Terahertz imaging and spectroscopy of large-area single-layer graphene

doi:10.1364/OE.19.000141

Terahertz imaging and spectroscopy of large-area single-layer graphene

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 Yun-Shik Lee »View Author Affiliations

Optics Express, Vol. 19, Issue 1, pp. 141-146 (2011)
http://dx.doi.org/10.1364/OE.19.000141

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▸ Article Outline
– Abstract
1. Introduction
2. Experiment
3. Power transmission: 2-D imaging and sheet conductivity calculation
4. Terahertz time-domain spectroscopy and conductivity spectra
5. Conclusion
– References and links

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Abstract

We demonstrate terahertz (THz) imaging and spectroscopy of a 15 × 15-mm² single-layer graphene film on Si using broadband THz pulses. The THz images clearly map out the THz carrier dynamics of the graphene-on-Si sample, allowing us to measure sheet conductivity with sub-mm resolution without fabricating electrodes. The THz carrier dynamics are dominated by intraband transitions and the THz-induced electron motion is characterized by a flat spectral response. A theoretical analysis based on the Fresnel coefficients for a metallic thin film shows that the local sheet conductivity varies across the sample from σ_s = 1.7 × 10⁻³ to 2.4 × 10⁻³ Ω⁻¹ (sheet resistance, ρ_s = 420 - 590 Ω/sq).

1. Introduction

Graphene is composed of a single-atom-thick layer of carbon atoms arranged in a two-dimensional honeycomb lattice [1

K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef] [PubMed]

]. The unique electronic structure of graphene gives rise to massless charge carriers and ballistic transport on a submicron scale at room temperature [2

A. H. Castro Neto, 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]

Y. Zhang, J. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005). [CrossRef] [PubMed]

]. The exceptional electronic properties of graphene have sparked intensive research into futuristic applications ranging from nanometer-scale switches to single molecule detection [4

K. Geim, “Graphene: Status and Prospect,” Science 324(5934), 1530–1534 (2009). [CrossRef] [PubMed]

–9

Y.-M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P. Avouris, “Operation of Graphene Transistors at Gigahertz Frequencies,” Nano Lett. 9(1), 422–426 (2009). [CrossRef]

]. In particular, the high electron mobility of graphene points to great potential for broadband communications and high-speed electronics operating at terahertz (THz) switching rates [10

H. Wang, D. Nezich, J. Kong, and T. Palacios, “Graphene frequency multipliers,” IEEE Electron Device Lett. 30(5), 547–549 (2009). [CrossRef]

–12

V. Ryzhii, “Terahertz plasma waves in gated graphene heterostructures,” Jpn. J. Appl. Phys. 45(35), L923–L925 (2006). [CrossRef]

]. Practical device applications require large-area graphene films, therefore, there is great interest in optimizing the growth of high-quality graphene films [13

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and Coherence in Patterned Epitaxial Graphene,” Science 312(5777), 1191–1196 (2006). [CrossRef] [PubMed]

–15

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009). [CrossRef] [PubMed]

] and probing the electronic properties of these films at ultrafast time scales. This interest motivates our current measurements of large-area graphene by THz imaging and time-domain spectroscopy.

So far, two methods of graphene fabrication have shown promising results for scalable production; (i) epitaxial growth on SiC substrates [13

] and (ii) chemical vapor deposition (CVD) on metal (Ni or Cu) layers [14

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009). [CrossRef] [PubMed]

,15

]. Epitaxial graphene on SiC has been studied by THz spectroscopy which yielded an estimate of carrier scattering time ~2 fs [16

H. Choi, F. Borondics, D. A. Siegel, S. Y. Zhou, M. C. Martin, A. Lanzara, and R. A. Kaindl, “Broadband electromagnetic response and ultrafast dynamics of few-layer epitaxial graphene,” Appl. Phys. Lett. 94(17), 172102 (2009). [CrossRef]

]. Growth of graphene by CVD onto Cu foil yields large-area graphene that is > 90% single layer [15

] and has recently been scaled up to the meter scale [17

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. Ri Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Özyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010). [CrossRef] [PubMed]

]. After wet transfer of graphene from Cu to a device substrate, typical carrier sheet density is n _2d ~4 × 10¹² cm⁻² [17

]. Reported sheet resistances of such single layer graphene vary widely, for example ρ _s = 150 Ω/sq [17

] versus 510 Ω/sq [18

Y. Lee, S. Bae, H. Jang, S. Jang, S.-E. Zhu, S. H. Sim, Y. I. Song, B. H. Hong, and J.-H. Ahn, “Wafer-Scale Synthesis and Transfer of Graphene Films,” Nano Lett. 10(2), 490–493 (2010). [CrossRef] [PubMed]

], corresponding to effective mobilities, μ = (ρ_s n _2d e)⁻¹ ~10,000 cm²s⁻¹V⁻¹ and 3,000 cm²s⁻¹V⁻¹ respectively.

In this paper, we present the first THz imaging and time-domain spectroscopy (TDS) of large area, single-layer graphene that is grown on Cu-foil and subsequently transferred to a substrate. We have measured the transmission of a pulsed, spatially-focused, broadband THz beam through the sample. Transmission is consistent with a sheet conductivity σ_s > 30σ _q = 30⋅e ²/4ℏ, i.e., at least 30 times larger than the optical sheet conductivity associated with interband transitions in graphene [19

K. F. Mak, M. Y. Sfeir, Y. Wu, C.-H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the Optical Conductivity of Graphene,” Phys. Rev. Lett. 101(19), 196405 (2008). [CrossRef] [PubMed]

]. Our measurements indicate that the optical response of graphene in the THz band is dominated by intraband transitions rather than interband transitions. The spectral response is flat, suggesting that our probe frequencies are well below the Drude roll-off frequency. By measuring THz transmission at discrete points across a graphene film we are able to map out sheet conductivity as a function of position. In contrast to conventional measurements of sheet conductivity, our THz imaging technique does not require patterning of graphene or fabrication of electrical contacts.

2. Experiment

Graphene was grown on Cu foil (Alfa Aesar, 25-μm thickness) at a temperature of 1000°C under a flow of methane (158 sccm) and hydrogen (6 sccm) inside a one-inch tube furnace [15

]. To promote growth of single-layer graphene the pressure of the CVD system was reduced to 5.5 Torr [15

]. To transfer the graphene from Cu to a Si wafer we used methods developed by previous authors [14

,15

]. High resistivity Si was used due to its high transparency to THz radiation. The top surface of the graphene-coated Cu foil was covered with PMMA (500nm thickness). The Cu was etched away by floating the sample in a FeCl₃-based solution (CE-200, Transene) leaving behind a PMMA-graphene film. The PMMA-graphene film was then washed in a series of six DI water baths and scooped out of solution using the Si substrate. The sample was allowed to air dry for 6 hours to promote adhesion of the graphene to the Si. Finally the PMMA was removed by a 6 hour soak in methylene chloride followed by 10 minute baths in acetone and IPA. After growth, the graphene on Si was verified to be predominately single-layer with low disorder by micro-Raman spectroscopy (Fig. 1 ) [20

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006). [CrossRef] [PubMed]

]. The position of the G-peak (1589 cm⁻¹) is consistent with a doping level ~4 x 10¹² cm⁻² [21

S. Pisana, M. Lazzeri, C. Casiraghi, K. S. Novoselov, A. K. Geim, A. C. Ferrari, and F. Mauri, “Breakdown of the adiabatic Born–Oppenheimer approximation in graphene,” Nat. Mater. 6(3), 198–201 (2007). [CrossRef] [PubMed]

]. Extensive characterization of control samples was also performed using micro-Raman spectroscopy and scanning electron microscopy. We consistently find that the growth method produces > 90% coverage of single layer graphene.

Fig. 1 Raman spectra from the graphene-on-Si sample. The background signal from bare Si has been subtracted. The integrated intensity of the 2D peak is more than double the G peak. There is no disorder-induced peak apparent at 1345 cm⁻¹. The same ratio of G peak to 2D peak was observed at multiple points across the graphene film.

We carried out two-dimensional raster scans of the graphene sample in a transmission geometry using broadband THz pulses. The broadband THz pulses were generated by optical rectification of femtosecond laser pulses in a 1-mm ZnTe crystal. The light source was a 1-kHz Ti:sapphire amplifier producing 800-nm femtosecond pulses (pulse energy, 1 mJ; pulse duration, 90 fs). The central frequency and the bandwidth of the THz pulses were 1 and 1.5 THz, respectively. THz pulses were focused onto the graphene/Si sample or the bare Si substrate. The beam size at the focus was 0.5 mm. The transmitted THz pulses were measured by either a L-He-cooled Si:Bolometer (sensitive to time-averaged THz power), or by electro-optic (EO) sampling using a 1-mm ZnTe crystal [22

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro‐optic sampling,” Appl. Phys. Lett. 69(16), 2321–2323 (1996). [CrossRef]

3. Power transmission: 2-D imaging and sheet conductivity calculation

Figure 2a shows transmitted THz power measured by the Si:Bolometer. The image covers a 26 × 41-mm² region. The pixel size is 0.4-mm and data was acquired with a 100-ms pixel integration time. The square-shaped graphene film (blue-green, average transmission: 0.39) is clearly resolved against the background of the Si substrate (bright-green, average transmission: 0.57). The THz response of the graphene film shows spatial inhomogeneity. The transmission varies from 0.36 (top right edge) to 0.41 (bottom left edge). We observed the transmission near the graphene edge in a 1.5 × 1.5-mm² region with 0.02-mm step size (Fig. 2b). The transmission drop across the boundary is as sharp as the spatial resolution of our probe, 0.5 mm (Fig. 2c).

Fig. 2 (a) THz transmission image of the graphene-on-Si sample over a 26 × 41-mm² region (pixel size is 0.4-mm). The graphene film and the Si substrate are shown in light blue and bright green, respectively. The red and dark-blue regions correspond to air and the aluminum sample mount, respectively. Measurements were made at room temperature in ambient conditions. (b) A higher definition image (1.5 × 1.5-mm²) taken with 0.02-mm steps shows an edge of the graphene. (c) The cross-section of the edge is shown.

From the relative power transmitted through graphene/Si versus bare Si we calculated the sheet conductivity σ_s of our single-layer graphene sample. The sample has a multi-layer structure consisting of graphene, Si, and air layers (Fig. 3 ) which we analyze using thin-film Fresnel coefficients and the Drude model. The graphene layer is treated as a zero-thickness conductive film, whereas the Si substrate is considered an optically thick dielectric medium. The high-resistivity Si substrate has refractive index n _Si = 3.42 and is nearly dispersionless in the THz regime. The transmission through the first interface (air→graphene→Si) is given by

t (σ_{S}) = \frac{2}{n_{S i} + 1 + Z_{0} σ_{S}},

(1)

and the internal reflection from the graphene interface is given by

r (σ_{S}) = \frac{n_{S i} - 1 - Z_{0} σ_{S}}{n_{S i} + 1 + Z_{0} σ_{S}},

(2)

where Z ₀ (376.7 Ω) is the vacuum impedance. The ratio of the total transmission of the graphene/Si sample to that of the Si substrate is given by

T_{r e l} (σ_{S}) = \frac{T_{G r - S i}}{T_{S i}} = {| \frac{t (σ_{s})}{t_{13}} |}^{2} \frac{1 - {| r_{34} r_{31} |}^{2}}{1 - {| r_{34} r (σ_{s}) |}^{2}},

(3)

where

t_{i j} = 2 n_{i} / (n_{i} + n_{j})

and

r_{i j} = (n_{i} - n_{j}) / (n_{i} + n_{j})

are the Fresnel coefficients with the refractive indices of n ₁ = n ₄ = n _air = 1 and n ₃ = n_Si = 3.42. There are no interference terms in Eq. (3) because multiple reflections are temporally separated (see Fig. 4a ). The measured values of local T _rel varied from 0.64 to 0.72 depending on position, from which we calculate the local sheet conductivity σ_s (x,y) = 1.7 x 10⁻³ to 2.4 x 10⁻³ Ω⁻¹ (ρ _s = 420 to 590 Ω/sq). These values are plotted in Fig. 3b. We speculate that spatial inhomogeneity in σ_s is caused by variations in doping level [23

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,” arXiv:1007.4623v1.

]. Variations in doping likely occur during the graphene transfer process. A clearer understanding of the causes of spatial variations in conductivity, and ways to improve the uniformity of transferred graphene films, is a subject for future work.

Fig. 3 (a) Multiple reflections at Air-Graphene-Si-Air interfaces: n ₁ = n ₄ = n _Air = 1 and n ₃ = n _Si = 3.42. (b) Relative THz transmission of graphene/Si versus sheet conductivity.

Fig. 4 (a) THz waveforms transmitted through air (black), silicon (red), and graphene on silicon (blue). (b-d) Amplitude spectra of the directly transmitted pulse (m = 1) and the first two internally reflected pulses (m = 2 and 3) through silicon (red) and graphene on silicon (blue). The spectrum of the pulse through air is added for comparison (Black line).

The measured sheet conductivity is more than 30 times greater than σ_q = e ²/4ℏ = 6.1 x10⁻⁵ Ω⁻¹ (σ_q is the optical conductivity of graphene due to interband transitions [19

K. F. Mak, M. Y. Sfeir, Y. Wu, C.-H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the Optical Conductivity of Graphene,” Phys. Rev. Lett. 101(19), 196405 (2008). [CrossRef] [PubMed]

]). We conclude that the measured sheet conductivity is dominated by intraband transitions and should closely reflect the dc electrical conductivity of the graphene sample. To compare our THz measurements of σ_s to conventional techniques we patterned 200 μm van der Pauw squares in the graphene film. Four-probe dc electrical measurements of these patterned graphene films yielded ρ_s ranging from 630 to 750 Ω/sq in reasonable agreement with the THz measurements. We propose three possible causes for the 30% increase in measured ρ_s , (i) grain-boundary scattering has a larger effect on the dc-electrical measurements than the THz measurements, (ii) small voids in the graphene film have a larger effect on the dc-electrical measurements than the THz measurements, (iii) the additional semiconductor processing steps required to pattern graphene and fabricate metal electrodes may reduce the doping level of the graphene, thereby increasing the measured ρ_s .

4. Terahertz time-domain spectroscopy and conductivity spectra

The reflection and transmission coefficients described in Eq. (1) and 2 can be determined as a function of frequency using THz time-domain spectroscopy (THz-TDS). Figure 4a shows a set of data including the THz waveforms through air (black), the Si substrate (red), and the graphene/Si sample (blue). The waveforms measured from both Si and graphene/Si consist of a series of single-cycle THz pulses. First, a directly transmitted pulse (m = 1), then subsequent “echos” corresponding to multiple reflections from the front and back sides of the Si substrate (m = 2, 3, 4…). The time delay between echoes is consistent with the thickness of the Si substrate (285 ± 5 μm). The amplitude difference between graphene/Si pulses and Si pulses becomes more pronounced as the pulses undergo more reflections. Figure 4b-d shows Fourier transforms of the m = 1, m = 2 and m = 3 waveforms respectively, obtained with a 6-ps time window corresponding to the time delay between echos. High-resolution Fourier transform of the entire waveform shows no sign of narrow spectral features other than the interference fringes of the periodic pulse train.

Combining Eqs. (1) and 2 with t _ij, and r _ij, the relative field transmission of the m-th pulse is predicted to be

t_{r e l}^{(m)} (σ_{S}) = \frac{E_{G - S i}^{(m)}}{E_{S i}^{(m)}} = \frac{t (σ_{S})}{t_{13}} {(\frac{r (σ_{S})}{r_{13}})}^{m - 1},

(4)

where

E_{G - S i}^{(m)}

is the electric field of the m-th pulse after transmission through graphene/Si and

E_{S i}^{(m)}

is the electric field of the m-th pulse after transmission through Si. Assuming σ_s = 2.04 × 10⁻³ Ω⁻¹ (the spatially-averaged sheet conductivity of graphene obtained from the power transmission measurement), Eq. (4) predicts

t_{r e l}^{(1)} = 0.852

t_{r e l}^{(2)} = 0.495

, and

t_{r e l}^{(3)} = 0.288

, in good agreement with the pulse-energy ratios (

t_{r e l}^{(m = 1, 2, 3)} = 0.855

0.454

, and

0.299

) seen in Fig. 4.

Figure 5 shows the relative transmission spectra through the graphene/Si sample for pulses m = 1 and m = 2 (i.e., transmission through graphene/Si relative to transmission through bare Si). The spectra are flat and in close agreement with the expected values

t_{r e l}^{(1)} = 0.852

and

t_{r e l}^{(2)} = 0.495

. The flat spectral response seen in Fig. 5 indicates that the period of the applied electric field (0.5-3 ps) is much longer than the room-temperature carrier scattering time in our graphene sample [16

,24

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of Scattering Rate and Minimum Conductivity in Graphene,” Phys. Rev. Lett. 99(24), 246803 (2007). [CrossRef]

Fig. 5 Relative amplitude transmission spectra of m = 1 (blue square) and m = 2 (red circle) pulses (graphene-on-Si transmission spectra divided by the Si transmission spectra). Solid lines at t_rel = 0.852 and 0.495 show the expected relative amplitude based on the spatial-average of our local sheet conductivity measurements σ_s = 2.04 × 10⁻³ Ω⁻¹. The experimental spectra were obtained by averaging the transmission through five different spots on the graphene.

5. Conclusion

We conclude that THz imaging and spectroscopy is of great use for rapidly characterizing the local free carrier dynamics in graphene. We have demonstrated that the strong THz absorption of graphene leads to high contrast imaging and the ability to accurately map sheet conductivity with sub-mm resolution over large areas.

Acknowledgments

The work at the Oregon State University is supported by Oregon Nanoscience and Microtechnologies Institute and by National Science Foundation (PHY-0449426). The work at Cornell was supported by the NSF through the Cornell Center for Materials Research (CCMR), the MARCO Focused Research Center on Materials, Structures, and Devices and the AFOSR. Sample Fabrication was performed at the Cornell node of the National Nanofabrication Infrastructure Network, which is supported by the National Science Foundation (Grant ECS-0335765).

References and links

1.	K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef] [PubMed]
2.	A. H. Castro Neto, 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]
3.	Y. Zhang, J. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005). [CrossRef] [PubMed]
4.	K. Geim, “Graphene: Status and Prospect,” Science 324(5934), 1530–1534 (2009). [CrossRef] [PubMed]
5.	G. Brumfiel, “Graphene gets ready for the big time,” Nature 458(7237), 390–391 (2009). [CrossRef] [PubMed]
6.	M. Dragoman and D. Dragoman, “Graphene-based quantum electronics,” Prog. Quantum Electron. 33(6), 165–214 (2009). [CrossRef]
7.	X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, “Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors,” Science 319(5867), 1229–1232 (2008). [CrossRef] [PubMed]
8.	L. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang, E. W. Hill, K. S. Novoselov, and A. K. Geim, “Chaotic Dirac Billiard in Graphene Quantum Dots,” Science 320(5874), 356–358 (2008). [CrossRef] [PubMed]
9.	Y.-M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P. Avouris, “Operation of Graphene Transistors at Gigahertz Frequencies,” Nano Lett. 9(1), 422–426 (2009). [CrossRef]
10.	H. Wang, D. Nezich, J. Kong, and T. Palacios, “Graphene frequency multipliers,” IEEE Electron Device Lett. 30(5), 547–549 (2009). [CrossRef]
11.	N. L. Rangel and J. M. Seminario, “Graphene terahertz generators for molecular circuits and sensors,” J. Phys. Chem. A 112(51), 13699–13705 (2008). [CrossRef] [PubMed]
12.	V. Ryzhii, “Terahertz plasma waves in gated graphene heterostructures,” Jpn. J. Appl. Phys. 45(35), L923–L925 (2006). [CrossRef]
13.	C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and Coherence in Patterned Epitaxial Graphene,” Science 312(5777), 1191–1196 (2006). [CrossRef] [PubMed]
14.	K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009). [CrossRef] [PubMed]
15.	X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009). [CrossRef] [PubMed]
16.	H. Choi, F. Borondics, D. A. Siegel, S. Y. Zhou, M. C. Martin, A. Lanzara, and R. A. Kaindl, “Broadband electromagnetic response and ultrafast dynamics of few-layer epitaxial graphene,” Appl. Phys. Lett. 94(17), 172102 (2009). [CrossRef]
17.	S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. Ri Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Özyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010). [CrossRef] [PubMed]
18.	Y. Lee, S. Bae, H. Jang, S. Jang, S.-E. Zhu, S. H. Sim, Y. I. Song, B. H. Hong, and J.-H. Ahn, “Wafer-Scale Synthesis and Transfer of Graphene Films,” Nano Lett. 10(2), 490–493 (2010). [CrossRef] [PubMed]
19.	K. F. Mak, M. Y. Sfeir, Y. Wu, C.-H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the Optical Conductivity of Graphene,” Phys. Rev. Lett. 101(19), 196405 (2008). [CrossRef] [PubMed]
20.	A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006). [CrossRef] [PubMed]
21.	S. Pisana, M. Lazzeri, C. Casiraghi, K. S. Novoselov, A. K. Geim, A. C. Ferrari, and F. Mauri, “Breakdown of the adiabatic Born–Oppenheimer approximation in graphene,” Nat. Mater. 6(3), 198–201 (2007). [CrossRef] [PubMed]
22.	A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro‐optic sampling,” Appl. Phys. Lett. 69(16), 2321–2323 (1996). [CrossRef]
23.	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,” arXiv:1007.4623v1.
24.	Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of Scattering Rate and Minimum Conductivity in Graphene,” Phys. Rev. Lett. 99(24), 246803 (2007). [CrossRef]

OCIS Codes
(320.7130) Ultrafast optics : Ultrafast processes in condensed matter, including semiconductors
(160.4236) Materials : Nanomaterials
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Spectroscopy

History
Original Manuscript: November 10, 2010
Revised Manuscript: December 14, 2010
Manuscript Accepted: December 15, 2010
Published: December 21, 2010

Citation
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 Yun-Shik Lee, "Terahertz imaging and spectroscopy of large-area single-layer graphene," Opt. Express 19, 141-146 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-1-141

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References

K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef] [PubMed]
A. H. Castro Neto, 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]
Y. Zhang, J. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005). [CrossRef] [PubMed]
K. Geim, “Graphene: Status and Prospect,” Science 324(5934), 1530–1534 (2009). [CrossRef] [PubMed]
G. Brumfiel, “Graphene gets ready for the big time,” Nature 458(7237), 390–391 (2009). [CrossRef] [PubMed]
M. Dragoman and D. Dragoman, “Graphene-based quantum electronics,” Prog. Quantum Electron. 33(6), 165–214 (2009). [CrossRef]
X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, “Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors,” Science 319(5867), 1229–1232 (2008). [CrossRef] [PubMed]
L. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang, E. W. Hill, K. S. Novoselov, and A. K. Geim, “Chaotic Dirac Billiard in Graphene Quantum Dots,” Science 320(5874), 356–358 (2008). [CrossRef] [PubMed]
Y.-M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P. Avouris, “Operation of Graphene Transistors at Gigahertz Frequencies,” Nano Lett. 9(1), 422–426 (2009). [CrossRef]
H. Wang, D. Nezich, J. Kong, and T. Palacios, “Graphene frequency multipliers,” IEEE Electron Device Lett. 30(5), 547–549 (2009). [CrossRef]
N. L. Rangel and J. M. Seminario, “Graphene terahertz generators for molecular circuits and sensors,” J. Phys. Chem. A 112(51), 13699–13705 (2008). [CrossRef] [PubMed]
V. Ryzhii, “Terahertz plasma waves in gated graphene heterostructures,” Jpn. J. Appl. Phys. 45(35), L923–L925 (2006). [CrossRef]
C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and Coherence in Patterned Epitaxial Graphene,” Science 312(5777), 1191–1196 (2006). [CrossRef] [PubMed]
K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009). [CrossRef] [PubMed]
X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009). [CrossRef] [PubMed]
H. Choi, F. Borondics, D. A. Siegel, S. Y. Zhou, M. C. Martin, A. Lanzara, and R. A. Kaindl, “Broadband electromagnetic response and ultrafast dynamics of few-layer epitaxial graphene,” Appl. Phys. Lett. 94(17), 172102 (2009). [CrossRef]
S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. Ri Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Özyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010). [CrossRef] [PubMed]
Y. Lee, S. Bae, H. Jang, S. Jang, S.-E. Zhu, S. H. Sim, Y. I. Song, B. H. Hong, and J.-H. Ahn, “Wafer-Scale Synthesis and Transfer of Graphene Films,” Nano Lett. 10(2), 490–493 (2010). [CrossRef] [PubMed]
K. F. Mak, M. Y. Sfeir, Y. Wu, C.-H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the Optical Conductivity of Graphene,” Phys. Rev. Lett. 101(19), 196405 (2008). [CrossRef] [PubMed]
A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006). [CrossRef] [PubMed]
S. Pisana, M. Lazzeri, C. Casiraghi, K. S. Novoselov, A. K. Geim, A. C. Ferrari, and F. Mauri, “Breakdown of the adiabatic Born–Oppenheimer approximation in graphene,” Nat. Mater. 6(3), 198–201 (2007). [CrossRef] [PubMed]
A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro‐optic sampling,” Appl. Phys. Lett. 69(16), 2321–2323 (1996). [CrossRef]
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,” arXiv:1007.4623v1.
Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of Scattering Rate and Minimum Conductivity in Graphene,” Phys. Rev. Lett. 99(24), 246803 (2007). [CrossRef]

Adam, S.
Ahn, J.-H.
An, J.
Avouris, P.
Bae, S.
Balakrishnan, J.
Banerjee, S. K.
Berger, C.
Bolotin, K.
Borondics, F.
Brown, N.
Brumfiel, G.
Cai, W.
Casiraghi, C.
Castro Neto, A. H.
Choi, H.
Choi, J.-Y.
Colombo, L.
Conrad, E. H.
Dai, H.
Das Sarma, S.
de Heer, W. A.
Dragoman, D.
Dragoman, M.
Farmer, D. B.
Ferrari, A. C.
First, P. N.
Geim, A. K.
Geim, K.
Hass, J.
Heinz, T. F.
Hill, E. W.
Hong, B. H.
Hwang, E. H.
Iijima, S.
Jang, H.
Jang, S.
Jenkins, K. A.
Jiang, D.
Jung, I.
Kaindl, R. A.
Katsnelson, M. I.
Kim, H.
Kim, J. M.
Kim, K. S.
Kim, P.
Kim, S.
Kim, Y.-J.
Kong, J.
Lanzara, A.
Lazzeri, M.
Lee, S.
Lee, S. Y.
Lee, Y.
Lei, T.
Li, T.
Li, X.
Lin, Y.-M.
Lui, C.-H.
Mak, K. F.
Marchenkov, A. N.
Martin, M. C.
Mauri, F.
Mayou, D.
Meyer, J. C.
Misewich, J. A.
Nah, J.
Nahata, A.
Naud, C.
Nezich, D.
Novoselov, K. S.
Özyilmaz, B.
Palacios, T.
Park, J.-S.
Peres, N. M. R.
Piner, R.
Pisana, S.
Piscanec, S.
Ponomarenko, L. A.
Rangel, N. L.
Ri Kim, H.
Roth, S.
Ruoff, R. S.
Ryzhii, V.
Scardaci, V.
Schedin, F.
Seminario, J. M.
Sfeir, M. Y.
Siegel, D. A.
Sim, S. H.
Small, J. P.
Song, Y. I.
Song, Z.
Stormer, H. L.
Tan, J. W.
Tan, Y.-W.
Tutuc, E.
Valdes-Garcia, A.
Velamakanni, A.
Wang, H.
Wang, X.
Weling, A. S.
Wu, X.
Wu, Y.
Xu, X.
Yang, D.
Yang, R.
Zhang, L.
Zhang, Y.
Zhao, Y.
Zheng, Y.
Zhou, S. Y.
Zhu, S.-E.

Appl. Phys. Lett.

H. Choi, F. Borondics, D. A. Siegel, S. Y. Zhou, M. C. Martin, A. Lanzara, and R. A. Kaindl, “Broadband electromagnetic response and ultrafast dynamics of few-layer epitaxial graphene,” Appl. Phys. Lett. 94(17), 172102 (2009). [CrossRef]
A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro‐optic sampling,” Appl. Phys. Lett. 69(16), 2321–2323 (1996). [CrossRef]

IEEE Electron Device Lett.

H. Wang, D. Nezich, J. Kong, and T. Palacios, “Graphene frequency multipliers,” IEEE Electron Device Lett. 30(5), 547–549 (2009). [CrossRef]

J. Phys. Chem. A

N. L. Rangel and J. M. Seminario, “Graphene terahertz generators for molecular circuits and sensors,” J. Phys. Chem. A 112(51), 13699–13705 (2008). [CrossRef] [PubMed]

Jpn. J. Appl. Phys.

V. Ryzhii, “Terahertz plasma waves in gated graphene heterostructures,” Jpn. J. Appl. Phys. 45(35), L923–L925 (2006). [CrossRef]

Nano Lett.

Y. Lee, S. Bae, H. Jang, S. Jang, S.-E. Zhu, S. H. Sim, Y. I. Song, B. H. Hong, and J.-H. Ahn, “Wafer-Scale Synthesis and Transfer of Graphene Films,” Nano Lett. 10(2), 490–493 (2010). [CrossRef] [PubMed]
Y.-M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P. Avouris, “Operation of Graphene Transistors at Gigahertz Frequencies,” Nano Lett. 9(1), 422–426 (2009). [CrossRef]

Nat. Mater.

S. Pisana, M. Lazzeri, C. Casiraghi, K. S. Novoselov, A. K. Geim, A. C. Ferrari, and F. Mauri, “Breakdown of the adiabatic Born–Oppenheimer approximation in graphene,” Nat. Mater. 6(3), 198–201 (2007). [CrossRef] [PubMed]
K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef] [PubMed]

Nat. Nanotechnol.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. Ri Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Özyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010). [CrossRef] [PubMed]

Nature

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009). [CrossRef] [PubMed]
Y. Zhang, J. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005). [CrossRef] [PubMed]
G. Brumfiel, “Graphene gets ready for the big time,” Nature 458(7237), 390–391 (2009). [CrossRef] [PubMed]

Phys. Rev. Lett.

K. F. Mak, M. Y. Sfeir, Y. Wu, C.-H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the Optical Conductivity of Graphene,” Phys. Rev. Lett. 101(19), 196405 (2008). [CrossRef] [PubMed]
A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006). [CrossRef] [PubMed]
Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of Scattering Rate and Minimum Conductivity in Graphene,” Phys. Rev. Lett. 99(24), 246803 (2007). [CrossRef]

Prog. Quantum Electron.

M. Dragoman and D. Dragoman, “Graphene-based quantum electronics,” Prog. Quantum Electron. 33(6), 165–214 (2009). [CrossRef]

Rev. Mod. Phys.

A. H. Castro Neto, 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]

Science

K. Geim, “Graphene: Status and Prospect,” Science 324(5934), 1530–1534 (2009). [CrossRef] [PubMed]
X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, “Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors,” Science 319(5867), 1229–1232 (2008). [CrossRef] [PubMed]
L. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang, E. W. Hill, K. S. Novoselov, and A. K. Geim, “Chaotic Dirac Billiard in Graphene Quantum Dots,” Science 320(5874), 356–358 (2008). [CrossRef] [PubMed]
X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009). [CrossRef] [PubMed]
C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and Coherence in Patterned Epitaxial Graphene,” Science 312(5777), 1191–1196 (2006). [CrossRef] [PubMed]

Other

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,” arXiv:1007.4623v1.

2010, Bae, Nat. Nanotechnol.
2010, Lee, Nano Lett.
2009, Castro Neto, Rev. Mod. Phys.
2009, Kim, Nature
2009, Li, Science
2009, Choi, Appl. Phys. Lett.
2009, Geim, Science
2009, Brumfiel, Nature
2009, Dragoman, Prog. Quantum Electron.
2009, Lin, Nano Lett.
2009, Wang, IEEE Electron Device Lett.
2008, Rangel, J. Phys. Chem. A
2008, Li, Science
2008, Ponomarenko, Science
2008, Mak, Phys. Rev. Lett.
2007, Pisana, Nat. Mater.
2007, Geim, Nat. Mater.
2007, Tan, Phys. Rev. Lett.
2006, Ferrari, Phys. Rev. Lett.
2006, Ryzhii, Jpn. J. Appl. Phys.
2006, Berger, Science
2005, Zhang, Nature
1996, Nahata, Appl. Phys. Lett.

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