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1 Oxygen-activated growth and bandgap tunability of large single-crystal bilayer graphene Yufeng Hao, Lei Wang, Yuanyue Liu, Hua Chen, Xiaohan Wang, Cheng Tan, Shu Nie, Ji Won Suk, Tengfei Jiang, Tengfei Liang, Junfeng Xiao, WenjingYe, Cory R. Dean, Boris I. Yakobson, Kevin F. McCarty, Philip Kim, James Hone, Luigi Colombo, Rodney S. Ruoff SUPPLEMENTARY METHODS Cu foil pretreatment, BLG growth, and transfer. Similar to our previous studies 19, two types of commercially available Cu foils were used in this work: (1) OR-Cu (Alfa-Aesar stock#46365, #13382, etc.) and (2) OF-Cu (Alfa-Aesar stock#46986, #42972, etc.). The O concentrations in (1) are ~10 2 atomic %; while in (2), they are below 10 6 atomic %, which is the detection limit of time-of-flight secondary ion mass spectrometry (TOF-SIMS). Both types of Cu foils were placed in acetic acid (CH 3 COOH) for 8 hours followed by blow-drying with nitrogen gas. Electrochemical polishing also cleans the Cu surface and has similar growth results. After cleaning, the Cu foils were made into a semi-sealed pocket (Fig. S1) and then loaded into the quartz tube of a low pressure CVD (LPCVD) system. The pockets were sitting directly in a quartz tube (lower panel of Fig. S1). The typical width of the pocket is ~18mm and the inner diameter of the quartz tube is ~22mm. In this way, when the pocket sits inside the tube, the distance between the bottom surface and the quartz tube wall is ~7 mm, NATURE NANOTECHNOLOGY 1

2 which is slightly smaller than that between the top surface and the wall, ~14 mm. In the LPCVD process, the growth environments of the top and bottom surfaces are similar. Also, the substrate configuration in this work is different from the sandwich structure (flat quartz plate/cu foil/quartz plate) or Cu tubes with both of their two ends open 32. Figure S1 Upper panel: Illustration of Cu pocket fabrication process flow. Lower panel: Placement of a Cu pocket in a quartz tube. The growth system was heated to 1035 C under a H 2 flow of 10 cm 3 per min (sccm), corresponding to 0.1 Torr, and annealed for 30 min; CH 4 was then introduced into the system for graphene growth. The typical P CH4 range is ~ Torr, and the growth time varied 2 NATURE NANOTECHNOLOGY

3 SUPPLEMENTARY INFORMATION from 10 to 500 min. Note that for "O 2 -treated OF-Cu", pure O 2 was used for different exposure time right before introducing CH 4 and the corresponding P O2 is Torr. After growth, the system was cooled down to room temperature while still under the H 2 and CH 4 flow. The bilayer and few-layer graphene films formed on the exterior surface of the Cu pockets were characterized and analyzed. The graphene domains/films were transferred onto dielectric surfaces, Si and h-bn, using a poly(methyl methacrylate) (PMMA)-assisted method 33 for Raman characterization and electrical device fabrication. Prior to transfer, the graphene surface was spin-coated with a layer of PMMA to provide mechanical support throughout the transfer process. The PMMA/graphene/Cu stack was then floated over an ammonium persulfate ((NH 4 ) 2 S 2 O 8, 0.5 M, Sigma Aldrich) aqueous solution to etch the Cu. The resulting graphene/pmma membranes are thoroughly rinsed with deionized water, and then transferred onto the target substrates. The PMMA was removed with acetone, then rinsed in isopropanol, and finally blow-dried with nitrogen gas. SEM images were taken with an FEI Quanta-600 FEG Environmental SEM with the accelerating voltage of 30 KV, and spot size of 5. Raman spectra and mapping images were taken from a WiTec Alpha 300 micro-raman imaging system. A 488 nm excitation laser with a 50 or 100 objective lens were used for the acquisition of Raman spectra and images. The spot size is nm, and the mapping step size is ~300nm. SUPPLEMENTARY NOTES A. Gas-flow dynamics of Cu pocket and its effects on graphene growth NATURE NANOTECHNOLOGY 3

4 (1) Cu pocket fabrication and gap size along the edges As shown in Fig. S1, a Cu pocket was made by first bending a Cu foil and then crimping & pressing the three open edges carefully by using metal tweezers. During the fabrication, no special mechanical machine was used to seal the edges. We first measured the gap size along the folded edges by cutting the pocket with scissors, which turns out to be undesirable since the folded edges were always smeared during the cutting, and thus no accurate gap size can be obtained. A focused ion beam (FIB, FEI Strata, Dual Beam235) was then used to cut, so that the real gap size at the edge could be revealed. We found that the gap size along the folded edges is typically in the range of a few μm (Fig. S2c). After annealing (1035 C, the growth temperature), the gap size was found to be reduced to nm (Fig. S2d) because the mechanical strength was reduced and the accumulated strain during the pocket fabrication process was released too. Gas exchange between the interior and exterior of the pocket is through this narrow gap. 4 NATURE NANOTECHNOLOGY

5 SUPPLEMENTARY INFORMATION Figure S2 The pocket was cut by scissors first a, and then focused ion beams were used to cut the local region as indicated by the blue-line box in b. The gap sizes before and after annealing are shown in c and d, respectively. (2) Gas equilibrium and Knudsen diffusion In the experimental environment, where the temperature is above 1000 C and the gas pressure is ~0.1 Torr, the calculated mean free path of CH 4 molecules is larger than 1mm 34. Hence the Knudsen number, which is defined as the ratio of the mean free path of CH 4 molecules to the gap size of the Cu pocket, is on the order of Such a high Knudsen number suggests that the diffusion of CH 4 from the exterior environment into the interior through the gap of the pocket is dominated by the collisions between CH 4 molecules and the gap sidewall, and is in the Knudsen diffusion regime. The diffusivity in the gap channel (indicated in Fig. S3a) is thus much lower than the diffusivity outside the Cu pocket. The diffusivity in the Knudsen diffusion regime depends on both the shape and dimensions of the channel. Monte Carlo simulation 35,36 provides a convenient way to calculate the diffusivity of CH 4 molecules inside the channel of the Cu pocket which is modelled as a nano-channel. In the simulation, the channel connects two infinitely large reservoirs of which the gas concentrations (or called number densities) are maintained at constant, but different values. When the system reaches the steady state, a linear density profile along the length of the channel is established and the number flux of gas molecules is measured. It is found that in the Knudsen diffusion regime, the number flux, J, follows the Fick s first law of diffusion, dn J= D, (1) dx NATURE NANOTECHNOLOGY 5

6 and the diffusivity D can be calculated based on the simulated number flux and the gradient of number density along the channel, dn dx. Using this method, the diffusivity of CH 4 molecules in a channel with a rectangular cross section of which the dimensions are 400 nm and 8 cm, respectively, is computed. The result is found to be close to that calculated from the formula for the diffusivity of gas molecules between two infinitely large parallel plates, which is derived based on ref. 37, 1 8K BT D = π HΛ p, (2) 4 πm where H is the gap size, 400nm, M is the molecular weight, and Λp a is a pre-factor calculated in ref. 37. In our experiments, the channel dimensions are: H = 400 nm, W = 8 cm (the edge length of a pocket), L = 2 mm (length of gap channel, Fig. S3a), and the volume of the Cu pocket is 2mm 3. The calculated diffusivity inside the channel is: D = m 2 /s, which is about 4 orders of magnitude lower than that outside the pocket, which is in the continuum gas transport regime. We then calculate the time it takes for the number density (equivalent to P CH4 ) of CH 4 molecules to equilibrate between the interior and the exterior of the pocket. The exterior environment is modelled as an infinitely large reservoir at, in which the number density of CH 4 molecules is maintained at a constant value. It is connected to the Cu pocket through the nano-channel with a length L. Assuming a uniformly distributed number density of CH 4 molecules in the interior environment of the pocket, the change of the number density of CH 4 6 NATURE NANOTECHNOLOGY

7 SUPPLEMENTARY INFORMATION molecules inside the Cu pocket,, is determined by the mass conservation law at the interface between the channel and the Cu pocket, nlt (,) nxt (,) V = D WH, (3) t x x= L where x is the coordinate along the length of the channel and is the number density of CH 4 molecules inside the channel. Since the volume of Cu pocket is much larger than that of the channel, the number density of CH 4 molecules in the pocket changes much slower than the time needed for the linear profile to be established along the channel. Hence at any time instant, the number density profile along the channel is nearly linear, and the gradient nxt (, ) x can be approximated by (, ) n0 n Lt L. Finally, equation (3) can be simplified as (, ) 0 dn( L,) t n Lt n V D WH dt L =. (4) The solution to Eq. (4) is = 1 characteristic time = = 136s. = 1, where the We plot the ratio of n(ch 4 ) between the interior and exterior as a function of time, as shown in Fig. S3b. From the calculation, we estimate that it takes about 4-8 min for the number density inside the pocket to get close to that of the exterior environment (such as 90% of the number density of CH 4 inside the pocket). As a comparison, different gap sizes, such as H = 300 nm, 800 nm, 3 μm, etc. were used to calculate the time. Results show that the time decreases with the NATURE NANOTECHNOLOGY 7

8 increased gap size. From the curve in Fig.S3c, the time decreases to a few seconds when the gap is more than a few μm. In summary, the narrow gap of a few hundred nm creates a stagnant growth environment in the interior of the pocket. Significantly low gas exchange rate occurs when the gap size is lower than about 1 μm. In addition, we are also aware that some CH 4 molecules are adsorbed on the Cu sidewall of the gap channel when diffusing into the pocket, which may further slow-down the gas exchange. Figure S3 a, A schematic drawing of the cross section of Cu pocket shows the CH 4 transport channel into the pocket interior environment. b, CH 4 molecule concentration ratio of interior environment to the exterior as a function of time for different gap size. c, The time needed for 90% equilibrium in CH 4 concentration between the interior and the exterior as a function of pocket gap size. 8 NATURE NANOTECHNOLOGY

9 SUPPLEMENTARY INFORMATION (3) The growth results from OF-Cu pocket The graphene domain growth starts from nuclei, the density of which is proportional to the P CH4 at the beginning of the growth 19,21,22. The P CH4 on the exterior surface of the pocket is immediately established as it is directly exposed to the flowing gases. However, as discussed above, P CH4 is low in the interior and takes a few minutes to reach equilibrium with the exterior. Therefore, the graphene nucleation density on the interior surface is lower than that on the exterior surface. Our experimental observations based on OF-Cu showed that the nucleation density on the interior surface is lower than that on the exterior surface (Fig. S4c and S4d). Therefore, the experimental observations are in agreement with the calculation results. After nucleation, the new C radicals predominantly contribute to the graphene growth instead of new nuclei formation due to the high barriers of nucleation compared to that of growth 21,24. In this way, the areal growth rate of graphene domains is proportional to the perimeter length of graphene domains. Therefore, high nucleation density of graphene leads to high graphene surface coverage rate. As a result, the graphene growth rate on the exterior surface remains higher than that on the interior surface even after P CH4 equilibrates between the interior and exterior surfaces. We consistently observed that the exterior surface of the pocket becomes fully covered with graphene earlier than the interior (Fig. S4). In addition, it is worth noting that both interior and exterior surfaces of OF-Cu were covered with only SLG, indicating that the growth is surface-limited. Note that the grown SLG on both interior and exterior surfaces of OF-Cu was confirmed by optical contrast and multiple Raman spectroscopy measurements after being transferred onto SiO 2 /Si substrates (data not shown). We did not find any BLG or few-layer graphene. NATURE NANOTECHNOLOGY 9

10 Figure S4 The parameter effects on the growth results of graphene on both interior and exterior surfaces of OF-Cu pockets. T=1035 C, growth time varies in different cases. B. Experimental study of BLG growth mechanism (1) The comparison of graphene growth between OR-Cu foils and OR-Cu pockets An OR-Cu foil and an OR-Cu pocket were placed side-by-side in the quartz tube for graphene growth (P CH4 = Torr) so that both were under the same growth conditions. The results for different growth times are shown in Fig. S5. After 30 min of growth, we find similar nucleation densities on the Cu foil and on the exterior surface of the OR-Cu pocket. This is expected since both the exterior surface of pocket and the foil surface are directly exposed to the growth atmosphere. We also observed that on the Cu foil, the nucleation density and growth rates of graphene on both top and bottom surfaces are similar. The 2 nd layer, up to ~5% of the whole surface area 38, does not grow larger once the surfaces are fully covered. In contrast, for the 10 NATURE NANOTECHNOLOGY

11 SUPPLEMENTARY INFORMATION Cu pocket, the nucleation density on the interior surface is much lower than that on Cu foil and the exterior surface of the pocket. Also, there is much larger areal coverage of additional layers growing on the exterior surface compared to the Cu foil. Furthermore, these additional layers continue to grow larger and thicker with time even after the exterior surface is fully covered with SLG. We observed that the growth of additional layers on the exterior surface does not stop until the SLG graphene fully covers the interior surface. This indicates that there is a connection between the growth on the two surfaces; even though they are separated by a Cu foil of 25 μm thick. Figure S5 An OR-Cu foil and an OR-Cu pocket were placed side-by-side for graphene growth. The SEM images of graphene growth results as a function of growth time. NATURE NANOTECHNOLOGY 11

12 (2) Control experiments show that the 2 nd layer growth is supported by C diffusion through Cu To elucidate how the growth of the 2 nd graphene layer on the exterior OR-Cu surface is influenced by the interior surface, we designed a two-step growth control experiment as schematically shown in Fig. S6. An OR-Cu foil was first fully covered on both surfaces with 12 C graphene using CVD. The graphene was then partially etched on one surface, and the foil wrapped into a pocket with the partially etched surface in the interior. A second growth was then carried out with 13 CH 4 ( Torr) for 30 min. In the etched area region, dendritic graphene domains formed on the interior surface (Fig. S6b) and hexagonal 2 nd layer domains appeared on the corresponding exterior surface regions (Fig. S6c). Raman mapping (insets of Fig. S6b and S6c) shows that these new domains on both surfaces are composed of 13 C, while the remaining graphene films are 12 C. In contrast, on the part of foil where both surfaces were covered by original 12 C-graphene, no new graphene domains were found on either surface. This control experiment unambiguously proves and demonstrates that the C source forming the 2 nd layer graphene is the C that dissolves from the exposed interior Cu surface and then diffuses through the Cu bulk to the exterior surface. It also reveals that graphene is an impermeable barrier to C atoms and hydrocarbon molecules, which prevents C diffusion through Cu while passivating the catalytic Cu surface, thus the 2 nd layer graphene cannot nucleate and grow on top of the 1 st layer, contrary to previous reports 14,17,18. Superficially, the exposed Cu area on the interior surface allows C to dissolve and diffuse in the Cu bulk to yield the 2 nd layer growth. However, further investigation suggests that the 2 nd layer growth is affected by oxygen (O) impurities present on the Cu surface. For example, when we intentionally increase the P CH4 in the growth system for the case of OR-Cu pocket, the 12 NATURE NANOTECHNOLOGY

13 SUPPLEMENTARY INFORMATION nucleation density and growth rate on the interior surface was found to be similar to that for the OF-Cu. However, as shown in Fig. S7, the 2 nd layer is formed only on the exterior surface of OR-Cu, suggesting that O is playing a critical role in the formation of dissolved C, versus none for the OF-Cu. Figure S6 a, Schematic of the control experiment. b and c, SEM images of the areas indicated in a. Insets in b and c are the corresponding 13 C Raman mapping, corresponding to peak intensity in the range of cm -1. The corresponding Raman spectra at different points were shown in Fig. S14. d, Schematic drawing of C diffusion processes for the BLG growth in the form of Cu pocket. Graphene domain edges (C sinks) were highlighted with dash-line boxes. NATURE NANOTECHNOLOGY 13

14 Figure S7 Control experiments. P CH4 for OF-Cu is Torr, while it is Torr for OR-Cu. The surface coverage is similar on both interior surfaces, but only on the exterior surface of OR-Cu, BLG domains were observed. The growth time is 60 minutes for OF-Cu, and 30 minutes for OR-Cu. (3) The driving force of C diffusion through the Cu bulk to the exterior surface. The whole growth process of graphene (both SLG and BLG) is a non-equilibrium process driven by the much lower energy of C in the graphene phase than that of the C radicals on the Cu surface, which is independent of the local graphene coverage. We point out that the driving force for C to diffuse through Cu bulk to the exterior surface to grow the 2 nd graphene layer is the higher C atom (or C radical) concentration on the interior surface than that on the exterior surface, which is the consequence of higher nucleation density of 2 nd layer on the exterior surface than that of SLG on the interior surface. A schematic drawing 14 NATURE NANOTECHNOLOGY

15 SUPPLEMENTARY INFORMATION (not to scale) regarding the process is shown in Fig. S6d. In our previous work 19 on the effect of oxygen on the nucleation density of graphene on Cu, we showed that the interior surface of the Cu pocket can be exposed to methane for many hours without nucleating new graphene domains, but becomes covered with a significant amount of C radicals. Therefore when the exterior surface is fully covered by 1 st layer graphene, the C atoms on the largely exposed interior Cu surface can diffuse either on the interior surface to the sparse graphene domain edges for their enlargement, or through the Cu bulk to the exterior surface to grow 2 nd layer graphene, with comparable diffusion energy barriers thanks to the help of oxygen (0.92eV vs. 1eV, Table S1). The nucleation density of 2 nd layer on the exterior surface is higher than that of SLG on the interior surface (this is a general characteristic, and can be seen in Figure 1b and 1c; Figure S5, S7, and S11, etc). Correspondingly, on the exterior surface there are more 2 nd layer domain edges, which are sinks for C incorporation into graphene lattice and thus keep the C radical concentration low. Consequently, more C is driven to diffuse through the Cu bulk to the exterior surface. Further, because the thickness of the Cu is only 25 μm, much smaller than the separation between graphene islands on the interior surface (~ mm), one can readily see that a significant fraction of C atoms will diffuse through the foil to the exterior surface to form the 2 nd layer graphene rather than diffusing to the growing domains on the interior surface. (4) The C bulk diffusion at the beginning of the growth. To provide a complete picture of the whole growth process, we comment here on the C diffusion at the beginning of the growth process. Nucleation and growth of 1 st layer graphene islands on the exterior surface of the OR-Cu pocket quickly proceeds through the wellestablished surface-mediated mechanism, similar to the case of Cu foil. It is also possible for the NATURE NANOTECHNOLOGY 15

16 CH x on the exterior surface of the OR-Cu pocket to completely dissociate and dissolve into the Cu bulk, followed by C diffusion to the interior surface. But such processes will unavoidably stop after the exterior surface being fully covered by graphene, which grows much faster than on the interior surface because of the asymmetric growth environment of the Cu pocket. We note that the bulk diffusion from the interior surface to the exterior surface is a critical pathway for the large 2 nd layer graphene growth, which is one of the main points in this work; while the diffusion in the reversed direction occurs only at the beginning of growth when the exterior surface is not fully covered with SLG, and is unimportant for the main claim of this paper. (5) The possibility of C diffusion through grain boundaries in polycrystalline Cu Multiple experimental and theoretical works presented in this work have clearly demonstrated that the 2 nd layer growth is closely associated with O, not Cu grain boundaries (GBs): oxygen can promote dissolution of C atoms into Cu, and then these C atoms diffuse through the Cu bulk for 2 nd layer growth. Furthermore, we did not find that the 2 nd layer domains preferentially grow along the Cu GBs: as shown in Figs.S8a and S9b, both high density and low density 2 nd layer domain growth are found to be independent of the Cu GBs; in a low magnification SEM image (Fig. S8c), the 2 nd layer domains can grow in regions more than one millimeter away from the Cu GBs, which demonstrates that the GB is not the dominant C diffusion pathway. These observations are in contrast to those in Ref NATURE NANOTECHNOLOGY

17 SUPPLEMENTARY INFORMATION Figure S8 The relationship between Cu grain boundaries and 2 nd layer growth sites. Note that in (c) the brightness contrast is due to the non-flatness of Cu surface at large-scale. (6) Domain shapes: Dendritic versus compact Different graphene domain shapes are the results of different growth kinetics. In the previous work 19, we have clearly confirmed that Cu surface O impurities play a critical role in determining the growth kinetics and hence the domain shapes. So the explanation is as follows: As grown on the OR-Cu, the 1st layer domains were always dendritic, indicating diffusionlimited growth. During the growth of the 1st layer, the surface oxygen species were depleted through the reactions: CH x + O CH x-1 + OH (x=4, 3, 2, 1). Thus the 2 nd layer domains were grown in an oxygen-free environment. The compact domain shapes are a direct consequence of the edge-attachment-limited growth kinetics in such an environment. This is consistent with our previous work. C. Optimization of growth parameters towards larger BLG domains NATURE NANOTECHNOLOGY 17

18 Since the BLG growth mechanism is established, further efforts were devoted to understand the effects of various growth parameters so as to achieve larger and more uniform 2 nd layer graphene, while suppressing thicker layer nucleation & growth. In this work, we investigate the effects of methane partial pressures and O 2 pretreatments on BLG growth, and to explore the optimal growth conditions of large BLG domains, as detailed below. Figure S9 Raman images show isotope-labeled BLG domains at different growth conditions. Lower inset is the growth rate plot at different P CH4. (1) 2 nd layer domain growth rates We measured the 2 nd layer domain growth rates. Using isotope-labeled growth at different conditions and Raman mapping (details can be found in Note E), we are able to visualize the time-resolved growth progress of the BLG (Fig. S9), and thus to extract the radial growth rates. We plotted the growth rates as a function of methane partial pressure (lower inset of Fig. S9), showing that the growth rates of individual 2 nd layer domains increase with P CH4. 18 NATURE NANOTECHNOLOGY

19 SUPPLEMENTARY INFORMATION (2) Effects of P CH4 As shown in Fig. S10, by adjusting P CH4, we found that the exposed interior Cu surface area, low P CH4, and proper growth time are critical for the formation of large and uniform BLG domains. At high P CH4 (~0.1Torr), due to the relatively high graphene nucleation density and growth rate on the interior surface, it is almost fully covered with graphene in ~15min. In this case, only small and sparse 2 nd layer domains (~10 μm in lateral size) are formed on the exterior surface, and these domains cannot grow larger because the graphene-covered interior surface prevents further C dissolution and diffusion. At medium P CH4 (~0.01Torr), the relatively low nucleation density and low growth rate on the interior surface leaves a relatively large area of exposed Cu. In this case, the 2 nd layer graphene domains are dominant and can grow to more than 50 μm in about 40 min. However, with time, more and more C atoms diffuse through the Cu. As a result, the 3 rd, 4 th, and even more layer also starts to grow. At low P CH4 (~ Torr), the nucleation density on the interior surface is very low, only about 0.5 mm -2 and the corresponding C that diffuses through the bulk and segregates onto the exterior surface is also low. In this case, the low C concentration leads to a film that is predominantly BLG and after 200min of growth, individual 2 nd layer domains can grow to ~ μm. NATURE NANOTECHNOLOGY 19

20 Figure S10 SEM images of graphene or BLG grown on surfaces of Cu pockets, showing the effects of methane partial pressure. 20 NATURE NANOTECHNOLOGY

21 SUPPLEMENTARY INFORMATION Figure S11 Optical images of large BLG domains and continuous films on SiO 2 /Si substrates. We demonstrate that at low P CH4 and after appropriate growth time, large area BLG and trilayer graphene can be achieved. Fig. S11 shows the optical images of individual domains and continuous films of large BLG and trilayer graphene (TLG) after being transferred onto Si substrates, which were grown at P CH4 =0.001Torr and different growth time. (3) Effects of O 2 pretreatments In this experimental comparison, we treat the OF-Cu substrates with O 2 at P O2 = Torr for different exposure time ranging from 20 s to 5 min. During growth the P CH4 was fixed at Torr in each case. The results are shown in Fig. S12. On the exterior surface of OF-Cu pockets, we do not observe any BLG growth for a wide range of growth parameters. However, once small amount of O 2 are introduced, say ~20 s before feeding CH 4, we immediately note a change in the growth behavior: on the interior surface, the graphene domain shape becomes fractal, distinct from the compact domains on pristine OF-Cu, in agreement with our previous work on SLG. On the exterior surface, we observed low density 2 nd layer domains with average size of about 10 μm. Obviously, this is the effect of oxygen activating the BLG growth as reported in this work. We also note that with the short O 2 exposure, the 2 nd layer domains do not grow larger than about 10 μm since the interior surface becomes fully covered with graphene in about 20 min. When the O 2 exposure time increases, i.e., the surface oxygen concentration increases prior to growth, the nucleation density of graphene domains on the interior surface decreases as NATURE NANOTECHNOLOGY 21

22 expected, the nucleation density of the 2 nd layer domains on the exterior surface decreased too, and thus the 2 nd layer domain size increases. Therefore O 2 treatment not only makes 2 nd layer growth possible, but also helps to improve the 2 nd layer domain growth by suppressing nucleation of graphene islands on both surfaces of the pocket. We plot the 2 nd layer domain size as a function of O 2 exposure time, as shown in the lower inset of Fig. S12. We find that after 180 s exposure, the 2 nd layer domain size can be up to about 660 μm, indicating that experimental conditions could be designed for further enlargement of the 2 nd layer domain size. Figure S12 SEM images of graphene or BLG grown on surfaces of Cu pockets, showing the effects of O 2 pretreatments. In each case, P CH4 =0.002 Torr. Lower inset is the 2 nd layer domain size as a function of O 2 exposure time. 22 NATURE NANOTECHNOLOGY

23 SUPPLEMENTARY INFORMATION We are aware that other growth parameters, such as P H2, Cu foil thickness, growth time, growth temperature, etc., may also affect the 2 nd layer growth. By tuning the combination of different parameters, we expect that further improvement in the growth of BLG can be achieved. D. Low-energy electron microscopy and low-energy electron diffraction Low-energy electron microscopy (LEEM) and low-energy electron diffraction (LEED) were utilized to investigate the crystallinity of BLG on the exterior surface of OR-Cu (Fig. S13). LEEM & LEED are also reliable and well-established tool to test the stacking sequence 40 (the 2 nd layer graphene above or below the 1 st layer): the LEED spot intensity from the under-layer is always weaker than that from the top-layer, which is a consequence of the strong attenuation of the incident electrons during transmission through the top-layer. The measurements were performed using an Elmitec LEEM III instrument. As-grown BLG-Cu samples were transferred through air into the instrument and then degassed at ~250 C overnight in ultra-high vacuum (base pressure < Torr). The analysis was performed at room temperature. Fig. S13a1 is a LEEM image of a region that contains a hexagonal island of BLG. The LEED patterns in a2 are from the whole 50 μm-sized view-field of a1, and thus the diffraction patterns can be associated with different domains of the 1 st layer. We can then obtain the dark field images, b1, b2, and b3, and re-build the color-coded 1 st layer (b4) with respect to crystal orientations and domain morphology. With this detailed but necessary background, we now turn to the key mechanistic issue of whether the 2 nd layer is next to the substrate or on top of the 1 st layer. NATURE NANOTECHNOLOGY 23

24 Figure S13 a, LEEM image and the corresponding LEED patterns of a BLG region. The electron energy is 3.2eV and 50eV for a1 and a2, respectively. b, Dark-field images obtained from the three sets of diffraction spots in a2, as indicated by red, green, and blue rings. b4, Map of the 1 st layer domains. The three colors represent domains with three different in-plane rotational orientations of the 1 st layer, as revealed by the dark-field LEEM images. The electron energy is 50eV for b1 to b3. Un-colored 1 st layer domains have a different, uncharacterized inplane rotation. c, Select-area LEED patterns taken from different regions (2 μm size) in a1, and the electron energy is 50 ev for each pattern in c. Note that the additional diffraction spots in each diffraction pattern result from the faceted Cu substrate. The Lower inset schematically shows the cross-section of this region, where different colors refer to different orientations of each domain. 24 NATURE NANOTECHNOLOGY

25 SUPPLEMENTARY INFORMATION Distinct from a2, the patterns in c1-c4 are from 2 μm regions, as indicated in a1 and the schematic drawing in the lower inset. From single-layer regions, c1 and c4 show one set of strong patterns, while c2 and c3 show two sets of patterns, respectively, since they are taken from bilayer regions. After comparison with domain morphology (b4) and diffraction pattern orientations (red spots in c1 and c2; blue spots in c3 and c4), we are able to confirm the red- and blue-coded spots are from 1 st layer and the green-coded spots from the 2 nd layer. The consistent and clear comparisons in each pattern can exclude any artifacts. We then compare the diffraction spot intensities between the 1 st and the 2 nd layers and thus conclude the 2 nd layer (with weaker intensity spots) is below the 1 st layer. In addition, we note that the (weak) diffraction spots of the 2 nd layer graphene had the same rotational alignment at all points examined in the hexagonal domain. This indicates that the hexagonal 2 nd layer is a single crystal, a general result found in our analysis of discrete 2 nd layer domains. In addition, by comparing the 2 nd layer domain shape with the corresponding diffraction pattern orientations, the 2 nd layer domains were found to be zigzag-edge-terminated, in accord with previous reports of hexagonal SLG domains on Cu 4,19. E. BLG characterizations using Raman spectroscopy and TEM (1) Raman spectroscopy characterizations Raman spectroscopy was used to study the characteristics of BLG and isotope-labeled BLG 6, 20, 23, 26, 41. Two well-established criteria were used to judge the characteristics of the BLG: (a) G band positions were used to determine the C isotope-labeling of the graphene regions. The peak at ~1580 cm -1 indicates 12 C graphene, and ~1525cm -1 indicates 13 C. If the peak is between 1525 and 1580cm -1, such as at ~1550cm -1, the film being mixed with both 12 C and 13 C; NATURE NANOTECHNOLOGY 25

26 in this work, no such regions were found. The co-existence of the two peaks (1525 and 1580cm -1 ) in bilayer regions indicates two possibilities: (i) one layer is formed by 12 C and the other is formed by 13 C graphene; (ii) the laser spot illuminates both 12 C and 13 C graphene regions bordering each other, which could be easily distinguished by Raman mapping in this work. (b) FWHM of 2D (G ) band was used to check the stacking orders of the BLG. When the FWHM was between 20-40cm -1, the region was considered as twisted BLG. If the FWHM is 50-55cm -1 (either 12 C or 13 C BLG) or cm -1 (one layer is 12 C and the other layer is 13 C), the region is considered as Bernal-stacking. Raman image is able to further visualize the spatial distributions of the layer number, stacking order, isotope distribution, domain size, domain shape, domain growth rate, domain boundary, etc, as shown in Fig. 1, Fig. 2, Fig. S6 and Fig. S9. Corresponding Raman spectra from Raman images are shown in Fig. S14. Figure S14 Raman spectra for the figure panels in the paper. AB in the panels refers to Bernal-stacking. 26 NATURE NANOTECHNOLOGY

27 SUPPLEMENTARY INFORMATION (2) Further explanations of isotope-labeled Raman images In order to highlight the 2 nd layer growth, we presented the zoom-in image in Fig. 2f, which shows only part of the 1 st layer domain. Here, we added the zoom-out image (Fig. S15), in which one complete 1 st layer domain is shown, and its adjacent 1 st layer domains are shown too. We also note that in Fig. 2f and 2j, the Raman images were taken according to the center of mass of the 2D peak in the range of 2500 cm cm -1. The brighter regions in the maps indicate that the center of mass of the peaks approach higher wavenumbers (lower panel in Fig. S15). We choose this Raman characteristic because it can clearly distinguish both layers of the isotope-labeled BLG. From the isotope-labeled Raman images, we are able to achieve more information regarding the growth mechanism, as follows: (a) The high 12 C surface coverage at the central region of the 1 st layer simply means that the first 12 C cycle grows faster in this selected area. Similarly, the nearly 1-to-1 ratio of C isotopes in the 2 nd layer domain suggests that this domain grows at a constant radial rate. The higher growth rate of the central part of 1 st layer domain during the 1st 12 C cycle is mainly due to the fact that the separation between it and the neighboring domains in the early stage of growth is larger than the C diffusion length, so that the growth of different domains are relatively independent of each other. As the domains keep growing and the distance between edges of neighboring domains becomes smaller than the C diffusion length, the surface concentration of C species between the two domains will be insufficient for each of them to maintain the same growth rate as before, hence the narrower isotopic rings in the subsequent cycles. Finally, all the domains merge together into a continuous graphene film. Detailed study of this phenomenon was reported in one of our previous works on SLG 42. In contrast, because the relatively small sizes of the 2 nd layer domains and the fact that they are typically well separated (edges of 2 nd layer domains are far NATURE NANOTECHNOLOGY 27

28 from edges of other 2 nd layer domains), they maintain a constant radial growth rate as indicated by the equal widths of the isotopic rings. (b) Further, we observe that after the first 6-7 isotope cycles (105 minutes of growth time), the 1 st layer domains on the exterior surface merge with adjacent domains and fully cover the Cu surface. However, because of a lower growth rate, the 2 nd layer domains continue to grow up to 12 cycles (180 minutes growth). The difference in growth kinetics for the two layers clearly shows that the enlargement of the 2 nd layer domains is not restricted by the full coverage of the 1 st layer graphene on the exterior Cu surface. This further suggests that the 2 nd layer growth is supported by the C bulk diffusion from the interior surface. 28 NATURE NANOTECHNOLOGY

29 SUPPLEMENTARY INFORMATION Figure S15 Zoom-out Raman image of Figure 2f. The growth progress of the whole domains of both layers was shown, and the grain boundary of the 1 st layer film is shown too. Note that this image was taken according to the center of mass of 2D peaks, and the corresponding Raman spectra at different regions were shown in the lower-right panel. (c) Sharp isotope labeled 2 nd layer graphene. In our previous work 23, the contrasting features between the isotope-labeled graphene films on Ni and on Cu strongly suggest that the extremely low C solubility in Cu restricts the whole growth processes, such as nucleation and diffusion, to happening only at surface. We emphasize that those samples were grown in the conventional geometry (i.e. same conditions on both sides of the Cu foil, such that there is no net flux of C through the foil). In contrast, in current work we intentionally utilize the asymmetric growth environment with a Cu pocket to promote the isothermal growth of the 2 nd layer. Multiple control experiments confirmed that small amounts of C can diffuse through the Cu bulk and segregate onto the exterior surface for the 2 nd layer growth. Interestingly, we found the similar isotopic rings. This appears to be different from the previous case. Here we revisit the scenario, and found that the occurrence of isotope rings are the results of extremely low C solubility, efficient diffusion both in bulk and along the interface between Cu and the 1st graphene layer. We note that significant isotope mixing requires that there is a C reservoir in the bulk of the metal substrate, i.e. the number of C atoms in the substrate bulk exceeds that in the graphene grown on it. 23 However, the C solubility in Cu is extremely low, so that even if there is mixing between 12 C and 13 C dissolved in the Cu foil, the amount is too small to give an obvious isotopemixing contrast from that of pure 12 C or 13 C regions. In other words, the total number of C atoms passing through the Cu foil and forming graphene on the exterior surface during one isotope NATURE NANOTECHNOLOGY 29

30 feeding cycle far exceeds that of saturating C atoms inside the Cu bulk. Therefore the minimal isotope mixing also indicates efficient C bulk diffusion at the elevated temperature. In addition, minor isotope mixing near the isotope ring boundaries cannot be completely excluded since the spatial resolution of the Raman mapping is ~300 nm. Last, the interface diffusion has been confirmed by the first-principles calculations, as detailed in Fig.3 of the main text and Note G. (3) TEM characterization Transmission electron microscopy and selected area electron diffraction (SAED) were used to further confirm the Bernal-stacking order. As shown in Fig. S16, only one set of six-fold diffraction pattern was exhibited from the area with 2D FWHM of 53 cm -1. Furthermore, the spot intensity of {2 1 10} is consistently higher than those of {01 10}, in agreement with previous characterization of Bernal-stacked BLG 11,43. Figure S16 a, SAED pattern of bilayer area with Raman 2D band FWHM ~53 cm -1. b, Profile plots of diffraction spot peak intensities along arrows in a. c, TEM image of folded edge, indicating that it is a BLG. 30 NATURE NANOTECHNOLOGY

31 SUPPLEMENTARY INFORMATION F. Estimation of C solubility and diffusivity in Cu bulk. (1) C solubility It is well known that the C solubility in Cu is extremely low, but our experimental observations have convinced that appreciable amounts of C can diffuse through the bulk for the 2 nd layer growth on the exterior surface of a pocket. In this way, it would be more informative if there is knowledge of C solubility in Cu at the growth temperature. However, C solubility is lack of consistent value in literature. In one of the most recent works, Lopez and Mittemeijer 25 measured the C solubility in Cu: 7.4 ± 0.5 at. ppm at 1020 C. One attempt to estimate the C solubility based on our own data is from the amount of 2 nd layer domains grown underneath a full-coverage SLG during the cooling down stage, which are from the segregation of the dissolved C in the Cu bulk (presumably saturated before the surfaces being fully passivated by SLG). Obviously we cannot use our Cu pockets for such estimates, since even though the Cu bulk is saturated with C, C atoms can continuously diffuse through Cu bulk to the exterior surface as long as the interior surface is not passivated with graphene. However, in our previous work 38 and the result of the control experiment in Fig. S5 of this work, we observed that there are always ~5% areas of BLG on SLG-covered Cu foil surface. These BLG domains should be formed by the segregated C from the saturated Cu foil. By using this data we may estimate the C solubility through the calculations as follows: Given the standard atomic weight of Cu ( g/mol) and the Cu density (8.96 g/cm 3 ), we obtain that in a Cu foil of 25 μm thick and 1cm 2 area, the number of Cu atoms is N Cu = The C sp2 bond distance is nm, and there are two C atoms in one graphene unit cell. So, in the area of 1 cm 2, there are C atoms in graphene if assuming full coverage. Considering the top and bottom surfaces of a Cu foil of 1cm 2 area and 5% coverage, we can get NATURE NANOTECHNOLOGY 31

32 that the number of C atoms in the 2 nd layer graphene on the Cu foil surface is N C = The solubility of C in Cu is therefore N C / N Cu = 1.8 at. ppm. This value is in the same order of magnitude as the value measured by Lopez and Mittemeijer 25. We nevertheless note that our number may be an underestimate since the Cu foil is not necessarily saturated with C during the growth, nor is it necessary that all C segregated from the bulk Cu to form the 2 nd layer graphene upon cooling. It is also safe to say, by following this estimation procedure, that the C dissolved in the bulk of our Cu pocket cannot lead to the significant growth of BLG that we observed. (2) C diffusivity The diffusivity for solid state diffusion is described by the Arrhenius formula: Δ kt D = D 0 e, where Δ is the microscopic kinetic energy barrier for a C atom to hop between adjacent lowest energy sites in bulk Cu. D 0 is given by 2 a D 0 = ν, 6 where a is the length of a hopping step and is equal to the Cu nearest neighbor distance 2.5 Å, 2 a 6 is from the assumption of 3D random walk, and ν is the attempt frequency, which is basically the atomic vibration frequency ~ Hz. With these numbers the C diffusivity is D = Δ kt 3 10 e cm 2 s NATURE NANOTECHNOLOGY

33 SUPPLEMENTARY INFORMATION When T=1300 K, Δ=1 ev (DFT calculation result in this work, Fig. 3d), the diffusivity of C in bulk Cu is found to be about cm 2 s -1. This value is comparable with the C diffusivity in γ-fe (fcc Fe), ~ cm 2 s -1 at ~1100 C (Ref. 44), indicating that C can efficiently diffuse inside Cu bulk. It is remarkable that although the C solubility of Fe is orders of magnitude larger than that of Cu, the diffusivity values of C in these two materials are comparable. This again points out that the diffusivity as a kinetic property is not necessarily strongly correlated with the solubility, which is a thermal equilibrium property. G. 2 nd Layer Growth Mechanism studied by First-Principles Calculations Besides the O-activated hydrocarbon dissociation on Cu, large 2 nd layer growth requires fast kinetics for (i) C diffusion in Cu bulk; (ii) C diffusion near the Cu-graphene interface. Overall, the Cu(111) surfaces with and without graphene top layer are adopted as an example to do the calculations. Since the Cu lattice cannot accommodate large C clusters [C-C dimer, CH x (x=1-4), etc.]; At the Cu-graphene interface, these species are also found energetically unfavorable 28,45. Therefore, in this work, only individual C atoms are calculated in various processes. We perform density functional theory (DFT) calculations using Projector Augmented Wave (PAW) pseudopotentials 46,47 and the VDW-DF functional, 48 as implemented in VASP. 49,50 The energy cutoff for the plane wave functions is 400 ev. All structures are relaxed until the force on each atom is < 0.01 ev/å. The Cu-graphene interface is modeled by a 4 4 Cu(111) surface cell with 4 layers, as shown in Fig. S17a. The bottom layer is fixed in the direction perpendicular to the surface Monkhorst-Pack (MP) k-points 51 are used (5 5 points in the surface plane and 1 along the surface normal direction) to sample the Brillouin zone. C atom in NATURE NANOTECHNOLOGY 33

34 Cu bulk is modeled by a 4 4 Cu(111) surface cell with 6 layers k-points are used. Vacuum spacing is kept larger than 15 Å in the direction perpendicular to the Cu or graphene surface. Figure S17 a, Model of Cu-graphene interface. C: black; Cu: orange. Blue-line arrows indicate the supercell. b-d, top-view and corresponding side-view of C monomer at FCC, HCP, and subsurface sites of graphene-cu interface, respectively. Note that the C monomer at Cu bridge sites of graphene-cu interface is unstable, and automatically fallen into subsurface, so no images shown here. The binding energy of C, shown in Table S1, is calculated as: E b = E(C+Cu) E(Cu) E(C), where E(C+Cu) is the total energy of the system which contains both C and Cu, E(Cu) is the energy of Cu substrate, and E(C) is the energy of an isolated C atom. The calculated binding energy values (E b ) of C monomer at various sites of Cu are listed in Table S1. The corresponding atomic-scale views are shown in Fig. S17b-d. Near the Cugraphene interface, C prefers to stay at the subsurface site (beneath one atomic layer of Cu 34 NATURE NANOTECHNOLOGY

35 SUPPLEMENTARY INFORMATION surface). This is consistent with previous reports 28,45,52 and indicates that after bulk diffusion, most C atoms should sit on the Cu subsurface. The energy of CH x for the without-o case, shown in Fig. 3, is calculated as: E = E(CH x +Cu) E(CH 4 +Cu) + x[e(cu+h)-e(cu)]; and for the with-o case: E = E(CH x +Cu) E(CH 4 +Cu) + x[e(cu+oh)-e(cu+o)]. Table S1 The calculated energetics and diffusion barriers of C atoms during various processes. The unit is ev/atom. Since Cu surface is not atomically smooth in real experiments, it is necessary to consider whether the surface defects would take effects on the dehydrogenation processes. Step edges have been found to be the most popular defects on Cu surface at elevated temperature. We calculated the dehydrogenation barriers from CH 4 to C monomers. The Cu step is modeled by cutting the Cu (111) surface along the <011> direction, with a spacing of 3*a*sqrt(3)/2 between the step edges (where a is the lattice parameter of Cu). The results are shown in Fig. S18a and compared with the results shown in Fig. 3c. We can clearly see that the step edge can only NATURE NANOTECHNOLOGY 35

36 slightly decrease the overall barrier from 4.3eV to 3.7eV, which is still significantly higher than the case with O assistance (1.4eV). It is therefore reasonable to conclude that Cu surface defects cannot efficiently catalyze methane dissociations either, while surface O is critical for this process. The binding energy of C atoms in Cu bulk was obtained based on the Cu interstitial positions, such as the C staying at the center of octahedral Cu atom cages. The value is slightly higher than that on Cu subsurface. So, this is in agreement with the low solubility of C in Cu bulk. The C monomer diffusion barrier in the bulk is ~1eV by hopping between adjacent octahedra (Fig. S18b). This value is lower than the graphene growth activation energy, which is up to 1.7eV 19. The bulk diffusion is thus not rate-limiting step for the 2 nd layer growth. It is worth noting that this relatively low kinetic barrier is not necessarily contradictory to the low C solubility in Cu, while the latter is a thermal equilibrium property. The reasonably low diffusion barriers allow for the massive C transport to underneath the 1 st graphene layer, finally leading to the formation of large 2 nd layer. Our calculation shows that on bare Cu, the C atom diffusion barrier along the subsurface is ~0.92eV. During the diffusion, one Cu atom is found to be slightly lifted up, as shown in Fig.3. In contrast, for graphene layer covered Cu, when the hopping of a C atom occurs along the subsurface, the distance between graphene over-layer and the lifted Cu atom is found to be ~2.1 Å. The charge density distribution also indicates the formation of weak chemical bond between the lifted Cu atom and graphene, which help to reduce the barrier to 0.45eV (Fig. 3d). The low barrier facilitated the C diffusion along the subsurface. In Fig. 3d, the charge density difference of the lifted Cu atom is defined as: 36 NATURE NANOTECHNOLOGY

37 SUPPLEMENTARY INFORMATION ρ(cu+substrate+graphene) - ρ(substrate+graphene) - ρ(cu atom), where the first term is the total charge density of the whole system, the second term is the charge density of the system without the lifted Cu atom (other atoms are in fixed positions), and the last term is the charge density of the isolated Cu atom. From the calculations, we established that at atomic-scale the C diffusion through Cu bulk and interface diffusion along the Cu subsurface are reasonable and can be incorporated into the graphene growth steps for the large 2 nd graphene layer. Figure S18 a, Cu (111) step edge dehydrogenation processes and the associated barriers. Inset shows the equilibrium positions of each CH x radical at Cu step edges. The red and black lines are for the ideal Cu and for the OR-Cu, respectively, as shown in Fig. 3c of the main text. b, C atom diffusion inside the Cu bulk. The three panels show the initial, transition, and final states of the hopping process. The Cu octahedron is found to be slightly distorted at the transition state. H. Device fabrication and transport measurements The fabrication process of the BLG devices was schematically shown in Fig. S19. First, the BLG domains were transferred onto h-bn/sio 2 /Si substrates (Step 1) by the PMMA-assisted method. Then, electron-beam lithography (EBL), reactive ion etching, and physical vapor NATURE NANOTECHNOLOGY 37

38 deposition processes were used to pattern the bubble-free area of the BLG into Hall bar geometry with Cr/Pd/Au electrodes (step 2 and 3). After that, another h-bn flake was transferred by the polymer transfer method on the top of the device (Step 4 and 5) as top-gate dielectrics, as described in Ref. 53. Finally the top-gate electrode (Cr/Pd/Au) was defined with EBL again (Step 6). Note that before top h-bn deposition, Raman spectroscopy was used to confirm that the device area is composed of Bernal-stacked BLG, where the FWHM of 2D peak is ~53cm -1 (Fig. S20), and the 2D peak shows the asymmetric characteristics and can be well fitted with four Lorentz components 20. Figure S19 Schematic drawing of the device fabrication process. The completed dual-gated Hall bar device was optically imaged with low- and highmagnifications, as shown in Fig. S20a and S20b. The atomic force microscopy (AFM) image before top h-bn layer deposition was shown in Fig. S20d. Samples were cooled in a variable temperature (1.7K 300K) liquid 4 He flow cryostat with samples in He vapor. Transport 38 NATURE NANOTECHNOLOGY

39 SUPPLEMENTARY INFORMATION measurements were acquired in a four-terminal geometry using a standard lock-in technique at 17Hz. Figure S20 a, b, The low- and high-magnification optical images of two devices encapsulated between two h-bn flakes. c, The schematic picture of the device cross section. d, AFM image of the device before top-gate dielectric deposition, as circled by the green dash-line in c. e, The Raman spectrum of the device area of the BLG. f, The Lorentz fitting of 2D band of the Bernalstacked BLG. On h-bn, we can clearly see the asymmetry of the 2D band. From the electrical transport measurement (Fig. S21), the extracted mobility is ~20,000 cm 2 V -1 S -1 at room temperature. At liquid He temperature, we can clearly observe the quantum Hall states at a magnetic field of 6 T with filling factors ν=±4, ±8, and ±12, in agreement with NATURE NANOTECHNOLOGY 39