Abstract

We describe a simple spectroscopic ellipsometer that uses a geometric phase shifter and a white-light source to generate a small number of phase-stepped intensities I(λ), which are recorded by a spectrometer. The ellipsometric angles ψ and Δ are easily calculated from these intensities at each wavelength simultaneously. We show that errors in Δ due to the nonideal behavior of the achromatic quarter-wave plate in the phase shifter can be made small by suitably adjusting the azimuth of the linearly polarized light incident on the sample. Two silicon dioxide films were measured with this instrument between 450 and 850 nm and yielded best fit film thicknesses of 1000.6±0.1Å and 20.6±0.1Å, in excellent agreement with those obtained using a commercial ellipsometer.

© 2012 Optical Society of America

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    [CrossRef]
  4. J. Opsal, J. Fanton, J. Chen, J. Leng, L. Wei, C. Uhrich, M. Senko, C. Zaiser, and D. E. Aspnes, “Broadband spectral operation of a rotating-compensator ellipsometer,” Thin Solid Films 313–314, 58–61 (1998).
    [CrossRef]
  5. J. A. Zapien, R. W. Collins, and R. Messier, “Multichannel ellipsometer for real time spectroscopy of thin film deposition from 1.5 to 6.5 eV,” Rev. Sci. Instrum. 71, 3451–3460 (2000).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. T. Wakayama, Y. Otani, and N. Umeda, “Birefringence dispersion measurement based on achromatic four points of geometric phase,” Opt. Eng. 45, 083603 (2006).
    [CrossRef]
  21. C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thick thickness measurement,” Opt. Commun. 273, 74–83 (2007).
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    [CrossRef]
  28. M. P. Kothiyal and C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
    [CrossRef]
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2010 (1)

2009 (1)

2008 (2)

H. C. Hsieh, Z. C. Jian, Y. L. Chen, P. J. Hsieh, and D. C. Su, “A method for measuring two-dimensional refractive index distribution by using Fresnel equations and phase-shifting interferometry,” Phys. Status Solidi C 5, 1016–1019 (2008).
[CrossRef]

W. Pin and A. Asundi, “Full-field retardation measurement of a liquid crystal cell with a phase shift polariscope,” Appl. Opt. 47, 4391–4395 (2008).
[CrossRef]

2007 (2)

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thick thickness measurement,” Opt. Commun. 273, 74–83 (2007).
[CrossRef]

H. Okabe, M. Hayakawa, H. Naito, A. Taniguchi, and K. Oka, “Spectroscopic polarimetry using channeled spectroscopic polarization state generator (CSPSG),” Opt. Express 15, 3093–3109 (2007).
[CrossRef]

2006 (1)

T. Wakayama, Y. Otani, and N. Umeda, “Birefringence dispersion measurement based on achromatic four points of geometric phase,” Opt. Eng. 45, 083603 (2006).
[CrossRef]

2004 (2)

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455–456, 120–123 (2004).
[CrossRef]

R. W. Collins, I. An, C. Chen, A. S. Ferlauto, and J. A. Zapien, “Advances in multichannel ellipsometric techniques for in-situ and real-time characterization of thin films,” Thin Solid Films 469–470, 38–46 (2004).
[CrossRef]

2000 (1)

J. A. Zapien, R. W. Collins, and R. Messier, “Multichannel ellipsometer for real time spectroscopy of thin film deposition from 1.5 to 6.5 eV,” Rev. Sci. Instrum. 71, 3451–3460 (2000).
[CrossRef]

1998 (3)

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

E. M. Frins, W. Dultz, and J. A. Ferrari, “Polarization-shifting method for step interferometry,” Pure Appl. Opt. 7, 53–60 (1998).
[CrossRef]

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Achromatic phase shifting by a rotating polarizer,” Opt. Commun. 154, 249–254 (1998).
[CrossRef]

1997 (1)

P. Hariharan, H. Ramachandran, K. A. Suresh, and J. Samuel, “The Pancharatnam phase as a strictly geometric phase: a demonstration using pure projections,” J. Mod. Opt. 44, 707–713 (1997).
[CrossRef]

1994 (2)

C. W. Chu, C. C. Lee, I. Y. Fu, J. C. Hsu, and Y. Y. Liou, “Phase shifting ellipsometry,” Jpn. J. Appl. Phys. 33, 4769–4772 (1994).
[CrossRef]

L. Y. Chen, X. W. Feng, Y. Su, H. Z. Ma, and Y. H. Qian, “Design of a scanning ellipsometer by synchronous rotation of the polarizer and analyzer,” Appl. Opt. 33, 1299–1305 (1994).
[CrossRef]

1992 (2)

C. C. Kim, P. M. Raccah, and J. W. Garland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[CrossRef]

P. Hariharan and M. Roy, “A geometric-phase interferometer,” J. Mod. Opt. 39, 1811–1815 (1992).
[CrossRef]

1990 (1)

1986 (1)

M. P. Kothiyal and C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
[CrossRef]

1985 (2)

1983 (1)

1975 (2)

An, I.

R. W. Collins, I. An, C. Chen, A. S. Ferlauto, and J. A. Zapien, “Advances in multichannel ellipsometric techniques for in-situ and real-time characterization of thin films,” Thin Solid Films 469–470, 38–46 (2004).
[CrossRef]

Aspnes, D. E.

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

D. E. Aspnes and A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975).
[CrossRef]

Asundi, A.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

Bungay, C. L.

J. N. Hilfiker, B. Johs, J. Hale, C. M. Herzinger, T. E. Tiwald, C. L. Bungay, R. A. Synowicki, G. K. Pribil, and J. A. Woollam, “Recent developments in spectroscopic ellipsometry for materials and process control,” in 46th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2003), pp. 365–370.

Chen, C.

R. W. Collins, I. An, C. Chen, A. S. Ferlauto, and J. A. Zapien, “Advances in multichannel ellipsometric techniques for in-situ and real-time characterization of thin films,” Thin Solid Films 469–470, 38–46 (2004).
[CrossRef]

Chen, J.

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

Chen, L. Y.

Chen, Y. L.

H. C. Hsieh, Z. C. Jian, Y. L. Chen, P. J. Hsieh, and D. C. Su, “A method for measuring two-dimensional refractive index distribution by using Fresnel equations and phase-shifting interferometry,” Phys. Status Solidi C 5, 1016–1019 (2008).
[CrossRef]

Chou, C.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thick thickness measurement,” Opt. Commun. 273, 74–83 (2007).
[CrossRef]

Chu, C. W.

C. W. Chu, C. C. Lee, I. Y. Fu, J. C. Hsu, and Y. Y. Liou, “Phase shifting ellipsometry,” Jpn. J. Appl. Phys. 33, 4769–4772 (1994).
[CrossRef]

Ciprian, D.

Collins, R. W.

R. W. Collins, I. An, C. Chen, A. S. Ferlauto, and J. A. Zapien, “Advances in multichannel ellipsometric techniques for in-situ and real-time characterization of thin films,” Thin Solid Films 469–470, 38–46 (2004).
[CrossRef]

J. A. Zapien, R. W. Collins, and R. Messier, “Multichannel ellipsometer for real time spectroscopy of thin film deposition from 1.5 to 6.5 eV,” Rev. Sci. Instrum. 71, 3451–3460 (2000).
[CrossRef]

De Martino, A.

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455–456, 120–123 (2004).
[CrossRef]

Delisle, C.

Drevillon, B.

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455–456, 120–123 (2004).
[CrossRef]

Dultz, W.

E. M. Frins, W. Dultz, and J. A. Ferrari, “Polarization-shifting method for step interferometry,” Pure Appl. Opt. 7, 53–60 (1998).
[CrossRef]

Fanton, J.

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

Feng, X. W.

Ferlauto, A. S.

R. W. Collins, I. An, C. Chen, A. S. Ferlauto, and J. A. Zapien, “Advances in multichannel ellipsometric techniques for in-situ and real-time characterization of thin films,” Thin Solid Films 469–470, 38–46 (2004).
[CrossRef]

Ferrari, J. A.

E. M. Frins, W. Dultz, and J. A. Ferrari, “Polarization-shifting method for step interferometry,” Pure Appl. Opt. 7, 53–60 (1998).
[CrossRef]

Frins, E. M.

E. M. Frins, W. Dultz, and J. A. Ferrari, “Polarization-shifting method for step interferometry,” Pure Appl. Opt. 7, 53–60 (1998).
[CrossRef]

Fu, I. Y.

C. W. Chu, C. C. Lee, I. Y. Fu, J. C. Hsu, and Y. Y. Liou, “Phase shifting ellipsometry,” Jpn. J. Appl. Phys. 33, 4769–4772 (1994).
[CrossRef]

Fujiwara, H.

H. Fujiwara, Spectroscopic Ellipsometry (Wiley, 2007).

Garcia-Caurel, E.

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455–456, 120–123 (2004).
[CrossRef]

Garland, J. W.

C. C. Kim, P. M. Raccah, and J. W. Garland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[CrossRef]

Hale, J.

J. N. Hilfiker, B. Johs, J. Hale, C. M. Herzinger, T. E. Tiwald, C. L. Bungay, R. A. Synowicki, G. K. Pribil, and J. A. Woollam, “Recent developments in spectroscopic ellipsometry for materials and process control,” in 46th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2003), pp. 365–370.

Hariharan, P.

P. Hariharan, H. Ramachandran, K. A. Suresh, and J. Samuel, “The Pancharatnam phase as a strictly geometric phase: a demonstration using pure projections,” J. Mod. Opt. 44, 707–713 (1997).
[CrossRef]

P. Hariharan and M. Roy, “A geometric-phase interferometer,” J. Mod. Opt. 39, 1811–1815 (1992).
[CrossRef]

Hayakawa, M.

Helen, S. S.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Achromatic phase shifting by a rotating polarizer,” Opt. Commun. 154, 249–254 (1998).
[CrossRef]

Herzinger, C. M.

J. N. Hilfiker, B. Johs, J. Hale, C. M. Herzinger, T. E. Tiwald, C. L. Bungay, R. A. Synowicki, G. K. Pribil, and J. A. Woollam, “Recent developments in spectroscopic ellipsometry for materials and process control,” in 46th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2003), pp. 365–370.

Hilfiker, J. N.

J. N. Hilfiker, B. Johs, J. Hale, C. M. Herzinger, T. E. Tiwald, C. L. Bungay, R. A. Synowicki, G. K. Pribil, and J. A. Woollam, “Recent developments in spectroscopic ellipsometry for materials and process control,” in 46th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2003), pp. 365–370.

Hlubina, P.

Hsieh, H. C.

H. C. Hsieh, Z. C. Jian, Y. L. Chen, P. J. Hsieh, and D. C. Su, “A method for measuring two-dimensional refractive index distribution by using Fresnel equations and phase-shifting interferometry,” Phys. Status Solidi C 5, 1016–1019 (2008).
[CrossRef]

Hsieh, P. J.

H. C. Hsieh, Z. C. Jian, Y. L. Chen, P. J. Hsieh, and D. C. Su, “A method for measuring two-dimensional refractive index distribution by using Fresnel equations and phase-shifting interferometry,” Phys. Status Solidi C 5, 1016–1019 (2008).
[CrossRef]

Hsu, J. C.

C. W. Chu, C. C. Lee, I. Y. Fu, J. C. Hsu, and Y. Y. Liou, “Phase shifting ellipsometry,” Jpn. J. Appl. Phys. 33, 4769–4772 (1994).
[CrossRef]

Hu, H. Z.

Huang, H. S.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thick thickness measurement,” Opt. Commun. 273, 74–83 (2007).
[CrossRef]

Jellison, G. E.

Jian, Z. C.

H. C. Hsieh, Z. C. Jian, Y. L. Chen, P. J. Hsieh, and D. C. Su, “A method for measuring two-dimensional refractive index distribution by using Fresnel equations and phase-shifting interferometry,” Phys. Status Solidi C 5, 1016–1019 (2008).
[CrossRef]

Johs, B.

J. N. Hilfiker, B. Johs, J. Hale, C. M. Herzinger, T. E. Tiwald, C. L. Bungay, R. A. Synowicki, G. K. Pribil, and J. A. Woollam, “Recent developments in spectroscopic ellipsometry for materials and process control,” in 46th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2003), pp. 365–370.

Kim, C. C.

C. C. Kim, P. M. Raccah, and J. W. Garland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[CrossRef]

Kothiyal, M. P.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Achromatic phase shifting by a rotating polarizer,” Opt. Commun. 154, 249–254 (1998).
[CrossRef]

M. P. Kothiyal and C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
[CrossRef]

M. P. Kothiyal and C. Delisle, “Rotating analyzer heterodyne ellipsometer: error analysis,” Appl. Opt. 24, 2288–2290 (1985).
[CrossRef]

M. P. Kothiyal and C. Delisle, “Shearing interferometer for phase shifting interferometry with polarization phase shifter,” Appl. Opt. 24, 4439–4442 (1985).
[CrossRef]

Lee, C. C.

C. W. Chu, C. C. Lee, I. Y. Fu, J. C. Hsu, and Y. Y. Liou, “Phase shifting ellipsometry,” Jpn. J. Appl. Phys. 33, 4769–4772 (1994).
[CrossRef]

Leng, J.

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

Liou, Y. Y.

C. W. Chu, C. C. Lee, I. Y. Fu, J. C. Hsu, and Y. Y. Liou, “Phase shifting ellipsometry,” Jpn. J. Appl. Phys. 33, 4769–4772 (1994).
[CrossRef]

Lunacek, J.

Ma, H. Z.

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

Messier, R.

J. A. Zapien, R. W. Collins, and R. Messier, “Multichannel ellipsometer for real time spectroscopy of thin film deposition from 1.5 to 6.5 eV,” Rev. Sci. Instrum. 71, 3451–3460 (2000).
[CrossRef]

Modine, F. A.

Naito, H.

Oka, K.

Okabe, H.

Opsal, J.

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

Otani, Y.

T. Wakayama, Y. Otani, and N. Umeda, “Birefringence dispersion measurement based on achromatic four points of geometric phase,” Opt. Eng. 45, 083603 (2006).
[CrossRef]

Pin, W.

Pribil, G. K.

J. N. Hilfiker, B. Johs, J. Hale, C. M. Herzinger, T. E. Tiwald, C. L. Bungay, R. A. Synowicki, G. K. Pribil, and J. A. Woollam, “Recent developments in spectroscopic ellipsometry for materials and process control,” in 46th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2003), pp. 365–370.

Qian, Y. H.

Raccah, P. M.

C. C. Kim, P. M. Raccah, and J. W. Garland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[CrossRef]

Ramachandran, H.

P. Hariharan, H. Ramachandran, K. A. Suresh, and J. Samuel, “The Pancharatnam phase as a strictly geometric phase: a demonstration using pure projections,” J. Mod. Opt. 44, 707–713 (1997).
[CrossRef]

Roy, M.

P. Hariharan and M. Roy, “A geometric-phase interferometer,” J. Mod. Opt. 39, 1811–1815 (1992).
[CrossRef]

Samuel, J.

P. Hariharan, H. Ramachandran, K. A. Suresh, and J. Samuel, “The Pancharatnam phase as a strictly geometric phase: a demonstration using pure projections,” J. Mod. Opt. 44, 707–713 (1997).
[CrossRef]

Senko, M.

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

Shamailov, S. S.

Sirohi, R. S.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Achromatic phase shifting by a rotating polarizer,” Opt. Commun. 154, 249–254 (1998).
[CrossRef]

Sommargren, G. E.

Studna, A. A.

Su, D. C.

H. C. Hsieh, Z. C. Jian, Y. L. Chen, P. J. Hsieh, and D. C. Su, “A method for measuring two-dimensional refractive index distribution by using Fresnel equations and phase-shifting interferometry,” Phys. Status Solidi C 5, 1016–1019 (2008).
[CrossRef]

Su, Y.

Suresh, K. A.

P. Hariharan, H. Ramachandran, K. A. Suresh, and J. Samuel, “The Pancharatnam phase as a strictly geometric phase: a demonstration using pure projections,” J. Mod. Opt. 44, 707–713 (1997).
[CrossRef]

Synowicki, R. A.

J. N. Hilfiker, B. Johs, J. Hale, C. M. Herzinger, T. E. Tiwald, C. L. Bungay, R. A. Synowicki, G. K. Pribil, and J. A. Woollam, “Recent developments in spectroscopic ellipsometry for materials and process control,” in 46th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2003), pp. 365–370.

Taniguchi, A.

Teng, H. K.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thick thickness measurement,” Opt. Commun. 273, 74–83 (2007).
[CrossRef]

Tiwald, T. E.

J. N. Hilfiker, B. Johs, J. Hale, C. M. Herzinger, T. E. Tiwald, C. L. Bungay, R. A. Synowicki, G. K. Pribil, and J. A. Woollam, “Recent developments in spectroscopic ellipsometry for materials and process control,” in 46th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2003), pp. 365–370.

Uhrich, C.

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

Umeda, N.

T. Wakayama, Y. Otani, and N. Umeda, “Birefringence dispersion measurement based on achromatic four points of geometric phase,” Opt. Eng. 45, 083603 (2006).
[CrossRef]

Wakayama, T.

T. Wakayama, Y. Otani, and N. Umeda, “Birefringence dispersion measurement based on achromatic four points of geometric phase,” Opt. Eng. 45, 083603 (2006).
[CrossRef]

Watkins, L. R.

Wei, L.

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

Woollam, J. A.

J. N. Hilfiker, B. Johs, J. Hale, C. M. Herzinger, T. E. Tiwald, C. L. Bungay, R. A. Synowicki, G. K. Pribil, and J. A. Woollam, “Recent developments in spectroscopic ellipsometry for materials and process control,” in 46th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2003), pp. 365–370.

Yu, C. J.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thick thickness measurement,” Opt. Commun. 273, 74–83 (2007).
[CrossRef]

Zaiser, C.

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

Zapien, J. A.

R. W. Collins, I. An, C. Chen, A. S. Ferlauto, and J. A. Zapien, “Advances in multichannel ellipsometric techniques for in-situ and real-time characterization of thin films,” Thin Solid Films 469–470, 38–46 (2004).
[CrossRef]

J. A. Zapien, R. W. Collins, and R. Messier, “Multichannel ellipsometer for real time spectroscopy of thin film deposition from 1.5 to 6.5 eV,” Rev. Sci. Instrum. 71, 3451–3460 (2000).
[CrossRef]

Appl. Opt. (8)

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[CrossRef]

P. Hariharan, H. Ramachandran, K. A. Suresh, and J. Samuel, “The Pancharatnam phase as a strictly geometric phase: a demonstration using pure projections,” J. Mod. Opt. 44, 707–713 (1997).
[CrossRef]

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C. W. Chu, C. C. Lee, I. Y. Fu, J. C. Hsu, and Y. Y. Liou, “Phase shifting ellipsometry,” Jpn. J. Appl. Phys. 33, 4769–4772 (1994).
[CrossRef]

Opt. Acta (1)

M. P. Kothiyal and C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
[CrossRef]

Opt. Commun. (2)

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Achromatic phase shifting by a rotating polarizer,” Opt. Commun. 154, 249–254 (1998).
[CrossRef]

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thick thickness measurement,” Opt. Commun. 273, 74–83 (2007).
[CrossRef]

Opt. Eng. (1)

T. Wakayama, Y. Otani, and N. Umeda, “Birefringence dispersion measurement based on achromatic four points of geometric phase,” Opt. Eng. 45, 083603 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Status Solidi C (1)

H. C. Hsieh, Z. C. Jian, Y. L. Chen, P. J. Hsieh, and D. C. Su, “A method for measuring two-dimensional refractive index distribution by using Fresnel equations and phase-shifting interferometry,” Phys. Status Solidi C 5, 1016–1019 (2008).
[CrossRef]

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E. M. Frins, W. Dultz, and J. A. Ferrari, “Polarization-shifting method for step interferometry,” Pure Appl. Opt. 7, 53–60 (1998).
[CrossRef]

Rev. Sci. Instrum. (2)

J. A. Zapien, R. W. Collins, and R. Messier, “Multichannel ellipsometer for real time spectroscopy of thin film deposition from 1.5 to 6.5 eV,” Rev. Sci. Instrum. 71, 3451–3460 (2000).
[CrossRef]

C. C. Kim, P. M. Raccah, and J. W. Garland, “The improvement of phase modulated spectroscopic ellipsometry,” Rev. Sci. Instrum. 63, 2958–2966 (1992).
[CrossRef]

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E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455–456, 120–123 (2004).
[CrossRef]

R. W. Collins, I. An, C. Chen, A. S. Ferlauto, and J. A. Zapien, “Advances in multichannel ellipsometric techniques for in-situ and real-time characterization of thin films,” Thin Solid Films 469–470, 38–46 (2004).
[CrossRef]

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

Other (6)

H. Fujiwara, Spectroscopic Ellipsometry (Wiley, 2007).

J. N. Hilfiker, B. Johs, J. Hale, C. M. Herzinger, T. E. Tiwald, C. L. Bungay, R. A. Synowicki, G. K. Pribil, and J. A. Woollam, “Recent developments in spectroscopic ellipsometry for materials and process control,” in 46th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2003), pp. 365–370.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

Thin Film Companion, Semiconsoft, Inc., Southborough, Mass. 01772, USA.

Picometer Ellipsometer, Beaglehole Instruments, Ltd., 32 Salamanca Road, Kelburn, Wellington 6012, New Zealand.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the white-light ellipsometer. P, polarizer; S: sample; G, goniometer; Q, quarter-wave plate; A, analyzer; λ, spectrometer.

Fig. 2.
Fig. 2.

Schematic of alternative form of the white-light ellipsometer. P, polarizer; H, half-wave plate; Q, quarter-wave plate; S, sample; G, goniometer; A, analyzer; λ, spectrometer.

Fig. 3.
Fig. 3.

Measured values of ψ and Δ for a 100 nm thick SiO2 film on a Si substrate at 70° AOI with the best fit curves to the data.

Fig. 4.
Fig. 4.

Measured values of ψ and Δ for a 2 nm thick SiO2 film on a Si substrate at 80° AOI with the best fit curves to the data.

Equations (27)

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[10]aexp(iα)+[01]b,
[ExEy]=[cos2AcosAsinAcosAsinAsin2A][1ii1][aexp(iα)b]=aexp(i[α+A])+ibexp(iA)[cosAsinA].
Ia2+b2+2absin(2A+α),
[ExEy]=[rpcosPrssinP]=[|rp|cosPexp(iΔ)|rs|sinP],
|rp|cosPa,
Δα,
|rs|sinPb.
I(λ,A)=I0{|rp|2cos2P+|rs|2sin2P+2|rp||rs|cosPsinPsin(2A+Δ)}.
I1(λ)=I0{|rp|2cos2P+|rs|2sin2P+2|rp||rs|cosPsinPsin(Δ)},
I2(λ)=I0{|rp|2cos2P+|rs|2sin2P+2|rp||rs|cosPsinPcos(Δ)},
I3(λ)=I0{|rp|2cos2P+|rs|2sin2P2|rp||rs|cosPsinPsin(Δ)},
I4(λ)=I0{|rp|2cos2P+|rs|2sin2P2|rp||rs|cosPsinPcos(Δ)},
Δ(λ)=tan1(I1I3I2I4).
Δ(λ)=tan1(2I1I2I33(I2I3)).
I1+I3=2I0{|rp|2cos2P+|rs|2sin2P},
I1I3=4I0|rp||rs|cosPsinPsinΔ,
I2I4=4I0|rp||rs|cosPsinPcosΔ.
r(λ)=2(I1+I3)(I1I3)2+(I2I4)2=|rp|2cos2P+|rs|2sin2P|rp||rs|cosPsinP=tan2ψcot2P+1tanψcotP.
tanψcotP=r±r242.
ψ(λ)=tan1IpIs
I(λ)=I0{|rp|2+|rs|2+2|rp||rs|sin(4H+Δ)}.
δα=γcosαcot2βγ24sin2α,
cot2β=(b2a2)2ab,
δ=π2+γ
δΔγcosΔ(tan2ψcot2P1)2tanψcotP.
δα=2ε(1+sinαcot2β)+4ε2cosαcot2βε2sin2α.
δΔ2ε(1+sinΔ[tan2Ptan2ψ2tanψtanP]).

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