The Dependence of Graphene Raman D-band on Carrier Density

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The Dependence of Graphene Raman D‑band on Carrier Density Junku Liu, Qunqing Li,* Yuan Zou, Qingkai Qian, Yuanhao Jin, Guanhong Li, Kaili Jiang, and Shoushan Fan State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China S Supporting Information *

ABSTRACT: Raman spectroscopy has been an integral part of graphene research and can provide information about graphene structure, electronic characteristics, and electron−phonon interactions. In this study, the characteristics of the graphene Raman D-band, which vary with carrier density, are studied in detail, including the frequency, full width half-maximum, and intensity. We find the Raman D-band frequency increases for hole doping and decreases for electron doping. The Raman D-band intensity increases when the Fermi level approaches half of the excitation energy and is higher in the case of electron doping than that of hole doping. These variations can be explained by electron−phonon interaction theory and quantum interference between different Raman pathways in graphene. The intensity ratio of Raman D- and G-band, which is important for defects characterization in graphene, shows a strong dependence on carrier density. KEYWORDS: Graphene, Raman spectroscopy, doping, carrier density, defect

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raphene,1,2 a two-dimensional plane of carbon atoms arranged in a honeycomb lattice, has led to many advances in two-dimensional physics3−8 and electronic device applications.9−15 In recent years, Raman spectroscopy has become an integral part of graphene research and an effective and indispensable tool in graphene research. The prominent Raman features in graphene are the Raman D-band (involving defects and the inside transverse optical branch (iTO) phonon at the vicinity of the K point), the Raman G-band (involving the phonon at the vicinity of the Brillouin zone center Γ) and the Raman 2D-band (involving two iTO phonon at the vicinity of K point),16 which provide the information of the defects, the doping, the strain, the number of layers and the electronic structure of graphene.16−24 Previously, most experiments and theories have shown that the Raman G and 2D-bands vary as a function of doping.18,19,25−31 Much of the research concerning the Raman D-band, which is assigned as a double resonance process that accompanies a defect and an iTO phonon,32−34 focuses on the effects of the defect.16,20,22−24,35 However, the effects of doping have not been reported previously. In this work, we investigate the variation of the graphene Raman D-band at different carrier densities by combining highly efficient ion-gel gate dielectric and in situ Raman measurements. The research is beneficial for both fundamental understanding of the origin of the Raman D-band and the © 2013 American Chemical Society

application of Raman techniques in graphene research. The experimental data show that the Raman D-band frequency increases in the case of hole doping and decreases for that of electron doping. The peak of the Raman D-band also becomes broader and then sharpens as the carrier density increases. Raman D-band intensity is enhanced when the Fermi level (| EF|) approaches half of the excitation energy, which has a similar trend to the behavior of the Raman G-band. While this behavior is in contrast to Raman 2D-band intensity, which decreases monotonically when |EF| increases. The intensities of Raman D- and G-band are higher for electron doping than for hole doping. We analyze these variations in the context of electron−phonon interaction theory and quantum interference28,34,36 between different Raman pathways in graphene. The intensity ratio of D- and G-band (ID/IG) has been used to quantify defects in graphene.23,24,35 Here we found this ratio also strongly depends on the carrier density. ID/IG reaches the minimum value when |EF| approaches the Dirac point and increases to the maximum value when |EF| approaches half of the excitation energy. Received: September 19, 2013 Revised: November 14, 2013 Published: November 27, 2013 6170

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Figure 1. (a) Illustration of an ion-gel top-gated graphene transistor on a SiO2/Si Substrate. (b) Transfer characteristic of the graphene transistor with ion-gel top-gate dielectric. (c) The dependence of the Fermi level and carrier density of the graphene on gate voltage. (d) Raman spectra of graphene with ion-gel top-gate dielectric, the arrows and stars indicate the Raman features from the graphene and ion-gel dielectric, respectively.

Figure 2. Raman spectra of graphene with ion-gel top-gate dielectric as a function of Raman shift and VG with 514 nm laser excitation. Raman Dband and G-band intensity is strongly enhanced as VG = 0 V (2|EF|→Eex) and the 2D-band peak intensifies as VG = −4 V (2|EF|→0).

Figure 1a shows a diagram of a typical device. The carrier density in graphene is controlled by the gate voltage (VG). In situ Raman spectra of the graphene with the ion-gel top-gate dielectric were measured by a LabRAM HR Raman spectrometer with 514 nm wavelength laser excitation (Eex = 2.41 eV) in the backscattering configuration using a 100× objective. The laser power measured from the objective was 3mW with a spot size of about 1 μm2. Figure 1b presents the transfer characteristics of a graphene transistor with an ion-gel top-gate dielectric, which has a charge neutral point (CNP) at −4 V. The resistance decreases from the CNP on both side because of electrons and holes doping. The relationship between the carrier density and the gate voltage satisfies37

VG − VG,CNP =

ℏv πn ne + F Cox e

(1)

where the first term on the right-hand side describes the carrier density induced by the top gate, the second term describes the effect of the quantum capacitance in graphene, VG is the gate voltage, VG.CNP is the CNP, Cox = 4.7 μF/cm2 is the dielectric capacitance per unit area, measured by controlling the graphene transistor using the top-gate and the back-gate simultaneously,37 and νF = 1.1 × 106 m/s is the Fermi velocity.38 The carrier density in the graphene channel approached 1014/cm2 at a gate voltage of 5 V, which allows investigation of graphene at high doping levels. The Fermi level is determined from the carrier density by the equation EF = ℏvF(πn)1/2. Figure 1(c) 6171

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Figure 3. (a,b) Typical inner scattering process with electrons first scattered by iTO phonons and by defects, respectively. (c) Measured and fitted (according to eq 2) frequency shift of Raman D-band as a function of carrier density for hole doping and electron doping. (d) Measured fwhm of the Raman D-band as a function of carrier density for hole doping and electron doping.

consequence strengthening/weakening of the phonons. This may be understood as an increase in electron density that can shield ions in the lattice and weaken the interactions among neighboring lattice ions. This contributes to the phonon frequency red shift at high electron doping levels. Conversely, hole doping equal to reduce the number of electrons in graphene, which strengthens the lattice ion interactions and results in a phonon frequency blue shift. Another effect of the carrier density on the behavior of the phonon is a dynamic effect from electron−phonon interactions, which leads to the phonon self-energy renormalization and modifies the frequency and lifetime of phonons. These two effects have been used to explain the G-band and 2D band behavior with carrier density.19,25 First, we check the frequency shift of Raman D-band using a phenomenological formulation from25

shows the dependence of the Fermi level and carrier density of the graphene layer on gate voltage. Figure 1(d) shows the Raman spectra of graphene with an ion-gel top-gate dielectric at VG = 0 V, the arrows and stars indicate the Raman features in the graphene and ion-gel dielectric material, respectively. Figure 2 shows a contour plot of the graphene Raman intensity as a function of Raman shift and gate voltage (Supporting Information Figure S1 shows real Raman spectra at different gate voltage). The frequency and intensity of the Raman G-band and 2D-band show a clear dependence on gate voltage. The Raman G-band features a blue shift in the case of both electron and hole doping (Supporting Information Figure S2a) and the Raman 2D-band is strengthened for hole doping and is weaken for electron doping (Supporting Information Figure S2b). These effects are consistent with recent experimental and theoretical reports19,25−27,29,30 and can be explained through phonon renormalization from electron− phonon coupling. The Raman G- and 2D-band show peak intensities at VG = 0 V (2|EF|→Eex) and VG = −4 V (2|EF|→0), respectively, which has been reported in ref 28 and explained through quantum interference between different Raman pathways. Here, we focus on the dependence of the graphene Raman D-band on carrier density. We find that the frequency of Raman D-band is strengthened for hole doping and is weakened for electron doping. The intensity of Raman D-band is strongly enhanced as VG approaches 0 and −8 V. The Raman D-band is assigned as a double resonance process involving defects and an iTO phonon at the vicinity of the K point. Figure 3a,b shows typical inner scattering process with electrons first scattered by iTO phonons and by defects, respectively. The Raman D-band is affected by iTO phonon and defects simultaneously. Figure 3c,d shows the dependence of the frequency shift and full width at half-maximum (fwhm) of the Raman D-band on the carrier density of graphene. The Raman D-band frequency shift, induced by electrochemical doping, was also observed in carbon nanotube.39 The variation of the carrier density in graphene has two major effects on this phonon.19,25 First, static effect is a modification of the equilibrium lattice parameter with a

Δω = a − bn − cn2 + dn3 + e |n|3/2

(2)

where Δω is the variation of the phonon frequency, n is the carrier density and a, b, c, d, and e are coefficients. This formulation takes into account the static effect. We fit the measured Raman D-band results shown in Figure 3c to obtain a = −0.201, b = −0.857, c = −0.225, d = 0.00341, and e = 0.807. The dynamic effect can also affect the Raman D-band phonon frequency, but this is expected to be negligible for the Raman D-band phonon in the vicinity of K-point. Therefore, the variation of the Raman-D band frequency can be explained mainly from the static effect. The fwhm of the Raman D-band indicates the decay lifetime of the iTO phonon in graphene, which is determined by the initial electronic state, final electron state and electron−phonon interactions. Figure 3d shows the fwhm of the Raman D-band first increases both for electron and hole doping, but decreases for heavy electron doping, which agrees with recent theoretical predictions for intervalley phonon scattering29 and is consistent with the fact that the Raman D-band is associated with an intervalley process. Although the experimental data agree with the theoretical prediction qualitatively, the measured fwhm departs from the theoretical prediction quantitatively, which 6172

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Figure 4. (a) Raman D-band intensity, (b) Raman G-band intensity, and (c) Raman 2D-band intensity as a function of Fermi level. (d) The phase of resonance factor Rk in Raman D-band process.

matrix element and resonance factor for a pathway starting at transition k, respectively. Eex = 2.41 eV is the excitation energy, γ is the energy broadening of the excited state, ℏωD = 0.167 eV is the Raman D-band energy, Ek, Ek′, and Ek″ are the intermediate states and Ek″ = Ek′ + hωD for a specific k. Electron scattering by a defect is an elastic scattering process and there is no energy change. All the Raman D-band pathways will interfere with each other and the Raman intensity depends on its phase relative to other pathways. The phase of a Raman pathway is determined by the resonance factor Rk. The phases of all the Raman D-band pathways are shown in Figure 4d. The phase varies rapidly as the intermediate state energy Ek close to Eex − ℏωD/2 and it hops from −π to π at Ek = Eex − ℏωD/2. Therefore, if all quantum pathways of the Raman D-band are allowed, they interfere destructively and thus decreases the Raman signal. While, if Ek = 2|EF| is increased to block the quantum pathways below Ek = Eex − ℏωD/2, the quantum interference is broken and the Raman intensity is enhanced. When Ek = 2|EF| > Eex, all the quantum pathways is blocked for Paul exclusion principle and the Raman intensity decreases rapidly. This trend agrees with the experimental data shown in Figure 4a. Furthermore, the asymmetry line-shape of the intensity peak agrees well with the enhanced intensity from interference. We also notice that the enhanced intensity for electron doping is higher than that for hole doping for the Raman Dand G-band, which are shown in Figure 4a,b. This may arise from the difference of the matrix elements Mk, which can be expressed as Mk = MoiMepMedMof, where Moi, Mof are the transition matrix elements for incoming and outcoming photons, respectively, and Mep, Med represent the transition matrix elements of phonon and defect scattering with the electron, respectively. Electron doping can enhance the electron−phonon interaction according to Coulomb law. By

may be due to the local density variation from self-doping, chemical absorption, and charge trapped in the substrate.18 Previously, most of the research on Raman D-band intensity focused on the edge of graphene and the type and the number of the defects.20,23,24,35,40 Here, we find that the Raman D-band intensity depends strongly on the carrier density of graphene, as show in Figure 4a. The enhanced intensity emerges as the Fermi level approaches −Eex/2 and Eex/2. Furthermore, the Raman D-band intensity for electron doping is higher than that for hole doping. These tendency of variations are similar to those of the Raman G-band intensity as show in Figure 4b. While the Raman 2D-band shows peak intensity at |EF| = 0 and then decreases as |EF| increases (Figure 4c). Quantum interference between different Raman pathways in graphene has recently been invoked to explain the variation of the Raman G-band and 2D-band intensity in graphene by Wang et al.28,34 This approach may also be suitable to explain the variation of the Raman D-band intensity. For the typical Raman D-band pathway shown in Figure 3a,b, the Raman D-band intensity can be described by28,34

I = |∑ MkR k|2 k

(3)

and ⎛ 1 Rk = ⎜ ⎝ (Eex ‐Ek ‐iγ )(Eex ‐ℏωD − Ek ′‐iγ )(Eex ‐ℏωD − Ek ‐iγ ) +

⎞ 1 ⎟ (Eex ‐Ek ‐iγ )(Eex ‐Ek ″‐iγ )(Eex ‐ℏωD − Ek ‐iγ ) ⎠

(4)

where the first term and the second term on the right-hand side describe the scattering process with electrons first scattered by iTO phonons and by defects, respectively. Mk and Rk are the 6173

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Figure 5. (a,b) The variation of the intensity ratio of ID/IG and I2D/IG, respectively, as a function of carrier density (or Fermi level).

The ion-gel dielectric was prepared by dispersing LiClO4 and PEO (MW 300 000) in methanol at a ratio of 0.012:0.1:4, as previously described.42 Then the mixture was heated and maintained at 45 °C with stirring until the suspension became uniform. This suspension was centrifuged and the resulting clear supernate was reserved. To form the ion-gel dielectric, the clear liquid was drop cast onto the graphene device followed by baking at 60 °C to remove residual methanol.

contrast, hole doping reduces the electron−phonon interaction. Therefore, Mep for electron doping is greater than that for hole doping and Raman intensity for electron doping is higher than that for hole doping. Figure 5a,b shows the dependence of the intensity ratio of ID/IG and I2D/IG on the carrier density. The variation of the intensity of Raman D- and 2D-band (Figure 4(a) and (c)) is much stronger than that of G-band (Figure 4(b)) and therefore ID/IG and I2D/IG depends strongly on the carrier density. The intensity ratio of ID/IG has the minimum value when 2|EF| approaches zero and then increases to the maximum value until 2|EF| = Eex. While the variation of the intensity ratio of I2D/IG is in contrast to that of ID/IG, which has the maximum value at 2| EF| = 0 and decreases monotonically as 2|EF| increases. That suggests there is a competition between Raman D-band and Raman 2D-band and is consistent with previous report.35 Therefore, the intensity ratio of ID/IG in graphene depends not only on defects density23,24,35 but also on the carrier density. Combining these two influences can help us to characterize the defects in graphene. In summary, we have shown that the prominent Raman Dband in graphene depends strongly on carrier density. Raman D-band frequency increases for hole doping and decreases for electron doping. The peak becomes broader and then sharpens as the electron or hole doping increases. These results can be explained by electron−phonon interactions in graphene. We found that the quantum interference between different Raman pathway leads to the enhanced Raman intensity at Ek = Eex − ℏωD/2 and the stronger electron−phonon interaction for electron doping give rise to higher Raman intensity for hole doping than that for electron doping. The strong dependence of ID/IG on carrier density must be considered when we use ID/ IG to characterize the defects in graphene. Experimental Details. Graphene was grown by chemical vapor deposition (CVD) on a 25 μm thick copper (Cu) foil (Alfa Aesar, item No.13382) at 1000 °C using a mixture of methane (CH4) and hydrogen (H2). A protective poly(methyl methacrylate) (PMMA) film was applied to the deposited graphene layers, and the PMMA/graphene film was transferred to SiO2/Si substrate by dissolving the Cu foil using a 1 M aqueous FeCl3 solution. The transfer process was completed by removing the PMMA with acetone.41 The graphene device was fabricated using a conventional top-down approach. Photolithography was used to define the source, drain, and gate electrode, and Cr/Au layers were then deposited in vacuum using an electron-beam system.

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ASSOCIATED CONTENT

S Supporting Information *

Raman spectra of graphene at different gate voltage and the frequency shift of Raman G- and 2D-band as a function of carrier density. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86 10 62796019. Fax: +86 10 62792457. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the National Basic Research Program of China (2012CB932301), National Natural Science Foundation of China (90921012).

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REFERENCES

(1) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6 (3), 183−191. (2) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306 (5696), 666−669. (3) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Nature 2005, 438 (7065), 197−200. (4) Zhang, Y. B.; Tan, Y. W.; Stormer, H. L.; Kim, P. Nature 2005, 438 (7065), 201−204. (5) Novoselov, K. S.; Jiang, Z.; Zhang, Y.; Morozov, S. V.; Stormer, H. L.; Zeitler, U.; Maan, J. C.; Boebinger, G. S.; Kim, P.; Geim, A. K. Science 2007, 315 (5817), 1379−1379. (6) Du, X.; Skachko, I.; Barker, A.; Andrei, E. Y. Nat. Nanotechnol. 2008, 3 (8), 491−495. (7) Du, X.; Skachko, I.; Duerr, F.; Luican, A.; Andrei, E. Y. Nature 2009, 462 (7270), 192−195. (8) Bolotin, K. I.; Ghahari, F.; Shulman, M. D.; Stormer, H. L.; Kim, P. Nature 2009, 462 (7270), 196−199. 6174

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(9) Rana, F.; George, P. A.; Strait, J. H.; Dawlaty, J. 33rd International Conference on Infrared, Millimeter and Terahertz Waves; IEEE: New York, 2008; Vols 1 and 2, pp 356−358. (10) Xia, F. N.; Mueller, T.; Lin, Y. M.; Valdes-Garcia, A.; Avouris, P. Nat. Nanotechnol. 2009, 4 (12), 839−843. (11) Bonaccorso, F.; Sun, Z.; Hasan, T.; Ferrari, A. C. Nat. Photonics 2010, 4 (9), 611−622. (12) Ju, L.; Geng, B. S.; Horng, J.; Girit, C.; Martin, M.; Hao, Z.; Bechtel, H. A.; Liang, X. G.; Zettl, A.; Shen, Y. R.; Wang, F. Nat. Nanotechnol. 2011, 6 (10), 630−634. (13) Liao, L.; Duan, X. F. Mater. Today 2012, 15 (7−8), 328−338. (14) Sensale-Rodriguez, B.; Yan, R. S.; Kelly, M. M.; Fang, T.; Tahy, K.; Hwang, W. S.; Jena, D.; Liu, L.; Xing, H. G. Nat. Commun. 2012, 3, 780. (15) Freitag, M.; Low, T.; Xia, F. N.; Avouris, P. Nat. Photonics 2013, 7 (1), 53−59. (16) Malard, L. M.; Pimenta, M. A.; Dresselhaus, G.; Dresselhaus, M. S. Phys. Rep. 2009, 473 (5−6), 51−87. (17) Ferrari, A. C.; Meyer, J. C.; Scardaci, V.; Casiraghi, C.; Lazzeri, M.; Mauri, F.; Piscanec, S.; Jiang, D.; Novoselov, K. S.; Roth, S.; Geim, A. K. Phys. Rev. Lett. 2006, 97, 187401. (18) Yan, J.; Zhang, Y. B.; Kim, P.; Pinczuk, A. Phys. Rev. Lett. 2007, 98, 166802. (19) Das, A.; Pisana, S.; Chakraborty, B.; Piscanec, S.; Saha, S. K.; Waghmare, U. V.; Novoselov, K. S.; Krishnamurthy, H. R.; Geim, A. K.; Ferrari, A. C.; Sood, A. K. Nat. Nanotechnol 2008, 3 (4), 210−215. (20) Casiraghi, C. Phys. Status Solidi RRL 2009, 3 (6), 175−177. (21) Yoon, D.; Moon, H.; Cheong, H.; Choi, J. S.; Choi, J. A.; Park, B. H. J. Korean Phys. Soc. 2009, 55 (3), 1299−1303. (22) Cancado, L. G.; Pimenta, M. A.; Neves, B.; Dantas, M.; Jorio, A. Phys. Rev. Lett. 2004, 93, 247401. (23) Lucchese, M. M.; Stavale, F.; Ferreira, E.; Vilani, C.; Moutinho, M.; Capaz, R. B.; Achete, C. A.; Jorio, A. Carbon 2010, 48 (5), 1592− 1597. (24) Cancado, L. G.; Jorio, A.; Ferreira, E.; Stavale, F.; Achete, C. A.; Capaz, R. B.; Moutinho, M.; Lombardo, A.; Kulmala, T. S.; Ferrari, A. C. Nano Lett. 2011, 11 (8), 3190−3196. (25) Lazzeri, M.; Mauri, F. Phys. Rev. Lett. 2006, 97, 266407. (26) Ando, T. J. Phys. Soc. Jpn. 2006, 75, 124701. (27) Pisana, S.; Lazzeri, M.; Casiraghi, C.; Novoselov, K. S.; Geim, A. K.; Ferrari, A. C.; Mauri, F. Nat. Mater. 2007, 6 (3), 198−201. (28) Chen, C. F.; Park, C. H.; Boudouris, B. W.; Horng, J.; Geng, B.; Girit, C.; Zettl, A.; Crommie, M. F.; Segalman, R. A.; Louie, S. G.; Wang, F. Nature 2011, 471 (7340), 617−20. (29) Sasaki, K.; Kato, K.; Tokura, Y.; Suzuki, S.; Sogawa, T. Phys. Rev. B 2012, 86, 201403. (30) Araujo, P. T.; Mafra, D. L.; Sato, K.; Saito, R.; Kong, J.; Dresselhaus, M. S. Phys. Rev. Lett. 2012, 109 (4), 046801. (31) Maciel, I. O.; Anderson, N.; Pimenta, M. A.; Hartschuh, A.; Qian, H. H.; Terrones, M.; Terrones, H.; Campos-Delgado, J.; Rao, A. M.; Novotny, L.; Jorio, A. Nat. Mater. 2008, 7 (11), 878−883. (32) Thomsen, C.; Reich, S. Phys. Rev. Lett. 2000, 85 (24), 5214−7. (33) Saito, R.; Jorio, A.; Souza, F. A.; Dresselhaus, G.; Dresselhaus, M. S.; Pimenta, M. A. Phys. Rev. Lett. 2002, 88 (2), 027401. (34) Maultzsch, J.; Reich, S.; Thomsen, C. Phys. Rev. B 2004, 70, 155403. (35) Jorio, A.; Lucchese, M. M.; Stavale, F.; Ferreira, E.; Moutinho, M.; Capaz, R. B.; Achete, C. A. J. Phys.: Condens. Mater. 2010, 22, 334204. (36) Sasaki, K. I.; Saito, R.; Dresselhaus, G.; Dresselhaus, M. S.; Farhat, H.; Kong, J. Phys. Rev. B 2008, 77, 245441. (37) Xu, H. L.; Zhang, Z. Y.; Xu, H. T.; Wang, Z. X.; Wang, S.; Peng, L. M. ACS Nano 2011, 5 (6), 5031−5037. (38) Chen, J. H.; Jang, C.; Xiao, S. D.; Ishigami, M.; Fuhrer, M. S. Nat. Nanotechnol. 2008, 3 (4), 206−209. (39) Souza, A. G.; Jorio, A.; Samsonidze, G. G.; Dresselhaus, G.; Saito, R.; Dresselhaus, M. S. Nanotechnology 2003, 14 (10), 1130− 1139.

(40) Eckmann, A.; Felten, A.; Mishchenko, A.; Britnell, L.; Krupke, R.; Novoselov, K. S.; Casiraghi, C. Nano Lett. 2012, 12 (8), 3925−30. (41) Li, X. S.; Cai, W. W.; An, J. H.; Kim, S.; Nah, J.; Yang, D. X.; Piner, R.; Velamakanni, A.; Jung, I.; Tutuc, E.; Banerjee, S. K.; Colombo, L.; Ruoff, R. S. Science 2009, 324 (5932), 1312−1314. (42) Lu, C. G.; Fu, Q.; Huang, S. M.; Liu, J. Nano Lett. 2004, 4 (4), 623−627.

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