The Role of Stable and Mobile Carbon Adspecies in Copper

Article pubs.acs.org/JPCC

The Role of Stable and Mobile Carbon Adspecies in CopperPromoted Graphene Growth S. Riikonen,*,† A. V. Krasheninnikov,‡,§ L. Halonen,† and R. M. Nieminen¶ †

Laboratory of Physical Chemistry, Department of Chemistry, University of Helsinki, P.O. Box 55, FI-00014, Helsinki, Finland Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076, Aalto, Finland ¶ Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076, Aalto, Finland § Department of Physics, University of Helsinki, P.O. Box 43, FI-00014, Finland ‡

ABSTRACT: Early stages of carbon monolayer nucleation on the copper (111) surface are systematically studied using densityfunctional theory calculations in the context of chemical vapor deposition and irradiation-mediated growth of graphene. By analyzing the kinetics of carbon atoms during their agglomeration, including surface, subsurface, and surface-to-bulk migration as well as dimer formation and diffusion, we draw a qualitative picture of the first stages of graphene growth on copper. The formation and migration of dimers and graphitic fragments happens at a much faster rate than the other competing processes, such as carbon migration into copper bulk and the dissociation of dimers into carbon monomers. To explain this tendency, which is an important factor in making copper such an effective graphene catalyst, we analyze in detail the electronic structure of dimers on surfaces and suggest that dimer stabilization and mobility stem from a delicate interplay between the carbon dimer σp bonding orbitals and copper d and s electrons. Our results emphasize the role of mobile carbon dimer intermediates during the growth of graphene on Cu, Ag, and Au surfaces by chemical vapor deposition and irradiation-mediated methods, in which carbon atoms are implanted into copper foils beyond the solubility limit.

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INTRODUCTION Graphene, a sheet of sp2-hybridized carbon atoms, has attracted an enormous amount of attention since its isolation by mechanical exfoliation.1 The interest in graphene sparked by its unique mechanical and electronic properties2,3 became not purely academic after a large-scale production of graphene was demonstrated.4−7 Nowadays, macroscopically large samples of graphene can be manufactured by chemical exfoliation,6,7 annealing of silicon carbide,8 heating solid carbon sources,9 and by the chemical-vapor deposition (CVD) method.4,5,10 Nearly all these techniques have been demonstrated to be suitable for the growth of two-dimensional carbon systems even before graphene became the hotspot in nanoresearch, e.g., growth of C monolayers on nickel surfaces was reported back in 1979,11 as well as on platinum in 1992 by hydrocarbon decomposition.12 The growth of graphene by CVD and related methods4,5,10,13−17 on metal surfaces has attracted particular attention, as it makes it possible to produce samples with areas up to 40 × 40 square inches, composed of predominantly © 2012 American Chemical Society

(up to 95%) of single layer graphene. Good electronic properties were observed due to a relatively small amount of defects,18 although numerous grain boundaries were found in the samples indicating that the growth process can be optimized, as confirmed by recent experiments.19 Another advantage of the CVD technique is that graphene grown on metals can easily be transferred to other substrates. Graphene has been grown on copper, nickel, cobalt, gold, and some other transition metals20 as well as on binary metal alloys.21 Recently, the growth of graphene on metal surfaces has become the subject of many theoretical studies.16,22−26 Among the different catalyst metals, copper has been most widely used. It is inexpensive when compared to Ir, Ru, and Au and the obtained graphene sheets are of good quality and predominantly monolayer.27 These also form continuously over Received: December 8, 2011 Revised: January 20, 2012 Published: January 26, 2012 5802

dx.doi.org/10.1021/jp211818s | J. Phys. Chem. C 2012, 116, 5802−5809

The Journal of Physical Chemistry C

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copper grain boundaries and step edges.19,28 It has been demonstrated that the low solubility of carbon in copper is a key factor in making copper an effective graphene catalyst: copper has a complete d-electron shell resulting in low chemical affinity with carbon. This leads to low carbon solubility and the absence of carbide phases.27 Because of the low solubility, graphene formation on copper is self-limiting: carbon precipitation from copper bulk is minimal, avoiding the formation of multiple graphene layers, while the first formed graphene layer passivates the copper surface.29 For a comprehensive description of such a surface-limited synthesis, kinetics of the first stages of graphene growth should be considered together with the solubility argument. There is an intimate relationship between carbon solubility near the surface and the kinetics of graphene formation as the carbon adspecies may either diffuse into the bulk or initiate the growth of graphitic structures.30 At the same time, although energetics of small clusters on copper has been studied at length,25 the diffusion of carbon species on and in copper has received much less attention (mostly in the context of carbon nanotube growth31), while kinetics effects may govern the graphene growth process. In addition to CVD growth, recent experiments32,33 demonstrate that single and multilayer graphene can be grown on metal foils by implanting carbon ions into the foils, followed by high-temperature annealing resulting in the migration of implanted atoms to the surface and eventually formation of graphene. The same technique has successfully been used for Cu.34 By controlling the implantation dose, one can grow up the desired number of layers. Moreover, by using spatially localized irradiation, the numbers of layers in different points of the sample can be varied in a controllable manner. Finally, irradiation with low-energy ethylene radicals was shown to be an effective way for growing graphene on low-reactivity metals.35 All of these require precise microscopic knowledge on the behavior of C atoms, not only on the top of metal surfaces but also in the subsurface regions. The aim of this work is to provide a comprehensive description of diffusion and reaction kinetics of the initial stages of graphene growth on a copper surface. By use of densityfunctional theory (DFT) calculations, we show that dimer formation and the subsequent graphene growth is by far the most favorable reaction in both energetic and kinetic terms, while the diffusion of species into the bulk happens at a much slower pace. By analyzing copper lattice relaxations, charge transfer from the copper lattice to carbon species and the stabilization of carbon in the subsurface region, we provide a comprehensive microscopic picture of the diffusion of carbon adspecies both close to the surface and in the bulk.

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Figure 1. Two different supercells (composed from atoms with a darker shade) used to study the adsorption and diffusion of carbon on the Cu(111) surface within the periodically repeated supercell scheme. The Cu(111) surface is viewed from above. The slabs were 9 layers thick for the 3 × 3 and 6 layers thick for the 4 × 6 slabs. The arrows indicate the surface lattice vectors.

We define adsorption energies Eads as Eads =

E(X *) − (E0 + nμ) E(X *) − E0 = −μ n n

(1)

where μ is the chemical potential of carbon, E(X*) the energy of the species (an atom or a dimer) adsorbed on the surface, and E0 the energy of the supercell without adsorbates. Quantity n is the number of carbon atoms in the adsorbed species; eq 1 then reflects the energy gain of adsorption per carbon atom. Two chemical potentials will be used; if not otherwise stated, μ is the energy of an isolated, spin-polarized carbon atom in vacuum (leading to negative adsorption energies). To compare some of our results to the data available in the literature, another chemical potential μ* is used, which is defined as the energy of graphene per carbon atom (leading typically to positive adsorption energies).31 Carbon Interstitials in Bulk Copper. The solution entalphy of carbon in bulk copper was studied by placing a carbon atom into an octahedral interstitial site, as illustrated in Figure 2. Carbon in a tetragonal site was tested as well, but the interstitial moved spontaneously into a neighboring octahedral site during the geometry optimization (earlier simulations36 carried out by semiempirical methods give the same qualitative picture). When the atomic geometry is relaxed, six neighboring copper atoms undergo slight displacements as listed in Table 1. From Table 1, we obtain a net charge transfer of 1.13 electrons from the copper lattice to the carbon atom and a solution entalphy of −5.31 eV, reflecting the moderate interaction of carbon with copper. When using the chemical potential μ*, this value is 2.39 eV, which is in good agreement with earlier theoretical results.31 Carbon diffusion in bulk Cu was studied by simulating the migration of the carbon atom between two neighboring octahedral sites. The diffusion process is illustrated in Figure 2. The transition state found using the NEB method is not a tetrahedral geometry, but an atomic configuration where carbon has again achieved an (approximate) octahedral coordination with copper, Figure 2b. This diffusion path is similar to the one found for another face-centered cubic (FCC) metal, the γ-iron.37 Details of atomic displacements in the transition state are given in Table 1. Rather large movement of neighboring atoms (α in Figure 2) is observed. A more detailed analysis of atomic displacements reveals that the stress on

RESULTS AND DISCUSSIONS

Bulk copper and the Cu(111) facet were simulated within the repeated supercell scheme. An isolated carbon interstitial in copper was modeled using a orthorhombic supercell of copper with dimensions of 12.8 Å × 13.4 Å × 12.6 Å and containing 180 copper atoms. Two surface supercells that were employed to model the Cu(111) facet are shown in Figure 1. The 3 × 3 supercell has been used earlier,31 but it is not large enough to account for the adsorbate-induced strain in the system, as we show below. 5803



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Figure 2. Carbon interstitial diffusion in bulk copper. Panel (a) shows two neighboring octahedral sites in the copper FCC lattice from different perspectives. The cage forming a tetrahedral site has been marked with blue color and one carbon atom has been adsorbed into an octahedral site. Panel (b) depicts the transition state of carbon atom between two octahedral sites (the same perspectives as in panel a). At the transition state, atoms marked with α undergo the largest displacements. The propagation of this distortion in the copper lattice is illustrated in panel (c). At the transition state, atom displacements are given in Ångstroms.

Table 1. Adsorption Energies per Carbon atom Eads as Given by Eq 1 and Interatomic Separations at the Adsorption Sites (as in Figure 3) and at the Transition States (Indicated with an Arrow)a site

4×6 Eads (eV)

3×3 Eads (eV)

Q3×3 (e−)

FCC

−5.04

−4.99

4.77

↓

(no TS)

−4.88

4.79

BRI

−5.28

−4.94

4.85

↓

(no TS)

−4.86

4.78

HCP

(not stable)

−4.94

4.75

BRI ↓

(no TS)

−4.65

5.05

A

−5.59

−5.42

5.15

↓

−5.07

−4.89

5.03

A′ ↓

(same as A) −4.16

−3.53

4.82

B′

−5.29

−5.26

5.13

−6.67

DIM

↓

−6.4

DIM′ Bulk (180 atoms)

−5.31

5.13

↓

−4.29

4.97

d3×3 (Å)

Δd3×3 (Å)

1.86 0.02 1.84 0.14 1.83 0.25 1.84 0.13 1.86 0.03

1.86 0.03 1.84 0.14 1.83 0.25 1.84 0.13 1.86 0.03

1.86 0.03 1.93 −0.17 2.08 −0.31 1.91 −0.12 1.86 0.03

2.12 −0.34

1.82 0.51 1.91 0.19 1.86 0.86

1.83 0.51 1.91 0.19 1.94 0.02

2.0 −0.29 1.91 0.19 1.97 0.16

2.03 −0.22 2.01 0.02 2.16 −0.21

1.83 0.76 1.95 0.14 1.96 −0.16 1.97 −0.16 2.03 0.0 2.04 −0.01

1.92 0.16 1.95 0.14 2.14 0.15 2.13 0.11 2.07 0.3 2.07 0.32

1.92 0.14 1.95 0.14 2.14 0.13 2.14 0.14 2.25 −0.3 2.21 −0.34

2.05 −0.03 1.95 0.07 1.29 (C)

1.93 0.13 1.81 0.53

1.93 0.1 1.82 0.51

1.93 0.1 2.09 −0.12

1.93 0.13 2.09 −0.14

2.25 −0.14 2.02 0.02 2.18 −0.13

2.02 0.02 2.34 −0.07

1.95 0.07

1.95 0.07

1.93 0.12 2.1 −0.14

1.93 0.1 2.1 −0.13

1.29 (C) 1.30 (C) 1.30 (C)

Bulk a

Values in bold letters (d) are the C−Cu distances, while values in normal letters (Δd) describe displacement of copper atoms projected into the C−Cu axis; positive (negative) values correspond to carbon repelling (attracting) the copper atoms. For the dimer (DIM), values for both carbon atoms have been tabulated. The row (Q) indicates the Bader occupation of the adsorbed carbon atom (Q = 4e− for an isolated carbon atom in vacuum). 5804



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Figure 3. The Cu(111) surface, top (a) and side (b) views. Copper atoms are shown as big white spheres. The green small spheres are surface adsorption sites. The FCC, HCP, TET, and BRI sites are inequivalent sites, while two equivalent sites are distinguished with a prime, for example BRI and BRI′ are neighboring equivalent sites. Dark spheres are the octahedral adsorption sites (bulk sites considered in Figure 2) and the nearest neighbor octahedral sites have been connected with lines.

Figure 4. Carbon energetics and minimum energy paths on the Cu(111) surface, subsurface and in the bulk. Labels (FCC, HCP, etc.) correspond to Figure 3. Results obtained using the 3 × 3 (blue) and the 4 × 6 (red) unit cells have been plotted. Results obtained for the dimer (“DIM”, using 3 × 3 unit cell) and for carbon diffusion in the bulk (using a 180 atom unit cell) are illustrated in the leftmost and rightmost parts of the figure, respectively. Energy values have been calculated using eq 1 and zero level has been adjusted to the adsorption energy of carbon at the A site as calculated in the 3 × 3 supercell. In the three lowermost insets, adsorption geometries in sites BRI and A′ have been depicted (top view): blue color marks nearest neighbors of the (BRI) carbon atom or alternatively, the two copper octahedrons (similar to Figure 2a) in a diffusion process (A→ A′,A′→B′). In the uppermost panel, the distortion of the copper lattice, when carbon is adsorbed in the BRI site has been illustrated.

atoms α is propagated in the copper lattice up to 5 Å along the (100) and equivalent directions (Figure 2c). The migration energy path with an activation energy of ∼1.0 eV is illustrated in Figure 2. The activation energy we obtain is more than 0.5 eV lower than the previously reported value,31 which can be attributed to the considerably larger supercell used in our work which minimizes finite-size elastic effects. Carbon Monomers on the Cu(111) Surface. Adsorption sites on the Cu(111) surface, subsurface, and deeper in the bulk are shown in Figure 3. The topmost sites are the FCC, HCP (hexagonal close-packed), and BRI (bridge) sites. Of these, the FCC and HCP sites are 3-fold, while the bri site is 2-fold coordinated to the neighboring copper atoms. The TET site is the bulk tetrahedral site which is located deeper in the bulk than the FCC site. The remaining sites (A,A′,B′) are bulk octahedral interstitials near the surface. Figure 4 shows the energetics of carbon adsorption and migration on and near the surface, as calculated for the 3 × 3 and 4 × 6 supercells. As evident from Figure 4, adsorption energies for the two cases are similar, while migration barriers differ substantially. In the 4 × 6 supercell, which is more adequate for simulations than the 3 × 3 supercell as we show below, the

HCP adsorption site is unstable. The FCC and BRI are also metastable sites; as seen from Figure 4, at finite temperatures, carbon diffuses directly to the subsurface A site. These features result from far-reaching lattice distortions into the (100) and equivalent directions, in analogy to the bulk case illustrated in Figure 2. The 4 × 6 supercell accommodates the resulting strain, giving more realistic results for surface and subsurface diffusion phenomena. The distortion propagating from atoms α also plays an important role in limiting the surface-to-bulk diffusion: As follows from the insets of Figure 4, on the path A→A′ the distortion propagates perpendicular to the surface, pushing one of the atoms tagged with α toward vacuum, while on the path A′→B′ the distortion propagates along the surface, creating strain with higher energy cost. This results in a lower migration barrier for diffusion along the surface and a higher one for the diffusion into the bulk. As can be seen in Figure 4, the high stability of carbon at the subsurface sites (A,A′) plays also an important role in creating a high surface-to-bulk migration barrier. The stabilization of carbon interstitials in the copper subsurface area can be understood with a few simple arguments: copper atoms at the topmost copper layer are the 5805



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least coordinated atoms on the Cu(111) surface, therefore pushing them toward vacuum should have a smaller energy cost;38 subsurface adsorbed carbon atoms take advantage of this greater flexibility and form an octahedrally symmetric copper surroundings with optimal bond lengths and maximal charge transfer; as evident from Table 1, largest charge transfer of more than one electron takes place at the subsurface sites, while the copper octahedron around the carbon atoms becomes almost symmetric. Finally, as is evident from the data presented in Table 1, a lower carbon atom concentration (4 × 6 supercell) gives systematically more stable carbon adsorption than higher (3 × 3 supercell) concentration. This difference is most significant (340 meV) at the metastable BRI site and least significant at the A and B sites (30−170 meV). There exists then a moderate repulsion between carbon atoms at high concentrations which we attribute to an elastic factor mediated by the copper lattice. The activation energies presented in Figure 4 and Table 1 (for the 3 × 3 supercell only) can be compared to those given in ref 31. Consistent with our results, the monomer migration barrier on the surface is small, less than 0.1 eV.24,31 For subsurface monomer diffusion within the 3 × 3 unit cell (0.55 eV,24 >0.5 eV31) we obtain a similar value (0.53 eV). Adsorption energies (using chemical potential μ*) for adatom, subsurface, and ad-dimer are (in eV) 2.71 (FCC), 2.28 (A), and 1.0 (DIM). These are in line with the values presented in Figure 1 of ref 31. Dimers. The adsorption configurations of C2 dimers and their migration are shown in Figure 5. Individual carbon atoms

Table 2. Spontaneous (Zero Activation Energy) Formation of Dimers from Nearby Adsorption Sitesa site

Eads (eV)

A + A′ A + FCC A + HCP FCC + HCP FCC + BRI BRI + BRI′

−5.36 → DIM −5.19 → DIM → DIM → DIM

a

A + FCC indicates that one carbon atom is adsorbed in site A, while another one in site FCC of Figure 3. → DIM indicates spontaneous dimer formation during the conjugent-gradient geometry optimization. Otherwise numeric values indicate the stable coadsorption energy (eV per carbon atom). Calculations were performed in the 3 × 3 unit cell.

evident from the lack of electron density between the molecule and the substrate) that has been “pushed” above the substrate d-electron “hump”39 (for similar molecule−substrate antibonding states, see for example Figure 3 of ref 39). The fact that the peak C is within the filled states and positioned well below the Fermi level has two desirable effects from the point of view of graphene synthesis: (1) it stabilizes the carbon dimer (the internal σp bonding orbital of the dimer), and (2) it reduces the interaction between the substrate and the molecule (it is a molecule−substrate antibonding state). We can further expect that for metals with a high d-band center (and high reactivity), the peak C is pushed above the Fermi level and will have an inverse effect (the dimer less stable, stronger dimer surface binding). However, for metals such as copper, silver, and gold, it should always remain below the Fermi level, in the energy interval dominated by the substrate s electrons. From Figure 6c, it is evident that substrate electronic states involved in peak C have the pronounced spherical shape of selectrons. The contribution from the surface also concentrates in the topmost copper layer. This is intriguing as the energy interval just above the “d hump” is known to host a surface state.40,41 Cu(111) surface states may then play a role in the stabilization of carbon dimers and graphitic fragments. To put these ideas on a firmer ground, we compared the behavior of a carbon dimer on Cu and Co surfaces. We chose the latter as a typical transition metal with a strong interaction between carbon and the metal atoms and repeated the simulations we did for the C dimer. Inset of panel (a) in Figure 6 shows the details of the electronic structure for the dimer adsorbed on Co(111); the peak C is now in the immediate vicinity of the Fermi level and only partially occupied. Finally, Figure 7 shows the relative energies of the carbon monomer and dimer in vacuum and on the (111) surface of copper and cobalt. As evident from Figure 7 that the dimer is stabilized more on copper than on cobalt. At the same time, it is less bound to copper than to cobalt surface.

Figure 5. Initial (DIM), transition (TS), and the final state (DIM′) of carbon dimer diffusion on the Cu(111) surface.

sit on the HCP and FCC sites while forming a carbon−carbon bond. In the transition state, both atoms sit on a BRI site and the activation energy for dimer migration is 0.27 eV. When individual carbon atoms are placed into nearby adsorption sites on the surface, a spontaneous (zero activation energy) dimer formation occurs for most coadsorption configurations (see Table 2). Our result for adsorption energy (1.03 eV using chemical potential μ*) is close to the value of ref 31 (∼1.3 eV), but our activation energy (0.27 eV) is significantly lower (∼0.5 eV31). To find out the key electronic factors for dimer stabilization, we studied the electronic structure at the adsorption geometry ”DIM“ in Figure 6. First of all, in panel (b) of Figure 6 one observes charge transfer from the copper substrate to the dimer σp bonding-type orbital, which stabilizes the C−C bond; this bonding orbital originating from the hybridization of p states is empty in an isolated (singlet state) carbon dimer. Next, we interpret using the Hammer−Nørskov d-band theory39 some of the salient features in Figure 6. Peak C in Figure 6a and the corresponding density of states visualized in Figure 6c can be interpreted as a molecule− substrate antibonding contribution (the antibonding nature is

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DISCUSSIONS

On the basis of our results, we can now draw a qualitative picture of the first stages of graphene growth on the Cu(111) surface. With regard to the CVD growth of graphene, a starting point where a large number of carbon monomers (created by CVD precursor decomposition) have adsorbed on the surface is considered. Immediately after carbon monomers have been adsorbed on the surface, these populate the subsurface octahedral sites (as 5806



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Figure 6. Details of the electronic structure for dimer adsorption on Cu(111). (a) Density of states, projected into copper atom centered d-orbitals (upper curve) and into the carbon atom centered sp orbitals (negative values, lower curve). Inset of panel (a) shows the same information for Co(111) surface. (b) Charge transfer Δρ between the copper surface and the carbon dimer. Δρ = ρCu+C2 − (ρCu + ρC2), where ρCu + ρC2, ρCu, and ρC2 are the self-consistent electron densities of adsorbed carbon including the copper surface, copper surface, and the isolated dimer, respectively. (c) Density of states integrated in a small energy interval around peak marked with letter C in panel (a). In panels (b) and (c), white arrows indicate the positions of carbon atoms, while white dots stand for copper atoms. In the rightmost panel, the used false-color scale is depicted; red and blue color indicate maximum and minimum values, respectively, for the electron density (c) and charge transfer (b).

Figure 8. Schematic illustration of formation of graphitic structures on the Cu(111) surface: the large white spheres present the Cu(111) top layer copper atoms, while the black spheres connected with lines are the carbon dimers (at an optimal adsorption site). Left panel: carbon dimers at nearby DIM sites (see Figure 5). Right panel: some of the dimers (3 and 4) have migrated to neighboring DIM sites, forming a graphitic network. Figure 7. Relative energies of a carbon monomer (dashed lines) and a carbon dimer in the singlet state (solid lines) in vacuum (black) and on copper (red) and cobalt (green). Energies are per carbon atom, as described by eq 1.

by incorporation of adatoms to the growing graphene layers.42−44 On the other hand, recent experimental45,46 and theoretical24,25,47 studies suggest the importance of larger carbon adspecies as the minimal units being incorporated into the growing graphene: on Ru(0001)45 and Ir(111)46 clusters of 5 carbon atoms have been proposed to act as reaction intermediates. Simulations suggest the formation of carbon atom “chains” on Ni(111)47 and Cu(111).25 Graphene is known to nucleate on Ru and Ir from atomic-sized steps, but on the other hand, atomic steps of these metals do not effectively trap carbon monomers but they do stabilize carbon dimers.24 In the same spirit, we emphasize the importance of stable and mobile reaction intermediates, such as carbon dimers which are energetically favorable and are formed spontaneously. In the dimer-based picture, the costly step of moving a monomer from the surface into the graphene boundary can be avoided. In particular, on Cu(111), persistent and mobile dimers are formed which are easily assembled into larger graphitic units. The tendency to form these kind of intermediates might be the key factor in making copper an effective graphene catalyst. From a detailed analysis of the electronic structure, an interplay of the substrate electronic states with the dimer σp-bonding orbital was observed: there is an electronic factor that stabilizes the internal C−C bonding of the carbon dimer, while at the same time reducing its interaction with copper. This could be an important mechanism in driving the formation of stable and mobile graphitic fragments on copper, gold and silver.

described by the 4 × 6 supercell in Figure 4, this reaction is spontaneous). Next, there are several competing processes, namely, (1) dimer formation, (2) dimer migration, (3) backdissociation of dimers into individual atoms, (4) migration of carbon along the surface, (5) migration of carbon atoms deeper into the bulk. On the basis of Figure 4 and Table 2 it is clear that processes (1) and (2) are dominant. In more detail, from Figure 4, we observe that (1) the formation of carbon dimers is exothermic and (2) the migration barrier for the dimer to move on the Cu(111) surface is small (Ea = 0.27 eV). Once the dimer is formed, it costs more energy to dissociate the dimer than to migrate it around the surface. Carbon dimers are then persistent and mobile. Finally, based on the adsorption geometries and transition state of the dimer in Figure 5, we show schematically in Figure 8 how migrating dimers could form larger graphitic structures on the Cu(111) facet. Two carbon dimers migrate to nearby adsorption sites at their optimal adsorption positions. This is a rapid process, as the migration barrier for carbon dimers is small, less than migration of C atoms in the subsurface area. In the vast majority of studies concerning the microscopic mechanism of graphene and carbon nanotube growth, a monomer-based picture has been considered. According to this picture, graphitic material emerges from atomic-sized steps 5807



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Newton scheme. This way the force residual for a stable geometry was ≤0.02 eV/Å. In all calculations a special Davidson block iteration scheme was used and symmetries of the adsorption geometries were not utilized. The standard “normal” accuracy was used. The nudged elastic band method (NEB)56 was used for finding reaction minimum energy paths. Spin polarization was excluded in calculations involving copper slabs; copper is nonmagnetic and the magnetic moments of molecular species typically vanish upon adsorption. Some test calculations including spin were performed for carbon monomer and dimer on copper which confirmed the magnetization to be less than 0.05 Bohr magnetons (μB).

Our results, especially for the diffusion of C interstitials in bulk Cu, should also shed light on irradiation-mediated graphene growth. After the implantation of C atoms well beyond the solubility limit has been done and sample temperature raised, the growth rate of graphene is determined by the migration rate of C interstitials toward the surface, which can be estimated provided that the migration barrier is known, as well as the concentration profile of interstitials after implantation. We notice that information on the diffusion rate may be important if a Cu foil with implanted C (or B/N) atoms is used for the CVD growth as doped graphene could be grown in this case.

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CONCLUSIONS In summary, by performing DFT calculations, we provided a qualitative microscopic picture of the diffusion of C atoms in bulk Cu, on the (111) surface and in the subsurface area. Contrary to previous calculations where smaller simulation cells were used, we minimized the finite-size effects by considering larger systems and analyzing lattice distortions, which made it possible to reliably estimate the migration barriers. The importance of the first subsurface layer in attracting and stabilizing the adsorbed carbon atoms and in creating a ratelimiting step for surface-to-bulk diffusion has been emphasized. Carbon may migrate rapidly below the topmost copper layer due to the flexibility of the topmost copper layer, while upon entering the copper bulk, it experiences a large barrier. We explained these phenomena with a carefull analysis of the copper lattice relaxations. Compared to these processes, signficantly more rapid ones are the dimer formation, dimer migration, and the formation of larger graphitic structures. We suggested that the rapid formation of many mobile and persistent reaction intermediates is the key factor in making copper an effective metal substrate for graphene growth. We further suggested, based on the dband theory, that the tendency to form these intermediates lies in the details of copper electronic structure and its interplay with the dimer σp bonding orbital. This observation may open the way for a deeper understanding of graphene synthesis and the fabrication of optimal catalysts.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We wish to thank the Center for Scientific Computing, for use of its computational resources. This work has been supported by the Academy of Finland through the FidiPro and the CoE (2006-2011) programs.

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REFERENCES

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METHODS

Bulk copper and the Cu(111) facets were simulated within the repeated supercell scheme. An isolated carbon interstitial in copper was modeled using the orthorhombic cubic supercell of bulk copper with dimensions of 12.8 Å × 13.4 Å × 12.6 Å. This large supercell contains 180 copper atoms. The Monkhorst− Pack (MP) sampling50 of 2 × 2 × 2 k-point grid was used. Two surface supercells that were employed to model the Cu(111) facet are represented in Figure 1. The 3 × 3 supercell was used earlier in the literature,31 while the elongated 4 × 6 supercell was constructed to relax lattice strain properly. Surface MP grids were 5 × 5 and 6 × 2 for the 3 × 3 and 4 × 6 supercells, respectively. All calculations were performed in the framework of the DFT, as implemented in VASP.51,52 Projector augmented waves53 and the Perdew−Burke−Ernzerhof generalized gradient approximation (GGA)54 were used. The cutoff energy of the plane wave basis was 420 eV. The smearing scheme in the electronic relaxation was the first order Methfessel−Paxton method.55 Conjugent-gradient relaxation of the geometry was performed, and if needed, the relaxation was continued with a 5808



Article

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The Role of Stable and Mobile Carbon Adspecies in Copper

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