Band-gap tuning of monolayer graphene by oxygen adsorption

CARBON

7 3 ( 2 0 1 4 ) 1 4 1 –1 4 5

Available at www.sciencedirect.com

ScienceDirect journal homepage: www.elsevier.com/locate/carbon

Band-gap tuning of monolayer graphene by oxygen adsorption Toru Takahashi a, Katsuaki Sugawara Takashi Takahashi a,b a b

b,* ,

Eiichi Noguchi a, Takafumi Sato a,

Department of Physics, Tohoku University, Sendai 980-8578, Japan WPI-Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

A R T I C L E I N F O

A B S T R A C T

Article history:

We have performed high-resolution angle-resolved photoemission spectroscopy of oxygen-

Received 2 October 2013

adsorbed monolayer graphene grown on 6H–SiC(0 0 0 1). We found that the energy gap

Accepted 12 February 2014

between the p and p* bands gradually increases with oxygen adsorption to as high as

Available online 19 February 2014

0.45 eV at the 2000 L oxygen exposure. A systematic shrinkage of the p* electron Fermi surface was also observed. The present result strongly suggests that the oxidization is a useful technique to create and control the band gap in monolayer graphene.  2014 Elsevier Ltd. All rights reserved.

1.

Introduction

Graphene, a single atomic layer of graphite, has attracted considerable attention because it exhibits several novel properties such as the massless Dirac fermions [1], ballistic transport [2], and the Berry’s phase [3]. The high-conducting and transparent nature is a large advantage for application to a transparent conducting electrode like indium tin oxide and fluorine tin oxide [4]. However, the absence of a band gap between the p and p* bands hinders further sophisticated application of graphene to advanced electronic devices. Intensive attempts have been performed to create a band gap in graphene. For example, it is well known that applying an external electric field to bilayer graphene produces a band gap by breaking the inversion symmetry between two layers [5–7]. In this case, however, the mobility of carriers is markedly reduced compared to that of monolayer graphene [7], likely due to the difference in the band structure near the Fermi level (EF). Since the high carrier mobility is a large advantage of using graphene and essential for realizing high-performance advanced devices, it is important to create

a band gap in monolayer graphene with keeping its high carrier mobility. Several methods to create a band gap in monolayer graphene have been proposed so far. It is known that graphene with modified edge structures such as nanoribbons [8–10] and quantum dots/antidotes [11,12] exhibits a characteristic feature indicative of a band-gap. However, this method has a difficulty in precisely tuning the band-gap magnitude since the edge structure is hard to be well controlled. Application of a uniaxial strain to a graphene sheet [13,14] can also open a band gap, but in this case a very strong strain is necessary to create a finite band gap with a desired magnitude for devices [14]. Adsorption of foreign atoms such as hydrogen [15,16], oxygen [17–21], and fluorine [22] onto graphene seems more controllable to create a band gap by altering the local chemical bonding. However, a systematic study for the relationship between the foreign-atom adsorption and the band-gap opening has not been performed, in particular, for graphene grown on a semiconductor substrate that is a basic platform of electronic devices. In this paper, we report a high-resolution angle-resolved photoemission spectroscopy (ARPES) study of oxygen-

* Corresponding author. E-mail address: [email protected] (K. Sugawara). http://dx.doi.org/10.1016/j.carbon.2014.02.049 0008-6223/ 2014 Elsevier Ltd. All rights reserved.

142

CARBON

7 3 ( 2 0 1 4 ) 1 4 1 –1 4 5

adsorbed monolayer graphene grown on SiC(0 0 0 1). We measured the change of band structure, with a special attention to the band-gap opening, with successive adsorption of oxygen to monolayer graphene. We found the oxygen-adsorption-induced band-gap opening and the systematic enlargement of the gap size with the adsorption amount. We also observed a systematic reduction of the density of states at EF, namely the carrier concentration, with oxygen adsorption.

2.

Experiments

Monolayer graphene was prepared by annealing a n-type Sirich 6H–SiC(0 0 0 1) single crystal by resistive heating at 1500 C [23]. The crystal was kept under Ar atmosphere of 0.1 MPa during the heating process to grow a large, flat sample [23,24]. By controlling the heating temperature and time, we selectively fabricated single layer graphene. The relatively large terrace size (5 lm) was observed by the atomic force microscopy. Sample surface was also characterized by low energy electron diffraction (LEED) and ARPES [23]. To oxidize monolayer graphene, it was exposed to cracked oxygen atoms, which is produced by heating 99.99995% pure O2 gas with a hot tungsten filament at the background pressure of 1.5 · 106 Torr [17]. We also tried the oxidation with noncracked oxygen and found that the oxidation efficiency is much higher in the case with cracked oxygen. After oxidizing monolayer graphene with cracked oxygen, we transferred the sample to the ARPES system without exposing the sample to the air. ARPES measurements were performed using a VGSCIENTA SES-2002 spectrometer with a high-flux helium discharge lamp and a toroidal grating monochromator. We used the He IIa resonance line (hn = 40.814 eV) to excite photoelectrons. The energy and angular resolutions were set at 16 meV and 0.2, respectively. The sample was kept at room temperature during the ARPES measurements. The Fermi level of samples was referred to that of a gold film deposited on the sample holder.

3.

Results and discussion

Fig. 1 shows the low-energy electron diffraction (LEED) pattern of monolayer graphene before and after the oxygen adsorption of 2000 Langmuir (L). As clearly seen in Fig. 1a, we find two different hexagonal structures, SiC(1 · 1) and graphene (1 · 1), which arise from the SiC substrate and

(a)

graphene (1x1)

(b)

graphene (1x1)

Si(1x1)

Si(1x1) 6 3x6 3R30

6 3x6 3R30

Fig. 1 – LEED patterns of (a) pristine and (b) oxygen-adsorbed (2000 L) monolayer graphene grown on SiC, measured with the primary electron energy of 150 eV.

monolayer graphene, respectively. It is clearly seen that the graphene (1 · 1) spots are rotated by 30 relative to the p p SiC(1 · 1) spots [23,25]. We also find the (6 3 · 6 3)R30 spot due to the buffer structure formed just above the SiC substrate [23,25]. After the oxygen exposure (Fig. 1b), the overall spectral intensity becomes slightly obscured while the position of spot looks unchanged. This suggests that oxygen atoms are randomly adsorbed on graphene surface and/or intercalated between graphene and buffer layer. We have p p not observed the ( 3 · 3)R30 superstructure unlike the case of previous study [18], which may be due to the difference in the sample fabrication and/or oxygen exposure conditions. Fig. 2 shows a comparison of experimental valence-band dispersions along the GKM high-symmetry line between pristine and oxygen-absorbed (2000 L) monolayer graphene. The experimental band structure was obtained by plotting the ARPES intensity as a function of wave vector and binding energy. The overall valence-band dispersions for the r and p bands appear to be essentially unchanged upon oxygen adsorption, as recognized by comparing the energy position of the bottom of the r band and the top of the p band at the K point, whereas the intensity distribution looks different, particularly at the binding-energy region of 4–10 eV, due to the contribution from the oxygen 2p orbital [26]. We have estimated the oxygen coverage at the 2000 L exposure from the intensity ratio of the O 2p and C 2s bands by taking into account the photo-ionization cross-section [27]. We obtained the oxygen coverage of about 28% in the O/C unit (%) at the 2000 L oxygen exposure. We use the coverage number based with this estimation instead of ‘‘Langmuir’’ in the later section of manuscript when the coverage number is more appropriate in explaining the experimental results. It is noted from Fig. 2a that the bright intensity near EF at the K point in pristine graphene, which originates from the p* band, is not seen in oxygen-adsorbed counterpart, likely due to a hole doping and the resultant upward shift of the overall valence band upon oxygen adsorption. To elucidate the change in the electronic state near EF in more detail, we have performed a systematic ARPES measurement around the K point as a function of oxygen exposure amount. Fig. 3a and b displays the evolution of Fermi surface and band dispersions near EF upon oxygen adsorption. In pristine graphene, we find a circular Fermi surface originating from the p* band, which is inherently unoccupied but looks electron-doped probably due to the charge transfer from the substrate [23,28]. As seen in Fig. 3, the oxygen adsorption causes a gradual shrinkage of the circular Fermi surface and a systematic upward shift of the p and p* bands, both of which are attributed to the carrier (hole) doping from adsorbed oxygen to graphene. It is remarked here that a finite density of states exists between the p and p* bands as seen in Fig. 3b. This is more clearly seen in a set of energy distribution curves (Fig. 3c), where a finite intensity remains between the p and p* bands. These in-gap states may originate from the edges and/ or the terrace defects [29] which enhances the incorporation of oxygen (note that further experimental studies are necessary to clarify this point). It is also noticed from Fig. 3b and c that the spectrum becomes broad in heavily-oxygenadsorbed samples, probably due to the enhanced impurity scattering by random potential of adsorbed oxygen atoms.

CARBON

(a)

(b)

EF

EF

2

2

4

Binding Energy (eV)

Binding Energy (eV)

143

7 3 (2 0 1 4) 1 4 1–14 5

6 8 10 12

4 6 8 10 high

12

14

14

16

16

low

Wave Vector

Wave Vector

Fig. 2 – Experimental valence-band structure along the GKM cut at 300 K for (a) pristine and (b) oxygen-adsorbed (2000 L) graphene. The band dispersion was obtained by plotting the ARPES intensity as a function of wave vector and binding energy. Arrow at EF at the K point in (a) indicates the weak signature of the p* band.

(a) 1.0 x 1013 (cm-2)

8.9 x 1012 (cm-2)

7.4 x 1012 (cm-2)

(c)

2.6 x 1012 (cm-2)

(d)

1.8

270 L

0L

-0.1

0.0

0.1-0.1

0.0

540 L

0.1-0.1

0.0 kx

2000 L

1200 L

0.1-0.1

-1)

0.1-0.1

0.0

0.0

0.1

Binding Energy (eV)

(b) EF 0.2 0.4

ED

2

2

2

2

2

Binding Energy (eV)

1.7

Intensity (arb. units)

ky

-1)

EF

0.2 0L 270 L 540 L 1200 L 2000 L

0.4

0.6

0.6 0.8

0.8 -0.1

0.0

0L 0.1

-0.1

0.0

270 L 0.1

-0.1

0.0 kx

-1)

540 L 0.1

-0.1

1200 L 0.0 0.1

2000 L

-0.1

0.0

0.1

0.8 0.6 0.4 0.2 EF Binding Energy (eV)

-0.1

0.0 kx

-1)

0.1

Fig. 3 – (a) Evolution of Fermi surface at the K point with oxygen adsorption in monolayer graphene. The experimental results until 1200 L were obtained with one sample by successive oxygen exposure while that for 2000 L was obtained with a different graphene sample prepared under the same condition. The total oxygen exposure (0–2000 L) and the carrier number estimated from the Fermi-surface volume are indicated. (b) Corresponding band dispersions near EF around the K point, obtained by dividing the ARPES intensity by the Fermi–Dirac distribution function convoluted with an instrumental resolution. 2D and ED indicate the band gap and the Dirac energy, respectively, where the Dirac energy is defined as the center of the band gap. (c) Energy distribution curves (EDCs) of monolayer graphene at the 270 L oxygen exposure shown in (b). (d) Experimental band dispersions for different oxygen exposures (circles), compared with its fitting results (solid lines) with the Dirac band dispersions with a rest mass term [33].

In addition to the change in the size of Fermi surface, the band gap (2D) between the p and p* bands, estimated from the energy difference between the top of the p band and the bottom of the p* band, also gradually increases with the oxygen adsorption from 0.2 eV for pristine graphene to 0.45 eV for the sample exposed to 2000 L oxygen. This clearly demonstrates that the oxygen adsorption not only causes the hole doping but also alters the band-gap magnitude. This shows a sharp contrast to the case of monolayer graphene deposited with Au, Sb, Bi, NO2, and F4-TCNQ molecules [30–32], where only a simple chemical-potential shift was observed. As seen in Fig. 3b, the bottom of p* band of the 2000 L sample looks to touch EF or be slightly above EF, suggesting that the heavily

oxygen-adsorbed monolayer graphene could be a semiconductor. Such a systematic change in the band dispersions is illustrated in Fig. 3d, where the experimental band dispersions (circles) obtained by fitting the energy distribution curves divided by the Fermi–Dirac distribution function are plotted together with the simulated band dispersions incorporating the rest mass term [33]. In Fig. 3d, one may recognize a peculiar behavior of the band dispersions upon the oxidation. The top of p band at first shifts toward the high binding energy from 0 L to 270 L, then turns to the low binding energy at the higher oxygen exposure (>540 L). This apparently peculiar behavior in the energy position of the top of the p band may be explained in terms of the combined effect of the

144

CARBON

7 3 ( 2 0 1 4 ) 1 4 1 –1 4 5

position of the Dirac point and the band-gap size. Namely, the Dirac point is gradually shifted upward with the oxidation while the energy gap is drastically increased at the early stage of oxidation (270 L) and is almost saturated at the higher oxygen exposure (>540 L). To evaluate more quantitatively the oxygen-induced change in the electronic state, we plot in Fig. 4 the band-gap magnitude and the electron carrier number estimated from the volume of the p* Fermi surface as a function of the total oxygen exposure (oxygen coverage). We find a general trend that the carrier density gradually decreases with oxygen exposure and vise versa for the band-gap magnitude. It is noticed here that the band-gap magnitude is not simply proportional to the oxygen exposure, being saturated at around 540 L (about 7% oxygen coverage), in sharp contrast to the carrier number which monotonically decreases even above 540 L. This suggests that the band gap magnitude and the carrier number are not closely correlated with each other as discussed later in detail. First, we discuss the origin of the observed band gap and its enhancement upon oxygen adsorption. The band gap of monolayer graphene is known to be produced by the nonequivalency between carbon A and B sites [33,34] induced by the symmetry breaking [35,36]. It has been theoretically argued that the oxygen atom alters the sp2 bonding scheme of carbon by locally eliminating the p orbital via the formation of the CAOAC bonding, leading to the creation of a band gap and its gradual increase with exposure amount [37–40]. The present experimental result is consistent with this theoretical prediction in a sense that the higher oxygen exposure creates the larger band gap, whereas the overall gap magnitude is much smaller than that from the theory (2D 3 eV in the calculations [37–40]). A possible reason for the suppressed band gap in the experiment may be the low concentration of CAOAC bonding in the present sample and/or the substrate effect. As seen in Fig. 4, the saturation of the band gap size

O/C ratio (%) 14

Band gap 2

28

0.6

1.2

0.5

1.0

0.4

0.8

0.3

0.6

0.2

0.4

0.1

0.2

0.0

0.0 0

270 540

1200 Langmuir (L)

Carrier number ( 1013 cm-2 )

(eV)

0

2000

Fig. 4 – Estimated band-gap size 2D (blue circle) and the carrier number (red circle) plotted as a function of the total oxygen exposure and the estimated oxygen coverage. The carrier number for the 2000 L sample is likely to be zero within our experimental uncertainties since the bottom of the p* band looks to be located above EF (see Fig. 3 (b)).

starts at around 540 L oxygen exposure. We ascribe this saturation to the low-concentration of CAOAC bonding. As described above, the 540 L oxygen exposure corresponds to the oxygen coverage of about 7% in the O/C unit. It has been theoretically proposed that the band gap of oxidized graphene strongly depends on the lattice constant [38,40]. The experimental fact that our oxidized graphene film has the lattice constant similar to that of graphene, as evidenced from the location of the K point, suggests that the expansion of CAC distance caused by the formation of CAOAC bonding would be markedly suppressed by the strong interaction between graphene and SiC substrate, leading to the observed suppression of the band-gap magnitude. A previous ARPES study [18] reported that the oxygen adsorption onto monolayer graphene at 500 C without using a heated W filament causes the shift of the Dirac point, but does not change the band-gap size. This shows a sharp contrast to the present ARPES study where both are markedly altered upon the oxygen exposure. This difference may be due to the effect of heated W filament which ‘‘cracks’’ molecular oxygen and produces atomic oxygen. Actually, when we stopped heating the W filament during the oxygen exposure, we observed a negligible change in the band-gap size, consistent with the previous study [18]. It is inferred that the simple molecular-oxygen adsorption onto graphene would cause only a charge (hole) transfer from oxygen to graphene with keeping the sp2 bonding scheme unchanged, while the strong adsorption with cracked oxygen (atomic oxygen) would destroy the sp2 local bonding by forming the CAOAC bond, resulting in the creation or enhancement of the band gap. As seen in Fig. 4, the band-gap size is saturated at around the 540 L oxygen exposure. This characteristic behavior of band gap may be understood in terms of two different processes of oxygen adsorption as described above. It is inferred that the CAOAC bond is efficiently formed by cracked oxygen at the early stage of oxygen adsorption (less that 540 L or about 7% oxygen coverage) to open the band gap, while adsorbed molecular oxygen continuously donate hole carriers to graphene in the all exposure region. This conjecture may be supported by the experimental result in Fig. 3 that the Dirac energy is continuously shifted upward even after the 540 L oxygen exposure. Finally it should be stressed that the precise control of the gap size and the resultant carrier concentration in oxidized monolayer graphene need a careful and precise tuning of several parameters such as the oxygen flow-rate, the duration time, the temperature of W filament, and the sample temperature.

4.

Conclusion

We reported the ARPES result for oxygen-adsorbed monolayer graphene. We found that the size of band gap gradually increases with oxygen adsorption to reach as high as 0.45 eV at the 2000 L-oxygen exposure (the estimated oxygen coverage of 28% in the O/C unit). The p* Fermi surface concomitantly shrinks with the oxygen adsorption and eventually vanishes, suggesting that the metal-to-semiconductor transition takes place in oxidized monolayer graphene. The present ARPES result provides a useful way to create and control the band gap in monolayer graphene, opening an important step

CARBON

7 3 (2 0 1 4) 1 4 1–14 5

toward feasible application of graphene-based nano-electronic devices.

Acknowledgements We thank T. J. Kleeman for his help in ARPES experiments. This work was supported by JSPS (KAKENHI 23224010 and 24740216) and MEXT (Grant-in-Aid for Scientific Research on Innovative Areas ‘‘Science of Atomic Layers’’ 25107003). R E F E R E N C E S

[1] Novoselov KS, Geim AK, Morozov SV, Jiang D, Katsnelson MI, Grigorieva IV, et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 2005;438:197–200. [2] Geim AK, Novoselov KS. The rise of graphene. Nat Mater 2007;6:183–91. [3] Zhang Y, Tan Y-W, Stormer HL, Kim P. Experimental observation of the quantum hall effect and Berry’s phase in graphene. Nature 2005;438:201–4. [4] Wang X, Zhi L, Mu¨llen K. Transparent, conductive graphene electrodes for dye-sensitized solar cells. Nano Lett 2008;8:323–7. [5] McCann E. Asymmetry gap in the electronic band structure of bilayer graphene. Phys Rev B 2006;74:161403R. [6] Castro EV, Novoselov KS, Morozov SV, Peres NMR, Lopes dos Santos JMB, Nilsson J, et al. Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect. Phys Rev Lett 2007;99:216802. [7] Oostinga JB, Heersche HB, Liu X, Morpurgo AF, Vandersypen LMK. Gate-induced insulating state in bilayer graphene devices. Nat Mater 2008;7:151–7. [8] Fujita M, Wakabayashi K, Nakada K, Kusakabe K. Peculiar localized state at zigzag graphite edge. J Phys Soc Jpn 1996;65:1920–3. [9] Nakada K, Fujita M, Dresselhaus G, Dresselhaus MS. Edge state in graphene ribbons: nanometer size effect and edge shape dependence. Phys Rev B 1996;54:17954–61. [10] Son Y-W, Cohen ML, Louie SG. Energy gaps in graphene nanoribbons. Phys Rev Lett 2006;97:216803. [11] Singh AK, Penev ES, Yakobson BI. Vacancy clusters in graphene as quantum dots. ACS Nano 2010;4:3510–4. [12] Fu¨rst JA, Pedersen JG, Flindt C, Mortensen NA, Brandbyge M, Pedersen TG, et al. Electronic properties of graphene antidot lattices. New J Phys 2009;11:095020. [13] Ni ZH, Yu T, Lu YH, Wang YY, Feng YP, Shen ZX. Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening. ACS Nano 2008;2:2301–5. [14] Ni ZH, Yu T, Lu YH, Wang YY, Feng YP, Shen ZX. Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening. ACS Nano 2009;3:483. [15] Balog R, Jørgensen B, Nilsson L, Andersen M, Rienks E, Bianchi M, et al. Bandgap opening in graphene induced by patterned hydrogen adsorption. Nature Mater 2010;9:315–9. [16] Elias DC, Nair RR, Mohiuddin TMG, Morozov SV, Blake P, Halsall MP, et al. Control of graphene’s properties by reversible hydrogenation: evidence for graphene. Science 2009;323:610–3. [17] Hossain MZ, Johns JE, Bevan KH, Karmel HJ, Liang YT, Yoshimoto S, et al. Chemically homogeneous and thermally reversible oxidation of epitaxial graphene. Nature Chem 2012;4:305–9. [18] Mathieu C, Lalmi B, Mentesß TO, Pallecchi E, Locatelli A, Latil S, et al. Effect of oxygen adsorption on the local properties of epitaxial graphene on SiC (0 0 0 1). Phys Rev B 2012;86:035435.

145

[19] Schulte K, Vinogradov NA, Ng ML, Ma˚rtensson N, Preobrajenski AB. Bandgap formation in graphene on Ir(1 1 1) through oxidation. Appl Surf Sci 2012;267:74–6. [20] Larciprete R, Ulstrup S, Lacovig P, Dalmiglio M, Bianchi M, Mazzola F, et al. Oxygen switching of the epitaxial graphene– metal interaction. ACS Nano 2012;6:9551–8. [21] Vinogradov NA, Schulte K, Ng ML, Mikkelsen A, Lundgren E, Ma˚rtensson N, et al. Impact of atomic oxygen on the structure of graphene formed on ir(1 1 1) and pt(1 1 1). J Phys Chem C 2011;115:9568–77. [22] Cheng S-H, Zou K, Okino F, Gutierrez HR, Gupta A, Shen N, et al. Reversible fluorination of graphene: evidence of a twodimensional wide bandgap semiconductor. Phys Rev B 2010;81:205435. [23] Sugawara K, Sato T, Kanetani K, Takahashi T. Semiconductormetal transition and band-gap tuning in quasi-free-standing epitaxial bilayer graphene on SiC. J Phys Soc Jpn 2011;80:024705. [24] Emtsev KV, Bostwick A, Horn K, Jobst J, Kellogg GL, Ley L, et al. Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide. Nat Mater 2009;8:203–7. [25] Forbeaux I, Themlin J-M, Debever J-M. Heteroepitaxial graphite on 6H–SiC(0001): interface formation through conduction-band electronic structure. Phys Rev B 1998;58:16396. [26] O’Brien ML, Koitzsch C, Nemanich RJ. Photoemission of the SiO2–SiC heterointerface. J Vac Sci Technol B 2000;18:1776–84. [27] Yeh JJ. Atomic Calculation of Photoionization Cross-Sections and Asymmetry Parameters. Langhorne, PE (USA): Gordon and Breach Science Publishers; 1993. [28] Riedl C, Coletti C, Iwasaki T, Zakharov AA, Starke U. Quasifree-standing epitaxial graphene on SiC obtained by hydrogen intercalation. Phys Rev Lett 2009;103:246804. [29] Rotenberg E, Bostwick A, Ohta T, McChesney JL, Seyller T, Horn K. Origin of the energy bandgap in epitaxial graphene. Nature Mater 2008;7:258–9. [30] Gierz I, Riedl C, Starke U, Ast CR, Kern K. Atomic hole doping of graphene. Nano Lett 2008;8:4603–7. [31] Zhou SY, Siegel DA, Fedorov AV, Lanzara A. Metal to insulator transition in epitaxial graphene induced by molecular doping. Phys Rev Lett 2008;101:086402. [32] Coletti C, Riedl C, Lee DS, Krauss B, Patthey L, Klitzing KV, et al. Charge neutrality and band-gap tuning of epitaxial graphene on SiC by molecular doping. Phys Rev B 2010;81:235401. [33] Hunt B, Sanchez-Yamagishi JD, Young AF, Yankowitz M, LeRoy BJ, Watanabe K, et al. Massive Dirac fermions and hofstadter butterfly in a van der waals heterostructure. Science 2013;340:1427–30. [34] Saito R, Dresselhaus G, Dresslelhaus MS. Physical Properties of Carbon Nanotubes. London: Imperial College Press; 1998. [35] Zhou SY, Gweon G-H, Fedorov AV, First PN, De Heer WA, Lee D-H, et al. Substrate-induced bandgap opening in epitaxial graphene. Nature Mater 2007;6:770–5. [36] Zhou SY, Siegel DA, Fedorov AV, Gabaly FE, Schmid AK, Castro Neto AH. Origin of the energy bandgap in epitaxial graphene. Nature Mater 2008;7:259–60. [37] Xu Z, Xue K. Engineering graphene by oxidation: a firstprinciples study. Nanotechnology 2010;21:045704. [38] Huang H, Li Z, She J, Wang W. Oxygen density dependent band gap of reduced graphene oxide. J Appl Phys 2012;111:054317. [39] Topsakal M, Ciraci S. Domain formation on oxidized graphene. Phys Rev B 2012;86:205402. [40] Pu HH, Rhim SH, Hirschmugl CJ, Gajdardziska-Josifovska M, Weinert M, Chen JH. Strain-induced band-gap engineering of graphene monoxide and its effect on graphene. Phys Rev B 2013;87:085417.