Oxidation-assisted graphene heteroepitaxy on copper foil

We propose an innovative, easy-to-implement approach to synthesize large-area singlecrystalline graphene sheets by chemical vapor deposition on copper foil. This method doubly takes advantage of residual oxygen present in the gas phase. First, by slightly oxidizing the copper surface, we induce grain boundary pinning in copper and, in consequence, the freezing of the thermal recrystallization process. Subsequent reduction of copper under hydrogen suddenly unlocks the delayed reconstruction, favoring the growth of centimeter-sized copper (111) grains through the mechanism of abnormal grain growth. Second, the oxidation of the copper surface also drastically reduces the nucleation density of graphene. This oxidation/reduction sequence leads to the synthesis of aligned millimeter-sized monolayer graphene domains in epitaxial registry with copper (111). The as-grown graphene flakes are demonstrated to be both single-crystalline and of high quality.


Introduction
Chemical vapor deposition (CVD) holds great promises for large-scale production of high-quality graphene. The very low carbon solubility in copper (Cu) makes it a very attractive catalyst for graphene CVD growth. 1 Low-pressure CVD leads to the self-limited growth of a graphene monolayer 2 while the same outcome can be obtained by atmospheric pressure CVD (APCVD) provided that the amount of injected hydrocarbon is carefully controlled (by working with highly-diluted hydrocarbons for instance). 3 However, graphene sheets produced by standard CVD on Cu are polycrystalline 2 and domain boundaries have a detrimental effect on transport properties of charge carriers in graphene. 4 Besides, large-scale single-crystalline monolayer graphene sheets constitute optimal building blocks for artificial layer stacking with a precise control of the interlayer rotation angle. Twisted bilayer graphene, formed from the stacking of two monolayer graphene sheets, has already demonstrated a range of interesting optoelectronic behaviors. 5,6,7,8 One approach to grow large-size graphene domains is a drastic lowering of the graphene nucleation density by various techniques such as: growth on resolidified Cu, 9 on Cu annealed at high pressure, 10 or by local feeding of carbon precursors. 11 The most popular method benefits from residual oxygen to suppress nucleation by superficially oxidizing Cu. 12,13,14,15,16 A recent study questions the role of Cu oxidation by rather attributing the effect to the removal of carbon contamination on the Cu surface. 17 The Cu(111) surface plane is very advantageous for graphene synthesis because its hexagonal lattice symmetry matches well the honeycomb lattice of graphene (lattice mismatch of ~4%), thereby enabling epitaxial graphene growth. A few publications (see Table S1 for more details) report on the formation of large Cu(111) grains spanning several millimeters starting from polycrystalline foils, 9,15,16,18 after annealing at temperatures close to the melting point of Cu (1088 °C), where the grain boundary mobility is high. After such thermal treatments, Cu naturally adopts the (111) crystallographic orientation since it is thermodynamically the most stable for face-centered cubic metals. 19,20 By contrast, Robinson et al. 20 report the formation of large Cu grains with a dominant (001) texture, the initial main orientation of the Cu foil. Following this line of thought, a novel method has emerged recently, in addition to the "single-domain" one. It consists in orienting the surface of initially polycrystalline Cu foils along the (111) orientation by long (several hours) thermal annealing at more than 1000 °C. The subsequent epitaxial growth of graphene conduces to the alignment of domains which ultimately merge to form a graphene film free of domain boundaries over several dozen centimeter squares. 21,22 Other more expensive, complicated techniques imply directly working on Cu(111) single crystals 23,24,25 or depositing a thin layer of copper epitaxially oriented on α-Al 2 O 3 (0001) 26,27,28 or MgO(111) substrates 29 .
The mechanism underlying the growth of large grains in materials is known as abnormal grain growth. 30,31 Cold-rolled metal foils are polycrystalline in nature. After annealing at high temperature, the process of primary recrystallization results in the formation of new dislocation-free grains. When subjected to further annealing at high temperature, the average grain size continues to increase because it is thermodynamically more favorable to reduce the total grain boundary energy. Gradually, larger grains grow at the expense of smaller ones via grain boundary migration (normal grain growth). In specific conditions, normal grain growth may give way to abnormal grain growth where a selective growth of a few "giant" grains occurs by absorbing the small neighboring ones. Abnormal grain growth can only proceed if normal grain growth is somehow inhibited, notably by grain boundary pinning. 30 In this work, we describe a new method, merging the advantages of the "single-domain" and epitaxial growth approaches, where we take advantage of residual oxygen in the gas phase. First, by slightly oxidizing the Cu surface, we induce grain boundary pinning and, in consequence, freezing of the thermal recrystallization process. Subsequent reduction of Cu under hydrogen suddenly unlocks the delayed reconstruction, favoring abnormal grain growth over normal grain growth. The posterior adjunction of methane leads to the aligned growth of large-area monolayer graphene domains. Compared to the usual hydrogen pre-growth annealing, this oxidation/reduction sequence is thus doubly beneficial: (1) the (111) reconstruction of Cu foils at the centimeter scale is greatly accelerated, allowing graphene domains to grow in an aligned way through epitaxial registry with the Cu substrate and, (2) the oxidation drastically reduces the nucleation density and promotes the growth of millimeter-sized monolayer graphene flakes.

Graphene growth
We start from Cu foil pieces with a size of 3×3 cm 2 (Alfa Aesar, reference number 13382: 25-µm-thick, purity 99.8%). The Cu pieces are cleaned in a 2:1 mixture of acetic acid and distilled water (see SI section 16 for more details), rinsed in distilled water, and blown-dry with nitrogen. More precisely, the sample is first put on a quartz boat and inserted into a quartz tube at room temperature. An argon flow of 2000 sccm is then fed into the tube for 15 min and the temperature of the hotwall furnace is increased to 1050 °C. Next, the quartz tube is introduced into the furnace and the argon flow decreased to 500 sccm, with the immediate (S#1:H 2 /S#2:H 2 ) or delayed addition of 20 sccm of hydrogen (S#1:noH 2 /S#2:H 2 ). After one hour in these conditions, dilute methane (5% in 95% of argon) is injected to grow graphene.
One hour later, the quartz tube is extracted from the furnace and left to cool down naturally (fast natural cooling) in the same gas mixture.

Graphene transfer
Graphene is transferred onto 300-nm-thick silicon dioxide/silicon substrates or TEM grids (Ted Pella, #01896N) by the widely used method based on poly(methyl methacrylate) (PMMA). After PMMA coating, the Cu foil is first partially etched in ammonium persulfate to remove graphene grown on the backside. After rinsing and rubbing the backside with a cleanroom wiper, the foil's etching is continued in a new persulfate solution. The PMMA/graphene stack is next rinsed thoroughly in distilled water and fished on the wanted support. The sample is left to dry overnight and, finally, PMMA is removed with acetone.
Additional details regarding the experimental techniques (scanning electron microscopy, energy-dispersive X-ray spectrometry, electron-backscattering diffraction, low-energy electron diffraction, X-ray photoelectron spectroscopy, micro-Raman spectroscopy, transmission electron microscopy) can be found in the supplementary information (SI).

Results and discussion
The temperature-time diagram shown in Figure 1a summarizes the so-called "standard" (small, misaligned domains) and novel (millimeter-sized, aligned domains) graphene growth conditions, with the corresponding argon and hydrogen flows. The unique difference between the two processes is the pre-growth annealing of the Cu foils: (1) a reductive annealing under argon and hydrogen 2,3,4,13 (dubbed S#1:H 2 /S#2:H 2 , see Figure 1a for the notations) or (2) an oxidative/reductive annealing under argon, then argon and hydrogen 12,13,15,16 (S#1:noH 2 /S#2:H 2 ). The results of the two pre-growth sequences are compared in the low magnification scanning electron microscopy (SEM) images displayed in Figure 1b and c. We observe that the slightly different thermal treatments result in radically dissimilar Cu foil morphologies. It is indeed clearly seen in Figure 1b that the S#1:H 2 /S#2:H 2 Cu foil is polycrystalline, as testified by the heterogeneous SEM contrast rendered by the diverse Cu grain orientations, due to electron channeling. On the other hand, the other Cu foil exhibits a nearly uniform contrast, as in Figure 1c (except for white lines due the rolling striations, darker contrast due to curving of the foil, and a few elongated grains). The systematic use of low magnification SEM to completely sweep the surface of three S#1:noH 2 /S#2:H 2 foils suggests the same qualitative conclusion: the foils present an almost completely unique crystallographic orientation. However, a few residual polycrystalline areas are seen, most of the time on the edges of the foil ( Figure S1a and b), or where it is strongly deformed ( Figure   S1c and d). In line with that observation, the reconstruction proves unstable on the edges of pieces cut from reconstructed 3×3 cm 2 samples when they are heated once again in the same conditions (Figure S1e and g). Strain created during the cutting causes the foil to return to a polycrystalline state on the edges. These observations evidence that deformations in the Cu foil play a very important role in the reconstruction. It is also noteworthy that the reconstruction is not purely superficial but rather extends throughout the whole thickness of the Cu foil, as proven by the SEM inspection of both sides of a reconstructed copper foil ( Figure S2). In a final control experiment, it is found out that an annealing under argon and hydrogen of at least four hours is necessary to reconstruct a 3×3 cm 2 Cu foil in a similar manner to the S#1:noH 2 /S#2:H 2 treatment ( Figure S3), meaning that the oxidative/reductive annealing helps to drastically shorten the recrystallization duration and consequently the cost of the whole process.
To unambiguously identify the crystalline structure and determine the size of the Cu grains, we perform electron-backscattering diffraction. First, as illustrated in Figure 2a, the analysis of a 3×3 cm 2 S#1:H 2 /S#2:H 2 foil shows that it is mainly (001)-oriented, as already reported by other works for Cu foils subjected to similar treatments [20,32]. Then, a 3×1 cm 2 Cu stripe cut from a 3×3 cm 2 S#1:noH 2 /S#2:H 2 foil is investigated in three distinct regions (see Figure 2b exhibiting a photograph of the stripe with color-coded circles locating the analyzed areas in the center and on the two edges). The corresponding inverse pole figure (IPF) maps exposed in Figure 1c Figure 1c. These small-sized rare grains are identified as (001)-oriented ( Figure   S4), in agreement with Ref. [21].  We now investigate the mechanism responsible for accelerating abnormal grain growth (see an illustration of abnormal grain growth in Figure S5). The sole difference between the two pre-growth annealings considered here is the suppression of hydrogen during S#1. In the absence of hydrogen and its reducing effect, it is known that trace amounts of oxygen are inevitably present in the atmosphere and affect CVD growth. 33,34 In consequence, we are naturally led to believe that oxygen plays a major role in the reconstruction of the Cu foil. To shed more light on the oxidation of Cu, energy-dispersive X-ray spectrometry (EDX) mapping is conducted on a Cu piece after the S#1:noH 2 thermal treatment (complementary Xray photoelectron spectroscopy data can be found in Figure S6a-d). The SEM image in Figure   3a reveals that the surface of the foil is scattered with micrometer-sized faceted inclusions, formed preferentially on the Cu grain boundaries. The corresponding EDX O K and Cu K elemental mappings (Figure 3b and c) disclose that oxygen is almost entirely concentrated in the crystalline inclusions, with a ~33% atomic concentration, matching the stoichiometry of Cu 2 O; while the dark background corresponds to very weakly oxidized Cu, with less than 1.5% in oxygen (see the corresponding spectra in Figure S7a and b). In Figure 2d, micro-Raman spectroscopy (µRS) further corroborates that the spectrum recorded on the particles corresponds to Cu 2 O 14,35 and that the background is weakly oxidized. Besides, the Ellingham diagram for the Cu/O 2 couple (4Cu + O 2 ↔ 2Cu 2 O) confirms that Cu 2 O is stable under the considered O 2 partial pressure and temperature conditions (see SI section 9 for more details). 36 Finally, in two complementary control experiments, we see that the average Cu grain size is not altered after prolonged (see Figure 3e-g and SI section 10) or repeated ( Figure S8a and b) S#1:noH 2 annealings, proving that the recrystallization is frozen. Based on the knowledge gained through the previous experiments, we propose the following scenario. During the first minutes of annealing under argon, the grain boundary mobility is high enough to enable the average Cu grain size to increase under the effect of the temperature (primary recrystallization). The conditions of temperature and residual oxygen partial pressure evolve in such a way that they become favorable to the formation of Cu 2 O inclusions. These particles end up pinning down the Cu grain boundaries, even provoking the stagnation of the recrystallization. These conditions are very propitious to abnormal grain growth. 30 So, when hydrogen is introduced in the reactor and the Cu grains are suddenly unpinned, the recrystallization is strongly driven to proceed by abnormal grain growth.
After unveiling the mechanism underlying the trigger of abnormal grain growth, we further investigate the growth of graphene on the (111)-reconstructed Cu foils. The standard conditions (growth following S#1:H 2 /S#2:H 2 ) lead to misaligned, monolayer graphene domains with a lateral size of 10-15 µm (apex to apex) as can be seen in the SEM image displayed in Figure 4a. This is commonly reported in the literature for graphene synthesized without any special pretreatment of the Cu foil. 3,13 Not content with accelerating the Cu (111) reconstruction, the S#1:noH 2 /S#2:H 2 pre-growth conditions also result in a spectacular size enlargement of the graphene flakes 13 beyond 1 millimeter (compared to 50-100 µm for Brown et al. 21 and Nguyen et al. 22 ), and, very interestingly, the different graphene domains are aligned ( Figure 4b). By contrast, unlike Zhou et al. 14 , it is found that the reverse pre-growth sequence (S#1:H 2 /S#2:noH 2 ) leads to a much higher nucleation density, resulting in smaller hexagons (< 50 µm) and in multilayer patches ( Figure S9). This is most probably due to a much higher number of Cu oxide particles formed during S#2:noH 2 which are preferential sites for graphene nucleation. 37 Annealing in hydrogen has indeed a short range polishing effect on the Cu foil, 13, 38 smoothing out Cu oxide particles and others defects (rolling striations, etc.), thereby strongly decreasing the nucleation density ( Figure S10). The top part of Figure 4c gives an additional illustration of merged graphene flakes aligned growth over ~7 mm. In the inset to Figure 4c, we also show one representative low-energy electron diffraction pattern acquired on the same sample (three others are available in Figure S11). They all display a single set of diffraction spots corresponding to the hexagonal symmetry of both the Cu(111) and graphene lattices aligned with each other. The small lattice mismatch and the relatively large size of the diffraction spots due to the uneven foil prevents from resolving the graphene and Cu(111) diffraction spots, as reported by Brown et al.. 21 The diffraction data strongly support the epitaxial alignment between the quasi-monocrystalline Cu(111) foil and graphene.

Conclusions
The present work details an innovative method to grow single-crystalline graphene sheets by CVD, where residual oxygen in the gas phase proves to be doubly advantageous. The superficial oxidation of cold-rolled polycrystalline Cu foils simultaneously (1) accelerates the foil recrystallization by abnormal grain growth in the (111) orientation and (2) drastically lowers the nucleation density. Growing graphene on such Cu(111) templates leads to high-quality monolayer single-crystalline graphene flakes spanning more than one millimeter, aligned at the centimeter scale. These results pave the way to facile, cheap CVD growth of domain-boundary-free graphene films of arbitrarily large dimensions.

2) Impacts of mechanical deformations on the recrystallization
The morphology of three 3×3 cm 2 foils is investigated in a systematic way (5×4 mm 2 windows every 5 mm, 36 measurement points in total for each foil). We illustrate that mechanical deformations in the Cu foil have a strong influence on the reconstruction. First, after the S#1:noH 2 /S#2:H 2 pregrowth treatment, the Cu foil often remains polycrystalline on the edges, and more specifically around the corners of the Cu foil (see Figure S1a,b), where the foil was stressed during its cutting with scissors from the larger 30×30 cm 2 as-received Cu foil. Moreover, it can be seen in Figure S1c that the region around an initial crumple in the foil also remains polycrystalline even after a S#1:noH 2 /S#2:H 2 annealing, while the piece is (111)-oriented everywhere else. Figure S1d shows a closeup view on the crumple with an optical microscope, where the crumple is much better seen than by scanning electron microscopy by the presence of shadows. The same elongated grain is evidenced in both pictures by a red-edged rectangle for facile comparison. These two observations evidence that it would be preferable to receive flat foils, instead of rolled ones, to avoid any manipulation during the unfurling which very often incurs folds and crumples in the foil, notwithstanding pleats already present in the as-received foil. We also believe that the final outcome of the annealing is in a large part determined by the internal strains in Cu foil, which is beyond our control. It is also interesting to note that, due to these "edge effects", the S#1:noH 2 /S#2:H 2 annealing of 1×1 cm 2 Cu pieces very often results in a very erratic reconstruction, either absent or very partial.
Finally, we have investigated what happens to a Cu piece cut from a larger (111)reconstructed one, when it is once again subjected to a S#1:noH 2 /S#2:H 2 pregrowth annealing (see Figure S1e,f). To help the reader to compare, a few identical grains are highlighted in red-edged rectangles. It is revealed that the (111) reconstruction is reversible on the edges of the piece that where stressed due to the cutting. Indeed, in Figure S1g, the top edge that was cut with scissors returns back to a polycrystalline state while the right one (uncut) remains (111)-oriented

3) Bulk reconstruction of the Cu foil
The recto and the verso of the same Cu foil treated by S#1:noH 2 /S#2:H 2 is examined at the exact same location in Figure S2. It clearly appears that both sides are identical even if the contrast of some grains is different due the uneven topography of the Cu foil. To help the reader, a few identical grains are highlighted in red-edged rectangles. The backside picture is flipped vertically to enable a direct comparison.

4) Prolonged Cu foil annealing in argon and hydrogen
Similar to the three 3×3 cm 2 S#1:noH 2 /S#2:H 2 Cu foils mentioned in the manuscript, this Cu foil annealed in argon and hydrogen during four hours (S#1 30 min + S#2 30 min+ S#3 180 min) is also scanned in 36 positions to get a global view. The two pictures in Figure S3a,b both evidence a uniform contrast (except for the (001) grains and the pleats), testimony to the reconstruction of the foil. Figure S3c reveals that, around a crumple, the foil remains polycrystalline. Figure S3: Two typical low magnification scanning electron microscopy images of a 3×3 cm 2 Cu foil annealed during four hours in argon and hydrogen. S8

6) Abnormal grain growth
As it is, a cold worked metal foil contains a large amount of dislocations introduced during plastic deformation. As pictured in Figure S5a, when exposed long enough at high temperature, the metal foil becomes fully recrystallized (primary recrystallization), meaning that new dislocation-free grains have formed. Upon further annealing, the average grain size keeps growing in a continuous manner, a process called normal grain growth (NGG, see Figure S5b). In peculiar circumstances (see Figure S5c), NGG can lead to abnormal grain growth (AGG) (also called secondary recrystallization). Contrary to NGG, AGG is a discontinuous phenomenon, resulting in a bimodal grain size distribution. More details can be found in Ref. [8]. The mechanism of AGG is clearly identified in the pictures shown in Figure  S5d,e.  Figure S5d). The corresponding stereographic triangle can be seen with the 001, 101, and 111 poles. S10

7) X-ray photoelectron spectroscopy data
Depth profile X-ray photoelectron spectroscopy (XPS) is performed to compare two foils subjected to S#1:H 2 /S#2:H 2 and S#1:noH 2 /S#2:H 2 , respectively. The analyses point out that there is no difference between the two samples: at the surface, peaks related to CuO, Cu 2 O, Cu(OH) 2 , and H 2 O show up with practically the same relative intensities, subsequent to interaction with oxygen and water present in the air 9 (see Figure S6a-d); in depth, Cu is not oxidized at all. It is worth noting that the manufacturer specifies a trace oxygen concentration of 0.01% in the Cu foil, well below the detection threshold of XPS. Next, the same XPS analysis is conducted on a Cu piece after the S#1:noH 2 thermal treatment, evidencing that, on the investigated thickness, Cu is weakly oxidized and the atomic oxygen concentration decreases progressively (see Figure S6e). The signal is integrated over a 250-µm-diameter spot and gives thus only average concentrations. Figure S6: X-ray photoelectron spectroscopy (XPS) depth profiles performed to compare two foils subjected to S#1:H 2 /S#2:H 2 (a) and S#1:noH 2 /S#2:H 2 (b), respectively. Cu is oxidized only at the surface of the samples. (c,d) Corresponding high-resolution core level spectra at the very surface of the two foils. XPS depth profiles carried out on a S#1:noH 2 Cu foil showing that Cu is oxidized in depth. S11 8) Energy-dispersive X-ray spectrometry spectra Figure S7: Energy-dispersive X-ray spectrometry spectra recorded on a Cu specimen subjected to S#1:noH 2 . Spectrum of (a) a Cu 2 O(111) inclusion and (b) the background. S12

9) Estimation of the oxygen partial pressure
First, we ensure that the flow inside the quartz tube is laminar. In that case, when argon is introduced, all the air in the tube is driven away without turbulence, gently pushed outside by argon. Therefore, argon does not mix with air, preserving its initial purity. The Reynolds number, Re, is a dimensionless number allowing to determine, given the rate and the geometry of the flow, if the regime is laminar or turbulent. For a flow in a pipe, it is given by the well-known formula: In the specific case of an argon flow, ρ = 1.7832 kg/m 3 and μ = 2.2×10 -4 kg/(m.s) (at 15 °C and 1013 mbar). We take into consideration the "worst case scenario" by taking the highest F value of 2 l/min (= 1/30×10 -3 m 3 /s) used in the process. Finally, with ɸ = 2.5×10 -2 m, we find Re = 13.8. This value is well below the value of 2300 generally considered for a transition to a turbulent flow. 10 Here again, we consider an upper bound for Re with respect to the temperature, since we consider the room temperature values of ρ and µ, and ρ varies as ~1/T while µ increases with increasing temperatures (~T 1/2 ), thus Re(1050 °C) << Re(15 °C).
In the case of a mixture of argon and hydrogen, the contribution of hydrogen can be neglected because it has a much smaller density compared with argon. In addition, the typical hydrogen flow used here (20 ml/min) is also much lower compared to the argon flow.
Based on the data provided by the argon cylinder supplier (Air liquide, purity alpha2 99.9995%), the amount of O 2 should be below 0.5 ppm. So we can estimate that the O 2 partial pressure p O2 is not greater than ~10 -7 bar. Based on the Ellingham diagram for the Cu/O 2 couple and considering p O2 = 10 -7 bar, we deduce that Cu 2 O is stable for any temperature lower than ~1050 °C. This is all the more true for any p O2 greater 10 -7 bar.

10) Cu foil annealing in argon alone
Cu foils are annealed in argon alone for 30 min, 1 h or 2 h to observe how the morphology of the sample evolves with the hydrogen-free annealing time. From Figure 2e-g of the main manuscript, it is seen that, obviously, the density in Cu 2 O(111) inclusions increases with the exposure duration to residual oxygen. These crystals are preferentially formed on the rolling striations, where Cu shows more defects, or along grain boundaries. More importantly, when comparing the surface morphology of each sample, it appears clearly that the average grain size stagnates at ~50 µm and does not increase after 30 min, even if a prolonged annealing of 2 h is performed, as though the recrystallization becomes somehow inhibited. In a second experiment, the same Cu piece is annealed twice in a row in the same conditions (S#1:noH 2 ). The inspection of the foil at the exact same place by scanning electron microscopy discloses that, as could be anticipated based on the previous observation, the grain morphology does not evolve in the least bit (see Figure S8a,b). The only notable difference lies in the larger number of inclusions adding to the ones already present.

11) Reverse pregrowth treatment
We evaluate the effect of a reverse pregrowth treatment (S#1:H 2 /S#2:noH 2 ) on the growth of graphene. For the same methane flow as the one used in Figure 3c of the main text (0.35 sccm), the growth following that treatment exhibits a full coverage by monolayer graphene with many multilayer graphene patches underneath (see Figure S9a). Figure S9b displays a scanning electron microscopy picture for an amount of methane decreased down to 0.2 sccm in order to obtain a partial coverage (in the same methane flow conditions, no growth occurs with the standard S#1:noH 2 /S#2:H 2 treatment). Even when the methane flow is decreased in that way, the coverage is almost complete, except for a few areas where it is possible to distinguish the edges of some hexagons only partially incorporated into the graphene film, or very occasionally isolated ones. The reduced methane flow allows determining that the typical hexagon size is below 50 µm. It is also worth noting that the Cu film is polycrystalline and the graphene flakes grow with random orientations.

13) Supplementary low-energy electron diffraction patterns
The graphene/Cu(111) specimen seen in Figure 3c of the main text is analyzed in several points randomly chosen all over its surface (~1 cm 2 ). It is found out that the sample presents a unique Cu(111) orientation. Graphene shows epitaxial alignment with respect to Cu(111), as testified by the unique set of LEED spots in Figure S11a-c. A weak misorientation is occasionally observed, as attested by the very faint ring in Figure S11d (white arrow), possibly related to the fact that the foil is not polished, thereby causing little graphene misorientation with respect to Cu(111). 7 Figure S11: Low-energy electron diffraction patterns recorded in random positions on the sample pictured in Figure 3c of the main text. S17

14) Micro-Raman spectroscopy statistics
In the average and standard deviation values given in the main text, we also include the data recorded on the edges of the hexagonal graphene domain. These data often show a large spread relative to the average value. Indeed, by excluding the edges, the standard deviation decreases. The average and standard deviation are calculated from more than 400 data points.  Table S2: Summary of the average and standard deviation of the 2D-band full width at half maximum, 2D-band shift, G-band shift, and 2D-band over G-band intensity ratio (I 2D /I G ) extracted from the micro-Raman mappings in Figure 4 of the main manuscript. S18 Figure S12 shows all the electron diffraction (ED) patterns recorded in nanobeam mode on the graphene flake shown in Figure 5a of the main text. All the ED patterns correspond to a graphene single crystal oriented along the [0001] zone axis. Between all the ED patterns, the rotation of the δ angle (defined in Figure 5b of the main text) is small, thus highlighting the single crystalline nature of the graphene flake. Figure S12: The 25 electron diffraction (ED) patterns recorded in nanobeam mode and through the holes of the TEM grid. Each ED pattern is labelled according to the location indicated in Figure 5a of the main text. In addition, the value of the δ angle (defined in Figure  5b of the main text) is given for each ED pattern. S19

16) Cleaning of the Cu foils
It is of great importance to properly prepare the Cu foils before growing graphene on top of it in order to achieve graphene films of the best quality. In the scientific literature, many different pretreatment techniques can be found: (1) chemical treatment in various liquids such as acetic acid, 11,12,13,14,15,16,17 solvents, 18 water, 19,20 inorganic acids (dilute HNO 3 , 11,19,21 dilute HCl, 21, 22 , 23 ), FeCl 3 , 11, 24 Cr or Ni etchants; 21 (2) electropolishing; 11,12,13,19,25 (3) chemical mechanical polishing. 26 More particularly, the removal of Cu oxide with acetic acid was shown to be very effective. 27 In the perspective of large-scale production, it also presents the distinctive asset not to involve complicated treatments or hazardous chemicals. On the other hand, many works reported in the literature deal with graphene growth on Alfa Aesar Cu foils (25-µm-thick; 99.8% purity; reference number 13382; explicitly mentioned in 11,12,14,15,18,19,20,23,24,25,28,29 ). However, it is rarely reported that these foils are in fact coated with a thin metallic oxide anticorrosion film. 16,25,29 It goes without saying that this coating must be entirely removed, without degrading the underlying Cu foil, prior to graphene synthesis.
Here, we consider the widely used Cu foils mentioned above (Alfa Aesar #13382). X-ray photoelectron spectroscopy was first used to assess the presence of contaminants on the foil's surface before any treatment (so-called "as-received" foil). Two different as-received samples (1×1 cm 2 ) are analyzed in two and three distinct spots randomly chosen, respectively. The concentration of the detected elements is determined from the survey scan (see Figure S13). The main detected elements are oxygen (O 1s) and carbon (C 1s), corresponding to organic contamination. The presence of chromium (Cr 2p) is also unambiguously identified, corresponding to a layer of chromium oxide (the anticorrosion coating mentioned above). In addition, peaks that can be attributed to calcium (Ca 2p; between 8 and 10%) and phosphorus (P 2p; around 6%) appear. Other contaminants such as nitrogen (N 1s) or chlorine (Cl 2p) are also found, albeit in very weak amounts (less than 1.5%). The concentrations in the different elements can be found in Table S3. In order to remove the observed contaminants, we have next tested simple recipes involving harmless chemicals such as glacial acetic acid (GAA; Acros Organics; >99.8% purity), distilled water (DW) or isopropyl alcohol (IPA): (1) GAA alone for 15 min; (2) DW alone for 15 min; (3) mixture of GAA and DW in a 1:1 ratio for 15 min; (4) GAA alone for 15 min followed by rinsing in IPA. All the treatments are performed at room temperature. Finally, the Cu pieces are gently blown dry with nitrogen. All the recipes leave the chromium oxide layer intact, as one would expect (see Figure S14a). The only technique being efficient in S20 removing calcium is the third one (GAA+DW) (see Figure S14b). Phosphorus is still present in all cases. The concentrations in the different elements are summarized in Table S3. Figure S14: (a) Cr 2p core level spectrum for the as-received, the GAA+DW cleaned, and the annealed Cu pieces, respectively. (b) X-ray photoelectron spectroscopy survey scan of a Cu sample cleaned in a mixture of glacial acetic acid and distilled water.

Scanning electron microscopy (SEM)/Energy-dispersive X-ray spectrometry (EDX):
The morphology and the size of the Cu grains and graphene domains are monitored with two different microscopes: a Jeol JSM-6010LV InTouchScope at low magnification (operated at an accelerating voltage of 5 kV and a spot size between 30 and 50, with a working distance of 25 mm to increase the field of view, in secondary electron mode) and a Jeol JSM-7500F at high resolution (operated at an accelerating voltage of 1 kV and an emission current of 5 µA, with a working distance of 3 mm, in secondary electron mode with a low gentle beam of 0.2 kV applied to the specimen). EDX mapping is performed with the Jeol JSM-7500F at 15 kV with a probe current of 1 nA and a resolution of 512×384 px.

Electron-backscattering diffraction (EBSD):
The analysis of the Cu foil crystal orientation is performed using a SEM ZeissSupra55 fitted with a HKL-Oxford Instruments EBSD system featuring the Nordlys II camera. Data analysis is realized using the associated Channel 5 software suit. EBSD data collection is operated at an accelerating voltage of 15 kV, a working distance of 11 mm, and a sample tilt of 70°. The out-of-plane inverse pole figure (IPF) maps are in the z direction, perpendicular to the Cu foil surface, while the in-plane IPF maps are in the y direction, parallel to the plane of the Cu foil (instead, the in-plane IPF maps could also be given in the x direction, the information being the same). The zero solutions (electron-backscattered diffraction patterns that cannot be indexed due to very poor quality) are replaced by an extrapolation based on the neighboring points. Figure Table S5: More details about the different inverse pole figure maps presented in this work.

Low-energy electron diffraction (LEED):
The LEED patterns are acquired in a ultrahigh-vacuum setup after outgassing the samples at 300 °C for one hour. The energy of the incident electrons is set to 70 eV, with an analysis spotsize of ~1 mm.

X-ray photoelectron spectroscopy (XPS):
A ThermoFisher Scientific K-alpha spectrometer is utilized. It is fitted with a monochromatized Al Kα1,2 x-ray source and a hemispherical deflector analyzer. The spectra are recorded at constant pass energy (150 eV for depth profiling and survey; 30 eV for high resolution spectra). A flood gun (low energy electrons and Ar + ions) is used during all the measurements. During the sputtering, the Ar + ion gun is operated at an accelerating voltage of 2 kV, with an erosion time of 5 s per cycle, and the analysis is done in snapshot mode. The XPS data are treated with the Avantage software. High resolution spectra are fitted by Gaussian-Lorentzian lineshapes with an Avantage "smart" background (i.e. a Shirley background in most cases, or a linear background in case the lineshape decreases with increasing binding energy). The diameter of the analyzed surface is 250 µm.

Micro-Raman spectroscopy (µRS):
A LabRam HR 800 confocal laser system from Horiba Jobin Yvon is used for the acquisition of the Raman spectra. The measurements are performed at room temperature with a laser wavelength of 514 nm in backscattering geometry. The spectra are acquired on a 950 µm by 1100 µm grid with a spacing of 30 µm between each measurement spot (totalizing 32×37 spectra). A 100× objective (NA = 0.95) is used to collect the signal. The incident power is kept below 1 mW to avoid any heating effect. High resolution (1800 lines/mm) gratings are used for the measurements (with a corresponding spectral resolution < 1 cm -1 ). For the data analysis, the spectra are first fitted with Lorentzian functions. Then, the full width at half maximum, the position, and the integrated intensities of the 2D and G bands are extracted from the resulting fits.

Transmission electron microscopy (TEM)/electron diffraction (ED):
The TEM experiments are performed by using a FEI Titan Cube operating at 80 kV and equipped with a C S image corrector. The analyses are performed at liquid-nitrogen temperature to hinder carbon contamination and electron-beam damages. The effective diameter of the area probed on the specimen during nanobeam electron diffraction is around 150 nm.