Abstract

We present a reflection-type terahertz time-domain spectroscopic ellipsometry (THz-TDSE) technique for measuring the complex dielectric constants of thin-film materials without replacement of the sample. THz-TDSE provides complex dielectric constants from the ratio of the complex amplitude reflection coefficients between p- and s- polarized THz waves. The measured dielectric constants of doped GaAs thin films show good agreement with predictions of the Drude model, even though the film thickness is of the order of a tenth of the penetration depth of the THz waves. In addition, we demonstrate the measurements of soft-phonon dispersion in SrTiO3 thin films deposited on a Pt layer. The obtained dielectric constants agree well with the predictions of a generalized harmonic oscillator model.

© 2011 Optical Society of America

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2009

N. Matsumoto, T. Fujii, K. Kageyama, H. Takagi, T. Nagashima, and M. Hangyo, Jpn. J. Appl. Phys. 48, 09KC11 (2009).
[CrossRef]

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, Appl. Phys. Lett. 95, 032102 (2009).
[CrossRef]

T. Hosokura, K. Kageyama, H. Takagi, and Y. Sakabe, J. Am. Ceram. Soc. 92, 253 (2009).
[CrossRef]

2005

K.-E. Peiponen, E. Gornov, Y. Svirko, Y. Ino, M. Kuwata-Gonokami, and V. Lucarini, Phys. Rev. B 72, 245109 (2005).
[CrossRef]

2004

H. Hirori, K. Yamashita, M. Nagai, and K. Tanaka, Jpn. J. Appl. Phys. 43, L1287 (2004).
[CrossRef]

2003

A. Pashkin, M. Kempa, H. Němec, F. Kadlec, and P. Kužel, Rev. Sci. Inst. 74, 4711 (2003).
[CrossRef]

2001

T. Nagashima and M. Hangyo, Appl. Phys. Lett. 79, 3917 (2001).
[CrossRef]

2000

A. A. Sirenko, C. Bernhard, A. Golnik, A. M. Clark, J.-H. Hao, W. Si, and X. X. Xi, Nature 404, 373 (2000).
[CrossRef] [PubMed]

1998

1997

1994

R. Fukasawa and S. Perkowitz, Phys. Rev. B 50, 14119(1994).
[CrossRef]

1990

D. M. Szmyd, P. Porro, A. Majerfeld, and S. Lagomarsino, J. Appl. Phys. 68, 2367 (1990).
[CrossRef]

1974

F. Gervais and B. Piriou, Phys. Rev. B 10, 1642 (1974).
[CrossRef]

Bernhard, C.

A. A. Sirenko, C. Bernhard, A. Golnik, A. M. Clark, J.-H. Hao, W. Si, and X. X. Xi, Nature 404, 373 (2000).
[CrossRef] [PubMed]

Clark, A. M.

A. A. Sirenko, C. Bernhard, A. Golnik, A. M. Clark, J.-H. Hao, W. Si, and X. X. Xi, Nature 404, 373 (2000).
[CrossRef] [PubMed]

Djurišic, A. B.

Elazar, J. M.

Fujii, T.

N. Matsumoto, T. Fujii, K. Kageyama, H. Takagi, T. Nagashima, and M. Hangyo, Jpn. J. Appl. Phys. 48, 09KC11 (2009).
[CrossRef]

Fujiwara, H.

H. Fujiwara, Spectroscopic Ellipsometry (Wiley, 2007), Chap. 2.
[CrossRef]

Fukasawa, R.

R. Fukasawa and S. Perkowitz, Phys. Rev. B 50, 14119(1994).
[CrossRef]

Gardona, M.

Gervais, F.

F. Gervais and B. Piriou, Phys. Rev. B 10, 1642 (1974).
[CrossRef]

Golnik, A.

A. A. Sirenko, C. Bernhard, A. Golnik, A. M. Clark, J.-H. Hao, W. Si, and X. X. Xi, Nature 404, 373 (2000).
[CrossRef] [PubMed]

Gornov, E.

K.-E. Peiponen, E. Gornov, Y. Svirko, Y. Ino, M. Kuwata-Gonokami, and V. Lucarini, Phys. Rev. B 72, 245109 (2005).
[CrossRef]

Grischkowsky, D.

T. I. Jeon and D. Grischkowsky, Appl. Phys. Lett. 72, 3032(1998).
[CrossRef]

Hangyo, M.

N. Matsumoto, T. Fujii, K. Kageyama, H. Takagi, T. Nagashima, and M. Hangyo, Jpn. J. Appl. Phys. 48, 09KC11 (2009).
[CrossRef]

T. Nagashima and M. Hangyo, Appl. Phys. Lett. 79, 3917 (2001).
[CrossRef]

Hao, J.-H.

A. A. Sirenko, C. Bernhard, A. Golnik, A. M. Clark, J.-H. Hao, W. Si, and X. X. Xi, Nature 404, 373 (2000).
[CrossRef] [PubMed]

Henn, R.

Herzinger, C. M.

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, Appl. Phys. Lett. 95, 032102 (2009).
[CrossRef]

Hirori, H.

H. Hirori, K. Yamashita, M. Nagai, and K. Tanaka, Jpn. J. Appl. Phys. 43, L1287 (2004).
[CrossRef]

Hofmann, T.

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, Appl. Phys. Lett. 95, 032102 (2009).
[CrossRef]

Hosokura, T.

T. Hosokura, K. Kageyama, H. Takagi, and Y. Sakabe, J. Am. Ceram. Soc. 92, 253 (2009).
[CrossRef]

Ino, Y.

K.-E. Peiponen, E. Gornov, Y. Svirko, Y. Ino, M. Kuwata-Gonokami, and V. Lucarini, Phys. Rev. B 72, 245109 (2005).
[CrossRef]

Jeon, T. I.

T. I. Jeon and D. Grischkowsky, Appl. Phys. Lett. 72, 3032(1998).
[CrossRef]

Kadlec, F.

A. Pashkin, M. Kempa, H. Němec, F. Kadlec, and P. Kužel, Rev. Sci. Inst. 74, 4711 (2003).
[CrossRef]

Kageyama, K.

N. Matsumoto, T. Fujii, K. Kageyama, H. Takagi, T. Nagashima, and M. Hangyo, Jpn. J. Appl. Phys. 48, 09KC11 (2009).
[CrossRef]

T. Hosokura, K. Kageyama, H. Takagi, and Y. Sakabe, J. Am. Ceram. Soc. 92, 253 (2009).
[CrossRef]

Kempa, M.

A. Pashkin, M. Kempa, H. Němec, F. Kadlec, and P. Kužel, Rev. Sci. Inst. 74, 4711 (2003).
[CrossRef]

Kircher, J.

Kuwata-Gonokami, M.

K.-E. Peiponen, E. Gornov, Y. Svirko, Y. Ino, M. Kuwata-Gonokami, and V. Lucarini, Phys. Rev. B 72, 245109 (2005).
[CrossRef]

Kužel, P.

A. Pashkin, M. Kempa, H. Němec, F. Kadlec, and P. Kužel, Rev. Sci. Inst. 74, 4711 (2003).
[CrossRef]

Lagomarsino, S.

D. M. Szmyd, P. Porro, A. Majerfeld, and S. Lagomarsino, J. Appl. Phys. 68, 2367 (1990).
[CrossRef]

Lucarini, V.

K.-E. Peiponen, E. Gornov, Y. Svirko, Y. Ino, M. Kuwata-Gonokami, and V. Lucarini, Phys. Rev. B 72, 245109 (2005).
[CrossRef]

Majerfeld, A.

D. M. Szmyd, P. Porro, A. Majerfeld, and S. Lagomarsino, J. Appl. Phys. 68, 2367 (1990).
[CrossRef]

Majewski, M. L.

Matsumoto, N.

N. Matsumoto, T. Fujii, K. Kageyama, H. Takagi, T. Nagashima, and M. Hangyo, Jpn. J. Appl. Phys. 48, 09KC11 (2009).
[CrossRef]

Nagai, M.

H. Hirori, K. Yamashita, M. Nagai, and K. Tanaka, Jpn. J. Appl. Phys. 43, L1287 (2004).
[CrossRef]

Nagashima, T.

N. Matsumoto, T. Fujii, K. Kageyama, H. Takagi, T. Nagashima, and M. Hangyo, Jpn. J. Appl. Phys. 48, 09KC11 (2009).
[CrossRef]

T. Nagashima and M. Hangyo, Appl. Phys. Lett. 79, 3917 (2001).
[CrossRef]

Nemec, H.

A. Pashkin, M. Kempa, H. Němec, F. Kadlec, and P. Kužel, Rev. Sci. Inst. 74, 4711 (2003).
[CrossRef]

Pashkin, A.

A. Pashkin, M. Kempa, H. Němec, F. Kadlec, and P. Kužel, Rev. Sci. Inst. 74, 4711 (2003).
[CrossRef]

Peiponen, K.-E.

K.-E. Peiponen, E. Gornov, Y. Svirko, Y. Ino, M. Kuwata-Gonokami, and V. Lucarini, Phys. Rev. B 72, 245109 (2005).
[CrossRef]

Perkowitz, S.

R. Fukasawa and S. Perkowitz, Phys. Rev. B 50, 14119(1994).
[CrossRef]

Piriou, B.

F. Gervais and B. Piriou, Phys. Rev. B 10, 1642 (1974).
[CrossRef]

Porro, P.

D. M. Szmyd, P. Porro, A. Majerfeld, and S. Lagomarsino, J. Appl. Phys. 68, 2367 (1990).
[CrossRef]

Rakic, A. D.

Richards, P. L.

Sakabe, Y.

T. Hosokura, K. Kageyama, H. Takagi, and Y. Sakabe, J. Am. Ceram. Soc. 92, 253 (2009).
[CrossRef]

Schubert, M.

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, Appl. Phys. Lett. 95, 032102 (2009).
[CrossRef]

Si, W.

A. A. Sirenko, C. Bernhard, A. Golnik, A. M. Clark, J.-H. Hao, W. Si, and X. X. Xi, Nature 404, 373 (2000).
[CrossRef] [PubMed]

Sirenko, A. A.

A. A. Sirenko, C. Bernhard, A. Golnik, A. M. Clark, J.-H. Hao, W. Si, and X. X. Xi, Nature 404, 373 (2000).
[CrossRef] [PubMed]

Svirko, Y.

K.-E. Peiponen, E. Gornov, Y. Svirko, Y. Ino, M. Kuwata-Gonokami, and V. Lucarini, Phys. Rev. B 72, 245109 (2005).
[CrossRef]

Szmyd, D. M.

D. M. Szmyd, P. Porro, A. Majerfeld, and S. Lagomarsino, J. Appl. Phys. 68, 2367 (1990).
[CrossRef]

Takagi, H.

N. Matsumoto, T. Fujii, K. Kageyama, H. Takagi, T. Nagashima, and M. Hangyo, Jpn. J. Appl. Phys. 48, 09KC11 (2009).
[CrossRef]

T. Hosokura, K. Kageyama, H. Takagi, and Y. Sakabe, J. Am. Ceram. Soc. 92, 253 (2009).
[CrossRef]

Tanaka, K.

H. Hirori, K. Yamashita, M. Nagai, and K. Tanaka, Jpn. J. Appl. Phys. 43, L1287 (2004).
[CrossRef]

Tiwald, T. E.

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, Appl. Phys. Lett. 95, 032102 (2009).
[CrossRef]

Williams, G. P.

Woollam, J. A.

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, Appl. Phys. Lett. 95, 032102 (2009).
[CrossRef]

Xi, X. X.

A. A. Sirenko, C. Bernhard, A. Golnik, A. M. Clark, J.-H. Hao, W. Si, and X. X. Xi, Nature 404, 373 (2000).
[CrossRef] [PubMed]

Yamashita, K.

H. Hirori, K. Yamashita, M. Nagai, and K. Tanaka, Jpn. J. Appl. Phys. 43, L1287 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

T. Nagashima and M. Hangyo, Appl. Phys. Lett. 79, 3917 (2001).
[CrossRef]

T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, Appl. Phys. Lett. 95, 032102 (2009).
[CrossRef]

T. I. Jeon and D. Grischkowsky, Appl. Phys. Lett. 72, 3032(1998).
[CrossRef]

J. Am. Ceram. Soc.

T. Hosokura, K. Kageyama, H. Takagi, and Y. Sakabe, J. Am. Ceram. Soc. 92, 253 (2009).
[CrossRef]

J. Appl. Phys.

D. M. Szmyd, P. Porro, A. Majerfeld, and S. Lagomarsino, J. Appl. Phys. 68, 2367 (1990).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

N. Matsumoto, T. Fujii, K. Kageyama, H. Takagi, T. Nagashima, and M. Hangyo, Jpn. J. Appl. Phys. 48, 09KC11 (2009).
[CrossRef]

H. Hirori, K. Yamashita, M. Nagai, and K. Tanaka, Jpn. J. Appl. Phys. 43, L1287 (2004).
[CrossRef]

Nature

A. A. Sirenko, C. Bernhard, A. Golnik, A. M. Clark, J.-H. Hao, W. Si, and X. X. Xi, Nature 404, 373 (2000).
[CrossRef] [PubMed]

Phys. Rev. B

F. Gervais and B. Piriou, Phys. Rev. B 10, 1642 (1974).
[CrossRef]

K.-E. Peiponen, E. Gornov, Y. Svirko, Y. Ino, M. Kuwata-Gonokami, and V. Lucarini, Phys. Rev. B 72, 245109 (2005).
[CrossRef]

R. Fukasawa and S. Perkowitz, Phys. Rev. B 50, 14119(1994).
[CrossRef]

Rev. Sci. Inst.

A. Pashkin, M. Kempa, H. Němec, F. Kadlec, and P. Kužel, Rev. Sci. Inst. 74, 4711 (2003).
[CrossRef]

Other

H. Fujiwara, Spectroscopic Ellipsometry (Wiley, 2007), Chap. 2.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for THz-TDSE.

Fig. 2
Fig. 2

Ellipsometric parameters (a) tan Ψ and (b) Δ of n- (open squares) and p-type (open circles) GaAs thin films, and complex dielectric constants of (c) n-type and (d) p-type GaAs thin films. Solid curves show the calculation results based on the Drude model. The inset in (b) shows waveforms of the p- and s-polarized THz waves reflected from the n-type GaAs thin film as a representative.

Fig. 3
Fig. 3

(a) Real and (b) imaginary parts of the dielectric constants for bulk [5] (open circles) and thin film of SrTiO 3 (open squares). The solid curves show calculation results for a generalized harmonic oscillator model.

Equations (1)

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r 012 ( p , s ) = r 01 ( p , s ) + r 12 ( p , s ) exp ( i 2 β ) 1 + r 01 ( p , s ) r 12 ( p , s ) exp ( i 2 β ) ,

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