Abstract

We constructed a double-modulation, reflection-type terahertz (THz) ellipsometer for precise measurement of the thickness of a paint film which is coated on a metal surface and which is not transparent to visible or mid-infrared light. The double-modulation technique enabled us to directly obtain two ellipsometric parameters, Δ(ω) and Ψ(ω), as a function of angular frequency, ω, with a single measurement while reducing flicker noise due to a pump laser. The bias voltage of a photoconductive antenna (PCA) used as a THz pulse emitter was modulated at 100 kHz, and a first lock-in amplifier (LA1) was connected to the output of an electro-optic (EO) signal-sampling unit. In addition, a wire-grid polarizer (WGP) was rotated at 100 Hz to conduct polarization modulation with a frequency of 200 Hz. The output signal from LA1 was fed into a second lock-in amplifier (LA2) that worked in synchronization with the rotating WGP (RWGP). By operating LA2 in a quadrature phase-detection mode, we were able to obtain in-phase and out-of-phase signals simultaneously, from which the two ellipsometric parameters for an isotropic sample could be derived at the same time while cancelling common-mode noise. The lower detection limit of the thickness measurement and the relative standard deviation (RSD) of a black paint film coated on an aluminum substrate were 4.3 µm and 1.4%, respectively. The possibility of determining all elements of the Jones matrix for an anisotropic material is also discussed.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Mittleman, Sensing with THz Radiation (Springer, 2003).
  2. D. E. Bray and D. McBride, Nondestructive Testing Techniques (John Wiley & Sons, 1992).
  3. T. Yasui, T. Yasuda, K. Sawanaka, and T. Araki, “Terahertz paintmeter for noncontact monitoring of thickness and drying progress in paint film,” Appl. Opt. 44(32), 6849–6856 (2005).
    [Crossref] [PubMed]
  4. T. Yasuda, T. Iwata, T. Araki, and T. Yasui, “Improvement of minimum paint film thickness for THz paint meters by multiple-regression analysis,” Appl. Opt. 46(30), 7518–7526 (2007).
    [Crossref] [PubMed]
  5. T. Yasui, Y. Kabetani, Y. Ohgi, S. Yokoyama, and T. Araki, “Absolute distance measurement of optically rough objects using asynchronous-optical-sampling terahertz impulse ranging,” Appl. Opt. 49(28), 5262–5270 (2010).
    [Crossref] [PubMed]
  6. T. Iwata, S. Yoshioka, S. Nakamura, Y. Mizutani, and T. Yasui, “Prediction of the thickness of a thin paint film by applying a modified partial-least-squares-1 method to data obtained in terahertz reflectometry,” J. Infrared Millim. Terahertz Waves 34(10), 646–659 (2013).
    [Crossref]
  7. K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
    [Crossref]
  8. T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, “Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation,” Rev. Sci. Instrum. 77(6), 063902 (2006).
    [Crossref]
  9. T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Hole diffusion profile in a p–p+ silicon homojunction determined by terahertz and midinfrared spectroscopic ellipsometry,” Appl. Phys. Lett. 95(3), 032102 (2009).
    [Crossref]
  10. T. Nagashima and M. Hangyo, “Measurement of complex optical constants of a highly doped Si wafer using terahertz ellipsometry,” Appl. Phys. Lett. 79(24), 3917–3919 (2001).
    [Crossref]
  11. D. K. George, A. V. Stier, C. T. Ellis, B. D. McCombe, J. Cerne, and A. G. Markelz, “Terahertz magneto-optical polarization modulation spectroscopy,” J. Opt. Soc. Am. B 29(6), 1406–1412 (2012).
    [Crossref]
  12. C. M. Morris, R. V. Aguilar, A. V. Stier, and N. P. Armitage, “Polarization modulation time-domain terahertz polarimetry,” Opt. Express 20(11), 12303–12317 (2012).
    [Crossref] [PubMed]
  13. D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient measurement of broadband terahertz optical activity,” Appl. Phys. Lett. 100(24), 241114 (2012).
    [Crossref]
  14. W. G. Golden, D. S. Dunn, and J. Overend, “A method for measuring infrared reflection—Absorption spectra of molecules adsorbed on low-area surfaces at monolayer and submonolayer concentrations,” J. Catal. 71(2), 395–404 (1981).
    [Crossref]
  15. S. P. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, D. Abbott, and X.-C. Zhang, “Double modulated differential THz-TDS for thin film dielectric characterization,” Microelectron. J. 33(12), 1033–1042 (2002).
    [Crossref]
  16. E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
    [Crossref]
  17. Y. Hirota, R. Hattori, M. Tani, and M. Hangyo, “Polarization modulation of terahertz electromagnetic radiation by four-contact photoconductive antenna,” Opt. Express 14(10), 4486–4493 (2006).
    [Crossref] [PubMed]
  18. H. Makabe, Y. Hirota, M. Tani, and M. Hangyo, “Polarization state measurement of terahertz electromagnetic radiation by three-contact photoconductive antenna,” Opt. Express 15(18), 11650–11657 (2007).
    [Crossref] [PubMed]
  19. N. Yasumatsu and S. Watanabe, “Precise real-time polarization measurement of terahertz electromagnetic waves by a spinning electro-optic sensor,” Rev. Sci. Instrum. 83(2), 023104 (2012).
    [Crossref] [PubMed]
  20. Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523–3525 (1995).
    [Crossref]
  21. Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69(8), 1026–1028 (1996).
    [Crossref]
  22. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland Personal Library, 1989).
  23. J. D. Holm and K. S. Champlin, “Microwave conductivity of silicon and germanium,” J. Appl. Phys. 39(1), 275–284 (1968).
    [Crossref]
  24. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–1119 (1983).
    [Crossref] [PubMed]

2013 (1)

T. Iwata, S. Yoshioka, S. Nakamura, Y. Mizutani, and T. Yasui, “Prediction of the thickness of a thin paint film by applying a modified partial-least-squares-1 method to data obtained in terahertz reflectometry,” J. Infrared Millim. Terahertz Waves 34(10), 646–659 (2013).
[Crossref]

2012 (4)

D. K. George, A. V. Stier, C. T. Ellis, B. D. McCombe, J. Cerne, and A. G. Markelz, “Terahertz magneto-optical polarization modulation spectroscopy,” J. Opt. Soc. Am. B 29(6), 1406–1412 (2012).
[Crossref]

C. M. Morris, R. V. Aguilar, A. V. Stier, and N. P. Armitage, “Polarization modulation time-domain terahertz polarimetry,” Opt. Express 20(11), 12303–12317 (2012).
[Crossref] [PubMed]

D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient measurement of broadband terahertz optical activity,” Appl. Phys. Lett. 100(24), 241114 (2012).
[Crossref]

N. Yasumatsu and S. Watanabe, “Precise real-time polarization measurement of terahertz electromagnetic waves by a spinning electro-optic sensor,” Rev. Sci. Instrum. 83(2), 023104 (2012).
[Crossref] [PubMed]

2010 (1)

2009 (1)

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Hole diffusion profile in a p–p+ silicon homojunction determined by terahertz and midinfrared spectroscopic ellipsometry,” Appl. Phys. Lett. 95(3), 032102 (2009).
[Crossref]

2007 (2)

2006 (2)

Y. Hirota, R. Hattori, M. Tani, and M. Hangyo, “Polarization modulation of terahertz electromagnetic radiation by four-contact photoconductive antenna,” Opt. Express 14(10), 4486–4493 (2006).
[Crossref] [PubMed]

T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, “Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation,” Rev. Sci. Instrum. 77(6), 063902 (2006).
[Crossref]

2005 (2)

T. Yasui, T. Yasuda, K. Sawanaka, and T. Araki, “Terahertz paintmeter for noncontact monitoring of thickness and drying progress in paint film,” Appl. Opt. 44(32), 6849–6856 (2005).
[Crossref] [PubMed]

E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
[Crossref]

2002 (1)

S. P. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, D. Abbott, and X.-C. Zhang, “Double modulated differential THz-TDS for thin film dielectric characterization,” Microelectron. J. 33(12), 1033–1042 (2002).
[Crossref]

2001 (1)

T. Nagashima and M. Hangyo, “Measurement of complex optical constants of a highly doped Si wafer using terahertz ellipsometry,” Appl. Phys. Lett. 79(24), 3917–3919 (2001).
[Crossref]

1998 (1)

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
[Crossref]

1996 (1)

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69(8), 1026–1028 (1996).
[Crossref]

1995 (1)

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523–3525 (1995).
[Crossref]

1983 (1)

1981 (1)

W. G. Golden, D. S. Dunn, and J. Overend, “A method for measuring infrared reflection—Absorption spectra of molecules adsorbed on low-area surfaces at monolayer and submonolayer concentrations,” J. Catal. 71(2), 395–404 (1981).
[Crossref]

1968 (1)

J. D. Holm and K. S. Champlin, “Microwave conductivity of silicon and germanium,” J. Appl. Phys. 39(1), 275–284 (1968).
[Crossref]

Abbott, D.

S. P. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, D. Abbott, and X.-C. Zhang, “Double modulated differential THz-TDS for thin film dielectric characterization,” Microelectron. J. 33(12), 1033–1042 (2002).
[Crossref]

Aguilar, R. V.

Alexander, R. W.

Araki, T.

Armitage, N. P.

Aschaffenburg, D. J.

D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient measurement of broadband terahertz optical activity,” Appl. Phys. Lett. 100(24), 241114 (2012).
[Crossref]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Castro-Camus, E.

E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
[Crossref]

Cerne, J.

Champlin, K. S.

J. D. Holm and K. S. Champlin, “Microwave conductivity of silicon and germanium,” J. Appl. Phys. 39(1), 275–284 (1968).
[Crossref]

Dunn, D. S.

W. G. Golden, D. S. Dunn, and J. Overend, “A method for measuring infrared reflection—Absorption spectra of molecules adsorbed on low-area surfaces at monolayer and submonolayer concentrations,” J. Catal. 71(2), 395–404 (1981).
[Crossref]

Ellis, C. T.

Esquinazi, P.

T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, “Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation,” Rev. Sci. Instrum. 77(6), 063902 (2006).
[Crossref]

Fraser, M. D.

E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
[Crossref]

George, D. K.

Golden, W. G.

W. G. Golden, D. S. Dunn, and J. Overend, “A method for measuring infrared reflection—Absorption spectra of molecules adsorbed on low-area surfaces at monolayer and submonolayer concentrations,” J. Catal. 71(2), 395–404 (1981).
[Crossref]

Hangyo, M.

Hattori, R.

Herzinger, C. M.

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Hole diffusion profile in a p–p+ silicon homojunction determined by terahertz and midinfrared spectroscopic ellipsometry,” Appl. Phys. Lett. 95(3), 032102 (2009).
[Crossref]

T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, “Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation,” Rev. Sci. Instrum. 77(6), 063902 (2006).
[Crossref]

Hewitt, T. D.

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69(8), 1026–1028 (1996).
[Crossref]

Hirota, Y.

Hofmann, T.

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Hole diffusion profile in a p–p+ silicon homojunction determined by terahertz and midinfrared spectroscopic ellipsometry,” Appl. Phys. Lett. 95(3), 032102 (2009).
[Crossref]

T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, “Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation,” Rev. Sci. Instrum. 77(6), 063902 (2006).
[Crossref]

Holm, J. D.

J. D. Holm and K. S. Champlin, “Microwave conductivity of silicon and germanium,” J. Appl. Phys. 39(1), 275–284 (1968).
[Crossref]

Iwata, T.

T. Iwata, S. Yoshioka, S. Nakamura, Y. Mizutani, and T. Yasui, “Prediction of the thickness of a thin paint film by applying a modified partial-least-squares-1 method to data obtained in terahertz reflectometry,” J. Infrared Millim. Terahertz Waves 34(10), 646–659 (2013).
[Crossref]

T. Yasuda, T. Iwata, T. Araki, and T. Yasui, “Improvement of minimum paint film thickness for THz paint meters by multiple-regression analysis,” Appl. Opt. 46(30), 7518–7526 (2007).
[Crossref] [PubMed]

Jagadish, C.

E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
[Crossref]

Johnston, M. B.

E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
[Crossref]

Kabetani, Y.

Lee, K.-S.

S. P. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, D. Abbott, and X.-C. Zhang, “Double modulated differential THz-TDS for thin film dielectric characterization,” Microelectron. J. 33(12), 1033–1042 (2002).
[Crossref]

Lloyd-Hughes, J.

E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
[Crossref]

Long, L. L.

Lu, T.-M.

S. P. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, D. Abbott, and X.-C. Zhang, “Double modulated differential THz-TDS for thin film dielectric characterization,” Microelectron. J. 33(12), 1033–1042 (2002).
[Crossref]

Makabe, H.

Markelz, A. G.

McCombe, B. D.

Mickan, S. P.

S. P. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, D. Abbott, and X.-C. Zhang, “Double modulated differential THz-TDS for thin film dielectric characterization,” Microelectron. J. 33(12), 1033–1042 (2002).
[Crossref]

Mizutani, Y.

T. Iwata, S. Yoshioka, S. Nakamura, Y. Mizutani, and T. Yasui, “Prediction of the thickness of a thin paint film by applying a modified partial-least-squares-1 method to data obtained in terahertz reflectometry,” J. Infrared Millim. Terahertz Waves 34(10), 646–659 (2013).
[Crossref]

Morris, C. M.

Munch, J.

S. P. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, D. Abbott, and X.-C. Zhang, “Double modulated differential THz-TDS for thin film dielectric characterization,” Microelectron. J. 33(12), 1033–1042 (2002).
[Crossref]

Nagashima, T.

T. Nagashima and M. Hangyo, “Measurement of complex optical constants of a highly doped Si wafer using terahertz ellipsometry,” Appl. Phys. Lett. 79(24), 3917–3919 (2001).
[Crossref]

Nakamura, S.

T. Iwata, S. Yoshioka, S. Nakamura, Y. Mizutani, and T. Yasui, “Prediction of the thickness of a thin paint film by applying a modified partial-least-squares-1 method to data obtained in terahertz reflectometry,” J. Infrared Millim. Terahertz Waves 34(10), 646–659 (2013).
[Crossref]

Ohgi, Y.

Ordal, M. A.

Overend, J.

W. G. Golden, D. S. Dunn, and J. Overend, “A method for measuring infrared reflection—Absorption spectra of molecules adsorbed on low-area surfaces at monolayer and submonolayer concentrations,” J. Catal. 71(2), 395–404 (1981).
[Crossref]

Prober, D. E.

D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient measurement of broadband terahertz optical activity,” Appl. Phys. Lett. 100(24), 241114 (2012).
[Crossref]

Santavicca, D. F.

D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient measurement of broadband terahertz optical activity,” Appl. Phys. Lett. 100(24), 241114 (2012).
[Crossref]

Sawanaka, K.

Schade, U.

T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, “Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation,” Rev. Sci. Instrum. 77(6), 063902 (2006).
[Crossref]

Schmuttenmaer, C. A.

D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient measurement of broadband terahertz optical activity,” Appl. Phys. Lett. 100(24), 241114 (2012).
[Crossref]

Schubert, M.

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Hole diffusion profile in a p–p+ silicon homojunction determined by terahertz and midinfrared spectroscopic ellipsometry,” Appl. Phys. Lett. 95(3), 032102 (2009).
[Crossref]

T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, “Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation,” Rev. Sci. Instrum. 77(6), 063902 (2006).
[Crossref]

Stier, A. V.

Talbayev, D.

D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient measurement of broadband terahertz optical activity,” Appl. Phys. Lett. 100(24), 241114 (2012).
[Crossref]

Tan, H. H.

E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
[Crossref]

Tani, M.

Tiwald, T. E.

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Hole diffusion profile in a p–p+ silicon homojunction determined by terahertz and midinfrared spectroscopic ellipsometry,” Appl. Phys. Lett. 95(3), 032102 (2009).
[Crossref]

Vedam, K.

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
[Crossref]

Ward, C. A.

Watanabe, S.

N. Yasumatsu and S. Watanabe, “Precise real-time polarization measurement of terahertz electromagnetic waves by a spinning electro-optic sensor,” Rev. Sci. Instrum. 83(2), 023104 (2012).
[Crossref] [PubMed]

Williams, M. R. C.

D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient measurement of broadband terahertz optical activity,” Appl. Phys. Lett. 100(24), 241114 (2012).
[Crossref]

Woollam, J. A.

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Hole diffusion profile in a p–p+ silicon homojunction determined by terahertz and midinfrared spectroscopic ellipsometry,” Appl. Phys. Lett. 95(3), 032102 (2009).
[Crossref]

Wu, Q.

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69(8), 1026–1028 (1996).
[Crossref]

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523–3525 (1995).
[Crossref]

Yasuda, T.

Yasui, T.

Yasumatsu, N.

N. Yasumatsu and S. Watanabe, “Precise real-time polarization measurement of terahertz electromagnetic waves by a spinning electro-optic sensor,” Rev. Sci. Instrum. 83(2), 023104 (2012).
[Crossref] [PubMed]

Yokoyama, S.

Yoshioka, S.

T. Iwata, S. Yoshioka, S. Nakamura, Y. Mizutani, and T. Yasui, “Prediction of the thickness of a thin paint film by applying a modified partial-least-squares-1 method to data obtained in terahertz reflectometry,” J. Infrared Millim. Terahertz Waves 34(10), 646–659 (2013).
[Crossref]

Zhang, X.-C.

S. P. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, D. Abbott, and X.-C. Zhang, “Double modulated differential THz-TDS for thin film dielectric characterization,” Microelectron. J. 33(12), 1033–1042 (2002).
[Crossref]

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69(8), 1026–1028 (1996).
[Crossref]

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523–3525 (1995).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (6)

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523–3525 (1995).
[Crossref]

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69(8), 1026–1028 (1996).
[Crossref]

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Hole diffusion profile in a p–p+ silicon homojunction determined by terahertz and midinfrared spectroscopic ellipsometry,” Appl. Phys. Lett. 95(3), 032102 (2009).
[Crossref]

T. Nagashima and M. Hangyo, “Measurement of complex optical constants of a highly doped Si wafer using terahertz ellipsometry,” Appl. Phys. Lett. 79(24), 3917–3919 (2001).
[Crossref]

D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient measurement of broadband terahertz optical activity,” Appl. Phys. Lett. 100(24), 241114 (2012).
[Crossref]

E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
[Crossref]

J. Appl. Phys. (1)

J. D. Holm and K. S. Champlin, “Microwave conductivity of silicon and germanium,” J. Appl. Phys. 39(1), 275–284 (1968).
[Crossref]

J. Catal. (1)

W. G. Golden, D. S. Dunn, and J. Overend, “A method for measuring infrared reflection—Absorption spectra of molecules adsorbed on low-area surfaces at monolayer and submonolayer concentrations,” J. Catal. 71(2), 395–404 (1981).
[Crossref]

J. Infrared Millim. Terahertz Waves (1)

T. Iwata, S. Yoshioka, S. Nakamura, Y. Mizutani, and T. Yasui, “Prediction of the thickness of a thin paint film by applying a modified partial-least-squares-1 method to data obtained in terahertz reflectometry,” J. Infrared Millim. Terahertz Waves 34(10), 646–659 (2013).
[Crossref]

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

Microelectron. J. (1)

S. P. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, D. Abbott, and X.-C. Zhang, “Double modulated differential THz-TDS for thin film dielectric characterization,” Microelectron. J. 33(12), 1033–1042 (2002).
[Crossref]

Opt. Express (3)

Rev. Sci. Instrum. (2)

N. Yasumatsu and S. Watanabe, “Precise real-time polarization measurement of terahertz electromagnetic waves by a spinning electro-optic sensor,” Rev. Sci. Instrum. 83(2), 023104 (2012).
[Crossref] [PubMed]

T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, “Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation,” Rev. Sci. Instrum. 77(6), 063902 (2006).
[Crossref]

Thin Solid Films (1)

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
[Crossref]

Other (3)

D. Mittleman, Sensing with THz Radiation (Springer, 2003).

D. E. Bray and D. McBride, Nondestructive Testing Techniques (John Wiley & Sons, 1992).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland Personal Library, 1989).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic block diagram of the double-modulation reflection-type THz ellipsometer. PCA: photoconductive antenna, TL1,2: THz lens, WGP1–4: wire grid polarizer, OAP: off-axis parabolic mirror, RWGP: rotational wire-grid polarizer, QWP: quarter-wave plate, RP: Rochon prism, OSC: oscillator, LA1,2: lock-in amplifier.

Fig. 2
Fig. 2

Timing diagram explaining the operation of the double-modulation THz ellipsometer. (a) Output pulse trains obtained from the Ti:Sapphire laser with a repetition frequency of 80 MHz, (b) bipolar-modulation signal with a frequency of 100 kHz applied to the PCA, (c) THz pulse trains emitted from the PCA, (d) THz pulse trains modulated by the RWGP (whose orientation angles are shown), (e) waveform of the THz pulse trains after passing through WGP3, (f) output signal obtained from LA1, and (g) and (h) the in-phase and out-of-phase reference signals, respectively, which were fed into LA2 for quadrature-phase detection and whose modulation frequency was 200 Hz.

Fig. 3
Fig. 3

Complex refractive index, n ˜ (ω)=n(ω)iκ(ω) , of a Si substrate as a function of frequency, where (a) and (b) show n(ω) and κ(ω) measured by the double-modulation THz ellipsometer, and (c) and (d) show those measured by the conventional single-modulation ellipsometer.

Fig. 4
Fig. 4

Time-domain waveforms (a) Ein(ω) and (b) Eout(ω) obtained from the LA2 as the in-phase and the out-of-phase output signals. Amplitude and phase spectra of (c) Ein(ω) and (d) Eout(ω), which were obtained from Fourier transformation of (a) and (b), respectively. (e) Ψ and (f) as a function of frequency, which were calculated from Eqs. (7) and (8), respectively. (g) Real part, n(ω), and (h) imaginary part, κ(ω), of the complex refractive index of the paint film as a function of frequency.

Fig. 5
Fig. 5

The ellipsometric parameters, Ψ(ω) (left column) and Δ(ω) (right column), for various thicknesses of paint coatings: (a) and (b) d = 102 µm, (c) and (d) d = 20.0 µm, (e) and (f) d = 10.4 µm, (g) and (h) d = 5.3 µm, and (i) and (j) d = 4.3 µm.

Tables (2)

Tables Icon

Table 1 Expressions for Ein(ω) and Eout(ω) derived from Eqs. (4) and (5), respectively, for various combinations of (θP, θA).

Tables Icon

Table 2 Measurement results of thicknesses of five paint coatings with an eddy-current meter and the double-modulated THz ellipsometer. unit: [µm]

Equations (14)

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

[ E p ( θ R ,ω) E s ( θ R ,ω) ]= P θ A P θ R S P θ P [ E p 0 (ω) E s 0 (ω) ],
P=[ cos 2 θ cosθsinθ cosθsinθ sin 2 θ ].
S=[ r ˜ pp (ω) r ˜ ps (ω) r ˜ sp (ω) r ˜ ss (ω) ],
E in (ω)= E i ( 0 ,ω) E i ( 90 ,ω),
E out (ω)= E i ( 45 ,ω) E i ( 45 ,ω).
ρ(ω)= r ˜ pp (ω) r ˜ ss (ω) =tan[Ψ(ω)]exp(iΔ(ω)),
E in (ω) E out (ω) = 1 2 ( E p 0 (ω)+ E s 0 (ω) )( r ˜ pp (ω)+ r ˜ ps (ω) ) 1 2 ( E p 0 (ω)+ E s 0 (ω) )( r ˜ sp (ω)+ r ˜ ss (ω) ) .
E in (ω) E out (ω) = r ˜ pp (ω) r ˜ ss (ω) =ρ(ω).
ρ(ω)= r ˜ pp (ω) r ˜ ss (ω) = 1 2 ( E p 0 (ω)+ E s 0 (ω) )( r ˜ pp (ω)+ r ˜ ps (ω) ) 1 2 ( E p 0 (ω)+ E s 0 (ω) )( r ˜ sp (ω)+ r ˜ ss (ω) ) = E out (ω) E in (ω) .
ρ ij (ω)= r ˜ ij (ω) r ˜ ss (ω) =tan[ Ψ ij (ω)]exp(iΔ (ω) ij ),  i, j= p, s.
( r ˜ pp (ω) r ˜ sp (ω) )= 1 E p 0 (ω) ( E in (ω) E out (ω) ) .
( r ˜ ps (ω) r ˜ ss (ω) )= 1 E s 0 (ω) ( E out (ω) E in (ω) ).
n ˜ (ω) 2 = { n(ω)iκ(ω) } 2 = sin 2 ϕ[ 1+ tan 2 ϕ ( 1ρ(ω) 1+ρ(ω) ) 2 ],
n ˜ (ω) 2 = ε ω p 2 ω 2 iΓω ,

Metrics