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1 Ultrafast growth of single-crystal graphene assisted by a continuous oxygen supply Xiaozhi Xu, Zhihong Zhang, Lu Qiu, Jianing Zhuang, Liang Zhang, Huan Wang, Chongnan Liao, Huading Song, Ruixi Qiao, Peng Gao, Zonghai Hu, Lei Liao, Zhimin Liao, Dapeng Yu, Enge Wang, Feng Ding, Hailin Peng, Kaihui Liu The supplementary information includes: Supplementary Figure 1-6 Supplementary Table 1 Supplementary Method 1-2 NATURE NANOTECHNOLOGY 1

2 Supplementary Fig. 1: Diffusive model of air flow in the narrow gap In our study, there is a narrow gap between the oxide substrate and the back side of the Cu foil. This gap has a height h ~ 15 μm(supplementary Fig. 1a), which is about more than 10 3 times less than the diameter of the furnace tube (DD~ 5cm) used in our CVD experiments (Supplementary Fig. 1b). According to theory of fluid dynamics, the viscous flow between the gap (νν) will be (DD h) 2 > 10 6 times slower than the flow through the furnace tube (VV) or νν VV < In our experimental design, VV is ~ 2 cm s and therefore ν < cm s. This indicates that time required for the air flow to go from one side of the gap to another side (length ~ 4cm) is ~ seconds or ~ 10 3 hours by viscous dynamics. Next let s consider the effect of molecule diffusion. The free path of the gaseous molecule under the experimental condition is λλ = kktt 2ππdd 2 PP = 0.2 μm, where kk is the Boltzmann constant, TT = 1300 K is the experimental temperature, dd = 0.4 nm is the diameter of CH4 molecular and PP = 10 5 Pa is the pressure of the system. The average velocity of molecule motion is <vv mm > = 3kkkk/mm ~ 10 3 m s, where m is the mass of the molecule (the mass of CH4 molecule is used for the estimation). So, the collision frequency between molecules can be estimated as ff = <v mm >/λ ~ Hz. A molecule to diffuse out of the gap should travel a distance of l~ 2 cm, therefore the average time for a molecule to diffuse out of the gap is tt = 1 ff (ll λλ) 2 = 2 s. which is extremely smaller than the time of the air flow passing through the gap. So, we conclude that the behaviour of the molecule in the gap is diffusive and trapping time is in the same order of magnitude as our experimental time (the graphene growth time is ~ 5 s in our experiments). 2 NATURE NANOTECHNOLOGY

3 SUPPLEMENTARY INFORMATION With the continuous release of the O from the oxide substrate, the concentration of the O confined in the gap can be many orders of magnitude higher than that on the front side of the Cu foil, which is exposed to the open space. This continuously present high O concentration can have two important effects. (1) As shown by our DFT calculations, the absorbed O will greatly promote the dissociation of CH4 on the Cu surface. (2) This O can also help to reduce the nucleation density and lower the barrier of carbon precursor attachment. The combination of these effects leads to high-rate growth of large-area single-crystal graphene. a air b Cu 15 μm D SiO 2 50 μm Supplementary Figure 1. Schematics of viscous fluid model of air flow in the narrow gap between Cu and oxide substrate. (a) Typical optical image of the cross-section of the structure. The gap between oxide and Cu foil is ~15 μm. (b) Schematic diagram of the viscous fluid model. NATURE NANOTECHNOLOGY 3

4 Supplementary Fig. 2: Graphene growth on Cu foil supported by other oxides and nonoxides We grew graphene on Cu foils supported by other oxides and non-oxides. 300 nm SiO2/Si and quartz substrates give out large circle-like graphene domains. But on Ta and SiC, graphene domains are all star-like with size of ~15 μm. a on SiO 2 /Si b on quartz 0.1 mm 0.1 mm c on Ta d on SiC 40 μm 40 μm Supplementary Figure 2. Optical images of graphene domains on back side of Cu foils supported by (a) 300 nnnn SiO2/Si, (b) quartz, (c) Ta and (d) SiC substrate. 4 NATURE NANOTECHNOLOGY

5 SUPPLEMENTARY INFORMATION Supplementary Fig. 3: Raman mapping of graphene domain Raman mapping was also adopted to demonstrate the quality and uniformity of the graphene domains in large area. Supplementary Fig. 3a is an optical image of a graphene domain transferred onto a 300 nm SiO2/Si substrate and the darker region is the graphene sample. Small black spots on the graphene are the residue of PMMA. G mode map and 2D mode map are shown in Supplementary Fig. 3b-c, the shapes of which are well consistent with the optical image (Supplementary Fig. 3a). The slight colour variation through the entire range of graphene indicates the uniformity of graphene domain. Supplementary Fig. 3d shows the D mode mapping of the graphene. The D mode signal is not detectable in the whole area and similar to the background, suggesting the high quality of graphene. a b G mode c 15 2D mode d D mode Supplementary Figure 3. Raman mapping of a graphene domain. (a) Optical image, (b) G band, (c) 2D band and (d) D band Raman mapping of the graphene domain transferred onto SiO2/Si substrate. NATURE NANOTECHNOLOGY 5

6 Supplementary Fig. 4: Electrical properties of graphene domain In order to evaluate the electrical properties of graphene, we fabricated back-gated graphene field-effect transistors on individual domains. A representative optical image of graphene device on SiO2/Si substrate is shown in Supplementary Fig. 4a. We conducted lowfield Hall measurements and the result is shown in Supplementary Fig. 4b. With n = (ee 1 ρρ xxxx ) and μ = (eeeeρρ xxxx ) 1, the mobility μ of the device was determined as 6300 cm 2 V 1 s 1 at hole side. The mobility is comparable to the mechanically exfoliated graphene in our experiment if we carry on the same transfer process. Additionally, the first Landau level (quantized filling factor υ = 6) of hole in graphene can be clearly identified. a b 1100 xx xy 4000 xx ( ) xy ( ) 10 μm B (T) Supplementary Figure 4. Electrical properties of graphene domain. (a) Optical image for back-gated graphene field-effect transistor device. (b) Hall measurement of graphene device. It shows a Hall mobility of 6300 cm 2 V 1 s 1. 6 NATURE NANOTECHNOLOGY

7 SUPPLEMENTARY INFORMATION Supplementary Fig. 5: Graphene growth on Cu foil sandwiched with oxide and non-oxide substrates A Cu foil was sandwiched with one oxide and one non-oxide substrates, ensuring the evaporation of Cu on both sides is suppressed, as depicted in Supplementary Fig. 5a-d. Under the same condition, we carried out the CVD growth of graphene. From the images shown in Supplementary Fig. 5e-h it is clearly seen that the size of graphene domains grown on the side facing fused silica is always much larger than the ones on the side facing graphite, Ta or SiC. By this result we can conclude that the ultrafast growth indeed mainly relies on the O released by the oxide, rather than the suppressed evaporation of Cu in the narrow gap between Cu and substrate. a b c d graphite SiO 2 Cu Cu SiO 2 graphite SiO 2 Cu Ta SiO 2 Cu SiC e face to SiO2 f face to graphite g face to Ta h face to SiC 0.2 mm 40 μm 40 μm 40 μm Supplementary Figure 5. Graphene growth on Cu foil sandwiched with oxide and nonoxide substrates. (a-d) Schematic diagrams of the sandwiched structure. (e-h) Optical image of graphene on Cu foils facing SiO2, graphite, Ta and SiC, respectively. NATURE NANOTECHNOLOGY 7

8 Supplementary Fig. 6: Morphologies of graphene domains under different feeding gas Under low flow of CH4, the graphene domains are of dendritic shape (Supplementary Fig. 6a). As the CH4 flow goes up graphene domains become compact (Supplementary Fig. 6b). When the CH4/H2 ratio increases further, the graphene domains become circle-like (Supplementary Fig. 6c). a CH 4 /H 2 = 1:40 CH 4 = 0.15 sccm b CH 4 /H 2 = 1:40 CH 4 = 1 sccm c CH 4 /H 2 = 1:4 CH 4 = 1 sccm 0.1 mm 0.1 mm 0.2 mm Supplementary Figure 6. Optical images of graphene domains on Cu foils with different feeding gas. 8 NATURE NANOTECHNOLOGY

9 SUPPLEMENTARY INFORMATION Supplementary Table 1. Reported growth rates of large CVD graphene single crystals on Cu foils Table 1 Reported growth rates of large CVD graphene single crystals on Cu foils Group Growth Rate (μm/s) Xiangfeng Duan Gong Gu Li Wang Zhengtang Luo Xiaoming Xie Rodney S. Ruoff James M. Tour Camilla Coletti Wenjun Zhang Kaihui Liu (this work) 60 NATURE NANOTECHNOLOGY 9

10 Supplementary Method 1: parameters for phase field simulations The phase field (PF) simulation used here is similar to that in Ref ( 6 ). The PF model consists of an order parameter ψψ and a concentration field cc. We denote ψψ = 1 for bare Cu surface and ψψ = 1 for graphene layer. The coupled PF equations for ψψ and cc read ττ ψψ = (κκκκ ) + (κκκκ ) + (κκ2 ψψ) + sin(ππππ) + φφ(cc cc eeee ) {1 + cos(ππππ)}, = DD 2 cc + FF cc 1 ττ ss 2. In the first equation, ττ ψψ is the characteristic time of attachment of the carbon species, and κκ = kk{1 + εε gg cos(nnnn)}, where kk is the constant average interface energy density, εε gg is the strength of the anisotropy, nn is the number of folding of symmetry, and θθ = tan 1 yyψψ xx ψψ is the angle between the grain edge and the x-axis. κκ. φφ is a coupling constant in the PF double-well potential, corresponding to the barrier height between ψψ = 1 and ψψ = 1, and cc eeee is the equilibrium concentration at which graphene and free carbon species can coexist in equilibrium. In the second equation, DD is the diffusion coefficient of the carbon species, FF is the flux and ττ ss is the mean lifetime of carbon species on the surface. In the last term, the factor -1/2 denotes that the unit of concentration must be monolayer (ML). To reasonably simulate the experimental conditions, by understanding that the C concentration on Cu substrate is usually low, we set cc eeee = On the other hand, we denote cc = FF ττ ss as the concentration at infinite distance, corresponding to the saturation concentration of the carbon species on Cu substrate, and we fix cc = 3cc eeee in our calculation. Since we suppose in the experiment that the most crucial difference between two sides of substrate lies in the different flux, we adjust FF and find the different growth behaviours, and then ττ ss = cc FF. Other parameters are: ττ ψψ = 1, kk = 2, εε gg = 0.04, nn = 6, φφ = 200, and DD = 120. The simulation is performed on a discrete lattice, with the spatial and time mesh being chosen Δxx = Δyy = 1 and Δtt = For each simulation, the initial 10 NATURE NANOTECHNOLOGY

11 SUPPLEMENTARY INFORMATION configuration is a spherical grain with radius of 10 at the centre of the simulation area, and both terms of incoming (FF) and outgoing ( cc ) of the carbon species are assumed to exist only in the ττ ss area of bare Cu substrate. As it is mentioned previously, the depletion zone is defined as the region where the C concentration is significantly lower than that in the area far from it. To assess this property in the framework of PFT, we designate the width of depletion zone as the distance of a stripe between 90% maximum concentration and 110% minimum concentration. The values of the width of depletion zone are presented in Fig. 4 in the text, where large numbers correspond to gentle concentration gradient. NATURE NANOTECHNOLOGY 11

12 Supplementary Method 2: calculations of CH4 dissociation on Cu(100) surface with and without O atoms In the theoretical part of this study, the metal surface is presented by a 4-atomic layer-thick slab model of the Cu(100) surface with periodic boundary condition (PBC). The PBC supercell is composed of 4 4 copper atoms on the x-y plan. To avoid the interaction between neighbouring images, the periodicity along z direction ensures a vacuum layer greater than 15 Å between neighbouring slabs. During the structure optimization, all the copper atoms of the bottom layer were fixed while all the other atoms were fully relaxed. Density functional theory (DFT) calculations were performed by using the Vienna ab initio Simulation Package (VASP) with projected augmented wave (PAW) method 13 describing the interactions between valence electrons and ion cores. Generalized gradient approximation (GGA) energy was adopted for the exchange-correlation interaction 14. To count the weak van der Waals interaction of the system during the calculations, the DFT-D2 method 15 was applied. A plane-wave cutoff energy of 400 ev was used and all the structures were fully relaxed with the energy and force convergence criteria of 10-4 ev and 10 2 ev A, respectively. The Brillouin zone was sampled with with the Monkhorst Pack mesh k-point 16. CH4 dissociation barriers and minimum energy paths (MEP) were calculated with climbing image nudged elastic band (CI-NEB) method 11, 13, NATURE NANOTECHNOLOGY

13 SUPPLEMENTARY INFORMATION References: 1 Zhou, H. L. et al. Chemical vapour deposition growth of large single crystals of monolayer and bilayer graphene. Nat Commun 4, 2096 (2013). 2 Mohsin, A. et al. Synthesis of Millimeter-Size Hexagon-Shaped Graphene Single Crystals on Resolidified Copper. Acs Nano 7, (2013). 3 Wang, C. C. et al. Growth of Millimeter-Size Single Crystal Graphene on Cu Foils by Circumfluence Chemical Vapor Deposition. Sci Rep-Uk 4, 4537 (2014). 4 Gan, L. & Luo, Z. T. Turning off Hydrogen To Realize Seeded Growth of Subcentimeter Single-Crystal Graphene Grains on Copper. Acs Nano 7, (2013). 5 Wu, T. R. et al. Triggering the Continuous Growth of Graphene Toward Millimeter-Sized Grains. Adv Funct Mater 23, (2013). 6 Hao, Y. F. et al. The Role of Surface Oxygen in the Growth of Large Single-Crystal Graphene on Copper. Science 342, (2013). 7 Yan, Z. et al. Toward the Synthesis of Wafer-Scale Single-Crystal Graphene on Copper Foils. Acs Nano 6, (2012). 8 Miseikis, V. et al. Rapid CVD growth of millimetre-sized single crystal graphene using a cold-wall reactor. 2D Mater 2, (2015). 9 Wang, H. et al. Controllable Synthesis of Submillimeter Single-Crystal Monolayer Graphene Domains on Copper Foils by Suppressing Nucleation. J Am Chem Soc 134, (2012). 10 Kresse, G. & Hafner, J. Ab-Initio Molecular-Dynamics for Open-Shell Transition-Metals. Phys Rev B 48, (1993). 11 Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science 6, (1996). 12 Wu, P. et al. Carbon Dimers as the Dominant Feeding Species in Epitaxial Growth and Morphological Phase Transition of Graphene on Different Cu Substrates. Phys Rev Lett 114, (2015). 13 Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59, (1999). 14 Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys Rev Lett 77, (1996). 15 Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem 27, (2006). 16 Monkhorst, H. J. & Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys Rev B 13, (1976). 17 Henkelman, G., Uberuaga, B. P. & Jonsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J Chem Phys 113, (2000). NATURE NANOTECHNOLOGY 13