Mechanisms of graphene growth on metal surfaces: theoretical perspectives.

Graphene Growth

Mechanisms of Graphene Growth on Metal Surfaces: Theoretical Perspectives Ping Wu, Wenhua Zhang, Zhenyu Li,* and Jinglong Yang*

From the Contents 1. Introduction ..............................................2 2. Graphene Growth on a Cu substrate ...........2 3. Graphene Growth on Other Substrates .....10 4. Conclusion and Outlook...........................12

small 2014, DOI: 10.1002/smll.201303680

Graphene is an important material with unique electronic properties. Aiming to obtain high quality samples at a large scale, graphene growth on metal surfaces has been widely studied. An important topic in these studies is the atomic scale growth mechanism, which is the precondition for a rational optimization of growth conditions. Theoretical studies have provided useful insights for understanding graphene growth mechanisms, which are reviewed in this article. On the mostly used Cu substrate, graphene growth is found to be more complicated than a simple adsorption-dehydrogenation-growth model. Growth on Ni surface is precipitation dominated. On surfaces with a large lattice mismatch to graphene, epitaxial geometry determin a robust nonlinear growth behavior. Further progresses in understanding graphene growth mechanisms is expected with intense theoretical studies using advanced simulation techniques, which will make a guided design of growth protocols practical.

© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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1. Introduction Graphene, a two-dimensional (2D) sheet of sp2-hybridized carbon atoms, has attracted extensive research interest due to its extraordinary physical and chemical properties promising for various applications.[1–4] Graphene is a zerogap semiconductor[5] with a very high carrier mobility up to 200000 cm2 V−1 s−1). It also possesses wonderful optical transparency with an very low adsorption (∼2.3%) of visible light.[6] Its thermal conductivity is as high as 5000 W mK−1 at room temperature and it can thus be used as a thermal management material in electronic devices.[7] Graphene is also one of the strongest materials ever measured with a breaking strength of 42 N m−1 and a Young’s modulus of 1012 N m−2.[8] Since it is an important material, a huge effort has been devoted to the synthesis of graphene. The famous mechanical exfoliation method[1,9] can provide high quality graphene samples, but it is not suitable for mass production. Solutionbased methods, such as direct chemical synthesis of graphene flakes[10] and reduction of graphene oxide,[11,12] are naturally scalable. However, the obtained graphene samples typically are either with a small size or carrying notable defects and residual functional groups. Graphene growth is a probable way to reach a reasonable balance between sample quality and process scalability. As an interesting example, epitaxial growth of graphene on silicon carbide (SiC) at high temperature has been reported.[13,14] A even more popular method is chemical vapor deposition (CVD) growth of graphene on metal surfaces.[15] Various substrate materials, including Ni,[16–18] Cu,[19–22] Ru,[23] Ir,[24,25] and their alloys,[26] have been used for CVD growth of graphene. At the same time, experimentally used carbon feedstock also ranges from gas (i.e. methane[27] and ethylene[21]), liquid (i.e. benzene[28]), to solid (i.e. poly(methyl methacrylate) (PMMA)[22] and amorphous-carbon thin films[29]). It is believed that any carbon-containing materials, such as food, insects, and waste, can be used to grow highquality graphene.[30] The most popular combination of carbon source and substrate is CH4 and Cu. Such a combination has been used with a roll-to-roll technique to produce highquality monolayer graphene of size as large as 30 inches,[31] which demonstrates that CVD growth has a great potential in graphene synthesis. The size, layer number, and quality of graphene samples are sensitive to various growth conditions, such as pressure, temperature, substrate morphology and so on. To optimize these parameters, it is very desirable to understand the growth mechanism at atomic details. Based on an isotope labeling experiment, two kinds of growth mechanisms have been proposed.[32] For substrate materials with large carbon solubility, such as Ni, a precipitation process is expected to be dominant during graphene growth. For those with negligible bulk carbon solubility, such as Cu, the growth should be surface mediated. However, beyond this general picture, little is known about the growth mechanisms, especially at atomic details. Theoretical studies provide an important means to reveal the atomic scale growth mechanisms. First principles calculations can reliably predict reaction energies and barriers

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for elementary processes. Notice that, although the general gradient approximation (GGA) of density functional theory (DFT) is widely used for this purpose, the inclusion of van der Waals (vdW) correction can also be very critical to reach a high accuracy in some cases.[33–35] Using first principles results as an input, kinetic Monte Carlo (kMC) simulation can then be performed to study the growth dynamics. Alternatively, molecular dynamics (MD) simulation can be used directly to observe relatively fast processes. Since first-principles MD is computationally very demanding, semi-empirical and empirical models are usually required in such studies. For carefully parameterized models, consistent results can generally be obtained.[36] Based on experimental observations, simple thermodynamic and kinetic analyses can also provide useful insights to understand growth mechanisms. All these kinds of attempts have been performed to provide a better understanding of graphene growth on metal surfaces. In this article, we review recent progresses in this direction. We start with studies on the experimentally most important Cu substrate. Then studies on other surfaces including Ni and Ir/Ru are briefly introduced. Finally, an outlook is given together with a brief summary.

2. Graphene Growth on a Cu substrate Cu was not a traditional catalyst for CVD growth of carbon nanomaterials. However, due to its superior layer-number controllability, Cu becomes the main substrate material in graphene growth.[20,32] Monolayer graphene can overgrow on polycrystalline copper with various facet features.[19] Although it is experimentally proven that graphene growth on Cu is a surface mediated process,[32] further information on the growth mechanism is mainly borrowed from studies on other traditional catalysts in CVD growth of carbon nanomaterials without verification. It’s supposed that there are mainly three steps in graphene growth on Cu surfaces: (i) decomposition of hydrocarbon catalyzed by Cu, (ii) nucleation of graphene from carbon atoms, and (iii) lateral extension of graphene nucleus via carbon atom attachment. Recently, all these stages have been studied theoretically, and useful new insights are obtained.

2.1. Dehydrogenation of Hydrocarbon Decomposition of feedstock molecules is traditionally expected to be occurred at the surface of catalyst in CVD growth. Gas phase reactions are typically neglected. In gas

P. Wu, Dr. W. Zhang, Prof. Z. Li, Prof. J. Yang Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics University of Science and Technology of China Hefei, Anhui 230026, China E-mail: [email protected]; [email protected] DOI: 10.1002/smll.201303680


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Mechanisms of Graphene Growth on Metal Surfaces: Theoretical Perspectives

phase, the first dehydrogenation step of methane is very endothermic with a calculated reaction energy of about 4.8 eV.[37] It is natural to expect that such a thermodynamically unfavorable process is not important in graphene growth. However, two other factors should also be considered here. First, the growth temperature is typically very high (about 1000 °C). Second, the Cu surface can act as a sink for active species such as CH3 radical, which then shifts the chemical equilibrium to the dehydrogenation direction. Both effects may make gas phase dynamics play a role in graphene growth. To quantitatively study these two effects, Li et al.[38] performed a thermodynamic analysis on the gas phase/solid state chemical equilibrium. With 15 gas phase species considered (H, H2, C, CH, CH2, CH3, CH4, C2, C2H, C2H2, C2H4, C2H6, C3, C4, and C5), the free energy as a function of mole numbers of different compounds can be minimized under the constrain of mass conservation to reach the chemical equilibrium. As shown in Figure 1a, in chemical equilibrium at low temperature, only molecules are observable. When the temperature increases to above 1000 K, radicals such as CH3 become not negligible. Therefore, at a typical growth temperature (1000 °C), gas phase dynamics may be important. When solid state carbon is included in the chemical equilibrium (Figure 1b), almost all CH4 is converted to solid carbon plus H2 and concentration of CH3 is significantly decreased, which is consistent with the sink effect of Cu surface to shift the chemical equilibrium to the methane decomposition direction. Based on the high-temperature data of Rodat et al.,[39] the methane conversion rate at a typical growth temperature is estimated to be on the order of magnitude of 1.0 s−1. If the residence time of the gas flow in the CVD tube is also at such a time scale, the gas compounds in the tube will be in a nonequilibrium steady state, and a gradient of active species concentration along the tube (Figure 1c) is expected. Consequently, Cu substrate placed at different positions in the tube will experience different chemical environments. Experiments with a Cu foil placed at seven different places in the tube (Figure 1d) have confirmed this conjecture. The thickness of graphene increases gradually from position 1 to position 7. Interestingly, if seven Cu foils are simultaneously placed in these seven positions, uniform monolayer graphene is achieved on all foils. This is a natural result of the sink effect of the Cu surfaces. Due to the consumption on upstream Cu foils, increase of active species concentrations at downstream positions is prohibited. This experiment thus clearly demonstrates that gas phase reactions should be considered in graphene growth on Cu surface. Although it can start in gas phase, dehydrogenation is more favorable on metal surfaces. On some active surfaces, such as Pd(100) and Ru(0001) surfaces, decomposition of CH4 becomes exothermic.[40,41] Even it is slightly endothermic on Ni(111) surface,[42] CH4 decomposition is expected to be kinetically favored by the high solubility of C in Ni. Based on these facts, it was supposed that CH4 will also be fully dehydrogenated on Cu surface to produce carbon atoms for further nucleation and growth of graphene. However, this is not necessarily true considering the much low catalysis activity of Cu. small 2014, DOI: 10.1002/smll.201303680

Zhenyu Li received his PhD degree in physical chemistry from University of Science and Technology of China (USTC) in 2004. Since then, he has been working as a postdoctoral researcher at University of Maryland, College Park and University of California, Irvine. In 2007, he joined the Hefei National Laboratory for Physical Sciences at the Microscale, USTC. Currently, he is a professor of chemistry at USTC. His research interests focus on theoretical design and computational characterization of materials and physical/chemical processes, mainly based on electronic structure calculation and molecular modeling. Jinlong Yang, currently a Changjiang professor of chemistry, executive dean of the School of Chemistry and Material Sciences of USTC, received his PhD degree in condensed matter physics from USTC in 1991. He is a fellow of the American Physics Society, the recipient of the young chemist award from Chinese Chemical Society and the national award (grade two) for natural science. His research interests focus on developing first principles methods and their application on clusters, nano structures, solid materials, surfaces, and interfaces.

Zhang et al.[37] checked the dehydrogenation energetics of CH4 on Cu surfaces. As shown in Figure 2a, all dehydrogenation steps on Cu(111) surface are endothermic, and the corresponding activation energy barriers range from 1.0 to 2.0 eV. The final product C+4H is already 3.60 eV higher in energy than the adsorbed CH4. Similar results has also been obtained by other groups.[43] On Cu(100) surface, there is also a large total energy increase (2.75 eV) for methane dehydrogenation.[37] At the same time, similar endothermic behavior is obtained for C2H4 decomposition on the Cu (111) surface. Therefore, atomic carbon is energetically very unfavorable on the Cu substrate. Notice that desorption is an important process to compete with dehydrogenation. For some precursor molecules, such as benzene, vdW interaction can thus play an important role in graphene growth.[35] The strongly unfavorable dehydrogenation thermodynamics on the Cu surface suggests that partially dehydrogenated species, such as CHx, will combine with each other before going to the final hydrogen-free product. First principles MD simulations found that C2H2 can be easily formed on CH covered Cu(111) surface (green circles in Figure 2b), while dehydrogenation of CH group has not been observed in a 3.5 picosecond trajectory with C–H bond length monitored (Figure 2c). Of course, to grow graphene, dehydrogenation should finally be completed. Computational results of Zhang et al.[37] suggest that it can be completed at a very late stage with large CxHy structures already formed. Such a possibility has been demonstrated in a surface assisted cyclodehydrogenation experiment.[44] Consistently, it was found that benzene can be formed by cyclotrimerization of C2H2 on Cu(110) surface, which is an exothermic reaction with a


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Figure 1. Calculated mole fractions of 15 gas phase species in chemical equilibrium from 500 to 1500 K (a) without and (b) with solid carbon included. Total pressure is 20 Torr, H/C = 26:5 (corresponding to H2/CH4 = 3:5). (c) Schematic of the density distribution of the active species derived from methane cracking along the tube. (d) Schematic of the CVD growth of graphene with Cu foils at seven different positions.[38] Reproduced with Permission. Copyright 2012, American Chemical Society (ACS).

moderate activation barrier of 0.79 eV.[45] It is thus reasonable to assume that dehydrogenation is a reaction involved during most of or even the whole graphene growth process.

2.2. Carbon clusters on Cu surface Before going to the nucleation stage, it is necessary to check the geometry and evolution dynamics of the possible carbon species on the surface. Although CxHy is expected to be extensively existed on Cu surface as discussed in section 2.1, most previous studies considered carbon clusters only. These results provide limited insights in understanding CVD growth of graphene on the Cu surface. Notice that, however, hydrogen free graphene growth using techniques such as molecular beam epitaxy (MBE) has also been reported in the literature.[46,47] Mechanisms in these processes involve only carbon clusters at an early stage. For carbon monomer, Mi et al.[48] checked stabilities of different adsorption sites on Cu (100), (110), and (111) surfaces, where the most stable adsorption sites are hollow, long bridge, and face-centered cubic (fcc) hollow, respectively. From (100) to (111) adsorption, the coordination number decreases from 4 to 3 and the adsorption energy decrease from 6.54 to 5.17 eV. Notice that the most stable adsorption site becomes the subsurface octahedral site if this degree of freedom is included, which further increases the adsorption energy by about 0.6 eV.[49,50] Diffusion barrier of carbon monomer on Cu(111) surface is negligible,[51] and it increases to 0.55 eV for hopping between subsurface octahedral sites via a tetrahedral site. Carbon dimer is more stable than monomer on Cu (100), (110), and (111) surfaces.[48] Diffusion barrier of carbon dimer


on Cu(111) surface is 0.44 eV[51] or lower.[52] Notice that the stability and mobility differences of carbon monomer and dimer on (100) and (111) surfaces can lead to an interesting graphene nanoribbon formation on Cu twin crystal, which can be described by a simple one dimensional (1D) diffusion equation.[53] For even larger carbon clusters, either linear or compact configurations can be formed on the surface. Due to the relatively stronger C–C interaction compared to C–Cu interaction, in a study of CN (N = 3–13), linear structures (Figure 3a) are always more stable than compact structures (Figure 3b).[54] Linear carbon chains form nanoarches with only two end atoms bonding with the surface. It becomes more stable as its length becomes longer. However, the energy difference between linear and compact configurations generally decreases with the increase of carbon atom number, which is desirable for an evolution from carbon linear clusters to graphene. Mobility of carbon nanoarches is expected to be relatively high, since a walk-with-legs diffusion mode[55] is available. To study the energetic trend in the evolution from carbon clusters to graphene, a reaction coordinate, CNC–C, defined as the average number of neighboring carbon atoms has been proposed.[48] CNC–C equals to 3 in graphene, 2 in an infinitely long chain, 1 in a carbon dimer, and 0 for a monomer. As shown in Figure 3c, for carbon monomer, the adsorption energy can be very different on different Cu surfaces. Along with the increasing of CNC–C, adsorptions become weaker and the differences between different surfaces gradually disappear. From a thermodynamic point of view, such a facet-insensitive behavior is consistent with the experimental observation that graphene can be effectively grown on polycrystalline copper foils.


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Figure 2. (a) Energy profile of the dehydrogenation processes of CH4 on Cu (111) and (100) surfaces. (b) Typical snapshot from a first principles MD simulation of a CH covered Cu (111) surface. (c) Bond length variation of a randomly chosen C-H bond in the MD trajectory.[37] Reproduced with Permission. Copyright 2011, ACS.

Comparing to its thermodynamics, kinetics of carbon cluster evolution on Cu surfaces is much less studied. The simplest procedure is the combination of two carbon monomer to form a dimer (1+1). If both monomers occupy a subsurface octahedral site, the 1+1 reaction associates a 0.32 eV barrier.[50] For two carbon monomers on surface hollow sites, since their diffusion is almost barrierless, one may expect that the corresponding 1+1 reaction also has a negligible barrier considering that monomer combination does not involve more bond-breaking events compared to monomer diffusion. However, geometry optimization leads to a significant structure relaxation when two carbon monomers are close enough to share a Cu atom.[51] small 2014, DOI: 10.1002/smll.201303680

In the relaxed structure one carbon atom goes to subsurface and the surface Cu atom shared by the two carbon atoms is pulled upward from the surface, which forms an almost linear C–Cu–C chain (Figure 4a). Accompanied with the increase of carbon coordination numbers, the adsorption energy of such a bridging-metal (BM) structure becomes 1.01 eV larger than that of two isolated carbon adatoms. The formation of the BM structure prohibits a straightforward monomer combination on the surface. One way to form dimer from the BM structure is moving the other carbon atom also to subsurface. Alternatively, if one carbon atom makes a detour, a dimer can be formed by sequentially conquering three energy barriers of 0.51, 0.64, and 0.37 eV. Formation of BM structures turns out to be an universal phenomenon on the Cu(111) surface. Generally, when a carbon monomer approaches a carbon cluster, the bridging Cu will be notably upshifted to form a BM structure. BM structure also formed in the combination reaction of C2H2 and CH on Cu(111) surface (Figure 4b). Formation of a BM structure increases the combination barrier. Therefore, carbon incorporation should not be barrierless on Cu(111), and it should be explicitly considered in studies of graphene growth. In a first principles MD trajectory at 800 K for 1/3 monolayer carbon atom covered Cu(111) surface, huge Cu surface structure relaxation upon C adsorption is observed and BM structures are very common on the rough surface. Therefore, the BM structure is expected to play an important role in graphene growth on Cu surface. The spontaneous formation of BM structures during approaching of carbon atoms can be understood by comparing the strengths of Cu–C and Cu–Cu interactions. When it is shared by two carbon atoms, a Cu atom gets a large coordination number and becomes relatively unstable. If Cu–C interaction is dominant, this Cu atom will be upshifted to make stronger Cu–C bonds, which is the driving force for BM structure formation. To predict the possibility of forming BM structure on other metal surface, the ratio between carbon atom adsorption energy and metal cohesive energy can be used as a good indicator for the competition between metalcarbon and metal-metal interactions. If this ratio is larger than 1.3, BM structure is expected to be formed spontaneously.[51] However, a ratio too large will make the adsorbed system very rigid, which can lead to a barrier ahead of the BM structure.

2.3. Graphene Nucleation Atomic details of the nucleation process during CVD growth of graphene on Cu surface are still mainly unknown. For small carbon clusters adsorbed on the Cu surface, generally the formation energy decreases with the cluster size. However, this does not necessarily mean that there is no nucleation barrier for graphene growth on Cu surface due to the following two reasons. First, the most stable configuration for small clusters is linear chain. A topological transition from one dimensional (1D) chain to 2D compact structure will experience a significant barrier. For example, there is an about 1.8 eV energy barrier for a C6 chain to form a ring.[54] At the same time,



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Figure 3. (a) Side views of the relaxed 1D nanoarch structures on Cu(111).[54] (b) Top views of the relaxed 2D compact structures on Cu(111).[54] (c) Adsorption energy versus CNC−C. The dashed lines envelop the most energetically stable configurations at different growth stages on various copper surfaces, in order to guide the eye.[48] Reproduced with Permission. Copyright 2011, American Institute of Physics (AIP) and 2012 American Physical Society (APS).

based on the analysis of carbon source dehydrogenation, graphene growth is not fed by carbon atoms.[37] Evolution of different CxHy species at the early stage of graphene growth is still unclear. A useful experimental technique to probe possible intermediates during the nucleation process is temperature programmed growth (TPG). In a TPG experiment, carbon source is deposited on metal surface at a low temperature, and the adsorbed system is then stepwise annealed up to a high temperature. On some active transition metal surfaces, such as Ir(111),[25] Rh(0001),[56] and Ru(0001),[57,58] uniform 2D clusters with a diameter about 1 nm were observed in graphene TPG experiments. To clarify the atomic structure of these magic clusters, which as a precursor may determine the nucleation process, Yuan et al.[59] calculated the ground state structure of adsorbed carbon clusters with 16-26 atoms. They found that the high symmetry (C3v) core-shell structured C21 (Figure 5a), which is a fraction of fullerene C60 possessing three isolated pentagons, is very stable on all four surfaces they studied, i.e. Rh(111), Ru(0001), Ni(111), and Cu(111). This result demonstrates that small 2D carbon clusters with sp2 network become more stable by incorporating one or more pentagons compared to those with only six-membered rings.[60] Pentagons introduced in small carbon clusters facilitate the formation of dome-shaped structure,[59–61] thus also enhance the binding between edge C atoms and the metal surfaces.


Although DFT calculations indicate that C21 is a very stable magic cluster also on the Cu(111) surface, TPG experiment observed different intermediate species on this surface.[62] Various carbon containing clusters, including small dimers, rectangles, and zigzag and armchair-like chains, are found to be the actual growth intermediates prior to the graphene formation. Based on an analysis of the scanning tunneling microscopy (STM) image, the small dimers are assigned as C2Hx. Zigzag and armchair like chains are composed of CH groups. Rectangles also have the same basic building block. A cluster with a structure shown in Figure 5b can successfully reproduce the experimentally observed STM image of rectangles according to a first principles simulation. Therefore, the nucleation process on Cu surface is expected to be very complicated, as indicated by the TPG confirmed partial dehydrogenation behavior. Interestingly, such a partial dehydrogenation behavior also provides us an opportunity of thermodynamic analysis on nucleation size.[37] The basic idea is that small carbon clusters are not stable without H. First principles calculations can give an estimation on how large an carbon cluster without hydrogen should be to be stable in a certain chemical environment. If we suppose that a nucleus is a 2D graphitic carbon cluster without hydrogen, such first principles calculations can give us a rough estimation on nucleation size (the lower bound). At a typical experimental growth temperature (1300 K), with the chemical equilibrium between CH4 and H2 in gas


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can be increased to as large as about 24 for χ = 1/20 (the red line in Figure 5c). Based on such a thermodynamic model, it becomes possible to predict the general behavior of the environmental effects on the nucleation size. For example, it is predicted that nucleation size is less sensitive to the partial pressure if ethylene is used as the carbon source. The experimental observed growth rate increase with the decrease of H2 concentration[63] is a natural result of the smaller nucleation size at higher CH4/H2 ratio. Lower CH4/H2 ratio leads to lower nucleation density, and higher quality of single layer samples.[64,65] The nucleation behavior has also been studied experimentally by checking the relationship between saturated nucleation density and temperature.[66,67] Although nucleation rate is expected to increase with temperature, nucleation density on Cu surface was observed to decrease with temperature. In an Arrhenius plot of the temperature dependent density of graphene nuclei, the slope gives an apparent Figure 4. BM structures for the (a) 1+1 and (b) C2H2+CH reactions. (c) A typical snapshot in nucleation activation energy. When the the 800 K MD trajectory for carbon monomer covered Cu(111) surface. A typical BM structure temperature is higher than 870 °C, the [ 51 ] is highlighted. Reproduced with Permission. Copyright 2010, AIP. apparent nucleation activation energy EHT is about 3-4 eV.[66,67] At lower temperature, phase, the relationship between the chemical potentials of C the activation energy ELT is about 1 eV.[67,68] Such a two regime behavior indicates that there are two and H in eV can be expressed as different nucleation mechanisms at high and low temperatures, which is proposed to be a result of the competition μC = −2 μ H − 10.152 + 0.112 ln χ (1) between the processes of adatom capture, surface diffusion, and re-evaporation.[67] In the high temperature regime, deswhere χ is the ratio of the partial pressures of CH4 and H2. orption rate is significant compared to the mobility of active The H chemical potential µH is readily related to the experi- carbon species. The nucleation is desorption controlled. At mental partial pressure of H2 within the ideal gas approxima- low temperature, the lifetime of an active carbon species tion. Therefore, at a fixed χ, µC during CVD growth is also on the surface is determined by nucleation and attachment related to the H2 partial pressure, as shown in Figure 5c. When events. Therefore, the kinetics enters a capture controlled a surface carbon species has a chemical potential higher than regime. µC (i.e., not in the yellow area), it is not stable and will react with H2. The chemical potential of an isolated atomic carbon on 2.4. Lateral Extension of Graphene Islands the surface can be approximated by its adsorption energy (4.85 eV, the horizontal line marked with C1 in Figure 5c). To access atomic details of the lateral extension of graphene Under most experimentally accessible pressures, it is much islands, one should first know what is the active species on the higher than µC. Therefore, atomic carbon is not stable. Carbon surface which will be attached to a graphene edge. Although chemical potential of graphene (the lowest horizontal line in it is expected to have a formula of CxHy as discussed in secFigure 5c) is lower than that of the source gases in most cases. tion 2.1, the dominant species is supposed to be carbon atom This is the thermodynamic driving force to grow graphene. It in most previous studies on graphene island growth. One becomes unstable only under very high pressures, where it is should also know what the structure of a graphene edge is during the growth. Possibilities of hydrogen saturation and expected to be etched by H2 to form CH4. Based on energy calculations for different 2D carbon edge reconstruction should be considered, and both of them clusters on the surface, a lower bound of the nucleation size are expected to depend on the chemical environment such can be estimated to be about six carbon atoms under a H2 as pressure and temperature. When both surface species and CH4 partial pressure of 10−5 and 2 × 10−4 bar, respec- and edge structure are known, first principles calculations tively. If the CH4/H2 ratio decreases, the nucleation size can be performed straightforwardly to obtain the energetics small 2014, DOI: 10.1002/smll.201303680



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Figure 5. (a) Structure of C21 and C24 clusters with reactive sites illustrated.[59] (b) Optimized structure of a rectangle on Cu(111).[62] (c) Relationship between µC and partial pressure of H2 during CVD growth of graphene on a Cu (111) surface at 1300 K with CH4 as the carbon source. Black line stands for χ = 1, blue line for χ = 20, and red line for χ = 1/20. Chemical potentials of carbon clusters adsorbed on the Cu (111) surface and that of graphene (Gr) are marked by horizontal lines. Yellow areas mark the stable zone with χ = 1. A typical experimental H2 partial pressure (10−5 bar) is marked by a vertical line.[37] Reproduced with Permission. Copyright 2011, 2012, 2013, ACS.

of attachment process. The graphene island shape can then be determined by a thermodynamic (Wulff construction) or kinetic analysis.[69] Alternatively, a coarse-grained phase-field model can be used to describe the diverse growth morphologies observed in experiment.[70] There are already several theoretical studies on the graphene island edge structure and stability. The possibility of hydrogen saturation is determined by the hydrogen chemical potential.[71] In a H-rich environment, graphene edges are expected to be hydrogen saturated, and vice versa. At the same time, graphene edges can be stabilized by reconstructions.[72] In vacuum, the armchair edge is stable while the metastable zigzag edge will be reconstructed into a line of pentagon-heptagon pairs. The situation changes on Cu surface, where the pristine zigzag edge can be well passivated by Cu atoms and become very stable.[73,74] If thermal fluctuation can well activate Cu atom diffusion on the surface, the armchair edge terminated by Cu atoms is thermodynamically favorable.[75] In fact, the interaction between graphene edge and the metal substrate is very important, which probably determines the final orientation of grown in an “edge epitaxy” manner.[76] For unconstructed edges, from armchair to zigzag orientations, their energy can be analytically expressed as a sinusoid function of the edge direction with a phase-shift constant determined by chemical environment.[73,77] For an arbitrary


edge direction χ, the edge energy γ per unit length can be obtained by a linear combination of armchair and zigzag edge energies

γ ( χ ) = 2γ A sin ( χ ) + 2γ Z cos ( 30 ° − χ )

(2)

It is then easy to show that, if the edge energies along the armchair and zigzag crystallographic directions differ by more than approximately 15%, either armchair or zigzag edge will dominate and a Wulff construction will give a hexagonal island.[73,77] Based on first principles calculations, the zigzag edge is significantly more stable than the armchair edge on Cu(111). Therefore, the equilibrium shape of a graphene island is a hexagon with only zigzag edges,[73,74] which is consistent with some experimental observations.[78–80] Notice that, however, a calculation for the Cu(100) surface suggested that these two edges have similar formation energies.[79] At the slow growth limit, the thermodynamic equilibrium assumed in Wulff construction will not be violated. However, when the growth process is far away from equilibrium, a kinetic extension to the Wulff construction should be adopted. In such a kinetic Wulff construction, the edge formation energy is substituted by growth rate, which can be estimated via first principles calculations. In a recent study,


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Figure 6. (a) Repeatable cycles of incorporating two C atoms onto Cu-termianted armchair graphene edges on the Cu(111) surface. The circled regions represent the growth site. All of the energy differences are in the unit of eV.[75] (b) Optimized structures of a SV (5DB) and a DV (5|8|5 and 555-777) in free-standing graphene. The most stable structure of (c) SV (3DBs) and (d) DV (M@4DBs) on the Cu(111) surface.[81] Reproduced with Permission. Copyright 2012, 2013, ACS.

incorporation of carbon atoms onto armchair and zigzag edges has been studied.[75] On Cu(111), each armchair-like site on the edge is expected to be passivated by a Cu atom, which significantly lowers the barrier of incorporating carbon atoms onto the graphene edge from 2.5 to 0.8 eV (Figure 6a) and therefore results in a very fast growth of the armchair edge. With atomic details at the armchair and zigzag edges known, growth rate for an arbitrary edge can be estimated by counting different types of active sites (kinks and armchair/ zigzag segments).[73,75] A kinetic Wulff construction then predicts also a hexagon with zigzag edges. In a nonequilibrium growth of graphene, defects are expected to be dynamically formed and healed. Single and double vacancies (SV and DV) have been considered by Wang et al.[81] In free-standing graphene, the ground state of SV has a pentagon-dangling bond (5-DB) structure (Figure 6b). The ground structure of DV is 555-777 with a metastable structure 5|8|5. On Cu(111) surface, SV tends to have three dangling bonds (3DBs), which are partially saturated by the surface (Figure 6c). For DV, there is already enough space to accommodate an additional Cu atom in the center with four dangling bonds (M@4DBs, Figure 6d). small 2014, DOI: 10.1002/smll.201303680

Mobility of these two structures on the surface is relatively low, and the healing process by the diffusion of vacancies out of a graphene domain is not practical. The 3DBs structure of SV can be healed by simply incorporating a new carbon atom. Therefore, the most critical process is the healing of the DV defect, where two carbon atoms are substituted by a Cu atom. Since Cu atom is involved in the C attachment process,[75] the possibility of DV formation is expected to be high. According to first principles calculations, DV healing by two C atoms which draws the embedded Cu atom out of the growth front has a barrier of 1.86 eV. At the temperature of 1300 K and the growth rate of 10−100 nm/s, the healing rate is estimated to be greater than 99.999%, which is consistent with the good graphene sample quality grown on Cu surface. Another interesting question at the island extension stage of graphene growth is whether it finally leads to a full coverage of graphene on the Cu surface. If we suppose that the adsorption and desorption rate are balanced after supersaturation is reached, graphene growth arises from the crystallization of a supersaturated fraction of carbon adatom concentration (the difference between the critical supersaturation level for nucleation and the equilibrium



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level for grown graphene, cnuc-ceq).[67] Then a saturated graphene area coverage (Asat) will be finally reached, which equals to (cnuc-ceq)/ρG with the atomic area density of graphene ρG being 0.382 Å−2. Only when Asat is larger than 1, complete coverage with a continuous graphene film will be obtained. To directly connect Asat with growth conditions, chemical equilibrium of main processes during growth should be considered. For graphene growth with CH4 as the carbon source, Kim et al.[82] wrote down three equilibrium constants. They are K1 for adsorption and desorption equilibrium of the CH4 decomposition reaction, K2 for adsorption and desorption of H2, and K3 for attachment and detachment of carbon atoms on edges of graphene islands. The coverage of graphene can be solved from the expressions of these three equilibrium constants AG ≈ 1 −

( PH ) 2 2

(3)

K 1 K 2 K 3 ρ s PCH 4

where ρs is the density of the surface sites on Cu (about 1.5×1019 m−2). Based on this expression, the saturation graphene coverage is mainly determined by two growth parameters, i.e. temperature (via equilibrium constants) and the ratio PCH4/(PH2)2.

3. Graphene Growth on Other Substrates Although Cu is currently the most interesting substrate material for CVD growth of graphene, many other surfaces have been used to grow graphene. Among them, Ni surface is a popular choice, since Ni has been widely used previously in CVD growth of carbon nanotubes.[83] Besides substrates like Cu and Ni with small lattice mismatch with graphene, some large transition metals have also been used to grow graphene, where a Moiré pattern will be formed.[84] Such a superstructure can be used as a template to grow regular nanoparticle lattice with various potential applications.[85] On the theoretical side, mechanism studies for graphene growth on substrates beyond Cu have also been reported, which will be briefly introduced below. 3.1. Precipitation dominated growth on Ni surface In contrast to Cu, Ni represents another kind of graphene growth substrate materials. The carbon solubility in Ni is very high, therefore precipitation will make a central role in graphene growth on Ni surface, which makes cooling rate an important growth parameter to control.[16] Although the main growth mechanism is different, similar theoretical methods as used for Cu are also applicable for Ni. According to MD simulations, methane molecules are dissociated into isolated carbon and hydrogen atoms via CH3 and CH fragments on Ni surface.[86] Small carbon clusters on Ni(111) surface also prefer to form linear chains, however this chains are crawling on the surface due to the stronger carbon-surface interaction. Such a configuration makes a chain-to-branched nucleation pathway available.[60,87] DFT energetic calculations predict a


transform from 1D carbon chain to 2D sp2 carbon network at carbon atom number N about 10 to 12.[88] Formation energy of carbon clusters on Ni(111) surface, E(N), can be fitted to a function of N. For chain structures, it is a linear function of N, while it is proportional to square root of N for 2D sp2 carbon network. The Gibbs free energy can be expressed as G(N) = E(N) – Δµ × N, where Δµ is the chemical potential difference between the crystalline phase and the carbon atoms dissolved in the Ni bulk. According to the classical nucleation theory, the maximum of G(N) gives the nucleus size N* and nucleation barrier G*. DFT calculations give an estimation of Δµ as 0.87 eV[87] or higher,[89] then the nucleation barrier goes to zero and the nucleus size becomes 1,[88] indicating a spontaneous growth during the cooling stage. When considering nucleation at step edge, it is also possible to estimate the nucleus size by fitting an analytical expression for strain energy and edge energy.[90] At the same time, by considering a crystallization process from amorphous carbon, the nucleus size has been estimated to be 0.68 nm.[36] To consider the possible strong structure relaxation of the Ni surface itself during the graphene growth process as demonstrated in previous studies on Cu surface,[51] MD simulations at the density-functional tight-binding (DFTB) level have been used to study the nucleation process for graphene growth on Ni surface.[91] As expected, the Ni surface is found to be highly malleable and mobile, and the carbon precipitation causes huge surface structure deformation. In cases with a high supersaturation, carbon clusters as graphene precursors have been observed to form beneath the Ni surface. Then, nucleation takes place via the following three steps. First, carbon chains are formed by the coalescence of carbon atoms below the surface. Then, these subsurface chains interact with each other to form irregular carbon clusters. Finally, the nucleation takes place by a simultaneous migration of these carbon clusters up to the surface. A transformation from irregular structure to sp2 network occurs simultaneously with the precipitation itself. At the same time, Monte Carlo simulations in the grand canonical ensemble (GCMC) have observed chains creeping on the surface and detached sp2 C layers with the increase of C chemical potential.[92] In another MD simulation, Haeckelite on Ni(111) surface is also found to be a metastable intermediate before graphene formation.[93] Carbon atoms can be explicitly provided during MD simulations, which generally corresponds to a far-from-equilibrium growth condition with a high precursor flux. Recently, such a MD study suggests that monolayer graphene can also be obtained on Ni surface if diffusion to bulk is effectively blocked.[94] Defect healing is expected to be also an important issue in graphene growth on the Ni surface. Similar to Cu, the DV defect with a Ni@4DBs structure plays an important role in the healing process. The same healing pathway as for Cu@4DBs by using two carbon atoms to push the metal atom away gives a larger barrier, indicating that the Ni surface may not be as efficient as the Cu surface for defect healing.[81] However, by stabilizing reaction intermediate, the activation energy for Stone-Wale defect healing still decreases from


small 2014, DOI: 10.1002/smll.201303680


4.10 eV for freestanding graphene to 2.88 eV on Ni(111) surface.[95] Beside first principles calculations, graphene defect healing has also been studied by tight-binding GCMC simulations.[96] By this way, it is not necessary to guess the type of the defects which can instead be automatically determined during the simulation. Numbers of different rings have been monitored during the simulations, and for healed graphene only six-membered rings exist. The Ni substrate is found to be helpful in healing of graphene by repeatedly breaking and reforming nickel-carbon chemical bonds around defects. In principle, more atomic details on defect healing can be obtained by MD simulations. A MD study using a reactive force field indicates that five- and seven-membered rings which are difficult to remove can be healed during the carbon incorporation process by the continuous breaking and reformation of C-C bonds.[97] At the same time, steps on the surface are found to be able to play an important role in healing those defects with a substrate Ni atom pulled up by several carbon atoms.[98]

3.2. Nonlinear growth on Ir and Ru Surfaces Ir substrate has also been used to grow high structural quality monolayer graphene with large-scale continuity over terraces and step edges.[24] Graphene grown on Ir(111) surface is typically well-aligned with the substrate, forming Moiré patterns.[84] However, the interaction between graphene and the Ir surface is not very strong and several graphene orientations can thus be formed. Typically, the majority phase (R0) nucleates first. Then, at the boundary of a growing R0 island, a 30o rotated phase (R30) can occasionally nucleate. Once nucleated, the R30 phase grows much faster than the R0 phase.[99] An interesting nonlinear behavior of the R0 phase growth has been observed using the low-energy electron microscopy (LEEM).[99] The growth velocity of a R0 domain satisfies n v ∝ ⎡⎢( c / c eq ) − 1 ⎤⎥ , where c and ceq are the adatom concentra⎣ ⎦ tion and its equilibrium value. Fitting experimental data gives n = 4.8 ± 0.5. Similar results have also been obtained for growth on the Ru surface.[99] This result indicates a synergetic effect involving several (∼5) carbon atoms. Such a process in principle can be well described by kinetic Monte Carlo (kMC) simulations. However, the growth conditions and material parameters conspire to render such simulations very difficult.[100] As an alternative, rate equations can be used to study the nonlinear growth of graphene on the Ru surface. A simple model is constructed to describe the quintic kinetics.[100] In this model, five carbon adatoms collide to form a C5 cluster first. These clusters migrate on the surface. When n such clusters collide, an immobile island is then formed. It is also supposed that islands grow mainly by the attachment of C5 clusters. Within this model, a set of rate equations can be written down. By fitting the evolution of the carbon adatom density obtained from the rate equations to experimental data, one can obtain n = 6. Notice that, however, with the fitted kinetic parameters, contribution to graphene growth small 2014, DOI: 10.1002/smll.201303680

from carbon atom attachment (DnN-K′N in ref.[100]) is about one order of magnitude greater than that from carbon cluster attachement (D′cN in ref.[100]). The rate equation approach has also been extended to include both gas-phase and surface elementary processes, which then enables a description on CVD growth of graphene.[101] Although conventional kMC simulation is impractical to describe the experimentally observed nonlinear growth behavior, a clever standing-on-the-front (SOF) kMC model has been developed recently to solve this problem.[55] By combining first principles calculations and SOF-kMC simulations, the nonlinear growth mechanism is successfully revealed. The obtained mechanism turns out to be very robust based on SOF-kMC numerical experiments. First principles calculations are performed first to get a general picture about the nonlinear growth behavior at the atomic scale. Structures and potential energies of small carbon clusters on Ir(111) surface up to 10 atoms have been calculated. Generally, nanoarches are the ground structures. Besides energies, diffusion barriers of different species are also calculated. With these data, equilibrium concentrations of different carbon clusters and their mobilities can be estimated. Clusters at different step edges are also studied. Dimer has a big thermodynamic driving force to attach at step edges. Stable 2D precursors have also been found at step edge, which is consistent with the experimental observation of the preference of step edge nucleation.[25] With possible carbon species on the surface known, their attachment to graphene edge is then studied. Due to lattice mismatch between graphene and the Ir substrate, different sites at the growth front of graphene are not equivalent. As shown in Figure 7a, carbon monomer attachment is exothermic only at eight of the ten graphene edge sites in a unit cell. Generally, when an attached carbon atom is sitting on the top of an Ir atom, the corresponding attachment process becomes endothermic. As a result, a gap is left at the graphene edge, and it can be readily bridged by a C5 cluster (a 0.70 eV exothermic process). Since the concentration of C5 is very low, this cluster attachment event will be the rate-determining process during graphene growth on Ir(111) surface. With the general physics obtained from first principles, kMC model can then be designed accordingly to obtain quantitative kinetics. To reduce the simulation cell size, the 2D space is divided into four regions (Figure 7b): the grown part, growth front, diffusion layer, and far field. The far field is a quasi-equilibrium homogeneous system of various carbon species, and the flux of different carbon species cross the diffusion layer to the graphene growth front. At the growth front, carbon species attachment and detachment are focused and other processes are compacted into effective carbon species fluxes. Therefore, a small simulation cell enclosing the growth front and moving with it can be used, which significantly reduce the simulation time. Other techniques, such as time scale separation, have been adopted to further improve the simulation efficiency. SOF-kMC simulations give a growth exponent of 5.25 (Figure 7c), which agrees well with the experiment.[99] Event analysis[102] shows that most attached C4 clusters are detached via smaller species, therefore net contribution of



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Figure 7. (a) Graphene nanoribbon with 8 of its 10 edge sites attached by carbon monomers and that with an additional C5 cluster. (b) Schematic diagram of the SOF-kMC model. (c) Graphene growth rates dependence on C monomer concentration obtained by kMC simulations.[55] (d) The dependence of growth exponent γ on heterogeneity level α.[102] Reproduced with Permission. Copyright 2012, ACS and 2013 APS.

C4 attachment to graphene growth is small. C5 attachment is the main event propagate the growth front at those sites carbon monomer detachment is much faster than its attachment. Contribution from C6 is much smaller but also not negligible, therefore the overall growth exponent is slightly larger than 5. An important merit of kMC simulation is that it can be used as a facility for numerical experiment. A heterogeneity level α is defined to represent difference between different growth sites.[102] When α is zero, all sites can be easily attached by carbon monomer, then a linear growth kinetics is expected. Interestingly, by gradually increase α, the growth exponent rapidly increases to 5 and then remains unchanged (Figure 7d). It means that the nonlinear growth behavior is not very sensitive to the details of atomic interactions, and the behavior determined by the Moiré pattern or lattice mismatch is very robust. That is why similar growth behavior has been observed experimentally on different metal surfaces. The robustness also provides us a powerful predictability. For example, simply by checking the epitaxial registry of the R30 phase, a growth exponent of 2 can be predicted. Such a geometry based prediction is consistent with first principles calculations.[55]


4. Conclusion and Outlook Over the past several years, our understanding to the mechanisms of graphene growth on metal surfaces has been significantly deepened due to an intense research effort from many theoretical and experimental groups. Graphene growth is strongly substrate dependent. For the most interested Cu substrate, some details about gas phase reactions, carbon source dehydrogenation, nucleation on the surface, and continue growth of graphene islands have been revealed. On Ni surface graphene growth is dominant by participation processes, very different from Cu. Lattice mismatch also plays an important role in graphene growth, and the resulted epitaxial pattern may determine the growth kinetics. To grow high quality graphene sample on Cu surface, nucleation density should be minimized. Besides improving substrate quality, this goal can also be reached by lowering CH4/H2 partial pressure ratio. At the same time, to enlarge graphene single crystalline domain, CH4 partial pressure over square of H2 partial pressure PCH 4 / PH2 2 cannot be minimized. Therefore, relatively low H2 partial pressure is encouraged in graphene growth with CH4 as carbon source on Cu surface. If another carbon source is preferred, using those


(

)

small 2014, DOI: 10.1002/smll.201303680


already have carbon hexagon and adsorb on the substrate more strongly generally leads to a lower growth temperature. Despite of the progresses already made, there are still many unknown issues in this active field of graphene growth. On one hand, most theoretical studies only focus on a specific issue in graphene growth, and a unified growth mechanism at the atomic level is still not available. On the other hand, CVD growth of graphene depends on many factors, including substrate, feedstock, temperature, pressure, etc. As a result, different growth processes may have totally different mechanisms, which makes the theoretical study very difficult. Some issues are commonly interested now, and they are certainly important topics for theoretical studies in the next few years. First, the influence of hydrogen on graphene growth is very important, especially on the Cu surface. Its effects have already been demonstrated in experiment.[103–105] However, the relevant atomic processes are mainly unknown. With CxHy on the surface, nucleation on Cu surface is expected to be very complicated. Second, layer number control is a very important but mainly untouched issue. Both on-top and underlayer growth of multilayer graphene have been observed experimentally,[106–109] which indicates the existence of multiple mechanisms. Third, quantitative growth kinetics provides a useful constrain for growth mechanism search, which has already been demonstrated by nonlinear growth of graphene on Ir and Ru surfaces. Another interesting example is the experimental observation that graphene growth on Cu(100) surface is attachment limited while it is diffusion limited on Cu(111) surface.[46,110] Such a counterintuitive result deserves a systematic theoretical study. At last, theoretical design of growth protocol is gradually becoming practical along with better understanding of the growth mechanisms. Recent examples include proposals for using alloyed surface to grow high quality graphene samples.[111,112] Currently, theoretical studies on graphene growth are mainly based on first principles calculations and empirical/ semiempirical molecular dynamics. Some other techniques, such as kMC simulation and phenomenological analysis, have also been used in previous studies. Development of more sophisticated multiscale theoretical models is expected to significantly promote researches in this field. It is also an urgent task to develop reliable empirical or semi-empirical force field for the Cu–C–H system. At the same time, advanced potential energy surface (PES) exploring algorithms, such as forward flux sampling,[113] may be useful in identifying the main nucleation pathway. Advanced theoretical modeling, together with experimental studies, will continue to deepen our understanding of graphene growth on metal surfaces.

Acknowledgements This work is partially supported by MOST (2011CB921404, 2014CB932700), by NSFC (21173202, 21222304, 21121003, 21233007, and 21103156), by CUSF, by CAS (XDB01020300), and by USTC-SCC, SCCAS, and Tianjin Supercomputer Centers.

small 2014, DOI: 10.1002/smll.201303680

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Received: November 28, 2013 Revised: February 26, 2014 Published online:


15

Graphene growth and properties on metal substrates.

Conversion of multilayer graphene into continuous ultrathin sp³-bonded carbon films on metal surfaces.

Construction of 2D atomic crystals on transition metal surfaces: graphene, silicene, and hafnene.

Si(001) surfaces.

Nucleation and Early Stages of Layer-by-Layer Growth of Metal Organic Frameworks on Surfaces.

Alkane activation on crystalline metal oxide surfaces.

Multiscale treatment of theoretical mechanisms for the protection of hydrogel surfaces from adhesive forces.

Thermally induced growth of ZnO nanocrystals on mixed metal oxide surfaces.

On the theoretical description of weakly charged surfaces.

Process-specific mechanisms of vertically oriented graphene growth in plasmas.

Low Temperature Metal Free Growth of Graphene on Insulating Substrates by Plasma Assisted Chemical Vapor Deposition.

Theoretical perspectives on the infectiousness of Ebola virus disease.

Quantitation of microbial growth on surfaces.

Theoretical perspectives on ion-channel electrostatics: continuum and microscopic approaches.

Correlation of metal decoration and topochemistry on protein surfaces.

Self-assembly of strongly dipolar molecules on metal surfaces.

Formation of carbyne and graphyne on transition metal surfaces.

Salt-Sensitive Hypertension: Perspectives on Intrarenal Mechanisms.

Electrically Responsive Surfaces: Experimental and Theoretical Investigations.

Oxygen-induced self-assembly of quaterphenyl molecules on metal surfaces.

Riemann Surfaces of Carbon as Graphene Nanosolenoids.

Rapid evolution of quantitative traits: theoretical perspectives.

Asymmetric light reflectance from metal nanoparticle arrays on dielectric surfaces.

Towards design rules for covalent nanostructures on metal surfaces.