Abstract

The effect of windows or lenses placed between the polarization-state generator and the polarization-state detector in a general ellipsometry measurement is examined. It is found that three parameters are required for describing the effects of the window retardation on the ellipsometry measurements. Two of these window parameters can be measured at the same time as the sample parameters if the sample is isotropic, but the third window parameter cannot be determined independently and must be measured separately. If the sample is anisotropic, then none of the windows parameters can be measured independently at the same time as the sample parameters. An example is given in which the strain-induced retardation in fused-silica focusing lenses is measured with a two-modulator generalized ellipsometer and the results are used to correct the sample data.

© 1999 Optical Society of America

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  1. A. A. Studna, D. E. Aspnes, L. T. Flores, B. J. Wilkens, J. P. Harbison, R. E. Ryan, “Low-retardance fused-quartz window for real-time optical applications in ultrahigh vacuum,” J. Vac. Sci. Technol. A 7, 3291–3294 (1989).
    [Crossref]
  2. R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029–2062 (1990).
    [Crossref]
  3. R. F. Spanier, R. G. Wolf, R. M. Loiterman, M. E. Haller, “Simultaneous multiple angle/multiple wavelength ellipsometer and method,” U.S. patent5,166,752 (24November1992).
  4. F. L. McCrackin, “Analyses and corrections of instrumental errors in ellipsometry,” J. Opt. Soc. Am. 60, 57–63 (1970).
    [Crossref]
  5. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  6. J. M. M. de Nijs, A. van Silfhout, “Systematic and random errors in rotating-analyzer ellipsometry,” J. Opt. Soc. A. 5, 773–781 (1988).
    [Crossref]
  7. G. E. Jellison, F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190–8198 (1997); “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184–8189 (1997).
    [Crossref]
  8. D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).
  9. R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, Chap. 22.
  10. R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller-Jones transfer matrix of polarization theory,” Opt. Commun. 38, 159–161 (1981).
    [Crossref]
  11. D. G. M. Anderson, R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” J. Opt. Soc. Am. A 11, 2305–2319 (1994).
    [Crossref]
  12. G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313–314, 33–39 (1998).
  13. B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
    [Crossref]
  14. G. E. Jellison, F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29, 959–974 (1990).
    [Crossref] [PubMed]
  15. R. M. A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2, 148–150 (1978).
    [Crossref] [PubMed]
  16. D. H. Goldstein, “Mueller matrix dual-rotating retarder polarimeter,” Appl. Opt. 31, 6676–6683 (1992).
    [Crossref] [PubMed]
  17. 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]
  18. G. E. Jellison, F. A. Modine, L. A. Boatner, “Measurement of the optical functions of uniaxial materials by two-modulator generalized ellipsometry: rutile (TiO2),” Opt. Lett. 22, 1808–1810 (1997).
    [Crossref]
  19. G. E. Jellison, L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
    [Crossref]
  20. G. E. Jellison, J. O. Ramey, L. A. Boatner, “The optical functions of BiI3 as measured by generalized ellipsometry,” Phys. Rev. B 59, 9718–9721 (1999).
    [Crossref]

1999 (1)

G. E. Jellison, J. O. Ramey, L. A. Boatner, “The optical functions of BiI3 as measured by generalized ellipsometry,” Phys. Rev. B 59, 9718–9721 (1999).
[Crossref]

1998 (3)

G. E. Jellison, L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (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]

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313–314, 33–39 (1998).

1997 (2)

1994 (1)

1992 (1)

1990 (2)

G. E. Jellison, F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29, 959–974 (1990).
[Crossref] [PubMed]

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

1989 (1)

A. A. Studna, D. E. Aspnes, L. T. Flores, B. J. Wilkens, J. P. Harbison, R. E. Ryan, “Low-retardance fused-quartz window for real-time optical applications in ultrahigh vacuum,” J. Vac. Sci. Technol. A 7, 3291–3294 (1989).
[Crossref]

1988 (1)

J. M. M. de Nijs, A. van Silfhout, “Systematic and random errors in rotating-analyzer ellipsometry,” J. Opt. Soc. A. 5, 773–781 (1988).
[Crossref]

1982 (1)

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[Crossref]

1981 (1)

R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller-Jones transfer matrix of polarization theory,” Opt. Commun. 38, 159–161 (1981).
[Crossref]

1978 (1)

1970 (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]

Anderson, D. G. M.

Aspnes, D. E.

A. A. Studna, D. E. Aspnes, L. T. Flores, B. J. Wilkens, J. P. Harbison, R. E. Ryan, “Low-retardance fused-quartz window for real-time optical applications in ultrahigh vacuum,” J. Vac. Sci. Technol. A 7, 3291–3294 (1989).
[Crossref]

Azzam, R. M. A.

Barakat, R.

D. G. M. Anderson, R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” J. Opt. Soc. Am. A 11, 2305–2319 (1994).
[Crossref]

R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller-Jones transfer matrix of polarization theory,” Opt. Commun. 38, 159–161 (1981).
[Crossref]

Bashara, N. M.

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

Boatner, L. A.

G. E. Jellison, J. O. Ramey, L. A. Boatner, “The optical functions of BiI3 as measured by generalized ellipsometry,” Phys. Rev. B 59, 9718–9721 (1999).
[Crossref]

G. E. Jellison, L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
[Crossref]

G. E. Jellison, F. A. Modine, L. A. Boatner, “Measurement of the optical functions of uniaxial materials by two-modulator generalized ellipsometry: rutile (TiO2),” Opt. Lett. 22, 1808–1810 (1997).
[Crossref]

Chipman, R. A.

R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, Chap. 22.

Collins, R. W.

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

Dalby, J. L.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[Crossref]

de Nijs, J. M. M.

J. M. M. de Nijs, A. van Silfhout, “Systematic and random errors in rotating-analyzer ellipsometry,” J. Opt. Soc. A. 5, 773–781 (1988).
[Crossref]

Drevillon, B.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[Crossref]

Flores, L. T.

A. A. Studna, D. E. Aspnes, L. T. Flores, B. J. Wilkens, J. P. Harbison, R. E. Ryan, “Low-retardance fused-quartz window for real-time optical applications in ultrahigh vacuum,” J. Vac. Sci. Technol. A 7, 3291–3294 (1989).
[Crossref]

Goldstein, D. H.

Haller, M. E.

R. F. Spanier, R. G. Wolf, R. M. Loiterman, M. E. Haller, “Simultaneous multiple angle/multiple wavelength ellipsometer and method,” U.S. patent5,166,752 (24November1992).

Harbison, J. P.

A. A. Studna, D. E. Aspnes, L. T. Flores, B. J. Wilkens, J. P. Harbison, R. E. Ryan, “Low-retardance fused-quartz window for real-time optical applications in ultrahigh vacuum,” J. Vac. Sci. Technol. A 7, 3291–3294 (1989).
[Crossref]

Jellison, G. E.

G. E. Jellison, J. O. Ramey, L. A. Boatner, “The optical functions of BiI3 as measured by generalized ellipsometry,” Phys. Rev. B 59, 9718–9721 (1999).
[Crossref]

G. E. Jellison, L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
[Crossref]

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313–314, 33–39 (1998).

G. E. Jellison, F. A. Modine, L. A. Boatner, “Measurement of the optical functions of uniaxial materials by two-modulator generalized ellipsometry: rutile (TiO2),” Opt. Lett. 22, 1808–1810 (1997).
[Crossref]

G. E. Jellison, F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190–8198 (1997); “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184–8189 (1997).
[Crossref]

G. E. Jellison, F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29, 959–974 (1990).
[Crossref] [PubMed]

Kliger, D. S.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

Lee, J.

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]

Lewis, J. W.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

Loiterman, R. M.

R. F. Spanier, R. G. Wolf, R. M. Loiterman, M. E. Haller, “Simultaneous multiple angle/multiple wavelength ellipsometer and method,” U.S. patent5,166,752 (24November1992).

Marbot, R.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[Crossref]

McCrackin, F. L.

Modine, F. A.

Perrin, J.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[Crossref]

Ramey, J. O.

G. E. Jellison, J. O. Ramey, L. A. Boatner, “The optical functions of BiI3 as measured by generalized ellipsometry,” Phys. Rev. B 59, 9718–9721 (1999).
[Crossref]

Randall, C. E.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

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]

Ryan, R. E.

A. A. Studna, D. E. Aspnes, L. T. Flores, B. J. Wilkens, J. P. Harbison, R. E. Ryan, “Low-retardance fused-quartz window for real-time optical applications in ultrahigh vacuum,” J. Vac. Sci. Technol. A 7, 3291–3294 (1989).
[Crossref]

Spanier, R. F.

R. F. Spanier, R. G. Wolf, R. M. Loiterman, M. E. Haller, “Simultaneous multiple angle/multiple wavelength ellipsometer and method,” U.S. patent5,166,752 (24November1992).

Studna, A. A.

A. A. Studna, D. E. Aspnes, L. T. Flores, B. J. Wilkens, J. P. Harbison, R. E. Ryan, “Low-retardance fused-quartz window for real-time optical applications in ultrahigh vacuum,” J. Vac. Sci. Technol. A 7, 3291–3294 (1989).
[Crossref]

van Silfhout, A.

J. M. M. de Nijs, A. van Silfhout, “Systematic and random errors in rotating-analyzer ellipsometry,” J. Opt. Soc. A. 5, 773–781 (1988).
[Crossref]

Violet, A.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[Crossref]

Wilkens, B. J.

A. A. Studna, D. E. Aspnes, L. T. Flores, B. J. Wilkens, J. P. Harbison, R. E. Ryan, “Low-retardance fused-quartz window for real-time optical applications in ultrahigh vacuum,” J. Vac. Sci. Technol. A 7, 3291–3294 (1989).
[Crossref]

Wolf, R. G.

R. F. Spanier, R. G. Wolf, R. M. Loiterman, M. E. Haller, “Simultaneous multiple angle/multiple wavelength ellipsometer and method,” U.S. patent5,166,752 (24November1992).

Appl. Opt. (3)

J. Opt. Soc. A. (1)

J. M. M. de Nijs, A. van Silfhout, “Systematic and random errors in rotating-analyzer ellipsometry,” J. Opt. Soc. A. 5, 773–781 (1988).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Vac. Sci. Technol. A (1)

A. A. Studna, D. E. Aspnes, L. T. Flores, B. J. Wilkens, J. P. Harbison, R. E. Ryan, “Low-retardance fused-quartz window for real-time optical applications in ultrahigh vacuum,” J. Vac. Sci. Technol. A 7, 3291–3294 (1989).
[Crossref]

Opt. Commun. (1)

R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller-Jones transfer matrix of polarization theory,” Opt. Commun. 38, 159–161 (1981).
[Crossref]

Opt. Lett. (2)

Phys. Rev. B (2)

G. E. Jellison, L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
[Crossref]

G. E. Jellison, J. O. Ramey, L. A. Boatner, “The optical functions of BiI3 as measured by generalized ellipsometry,” Phys. Rev. B 59, 9718–9721 (1999).
[Crossref]

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]

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

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[Crossref]

Thin Solid Films (1)

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313–314, 33–39 (1998).

Other (4)

R. F. Spanier, R. G. Wolf, R. M. Loiterman, M. E. Haller, “Simultaneous multiple angle/multiple wavelength ellipsometer and method,” U.S. patent5,166,752 (24November1992).

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

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, Chap. 22.

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Figures (1)

Fig. 1
Fig. 1

Measured W, S 0, and S 1 parameters and the associated error limits. The solid curves through the data points show the fit to the Cauchy dispersion formula.

Tables (1)

Tables Icon

Table 1 Fitted Parameters for the Cauchy Dispersion Relation for the Window Strain Parameters W, S0, and S1

Equations (34)

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

S=IoQUV=IoI0-I90I45-I-45Irc-Ilc,
IoQ2+U2+V21/2,
I=SPSDMSPSG,
J=rpprpsrsprss=rssρppρpsρsp1,
MJ=A·JJ*·A-1,
A=1001100-101100-ii0.
M=m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44=1-N00-N10000CS00-SC,
N=cos2ψ,
S=sin2ψsin Δ,
C=sin2ψcos Δ.
ρpp=rpprss=tanψexpiΔ=C+iS1+N.
ρsp=rsprss=Csp+iSsp1+N,
ρps=rpsrss=Cps+iSps1+N.
N2+S2+C2+Ssp2+Csp2+Sps2+Cps2=1.
MW=1000010-SW001CW0SW-CW1,
MG=MW1MMW0=1-N0S0N-N1S1S-S0-S1C0S0SC-WSS+WC-S1NS1+S0C-S+WCC-WS,
=M+MWt=1-N00-N10000CS00-SC+000S0N00S1S-S0-S1C0S0S-WSWC-S1NS1+S0W-WC-WS,
m13=Csp+CCps+SSps1+N,
m14=Ssp+CSps-SCps1+N+NS0,
m23=-Csp+CCps+SSps1+N+SS1,
m24=-Ssp+CSps-SCps1+N-S0-CS1,
m31=Cps+CCsp+SSsp1+N,
m41=-Sps+CSsp-SCsp1+N-NS1,
m32=-Cps+CCsp+SSsp1+N+SS0,
m42=Sps+CSsp-SCsp1+N+S1+CS0.
Ssp2+Csp2+Sps2+Cps2+N2+S2+C2=1,
Ssp2+Csp2+Sps2+Cps2  N2+S2+C2,
M1urM2urM3urM4ur=010-110-10SXCXSXCXCX-SXCX-SXm13m14m23m24=SspCspSpsCps+1+N0-CSS02+C-SC2-S2X2SCXS12,
M1llM2llM3llM4ll=SXCXSXCXCX-SXCX-SX0-10110-10m31m41m32m42=SspCspSpsCps+1+N0C-SS02+C-S1+N0S12,
SM3ur-M3ll=CM4ll-M4ur=-SCS0+CS1/1-N.
I=Idc+Is sin2θa+Ic cos2θa,
IsIdc=C-WSsin2θp+SS0 cos2θp1-N cos2θp,
IcIdc=SS1 sin2θp+cos2θp-N1-N cos2θp,
W=EA0W+A1WE2+A2WE4,

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