Abstract

Terahertz time-domain spectroscopy (THz–TDS) relies heavily on knowing precisely the thickness or refractive index of a material. In practice, one of these values is assumed to be known, or their product is numerically optimized to converge on suitable values. Both approaches are prone to errors and may mask some real features or properties of the material being studied. To eliminate these errors, we use THz–TDS in reflection geometry to accurately and independently determine both thickness and refractive index by illuminating the step-edge of a substrate atop a metal stage. This method relies solely on the relative time delay among three reflected pulses, and therefore forgoes the need for optimization or assumption of substrate parameters.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. E. Dadrasnia and H. Lamela, “Terahertz conductivity characterization of nanostructured graphene-like films for optoelectronic applications,” J. Nanophotonics 9(1), 093598 (2015).
    [Crossref]
  2. P. R. Whelan, K. Iwaszczuk, R. Z. Wang, S. Hofmann, P. Bøggild, and P. U. Jepsen, “Robust mapping of electrical properties of graphene from terahertz time-domain spectroscopy with timing jitter correction,” Opt. Express 25(3), 2725–2732 (2017).
    [Crossref]
  3. A. J. Fitzgerald, E. Pickwell-MacPherson, and V. P. Wallace, “Use of finite difference time domain simulations and Debye theory for modelling the terahertz reflection response of normal and tumour breast tissue,” PLoS One 9(7), e99291 (2014).
    [Crossref] [PubMed]
  4. K. Shiraga, T. Suzuki, N. Kondo, K. Tanaka, and Y. Ogawa, “Hydration state inside HeLa cell monolayer investigated with terahertz spectroscopy,” Appl. Phys. Lett. 106(25), 5 (2015).
    [Crossref]
  5. Y. Zhou, L. Zhu, M. Qi, X. Xu, J. Bai, Z. Ren, and L. Wang, “Terahertz wave reflection impedance matching properties of graphene layers at oblique incidence,” Carbon 96(1), 1129–1137 (2016).
    [Crossref]
  6. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
    [Crossref]
  7. L. Duvillaret, F. Garet, and J. Coutaz, “Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,” Appl. Opt. 38(2), 409–415 (1999).
    [Crossref]
  8. W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Material parameter extraction for terahertz time-domain spectroscopy using fixed-point iteration,” Proc. SPIE 5840(1), 221–231 (2005).
    [Crossref]
  9. I. Pupeza, R. Wilk, and M. Koch, “Highly accurate optical material parameter determination with THz time-domain spectroscopy,” Opt. Express 15(7), 4335–4350 (2007).
    [Crossref] [PubMed]
  10. J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, “Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon,” J. Opt. Soc. Am. B 21(7), 1379–1386 (2004).
    [Crossref]
  11. C.-Y. Jen and C. Richter, “Sample thickness measurement with THz-TDS: Resolution and implications,” J. Infrared Milli. Terahz. Waves 35(10), 840–859 (2014).
    [Crossref]
  12. P. Jepsen, U. Møller, and H. Merbold, “Investigation of aqueous alcohol and sugar solutions with reflection terahertz time-domain spectroscopy,” Opt. Express 15(22), 14717–14737 (2007).
    [Crossref] [PubMed]
  13. S. Fan, E. P. J. Parrott, B. S. Y. Ung, and E. Pickwell-MacPherson, “Calibration method to improve the accuracy of THz imaging and spectroscopy in reflection geometry,” Photonics Res. 4(3), A29 (2016).
    [Crossref]
  14. W. E. Lai, H. W. Zhang, Y. H. Zhu, and Q. Y. Wen, “A novel method of terahertz spectroscopy and imaging in reflection geometry,” Appl. Spectrosc. 67(1), 36–39 (2013).
    [Crossref] [PubMed]
  15. T.-I. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78(6), 1106–1109 (1997).
    [Crossref]
  16. K. Willis, S. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013).
    [Crossref]

2017 (1)

2016 (2)

Y. Zhou, L. Zhu, M. Qi, X. Xu, J. Bai, Z. Ren, and L. Wang, “Terahertz wave reflection impedance matching properties of graphene layers at oblique incidence,” Carbon 96(1), 1129–1137 (2016).
[Crossref]

S. Fan, E. P. J. Parrott, B. S. Y. Ung, and E. Pickwell-MacPherson, “Calibration method to improve the accuracy of THz imaging and spectroscopy in reflection geometry,” Photonics Res. 4(3), A29 (2016).
[Crossref]

2015 (2)

E. Dadrasnia and H. Lamela, “Terahertz conductivity characterization of nanostructured graphene-like films for optoelectronic applications,” J. Nanophotonics 9(1), 093598 (2015).
[Crossref]

K. Shiraga, T. Suzuki, N. Kondo, K. Tanaka, and Y. Ogawa, “Hydration state inside HeLa cell monolayer investigated with terahertz spectroscopy,” Appl. Phys. Lett. 106(25), 5 (2015).
[Crossref]

2014 (2)

A. J. Fitzgerald, E. Pickwell-MacPherson, and V. P. Wallace, “Use of finite difference time domain simulations and Debye theory for modelling the terahertz reflection response of normal and tumour breast tissue,” PLoS One 9(7), e99291 (2014).
[Crossref] [PubMed]

C.-Y. Jen and C. Richter, “Sample thickness measurement with THz-TDS: Resolution and implications,” J. Infrared Milli. Terahz. Waves 35(10), 840–859 (2014).
[Crossref]

2013 (2)

W. E. Lai, H. W. Zhang, Y. H. Zhu, and Q. Y. Wen, “A novel method of terahertz spectroscopy and imaging in reflection geometry,” Appl. Spectrosc. 67(1), 36–39 (2013).
[Crossref] [PubMed]

K. Willis, S. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013).
[Crossref]

2011 (1)

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
[Crossref]

2007 (2)

2005 (1)

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Material parameter extraction for terahertz time-domain spectroscopy using fixed-point iteration,” Proc. SPIE 5840(1), 221–231 (2005).
[Crossref]

2004 (1)

1999 (1)

1997 (1)

T.-I. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78(6), 1106–1109 (1997).
[Crossref]

Abbott, D.

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Material parameter extraction for terahertz time-domain spectroscopy using fixed-point iteration,” Proc. SPIE 5840(1), 221–231 (2005).
[Crossref]

Bai, J.

Y. Zhou, L. Zhu, M. Qi, X. Xu, J. Bai, Z. Ren, and L. Wang, “Terahertz wave reflection impedance matching properties of graphene layers at oblique incidence,” Carbon 96(1), 1129–1137 (2016).
[Crossref]

Bøggild, P.

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
[Crossref]

Coutaz, J.

Dadrasnia, E.

E. Dadrasnia and H. Lamela, “Terahertz conductivity characterization of nanostructured graphene-like films for optoelectronic applications,” J. Nanophotonics 9(1), 093598 (2015).
[Crossref]

Dai, J.

Duvillaret, L.

Fan, S.

S. Fan, E. P. J. Parrott, B. S. Y. Ung, and E. Pickwell-MacPherson, “Calibration method to improve the accuracy of THz imaging and spectroscopy in reflection geometry,” Photonics Res. 4(3), A29 (2016).
[Crossref]

Ferguson, B.

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Material parameter extraction for terahertz time-domain spectroscopy using fixed-point iteration,” Proc. SPIE 5840(1), 221–231 (2005).
[Crossref]

Fitzgerald, A. J.

A. J. Fitzgerald, E. Pickwell-MacPherson, and V. P. Wallace, “Use of finite difference time domain simulations and Debye theory for modelling the terahertz reflection response of normal and tumour breast tissue,” PLoS One 9(7), e99291 (2014).
[Crossref] [PubMed]

Garet, F.

Grischkowsky, D.

Hagness, S.

K. Willis, S. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013).
[Crossref]

Hofmann, S.

Iwaszczuk, K.

Jen, C.-Y.

C.-Y. Jen and C. Richter, “Sample thickness measurement with THz-TDS: Resolution and implications,” J. Infrared Milli. Terahz. Waves 35(10), 840–859 (2014).
[Crossref]

Jeon, T.-I.

T.-I. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78(6), 1106–1109 (1997).
[Crossref]

Jepsen, P.

Jepsen, P. U.

Knezevic, I.

K. Willis, S. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013).
[Crossref]

Koch, M.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
[Crossref]

I. Pupeza, R. Wilk, and M. Koch, “Highly accurate optical material parameter determination with THz time-domain spectroscopy,” Opt. Express 15(7), 4335–4350 (2007).
[Crossref] [PubMed]

Kondo, N.

K. Shiraga, T. Suzuki, N. Kondo, K. Tanaka, and Y. Ogawa, “Hydration state inside HeLa cell monolayer investigated with terahertz spectroscopy,” Appl. Phys. Lett. 106(25), 5 (2015).
[Crossref]

Lai, W. E.

Lamela, H.

E. Dadrasnia and H. Lamela, “Terahertz conductivity characterization of nanostructured graphene-like films for optoelectronic applications,” J. Nanophotonics 9(1), 093598 (2015).
[Crossref]

Merbold, H.

Mickan, S. P.

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Material parameter extraction for terahertz time-domain spectroscopy using fixed-point iteration,” Proc. SPIE 5840(1), 221–231 (2005).
[Crossref]

Møller, U.

Ogawa, Y.

K. Shiraga, T. Suzuki, N. Kondo, K. Tanaka, and Y. Ogawa, “Hydration state inside HeLa cell monolayer investigated with terahertz spectroscopy,” Appl. Phys. Lett. 106(25), 5 (2015).
[Crossref]

Parrott, E. P. J.

S. Fan, E. P. J. Parrott, B. S. Y. Ung, and E. Pickwell-MacPherson, “Calibration method to improve the accuracy of THz imaging and spectroscopy in reflection geometry,” Photonics Res. 4(3), A29 (2016).
[Crossref]

Pickwell-MacPherson, E.

S. Fan, E. P. J. Parrott, B. S. Y. Ung, and E. Pickwell-MacPherson, “Calibration method to improve the accuracy of THz imaging and spectroscopy in reflection geometry,” Photonics Res. 4(3), A29 (2016).
[Crossref]

A. J. Fitzgerald, E. Pickwell-MacPherson, and V. P. Wallace, “Use of finite difference time domain simulations and Debye theory for modelling the terahertz reflection response of normal and tumour breast tissue,” PLoS One 9(7), e99291 (2014).
[Crossref] [PubMed]

Pupeza, I.

Qi, M.

Y. Zhou, L. Zhu, M. Qi, X. Xu, J. Bai, Z. Ren, and L. Wang, “Terahertz wave reflection impedance matching properties of graphene layers at oblique incidence,” Carbon 96(1), 1129–1137 (2016).
[Crossref]

Rainsford, T.

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Material parameter extraction for terahertz time-domain spectroscopy using fixed-point iteration,” Proc. SPIE 5840(1), 221–231 (2005).
[Crossref]

Ren, Z.

Y. Zhou, L. Zhu, M. Qi, X. Xu, J. Bai, Z. Ren, and L. Wang, “Terahertz wave reflection impedance matching properties of graphene layers at oblique incidence,” Carbon 96(1), 1129–1137 (2016).
[Crossref]

Richter, C.

C.-Y. Jen and C. Richter, “Sample thickness measurement with THz-TDS: Resolution and implications,” J. Infrared Milli. Terahz. Waves 35(10), 840–859 (2014).
[Crossref]

Shiraga, K.

K. Shiraga, T. Suzuki, N. Kondo, K. Tanaka, and Y. Ogawa, “Hydration state inside HeLa cell monolayer investigated with terahertz spectroscopy,” Appl. Phys. Lett. 106(25), 5 (2015).
[Crossref]

Suzuki, T.

K. Shiraga, T. Suzuki, N. Kondo, K. Tanaka, and Y. Ogawa, “Hydration state inside HeLa cell monolayer investigated with terahertz spectroscopy,” Appl. Phys. Lett. 106(25), 5 (2015).
[Crossref]

Tanaka, K.

K. Shiraga, T. Suzuki, N. Kondo, K. Tanaka, and Y. Ogawa, “Hydration state inside HeLa cell monolayer investigated with terahertz spectroscopy,” Appl. Phys. Lett. 106(25), 5 (2015).
[Crossref]

Ung, B. S. Y.

S. Fan, E. P. J. Parrott, B. S. Y. Ung, and E. Pickwell-MacPherson, “Calibration method to improve the accuracy of THz imaging and spectroscopy in reflection geometry,” Photonics Res. 4(3), A29 (2016).
[Crossref]

Wallace, V. P.

A. J. Fitzgerald, E. Pickwell-MacPherson, and V. P. Wallace, “Use of finite difference time domain simulations and Debye theory for modelling the terahertz reflection response of normal and tumour breast tissue,” PLoS One 9(7), e99291 (2014).
[Crossref] [PubMed]

Wang, L.

Y. Zhou, L. Zhu, M. Qi, X. Xu, J. Bai, Z. Ren, and L. Wang, “Terahertz wave reflection impedance matching properties of graphene layers at oblique incidence,” Carbon 96(1), 1129–1137 (2016).
[Crossref]

Wang, R. Z.

Wen, Q. Y.

Whelan, P. R.

Wilk, R.

Willis, K.

K. Willis, S. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013).
[Crossref]

Withayachumnankul, W.

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Material parameter extraction for terahertz time-domain spectroscopy using fixed-point iteration,” Proc. SPIE 5840(1), 221–231 (2005).
[Crossref]

Xu, X.

Y. Zhou, L. Zhu, M. Qi, X. Xu, J. Bai, Z. Ren, and L. Wang, “Terahertz wave reflection impedance matching properties of graphene layers at oblique incidence,” Carbon 96(1), 1129–1137 (2016).
[Crossref]

Zhang, H. W.

Zhang, J.

Zhang, W.

Zhou, Y.

Y. Zhou, L. Zhu, M. Qi, X. Xu, J. Bai, Z. Ren, and L. Wang, “Terahertz wave reflection impedance matching properties of graphene layers at oblique incidence,” Carbon 96(1), 1129–1137 (2016).
[Crossref]

Zhu, L.

Y. Zhou, L. Zhu, M. Qi, X. Xu, J. Bai, Z. Ren, and L. Wang, “Terahertz wave reflection impedance matching properties of graphene layers at oblique incidence,” Carbon 96(1), 1129–1137 (2016).
[Crossref]

Zhu, Y. H.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

K. Shiraga, T. Suzuki, N. Kondo, K. Tanaka, and Y. Ogawa, “Hydration state inside HeLa cell monolayer investigated with terahertz spectroscopy,” Appl. Phys. Lett. 106(25), 5 (2015).
[Crossref]

K. Willis, S. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013).
[Crossref]

Appl. Spectrosc. (1)

Carbon (1)

Y. Zhou, L. Zhu, M. Qi, X. Xu, J. Bai, Z. Ren, and L. Wang, “Terahertz wave reflection impedance matching properties of graphene layers at oblique incidence,” Carbon 96(1), 1129–1137 (2016).
[Crossref]

J. Infrared Milli. Terahz. Waves (1)

C.-Y. Jen and C. Richter, “Sample thickness measurement with THz-TDS: Resolution and implications,” J. Infrared Milli. Terahz. Waves 35(10), 840–859 (2014).
[Crossref]

J. Nanophotonics (1)

E. Dadrasnia and H. Lamela, “Terahertz conductivity characterization of nanostructured graphene-like films for optoelectronic applications,” J. Nanophotonics 9(1), 093598 (2015).
[Crossref]

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

Laser Photonics Rev. (1)

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
[Crossref]

Opt. Express (3)

Photonics Res. (1)

S. Fan, E. P. J. Parrott, B. S. Y. Ung, and E. Pickwell-MacPherson, “Calibration method to improve the accuracy of THz imaging and spectroscopy in reflection geometry,” Photonics Res. 4(3), A29 (2016).
[Crossref]

Phys. Rev. Lett. (1)

T.-I. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78(6), 1106–1109 (1997).
[Crossref]

PLoS One (1)

A. J. Fitzgerald, E. Pickwell-MacPherson, and V. P. Wallace, “Use of finite difference time domain simulations and Debye theory for modelling the terahertz reflection response of normal and tumour breast tissue,” PLoS One 9(7), e99291 (2014).
[Crossref] [PubMed]

Proc. SPIE (1)

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Material parameter extraction for terahertz time-domain spectroscopy using fixed-point iteration,” Proc. SPIE 5840(1), 221–231 (2005).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 Fractional reflection at substrate step-edge.
Fig. 2
Fig. 2 Time-domain measurement results.
Fig. 3
Fig. 3 Complex refractive index of Si wafers with different resistivities.

Tables (1)

Tables Icon

Table 1 Thicknesses L and refractive indices nsub for Si wafers with different resistivities ρ.

Equations (14)

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

Δ t = t stage t main
c Δ t = 2 L sub cos θ i ( 2 L sub cos θ i sin θ i ) sin θ i
= 2 L sub cos θ i
L sub = c Δ t 2 cos θ i
Δ t = t echo t main
c Δ t = 2 L sub cos θ t n sub ( 2 L sub cos θ t sin θ t ) sin θ i
n sub sin θ t = n air sin θ i
n sub cos θ t = ( n sub 2 sin 2 θ i ) 1 / 2
c Δ t = 2 L sub cos θ t n sub 2 L sub cos θ t n sub sin 2 θ t
= 2 L sub n sub cos θ t
n sub = [ ( c Δ t 2 L sub ) 2 + sin 2 θ i ] 1 / 2
| E ˜ echo | | E ˜ main | exp ( j [ ϕ echo ϕ main ] ) = T air sub R sub air T sub air R air sub exp ( j 2 ω c n ˜ sub L sub cos θ t )
n sub = [ ( c [ ϕ echo ϕ main ] 2 ω L sub ) 2 + sin 2 θ i ] 1 / 2
κ sub = c 2 ω L sub cos θ t ( log [ | E ˜ echo | | E ˜ main | ] log [ T air sub T sub air ] )

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