Oxygen-Promoted Chemical Vapor Deposition of Graphene on

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Oxygen-Promoted Chemical Vapor Deposition of Graphene on Copper: A Combined Modeling and Experimental Study Bharathi Madurai Srinivasan,†,□ Yufeng Hao,*,‡,□ Ramanarayan Hariharaputran,† Shanti Rywkin,§ James C. Hone,∥ Luigi Colombo,⊥ Rodney S. Ruoff,*,# and Yong-Wei Zhang*,† ACS Nano Downloaded from pubs.acs.org by UNIV OF SOUTH DAKOTA on 08/28/18. For personal use only.

†

Institute of High Performance Computing, A*STAR, Singapore 138632, Singapore National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China § Department of Science, Borough of Manhattan Community College, The City University of New York, New York, New York 10007, United States ∥ Department of Mechanical Engineering, Columbia University, New York, New York 10027, United States ⊥ Texas Instruments, Dallas, Texas 75243, United States # Center for Multidimensional Carbon Materials, Institute for Basic Science, Ulsan National Institute of Science and Technology, Ulsan 689-798, Korea ‡

S Supporting Information *

ABSTRACT: Mass production of large, high-quality single-crystalline graphene is dependent on a complex coupling of factors including substrate material, temperature, pressure, gas flow, and the concentration of carbon and hydrogen species. Recent studies have shown that the oxidation of the substrate surface such as Cu before the introduction of the C precursor, methane, results in a significant increase in the growth rate of graphene while the number of nuclei on the surface of the Cu substrate decreases. We report on a phase-field model, where we include the effects of oxygen on the number of nuclei, the energetics at the growth front, and the graphene island morphology on Cu. Our calculations reproduce the experimental observations, thus validating the proposed model. Finally, and more importantly, we present growth rate from our model as a function of O concentration and precursor flux to guide the efficient growth of large single-crystal graphene of high quality KEYWORDS: oxygen concentration, growth rate, nucleation density, phase-field model, chemical vapor deposition

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Single-crystalline graphene has been observed on both single-crystal and polycrystalline Cu surfaces from a single nucleus. Growing graphene on single-crystal Cu(111) is desirable since in this case the nuclei are rotationally aligned in comparison to other Cu crystal orientations. Growth on polycrystalline Cu or nonoriented crystals would require the control of the nucleation density to achieve large graphene single crystals since the presence of a large number of misoriented crystals would give rise to the formation of grain boundaries upon merging; grain “stitching” upon closure could

rowth of large single-crystalline graphene is an important research topic since its mechanical and electronic performances are superior to its polycrystalline counterpart.1−4 Among many growth techniques, chemical vapor deposition (CVD) on copper (Cu) substrates has attracted significant interest due to the ease of growing monolayers of graphene,5−8 high crystalline quality, and ease of transfer after growth in comparison to other substrate materials with a focus on growing large single-crystalline graphene.9−12 In these studies, the effects of various parameters, such as flow and pressure of precursor gases, temperature, the overall C:H ratio, Cu surface preparation, and pregrowth annealing,4,13−17 among other factors, were studied. © XXXX American Chemical Society

Received: June 12, 2018 Accepted: August 20, 2018

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DOI: 10.1021/acsnano.8b04460 ACS Nano XXXX, XXX, XXX−XXX

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Cite This: ACS Nano XXXX, XXX, XXX−XXX

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PHASE-FIELD MODEL The phase-field model consists of an order parameter ψ, which takes a value of 1 on the graphene island and −1 on the Cu substrate. For a concentration c of the active carbon (C) species, we define the concentration field u = c − ceq, where ceq is the equilibrium concentration. Using the free energy functional /(ψ ) given below,31

also give rise to low-angle grain boundaries in the case of Cu(111) because of nonflat surfaces.18,19 Therefore, it would be desirable to have a very low nucleation density and an increased growth rate of individual islands so as to grow single crystals in as short amount of time as possible to meet production and cost requirements. In addition, it is of great importance to understand various growth factors and their influence on the number of nuclei and the growth rate of graphene islands. Recent studies have shown that oxygen on Cu foil affects the production of large-area single-crystalline graphene islands significantly.8,20−22 It was found that the O species present in Cu surfaces (in “about the right concentration”) have two major effects: first, O reduces the nucleation density by passivating the active nucleation sites on the substrate surface; and second, O increases the growth rate of the islands by reducing the attachment barrier of C atoms at the graphene growth front. Kraus et al.22 showed that removal of the carbon present in the Cu substrate by oxidation a priori decreases the nucleation density of graphene to a large extent during CVD. They also showed that such a reduction is mainly caused by the removal of carbon from the substrate rather than the presence of O in the foil. Braeuninger-Weimer et al.23 also showed that pretreatment of the Cu foil by removing the extrinsic and intrinsic carbon impurities by oxidation significantly decreases the nucleation density of graphene during CVD growth. The concentration of O is thus a fundamentally important variable in enabling high graphene growth rates on Cu.19−25 Although the atomic scale effects of O are established, how the O species affect the growth and the resulting graphene films and how they interact with other variables during the growth process are essentially unknown. Up until now, most of the graphene has been grown in CVD chambers with poor vacuum control, and in most cases, there was always an oxygen (air) background pressure. Recently, Terasawa and Saiki25 investigated the role of intentional vapor phase O during the growth of graphene. They found that as the O2 partial pressure increased, the nucleation density on the Cu substrate is monotonically decreased, and a high growth rate was achieved, agreeing with results of Hao et al.,8 where the Cu was either preoxidized or doped with oxygen. Xu et al.19,20 further took advantage of O for ultrafast growth of graphene on Cu/oxide (silica and sapphire) substrates. These studies further highlight the importance of O and call for a complete understanding of the effects of O in growing large, singlecrystalline graphene. Phase-field models have proven helpful in understanding the dynamics and evolution of morphology of materials growing under various conditions26−29 and recently in the case of modeling graphene growth.8,19,30 Here, we employ a phasefield model incorporating the effect of O at the growth front to study in detail detailed dynamics of the growth and the resultant morphology of of graphene islands on a Cu(111) substrate. To test our model, we carry out CVD growth of graphene on both O-free (OF) and also O-rich copper (ORCu) to observe the effects of O on the growth rate and graphene island morphology. Our calculations not only agree with our CVD experimental observations but also provide important guidelines for the high growth rate of high-quality and large single-crystal graphene.

/(ψ ) =

∮ jijjkκ 2(∇ψ )2 − π1 cos[π(ψ − ψ0)]

y + λu{ψ + sin[π (ψ − ψ0)]}zzz d1 V {

(1)

the evolution equations are written as τψ

∂ψ δ/ =− ∂t δψ

(2)

and u 1 ∂ψ ∂u = D∇2 u − +F− 2 ∂t ∂t τl

(3)

Here, τψ is the characteristic attachment time of the active C species at the graphene step-edge on copper and τl is the mean lifetime. For typical CVD growth, τψ ≪ τl. The flux of the active C species arriving at the surface is F, κ2 corresponds to the step-edge energy of graphene on the copper surface, the diffusion coefficient of the active C species on Cu is given by D, λ is a dimensionless coupling constant, and ψ0 = 0 is the initial value of ψ. Clearly, the model parameters, such as τψ, F, and D, determine the growth morphology and growth rate. In this work, we focus on the growth of graphene islands by CVD growth on the Cu(111) substrate. We consider that the transport and diffusion are isotropic, and the anisotropy of graphene step energy determines the morphological symmetry of graphene islands. Hence, κ2 = k2{1 + εg cos(mθ)}, where k2 is the average step energy, εg is the strength of the energy anisotropy, and m represents the symmetry of the step energy. In our simulations, we assume that the substrate surface is single crystalline. In this work, we choose m = 6, which gives rise to hexagonal or six-lobe island shapes, prevalent in literature and our experimental works.8,32,33 Note that shape variations due to the Cu surface crystalline orientations were analyzed by Meca et al.30 As discussed above, O has been reported to reduce the attachment energy barrier at the graphene growth front (also called the edge) and to reduce the nucleation density.8,22,23,25 In our simulations, these two effects are treated separately. Since the basic functions of oxygen in graphene growth are not entirely clear, here, we select these two effects to examine the functions of oxygen in the ultrafast growth of graphene domains. Our previous study revealed that O was able to reduce the edge attachment barrier of C species, facilitate C incorporation at the growth edge, and accelerate graphene growth.8 The characteristic attachment time τψ is determined by the energy barrier for the attachment of C atoms and the concentration of O atoms at the graphene edge. Clearly, the smaller the attachment energy barrier, the smaller the τψ value; meanwhile, the higher the O concentration at the edge, the faster the graphene growth.20 In the following, we present a model that quantifies the relation of the graphene edge growth velocity with the attachment energy barrier and the concentration of the surface O atoms. B


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Figure 1. Change in the morphology of graphene islands from simulations with increasing O concentration for (a) cO = 0, (b) cO = 0.0005, (c) cO = 0.001, and (d) cO = 0.002. For all the cases, D = 5 and F = 0.0004. (e) Experimental graphene islands without O. (f−h) Experimental graphene islands with increasing O content on the Cu surface.

τC τψ = ÄÅ ÅÅ ÅÅ1 − f (cO) + f (cO) exp ÅÅÇ

ji ΔE zyz τO = τC expjjj− z j kBT zz k {

(4)

uGr τc

as

τC ÉÑ = ÑÑ [1 + aocO] ÑÑ ÑÑÖ

ψ

(9)

ΔE kBT

the characteristic time τψ decreases as cO increases. For example, using the experimental values of ΔE = 0.84 eV and cO = 0.0001,5−7 we see that the characteristic attachment time is reduced to τψ = 0.85τC at T = 1035 °C. Using eq 9 for τψ, we can rewrite eq 2 as τc

∂ψ δ= −[1 + aocO] ∂t δψ

(10)

To model the influence of cO on the growth rate of graphene islands on the Cu surface, we solve the coupled eqs 3 and 10.

RESULTS AND DISCUSSIONS A recent study by Zhang et al.35 has shown that apart from surface oxygen other parameters, including the partial pressure of methane, PCH4, and growth temperature, T, also significantly influence the ultrafast growth of single-crystalline graphene. Hence, here, we not only investigate the role of the surface O concentration, cO, but also those of flux, F, of carbon species, which depends strongly on PCH4, and the effect of diffusivity of C species, D, which depends on the growth temperature, the island growth rate, and morphology.

ÉÑ ÑÑ ÑÑ ÑÑÖ

( ) ΔE kBT

ΔE kBT

ΔE kBT

( ) From the above equation, we see that

where ao = exp

(6)

Using eq 4, we can recast eq 6 as ÄÅ ÅÅ ÅÅ1 − f (cO) + f (cO) exp Å Gr Å ρvn = u Ç τC

τC τψ = ÄÅ ÅÅ ÅÅ1 + cO exp ÅÅÇ

( )

(5)

1 − f (cO) Gr f (cO) Gr u + u τc τO

(8)

( ), we can rewrite τ

of 1035 °C and the fact that 1 ≪ exp

where ρ is the density of the graphene layer. In the case of ORCu, the O atoms at the growth edge can reduce the attachment barrier of the C species. Let the function f(cO) denote the ratio of the number of C atoms at the edge that are promoted by O atoms to the number of the total C atoms at the growth edge. Then, we can rewrite the above equation as ρvn =

ΔE kBT

From the experimentally measured growth rates and firstprinciples calculations,8 the growth activation energy was found to be 0.84 eV lower for the OR-Cu. From previous study,8 we know that the O atom has a critical role in reducing the attachment barrier and its concentration is about 10−2 at. %. Here, we choose f(cO) = cO. Using the growth temperature

where kB is the Boltzmann constant and T is the absolute temperature. Clearly, an increase in O concentration facilitates the attachment of the C species at the growth front and, thus, increases the growth velocity of the graphene island. In the following, we present our formulation to include the effect of surface O concentration cO on the growth rate in our model given in eqs 2 and 3. Let uGr be the concentration field of the C species at the growth front, which is defined as uGr = Ω(cGr − Gr cCu eq ), where c is the density of C species at the growth front, Cu ceq is the equilibrium density of the C species on Cu substrate, and Ω is the atomic volume. In the absence of surface O atoms, the first-order growth velocity vn can be written as34 ρvn =

ÑÉ

( )ÑÑÑÑÑÑÖ

Let τψ = τc be the attachment time of the C species in the absence of O and τψ = τO be that in the presence of O. If EC and EO are the corresponding energy barriers, the energy barrier reduction is ΔE = EC − EO. Then, we can write τO as

(7)

From eq 7, we can define the characteristic time τψ as C


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Figure 2. Change in the morphology of graphene islands from simulations with flux for (a) F = 0.02, (b) F = 0.002, (c) F = 0.0008, and (d) F = 0.00005. Note that a simulation box of 1024 × 1024 is used for (d). For all the cases, D = 5 and cO = 0.001. (e−h) Experimental graphene islands with decreasing PCH4.

Role of Oxygen Concentration cO. According to eq 10, an increase in cO increases the edge attachment rate. Hence, it is expected that an increase in cO will cause the growth regime to change from an attachment-limited regime toward a diffusion-limited regime.8 The simulation results at various values of cO for τc = 4.0, F = 0.0004, and D = 6 are given in Figure 1(a)−(d). In these panels, cO is increased from 0 (Figure 1(a)) to 0.001 (Figure 1(d)). As the cO value increases, the hexagonal shape (Figure 1(a)) changes to a star-like pattern (Figure 1(b)). Upon further increase of cO, a dendritic structure develops as shown in Figures 1(c) and (d). Experimentally, we observe the same results as the oxygen concentration, cO, is increased, as shown in Figure 1(e)−(h). When we increase the O2 exposure time from 5 s to 2 min, the graphene island shape changes from hexagonal to star-like and then to dendritic (Figure 1(e) and (d)). Clearly, the simulated and experimental graphene island morphological evolution show the same qualitative behavior as the O concentration is increased. In particular, both our simulation and experimental results show that for a given deposition flux and temperature an increase in the O exposure time causes the growth dynamics toward a diffusion-limited regime.8 Role of Deposition Flux. The evolution of graphene island morphology with a decrease in deposition flux F is shown in Figure 2(a)−(d). For the simulation with cO = 0.001 and D = 5, it is seen that the graphene island starts from a mixed rounded hexagonal island at F = 0.02 (Figure 2(a)) then forms a star-shaped island at F = 0.002, as shown in Figure 2(b). When F is decreased further, the island becomes dendritic at F = 0.0008, as shown in Figure 2(c). For a very small value of F = 0.00005, the island takes a hexagonal shape with dendritic edges, as shown in Figure 2(d). In our experiments, the partial pressure of the CH4 precursor determines the deposition flux. For a given O2 exposure time and growth temperature, a decreasing deposition flux or reducing CH4 partial pressure causes the island morphology to transition from a mixed rounded hexagonal island to a star island, then to a dendritic island, and further to a hexagonal island with dendritic edges as shown in Figure 2(e)−(h), in qualitative agreement with the simulation results. In addition, for a given O2 exposure time and growth temperature, both our

simulation and experimental results suggest that a decrease in the CH4 partial pressure or the deposition flux leads the island shape to become more dendritic, thus causing the growth regime to move from an edge-attachment-limited regime toward a diffusion-limited regime again, consistent with the simulation results. Role of Diffusivity. Here, we study the effect of the C diffusivity on the graphene island morphology. In general, the diffusivity D is dependent on the temperature according to the Arrhenius equation. Thus, it is expected that the diffusivity, D, of C species on the Cu surface should depend on the temperature. The island morphology simulated at D = 8 is shown in Figure 3(a), and that at D = 4 is shown in Figure 3(b) with cO = 0.001 and F = 0.0008 for the two diffusivity simulations. It is seen that as D decreases, the island goes from a star shape to a more dendritic star shape. By comparing these simulated morphologies obtained at high and low diffusivities as shown in Figure 3(a) and (b) with the experimental results

Figure 3. Change in the morphology of the graphene island with diffusivity D. (a, b) Change in the simulated morphology with D = 8 and D = 4 for cO = 0.001 and F = 0.0008. Here, the simulation box size is 256 × 256. (c, d) Graphene islands observed experimentally at two different temperatures. D


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simulation results suggests that the process space of the combined effects of oxygen concentration and deposition flux on the growth morphologies beyond the experimental ranges could be explored. The predicted morphologies for wider ranges of cO, F, and D are listed in Tables 1−3 and S1 in the

at high and low temperatures as shown in Figure 3(c) and (d), respectively, we see that they follow the same trend. It is noted that the widths of the domain interfaces shown in Figures 1−3 are different. This difference arises from our numerical solutions: We have used the same time and space steps in our simulations, but the time and space scales under different growth conditions are different. However, our numerical results have shown that further reduction in the time and space steps does not change the growth morphology and growth rate. Role of Nucleation Density. In the above simulations, we used a single pre-existing nucleus to study the role of the model parameters. Here, we present the results of the simulations at different nucleation densities. In our simulations, the nucleation density is changed by adding more pre-existing nuclei (each with a 10 unit radius) in a simulation box of dimensions 2048 × 2048. Figure 4(a) and (b) show the

Table 1. Morphologies of Graphene Islands Predicted from Phase-Field Simulationsa

a F is the deposition flux and cO is the oxygen concentration. D = 5 for all the simulation cases. * indicates that the simulation box size is 1024 × 1024.

Figure 4. (a and b) Isotope-labeled Raman maps for graphene island growth from experiments. Simulation results for the evolution of graphene islands with (c) two nuclei and (d) 20 nuclei.

Supporting Information. These results show that when F is very high, the deposition flux arriving at the edges completely dominates the growth, and hence a circular island is always observed, as shown at the top right column of Table 1. As F is

graphene island shape as obtained by Raman mapping of graphene grown using sequential isotopes of carbon, 12CH4 and 13CH4, where some of the nuclei have fused together during growth. We also plotted the growth fronts from our simulations in Figure 4(c) and (d). A similar fusion of islands can be seen in the case of two pre-existing nuclei (Figure 4(c)). In Figure 4(d), we started with 20 nuclei where most of the islands had fused together with the adjacent islands, similar to those in the experiments (Figure 4(b)). Such fusion of islands, especially in Figure 4(a) and (c), clearly resulted in polycrystalline graphene with multiple grains and grain boundaries, whereas in the case of Figure 4(b) and (d), it is possible that some islands fused into a single grain given the alignment of the hexagonal grains. For a higher nucleation density, we see more fused islands and thus more grains in polycrystalline graphene. Hence, our simulations not only produce the experimental observations and but also highlight the importance of controlling the nucleation density in order to achieve large-area, single-crystal islands, where grain boundaries are minimized. Role of Oxygen Concentration, Deposition Flux, and Diffusivity. The agreement between our experimental and

Table 2. Change of Graphene Island Morphology with Flux (F) and Diffusivity (D)a

a

As D is dependent on temperature, an increase in D is related to an increase in temperature. An increase in D results in a more regular shape. Here cO = 0.001 and * indicates that the simulation box size is 1024 × 1024. E


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of step energy anisotropy and promotes the dendritic feature of the island, as shown in Figure 2 and Tables 1, 3, and S1 in the Supporting Information. The scale bars for these simulation figures in Tables 1−3 and S1 have not been included since, due to small size of the figures, the scale bars are not clearly visible. Here, we would like to point out that for the entire range of PCH4 values used in our experiments the fully circular morphology observed in the simulations was not observed. However, the fully circular morphology was observed by Xu et al.20 The reason for this is that in the experiments reported by Xu et al.20 the PCH4 is much higher than those used in our experiments. Our simulations clearly show the important roles played by the various growth parameters and their relationship in controlling the island morphology during growth. It is expected that Tables 1−3 and S1 may serve as a useful guide for achieving large-area, high-quality graphene single crystals. Growth Rate. From eqs 3 and 10, it is seen that the growth rate of graphene islands is affected by the attachment energy barrier, the growth temperature, and the O concentration at the growth front. Our simulations show that, in general, the island lateral size increases linearly with time. An example is presented in Figure 5(a); the growth of a single graphene island is shown for F = 0.0004 and cO = 0.001, starting from t = 2τψ to t = 42τψ in steps of 8τψ. The graphene island evolves from initially a 6-fold star-like shape to a 6-fold dendritic island in a linear manner, as confirmed by the linear growth of the island radius with time, shown in Figure 5(c) with (+). This linear growth of the island morphologies agrees with the isotope-labeled Raman maps of the growing graphene islands in our experiments, as shown in Figure 5(b). The domain radius of the graphene islands from our simulations is shown in Figure 5(c) for a single nucleus (+) and two nuclei (*), with the same parameters used in Figure 5(a). The domain radius reported here is the radius of the circle of the same area as the total area of the graphene island(s). The linear growth for the single nucleus is in excellent agreement with the radial growth rate from the experiments at the early stage where the growth of the graphene islands is not influenced by the adjacent islands.8 In the case of two nuclei, when the islands are far apart at the initial stage, the radius shows a linear growth. As the domains grow and approach each other, the growth of individual islands slows down as the two islands start to compete for the same flux of C species. A similar slowdown of growth is also observed in our experiments as the nucleation density increases.8

Table 3. Change of Graphene Island Morphology with Oxygen Concentration (cO) and diffusivity (D)a

a

An increase of cO results in more dendritic morphology, and the reverse is true for increasing D. Here F = 5 × 10−4.

reduced, for a given D, the island shape is increasingly controlled by the graphene step-energy anisotropy. As a result, a regular hexagon is observed. Upon further decreasing F, the growth becomes diffusion controlled and a dendritic shape begins to develop. For very low values of F, as the island grows, there is sufficient time for the diffusion of C species, resulting in regular shape, albeit with rough edges. These trends can be clearly seen from the right column to the left column in Tables 1 and S1 for all cO. Similarly, we can also predict the changes in graphene island morphology with the parameters F and D and the parameters cO and D. For example, the predicted morphologies for a range of the parameters F and D with cO = 0.001 are given in Table 2, and for a range of the parameters cO and D with F = 5 × 10−4 are given in Table 3. In general, for a given cO, the morphology of a growing island is determined by the ratio of deposition flux and diffusivity, F/D, as evidenced by the morphologies in Figures 1−3 and Tables 1−3 and S1. When the ratio of F/D is high, the growth falls into the attachment-limited regime; as a result, the effects of step energy anisotropy and the dendritic feature tend to be suppressed. However, when the ratio of F/D is low, the growth is in the diffusion-limited regime, and as a result, the effect of step energy anisotropy is strong and the dendritic feature becomes pronounced. When the F/D ratio is fixed, the attachment rate at the growing edge is increased with increasing cO, causing a shift from the growth-limited regime toward the diffusion-limited regime. This enhances the effect

Figure 5. (a) Growth of graphene islands from simulations with F = 0.0004 and cO = 0.001 from t = 2τψ to 42τψ in steps of 8τψ and (b) isotope-labeled Raman maps from experiments. (c) Domain radius of a single nucleus (+) and two nuclei (*) as a function of time. F


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Figure 6. (a) Growth rate of a single nucleus as a function of F for cO = 0.01 (+), cO = 0.004 (×), and cO = 0.0 (○). (b) Growth rate as a function of flux for various nucleation densities at cO = 0.001.

and multiple nuclei. For the case of multiple nuclei, the growth rate is averaged over all the islands. In all of these cases, the growth rate increases with flux as expected. But, for a given flux value, we see that the growth rate decreases with increasing nuclei density. As the nucleation density increases, more islands compete for the same flux of C atoms, and hence the effective flux for each of the islands decreases, leading to the reduction in the growth rate of individual islands.

The good matches between our simulation and experimental results both in the early stage and in the presence of adjacent nuclei allow us to further examine the graphene growth rates. To achieve the conditions for the ultrafast growth of large graphene single crystals, it is essential to study the growth rate of individual islands at various growth conditions. From eq 10, we see that a decrease in the attachment energy barrier and an increase in diffusivity or O concentration can independently increase the growth rate. In various experiments conducted on the CVD growth of graphene on Cu foil, the reported growth rate can vary remarkably from 0.03 to 60 μm/s, with the highest being 2000 times the lowest.20 The ultrafast growth rate reported by Xu et al.20 was attributed to the fact that the Cu foil was on an oxide substrate, which continuously supplied O to the growth surface, and the predominant role of O was assumed to reduce the energy barrier for dissociation of CH4 on the Cu foil, which resulted in a high carbon flux available for growth and hence increased the growth rate. Here, we perform simulations by changing both the oxygen concentration and the carbon flux to examine the roles of both carbon flux and O concentration in the fast growth of single-crystalline graphene. Figure 6(a) shows the single island growth rate vs the flux F at three O concentrations, cO = 0.01 (+), cO = 0.004 (×), and cO = 0.0 (○). It is clear that an increase of either cO or F is able to lead to an increase in the growth rate. For a constant F, an increase in cO by 1 order is able to result in roughly 1 order of increase in the growth rate, while for a constant cO, an increase in F by 2 orders of magnitude is able to result in an increase in the growth rate of about 1 order of magnitude. Below, we would like to make a more quantitative comparison between the simulated growth rate and that measured experimentally.20 To do so, we use the lowest growth rate (0.03 μm/s)20,36 to rescale the lowest growth rate at F = 0.0002 and cO = 0.0 from our simulation, as shown in Figure 6(a). Using this scaling, we see that the growth rate can be increased to 30 μm/s at F = 0.8 and cO = 0.01. Hence the highest growth rate obtained at F = 0.8 and cO = 0.01 is about 3 orders higher than the lowest growth rate at F = 0.0002 and cO = 0.0 (see Figure 6). These results clearly show that the increase in both carbon flux and oxygen mechanism can adequately explain the increase in the growth rate by 3 orders of magnitude observed in the experiments,8,20,36 and the increases in both the flux F and the O concentration cO are essential to capture the ultrafast growth observed in experiments. As mentioned above, the growth rate of individual islands is also affected by the nucleation density. Figure 6(b) shows the change in growth rate with flux for the cases of a single nucleus

CONCLUSION We have performed phase-field simulations on the CVD of graphene to investigate the growth dynamics and evolution of the islands on Cu in the presence of surface O. We have modified the phase-field model by explicitly considering the reduction of the attachment barrier at the growth front due to the presence of O and also its concentration. The simulations of the morphology evolution and growth rate agree well with those from our and also others’ experimental results. Building on this, we performed systematic phase-field simulations, which are well beyond the reach of current experiments, to reveal a more complete picture on the growth of graphene islands under various conditions. It is expected that our detailed simulation results presented here may serve as a guide in choosing optimal conditions for the fast production of large, single-crystalline graphene by the CVD method. METHODS Simulation Methods. We solve the evolution eqs 3 and 10 using a discrete Fourier transform37 with periodic boundary conditions in the x and y axes. The unit of length is defined using κ2 = 1, and the time is measured in units of τψ.38 In the simulations, we choose k2 = 2, εg = 0.01, τl = 1 000 000, λ = 10, Δx = Δy = 1, and Δt = 0.01. We start with a seed nucleus with a radius of 10 units and a simulation box of 256 × 256 unless otherwise mentioned. In all the simulations, we use ΔE = 0.84 eV, T = 1035 °C, and τc = 4.0. Experimental Procedure. We use a a hot-wall low-pressure CVD system for graphene growth. Briefly, we loaded 25 μm thick Cu foils (Alfa-Aesar, product number 46365) into the one-inch-diameter quartz tube at the center of the furnace. We then evacuated the tube to a vacuum of less than 10−6 Torr, heated the furnace to 1035 °C under a H2 flow of 10 sccm, and annealed the Cu foil for ∼20 min at a total pressure of about 1 × 10−1 Torr. Methane gas was then flowed into the system with a flow rate ranging from 0.1 to 10 sccm (the PCH4 range is from 1 × 10−3 to 5 × 10−2 Torr) for the growth of graphene and the growth duration varying from 10 to 800 min. The OR-Cu was exposed to pure O2 for a duration ranging from 10 s to 5 min prior to the growth step (CH4 flowing), and the corresponding PO2 was 1 × 10−3 Torr. We cooled the system after growth to room temperature with the H2 and CH4 flows. We characterized the grown graphene islands on the Cu foil by scanning electron microscopy and Raman G


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spectroscopy. The typical Raman spectrum (Figure S1 in the Supporting Information) of the graphene sample has clearly shown its high crystalline quality.

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.8b04460. Morphologies of the graphene islands predicted by the phase-field model for a range of values of flux, oxygen concentration, and diffusivity and a Raman spectrum of graphene after being transferred onto Si substrates (PDF)

AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected]. *E-mail: ruoffl[email protected]. *E-mail: [email protected]. ORCID

Yufeng Hao: 0000-0001-7758-5244 Author Contributions □

B. M. Srinivasan and Y. Hao contributed equally to this work.

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The work was supported by National Key R&D Program of China (2018YFA0305800), National Science Foundation of China (51772145), and National Thousand Young Talents Program. This work in Singapore was supported in part by a grant from the Science and Engineering Research Council (152-70-00017), the Agency for Science, Technology and Research (A*STAR), Singapore. The computing resources were obtained from the A*STAR Computational Resource Centre, Singapore. The work in the United States was supported by South West Academy of Nanoelectronics of the Nanoelectronics Research Initiative. We thank Z. Han for technical assistance in preparing Table S1. REFERENCES (1) Huang, P. Y.; Ruiz-Vargas, C. S.; van der Zande, A. M.; Whitney, W. S.; Levendorf, M. P.; Kevek, J. W.; Garg, S.; Alden, J. S.; Hustedt, C. J.; Zhu, Y.; Park, J.; McEuen, P. L.; Muller, D. A. Grains and Grain Boundaries in Single-Layer Graphene Atomic Patchwork Quilts. Nature 2011, 469, 389−392. (2) Suk, J. W.; Mancevski, V.; Hao, Y.; Liechti, K. M.; Ruoff, R. S. Fracture of Polycrystalline Graphene Membranes by In Situ Nanoindentation in a Scanning Electron Microscope. Phys. Status Solidi RRL 2015, 9, 564−569. (3) Pantelic, R. S.; Suk, J. W.; Hao, Y.; Ruoff, R. S.; Stahlberg, H. Oxidative Doping Renders Graphene Hydrophilic, Facilitating Its Use as a Support an Biological TEM. Nano Lett. 2011, 11, 4319−4323. (4) Yu, Q.; Jauregui, L. A.; Wu, W.; Colby, R.; Tian, J.; Su, Z.; Cao, H.; Liu, Z.; Pandey, D.; Wei, D.; Chung, T. F.; Peng, P.; Guisinger, N. P.; Stach, E. A.; Bao, J.; Pei, S. S.; Chen, Y. P. Control and Characterization of Individual Grains and Grain Boundaries in Graphene Grown by Chemical Vapour Deposition. Nat. Mater. 2011, 10, 443−449. (5) Li, X.; Cai, W.; An, J.; Kim, S.; Nah, J.; Yang, D.; Piner, R.; Velamakanni, A.; Jung, I.; Tutuc, E.; Banerjee, S. K.; Colombo, L.; Ruoff, R. S. Large-Area Synthesis of High-Quality and Uniform Graphene Films On Copper Foils. Science 2009, 324, 1312−1314. H


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Oxygen-Promoted Chemical Vapor Deposition of Graphene on

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