Elementary Process for CVD Graphene on Cu(110): Size-selective Carbon Clusters

Revealing the graphene growth mechanism at the atomic-scale is of great importance for achieving high quality graphene. However, the lack of direct experimental observation and density functional theory (DFT) verification hinders a comprehensive understanding of the structure of the carbon clusters and evolution of the graphene growth on surface. Here, we report an in-situ low-temperature scanning tunneling microscopy (LT-STM) study of the elementary process of chemical vapor deposition (CVD) graphene growth via thermal decomposition of methane on Cu(110), including the formation of monodispersed carbon clusters at the initial stage, the graphene nucleation and the ripening of graphene islands to form continuous graphene film. STM measurement, supported by DFT calculations, suggests that the carbon clusters on the surface are C2H5. It is found that graphene layers can be joined by different domains, with a relative misorientation of 30°. These graphene layers can be decoupled from Cu(110) through low temperature thermal cycling.

mechanism 14,[33][34][35][36][37][38][39][40][41][42][43] . Using first-principle calculations, Chen et al. found on flat surfaces of Ir(111) and Ru(0001), two carbon atoms repel each other; while they prefer to form a dimer on Cu(111) 37 . Zhang et al. also revealed that C 2 H 2 can be easily formed on a Cu(111) surface, which represents a more favorable reaction path compared to CH dissociation 38 . By careful optimization of the supported carbon clusters C N on Ni(111), Gao et al. indicated a ground state structure transition from a one-dimensional (1D) carbon chain to a two-dimensional (2D) sp 2 carbon network at N , 10-12 40 ; while Wesep and co-workers proposed an energetic preference for the formation of stable 1D carbon nanoarches consisting of 3-13 atoms on Cu(111) surface 43 . Explored by ab initio calculations, Yuan et al. showed that the core-shell C 21 is a very stable magic carbon cluster on Rh(111), Ru(0001), Ni(111) and Cu(111) surfaces 42 . Zangwill et al. predicted that an immobile island composed of six five-atom carbon clusters as the smallest stable precursor to graphene growth on metals 41 . Despite these inspiring achievements, most of these theoretical studies only address the number of carbon atoms, and the precise determination of hydrogen atoms within the cluster is rare. Moreover, very little of the growth mechanism in the initial nucleation stages of carbon atoms has been revealed experimentally 15,16,44 . In this regard, atomic-scale characterization of a complete process of graphene growth in combination with theoretical calculations is of great importance, for both fundamental interest and achieving high quality graphene.
Here, we report an atomic scale characterization of the elementary process of CVD graphene growth via thermal decomposition of methane (CH 4 ) on Cu(110) using low-temperature scanning tunneling microscopy (LT-STM), including the formation of monodispersed carbon clusters at low temperature, nucleation and ripening of graphene islands at high temperature. Combined with first principles calculations, the monodispersed carbon clusters are identified as C 2 H 5 . Different domains stitch together to form a graphene layer, with a preference angle of 30u at the grain boundaries. These graphene layers can be decoupled from Cu(110) through low temperature thermal cycling.

Results
As shown by the high magnification STM image in Fig. 1a, upon the deposition of CH 4 at room temperature (RT) and subsequent annealing at 480uC in CH 4 at a pressure of 2 3 10 25 mbar for 50 min, the Cu(110) surface was almost decorated with carbon clusters of monodispersed size. Each carbon cluster appears as a bright spot with an identical size of 0.4 nm. Careful inspection of the STM image reveals that the surface is decorated by isolated but well-defined superstructures, where the carbon clusters are adsorbed in an epitaxial relationship with the underling Cu(110). As indicated by the dashed lines in Fig. 1a, the minimum distance between two neighboring row is 2a 0 of 0.512 nm; while it is 2b 0 of 0.723 nm between two columns (a 0 and b 0 are the unit cell dimensions of Cu(110)). It can also be revealed that the carbon cluster arrays are aligned precisely with the crystal orientation of the underlying Cu(110). The carbon cluster at this low coverage was referred to as ''cluster 1'' with a density around 2.70 3 10 14 /cm 2 . Previous theoretical studies proposed that carbon dimmers are energetically favorable on the Cu surface [37][38][39] . Therefore, we tentatively assign these carbon clusters as carbon dimers (C 2 H x ).
Further increasing the coverage of the carbon clusters can result in the formation of a hexagonally close packed structure, as shown in Fig. 1b. The coverage of the carbon clusters can be increased through low temperature thermal cycling as described in the supporting information. Some gaps can still be observed between the ordered domains. However, the carbon clusters in each ordered domain posses the unit cell with a 5 0.515 nm, b 5 0.500 nm and an inclusion angle of 60u, as indicated by arrows A and B. Upon saturation of the carbon clusters on the surface, they formed highly ordered close packed structure over the surface, as shown in Fig. 1c. The unit cell  was further reduced to c 5 0.450 nm, d 5 0.480 nm with an unchanged inclusion angle of 60u. At this stage, the carbon cluster density was increased to 10.9 3 10 14 /cm 2 , referred to as ''cluster 2''. In this regime, the arrangement is supposed to be cluster-cluster interaction dominated. Some brighter lines can be frequently observed, induced by the stress relaxation at high cluster coverage with increased lateral inter-cluster interaction.
Annealing the Cu(110) surface at high temperature at 550uC in CH 4 at a pressure of 2 3 10 25 mbar for 130 min can promote the nucleation of small graphene flakes. As shown in Fig. 1d, at this stage the carbon clusters co-exist with the small graphene flakes which are indicated as ''G''. The high magnification STM image in Fig. 1e reveals that the clusters on Cu(110) are ''cluster 2''. The directions of the unit cell are indicated by arrows E and F, with lateral dimensions of e 5 0.450 nm, f 5 0.480 nm and an inclusion angle of 60u. The bright stripes inserted between these clusters are clean Cu(110) surface but with a 1 3 2 superstructure as highlighted by the red dotted line in Fig. 1e. Figure 1f shows the atomically resolved STM image of the 1 3 1 graphene lattice, and the crystal orientation of the underlying Cu(110) is indicated in the lower right corner.
To obtain the atomic structure of the carbon clusters, the adsorption of various carbon clusters on Cu(110) were simulated using DFT. First, the stability of C 1 H x (0 , 4) and C 2 H x (0 , 6) clusters on Cu (110) were studied. We define the formation energy in equation (1) where E tot is the total energy of the adsorbed system, E sub is the energy of clean Cu (110) substrate, m i and n i (i 5 C, H) represent chemical potential and the number of atoms in the cluster, respectively. Considering the equilibrium of CH 4 and H 2 , the relationship of m H and m C in unit of electron volt can be obtained as equation (2) by the process described in the supporting information: Here, x is the ratio of the partial pressures of CH 4 and H 2 .
For each carbon cluster species, the most stable adsorption configuration was found by checking different adsorption sites on Cu(110) surface, including the hollow site (H-site), bridge-long site (B long site), bridge-short site (B short site) and Top site (T-site) 45 . Figure 2 shows the formation energy of various carbon cluster species as a function of the chemical potential of H (thus the partial pressure of H 2 ). The x here was set to be 2051; we also tested x 5 1520, which gave similar results.
From Fig. 2, it is easy to find that clusters C 2 H 6 and C 2 H 5 are the two most stable species under all physical H 2 partial pressure. Although the formation energy of C 2 H 6 is very large, as a close shell molecule, its adsorption energy is expected to be very small, and it's hence easy to desorb from Cu(110) at high temperature. The average lifetime of C 2 H 6 and C 2 H 5 can be estimated by their adsorption energy E a via t a~1 u 0 e Ea=kT 46 . According to our calculations, adsorption energy of C 2 H 6 and C 2 H 5 on Cu(110) surface are 0.41 and 2.85 eV, respectively. u 0 is about 10 13 s 21 . Therefore, their average lifetime on the surface at 480uC is 5.5 3 10 211 and 1.2 3 10 6 s, respectively. Such a short lifetime makes C 2 H 6 not be able to be observed by STM. Therefore, C 2 H 5 could be the most possible abundant species from the thermodynamic point of view. STM images of several partially dehydrogenated carbon dimer species were also simulated using the Tersoff and Hamann approximation 47 . Figure 3 shows the optimized structures and simulated STM images of C 2 , C 2 H 4 , C 2 H 5 and C 2 H 6 . The optimized unit cell of the carbon cluster is 2a 0 5 0.504 nm, 2b 0 5 0.713 nm. Among these carbon clusters, the simulated STM image of C 2 H 5 is in good agreement with the experimental results. All other stable species cannot reproduce the experimental circular shape. Hence, the basic structures of the carbon clusters are elucidated by the STM images in combination with DFT calculations as C 2 H 5 .
Large graphene flakes can be achieved through low temperature thermal cycling process as described in the supporting information. Figure 4a shows a large scale STM image of a flake of graphene film on Cu(110) interconnected by two graphene grains, forming a grain boundary in between as indicated by the red ellipse. Close-up (Fig. 4b) and the corresponding atomic-resolution STM images (Fig. 4c) reveal that the two graphene grains are stitched together to form a continuous film with a relative misorientation of 30u. The detailed atomic structure at the grain boundary cannot be identified  Optimized structures (left panels) and simulated STM images (right panels) of (a, b) C 2 , (c, d) C 2 H 4 , (e, f) C 2 H 5 , and (g, h) C 2 H 6 . The integrated density of states from 0.25 V below E F to the Fermi level is used to simulate the STM image, which represents the HOMO of the carbon clusters.
www.nature.com/scientificreports SCIENTIFIC REPORTS | 4 : 4431 | DOI: 10.1038/srep04431 from our STM image, but it has been theoretically proposed and experimentally conformed as a series of pentagons, heptagons and distorted hexagons 25,48 . The graphene grows in different orientations with respect to the underlying lattice, resulting in two different moiré patterns. As shown in Fig. 4c, the lower right panel shows a moiré superstructure almost aligned with the underlying Cu(110) lattice, referred to as R0 phase. The graphene lattice of the upper left panel shows a different moiré pattern with a larger periodic modulation and is rotated by 30u from the lower R0 phase, referred to as R30 phase. Supplementary Fig. S3 on line shows a graphene film joined by multi-domains taken from a different location on Cu(110), which also shows a 30u misorientation. The preference of around 30u misorientation between two domains has also been reported by other groups 19,25 . For graphene grown on Ru(0001), only one orientation can be observed, due to the strong interaction between graphene and Ru 29 . The two dominating orientations observed here and the fact that graphene can grow continuously across Cu step edges could indicate a weaker graphene-Cu interaction when compared with Ru.
As described in the supporting information, during the experiment, we introduced the low temperature thermal cycling method to increase the carbon cluster coverage. Figure 4d shows the STM image of large flakes of graphene coexisting with carbon clusters on Cu(110). After repeating several cycles of low temperature thermal cycling, the graphene flakes on the surface possess two stripe-shaped contrasts. Comparison between Supplementary Fig. S2 on line and Fig. 4d reveals that the appearance of those bright stripes are same with the previous small graphene islands; while the dark stripes are newly produced during the low temperature thermal cycling. Close up STM image in Supplementary Fig. S4 on line and Fig. 4f reveals that the bright and dark stripes alternated between each other with a continuous boundary. As shown in Fig. 4e, the bright stripes (BG) show moiré pattern resembling the underlying Cu(110); while the dark stripes (DG) display prefect hexagonal graphene lattice. These contrasts result from the modulation by different interactions with the underlying Cu(110). The appearance of the prefect hexagonal graphene lattice in DG suggests that the graphene in this region is physically decoupled from the underlying Cu(110).
The formation of such physically decoupled graphene can arise from the intercalation at the graphene/Cu(110) interface by hydrogen atoms released from CH 4 decomposition, similar to the previously reported hydrogen 49 , lithium 50 , oxygen 51 , and fluorine intercalation to form quasi-free-standing graphene 52 ; or from the strain relief during the annealing/cooling cycles due to the different thermal expansion of graphene film and Cu substrate 53 . More controlled experiment and detailed theoretical calculations will be carried out to unravel the decoupling mechanism.

Discussion
Through the combination of the LT-STM and DFT calculations, we reveal the elementary process of graphene growth on Cu(110) surface via thermal decomposition of CH 4 . Low temperature annealing (.480uC) in CH 4 results in the formation of carbon clusters at the initial stage; further high temperature annealing (.550uC) activates the graphene nucleation; prolonged annealing in the absence of CH 4 propels the diffusing and ripening of these graphene island to form continuous graphene films extended over the surface. Low temperature thermal cycling induced decoupling of graphene from Cu(110) has also been demonstrated. Our systematic investigations identify the fundamental carbidic building blocks by STM measurement, and further elucidate their atomic structures through DFT calculations. Our work could lay the foundation for providing rational design rules for synthesis of large area single crystalline graphene films.

Methods
Growth of graphene on Cu(110). Graphene was grown on a single crystal Cu(110) via thermal decomposition of CH 4 . Prior to the deposition of CH 4 , Cu(110) substrate was cleaned by a few cycles of Ar 1 ion bombardment and subsequent annealing at 530uC. The CH 4 gas was introduced into the growth chamber through a leak valve, and the pressure was monitored by a cold cathode gauge. A typical growth procedure is as follows: the Cu(110) substrate was exposed to CH 4 at a pressure of 2 3 10 25 mbar for 20 min; annealing the sample at 480uC in CH 4 at a pressure of 2 3 10 25 mbar resulted in the formation of carbon clusters; further annealing the sample in the absence of CH 4 at 550uC initiated the graphene nucleation; prolonged annealing without CH 4 at higher temperature up to 720uC propelled the ripening of graphene islands.
Characterization of graphene in UHV LT-STM. The LT-STM experiments were carried out in a custom-built multichamber ultra-high-vacuum (UHV) system with base pressure better than 1.0 3 10 210 mbar, housing an omicron LT-STM interfaced to a Nanonis controller. All STM imaging were performed at 77 K using constant current mode with an electrochemically etched tungsten tip. All the bias voltage was applied to the tip 54 .
Structural models of clusters on Cu (110) surface. Stability of C 1 H x (0 , 4) or C 2 H x (0 , 6) clusters on Cu (110) surface were studied using DFT calculations. A 5-layer slab with a 20 Å vacuum layer was used as the substrate. The bottom layer was fixed to its bulk configuration and all other atoms were fully relaxed. A (3 3 4) supercell was chosen to make sure that clusters were separated to their neighboring clusters by more than 10 Å . In STM simulation, a (2 3 2) supercell was chosen according to the experimental coverage.
Calculation details. All the calculations were performed using DFT implemented in the Vienna Ab Initio Simulation Package (VASP) within the generalized gradient approximation 55,56 plus DFT-D2 van der Waals (vdW) correction 57 . The exchangecorrelation functional of Perdew-Burke-Ernzerhof 58 and the projector-augmented wave 59 methods were used. The plane-wave basis cutoff energy was set to 500 eV. The criteria of convergence for energy and force were set to 10 25 eV and 0.02 eV/Å . For the (3 3 4) and (2 3 2) models, (7 3 7 3 1) and (10 3 14 3 1) k-point grids were used, respectively. STM images were simulated using the Tersoff and Hamann approximation 47 . The lattice parameter of bulk Cu was optimized to be 3.564 Å 60 .