Abstract

We demonstrate a method for reliably determining the electrical properties of graphene including the carrier scattering time and carrier drift mobility from terahertz time- domain spectroscopy measurements (THz-TDS). By comparing transients originating from directly transmitted pulses and the echoes from internal reflections in a substrate, we are able to extract electrical properties irrespective of random time delays between pulses emitted in a THz-TDS setup. If such time delays are not accounted for they can significantly influence the extracted properties of the material. The technique is useful for a robust determination of electrical properties from THz-TDS measurements and is compatible with substrate materials where transients from internal reflections are well-separated in time.

© 2017 Optical Society of America

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  1. J. L. Tomaino, A. D. Jameson, J. W. Kevek, M. J. Paul, A. M. van der Zande, R. A. Barton, P. L. McEuen, E. D. Minot, and Y.-S. Lee, “Terahertz imaging and spectroscopy of large-area single-layer graphene,” Opt. Express 19(1), 141–146 (2011).
    [Crossref] [PubMed]
  2. J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
    [Crossref]
  3. I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
    [Crossref] [PubMed]
  4. J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
    [Crossref] [PubMed]
  5. J. D. Buron, D. M. A. Mackenzie, D. H. Petersen, A. Pesquera, A. Centeno, P. Bøggild, A. Zurutuza, and P. U. Jepsen, “Terahertz wafer-scale mobility mapping of graphene on insulating substrates without a gate,” Opt. Express 23(24), 30721–30729 (2015).
    [Crossref] [PubMed]
  6. J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
    [Crossref]
  7. M. J. Paul, J. L. Tomaino, J. W. Kevek, T. Deborde, Z. J. Thompson, E. D. Minot, and Y. S. Lee, “Terahertz imaging of inhomogeneous electrodynamics in single-layer graphene embedded in dielectrics,” Appl. Phys. Lett. 101(9), 091109 (2012).
    [Crossref]
  8. J. D. Buron, F. Pizzocchero, P. U. Jepsen, D. H. Petersen, J. M. Caridad, B. S. Jessen, T. J. Booth, and P. Bøggild, “Graphene mobility mapping,” Sci. Rep. 5, 12305 (2015).
    [Crossref] [PubMed]
  9. C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
    [Crossref] [PubMed]
  10. M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
    [Crossref]
  11. P. Kužel, H. Němec, F. Kadlec, and C. Kadlec, “Gouy shift correction for highly accurate refractive index retrieval in time-domain terahertz spectroscopy,” Opt. Express 18(15), 15338–15348 (2010).
    [Crossref] [PubMed]
  12. P. Braeuninger-Weimer, B. Brennan, A. J. Pollard, and S. Hofmann, “Understanding and controlling Cu catalyzed graphene nucleation: the role of impurities, roughness and oxygen scavenging,” Chem. Mater. 28(24), 8905–8915 (2016).
    [Crossref]
  13. R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
    [Crossref] [PubMed]
  14. P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
    [Crossref]
  15. J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
    [Crossref] [PubMed]
  16. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
    [Crossref]
  17. M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48(5), 1592–1597 (2010).
    [Crossref]

2016 (2)

P. Braeuninger-Weimer, B. Brennan, A. J. Pollard, and S. Hofmann, “Understanding and controlling Cu catalyzed graphene nucleation: the role of impurities, roughness and oxygen scavenging,” Chem. Mater. 28(24), 8905–8915 (2016).
[Crossref]

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

2015 (3)

J. D. Buron, D. M. A. Mackenzie, D. H. Petersen, A. Pesquera, A. Centeno, P. Bøggild, A. Zurutuza, and P. U. Jepsen, “Terahertz wafer-scale mobility mapping of graphene on insulating substrates without a gate,” Opt. Express 23(24), 30721–30729 (2015).
[Crossref] [PubMed]

J. D. Buron, F. Pizzocchero, P. U. Jepsen, D. H. Petersen, J. M. Caridad, B. S. Jessen, T. J. Booth, and P. Bøggild, “Graphene mobility mapping,” Sci. Rep. 5, 12305 (2015).
[Crossref] [PubMed]

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

2014 (1)

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

2012 (4)

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

M. J. Paul, J. L. Tomaino, J. W. Kevek, T. Deborde, Z. J. Thompson, E. D. Minot, and Y. S. Lee, “Terahertz imaging of inhomogeneous electrodynamics in single-layer graphene embedded in dielectrics,” Appl. Phys. Lett. 101(9), 091109 (2012).
[Crossref]

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
[Crossref] [PubMed]

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

2011 (2)

J. L. Tomaino, A. D. Jameson, J. W. Kevek, M. J. Paul, A. M. van der Zande, R. A. Barton, P. L. McEuen, E. D. Minot, and Y.-S. Lee, “Terahertz imaging and spectroscopy of large-area single-layer graphene,” Opt. Express 19(1), 141–146 (2011).
[Crossref] [PubMed]

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

2010 (2)

P. Kužel, H. Němec, F. Kadlec, and C. Kadlec, “Gouy shift correction for highly accurate refractive index retrieval in time-domain terahertz spectroscopy,” Opt. Express 18(15), 15338–15348 (2010).
[Crossref] [PubMed]

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48(5), 1592–1597 (2010).
[Crossref]

2009 (2)

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

2007 (1)

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Achete, C. A.

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48(5), 1592–1597 (2010).
[Crossref]

Alexander-Webber, J. A.

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

Barton, R. A.

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

J. L. Tomaino, A. D. Jameson, J. W. Kevek, M. J. Paul, A. M. van der Zande, R. A. Barton, P. L. McEuen, E. D. Minot, and Y.-S. Lee, “Terahertz imaging and spectroscopy of large-area single-layer graphene,” Opt. Express 19(1), 141–146 (2011).
[Crossref] [PubMed]

Bechtel, H. A.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Blake, P.

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Bogani, L.

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

Bøggild, P.

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

J. D. Buron, D. M. A. Mackenzie, D. H. Petersen, A. Pesquera, A. Centeno, P. Bøggild, A. Zurutuza, and P. U. Jepsen, “Terahertz wafer-scale mobility mapping of graphene on insulating substrates without a gate,” Opt. Express 23(24), 30721–30729 (2015).
[Crossref] [PubMed]

J. D. Buron, F. Pizzocchero, P. U. Jepsen, D. H. Petersen, J. M. Caridad, B. S. Jessen, T. J. Booth, and P. Bøggild, “Graphene mobility mapping,” Sci. Rep. 5, 12305 (2015).
[Crossref] [PubMed]

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Booth, T.

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

Booth, T. J.

J. D. Buron, F. Pizzocchero, P. U. Jepsen, D. H. Petersen, J. M. Caridad, B. S. Jessen, T. J. Booth, and P. Bøggild, “Graphene mobility mapping,” Sci. Rep. 5, 12305 (2015).
[Crossref] [PubMed]

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Braeuninger-Weimer, P.

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

P. Braeuninger-Weimer, B. Brennan, A. J. Pollard, and S. Hofmann, “Understanding and controlling Cu catalyzed graphene nucleation: the role of impurities, roughness and oxygen scavenging,” Chem. Mater. 28(24), 8905–8915 (2016).
[Crossref]

Brennan, B.

P. Braeuninger-Weimer, B. Brennan, A. J. Pollard, and S. Hofmann, “Understanding and controlling Cu catalyzed graphene nucleation: the role of impurities, roughness and oxygen scavenging,” Chem. Mater. 28(24), 8905–8915 (2016).
[Crossref]

Burghard, M.

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

Buron, J. D.

J. D. Buron, F. Pizzocchero, P. U. Jepsen, D. H. Petersen, J. M. Caridad, B. S. Jessen, T. J. Booth, and P. Bøggild, “Graphene mobility mapping,” Sci. Rep. 5, 12305 (2015).
[Crossref] [PubMed]

J. D. Buron, D. M. A. Mackenzie, D. H. Petersen, A. Pesquera, A. Centeno, P. Bøggild, A. Zurutuza, and P. U. Jepsen, “Terahertz wafer-scale mobility mapping of graphene on insulating substrates without a gate,” Opt. Express 23(24), 30721–30729 (2015).
[Crossref] [PubMed]

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Capaz, R. B.

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48(5), 1592–1597 (2010).
[Crossref]

Caridad, J. M.

J. D. Buron, F. Pizzocchero, P. U. Jepsen, D. H. Petersen, J. M. Caridad, B. S. Jessen, T. J. Booth, and P. Bøggild, “Graphene mobility mapping,” Sci. Rep. 5, 12305 (2015).
[Crossref] [PubMed]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Centeno, A.

Cervetti, C.

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

Chae, S. J.

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
[Crossref] [PubMed]

Chen, C. F.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Choi, H.

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
[Crossref] [PubMed]

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

Cooke, D. G.

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Crommie, M. F.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Deborde, T.

M. J. Paul, J. L. Tomaino, J. W. Kevek, T. Deborde, Z. J. Thompson, E. D. Minot, and Y. S. Lee, “Terahertz imaging of inhomogeneous electrodynamics in single-layer graphene embedded in dielectrics,” Appl. Phys. Lett. 101(9), 091109 (2012).
[Crossref]

Dressel, M.

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

Ferreira, E. H. M.

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48(5), 1592–1597 (2010).
[Crossref]

Geim, A. K.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Geng, B.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Girit, C.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Gorshunov, B.

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

Guinea, F.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Hansen, O.

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Hao, Z.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Heintze, E.

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

Hilke, M.

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Hill, E. W.

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Hofmann, S.

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

P. Braeuninger-Weimer, B. Brennan, A. J. Pollard, and S. Hofmann, “Understanding and controlling Cu catalyzed graphene nucleation: the role of impurities, roughness and oxygen scavenging,” Chem. Mater. 28(24), 8905–8915 (2016).
[Crossref]

Horng, J.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Hoyer, A.

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

Jameson, A. D.

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

J. L. Tomaino, A. D. Jameson, J. W. Kevek, M. J. Paul, A. M. van der Zande, R. A. Barton, P. L. McEuen, E. D. Minot, and Y.-S. Lee, “Terahertz imaging and spectroscopy of large-area single-layer graphene,” Opt. Express 19(1), 141–146 (2011).
[Crossref] [PubMed]

Jansen, C.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

Jepsen, P. U.

J. D. Buron, F. Pizzocchero, P. U. Jepsen, D. H. Petersen, J. M. Caridad, B. S. Jessen, T. J. Booth, and P. Bøggild, “Graphene mobility mapping,” Sci. Rep. 5, 12305 (2015).
[Crossref] [PubMed]

J. D. Buron, D. M. A. Mackenzie, D. H. Petersen, A. Pesquera, A. Centeno, P. Bøggild, A. Zurutuza, and P. U. Jepsen, “Terahertz wafer-scale mobility mapping of graphene on insulating substrates without a gate,” Opt. Express 23(24), 30721–30729 (2015).
[Crossref] [PubMed]

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Jessen, B. S.

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

J. D. Buron, F. Pizzocchero, P. U. Jepsen, D. H. Petersen, J. M. Caridad, B. S. Jessen, T. J. Booth, and P. Bøggild, “Graphene mobility mapping,” Sci. Rep. 5, 12305 (2015).
[Crossref] [PubMed]

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

Jiang, D.

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Jorio, A.

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48(5), 1592–1597 (2010).
[Crossref]

Kadlec, C.

Kadlec, F.

Kern, K.

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

Kevek, J. W.

M. J. Paul, J. L. Tomaino, J. W. Kevek, T. Deborde, Z. J. Thompson, E. D. Minot, and Y. S. Lee, “Terahertz imaging of inhomogeneous electrodynamics in single-layer graphene embedded in dielectrics,” Appl. Phys. Lett. 101(9), 091109 (2012).
[Crossref]

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

J. L. Tomaino, A. D. Jameson, J. W. Kevek, M. J. Paul, A. M. van der Zande, R. A. Barton, P. L. McEuen, E. D. Minot, and Y.-S. Lee, “Terahertz imaging and spectroscopy of large-area single-layer graphene,” Opt. Express 19(1), 141–146 (2011).
[Crossref] [PubMed]

Kidambi, P. R.

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

Koch, M.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

Kužel, P.

Lee, Y. H.

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
[Crossref] [PubMed]

Lee, Y. S.

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

M. J. Paul, J. L. Tomaino, J. W. Kevek, T. Deborde, Z. J. Thompson, E. D. Minot, and Y. S. Lee, “Terahertz imaging of inhomogeneous electrodynamics in single-layer graphene embedded in dielectrics,” Appl. Phys. Lett. 101(9), 091109 (2012).
[Crossref]

Lee, Y.-S.

Lim, S.

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
[Crossref] [PubMed]

Lobanov, S.

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

Lucchese, M. M.

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48(5), 1592–1597 (2010).
[Crossref]

Mackenzie, D. M. A.

Maeng, I.

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
[Crossref] [PubMed]

Martin, M.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

McEuen, P. L.

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

J. L. Tomaino, A. D. Jameson, J. W. Kevek, M. J. Paul, A. M. van der Zande, R. A. Barton, P. L. McEuen, E. D. Minot, and Y.-S. Lee, “Terahertz imaging and spectroscopy of large-area single-layer graphene,” Opt. Express 19(1), 141–146 (2011).
[Crossref] [PubMed]

Minot, E. D.

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

M. J. Paul, J. L. Tomaino, J. W. Kevek, T. Deborde, Z. J. Thompson, E. D. Minot, and Y. S. Lee, “Terahertz imaging of inhomogeneous electrodynamics in single-layer graphene embedded in dielectrics,” Appl. Phys. Lett. 101(9), 091109 (2012).
[Crossref]

J. L. Tomaino, A. D. Jameson, J. W. Kevek, M. J. Paul, A. M. van der Zande, R. A. Barton, P. L. McEuen, E. D. Minot, and Y.-S. Lee, “Terahertz imaging and spectroscopy of large-area single-layer graphene,” Opt. Express 19(1), 141–146 (2011).
[Crossref] [PubMed]

Moutinho, M. V. O.

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48(5), 1592–1597 (2010).
[Crossref]

Nemec, H.

Nielsen, P. F.

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Novoselov, K. S.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Paul, M. J.

M. J. Paul, J. L. Tomaino, J. W. Kevek, T. Deborde, Z. J. Thompson, E. D. Minot, and Y. S. Lee, “Terahertz imaging of inhomogeneous electrodynamics in single-layer graphene embedded in dielectrics,” Appl. Phys. Lett. 101(9), 091109 (2012).
[Crossref]

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

J. L. Tomaino, A. D. Jameson, J. W. Kevek, M. J. Paul, A. M. van der Zande, R. A. Barton, P. L. McEuen, E. D. Minot, and Y.-S. Lee, “Terahertz imaging and spectroscopy of large-area single-layer graphene,” Opt. Express 19(1), 141–146 (2011).
[Crossref] [PubMed]

Peres, N. M. R.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Pesquera, A.

Petersen, D. H.

J. D. Buron, D. M. A. Mackenzie, D. H. Petersen, A. Pesquera, A. Centeno, P. Bøggild, A. Zurutuza, and P. U. Jepsen, “Terahertz wafer-scale mobility mapping of graphene on insulating substrates without a gate,” Opt. Express 23(24), 30721–30729 (2015).
[Crossref] [PubMed]

J. D. Buron, F. Pizzocchero, P. U. Jepsen, D. H. Petersen, J. M. Caridad, B. S. Jessen, T. J. Booth, and P. Bøggild, “Graphene mobility mapping,” Sci. Rep. 5, 12305 (2015).
[Crossref] [PubMed]

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Pizzocchero, F.

J. D. Buron, F. Pizzocchero, P. U. Jepsen, D. H. Petersen, J. M. Caridad, B. S. Jessen, T. J. Booth, and P. Bøggild, “Graphene mobility mapping,” Sci. Rep. 5, 12305 (2015).
[Crossref] [PubMed]

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

Pollard, A. J.

P. Braeuninger-Weimer, B. Brennan, A. J. Pollard, and S. Hofmann, “Understanding and controlling Cu catalyzed graphene nucleation: the role of impurities, roughness and oxygen scavenging,” Chem. Mater. 28(24), 8905–8915 (2016).
[Crossref]

Scheller, M.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

Shen, Y. R.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Son, J. H.

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
[Crossref] [PubMed]

Stavale, F.

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48(5), 1592–1597 (2010).
[Crossref]

Sun, J.

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Tappertzhofen, S.

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

Thompson, Z. J.

M. J. Paul, J. L. Tomaino, J. W. Kevek, T. Deborde, Z. J. Thompson, E. D. Minot, and Y. S. Lee, “Terahertz imaging of inhomogeneous electrodynamics in single-layer graphene embedded in dielectrics,” Appl. Phys. Lett. 101(9), 091109 (2012).
[Crossref]

Tomaino, J. L.

M. J. Paul, J. L. Tomaino, J. W. Kevek, T. Deborde, Z. J. Thompson, E. D. Minot, and Y. S. Lee, “Terahertz imaging of inhomogeneous electrodynamics in single-layer graphene embedded in dielectrics,” Appl. Phys. Lett. 101(9), 091109 (2012).
[Crossref]

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

J. L. Tomaino, A. D. Jameson, J. W. Kevek, M. J. Paul, A. M. van der Zande, R. A. Barton, P. L. McEuen, E. D. Minot, and Y.-S. Lee, “Terahertz imaging and spectroscopy of large-area single-layer graphene,” Opt. Express 19(1), 141–146 (2011).
[Crossref] [PubMed]

Van Der Zande, A. M.

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

J. L. Tomaino, A. D. Jameson, J. W. Kevek, M. J. Paul, A. M. van der Zande, R. A. Barton, P. L. McEuen, E. D. Minot, and Y.-S. Lee, “Terahertz imaging and spectroscopy of large-area single-layer graphene,” Opt. Express 19(1), 141–146 (2011).
[Crossref] [PubMed]

Van Veldhoven, Z. A.

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

Vilani, C.

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48(5), 1592–1597 (2010).
[Crossref]

Wang, F.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Wang, R.

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

Whelan, P. R.

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

Whiteway, E.

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Yang, R.

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Yurgens, A.

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Zettl, A.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Zhang, Y.

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Zhukova, E.

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

Zurutuza, A.

ACS Appl. Mater. Interfaces (1)

R. Wang, P. R. Whelan, P. Braeuninger-Weimer, S. Tappertzhofen, J. A. Alexander-Webber, Z. A. Van Veldhoven, P. R. Kidambi, B. S. Jessen, T. Booth, P. Bøggild, and S. Hofmann, “Catalyst interface engineering for improved 2D film lift-off and transfer,” ACS Appl. Mater. Interfaces 8(48), 33072–33082 (2016).
[Crossref] [PubMed]

Adv. Mater. (1)

C. Cervetti, E. Heintze, B. Gorshunov, E. Zhukova, S. Lobanov, A. Hoyer, M. Burghard, K. Kern, M. Dressel, and L. Bogani, “Sub-terahertz frequency-domain spectroscopy reveals single-grain mobility and scatter influence of large-area graphene,” Adv. Mater. 27(16), 2635–2641 (2015).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

M. J. Paul, J. L. Tomaino, J. W. Kevek, T. Deborde, Z. J. Thompson, E. D. Minot, and Y. S. Lee, “Terahertz imaging of inhomogeneous electrodynamics in single-layer graphene embedded in dielectrics,” Appl. Phys. Lett. 101(9), 091109 (2012).
[Crossref]

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91(6), 063124 (2007).
[Crossref]

Carbon (1)

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48(5), 1592–1597 (2010).
[Crossref]

Chem. Mater. (1)

P. Braeuninger-Weimer, B. Brennan, A. J. Pollard, and S. Hofmann, “Understanding and controlling Cu catalyzed graphene nucleation: the role of impurities, roughness and oxygen scavenging,” Chem. Mater. 28(24), 8905–8915 (2016).
[Crossref]

J. Infrared Millim. Terahertz Waves (1)

J. L. Tomaino, A. D. Jameson, M. J. Paul, J. W. Kevek, A. M. Van Der Zande, R. A. Barton, H. Choi, P. L. McEuen, E. D. Minot, and Y. S. Lee, “High-contrast imaging of graphene via time-domain terahertz spectroscopy,” J. Infrared Millim. Terahertz Waves 33(8), 839–845 (2012).
[Crossref]

Nano Lett. (3)

J. D. Buron, F. Pizzocchero, B. S. Jessen, T. J. Booth, P. F. Nielsen, O. Hansen, M. Hilke, E. Whiteway, P. U. Jepsen, P. Bøggild, and D. H. Petersen, “Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe,” Nano Lett. 14(11), 6348–6355 (2014).
[Crossref] [PubMed]

I. Maeng, S. Lim, S. J. Chae, Y. H. Lee, H. Choi, and J. H. Son, “Gate-controlled nonlinear conductivity of Dirac fermion in graphene field-effect transistors measured by terahertz time-domain spectroscopy,” Nano Lett. 12(2), 551–555 (2012).
[Crossref] [PubMed]

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping,” Nano Lett. 12(10), 5074–5081 (2012).
[Crossref] [PubMed]

Opt. Commun. (1)

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

Opt. Express (3)

Phys. Rev. B – Condens. Matter Mater. Phys. (1)

J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B – Condens. Matter Mater. Phys. 83(16), 1–5 (2011).
[Crossref]

Rev. Mod. Phys. (1)

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Sci. Rep. (1)

J. D. Buron, F. Pizzocchero, P. U. Jepsen, D. H. Petersen, J. M. Caridad, B. S. Jessen, T. J. Booth, and P. Bøggild, “Graphene mobility mapping,” Sci. Rep. 5, 12305 (2015).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Waveform of THz pulses after transmission through a Si substrate without and with graphene. The inset shows how different echoes are generated by internal reflections in the substrate. (b) Sheet conductivity spectra for graphene on Si extracted from the first echo together with fits to the Drude model. (c) Optical map of the graphene sample combined with map of σ1 from the directly transmitted pulse averaged from 0.8 to 0.9 THz. White arrows indicate the scanning direction during the THz-TDS measurement and the grey box illustrates the area chosen for performing timing jitter corrections. White crosses mark different areas used as sample reference points. (d) A representative Raman spectrum from the sample shown in (c) with a histogram of Raman I(D)/(G) peak ratios in the inset.

Fig. 2
Fig. 2

(a) Time delay between individual waveforms measured in dry air. Inset shows one waveform. (b) Sheet conductivity spectra for graphene on Si extracted from the directly transmitted pulse and the first echo. (c) Sheet conductivity spectra from same pixel as (b) after correction for timing jitter. (d) Timing jitter delay in each pixel from the highlighted area in Fig. 1(c).

Fig. 3
Fig. 3

Histograms of (a-c) τsc and (d-f) µdrift for graphene extracted from the directly transmitted pulse from the area highlighted in Fig. 1(c). The five colors corresponds to properties calculated using five different reference areas on the sample, respectively and are plotted on top of each other. (a,d) Full fit after correction for timing jitter, (b,e) Full fit uncorrected, (c,f) Real-part fit after correction for timing jitter. Average values and standard deviations shown on plots cover all five data sets.

Fig. 4
Fig. 4

Comparisons of electrical properties of graphene extracted from THz-TDS measurements using a full fit (FF) to the Drude model and only fitting to the real-part fit (RF) including non-corrected (ucorr) data and data after correction (corr) for timing jitter. (0) refers to data from directly transmitted pulses and (1) to the first reflected echo. (a) σDC. (b) τsc. (c) Ns. (d) µdrift. The bars show the average value based on measurements from five different reference areas with error bars showing the standard deviation.

Equations (6)

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T ˜ film (0) (ω)= E ˜ film (0) (ω) E ˜ sub (0) (ω) = E 0 t ˜ film t ˜ sub,air e iδ E 0 t ˜ air,sub t ˜ sub,air e iδ = t ˜ film t ˜ air,sub ,
σ ˜ s (0) (ω)= 1 Z 0 ( n A T ˜ (0) film (ω) n A ),
σ ˜ s (1) (ω)= ± n A n A 2 +4 n A 2 n B T ˜ (1) film (ω)+4 n B 2 T ˜ (1) film (ω) n A 2 2 n A n B T ˜ (1) film (ω) 2 n B Z 0 T ˜ (1) film (ω) ,
σ ˜ s (ω)= σ DC 1iω τ sc .
N s = π 2 e 4 ν F 2 ( σ DC τ sc ) 2 ,
μ drift = σ DC e N s ,

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