Structural and Electronic Properties of Oxidized Graphene
aa r X i v : . [ c ond - m a t . m e s - h a ll ] A ug Structural and Electronic Properties of Oxidized Graphene
Jia-An Yan, Lede Xian, and M. Y. Chou
School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, U.S.A. (Dated: August 18, 2018)We have systematically investigated the effect of oxidation on the structural and electronic proper-ties of graphene based on first-principles calculations. Energetically favorable atomic configurationsand building blocks are identified, which contain epoxide and hydroxyl groups in close proximitywith each other. Different arrangements of these units yield an LDA band gap over a range of afew eV. These results suggest the possibility of creating and tuning the band gap in graphene byvarying the oxidation level and the relative amount of epoxide and hydroxyl functional groups onthe surface.
The prospects of graphene-based nanoelectronics [1, 2]have stimulated extensive research activities in recentyears. Pristine graphene, with two linear bands cross-ing at the Dirac point, is a zero-gap material. There-fore, much effort has been devoted to creating an energygap in graphene-based materials for device applications[3, 4, 5, 6, 7, 8, 9]. In particular, an energy gap can beachieved through either nanopatterning [4, 6] or chemicalfunctionalization [7, 8, 9]. The latter has a greater ad-vantage because of the ease to scale up in the production.A recent experiment has successfully generated a metal-semiconductor-metal junction using epitaxial grapheneand a single functionalized graphene sheet (FGS) [7].Analogous to the combination of Si and SiO in the cur-rent generation of microelectronics, the FGS has the po-tential of being seamlessly integrated with graphene inthe fabrication of future nanoelectronics devices. Oneway to produce FGSs is by exfoliation from graphite ox-ide (GO), which can have different compositions withvarious oxidation levels depending on the synthesis pro-cesses and conditions. Currently, GO is of particular in-terest to scientists since chemical reduction of GO hasbeen demonstrated as a promising solution-based routefor mass production of graphene [10, 11, 12, 13, 14, 15].The electronic properties of the oxidized layers dependon the detailed chemical structure, which remains un-resolved for GO for more than a century with variousstructural models proposed in the literature [16, 17, 18,19, 20]. Increased conductivity was observed during thereduction of an oxidized graphene sheet prepared fromGO [8], but the atomic origin of this behavior is stillunknown. A recent high-resolution solid-state C-NMRmeasurement [21] has confirmed the existence of C-OH(hydroxyl), C-O-C (epoxide), and sp C units on theselayers. The data further indicate that a large fraction of sp C atoms are bonded directly to C atoms in the hy-droxyl and epoxide groups, and that a large fraction of Catoms in the hydroxyl and epoxide units are bonded toeach other. In order to fully establish the atomic config-urations and related electronic properties in this impor-tant material, we report results from first-principles cal-culations that provide a clear picture of the energeticallyfavorable building blocks and stable phases. Interest- ingly, various energy gap values are found for structureswith different O concentrations, suggesting that the gapis highly tunable by varying the amount of hydroxyl andepoxide on the graphene sheet.Our theoretical study focuses on the following two keyissues: (i) how these functional groups arrange them-selves on graphene, and (ii) how these arrangementsaffect the electronic properties of the graphene sheet.The calculations were carried out using the local-densityapproximation (LDA) within density-functional theorywith a plane-wave basis set as implemented in the Vi-enna Ab-initio Simulation Package (VASP) [22]. Van-derbilt ultrasoft pseudopotentials [23] are employed. Allcalculations are done with a plane-wave cutoff energy of500 eV. Results shown in Fig. 1 are obtained using a5 × × × k -point sampling.The 5 × × − eV per cell and the force on each atomis less than 0.02 eV/˚A.A single functional group of epoxide or hydroxyl ongraphene can induce significant local distortion. With anew bond formed between C and O, the bonding char-acteristics of the connecting C atoms change from pla-nar sp to distorted sp hybridization. The structureobtained in our calculation is in good agreement withthat reported in previous theoretical studies [24, 25]. Ofparticular interest is the distribution of these functionalgroups on graphene. A recent atomic force microscope(AFM) measurement showed that the oxidized graphenesheets appear to have a thickness equal to integer mul-tiples of h ≈ FIG. 1: (Color online) Atomic configurations and energiesof various favorable combinations of epoxide and hydroxylgroups on the graphene surface. The energy shown is calcu-lated using a 5 × units in various ways, and the results calculated using a5 × sp C atoms(denoted by C ∗ , corresponding to C atoms not bonded toO), epoxide (C O), and the 1,2-hydroxyl pair [C (OH) with the connecting C atoms included]. The repre-sentative stoichiometry is C ∗ − x − y (C O) x [C (OH) ] y , orequivalently C x + y O x (OH) y , with 0 ≤ x ≤
1, 0 ≤ y ≤
1, and 0 ≤ x + y ≤
1. The ordered phases we have calcu-lated are marked on a ternary diagram shown in Fig. 2(a),where the dashed lines indicate phases with the same ra-tio of epoxide versus the hydroxyl pair. For each phasewe investigated, the structure was optimized by explor-ing various different local arrangements of the epoxideand hydroxyl groups. The lattice parameters and atomiccoordinates are fully relaxed. The formation energy isdefined in the usual way for a ternary system:∆ E [ x, y ] = E [C x + y O x (OH) y ] − (1 − x − y ) E [C ∗ ] − xE [C O] − yE [C (OH) ] , (1)where E [Z] represents the energy of a periodic phase Z.These formation energies are shown in Fig. 2(b) for the“binary” phases and for phases along each dashed line inFig. 2(a).For the fully oxidized phases in which all C atoms arebonded to O in either an epoxide or a 1,2-hydroxyl pair,low-energy “binary” phases with mixed epoxide and hy-droxyl compositions are found (top panel of Fig. 2(b)).These fully oxidized phases have a lattice expansion ofthe order of 2-3 %, and an LDA energy gap of 2.8 - 4.2eV. With a negative formation energy, these intermedi-ate phases are stable against separation into pure epoxideand pure hydroxyl phases. These stable phases includeC O (OH) , C O(OH) , and C O(OH) , with an epox-ide to hydroxyl ratio of 1:1, 1:2, and 1:4, respectively.As an example, the structure of C O (OH) is shownin Fig. 3(a), in which one can easily identify the follow-ing key features: the 1,2-hydroxyl pairs are connected toform a chain-like structure on both sides of the sheet insuch a way that the interaction associated with hydro-gen bonds can be maximized; and O atoms are drawnto the remaining C atoms in the same hexagonal ringsto form epoxides in the close proximity. The other twofully oxidized phases, C O(OH) , and C O(OH) followthe same pattern for their atomic arrangements. Thesefeatures turn out to be quite energetically favorable inconstructing phases with intermediate compositions, aswill be discussed below. The epoxide-only phase, C O, C n OC n O (OH) C n O(OH) C n O(OH) C n (OH) E ne r g y G ap ( e V ) O/C Ratio (c) -0.10.00.1-0.10.00.1-0.10.00.1 0.0 0.2 0.4 0.6 0.8 1.0-0.2-0.10.00.00.1 0.0 0.2 0.4 0.6 0.8 1.00.00.1 C n O(OH) C * =0 C OC n O (OH) F o r m a t i on E ne r g y ( e V ) C n O C O composition C (OH) C n (OH) C* Composition C n O(OH) C O(OH) C O(OH) C O (OH) C O(OH) C (OH) C OC OC O(OH) C O (OH) C*C OC (OH) C O (b)(a) FIG. 2: (Color online) (a) Ternary diagram showing ordered phases on the graphene surface with different amounts of sp Carbon (C ∗ ), epoxide (C O), and the 1,2-hydroxyl pair (C (OH) ). The phases investigated in this study are marked on thediagram, with dashed lines indicating those with the same relative amount of epoxide and hydroxyl pairs. (b) Formation energyas defined in Eq. (1) for different phases marked in the ternary diagram in (a). (c) Energy gap as a function of the overalloxygen-to-carbon ratio for different phases. is shown in Fig. 3(b), in which the O atoms follow the ar-rangements in Fig. 1(a) and stay in rows on opposite sidesof the sheet [27]. The buckling is symmetrically compen-sated. For lower-concentration epoxide-only phases, theopening of the three-membered epoxide ring by breakingthe C-C bond to release strain as proposed previously [24]turns out to be energetically favorable, together with theformation of O rows.Apart from the fully oxidized “binaries” shown in thetop panel of Fig. 2(b), we are not able to find other or-dered phases with a negative formation energy. There-fore, the T=0 lowest-energy configuration of the oxidizedgraphene sheet is likely to be a combination of fully ox-idized regions and the clean graphene phase. This con-figuration has not been observed experimentally at fi-nite temperature. Possible reasons include the following:the entropy term could be important at finite tempera-ture; the oxidization process is a highly non-equilibriumone; and the covalent bonding in the epoxide and hy-droxyl units largely reduces their mobility on the surface.Therefore, domains of various intermediate phases maystill be found in the sample under experimental condi-tions. The relative amount of epoxide and hydroxyl unitson the graphene sheet depends on the sample preparationprocess and can vary over a wide range. Here we focuson phases along each dashed line in Fig. 2(a), in which the relative amount of epoxide and hydroxyl units on thesurface is a constant. After exploring various atomic con-figurations, the lowest-energy periodic structure of theseintermediate phases found in our calculation containsstrips of epoxide and hydroxyl combinations with cleangraphene ribbons in between. An example, the structureof C O (OH) , is shown in Fig. 3(c), which contains sep-arate regions of sp and sp carbon. The sp strips con-sist of double hydroxyl chains and neighboring epoxides.The formation energies for the periodic phases with var-ious intermediate compositions constructed in this fash-ion are shown in Fig. 2(b). The strips interact weaklywhen separated by carbon ribbons, which explains whythe formation energies of these phases fall on a straightline in Fig. 2(b) when the C ∗ composition is larger thanabout 0.4. (Phases with different C ∗ compositions havedifferent strip separations.) With the formation energiesfalling on a straight line, many of these phases are ex-pected to coexist on the surface. It is energetically favor-able for these strips to coalesce, since the fully oxidizedphase has a lower formation energy. However, this pro-cess may not be completed during the oxidation process.The current results indicate that the configurationsinvestigated in previous density-functional calculations[25] for oxidized graphene sheets containing both theepoxy and hydroxyl groups may not be energetically FIG. 3: (Color online) Atomic structures for selected phases.(a) Fully-oxidized phase of C O (OH) . (b) Fully-oxidizedepoxide-only phase C O with oxygen rows on both sides ofthe plane. (c) C O (OH) structure with hydroxyl-epoxidestrips separated by sp carbon. C and O atoms are repre-sented by large spheres and H by small spheres and the dashedrectangles indicate the respective unit cells. The hydrogenbonds in the hydroxyl chains above the plane are indicatedby dashed lines. favorable for a given composition. In our calculation,we find that the formation of hydroxyl chains result-ing from hydrogen-bond interaction between neighbor-ing 1,2-hydroxyl pairs greatly lowers the energy andthat the epoxides are grouped next to these hydroxylchains. The epoxide and hydroxyl units randomly de-posited on the surfaces are expected to arrange them-selves locally following these preferred patterns, givingrise to patches of sp carbon surrounded by fully oxidizedepoxide+hydroxyl regions or vice versa. The possible ex-istence of pure graphene ribbons was proposed previously[28] in order to explain the shift of the Raman peaks inGO and FGSs. The current study provides a strong sup-port for this picture based on extensive first-principlescalculations.The finite region of sp carbon has a consequence in theelectronic structure. Without knowing the exact atomicarrangements at various compositions, we use the resultsof the ordered structures investigated above to providean estimate for this effect. The calculated LDA energygaps associated with the ordered phases considered inFig. 2(a) as a function of the overall O/C ratio are shownin Fig. 2(c). The data-point symbols are the same as those in other parts of Fig. 2. An LDA energy gap ofthe size ranging from zero to 4 eV can be found for therange of O concentration we considered. The gap rangeincludes both semiconducting and insulating phases, andthe gap size is dictated by the width of the grapheneribbons in the ordered phases we studied. (It is wellknown that an LDA calculation underestimates the en-ergy gap, and the real gap value is expected to be larger.)A few vanishing band gap values are associated with arm-chair ribbons with 3 n +2 rows of atoms ( n is an integer)or zigzag ribbons with an even number of atomic rows.These may be considered as special cases. The overallband-gap results suggest a promising and practical wayto tune the energy gap in FGSs by varying the degree ofoxidization, which is feasible experimentally, and possi-bly the location of the oxidized regions.In summary, with first-principles calculations we havestudied the structure and energetics of oxidation func-tional groups (epoxide and hydroxyl) on single-layergraphene, and the induced changes in the electronic prop-erties. We find that it is energetically favorable for thehydroxyl and epoxide groups to aggregate together andto form specific types of strips with sp carbon regions inbetween. An LDA band gap ranging from a few tenths ofan eV to 4 eV can be obtained by changing the oxidationlevel and the location of the oxidized region, suggest-ing a great potential to tune the energy gap in graphenethrough controlled oxidation processes.We acknowledge stimulating discussions with W. deHeer, C. Berger, X. Wu, and M. Sprinkle. J.A.Y.thanks D. Pandey for sending the preprint of their pa-per. This work is supported by the Department of En-ergy (Grant No. DE-FG02-97ER45632). L. X. acknowl-edges support from the Georgia Tech MRSEC funded bythe National Science Foundation (Grants No. DMR-08-20382). This research used computational resources atthe National Energy Research Scientific Computing Cen-ter, which is supported by the Office of Science of the U.S.Department of Energy under Contract No. DE-AC02-05CH11231, and the National Science Foundation Ter-aGrid resources provided by the Texas Advanced Com-puting Center (TACC). [1] W. A. de Heer et al. , Solid State Commun. , 92(2007).[2] A. K. Geim and K. S. Novoselov, Nature Materials , 183(2007).[3] T. Ohta et al. , Science , 951 (2006).[4] M. Y. Han et al. , Phys. Rev. Lett. , 206805 (2007).[5] G. Giovannetti et al. , Phys. Rev. B , 073103 (2007).[6] X. Li et al. , Science , 1229 (2008).[7] X. Wu et al. , Phys. Rev. Lett. , 026801 (2008).[8] I. 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