Contrasting Behavior of Carbon Nucleation in the Initial Stages of Graphene Epitaxial Growth on Stepped Metal Surfaces
aa r X i v : . [ c ond - m a t . m e s - h a ll ] D ec Contrasting Behavior of Carbon Nucleation in the Initial Stages of Graphene Epitaxial Growth onStepped Metal Surfaces
Hua Chen,
1, 2
Wenguang Zhu,
1, 2 and Zhenyu Zhang
2, 1 Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996 Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (Dated: June 1, 2018)Using first-principles calculations within density functional theory, we study the energetics and kinetics ofcarbon nucleation in the early stages of epitaxial graphene growth on three representative stepped metal surfaces:Ir(111), Ru(0001), and Cu(111). We find that on the flat surfaces of Ir(111) and Ru(0001), two carbon atomsrepel each other, while they prefer to form a dimer on Cu(111). Moreover, the step edges on Ir and Ru surfacescannot serve as effective trapping centers for single carbon adatoms, but can readily facilitate the formation ofcarbon dimers. These contrasting behaviors are attributed to the delicate competition between C-C bonding andC-metal bonding, and a simple generic principle is proposed to predict the nucleation sites of C adatoms onmany other metal substrates with the C-metal bond strengths as the minimal inputs.
PACS numbers: 68.35.Fx, 68.43.Bc, 68.43.Hn
Since its first isolation, graphene has attracted rapidly grow-ing research interest because of its various intriguing prop-erties and potential applications in future electronics [1, 2].However, a route towards scalable mass production of qual-ity graphene for industrial use is still lacking. Among manynewly developed techniques, epitaxial growth of grapheneon metal surfaces offers a promising avenue [3, 4, 5, 6,7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. Large size andgood quality graphene samples have been prepared on vari-ous metal surfaces [3, 4, 5, 6, 7, 8, 9]. The success in trans-ferring the epitaxial graphene grown on Ni and Cu surfacesto insulating substrates makes this method even more attrac-tive [7, 9]. Additionally, various aspects about the growthmechanisms of graphene have been revealed in recent stud-ies of representative carbon/metal systems. For example, thegrowth of graphene on Ir(111) and Ru(0001) substrates is fedby the supersaturated two-dimensional (2D) gas of carbonadatoms, and a multi-carbon cluster attachment mechanismhas been proposed [10, 11, 12], with minimal effect of hydro-gen [11, 13]. On a Cu substrate, graphene is found to growthrough a surface adsorption process, while on Ni it is by car-bon segregation or precipitation [14].Despite these preliminary achievements, very little has beenrevealed about the growth kinetics, especially in the initial nu-cleation stages of carbon adatoms. Experimentally it has beenfound that carbon nucleation starts from the lower edges ofsteps on Ir(111) [15] and Ru(0001) [10] surfaces, but it is un-clear why and to what extent nucleation at the step edges ispreferred over terraces. Determination of nucleation sites iscrucial in improving both the quality and quantity of epitax-ial graphene. In the growth of graphene on Ru(0001), mul-tiple nucleation on terraces can easily degrade the quality ofgraphene because defects will form at the interfaces of sep-arately nucleated graphene islands [11]. In graphene growthon Ir(111), the nucleation sites must not be too sparse, becauseotherwise rotated graphene domains are more likely to growat the boundaries of the major phase of the islands that arealigned with the substrate [16, 17]. Quantity-wise, in order to eventually achieve mass production for industrial applica-tions, it is more desirable for nucleation of graphene islandsto take place over the entire substrate rather than only at theedges of preexisting steps. In light of these aspects, a gen-eral guiding principle of determining the nucleation sites ondifferent substrates will be highly beneficial.In this Letter, we present a comparative study of the ener-getics and kinetics in the initial stages of epitaxial graphenegrowth on three representative stepped metal surfaces, usingfirst-principles calculations within density functional theory(DFT). We find that, whereas the interaction between twoadatoms is attractive on flat Cu(111), leading to easy ad-dimerformation, it becomes repulsive on flat Ir(111) and Ru(0001),making ad-dimer formation improbable. On the other hand,even though the steps on Ir(111) and Ru(0001) cannot serveas effective trapping centers for single carbon adatoms, suchsteps can readily facilitate the formation of carbon dimers attheir lower edges. We rationalize these contrasting kineticbehaviors of carbon adatom diffusion and nucleation basedon the delicate competition between the C-C bonding and C-metal bonding, and generalize this picture to predict the initialgrowth stages of graphene on different metal substrates.In our studies, we use the Vienna ab initio simulation pack-age (VASP) [18] with PAW potentials [19] and the general-ized gradient approximation (PBE-GGA) [20] for exchange-correlation potential. All the metal surfaces are modeled bya 6-layer slab, with atoms in the lower 3 layers fixed in theirrespective bulk positions. A (2 × squared surface unit cellis used to describe the Ir(111) , Ru(0001) and Cu(111) sur-faces. We use (322) and (332) surfaces to model the steppedIr(111) and Cu(111) surfaces, which contains { } (A-type)and { } (B-type) microfacets, respectively. The steppedRu(0001) surface is modeled by a vicinal surface with its nor-mal along the h i direction, which contains alternatingA- and B-type steps. All the terrace widths are ∼ × × for steppedRu(0001), and × × for all the other cases [21]. We use theclimbing image nudged elastic band (CINEB) method [22] to U L U U R L U (c) Ru A-step (d) Ru B-stepU U R L E C ( e V ) U
1b 0.71
R L L (a) Ir A-step U U R L L (b) Ir B-step E C ( e V ) E C ( e V ) E C ( e V ) L U R L L L L U U RL L L L L L L L L L L FIG. 1: (Color online)
Top views of adsorption sites and bindingenergies of a C adatom around (a) Ir A-step, (b) Ir B-step , (c) RuA-step, and (d) Ru B-step. The solid curves represent C diffusionprofiles. The vertical dashed line represents the position of step edge,and the horizontal dot-dashed line indicates the C binding energy onflat surfaces. Definition of labels: U - upper terrace, L - lower terrace,R - ridge site where C only binds to atoms in the ridge of a step edge;b - hcp site, c - fcc site. determine the energy barriers of the various kinetic processes.We first consider the adsorption and diffusion of isolatedcarbon atoms on flat metal surfaces. The most stable adsorp-tion sites and the corresponding binding energies, defined by △ E C = E C / subst − E C − E subst , on Ir(111), Ru(0001) andCu(111) are hcp (-7.44 eV), hcp (-7.66 eV) (in agreementwith previous calculations [10, 11]), and subsurface intersti-tial (-5.66 eV), respectively. The stronger binding on the othertwo substrates and the weaker binding on Cu(111) are consis-tent with the d -band model [23]: on Cu(111), the C adatommainly interacts with the free-electron like surface states ofCu, whose d -shell is completely filled; whereas on Ir(111) orRu(0001), the stronger binding originates from the hybridiza-tion between the sp orbitals of carbon and the half-filled d -band of the substrate. On Ir(111) and Ru(0001), the energyin the metastable fcc sites are 0.25 eV and 0.74 eV higher,respectively. On Cu(111), the metastable sites on the surface(fcc, hcp, bridge) are less stable than the subsurface interstitialsites by ∼ ε a ) betweena stable and the nearest metastable states are 0.75 eV, 0.87 eVand 0.66 eV on Ir(111), Ru(0001), and Cu(111), respectively.We next investigate the adsorption and diffusion of singleC adatoms at step edges of Ir(111) and Ru(0001). The resultsfor the case of Cu(111) will be reported in a separate work[24], as will be explained later. As shown in Fig. 1, the calcu-lated binding energies at step edges are not much larger thanthose on flat surfaces. The same is true for the kinetic barri-ers. Considering the high growth temperatures in experiments B i nd i n g E n e r g y ( e V ) C-C Distance (Å)
C C dimer
FIG. 2: (Color online)
Binding energies of two C adatoms on flatmetal surfaces as a function of their separation distance. Data pointsaround the vertical dashed line correspond to the formation of Cdimers. Inset shows the top view of a C dimer on a close-packedmetal surface. Kinetic barriers are not shown. ( ∼ △ E = E / subst − E C − E subst , as a func-tion of the separation distance. One can immediately noticethat on Ir(111) and Ru(0001) the formation of C dimers isenergetically unfavorable, but on Cu(111), dimers are muchmore stable than separate C adatoms by over 2 eV. More-over, the energy barrier of forming a dimer for two neigh-boring C adatoms is only 0.32 eV on Cu(111), which is muchsmaller than those on Ir(111) (1.37 eV) and Ru(0001) (1.49eV). These findings suggest that on Ir(111) and Ru(0001),C adatoms are mutually repulsive and cannot form dimers,whereas on Cu(111) they strongly attract each other, leadingto the formation of dimers and larger islands. B i nd i n g E n e r g y ( e V ) C-C Distance (Å) (a) (b)(c) Ir A-step (d) Ir B-step(e) Ru A-step (f) Ru B-step(g) Cu A-step (h) Cu B-step
FIG. 3: (Color online) (a) and (b) Top- and side-view of the moststable configuration of a C dimer at the lower edge of a (a) A-step and(b) B-step. (c-h) Binding energies of two carbon adatoms with oneC atom fixed at the lower step edge and another moving on the upperterrace, the lower terrace and along the lower step edge, respectively.Horizontal axis is their separation distance. Vertical dashed line ineach panel shows where a C dimer is formed, and horizontal dot-dashed line shows the binding energy of two separate C adatoms onflat surfaces.TABLE I: Binding energy difference between a C dimer at lower stepedges ( E dimer / step ) and (1) two separate C adatoms on flat surfaces( E / flat ) and (2) a C dimer on flat surfaces ( E dimer / flat ). (The unitis in eV).Energy difference Ir Ru CuStep A B A B A B E dimer / step − E dimer / flat -1.31 -1.19 -1.09 -0.68 -0.64 -0.28 E dimer / step − E / flat -0.44 -0.33 -0.46 -0.15 -2.54 -2.18 Now that the nucleation sites on Cu(111) have been iden-tified, we next show that on Ir(111) and Ru(0001) nucleationcan be readily facilitated by the step edges. Table I comparesthe binding energies of a C dimer at lower step edges with thecases of a dimer on flat surfaces and two separate C adatomson flat surfaces, showing that dimers at step edges are not onlymuch more stable than on flat surfaces, but also more stablethan two separate C adatoms. Therefore, even though on flatIr and Ru surfaces C dimerization is not preferred, C adatomsattract each other at lower edges of the surface steps. To betterillustrate this, we plot the binding energies of two C adatoms on stepped metal surfaces with their separation in Fig. 3. Inall cases, there is a deep potential well upon the formation ofa C dimer at lower step edges.Summarizing the above results, we have shown that onIr(111) and Ru(0001), nucleation of C adatoms first occursat substrate step edges, in agreement with existing experi-ments [10, 15]; whereas on Cu(111), our results predict thatC adatoms should nucleate everywhere on the surface. Wenote that even though there is also a deeper potential well forthe C dimer formation at the Cu(111) steps, such steps are notso crucial in the nucleation of C adatoms on Cu, because Cadatoms are already strongly attractive to each other on theterraces and readily form dimers before they can reach a stepedge. For the same reason we ignored the discussion aboutCu(111) steps in the study of single C adatoms above.For C adatoms on Ir(111) and Ru(0001), this exceptionaltendency towards dimerization at substrate step edges is re-lated to the special local bonding geometry of a C dimer atthose sites. In Figs. 3 (a) and (b) the bonding geometries ofa C dimer at A-type and B-type step edges are shown, re-spectively. By comparing those with a C dimer on flat sur-faces shown in the inset of Fig. 2, one can observe that thebonds in the latter case are severely twisted. Since the cova-lent bonds are highly directional and it is energetically costlyto change the relative bond angles, the relaxation of the cova-lent bonds by the step geometry leads to the extra stability ofthe C dimers.The contrasting behavior of the interacting C adatoms onflat close-packed Ir(111), Ru(0001), and Cu(111) surfaces canbe attributed to the competition between the C-C and C-metalinteractions. The C-C bond lengths of carbon dimers on flatIr(111), Ru(0001) and Cu(111) surfaces are 1.397 ˚A, 1.376˚A, and 1.299 ˚A, respectively, which are very close to thelength of a C-C double bond (1.34 ˚A). A double bond re-quires two bonding electrons from each C adatom, but onecarbon adatom has only four valence electrons and three near-est metal neighbors on the surface. So intuitively, the forma-tion of a C dimer will weaken the C-metal bonding becauseof less bonding electrons. Therefore, if the C-metal bonds arevery strong, which is the case of Ir and Ru, the dimer forma-tion is not energetically favorable. Conversely, in the case ofCu where C-metal bonding is weak, formation of a dimer ispreferred for two C adatoms.Next we show that the above picture is not limited to thethree representative cases, but can be generalized into a simpleguiding principle. To this end, we compare the binding ener-gies of C adatoms and C dimers on the close-packed surfacesof various transition metals, as shown in Fig. 4. It is apparentthat the weaker the C-metal interaction is, the more preferredthe C dimers are. In all the cases of noble metals, which haveclosed d -shells and strong free-electron like surface states, Cdimerization is preferred. The relative strength of C-metaland C-C interactions largely determines whether the net in-teraction between C adatoms is attractive or repulsive. Thedimer-preferred and dimer-not-preferred systems are essen-tially separated by the vertical dashed line corresponding to E C (eV) E d i m e r - E C ( e V ) dimer not preferreddimer preferred FIG. 4: (Color online) . Binding energy difference between a Cdimer ( △ E dimer ) and two separate C adatoms ( △ E C ) with respectto △ E C on close-packed transition metal surfaces. Vertical dashedline corresponds to the binding energy of a C-C double bond (-6.33eV) [29]. the energy of a C-C double bond (-6.33 eV) [29]. The de-viation from this trend may be, for example, because of thevariation in bonding nature or geometrical effects. Based onthe results presented earlier and the prototypical nature of thesystems we have studied therein, we can further conclude thatfor those systems in which C dimers are not preferred on ter-races, C nucleation should first occur at substrate step edges.Thus, our study makes it possible to predict where the initialnucleation should happen armed solely with the knowledge ofthe binding energy of C adatoms to the metal substrate.This generic principle can lead to many strong predictions.For example, in the strong C-metal binding regime, a flat sub-strate with scarce steps may not result in growth of qualitygraphene because of the simultaneous nucleation at multiplesites on the terraces [10], a somewhat counterintuitive conclu-sion. In the weak C-metal binding regime, epitaxy on single-crystal flat Cu(111) is more likely to yield graphene with thedesired high quality and potential mass production, because Cadatoms prefer to nucleate everywhere, and the mismatch ofgraphene with Cu substrate is very small.We finally emphasize on another salient prediction of thepresent study. The most stable configuration of a C dimerat A- or B-type step edges are shown in Figs.3 (a) and (b),with the dimers bridging the step ridge and the lower terraceperpendicular to the step. Experimentally it is already possi-ble to prepare near-perfect vicinal surfaces containing regu-lar straight step arrays by precise control of the miscut [30].Therefore on Ir(111), Ru(0001), and other metal surfaces withstrong C-metal bonding, growth of straight graphene nanorib-bons with zigzag edges are likely to be obtained from theregularly spaced C dimer arrays formed along the A- or B-type steps in the nucleation stage. This suggestion may of-fer a potentially more attractive route for mass production ofhighly ordered graphene nanoribbons with zigzag edges than the known approaches [31, 32].In summary, we have performed a comparative study of theenergetics and kinetics of carbon adatoms on stepped Ir(111),Ru(0001) and Cu(111) surfaces, with intriguing predictions.We have found that the substrate step edges cannot effectivelycapture single C adatoms, and two carbon adatoms dislikeforming dimers on flat Ir(111) and Ru(0001) surfaces either,though they strongly attract each other on Cu(111). How-ever, the lower edges of steps on Ir(111) and Ru(0001) canreadily mediate the formation of C dimers. These findingshave been rationalized by considering the competition be-tween the carbon-carbon and carbon-metal bonds. 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