Abstract

Biplate compensators made from MgF2 are being used increasingly in rotating-element single-channel and multichannel ellipsometers. For the measurement of accurate ellipsometric spectra, the compensator must be carefully (i) aligned internally to ensure that the fast axes of the two plates are perpendicular and (ii) calibrated to determine the phase retardance δ versus photon energy E. We present alignment and calibration procedures for multichannel ellipsometer configurations with special attention directed to the precision, accuracy, and reproducibility in the determination of δ(E). Run-to-run variations in external compensator alignment, i.e., alignment with respect to the incident beam, can lead to irreproducibilities in δ of ∼0.2°. Errors in the ellipsometric measurement of a sample can be minimized by calibrating with an external compensator alignment that matches as closely as possible that used in the measurement.

© 2001 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  7. W. A. Shurcliff, Polarized Light: Production and Use (Harvard University, Cambridge, Mass., 1962).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. N. V. Nguyen, B. S. Pudliner, I. An, R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry: applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8, 919–931 (1991).
    [CrossRef]
  19. I. An, J. Lee, B. Hong, R. W. Collins, “Simultaneous determination of reflectance spectra along with {ψ(E),Δ(E)} in multichannel ellipsometry: applications to instrument calibration and reduction of real-time data,” Thin Solid Films 313–314, 79–84 (1998).
    [CrossRef]
  20. T. M. Cotter, M. E. Thomas, W. J. Tropf, “Magnesium fluoride (MgF2),” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, New York, 1991), pp. 899–918.
  21. J. Lee, J. Koh, R. W. Collins, “Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and films,” Rev. Sci. Instrum. 72, 1742–1754 (2001).
    [CrossRef]
  22. P. Chindaudom, K. Vedam, “Optical characterization of inhomogeneous transparent films on transparent substrates by spectroscopic ellipsometry, '’ in Optical Characterization of Real Surface and Films, K. Vedam, ed. (Academic, New York, 1994), pp. 191–247.
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    [CrossRef]

2001 (1)

J. Lee, J. Koh, R. W. Collins, “Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and films,” Rev. Sci. Instrum. 72, 1742–1754 (2001).
[CrossRef]

1999 (1)

1998 (3)

J. Lee, P. I. Rovira, I. An, R. W. Collins, “Rotating-compensator multichannel ellipsometry: applications for real time Stokes vector spectroscopy of thin film growth,” Rev. Sci. Instrum. 69, 1800–1810 (1998).
[CrossRef]

I. An, J. Lee, B. Hong, R. W. Collins, “Simultaneous determination of reflectance spectra along with {ψ(E),Δ(E)} in multichannel ellipsometry: applications to instrument calibration and reduction of real-time data,” Thin Solid Films 313–314, 79–84 (1998).
[CrossRef]

J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
[CrossRef]

1994 (2)

1991 (1)

1990 (1)

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

1988 (1)

1981 (1)

1978 (2)

1975 (1)

P. S. Hauge, F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[CrossRef]

1974 (1)

1971 (1)

1957 (1)

An, I.

J. Lee, P. I. Rovira, I. An, R. W. Collins, “Rotating-compensator multichannel ellipsometry: applications for real time Stokes vector spectroscopy of thin film growth,” Rev. Sci. Instrum. 69, 1800–1810 (1998).
[CrossRef]

I. An, J. Lee, B. Hong, R. W. Collins, “Simultaneous determination of reflectance spectra along with {ψ(E),Δ(E)} in multichannel ellipsometry: applications to instrument calibration and reduction of real-time data,” Thin Solid Films 313–314, 79–84 (1998).
[CrossRef]

N. V. Nguyen, B. S. Pudliner, I. An, R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry: applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8, 919–931 (1991).
[CrossRef]

Aspnes, D. E.

J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
[CrossRef]

D. E. Aspnes, “Effects of component optical activity in data reduction and calibration of rotating-analyzer ellipsometers,” J. Opt. Soc. Am. 64, 812–819 (1974).
[CrossRef]

D. E. Aspnes, “Alignment of an optically active biplate compensator,” Appl. Opt. 10, 2545–2546 (1971).
[CrossRef] [PubMed]

Azzam, R. M. A.

Bashara, N. M.

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

Bennett, H. E.

J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. 10-1–10-164.

Bennett, J. M.

J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. 10-1–10-164.

Cahan, B. D.

Chen, J.

J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
[CrossRef]

Chindaudom, P.

P. Chindaudom, K. Vedam, “Optical characterization of inhomogeneous transparent films on transparent substrates by spectroscopic ellipsometry, '’ in Optical Characterization of Real Surface and Films, K. Vedam, ed. (Academic, New York, 1994), pp. 191–247.

Clarke, D.

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).

Collins, R. W.

J. Lee, J. Koh, R. W. Collins, “Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and films,” Rev. Sci. Instrum. 72, 1742–1754 (2001).
[CrossRef]

R. W. Collins, J. Koh, “Dual rotating-compensator multichannel ellipsometer: instrument design for real-time Mueller matrix spectroscopy of surfaces and films,” J. Opt. Soc. Am. A 16, 1997–2006 (1999).
[CrossRef]

I. An, J. Lee, B. Hong, R. W. Collins, “Simultaneous determination of reflectance spectra along with {ψ(E),Δ(E)} in multichannel ellipsometry: applications to instrument calibration and reduction of real-time data,” Thin Solid Films 313–314, 79–84 (1998).
[CrossRef]

J. Lee, P. I. Rovira, I. An, R. W. Collins, “Rotating-compensator multichannel ellipsometry: applications for real time Stokes vector spectroscopy of thin film growth,” Rev. Sci. Instrum. 69, 1800–1810 (1998).
[CrossRef]

R. A. Yarussi, A. R. Heyd, H. V. Nguyen, R. W. Collins, “Multichannel transmission ellipsometer for characterization of anisotropic optical materials,” J. Opt. Soc. Am. A 11, 2320–2330 (1994).
[CrossRef]

N. V. Nguyen, B. S. Pudliner, I. An, R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry: applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8, 919–931 (1991).
[CrossRef]

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

Cotter, T. M.

T. M. Cotter, M. E. Thomas, W. J. Tropf, “Magnesium fluoride (MgF2),” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, New York, 1991), pp. 899–918.

de Nijs, J. M. M.

Dill, F. H.

P. S. Hauge, F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[CrossRef]

El Ghemmaz, A.

Fanton, J.

J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
[CrossRef]

Grainger, J. F.

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).

Hauge, P. S.

P. S. Hauge, “Mueller matrix ellipsometry with imperfect compensators,” J. Opt. Soc. Am. 68, 1519–1528 (1978).
[CrossRef]

P. S. Hauge, F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[CrossRef]

Heyd, A. R.

Hong, B.

I. An, J. Lee, B. Hong, R. W. Collins, “Simultaneous determination of reflectance spectra along with {ψ(E),Δ(E)} in multichannel ellipsometry: applications to instrument calibration and reduction of real-time data,” Thin Solid Films 313–314, 79–84 (1998).
[CrossRef]

Kleim, R.

Koh, J.

J. Lee, J. Koh, R. W. Collins, “Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and films,” Rev. Sci. Instrum. 72, 1742–1754 (2001).
[CrossRef]

R. W. Collins, J. Koh, “Dual rotating-compensator multichannel ellipsometer: instrument design for real-time Mueller matrix spectroscopy of surfaces and films,” J. Opt. Soc. Am. A 16, 1997–2006 (1999).
[CrossRef]

Kunstler, L.

Lee, J.

J. Lee, J. Koh, R. W. Collins, “Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and films,” Rev. Sci. Instrum. 72, 1742–1754 (2001).
[CrossRef]

I. An, J. Lee, B. Hong, R. W. Collins, “Simultaneous determination of reflectance spectra along with {ψ(E),Δ(E)} in multichannel ellipsometry: applications to instrument calibration and reduction of real-time data,” Thin Solid Films 313–314, 79–84 (1998).
[CrossRef]

J. Lee, P. I. Rovira, I. An, R. W. Collins, “Rotating-compensator multichannel ellipsometry: applications for real time Stokes vector spectroscopy of thin film growth,” Rev. Sci. Instrum. 69, 1800–1810 (1998).
[CrossRef]

Leng, J.

J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
[CrossRef]

Nguyen, H. V.

Nguyen, N. V.

Opsal, J.

J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
[CrossRef]

Pudliner, B. S.

Radman, D. M.

Rovira, P. I.

J. Lee, P. I. Rovira, I. An, R. W. Collins, “Rotating-compensator multichannel ellipsometry: applications for real time Stokes vector spectroscopy of thin film growth,” Rev. Sci. Instrum. 69, 1800–1810 (1998).
[CrossRef]

Sekera, Z.

Senko, M.

J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
[CrossRef]

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light: Production and Use (Harvard University, Cambridge, Mass., 1962).

Thomas, M. E.

T. M. Cotter, M. E. Thomas, W. J. Tropf, “Magnesium fluoride (MgF2),” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, New York, 1991), pp. 899–918.

Tropf, W. J.

T. M. Cotter, M. E. Thomas, W. J. Tropf, “Magnesium fluoride (MgF2),” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, New York, 1991), pp. 899–918.

Uhrich, C.

J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
[CrossRef]

van Silfhout, A.

Vedam, K.

P. Chindaudom, K. Vedam, “Optical characterization of inhomogeneous transparent films on transparent substrates by spectroscopic ellipsometry, '’ in Optical Characterization of Real Surface and Films, K. Vedam, ed. (Academic, New York, 1994), pp. 191–247.

Wei, L.

J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
[CrossRef]

Yarussi, R. A.

Zaiser, C.

J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (5)

Opt. Commun. (1)

P. S. Hauge, F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (3)

J. Lee, P. I. Rovira, I. An, R. W. Collins, “Rotating-compensator multichannel ellipsometry: applications for real time Stokes vector spectroscopy of thin film growth,” Rev. Sci. Instrum. 69, 1800–1810 (1998).
[CrossRef]

J. Lee, J. Koh, R. W. Collins, “Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and films,” Rev. Sci. Instrum. 72, 1742–1754 (2001).
[CrossRef]

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

Thin Solid Films (2)

J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
[CrossRef]

I. An, J. Lee, B. Hong, R. W. Collins, “Simultaneous determination of reflectance spectra along with {ψ(E),Δ(E)} in multichannel ellipsometry: applications to instrument calibration and reduction of real-time data,” Thin Solid Films 313–314, 79–84 (1998).
[CrossRef]

Other (6)

T. M. Cotter, M. E. Thomas, W. J. Tropf, “Magnesium fluoride (MgF2),” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, New York, 1991), pp. 899–918.

P. Chindaudom, K. Vedam, “Optical characterization of inhomogeneous transparent films on transparent substrates by spectroscopic ellipsometry, '’ in Optical Characterization of Real Surface and Films, K. Vedam, ed. (Academic, New York, 1994), pp. 191–247.

W. A. Shurcliff, Polarized Light: Production and Use (Harvard University, Cambridge, Mass., 1962).

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).

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

J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. 10-1–10-164.

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Figures (4)

Fig. 1
Fig. 1

Spectra in the ellipsometric angle ψ=ψC for a zero-order MgF2 biplate compensator measured with a rotating-analyzer single-channel ellipsometer in the straight-through PCAr configuration. The top and bottom spectra were measured before and after an internal alignment procedure to ensure that the fast axes of the two MgF2 plates are perpendicular.

Fig. 2
Fig. 2

(a) Measured (open circles) and best-fit (line) phase-retardance spectra for the aligned MgF2 compensator of Fig. 1, obtained with a rotating-compensator multichannel ellipsometer in the straight-through PCrA configuration. (b) Differences between the experimental and the best-fit spectra in δ measured in the straight-through configuration for the MgF2 compensator by using three different multichannel instruments: PrCA (solid circles), PCrA (open circles), and PC1rC2rA (open triangles). The best-fit spectra in δ differ for these configurations owing to small differences in the experimental spectra as shown in Fig. 3.

Fig. 3
Fig. 3

Differences between the experimental δ spectra of the aligned MgF2 compensator of Fig. 1, measured with three different straight-through multichannel ellipsometer configurations. In (a), the solid (open) circles were obtained by subtracting the δ spectra measured in the PCrA and PrCA (PC1rC2rA) configurations. For each pair of δ spectra, the overall source configuration and system alignment remained unchanged. In (b), the difference is shown between the spectra in δ measured in the PCrA-ellipsometer configuration before [PrCA(1)] and after [PrCA(2)] a major system realignment.

Fig. 4
Fig. 4

Simulated errors in ψ (right scale) and Δ (left scale) propagated from a photon energy independent error in δ of 0.2° for (a) c-Si, (b) Al, and (c) SiO2. To obtain these data, the best-fit results for δ(E) in Fig. 2(a) were used. In addition, the polarizer angle P was optimized to minimize the average error in ψ by using the values of P=ψ=25°, 42.5°, and 21° in (a), (b), and (c), respectively.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

|B4| (α42+β42)1/2=p|cos 2χ|sin2(δ/2)1+p cos2(δ/2) cos 2χ cos 2(A-Q),
δ=2 cos-1(1-|B4|)[1+|B4|cos 2(A-P)]1/2.
δ=2 tan-1|B8||B20|1/2.
δ(E)=(360/1239.8)dEk=15akEk-1,
|B4|-1=γ0+γ2cos 2A+2sin 2A,
γ0=[p sin2(δ/2)]-1,
γ2=±cos 2AScot2(δ/2),
2=±sin 2AScot2(δ/2),
δ=2 tan-11γ22+221/2.

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