How the Orientation of Graphene Is Determined during Chemical

Letter pubs.acs.org/JPCL

How the Orientation of Graphene Is Determined during Chemical Vapor Deposition Growth Xiuyun Zhang,† Ziwei Xu,† Li Hui,*,‡ John Xin,*,† and Feng Ding*,† †

Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hong Kong, China Key Laboratory of Liquid Structure and Heredity of Materials, Ministry of Education, Shandong University, Jinan 250061, People’s Republic of China

‡

S Supporting Information *

ABSTRACT: We present a theoretical study on the determination of graphene orientation on the catalyst surface in chemical vapor deposition growth. Our study reveals that the interaction between the graphene wall and catalyst surface is weak and not sensitive to the orientation of graphene. The graphene edge−catalyst interaction is strong and sensitively depends on the graphene orientation. Therefore, the graphene edge− catalyst interaction is responsible for the orientation determination of a small graphene island in the early stage of graphene growth, and such an orientation can be inherited by the matured graphene due to the high barrier of graphene island rotation. On the basis of the mechanism of graphene orientation determination, various controversial-like experimental puzzles have been well-explained, and a potential of synthesizing large-area single-crystalline graphene on either single-crystalline or polycrystalline catalyst surfaces is revealed. SECTION: Surfaces, Interfaces, Porous Materials, and Catalysis

G

of a GB would mostly be different. Therefore, we would expect a graphene GB, which is characterized as a linear pentagonheptagon (5|7) chain,16−18 to appear at every GB of the catalyst surface. In other words, the grown graphene would copy the grain map of the polycrystalline catalyst surface, and the mean size of the graphene domains would not be greater than that of the catalyst surface. The above analysis indicates that for epitaxial growth the control of the grain size of the catalyst surface is crucial for high-quality graphene CVD synthesis. It also indicates that synthesized graphene with larger average domain size than that of the catalyst surface can be expected only for nonepitaxial growth and for that reason strict epitaxial growth is a disadvantage for high-quality graphene synthesis. Therefore, exploring the determination of graphene orientation of graphene CVD growth is crucial and pressing for experimental design. As a first step, we would like to review some experimental observations about graphene CVD growth: (i) In experiments, continuous single-crystalline graphene domains crossing the grain borders of the polycrystalline catalyst surfaces were frequently observed, usually with a change of the Moiré pattern. For example, singlecrystalline graphene domains have been observed crossing adjacent facets on Ni6 or Cu7 surfaces.

raphene has recently attracted overwhelming research interest due to its exotic physical, chemical, and electronic properties and its numerous potential applications.1,2 Because the synthesis of high-quality graphene is a prerequisite to realize most of these applications, a great number of efforts have been dedicated to exploring the optimum method of graphene synthesis.1−5 The chemical vapor deposition (CVD) method has been considered to be most promising for high-quality, large-area, single- or few-layer graphene synthesis because of the involving of metal catalyst and the large number of tunable factors (temperature, type, and partial pressure of feedstock and/or carrier gases, type of catalyst, etc.).6−25 In most previous studies, graphene CVD growth has been reported as an epitaxial process. The primary evidence of epitaxial growth is the observation of the regular Moiré pattern of the grown graphene on the catalyst surface.6−9 However, it should be noted that the Moiré pattern can be formed by overlaying two regular lattices at any angle,26,27 whereas epitaxy refers to the deposition of a crystalline overlayer on a crystalline substrate, where the overlayer is in registry with the substrate. In epitaxial growth, the overlayer normally has one or a few preferred orientations that correspond to minima of the overlayer− substrate interaction energy surface.28 So, in principle, the observation of a regular Moiré pattern cannot be interpreted as evidence of graphene epitaxial growth. In most experiments of graphene CVD growth, the used catalysts are polycrystalline with numerous grain boundaries (GBs). If graphene growth is epitaxial, or in registry with the substrate, then the orientations of the graphene on either side © 2012 American Chemical Society

Received: July 24, 2012 Accepted: September 14, 2012 Published: September 14, 2012 2822

dx.doi.org/10.1021/jz301029g | J. Phys. Chem. Lett. 2012, 3, 2822−2827

The Journal of Physical Chemistry Letters

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where (a1, a2) are two base vectors of the pristine graphene and (n, m) are the rotation indexes. As an example, the (2, 1) superstructure is shown in Figure 1. Because the symmetry of

(ii) High-quality graphene with an average single-crystalline domain size greater than that of the catalyst surface has been synthesized. For example, Li et al. have synthesized graphene with a domain size up to a millimeter on a polycrystalline Cu foil.10 (iii) During the initial nucleation stage, small graphene islands are observed well-aligned along a few specific directions on the catalyst surface.11,12 (iv) Evidence of the orientation correlation between graphene and catalyst surface is frequently shown. For example, the abundance of low (∼7°) and high (∼30°) mismatching angles has been observed for graphene growth on Cu(111) and Cu(100) surfaces,13,14 and the graphene grown on Ir(111) surface tends to have a misorientation angle of ±2.6°.9 (v) The statistics of the domain mismatching angles on both sides of a GB in graphene grown on a Cu surface show a multipeak shape, indicating an orientation correlation between adjacent graphene islands.15−18 Among these observations, (i) and (ii) undoubtedly indicate that the graphene CVD growth is not a strict epitaxial process in most cases. This can be easily understood by the weak van der Waals (VDW) interaction between the graphene wall and the catalyst surfaces (30−100 meV/atom for most metal surfaces). (iii)−(v) point to the opposite conclusion, that the orientation of the synthesized graphene is highly correlated with the crystalline orientation of the catalyst surface, which may be considered to be a consequence of epitaxial growth. In this study, using the Cu(111) surface as an example, we explored the orientation-dependent graphene wall−catalyst (GW−C) and graphene edge−catalyst (GE−C) interactions with the density functional theory (DFT) calculations. The results showed that the weak GW−C interaction is less important than the strong GE−C interaction in the orientation determination of the small graphene islands. In the subsequent graphene growth, due to the high activation barriers of graphene island rotation, the grown graphene intends to inherit the orientation of its infant stage. Given this, all abovementioned controversial-like experimental observations (i−v) are satisfactorily explained, and strategies of growing graphene with large single-crystalline domains on both single crystalline and polycrystalline catalyst surfaces are proposed. Two types of graphene−catalyst interactions, GW−Cu interaction and GE−Cu interaction, as functions of graphene orientation, are explored. The Cu(111) surface has very similar lattice constants to the graphene (0. 256 nm for Cu vs 0.246 nm for graphene). We neglected their difference and use the graphene lattice for the whole system in the modeling to avoid the extra strain on graphene. To explore the orientation dependence of graphene wall−catalyst interactions, we rotated the graphene on Cu(111) substrate. Although most rotation angles, θ, lead to a very large unit cell sizes of the superstructure, some specific rotation angles determined by a pair of indexes (n, m) correspond reasonable small unit cell sizes. Mathematically, the rotation angle (θ) and the unit cell vectors (V1, V2) can be written as26,27 2

Figure 1. Scheme of the unit cell of graphene@Cu(111) superstructure with (n, m) = (2,1). The black and orange balls represent the C and Cu atoms, respectively.

the graphene is C6v, these relative rotation angles can be restricted in the range of 0−60°.27 Moreover, because of the graphene’s symmetry of reflection, a structure with rotation angle, θ, ranging from 30 to 60° is equivalent to the smaller one, 60° − θ, within 0−30°. Considering the limitation of computational resources, only superstructures with relative small unit cell sizes are selected. They are (n, m) = (2,1), (3,1), (3,2), (5,1), (4,3), (6,1), (5,3), (5,4), (7,2) and (8,1), (8,3), corresponding to the rotation angles of θ = 21.8, 27.8, 13.2, 17.9, 9.4, 15.2, 16.4, 7.3, 24.4, 11.7, and 29.4°, respectively.

Figure 2. Optimized distance of graphene from the top layer of the Cu(111) surface (a) and the binding energy of the graphene on the Cu(111) surface (b) as a function of rotation angle.

Figure 2 shows the optimized graphene wall−Cu distance and the GW−Cu adhesion energy, EGW−Cu, as functions of rotation angle θ. The GW−Cu interaction is defined as EGW − Cu = [EG + ECu − EG@Cu]/N

2

n + 4nm + m cos(θ) = 2(n2 + nm + m2)

where EG, ECu, and EG@Cu represent the energies of freestanding graphene, the Cu(111) substrate, and the graphene@ Cu(111) surface, respectively, and N is the number of C atoms per unit cell. As shown in Figure 2b, EGW−Cu is in the range of 30−35 meV/C atom, and the configuration of no rotation (θ = 0°) corresponds to the strongest binding of 35 meV/C atom

(1)

V1 = na1 + ma 2,

(2a)

V2 = −na1 + (m + n)a 2

(2b)

(3)

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similar behavior, but the rotation barriers of the two TSs are much greater (1.96 and 5.18 eV, respectively). The low-energy transition state (TS-1) corresponds to a configuration of perfect alignment between the graphene and the substrate (θ = 0°), whereas the high-energy transition state (TS-2) corresponds a configuration with maximum mismatching angle (θ = 30°). Certainly such a strong binding and the high barriers between the minima are sufficient to overcome the thermal activation energy (kT ≈0.1 eV) and constrain small graphene islands along a specific direction. The above analysis suggests that the graphene edge−catalyst interaction, EGE−C, is the dominating factor for graphene orientation determination in CVD growth. However, we must note that the EGE−C is proportional to the number of graphene edge atoms

and the smallest GW−Cu distance (3.19 Å). In contrast, the weakest binding, around 30 meV/C atom, appears at θ = 17.9°. The amplitude of the fluctuation, ΔEGW−Cu, is only 5 meV/C atom. At a typical graphene CVD growth temperature, (T ≈ 1000 °C), the thermal activation energy kT ≈ 0.1 eV (where k is the Boltzmann constant) is significantly greater than ΔEGW−Cu. Therefore, for a small graphene island, the weak GW−Cu interaction should not be sufficient to constrain its growth along a specific orientation. However, this contradicts the experimental observation (iii) that small graphene islands are actually perfectly aligned on a catalyst surface. So there must be other causes that lead to the alignment of small graphene islands on catalyst surfaces. Figure 3 shows the energy profiles of two small graphene islands, C24 and C54, rotating on a Cu(111) surface. Mimicking

EGE − C ≈ γ × NE = γ × √(6N)

(5)

where γ is the formation energy of the graphene edge on a metal surface in the units of eV/edge atom, and NE = √6N is the number of edge atoms of a graphene island, which is estimated by counting the edge carbon atoms of hexagonal graphene patches.29 The weak graphene wall−catalyst interaction, EGW−C, is proportional to the number of total C atoms in the graphene island EGW − C ≈ σ × N

where σ is the adhesion energy between the graphene wall and the metal surface, measured in the units of eV/atom. Clearly, during the growth of a graphene island, EGW−C would eventually exceed EGE−C, and thus the energetically preferred orientation of a large graphene island should be determined by the EGW−C. The critical size (Nc ), above which E GW−C dominates the energetically preferred orientations of the island, can be estimated by solving the equation EGE−C = EGW−C. From eqs 5 and 6 we have the expression of NC as

Figure 3. Energy profiles of C24 (the up panel) and C54 (the lower panel) clusters rotating on the Cu(111) surface, where θ is defined as the angle between graphene zigzag direction and the (2,1,1) direction of the Cu(1,1,1) surface. Both of the rotations of the C24 or C54 on the Cu(111) surface have a C6v symmetry, and thus the energy profiles have a periodicity of 360°/6 = 60°. For each, two symmetric local minima at θ ≈ ±10 + 60° × i (i = 0, 1, 2, 3, 4, 5) are identified (marked as I and II), and two TSs located at θ = 60° × i (TS-1) and 30 + 60° × i (TS-2) are identified.

NC = 6(γ /σ )2

(7)

In the case of graphene on a Cu(111) surface, σ = 0.035 eV/ atom, γ ≈ 1.43 eV/edge atom and thus Nc(G@Cu(111)) ≈ 10 000. As summarized in Table 1, for most catalysts used for graphene CVD growth, the ranges of γ and σ are 1.33 to 2.4 eV/edge atom (calculated by using C24 as an example of a graphene island) and 0.03 to 0.2 eV/atom, respectively. The calculated Nc ranges from 800 to 11 000 atoms, and the critical size of a graphene island ranges from 5 to 20 nm.

the graphene CVD growth condition, the edge C atoms are not saturated with H or other functional groups.24,25 Thus there is a strong interaction between these active edge C atoms and the metal surface. The graphene edge−catalyst (GE−Cu) interaction is defined as EGE − Cu = [ECN + ECu − ECN@Cu]/NE

(6)

Table 1. Graphene Wall−Metal Interaction (σ, Calculated in This Study and from the Literature), Graphene Edge−Metal Interaction (γ, Calculated in This Study), and the Critical Size of Graphene Islands on Various Metal Surfaces

(4)

where ECN, ECu, and ECN@Cu represent the energies of the CN island, the Cu substrate, and CN@Cu(111), respectively. NE is the number of C atoms that appear on the edge of the CN cluster. In sharp contrast with the weak GW−Cu interaction (EGW−Cu), the optimized GE−Cu interactions of C24 and C54 on the Cu(111) surface are 1.43 and 1.91 eV per edge atom, respectively, which is about two orders of magnitude greater than EGW−Cu. In the energy profile of C24, there are two symmetric local minimums (at θ ≈ ±10°) and two transition states (TSs:TS-1, TS-2) between them (0.21 eV at θ = 0° and 0.96 eV at θ = 30°). The energy profile of C54 shows very

metal surface

range of Nc (the size range of critical island)

Cu(111)

0.035, 0.062,20 0.03021

1.43

Pt(111)

0.033,190.068,200.04621

1.33

Ni(111)

0.164, 0.123,19 0.141,20 0.067,22 0.13321 0.139,21 0.255 0.175,19 0.16023

1.97

3000−11 000 (10−19 nm) 2300−10 000 (8.7−18 nm) 800−6000 (5.2−14 nm)

2.34 2.32

1700−2300 (7.5−8.8 nm) 1054−1270 (5.9−6.5 nm)

Ru(0001) Co(111) 2824

σ (eV/atom)

γ (eV/ edge atom)



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Figure 4. (a) Potential energy surface of a C1014 cluster adsorbed on Cu(111) surfaces at different rotation angles (θ) with respect to lowest energy structure. The rotation angle (θ) stands for the angle of relative rotation of the graphene island on the Cu(111) substrate. (b) C1024@Cu(111) configuration.

Figure 5. (a−c) Illustration of single-crystalline graphene growth on a polycrystalline catalyst surface via the edge epitaxial mechanism. (d) Multicrystalline graphene will be formed on a polycrystalline catalyst surface if the growth is a strict epitaxial process.

When a graphene island grows large enough (i.e., when N > NC), EGW−C dominates the graphene−C catalyst interaction potential energy surface such that EG−C = EGE−C + EGW−C. In this case, there is the potential for a large graphene island to align along a specific direction that corresponds to the minimum of EGW−C, such as θ = 0° for the G@Cu(111) (Figure 2). For such a transition to occur, the barrier of the graphene island rotation must be overcome. As seen in Figure 3a, the two barriers of a C24 island rotation on a Cu(111) surface are 0.21 and 0.96 eV when rotating it within a periodicity of 0 ≤ θ ≤ 60°, respectively. At the temperature of graphene CVD growth (kT ≈ 0.1 eV), such barriers can be overcome by the thermal activation energy in a short period of time. However, the barrier of graphene island rotation increases as the island grows larger. For C54, the barriers become 1.96 and 5.18 eV, respectively. Such high barriers are expected because there are 18 dangling C atoms strongly bonded to the metal surface, giving a total binding energy of ∼27 eV. Although the small barrier (∼1.96 eV) may still be overcome, overcoming the larger one is impossible, which means that the C54 island has lost some freedom of rotation on the Cu(111) surface. For the rotation of larger graphene islands up to the critical size NC, the use of the DFT method is too expensive, so we apply the reactive force field (ReaxFF) in LAMMPS package30,31 to study the potential energy surface of a C1014 island, which is about the lower limit of the critical size NC on a Cu(111) surface. The results are presented in Figure 4. First, there are more than 10 energy minima in a periodicity of 0 ≤ θ ≤ 60°. Second, the energy barriers between two minima are normally greater than 50 eV. Although the ReaxFF may overestimate the barrier of graphene island rotation, we are confident that such an island on a Cu(111) surface can be easily trapped by one of the local minima and could not rotate itself during graphene CVD growth. Therefore, the orientation of

such an island would not be changed during the later stages of growth. Because the critical size of a graphene island on a Cu(111) surface is 3000−11 000, we conclude that the orientation of a growing graphene island on a Cu(111) surface is determined in its infant stage, when the EGE−C dominates the EG−C potential energy surface. On the basis of this conclusion, if all graphene islands have very similar infant age experiences, then we can expect an epitaxial-like graphene growth on metal terraces; that is, graphene islands grown on the same terrace will have the same orientation and vice versa. Because the graphene edge− catalyst interaction dominates the orientation of the growing graphene, we mimic the term “van der Waals epitaxy”, used for the growth behavior dominated by the weak van der Waals (VDW) interaction,32 and name this growth behavior “edge epitaxy (EE)”. The EE mechanism of graphene growth can be used to explain all of the experimental facts (i−v) in the following way: (i) There is no lattice registry between grown graphene and the catalyst surface because the EGW−C is weak and orientation-insensitive. Because the barrier of a graphene island rotation on a metal surface is high, a graphene island will not change its orientation when crossing the GB of the metal surface (Figure 5a→b). Furthermore, the high formation energy of the GB in graphene (∼4 to 5 eV/nm)12,33 and the lack of a driving force should be enough to prevent the creation of a GB formation when a growing graphene is crossing a GB of the metal surface. Thus, as a consequence of a single-crystalline graphene lying over a GB of a catalyst surface, the graphene Moiré patterns on both sides will usually be changed (Figure 5c). This is in sharp contrast with the strict graphene epitaxal growth, in which a GB appears at every boundary between catalyst domains (Figure 5d). 2825



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vdW-DF give close results; considering the large systems we studied and expensive computational expense, we choose LDA in this study. The interaction between valence electrons and ion cores is described by the projected-augmented wave (PAW) method.38,39 The energy cutoff for the plane-wave functions is 400 eV, and the force acting on each atom of

How the Orientation of Graphene Is Determined during Chemical

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