the role of stable and mobile carbon adspecies in …ark/publ/jp211818s-1.pdfthe role of stable and...

The Role of Stable and Mobile Carbon Adspecies in Copper-Promoted Graphene GrowthS. 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 density-functional theory calculations in the context of chemical vapor deposition and irradiation-mediated growth of graphene. Byanalyzing the kinetics of carbon atoms during their agglomeration, including surface, subsurface, and surface-to-bulk migration aswell as dimer formation and diffusion, we draw a qualitative picture of the first stages of graphene growth on copper. Theformation 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, whichis an important factor in making copper such an effective graphene catalyst, we analyze in detail the electronic structure of dimerson surfaces and suggest that dimer stabilization and mobility stem from a delicate interplay between the carbon dimer σp bondingorbitals and copper d and s electrons. Our results emphasize the role of mobile carbon dimer intermediates during the growth ofgraphene on Cu, Ag, and Au surfaces by chemical vapor deposition and irradiation-mediated methods, in which carbon atoms areimplanted into copper foils beyond the solubility limit.

■ INTRODUCTIONGraphene, a sheet of sp2-hybridized carbon atoms, has attractedan enormous amount of attention since its isolation bymechanical exfoliation.1 The interest in graphene sparked byits unique mechanical and electronic properties2,3 became notpurely academic after a large-scale production of graphene wasdemonstrated.4−7 Nowadays, macroscopically large samples ofgraphene can be manufactured by chemical exfoliation,6,7

annealing of silicon carbide,8 heating solid carbon sources,9 andby the chemical-vapor deposition (CVD) method.4,5,10 Nearlyall these techniques have been demonstrated to be suitable forthe growth of two-dimensional carbon systems even beforegraphene became the hotspot in nanoresearch, e.g., growth of Cmonolayers on nickel surfaces was reported back in 1979,11 aswell as on platinum in 1992 by hydrocarbon decomposition.12

The growth of graphene by CVD and related meth-ods4,5,10,13−17 on metal surfaces has attracted particularattention, as it makes it possible to produce samples withareas up to 40 × 40 square inches, composed of predominantly

(up to 95%) of single layer graphene. Good electronicproperties were observed due to a relatively small amount ofdefects,18 although numerous grain boundaries were found inthe samples indicating that the growth process can beoptimized, as confirmed by recent experiments.19 Anotheradvantage of the CVD technique is that graphene grown onmetals can easily be transferred to other substrates. Graphenehas been grown on copper, nickel, cobalt, gold, and some othertransition metals20 as well as on binary metal alloys.21 Recently,the growth of graphene on metal surfaces has become thesubject of many theoretical studies.16,22−26

Among the different catalyst metals, copper has been mostwidely used. It is inexpensive when compared to Ir, Ru, and Auand the obtained graphene sheets are of good quality andpredominantly monolayer.27 These also form continuously over

Received: December 8, 2011Revised: January 20, 2012Published: January 26, 2012

Article

pubs.acs.org/JPCC

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

pubs.acs.org/JPCC

copper grain boundaries and step edges.19,28 It has beendemonstrated that the low solubility of carbon in copper is akey factor in making copper an effective graphene catalyst:copper has a complete d-electron shell resulting in low chemicalaffinity with carbon. This leads to low carbon solubility and theabsence of carbide phases.27 Because of the low solubility,graphene formation on copper is self-limiting: carbonprecipitation from copper bulk is minimal, avoiding theformation of multiple graphene layers, while the first formedgraphene layer passivates the copper surface.29

For a comprehensive description of such a surface-limitedsynthesis, kinetics of the first stages of graphene growth shouldbe considered together with the solubility argument. There isan intimate relationship between carbon solubility near thesurface and the kinetics of graphene formation as the carbonadspecies may either diffuse into the bulk or initiate the growthof graphitic structures.30 At the same time, although energeticsof small clusters on copper has been studied at length,25 thediffusion of carbon species on and in copper has received muchless attention (mostly in the context of carbon nanotubegrowth31), while kinetics effects may govern the graphenegrowth process.In addition to CVD growth, recent experiments32,33

demonstrate that single and multilayer graphene can begrown on metal foils by implanting carbon ions into the foils,followed by high-temperature annealing resulting in themigration of implanted atoms to the surface and eventuallyformation of graphene. The same technique has successfullybeen used for Cu.34 By controlling the implantation dose, onecan grow up the desired number of layers. Moreover, by usingspatially localized irradiation, the numbers of layers in differentpoints of the sample can be varied in a controllable manner.Finally, irradiation with low-energy ethylene radicals was shownto be an effective way for growing graphene on low-reactivitymetals.35 All of these require precise microscopic knowledge onthe behavior of C atoms, not only on the top of metal surfacesbut also in the subsurface regions.The aim of this work is to provide a comprehensive

description of diffusion and reaction kinetics of the initial stagesof graphene growth on a copper surface. By use of density-functional theory (DFT) calculations, we show that dimerformation and the subsequent graphene growth is by far themost favorable reaction in both energetic and kinetic terms,while the diffusion of species into the bulk happens at a muchslower pace. By analyzing copper lattice relaxations, chargetransfer from the copper lattice to carbon species and thestabilization of carbon in the subsurface region, we provide acomprehensive microscopic picture of the diffusion of carbonadspecies both close to the surface and in the bulk.

■ RESULTS AND DISCUSSIONS

Bulk copper and the Cu(111) facet were simulated within therepeated supercell scheme. An isolated carbon interstitial incopper was modeled using a orthorhombic supercell of copperwith dimensions of 12.8 Å × 13.4 Å × 12.6 Å and containing180 copper atoms. Two surface supercells that were employedto model the Cu(111) facet are shown in Figure 1. The 3 × 3supercell has been used earlier,31 but it is not large enough toaccount for the adsorbate-induced strain in the system, as weshow below.

We define adsorption energies Eads as

=* − + μ

=* −

− μEE X E n

nE X E

n( ) ( ) ( )

ads0 0

(1)

where μ is the chemical potential of carbon, E(X*) the energyof the species (an atom or a dimer) adsorbed on the surface,and E0 the energy of the supercell without adsorbates. Quantityn is the number of carbon atoms in the adsorbed species; eq 1then reflects the energy gain of adsorption per carbon atom.Two chemical potentials will be used; if not otherwise stated, μis the energy of an isolated, spin-polarized carbon atom invacuum (leading to negative adsorption energies). To comparesome of our results to the data available in the literature,another chemical potential μ* is used, which is defined as theenergy of graphene per carbon atom (leading typically topositive adsorption energies).31

Carbon Interstitials in Bulk Copper. The solutionentalphy of carbon in bulk copper was studied by placing acarbon atom into an octahedral interstitial site, as illustrated inFigure 2. Carbon in a tetragonal site was tested as well, but theinterstitial moved spontaneously into a neighboring octahedralsite during the geometry optimization (earlier simulations36

carried out by semiempirical methods give the same qualitativepicture). When the atomic geometry is relaxed, six neighboringcopper atoms undergo slight displacements as listed in Table 1.From Table 1, we obtain a net charge transfer of 1.13 electronsfrom the copper lattice to the carbon atom and a solutionentalphy of −5.31 eV, reflecting the moderate interaction ofcarbon with copper. When using the chemical potential μ*, thisvalue is 2.39 eV, which is in good agreement with earliertheoretical results.31

Carbon diffusion in bulk Cu was studied by simulating themigration of the carbon atom between two neighboringoctahedral sites. The diffusion process is illustrated in Figure2. The transition state found using the NEB method is not atetrahedral geometry, but an atomic configuration wherecarbon has again achieved an (approximate) octahedralcoordination with copper, Figure 2b. This diffusion path issimilar to the one found for another face-centered cubic (FCC)metal, the γ-iron.37 Details of atomic displacements in thetransition state are given in Table 1. Rather large movement ofneighboring atoms (α in Figure 2) is observed. A more detailedanalysis of atomic displacements reveals that the stress on

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

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp211818s | J. Phys. Chem. C 2012, 116, 5802−58095803

Figure 2. Carbon interstitial diffusion in bulk copper. Panel (a) shows two neighboring octahedral sites in the copper FCC lattice from differentperspectives. 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, atomsmarked with α undergo the largest displacements. The propagation of this distortion in the copper lattice is illustrated in panel (c). At the transitionstate, 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 inFigure 3) and at the Transition States (Indicated with an Arrow)a

site Eads4 × 6 (eV) Eads

3 × 3 (eV) Q3×3 (e−) d3×3 (Å) Δd3×3 (Å)

FCC −5.04 −4.99 4.77 1.86 1.86 1.860.02 0.03 0.03

↓ (no TS) −4.88 4.79 1.84 1.84 1.930.14 0.14 −0.17

BRI −5.28 −4.94 4.85 1.83 1.83 2.08 2.120.25 0.25 −0.31 −0.34

↓ (no TS) −4.86 4.78 1.84 1.84 1.910.13 0.13 −0.12

HCP (not stable) −4.94 4.75 1.86 1.86 1.860.03 0.03 0.03

BRI↓ (no TS) −4.65 5.05 1.82 1.83 2.0 2.03 2.25

0.51 0.51 −0.29 −0.22 −0.14A −5.59 −5.42 5.15 1.91 1.91 1.91 2.01 2.02 2.02

0.19 0.19 0.19 0.02 0.02 0.02↓ −5.07 −4.89 5.03 1.86 1.94 1.97 2.16 2.18 2.34

0.86 0.02 0.16 −0.21 −0.13 −0.07A′ (same as A)↓ −4.16 −3.53 4.82 1.83 1.92 1.92 2.05

0.76 0.16 0.14 −0.03B′ −5.29 −5.26 5.13 1.95 1.95 1.95 1.95 1.95 1.95

0.14 0.14 0.14 0.07 0.07 0.07DIM −6.67 1.96 2.14 2.14 1.29 (C)

−0.16 0.15 0.131.97 2.13 2.14 1.29 (C)

−0.16 0.11 0.14↓ −6.4 2.03 2.07 2.25 1.30 (C)

0.0 0.3 −0.32.04 2.07 2.21 1.30 (C)

−0.01 0.32 −0.34DIM′

Bulk (180 atoms) −5.31 5.13 1.93 1.93 1.93 1.93 1.93 1.930.13 0.1 0.1 0.13 0.12 0.1

↓ −4.29 4.97 1.81 1.82 2.09 2.09 2.1 2.10.53 0.51 −0.12 −0.14 −0.14 −0.13

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



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 ismore than 0.5 eV lower than the previously reported value,31

which can be attributed to the considerably larger supercellused 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 bulkare shown in Figure 3. The topmost sites are the FCC, HCP(hexagonal close-packed), and BRI (bridge) sites. Of these, theFCC and HCP sites are 3-fold, while the bri site is 2-foldcoordinated to the neighboring copper atoms. The TET site isthe bulk tetrahedral site which is located deeper in the bulkthan the FCC site. The remaining sites (A,A′,B′) are bulkoctahedral interstitials near the surface. Figure 4 shows theenergetics of carbon adsorption and migration on and near thesurface, as calculated for the 3 × 3 and 4 × 6 supercells. Asevident from Figure 4, adsorption energies for the two cases aresimilar, 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 alsometastable sites; as seen from Figure 4, at finite temperatures,carbon diffuses directly to the subsurface A site. These featuresresult from far-reaching lattice distortions into the (100) andequivalent directions, in analogy to the bulk case illustrated inFigure 2. The 4 × 6 supercell accommodates the resultingstrain, giving more realistic results for surface and subsurfacediffusion phenomena. The distortion propagating from atoms αalso plays an important role in limiting the surface-to-bulkdiffusion: As follows from the insets of Figure 4, on the pathA→A′ the distortion propagates perpendicular to the surface,pushing one of the atoms tagged with α toward vacuum, whileon the path A′→B′ the distortion propagates along the surface,creating strain with higher energy cost. This results in a lowermigration barrier for diffusion along the surface and a higherone for the diffusion into the bulk. As can be seen in Figure 4,the high stability of carbon at the subsurface sites (A,A′) playsalso an important role in creating a high surface-to-bulkmigration barrier.The stabilization of carbon interstitials in the copper

subsurface area can be understood with a few simplearguments: copper atoms at the topmost copper layer are the

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 surfaceadsorption sites. The FCC, HCP, TET, and BRI sites are inequivalent sites, while two equivalent sites are distinguished with a prime, for exampleBRI and BRI′ are neighboring equivalent sites. Dark spheres are the octahedral adsorption sites (bulk sites considered in Figure 2) and the nearestneighbor 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 toFigure 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 ascalculated in the 3 × 3 supercell. In the three lowermost insets, adsorption geometries in sites BRI and A′ have been depicted (top view): blue colormarks 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.



least coordinated atoms on the Cu(111) surface, thereforepushing them toward vacuum should have a smaller energycost;38 subsurface adsorbed carbon atoms take advantage of thisgreater flexibility and form an octahedrally symmetric coppersurroundings with optimal bond lengths and maximal chargetransfer; as evident from Table 1, largest charge transfer ofmore than one electron takes place at the subsurface sites, whilethe copper octahedron around the carbon atoms becomesalmost symmetric.Finally, as is evident from the data presented in Table 1, a

lower carbon atom concentration (4 × 6 supercell) givessystematically 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 theA and B sites (30−170 meV). There exists then a moderaterepulsion between carbon atoms at high concentrations whichwe 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 givenin ref 31. Consistent with our results, the monomer migrationbarrier on the surface is small, less than 0.1 eV.24,31 Forsubsurface monomer diffusion within the 3 × 3 unit cell (0.55eV,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), and1.0 (DIM). These are in line with the values presented inFigure 1 of ref 31.Dimers. The adsorption configurations of C2 dimers and

their migration are shown in Figure 5. Individual carbon atoms

sit on the HCP and FCC sites while forming a carbon−carbonbond. In the transition state, both atoms sit on a BRI site andthe activation energy for dimer migration is 0.27 eV. Whenindividual carbon atoms are placed into nearby adsorption siteson the surface, a spontaneous (zero activation energy) dimerformation occurs for most coadsorption configurations (seeTable 2). Our result for adsorption energy (1.03 eV usingchemical potential μ*) is close to the value of ref 31 (∼1.3 eV),but our activation energy (0.27 eV) is significantly lower (∼0.5eV31).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 oneobserves charge transfer from the copper substrate to the dimerσp bonding-type orbital, which stabilizes the C−C bond; thisbonding orbital originating from the hybridization of p states isempty in an isolated (singlet state) carbon dimer. Next, weinterpret using the Hammer−Nørskov d-band theory39 some ofthe 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

evident from the lack of electron density between the moleculeand the substrate) that has been “pushed” above the substrated-electron “hump”39 (for similar molecule−substrate antibond-ing 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 effectsfrom the point of view of graphene synthesis: (1) it stabilizesthe carbon dimer (the internal σp bonding orbital of the dimer),and (2) it reduces the interaction between the substrate and themolecule (it is a molecule−substrate antibonding state). Wecan further expect that for metals with a high d-band center(and high reactivity), the peak C is pushed above the Fermilevel and will have an inverse effect (the dimer less stable,stronger dimer surface binding). However, for metals such ascopper, silver, and gold, it should always remain below theFermi level, in the energy interval dominated by the substrate selectrons.From Figure 6c, it is evident that substrate electronic states

involved in peak C have the pronounced spherical shape of s-electrons. The contribution from the surface also concentratesin the topmost copper layer. This is intriguing as the energyinterval just above the “d hump” is known to host a surfacestate.40,41 Cu(111) surface states may then play a role in thestabilization 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 chosethe latter as a typical transition metal with a strong interactionbetween carbon and the metal atoms and repeated thesimulations 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); thepeak C is now in the immediate vicinity of the Fermi level andonly partially occupied. Finally, Figure 7 shows the relativeenergies of the carbon monomer and dimer in vacuum and onthe (111) surface of copper and cobalt. As evident from Figure7 that the dimer is stabilized more on copper than on cobalt. Atthe same time, it is less bound to copper than to cobalt surface.

■ DISCUSSIONS

On the basis of our results, we can now draw a qualitativepicture of the first stages of graphene growth on the Cu(111)surface. With regard to the CVD growth of graphene, a startingpoint where a large number of carbon monomers (created byCVD precursor decomposition) have adsorbed on the surface isconsidered.Immediately after carbon monomers have been adsorbed on

the surface, these populate the subsurface octahedral sites (as

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

Table 2. Spontaneous (Zero Activation Energy) Formationof Dimers from Nearby Adsorption Sitesa

site Eads (eV)

A + A′ −5.36A + FCC → DIMA + HCP −5.19FCC + HCP → DIMFCC + BRI → DIMBRI + BRI′ → DIM

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



described by the 4 × 6 supercell in Figure 4, this reaction isspontaneous). Next, there are several competing processes,namely, (1) dimer formation, (2) dimer migration, (3) back-dissociation of dimers into individual atoms, (4) migration ofcarbon along the surface, (5) migration of carbon atoms deeperinto the bulk. On the basis of Figure 4 and Table 2 it is clearthat processes (1) and (2) are dominant. In more detail, fromFigure 4, we observe that (1) the formation of carbon dimers isexothermic and (2) the migration barrier for the dimer to moveon the Cu(111) surface is small (Ea = 0.27 eV). Once the dimeris formed, it costs more energy to dissociate the dimer than tomigrate it around the surface. Carbon dimers are then persistentand mobile.Finally, based on the adsorption geometries and transition

state of the dimer in Figure 5, we show schematically in Figure8 how migrating dimers could form larger graphitic structureson the Cu(111) facet. Two carbon dimers migrate to nearbyadsorption sites at their optimal adsorption positions. This is arapid process, as the migration barrier for carbon dimers issmall, 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, amonomer-based picture has been considered. According tothis picture, graphitic material emerges from atomic-sized steps

by incorporation of adatoms to the growing graphenelayers.42−44 On the other hand, recent experimental45,46 andtheoretical24,25,47 studies suggest the importance of largercarbon adspecies as the minimal units being incorporated intothe growing graphene: on Ru(0001)45 and Ir(111)46 clusters of5 carbon atoms have been proposed to act as reactionintermediates. Simulations suggest the formation of carbonatom “chains” on Ni(111)47 and Cu(111).25 Graphene isknown to nucleate on Ru and Ir from atomic-sized steps, but onthe other hand, atomic steps of these metals do not effectivelytrap carbon monomers but they do stabilize carbon dimers.24

In the same spirit, we emphasize the importance of stable andmobile reaction intermediates, such as carbon dimers which areenergetically favorable and are formed spontaneously. In thedimer-based picture, the costly step of moving a monomer fromthe surface into the graphene boundary can be avoided. Inparticular, on Cu(111), persistent and mobile dimers areformed which are easily assembled into larger graphitic units.The tendency to form these kind of intermediates might be thekey factor in making copper an effective graphene catalyst.From a detailed analysis of the electronic structure, an interplayof the substrate electronic states with the dimer σp-bondingorbital was observed: there is an electronic factor that stabilizesthe internal C−C bonding of the carbon dimer, while at thesame time reducing its interaction with copper. This could bean important mechanism in driving the formation of stable andmobile graphitic fragments on copper, gold and silver.

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 forCo(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 thepositions of carbon atoms, while white dots stand for copper atoms. In the rightmost panel, the used false-color scale is depicted; red and blue colorindicate maximum and minimum values, respectively, for the electron density (c) and charge transfer (b).

Figure 7. Relative energies of a carbon monomer (dashed lines) and acarbon dimer in the singlet state (solid lines) in vacuum (black) andon copper (red) and cobalt (green). Energies are per carbon atom, asdescribed by eq 1.

Figure 8. Schematic illustration of formation of graphitic structures onthe Cu(111) surface: the large white spheres present the Cu(111) toplayer copper atoms, while the black spheres connected with lines arethe carbon dimers (at an optimal adsorption site). Left panel: carbondimers at nearby DIM sites (see Figure 5). Right panel: some of thedimers (3 and 4) have migrated to neighboring DIM sites, forming agraphitic network.



Our results, especially for the diffusion of C interstitials inbulk Cu, should also shed light on irradiation-mediatedgraphene growth. After the implantation of C atoms wellbeyond the solubility limit has been done and sampletemperature raised, the growth rate of graphene is determinedby the migration rate of C interstitials toward the surface, whichcan be estimated provided that the migration barrier is known,as well as the concentration profile of interstitials afterimplantation. We notice that information on the diffusionrate may be important if a Cu foil with implanted C (or B/N)atoms is used for the CVD growth as doped graphene could begrown in this case.

■ CONCLUSIONS

In summary, by performing DFT calculations, we provided aqualitative microscopic picture of the diffusion of C atoms inbulk Cu, on the (111) surface and in the subsurface area.Contrary to previous calculations where smaller simulation cellswere used, we minimized the finite-size effects by consideringlarger systems and analyzing lattice distortions, which made itpossible 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 rate-limiting step for surface-to-bulk diffusion has been emphasized.Carbon may migrate rapidly below the topmost copper layerdue to the flexibility of the topmost copper layer, while uponentering the copper bulk, it experiences a large barrier. Weexplained these phenomena with a carefull analysis of thecopper lattice relaxations.Compared to these processes, signficantly more rapid ones

are the dimer formation, dimer migration, and the formation oflarger graphitic structures. We suggested that the rapidformation of many mobile and persistent reaction intermediatesis the key factor in making copper an effective metal substratefor graphene growth. We further suggested, based on the d-band theory, that the tendency to form these intermediates liesin the details of copper electronic structure and its interplaywith the dimer σp bonding orbital. This observation may openthe way for a deeper understanding of graphene synthesis andthe fabrication of optimal catalysts.

■ METHODS

Bulk copper and the Cu(111) facets were simulated within therepeated supercell scheme. An isolated carbon interstitial incopper was modeled using the orthorhombic cubic supercell ofbulk copper with dimensions of 12.8 Å × 13.4 Å × 12.6 Å. Thislarge 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 supercellwas used earlier in the literature,31 while the elongated 4 × 6supercell was constructed to relax lattice strain properly. SurfaceMP grids were 5 × 5 and 6 × 2 for the 3 × 3 and 4 × 6supercells, respectively.All calculations were performed in the framework of the

DFT, as implemented in VASP.51,52 Projector augmentedwaves53 and the Perdew−Burke−Ernzerhof generalized gra-dient approximation (GGA)54 were used. The cutoff energy ofthe plane wave basis was 420 eV. The smearing scheme in theelectronic relaxation was the first order Methfessel−Paxtonmethod.55 Conjugent-gradient relaxation of the geometry wasperformed, and if needed, the relaxation was continued with a

Newton scheme. This way the force residual for a stablegeometry was ≤0.02 eV/Å. In all calculations a specialDavidson block iteration scheme was used and symmetries ofthe 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 copperslabs; copper is nonmagnetic and the magnetic moments ofmolecular species typically vanish upon adsorption. Some testcalculations including spin were performed for carbonmonomer and dimer on copper which confirmed themagnetization to be less than 0.05 Bohr magnetons (μB).

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe wish to thank the Center for Scientific Computing, for useof its computational resources. This work has been supportedby the Academy of Finland through the FidiPro and the CoE(2006-2011) programs.

■ REFERENCES(1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang,Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric field effect inatomically thin carbon films. Science 2004, 306, 666−669.(2) Geim, A. K.; Novoselov, K. S. The rise of graphene. Nat. Mater.2007, 6, 183−191.(3) Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.;Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys.2009, 81, 109−162.(4) Li, X.; Cai, W.; An, J.; Kim, S.; Nah, J.; Yang, D.; Piner, R.;Velamakanni, A.; Jung, I.; Tutuc, E. Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils. Science 2009,324, 1312−1314.(5) Bae, S.; Kim, H.; Lee, Y.; Xu, X.; Park, J.-S.; Zheng, Y.;Balakrishnan, J.; Lei, T.; Ri Kim, H.; Song, Y. I. Roll-to-roll productionof 30-in. graphene films for transparent electrodes. Nat. Nanotechnol.2010, 5, 574−578.(6) Choucair, M.; Thordarson, P.; Stride, J. A. Gram-scale productionof graphene based on solvothermal synthesis and sonication. Nat.Nanotechnol. 2009, 4, 30−33.(7) Hernandez, Y.; Nicolosi, V.; Lotya, M.; Blighe, F. M.; Sun, Z.; De,S.; McGovern, I. T.; Holland, B.; Byrne, M.; Gun’ko, Y. K. High-yieldproduction of graphene by liquid-phase exfoliation of graphite. Nat.Nanotechnol. 2008, 3, 563−568.(8) Berger, C.; Song, Z.; Li, X.; Wu, X.; Brown, N.; Naud, C.; Mayou,D.; Li, T.; Hass, J.; Marchenkov, A. N. Electronic confinement andcoherence in patterned epitaxial graphene. Science 2006, 312, 1191−1196.(9) Sun, Z.; Yan, Z.; Yao, J.; Beitler, E.; Zhu, Y.; Tour, J. M. Growthof graphene from solid carbon sources. Nature 2010, 468, 549−552.(10) Kim, K. S.; Zhao, Y.; Jang, H.; Lee, S. Y.; Kim, J. M.; Kim, K. S.;Ahn, J.-H.; Kim, P.; Choi, J.-Y.; Hong, B. H. Large-scale patterngrowth of graphene films for stretchable transparent electrodes. Nature2009, 457, 706−710.(11) Eizenberg, M.; Blakely, J. M. Carbon monolayer phasecondensation on Ni(111). Surf. Sci. 1979, 82, 228−236.(12) Land, T.; Michely, T.; Behm, R.; Hemminger, J.; Comsa, G.STM investigation of single layer graphite structures produced onPt(111) by hydrocarbon decomposition. Surf. Sci. 1992, 264, 261−270.



mailto:[email protected]

(13) Eom, D.; Prezzi, D.; Rim, K. T.; Zhou, H.; Lefenfeld, M.; Xiao,S.; Nuckolls, C.; Hybertsen, M. S.; Heinz, T. F.; Flynn, G. W. Structureand Electronic Properties of Graphene Nanoislands on Co(0001).Nano Lett. 2009, 9, 2844−2848.(14) Oznuluer, T.; Pince, E.; Polat, E. O.; Balci, O.; Salihoglu, O.;Kocabas, C. Synthesis of graphene on gold. Appl. Phys. Lett. 2011, 98,183101.(15) Rodríguez-Manzo, J. A.; Pham-Huu, C.; Banhart, F. Graphenegrowth by a metal-catalyzed solid-state transformation of amorphouscarbon. ACS Nano 2011, 5, 1529−1534.(16) Lahiri, J.; Miller, T. S.; Ross, A. J.; Adamska, L.; Oleynik, I. I.;Batzill, M. Graphene growth and stability at nickel surfaces. New J.Phys. 2011, 13, 025001.(17) Pletikosic, I.; Kralj, M.; Pervan, P.; Brako, R.; Coraux, J.;N’Diaye, A. T.; Busse, C.; Michely, T. Dirac cones and minigaps forgraphene on Ir(111). Phys. Rev. Lett. 2009, 102, 056808.(18) Banhart, F.; Kotakoski, J.; Krasheninnikov, A. V. StructuralDefects in Graphene. ACS Nano 2011, 5, 26−41.(19) Yu, Q.; Jauregui, L. A.; Wu, W.; Colby, R.; Tian, J.; Su, Z.; Cao,H.; Liu, Z.; Pandey, D.; Wei, D. Control and characterization ofindividual grains and grain boundaries in graphene grown by chemicalvapour deposition. Nat. Mater. 2011, 10, 443−449.(20) Wintterlin, J.; Bocquet, M.-L. Graphene on metal surfaces. Surf.Sci. 2009, 603, 1841−1852.(21) Dai, B.; Fu, L.; Zou, Z.; Wang, M.; Xu, H.; Wang, S.; Liu, Z.Rational design of a binary metal alloy for chemical vapour depositiongrowth of uniform single-layer graphene. Nat. Commun. 2011, 2, 522.(22) Saadi, S.; Abild-Pedersen, F.; Helveg, S.; Sehested, J.;Hinnemann, B.; Appel, C. C.; Nørskov, J. K. On the role of metalstep-edges in graphene growth. J. Phys. Chem. C 2010, 114, 11221−11227.(23) Gao, J.; Yip, J.; Zhao, J.; Yakobson, B. I.; Ding, F. GrapheneNucleation on Transition Metal Surface: Structure transformation androle of the metal step edge. J. Am. Chem. Soc. 2011, 133, 5009−5015.(24) Chen, H.; Zhu, W.; Zhang, Z. Contrasting behavior of carbonnucleation in the initial stages of graphene epitaxial growth on steppedmetal surfaces. Phys. Rev. Lett. 2010, 104, 186101.(25) Wesep, R. G. V.; Chen, H.; Zhu, W.; Zhang, Z. Communication:Stable carbon nanoarches in the initial stages of epitaxial growth ofgraphene on Cu(111). J. Chem. Phys. 2011, 134, 171105.(26) Karoui, S.; Amara, H.; Bichara, C.; Ducastelle, F. Nickel-AssistedHealing of Defective Graphene. ACS Nano 2010, 4, 6114−6120.(27) Mattevi, C.; Kim, H.; Chhowalla, M. A review of chemicalvapour deposition of graphene on copper. J. Mater. Chem. 2011, 21,3324−3334.(28) Rasool, H. I.; Song, E. B.; Allen, M. J.; Wassei, J. K.; Kaner, R.B.; Wang, K. L.; Weiller, B. H.; Gimzewski, J. K. Continuity ofgraphene on polycrystalline copper. Nano Lett. 2011, 11, 251−256.(29) Li, X.; Cai, W.; Colombo, L.; Ruoff, R. S. Evolution of graphenegrowth on Ni and Cu by carbon isotope labeling. Nano Lett. 2009, 9,4268-4272, PMID: 19711970.(30) McCarty, K. F.; Feibelman, P. J.; Loginova, E.; Bartelt, N. C.Kinetics and thermodynamics of carbon segregation and graphenegrowth on Ru(0001). Carbon 2009, 47, 1806−1813.(31) Yazyev, O. V.; Pasquarello, A. Effect of metal elements incatalytic growth of carbon nanotubes. Phys. Rev. Lett. 2008, 100,156102.(32) Baraton, L.; He, Z.; Lee, C. S.; Maurice, J.-L.; Cojocaru, C. S.;Gourgues-Lorenzon, A.-F.; Lee, Y. H.; Pribat, D. Synthesis of few-layered graphene by ion implantation of carbon in nickel thin films.Nanotechnology 2011, 22, 085601.(33) Garaj, S.; Hubbard, W.; Golovchenko, J. A. Graphene synthesisby ion implantation. Appl. Phys. Lett. 2010, 97, 183103.(34) Bolotin, K., unpublished.(35) Martínez-Galera, A. J.; Brihuega, I.; Gomez-Rodríguez, J. M.Ethylene irradiation: a new route to grow graphene on low reactivitymetals. Nano Lett. 2011, 11, 3576−3580.

(36) Ellis, D. E.; Mundim, K. C.; Fuks, D.; Dorfman, S.; Berner, A.Interstitial carbon in copper: Electronic and mechanical properties.Phil. Mag. B 2010, 79, 1615−1630.(37) Jiang, D. E.; Carter, E. A. Carbon dissolution and diffusion inferrite and austenite from first principles. Phys. Rev. B 2003, 67,214103.(38) Riikonen, S.; Halonen, L. α-iron facet with enhanced carbonmobility. Phys. Rev. B 2011, 83, 235423.(39) Hammer, B. Special sites at noble and late transition metalcatalysts. Top. Catal. 2006, 37, 3−16.(40) Kevan, S. D.; Gaylord, R. H. High-resolution photoemissionstudy of the electronic structure of the noble-metal (111) surfaces.Phys. Rev. B 1987, 36, 5809−5818.(41) Euceda, A.; Bylander, D. M.; Kleinman, L. Self-consistentelectronic structure of 6- and 18-layer Cu(111) films. Phys. Rev. B1983, 28, 528−534.(42) Bengaard, H. S.; Nørskov, J. K.; Sehested, J.; Clausen, B. S.;Nielsen, L. P.; Molenbroek, A. M.; Rostrup-Nielsen, J. R. Steamreforming and graphite formation on Ni catalysts. J. Catal. 2002, 209,365−384.(43) Helveg, S.; Lopez-Cartes, C.; Sehested, J.; Hansen, P. L.;Clausen, B. S.; Rostrup-Nielsen, J. R.; Abild-Pedersen, F.; Nørskov, J.K. Atomic-scale imaging of carbon nanofibre growth. Nature 2004,427, 426−429.(44) Abild-Pedersen, F.; Nørskov, J. K.; Rostrup-Nielsen, J. R.;Sehested, J.; Helveg, S. Mechanisms for catalytic carbon nanofibergrowth studied by ab initio density functional theory calculations. Phys.Rev. B 2006, 73, 115419.(45) Loginova, E.; Bartelt, N. C.; Feibelman, P. J.; McCarty, K. F.Evidence for graphene growth by C cluster attachment. New J. Phys.2008, 10, 093026.(46) Loginova, E.; Bartelt, N. C.; Feibelman, P. J.; McCarty, K. F.Factors influencing graphene growth on metal surfaces. New J. Phys.2009, 11, 063046.(47) Amara, H.; Bichara, C.; Ducastelle, F. Understanding thenucleation mechanisms of carbon nanotubes in catalytic chemicalvapor deposition. Phys. Rev. Lett. 2008, 100, 056105.(48) Begtrup, G. E.; Gannett, W.; Meyer, J. C.; Yuzvinsky, T. D.;Ertekin, E.; Grossman, J. C.; Zettl, A. Facets of nanotube synthesis:High-resolution transmission electron microscopy study and densityfunctional theory calculations. Phys. Rev. B 2009, 79, 205409.(49) Riikonen, S.; Krasheninnikov, A. V.; Nieminen, R. M.Submonolayers of carbon on α − Fe facets: An ab initio study. Phys.Rev. B 2010, 82, 125459.(50) Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zoneintegrations. Phys. Rev. B 1976, 13, 5188−5192.(51) Kresse, G.; Hafner, J. Ab initio molecular dynamics for liquidmetals. Phys. Rev. B 1993, 47, 558−561.(52) Kresse, G.; Furthmuller, J. Efficient iterative schemes for abinitio total-energy calculations using a plane-wave basis set. Phys. Rev. B1996, 54, 11169−11186.(53) Blochl, P. E. Projector augmented-wave method. Phys. Rev. B1994, 50, 17953−17979.(54) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradientapproximation made simple. Phys. Rev. Lett. 1996, 77, 3865−3868.(55) Methfessel, M.; Paxton, A. T. High-precision sampling forBrillouin-zone integration in metals. Phys. Rev. B 1989, 40, 3616−3621.(56) Henkelman, G.; Uberuaga, B. P.; Jonsson, H. A climbing imagenudged elastic band method for finding saddle points and minimumenergy paths. J. Chem. Phys. 2000, 113, 9901−9904.



the role of stable and mobile carbon adspecies in …ark/publ/jp211818s-1.pdfthe role of stable and...

Documents