R y , R x = r x r x * ,             R y = r y r y * ,
R = R 01 + T 01 2 R 12 exp ( - 2 δ ) × [ 1 + R 01 R 12 exp ( - 2 δ ) + ] , R = R 01 + T 01 2 R 12 exp ( - 2 δ ) 1 - R 01 R 12 exp ( - 2 δ ) = R 01 + a .
s 2 = E x E y * + E y E x * = I 0 sin 2 α Re ( r x r y * ) .
s 2 = [ Re ( r x r y * ) 01 + Re b ] I 0 , b = ( t x t y * ) 01 2 ( r x r y * ) 12 exp ( - 2 δ ) 1 - ( r x r y * ) 01 ( r x r y * ) 12 exp ( - 2 δ ) , s 2 s 0 = 2 Re [ ( r x r y * ) 01 + b ] R x + R y = sin 2 ψ cos Δ .
s 3 = i ( E x E y * - E y E x * ) = I 0 sin 2 α Im [ ( r x r y * ) 01 + b ] , s 3 s 0 = 2 Im [ ( r x r y * ) 01 + b ] R x + R y = sin 2 ψ sin Δ , tan Δ = Im [ ( r x r y * ) 01 + b ] Re [ ( r x r y * ) 01 + b ] .
cos Δ = Re [ ( r x r y * ) 01 + b ] [ ( r x r y * ) 01 + b ] = s 2 P Ph s 0 sin 2 ψ , sin Δ = Im [ ( r x r y * ) 01 + b ] [ ( r x r y * ) 01 + b ] = s 3 P Ph s 0 sin 2 ψ .

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