Edge-controlled growth and kinetics of single-crystalgraphene domains by chemical vapor depositionTeng Maa, Wencai Rena,1, Xiuyun Zhangb, Zhibo Liua, Yang Gaoa, Li-Chang Yina, Xiu-Liang Maa, Feng Dingb,c,1,and Hui-Ming Chenga,1

aShenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, People’s Republic ofChina; bInstitute of Textiles and Clothing, Hong Kong Polytechnic University, Kowloon, Hong Kong, People’s Republic of China; and cBeijing ComputationalScience Research Center, Hai-Dian District, Beijing 100084, People’s Republic of China

Edited by Hongjie Dai, Stanford University, Stanford, CA, and accepted by the Editorial Board November 4, 2013 (received for review July 6, 2013)

The controlled growth of large-area, high-quality, single-crystalgraphene is highly desired for applications in electronics andoptoelectronics; however, the production of this material remainschallenging because the atomistic mechanism that governs gra-phene growth is not well understood. The edges of graphene,which are the sites at which carbon accumulates in the two-dimensional honeycomb lattice, influence many properties, includ-ing the electronic properties and chemical reactivity of graphene,and they are expected to significantly influence its growth. Wedemonstrate the growth of single-crystal graphene domains withcontrolled edges that range from zigzag to armchair orientationsvia growth–etching–regrowth in a chemical vapor deposition pro-cess. We have observed that both the growth and the etchingrates of a single-crystal graphene domain increase linearly withthe slanted angle of its edges from 0° to ∼19° and that the ratesfor an armchair edge are faster than those for a zigzag edge. Suchedge-structure–dependent growth/etching kinetics of graphenecan be well explained at the atomic level based on the concentra-tions of the kinks on various edges and allow the evolution andcontrol of the edge and morphology in single-crystal graphenefollowing the classical kinetic Wulff construction theory. Usingthese findings, we propose several strategies for the fabricationof wafer-sized, high-quality, single-crystal graphene.

two-dimensional materials | crystal growth

Graphene, a one-atom-thick, two-dimensional (2D) crys-tal, has attracted increasing interest because of its in-

teresting properties, which include a large carrier mobility,high transparency, extremely high thermal conductivity, andhigh tensile strength (1–3). Wafer-sized single-crystal grapheneis highly desired and required for numerous applications, especiallyin electronics and optoelectronics, because grain boundariesbetween the graphene domains markedly degrade its qualityand properties (4–8). Chemical vapor deposition (CVD) hasshown great potential for growing large-sized single-crystal gra-phene domains (8–12); however, the growth rate with CVD islow, typically less than 20 μm/min, which is obviously not con-ducive to the fabrication of wafer-sized single crystals. In addition,the graphene produced by CVD suffers from poor controllabilityand low quality. For example, only zigzag (ZZ) or randomlyoriented edges have been fabricated via CVD, and the elec-tron mobility in CVD-produced graphene is substantially lowerthan that in mechanically exfoliated graphene (13). Understandingthe atomistic mechanism that governs graphene growth is nec-essary for the controlled growth of wafer-sized, high-quality,single-crystal graphene. The edge structure of graphene has beenshown to significantly influence its various fundamental prop-erties, such as its electronic and magnetic properties, its edgestability, and its chemical reactivity (14–18). Similarly, the gra-phene edges, as the sites at which carbon accretion to the two-dimensional honeycomb lattice occurs, likely influence the graphenegrowth (19–21).

We report the growth of single-crystal graphene domains withcontrolled edges with orientations that range from ZZ to arm-chair (AC) via a CVD growth–etching–regrowth (G–E–RG) pro-cess. We observed that both the graphene growth and etching viaCVD are strongly dependent on the edge structure. Such growth/etching behavior is well explained at the atomic level given theconcentrations of kinks on the various edges and allows the evo-lution and control of the graphene edges and the morphologyaccording to the classical kinetic Wulff construction (KWC) theory.Thus, we explain the commonly observed ZZ edges and low gra-phene growth rate under CVD and propose several strategies forthe fabrication of wafer-sized, high-quality, single-crystal graphene.

ResultsMorphology, Edge Evolution, and Control over Single-Crystal Graphenein CVD. We used ambient CVD with a platinum foil substrate toinvestigate the morphology evolution and to tune the edgestructure of single-crystal graphene domains. In a typical G–E–RG process, only the methane flow rate was changed to inducethe growth, etching, and regrowth of the graphene; all otherparameters were held constant (SI Appendix, Fig. S1). The ex-periments were highly reproducible, and most of the graphenedomains obtained over a given reaction time exhibited similarstructures (SI Appendix, Figs. S2 and S3). The morphology of thegraphene domains on Pt was characterized by scanning electronmicroscopy (SEM), and the edge structure of the graphene domains

Significance

Controlled synthesis of wafer-sized single crystalline high-quality graphene is a great challenge of graphene growth bychemical vapor deposition because of the complicated kineticsat edges that govern the growth process. Here we report thesynthesis of single-crystal graphene domains with tunableedges from zigzag to armchair via a growth–etching–regrowthprocess. Both growth and etching of graphene are stronglydependent on the edge structure. This growth/etching behav-ior is well explained at the atomic level, given the concen-trations of kinks on various edges, and allows control ofgraphene edges and morphology according to the classical ki-netic Wulff construction theory. This work provides a deepunderstanding of the fundamental problems that limit gra-phene growth by chemical vapor deposition.

Author contributions: W.R. and H.-M.C. designed research; T.M., W.R., X.Z., and F.D.performed research; Z.L. and X.-L.M. contributed new reagents/analytic tools; T.M.,W.R., X.Z., Z.L., Y.G., L.-C.Y., F.D., and H.-M.C. analyzed data; and T.M., W.R., F.D., andH.-M.C. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. H.D. is a guest editor invited by the EditorialBoard.1To whom correspondence may be addressed. E-mail: wcren@imr.ac.cn, feng.ding@polyu.edu.hk, or cheng@imr.ac.cn.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1312802110/-/DCSupplemental.

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was identified via Raman spectroscopy, transmission electron mi-croscopy (TEM), and selective area electron diffraction (SAED)after being transferred onto Si/SiO2 (280 nm thick) substrate ora TEM grid, using a bubbling transfer method (SI Appendix, TablesS1 and S2 and Figs. S4–S12).Fig. 1 shows the typical structure of single-crystal graphene

domains obtained at various reaction times during a CVDG–E–RGprocess. Hexagonal, single-crystal graphene domains with ZZedges were grown on the Pt surface with a relatively high methaneflow rate [3.7 standard-state cubic centimeter per minute (sccm)](Fig. 1A and SI Appendix, Figs. S4 and S5). As the reaction timewas increased, the domain size increased, whereas the ZZ edgestructure remained unchanged (Fig. 1B). Surprisingly, when weslightly reduced the methane flow rate from 3.7 sccm to 3.3 sccm,the graphene domains switched from growing to being etched.When the etching time was increased, the domain size decreased,and the morphology and edge structure changed (Fig. 1 C–G).First, two new slanted edges gradually formed at each vertex ofthe ZZ-edged hexagonal domain (Fig. 1C and SI Appendix, Fig.S13). Then, 12 new slanted edges moved inward, toward the ACdirection. Eventually, the ZZ edges disappeared, leavinga dodecagonal domain with 12 identical slanted edges (Fig. 1Dand SI Appendix, Fig. S6). During further etching, these 12slanted edges moved inward and gradually became armchair-like(Fig. 1E and SI Appendix, Fig. S7), eventually transforming into

slanted edges with an ∼19° angle from the ZZ edge (Fig. 1F andSI Appendix, Figs. S8, S9, and S14). After that, the edge directionremained almost unchanged (Fig. 1G), although the graphenedomain continuously shrank. Hereafter, we refer to this specificedge structure as S19. It is also found that the etching rate of thegraphene domains increases with the flow rate ratio of H2/CH4(SI Appendix, Figs. S2 and S15 and Table S3). Combined with thehigh catalytic ability of Pt for the dissociation of H2 to formactive atomic H, we suggest that the atomic H plays an im-portant role in the etching of graphene domains in our system.By simply increasing the methane flow rate from 3.3 sccm to

3.5 sccm, we apparently induced regrowth of the etched gra-phene domains (Fig. 1 H–L). First, the 12 slanted outer edges ofthe dodecagonal domain change to alternating AC and ZZ edges(Fig. 1H). Then, the six AC edges gradually shorten, whereas thesix ZZ edges become longer (Fig. 1 I–K and SI Appendix, Figs.S10 and S11). Finally, the graphene domain is transformed intoa hexagon with ZZ edges (Fig. 1L and SI Appendix, Fig. S12).The hexagonal domain grows continuously with increasing re-action time but without any change to its morphology or edgestructure (SI Appendix, Fig. S16), which is the same as that ob-served in Fig. 1 A and B.In addition to the evolution of the outer edge structure, a

perfect hexagonal hole in the ZZ edges appears at the center ofthe dodecagonal domain and quickly expands; however, the ZZ

Fig. 1. Morphology and edge evolution of single-crystal graphene domains grown on a Pt surface during the G–E–RG process. (A and B) The growth stage:scanning electron microscopy (SEM) images of the hexagonal single-crystal graphene domain grown in a gas flow of 700 sccm hydrogen and 3.7 sccmmethane with growth times of (A) 15 min and (B) 30 min. (C–G) The etching stage: SEM images depict a change in the single-crystal graphene domain witha gas flow of 700 sccm hydrogen and 3.3 sccm methane from B etched for (C) 4 min, (D) 7 min, (E) 10 min, (F) 11.5 min, and (G) 12 min. (H–L) The regrowthstage: SEM images of the single-crystal graphene domain regrown in a gas flow of 700 sccm hydrogen and 3.5 sccm methane from G with a regrowth time of(H) 0.5 min, (I) 2 min, (J) 3 min, (K) 5 min, and (L) 9 min. In all images, the ZZ edge of the graphene domain is oriented along the horizontal direction.

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edge structure remains unchanged during the etching process(Fig. 1 E–G). The formation of the hole likely results from thestructural defects formed during the graphene nucleation (22),and its unchanged edge directions, combined with the results ofRaman spectroscopy analysis, provide strong evidence related tothe crystallographic orientation of the outer edge. During theregrowth process, the inner hole shrinks and eventually dis-appears after its morphology evolves from a ZZ-edged hexagon(Fig. 1G) to a dodecagon with identical slanted edges (Fig. 1H)and then to a dodecagon with near-AC edges (Fig. 1I). Thisevolution is identical to that of the etching process at the outeredges of the hexagonal domains depicted in Fig. 1 C–G.

Edge-Structure–Dependent Growth and Etching of Single-CrystalGraphene. To achieve a quantitative understanding of the gra-phene growth and etching, we further studied the size evolutionof the single-crystal graphene domains as a function of the re-action time during the etching and regrowth processes. Fig. 2Aclearly demonstrates that the size evolution of the graphenedomains as a function of time exhibits a nonlinear behavior.During the etching process, the shrinking of the single-crystalgraphene domains accelerates. In contrast, the domains growmore and more slowly and eventually reach a constant growthrate after all of the edges have changed to ZZ during regrowth.A constant growth rate is also observed during the growth of theZZ-edged hexagonal graphene domain (SI Appendix, Fig. S17).Because either the etching or the regrowth was performed underconstant experimental conditions and was accompanied by acontinuous edge evolution, the rates of both etching and regrowthmust be edge-structure dependent. By fitting these data, we canobtain the etching and regrowth rates of a domain as a function ofthe average edge slanted angle, θ. The plots in Fig. 2B show alinear relationship between the etching/regrowth rate and θ,

RE=GðθÞ=RE=G0 + βE=G × θ;     for  0≤ θ≤ 198; [1]

where RE/G0 is the etching/regrowth rate of the ZZ edge, and βE/Gis a constant. Of the edges, the S19 exhibits the highest etchingand regrowth rates, which are two and six times greater than thatof the ZZ edge, respectively. Moreover, the AC edge grows fasterthan the ZZ edge (SI Appendix, Fig. S18).

Theoretical Calculation. During the growth/etching of a graphenedomain, the kinetics are determined by the addition/removal of

carbon atoms onto/from the graphene edges. Both the AC andthe ZZ edges are straight, with all edge carbon atoms located ina straight line. Therefore, the growth/etching of a straight AC/ZZedge must be initiated by the formation of a nucleus or dent (Fig.3 A and B). The height/depth of a nucleus/dent on a ZZ edge(hZZ) is 2.13 Å, whereas that on an AC edge (hAC) is smaller at1.23 Å. Therefore, the nucleus or dent on a ZZ edge may havehigher formation energy than that on an AC edge. A slantedgraphene edge can be considered as an AC or ZZ edge with kinks(Fig. 3 C–E). The addition or removal of carbon atoms onto/froma kink site leads to an only one-step propagation of the kink; anycorresponding change in the formation energy should thus benegligible. Therefore, the kink sites are the most active for carbonaddition or removal onto/from a graphene edge. If the graphenegrowth is attachment limited and all possibilities for carbon ad-dition/removal onto/from an arbitrary graphene edge with aslanted angle θ are considered, then a simplified formula for theedge orientation-dependent growth/etching rate is (19, 21, 23, 24)

RðθÞ ≈ nZZðθÞ p expð−EZZ=kTÞ+ nACðθÞexpð−EAC=kTÞ+ nKðθÞ;[2]

where nZZ(θ), nAC(θ), and nK(θ) are the concentrations of the ZZsites, the AC sites, and the kinks, respectively, along the edge.The calculated formation energies of the ZZ and AC nuclei on

a Pt(111) surface are 2.24 eV and 1.60 eV, respectively (Fig. 3Fand SI Appendix), which is in agreement with the aforemen-tioned analysis. Both of these energies are substantially greaterthan the thermal energy, kT ≈ 0.1 eV, at the graphene growthtemperature. Thus, the values of the first and second terms inEq. 2 are substantially smaller than that of the third term unlessnK(θ) = 0. Therefore, the growth/etching rate of a slanted edge islinearly proportional to the concentration of its kinks. As de-scribed in the literature (19, 20), the edge with a slanted angle ofθ = 19.107° has the largest kink concentration, and the kinkconcentration on the edges increases or decreases linearly with θfor θ in the range of 0°–19.107° or 19.107°–30° (SI Appendix, Fig.S19). Given Eq. 2, a linear relationship is expected between thegrowth/etching rate and θ for a slanted edge of θ = 19.107° withthe highest growth/etching rate of all edge types:

RðθÞ≈ nKðθÞ= θ=hZZ;     for  08< θ< 19:1078

RðθÞ≈ nKðθÞ= ð308− θÞ=hAC;     for  19:1078< θ< 308:[3]

Given the larger barrier for initiating nucleation, the growth/etching rate of the ZZ edge must be slower than that of theAC edge. Therefore, the growth/etching rate of the grapheneedges follows the order (23)

RS19 >RSL >RAC >RZZ; [4]

where RS19, RSL, RAC, and RZZ are the growth/etching rates ofthe S19, the other slanted, the AC, and the ZZ edges, respec-tively. These results are in perfect agreement with our experi-mental observations shown above.

DiscussionThe aforementioned morphology evolution can be well ex-plained by the classical theory of crystal growth (Fig. 3 G–I andSI Appendix, Figs. S20–S22). The morphology of a grown/etchedcrystal surface is governed by the dynamics of addition or re-moval of atoms, which is strongly dependent on the type ofsurface. However, in 2D graphene, the surface degenerates intolinear edges. During the growth process, according to the KWCtheory (25), the edges that grow rapidly become smaller; even-tually, only the edges with the slowest growth rate (the ZZ edge)survive (Fig. 3 G and I). In contrast, during the etching process,

Fig. 2. Edge-structure–dependent growth/etching of single-crystal graphenedomains. (A) Evolution of the size of single-crystal graphene domains asa function of the reaction time during etching and regrowth. The blue andred lines represent the fitting curves. Tens of graphene domains with thesame structure were measured for each condition; the error bars indicate thevariation in size. The typical graphene structure obtained at the measuredreaction time (denoted with letters from B to N) is presented in Fig. 1 B–L andin SI Appendix, Fig. S16. (B) The rates of etching and regrowth of the gra-phene domains as functions of the average slanted angle θ. θ = Σθili/Σli, whereθi is the slanted angle relative to the ZZ direction of an edge in a graphenedomain, and li is the length of the corresponding edge. The red and blue linesrepresent the linear fits of the data.

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the edges with a slow etching rate disappear, and those with thehighest etching rate (the S19 edges) eventually dominate the cir-cumference of the graphene domain (Fig. 3 G and H). Thegrowth/etching from the vertexes of a graphene domain leads tothe formation of various edges, including ZZ, AC, and slantededges (θ = 0° to ∼19°). However, the evolution of the hole isopposite to that of the outer circumference of a 2D crystal becausethe hole-edge propagation during etching equals the growth of theouter circumference and vice versa. Therefore, the edge-structure–dependent growth/etching rate determines the edge and mor-phology evolution of the graphene domains during both CVDgrowth and etching processes.These results indicate that graphene edges do not maintain

a constant orientation during both CVD growth and etching andthat the morphology of the graphene domains is not determinedby nucleation; the morphology is rather determined by the dy-namics of the addition/removal of carbon atoms onto/from theiredges. Such unique growth/etching behavior of graphene differsnoticeably from that of its one-dimensional counterpart, single-walled carbon nanotubes, whose chirality and growth rate remainunchanged over time under the same conditions because of theircylindrical topology (19, 23). This unique growth/etching behavior

of graphene allows us to tune the morphology and edge structureof single-crystal graphene domains by simply changing the reactiontime and the flow rate of the carbon feedstock. Because the rap-idly growing slanted edges disappear quickly, the growth of single-crystal graphene domains is largely governed by the addition ofcarbon atoms onto the surviving ZZ edges with the slowest growthrate. Thus, the observed average growth rate of single-crystalgraphene domains is relatively low, especially over long reactiontimes (8–12). We suggest that an increase in the growth temper-ature and the use of substrates with low ZZ nucleus formationenergies provide two possibilities for increasing the graphenegrowth rate because these approaches can potentially increase theaddition rate of carbon atoms onto the ZZ edges. In our experi-ments, for example, the average growth rate of single-crystalgraphene on Pt increased approximately twofold at the highergrowth temperature of 1,070 °C, even at a low methane flow rateof 3.0 sccm. The average growth rate of single-crystal graphene onliquid Cu can reach 50 μm/min at 1,080–1,160 °C (26).In addition, the regrown graphene domains are defect-free (SI

Appendix, Fig. S12), which indicates the perfect incorporation ofcarbon atoms onto the domain edges. We further confirmed thehigh quality of the regrown graphene domains via etching (Fig. 4).

Fig. 3. Theoretical analyses of the growth and etching behaviors of single-crystal graphene domains. (A and B) Nucleus, dent, and kink formation on the (A)AC and (B) ZZ edges. (C and D) A slanted edge can be viewed as an AC or a ZZ edge with a series of kinks. (E) The slanted edge 19.1° from the ZZ directionexhibits the highest concentration of kinks (23). The kink sites and normal AC or ZZ sites are marked by the solid triangles and circles, respectively. (F) Themodels used to calculate the formation energies of the kinks on the ZZ and AC edges on the Pt(111) surface. For details of the calculation, see SI Appendix. (G)Illustration of the 2D KWC during crystal growth (indicated by the outward arrow) and etching (indicated by the inward arrow). The red and blue edgesrepresent slower and faster growth/etching, respectively. (H and I) Illustrations of the edge and morphology evolution during (H) etching and (I) regrowth, asobtained by 2D KWC analyses (SI Appendix). The red, blue, and green lines represent the ZZ, AC, and S19 edges, respectively.

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As shown in Fig. 1 E–G, a hole typically appears in the centerof the as-grown single-crystal graphene domain after a givenetching time because of the structural defects that form duringgraphene nucleation (22). In contrast, visible holes do not appearin the regrown graphene domains during etching even after theirouter edges have transformed into S19 (Fig. 4B and SI Appendix,Fig. S23), and the Raman spectra of these domains do not showstrong defect-related D peaks (1,300∼1,400 cm−1) (Fig. 4C);these results suggest a complete healing of the structural defectsduring regrowth. Therefore, the regrowth of graphene providesan effective method for healing defects and improving the qualityof defective single-crystal graphene. In addition, the density ofthe graphene domains can be tuned via etching (SI Appendix,Fig. S23). We eventually obtained a single graphene domain byextending the etching time. Therefore, the observed high re-versibility of the graphene etching and regrowth, combined withthe varying activation energies for graphene nucleation and growth(27), enables the CVD fabrication of wafer-sized, high-qualitysingle-crystal graphene.

ConclusionsWe report an experimental and theoretical study of the growthkinetics of single-crystal graphene during a CVD growth–etching–regrowth process. We found that the graphene edges and mor-phologies are not determined by the nucleation but are kinetically

controlled during the CVD process and that defects in the gra-phene can be healed through an etching–regrowth process. Weobserved that the growth/etching rate of the graphene edges fol-lows the order RS19 > RSL > RAC > RZZ and increases linearly withthe slanted angles within 0°−19° relative to the ZZ direction.These results are explained theoretically at the atomic level by thedifferent kink concentrations on various edges (23). Such edge-structure–dependent growth and etching behaviors combined withthe KWC theory explain the edge and morphology evolution andthe experimental observations that, with respect to the preparationof single-crystal graphene via the CVD process, the ZZ edge isdominant, and the graphene growth rate is low. This work pro-vides a deeper understanding of the fundamental problems thatlimit the applications of CVD-grown graphene, and we haveproposed several strategies for the fabrication of wafer-sized, high-quality, single-crystal graphene.

MethodsCVD Growth of Graphene. A typical G–E–RG experiment includes three stages:growth, etching, and regrowth (SI Appendix, Fig. S1). For graphene growth,a piece of Pt foil (180 μm thick, 99.9 wt% metal basis) was rinsed with ac-etone, water, and ethanol in sequence for 40 min each. The foil was thenloaded into a fused-silica reaction tube (inner diameter: 22 mm) and heatedto 1,040 °C under the protection of 200 sccm H2; the Pt foil was annealed at1,040 °C for 10 min in H2 to remove any residual carbon or organic sub-stances. Growth was then initiated and maintained for a certain time undera mixture of gaseous CH4 (3.7 sccm) and H2 (700 sccm). After the graphenegrowth stage, the CH4 flow rate was reduced from 3.7 sccm to 3.3 sccm forgraphene etching; the other parameters were held constant. After thegraphene was etched, we regrew the graphene by increasing the CH4 flowrate from 3.3 sccm to 3.5 sccm while holding all other parameters constant.The reaction time for each stage was recorded from the point at which theCH4 flow rate was altered.

Characterization. To investigate the structure of the single-crystal graphenedomains obtained after a given reaction time, the Pt foil was quickly removedfrom the high-temperature zone. The furnace was shut down, and the CH4

flowwas stopped after the furnace temperature decreased to less than 600 °C.Such operations ensure a rapid quenching of the reactions and allow thestructure to be captured after a given time. Then, the Pt foil covered by thegraphene domains was taken out for morphological analysis of the graphenevia SEM (Nova NanoSEM 430, acceleration voltage of 15 kV). The graphenedomains were then transferred onto a Si/SiO2 (280 nm thick) substrate ora TEM grid, using a bubbling transfer method for optical (Nikon LV100D) andRaman analyses (JY HR800) or TEM (FEI Tecnai T12, 120 kV) observations andSAED measurements to identify their edge structures (SI Appendix). Becausethe bubbling transfer process does not cause any structural change in the Ptsubstrate (8), the same Pt substrate was reused in additional growth experi-ments after the graphene transfer.

Calculations. The formation energies of the ZZ and AC nuclei were calculatedwithin the density functional theory framework, as implemented using theVienna Ab initio simulation package (SI Appendix).

ACKNOWLEDGMENTS. This work was supported by the National ScienceFoundation of China (Grants 51325205, 51290273, 51172240, 51221264,and 50972147), the Ministry of Science and Technology of China (Grant2012AA030303), and the Chinese Academy of Sciences (Grant KGZD-EW-303-1).

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