Morphology Evolution of Graphene during Chemical Vapor Deposition

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Morphology Evolution of Graphene during Chemical Vapor Deposition Growth—A Phase Field Theory Simulation Jianing Zhuang, Wen Zhao, Lu Qiu, John H. Xin, Jichen Dong, and Feng Ding J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00761 • Publication Date (Web): 28 Mar 2019 Downloaded from http://pubs.acs.org on March 28, 2019

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The Journal of Physical Chemistry

Morphology Evolution of Graphene during Chemical Vapor Deposition Growth—A Phase Field Theory Simulation Jianing Zhuang†, Wen Zhao†,‡, Lu Qiu†,‡,§, John Xin†, Jichen Dong*,†,‡, Feng Ding*,†,‡,§ † Institute ‡ Center

of Textiles and Clothing, Hong Kong Polytechnic University, Hong Kong, China

for Multidimensional Carbon Materials, Institute for Basic Science, Ulsan, Republic of

Korea § School

of Materials Science and Engineering, Ulsan National Institute of Science and Technology, Ulsan, Republic of Korea

ABSTRACT: In chemical vapor deposition (CVD) growth, depending on the growth condition, graphene islands present various shapes, such as circular, hexagonal, square, rectangular star-like and fractal. We present a systematic phase field model (PFM) study to explore the role of three key factors, carbon flux, precursor concentration on metal surface, and diffusion of carbon precursors, on the determination of the graphene domain shape. We find the size of the depletion zone, i.e., the area with carbon precursor concentration gradient around the circumference of the growing graphene island, is of critical importance. In case of no depletion zone or the size of depletion zone is much larger than that of the graphene island, the graphene island will present a shape of regular hexagon. While star-like graphene islands will form if the size of the depletion

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zone is compatible to that of the graphene island. Further increasing the size of the graphene island will lead to a fractal-like graphene island with multi-scaled branches. Although extremely small depletion zone will lead to a graphene island in regular shapes, its edges are found to be rough. The three key parameters affects the shape of graphene by tuning the size of depletion zone. Based on this study, a series experimental puzzles are properly explained and the conditions of growing high quality graphene emerge.

INTRODUCTION Graphene1, the flagship of two-dimensional (2D) materials, has attracted great interest for a decade because of its unique properties2-3 and promising applications4-6. To synthesize large-area highquality graphene films is of top priority towards its high-end applications. The fast chemical vapor deposition (CVD) growth of graphene, normally on a catalytic metal substrate7-8, has been proved most promising for large-area high-quality graphene production at a reasonable low price. For example, on Cu substrates, the growth rate of single-crystal graphene has been improved to be 60 μm/s9 and wafer-sized graphene has been synthesized via different approaches10-11. Besides Cu, many other transition metals or their alloys have been used to catalyze graphene CVD growth and various growth behaviors are observed. Based on previous theoretical calculations12, these metal substrates can be divided into two categories, the less active coinage metals (e.g., Cu, Au and Ag) and the more active late-transition metals (Ni, Co, Fe, Pd, Pt, Ru, Rh, Ir, etc.). The grown graphene on the latter ones usually present regular domain shape, such as hexagons with a six-fold symmetry, triangles with three-fold symmetry, or rectangles with a two-fold symmetry, on Ni13, Co14, Pt15, Ir(111)16, and Ru(0001)17 surfaces but star-like or fractal shaped graphene islands are


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rarely seen. However, despite the regular shaped graphene domains grown under certain conditions18, a variety of concave shapes, e.g., fractal or star-like ones, were frequently observed on Cu10, 19-24 and Au25 substrates. The formation of star-like or fractal graphene island is as a consequence of diffusion-limited growth, where a concentration gradient appears around the edge of the domain and a protrusion of the domain will grow faster because of the increased carbon concentration around it. However, the detailed mechanism that governs the graphene morphology evolution in the CVD growth is still pending. For example, varying carbon flux, carbon precursor diffusion or the concentration of precursor on the substrate could affect the concentration gradient significantly but which one plays the dominating role and how do they interplay with each other during graphene CVD growth are far from well understood. To achieve a deep understanding on the mechanism that governs the graphene domains’ evolution, we turn to the help of phase field theory, a mathematical model for solving interfacial problems. The central idea of PFM is to use an order parameter to distinguish different phases and reproduce the interfacial dynamics, which is powerful to study the morphology evolution during crystal growth26-30. Compared to other methods, such as density functional theory (DFT), molecular dynamics (MD) and kinetic Monte Carlo (KMC) simulations, the most significant advantage of PFM simulation is the very large crystal size that it can deal with, by neglecting the atomic details of the structure. In Ref.20, the authors explained different graphene morphologies on pure Cu and Cu-oxidized substrates, respectively, by varying the carbon precursor flux and the characteristic time of precursor attachment in the PFM. In Ref.31, the authors used PFM to obtain various nonregular shapes by assuming the anisotropy of diffusion of carbon species on the Cu substrate. In Ref.32, a PFM simulation is used to explain different supply of carbon species in single- and bilayer graphene growth. In Ref.9, the PFM results showed that an increase of carbon flux leads to a


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shape evolution from fractal to regular polygon. Although many theoretical efforts have been dedicated to understand the graphene domain shape evolution, a systematic theoretical exploration haven’t been done and the questions, such as why fractal-like graphene domains only appear on Cu or Au surfaces and, under which conditions the domains may change from fractal to regular shape on Cu surface, haven’t been well answered yet. The present paper aims to use PFM simulations to give a clear picture on graphene domain evolution. By studying the effects of three important parameters, carbon flux, precursor concentration on metal surface, and diffusion of carbon precursors, we systematically explored the necessary conditions of forming fractal-like graphene domains and the parameter space of forming various shaped graphene domains. METHODS In the PFM of graphene CVD growth, we regard the free carbon species on metal substrate and the graphene domain as two phases, characterized by the order parameter 𝜓 (𝜓 = -1 for free carbon species on metal substrate and 𝜓 = +1 for graphene). The order parameter 𝜓 = 𝜓(𝑥,𝑦,𝑡) is a function defined in the 2D space which includes the effects of concentration field, free energy, symmetry, diffusion, etc. It varies smoothly between phases with a diffused interface of finite width. By solving the equation

∂𝜓 ∂𝑡

= 𝑓(𝜓), we can obtain the evolution of phase interface. The

phase field simulation in the present paper is in accordance with Ref.9, with a slight modification by physical consideration. The coupled PFM equations for 𝜓 and the concentration field 𝑐 read (1 ∂ ∂𝜓 ∂ ∂𝜓 ∂𝜓 𝜏𝜓 = ― 𝜅𝜅′ + 𝜅𝜅′ + ∇ ∙ (𝜅2∇𝜓) + sin (𝜋𝜓) + 𝜑(𝑐 ― 𝑐𝑒𝑞){1 + cos (𝜋𝜓)} ∂𝑡 ∂𝑥 ∂𝑦 ∂𝑦 ∂𝑥 )

(

) (

)


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(2

∂𝑐 1∂𝜓 = 𝐷∇2𝑐 + 𝐹↓ ― 𝐹↑ ― ∂𝑡 2 ∂𝑡

)

In Eq. (1), 𝜏𝜓 is the characteristic time of attachment of the carbon species. 𝜅2 is the gradient energy term which includes the anisotropy of the graphene edge energy by 𝜅2 = 𝑘2

{1 + 𝜀𝑔cos (𝑛𝜃)}, where 𝑘 is the constant average interface energy density, 𝜀𝑔 the strength of the anisotropy, 𝑛 the number of folding of symmetry which equals 6 for six-fold anisotropy, and 𝜃 = ∂𝑦𝜓

∂𝜅

tan ―1 ∂𝑥𝜓 is the angle between the grain edge and the x-axis. 𝜅′ ≡ ∂𝜃. 𝜑 is a coupling constant in the PFM double-well potential, corresponding to the barrier height between 𝜓 = -1 and 𝜓 = +1, and 𝑐𝑒𝑞 is the equilibrium concentration of carbon species when graphene and free carbon species coexist in equilibrium. In Eq. (2), 𝐷 is the diffusion coefficient of the carbon species, 𝐹 the flux and 𝜏𝑠 the mean lifetime of carbon species on the surface. In the last term, the factor -1/2 denotes that the unit of concentration must be monolayer (ML). We denote 𝒄∞ as the concentration at infinite distance, which is also the saturation concentration of the carbon species on Cu substrate. We fix 𝑐∞ = 3𝑐𝑒𝑞 in our calculation. This consideration is based on the La Mer theory of nucleation33 that is also experimentally verified in graphene growth34, and we assume that 𝑐∞ is the same order of magnitude as nucleation concentration. The incoming flux of the carbon species arriving at the metal surface is defined as 𝐹↓ =

𝒄∞

𝝉𝒔 ,

𝒄

and the outcoming one as 𝐹↑ = 𝝉𝒔. Both 𝐹↓ and

𝐹↑ flux are assumed to exist only in bare metal substrate. The equations are discretized in both space and time, which is simulated on a 512×512 discrete lattice, with the spatial and time mesh chosen as Δ𝑥 = Δ𝑦 = 1 and Δ𝑡 = 0.01. An exception is made for the simulation shown in Figure 1, where a 1000×1000 discrete lattice is used. For each


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simulation, the initial configuration is a circular grain with radius 𝑟(𝑡 = 0) = 10 at the center of the lattice, and the initial concentration 𝑐(𝑡 = 0) = 𝑐∞ = 3𝑐𝑒𝑞 everywhere. The fixed parameters (dimensionless) in our simulations are: 𝜏𝜓 = 10, 𝑘 = 2, 𝜀𝑔 = 0.04, and 𝜑 = 200, and we generally adjust 𝐷, 𝐹↓, and 𝑐𝑒𝑞. RESULTS OF PFM SIMULATION Firstly, let’s simulate the evolution of a graphene island during growth. We take a small circular graphene domain as a seed to begin the simulation. Figure 1a shows the evolution of domain size and shape, under a typical self-limited growth condition (equilibrium precursor concentration 𝑐𝑒𝑞 = 0.01, diffusion coefficient D = 12, and incoming carbon flux 𝐹↓ = 0.015). In the figure, domains with no larger than 1/32 coverage are properly zoomed in to make clear views. Figure 1b shows the corresponding local concentration 𝑐 during the growth. Interestingly, we find that during the graphene growth, as accompanied by the decrease of the ratio of the length of depletion zone (L) to the diameter of the graphene island (D), the graphene island changes from a regular hexagon to a start-like shape and then to a fractal shape with small branches and finally to a hexagon with very rough edges. Here, L is defined as L= x2-x1, where c(x1) and c(x2) in the concentration profile lines shown in Figure 1b equal to cmin+0.1×(cmax-cmin) and cmax-0.1×(cmax-cmin), respectively, with both x1 and x2 ≥500, and cmin/max to be the lowest/highest precursor concentration along the concentration profile. D is defined as the distance between two opposing vertices of the graphene island. It can be seen that, at the initial stage (L/D ~ 0.42), the graphene island evolves to a hexagonal shape. With the growth of the graphene island (during which L/D reduces from 0.42 to 0.13), star-like graphene island is formed. During further growth of the graphene island (where L/D reduces from 0.13 to 0.09), the protrusions along the circumference of the graphene island


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become more obvious, and small branches are formed. Finally, if the graphene island grows large enough (L/D decreases from 0.09 to 0.01), numerous branches along the circumference of the graphene island are formed, and the hexagonal graphene island shows very rough edges, with the distance between two neighboring branches at the scale of L. As will be discussed in detail below, the morphology evolution of the graphene island is due to the change of precursor concentration distribution along the island circumference, as driven by L/D.

Figure 1. Phase field simulations of graphene shape (a) and concentration (b) evolution from regular to fractal as the domain size increases. Domains no larger than 1/32 coverage are properly zoomed in to make clear views (upper insets). Selected areas (red rectangles) in the domains with a 1/8 and 1/2 coverages are zoomed in to clearly show the rough edges. Panels from left to right respectively show the size reaching 1/2𝑛 (𝑛 = 9, 8, …,1, except 2) of the simulation unit cell, with fixed parameters, equilibrium concentration 𝑐𝑒𝑞 = 0.01, diffusion coefficient 𝐷 = 12, and incoming flux 𝐹↓ = 0.015. In this simulation, 1000×1000 grids are used. In (b), the concentration profile is shown along the line y=500 at the map, with the y axis for the profile ranging from 0% to 3.25%. In addition, L/D is also shown below (b). During the growth process, L shows no obvious change, with a value of ~10.


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Figure 2a and 2b respectively present the domain shapes and concentration of the carbon precursor on the substrate, simulated with different combinations of equilibrium precursor concentration 𝑐𝑒𝑞 (or 𝑐∞ as the ratio of 𝑐∞/𝑐𝑒𝑞 = 3 was maintained in the simulation) and incoming carbon flux 𝐹↓ with a fixed diffusion coefficient, D = 12. We can clearly see that, high 𝐹↓ and low 𝑐𝑒𝑞 lead to regular graphene shape with a six-fold symmetry while low 𝐹↓ and high 𝑐𝑒𝑞 result in fractal shape. In first three rows, or at a low 𝐹↓, increasing the 𝑐𝑒𝑞 gradually tunes the domain shape from hexagon to star-like, and then to fractal-like. When 𝐹↓ is large enough, no depletion zone (the area with carbon precursor concentration gradient) appears around the graphene island and only regular graphene islands are formed. In Figure 2b, we can see that the formation of non-regular graphene shape is always related to the obvious concentration gradient, where the concentration at edge is lower than 𝑐∞. Based on this we can understand the above results qualitatively. With a large carbon flux, all the consumed carbon precursors around the edge of graphene can be easily replaced by the precursor deposition from gas phase and, therefore, no significant depletion zoon or concentration gradient will be formed around a growing graphene. So, the grown graphene islands are in hexagonal shape due to the six-fold symmetry of the graphene. At a low carbon concentration, i.e. smaller 𝑐𝑒𝑞 or 𝑐∞, the growth of graphene must be very slow and, therefore, the small amount of consumed carbon precursors on the surface can be easily replaced by the carbon flux. Thus, there will be no significant concentation gradient around the edge of a growing graphene. So, the regular shaped graphene islands tend to be formed. At high 𝑐𝑒𝑞 and low carbon flux, the carbon precursors consumed by graphene growth around the island can not be efficiently supplemented by carbon flux. Consequently, an obvious carbon


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precursor concentration gradient is developed around the circumference of the graphene island, which leads the island to evolve to be fractal.

Figure 2. Phase field simulations with fixed D = 12 and varying 𝐹↓ and equilibrium carbon precursor concentration 𝑐𝑒𝑞 (or saturated concentration 𝑐𝑒𝑞). Simulated graphene domains (a) and corresponding precursor concentration distribution (b).

Figure 3a and 3b respectively present the graphene islands and the corresponding distribution of precursor concentrations on the metal surface simulated at different diffusion coefficient D and incoming carbon flux 𝐹↓ but fixing a fixed equilibrium concentration (𝑐𝑒𝑞 = 2%). In the first three rows, or at a lower 𝐹↓, we can see that graphene islands are in fractal shapes at a lower D while the shape gradually becomes star-like and then hexagonal with the increase of D,


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which supports that the diffusion-limited growth facilitates the fractal shaped graphene islands. While, in the fourth and fifth rows, or at a higher 𝐹↓, a surprising transition with the increase of D from very small to very large (from 6 to 12,800) is shown. The simulated graphene is in a hexagonal shape at a very large D due the fast diffusion of the carbon precursor on the substrate, as expected. Keeping decreasing D gradually leads to a transition to star-like and fractal domains. But, surprisingly, at a very small diffusion coefficient, the simulated graphene presents the hexagonal shape again. In the concentration map, we can see that an obvious depletion zoon appears around each star-like or fractal graphene island with mediate diffusion coefficient D. As D decreasing, although the slow diffusion of carbon precursor on the substrate lead to a large concentration difference near the graphene edge and at a far area, the width of the depletion zoon becomes smaller and smaller simultaneously. Finally, the depletion zoon disappears at an extremely low diffusion rate and the shape of the simulated graphene becomes regular hexagonal. This result clearly shows that the size of the depletion zoon around the graphene domain is of critical importance for the formation of star-like or fractal shaped graphene islands.


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Figure 3. The phase field simulations with fixed 𝑐𝑒𝑞 = 2% and varying 𝐹↓ and D. The simulated graphene islands (a) and the corresponding precursor concentration on the substrate (b).

DISCUSSIONS


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Figure 4. Upper panels are the concentration maps of phase field simulations with fixed 𝑐𝑒𝑞 = 2% and varying 𝐹↓ and D. Lower panels are experimental observations21 (Copyright © 2013, Springer Nature).

In Figure 4, we show a comparison between the typical simulation results and experimental observations21, from which a perfect agreement of their shapes is shown. The comparison validates our simulation and reveals the concentration gradient around each graphene islands that cannot be seen experimentally35. From this we demonstrate that the width of the depletion zone plays a central role in the shape determination of the graphene islands. As each protrusion of a fractal structure corresponds to a large concentration area, the distance between two neighboring protrusions corresponds to the width of a typical depletion zone. Based on the size of the depletion zone (L) and that of the graphene island (D), the graphene growth can be classified into four different cases: (i)

If the depletion zone is much larger than the graphene island, L/D ≫ 1, the graphene circumference is in a homogeneous environment. So, the growth of the graphene is attachment limited and the shape of the graphene island will be determined by the


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kinetic Wulff construction. Under such a growth condition, regular graphene domain will be formed. (ii)

If the depletion zone is of the similar size of the graphene island, L/D ~ 1, the precursor concentration around the circumference of the graphene will be different and those protrusions will be in an environment with larger precursor concentration and grow faster. So, in this case the star-like domains will be formed.

(iii)

If the depletion zone is a few times smaller than the size of the graphene, L/D < 1, the concentration gradient around each protrusion will be further disturbed and branches with neighboring distance close to the width of depletion zone will be formed. So, clear fractal-like graphene domains will be formed.

(iv)

If the depletion zone is orders of magnitude smaller than the size of the graphene, L/D ≪ 1, the distances between branches becomes negligible and the space between them will be eventually filled by the newly grown graphene. So, graphene of regular shapes will form but the edges of it are not perfect flat at atomic level.

Above results clearly showed that the shape of graphene islands is controlled by the size of depletion zone, and all other experimental factors, such as the coverage of graphene, concentration of precursors on the surface and the precursor flux affects the shape of the graphene through the change of the depletion zone around the graphene domain. First, let’s consider the growth of graphene from a tiny nucleus to a large domain in a specific environment, the size of the depletion zone is a constant, but the graphene island become larger and larger. So, during growth the ratio between the size of depletion zone and the diameter of the


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graphene island, L/D, must go through all the four zones with L/D ≫ 1, ~1, < 1, ≪1, respectively, and the corresponding shape evolutions, from regular hexagon to star-like and fractal shapes, should be seen in sequence during growth. So, graphene island’s shape evolution shown in Figure 1 can be easily understood. Before further analysis, let’s consider the corresponding experimental conditions of each combination of parameters qualitatively: a. A large incoming flux of carbon species 𝐹↓ corresponds to a large flow of carbon precursors such as CH4 or C2H2 and active substrate (e.g., Ni, Fe, Co, Pd, Pt, Ru, Rh, Ir), which is able to decompose the feedstock efficiently. b. Experimentally, a large flow of H2 will etch the carbon species on the substrate quickly and, therefore, can be regarded as a decrease the lifetime of carbon precursor on substrate (𝜏𝑠) and a low saturated concentration of precursor on the substrate 𝑐∞. c. The diffusion coefficient D is determined by the property of the substrate, especially the interaction between metal and carbon species. For example, a liquid metal substrate should have larger D than a solid one due to the fast motion of all atoms. With this understanding, we can easily explain the growth behavior of graphene in various experimental conditions as stated before. In case the catalyst surface is highly active, such as the Ni, Co, Fe, Pt, Pd, Ru, Rh, Ir, the fast decomposition of the feedstock results in a very large carbon flux and negligible concentration difference on the metal surface. So, only regular graphene islands are seen on the surface of these metals because of the smear of the depletion zone. In case the metal is not very active, such as Au or Cu, or with very limited precursor feeding, the slow carbon


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flux is not able to fill the depletion zone around a growing graphene island with enough carbon precursor and, therefore, the diffusion of carbon precursor is critical to support the fast graphene growth and the graphene growth becomes self-limited and diffusion limited. Under such a condition, if the size of the depletion zone is comparable with the size of the graphene, star-like or fractal graphene islands will be seen. It is worth noting that the large carbon flux can be achieved by increasing the concentration of carbon feedstock, such as CH4 or replace CH4 with more active species, such as C2H2 or alcohol. As observed in many experiments, the graphene growth in increased feedstock concentration or the active carbon species mostly leads to regular graphene domains36-37. Besides, the increase of H2 flow in experiments, which corresponds the decrease of 𝜏𝑠 and hence 𝑐𝑒𝑞 in our simulation, also leads to the shape variation from fractal like domain to regular hexagons, as observed in Wu’s experiments for graphene growth on liquid Cu surface under a very low flux of CH421. With the increase of H2 partial pressure, the growth rate of graphene decreases significantly, which allows for effective supplementation of carbon precursors around the graphene island through diffusion and thus shrinkage of the depletion zone. Therefore, much smaller graphene islands of regular hexagonal shapes than fractal graphene islands formed under a lower H2 partial pressure are formed21. Vlassiouk et al. has also observed similar phenomenon for graphene growth on Cu foils38. On liquid Cu surface, fast diffusion of carbon precursors would prohibit the formation of depletion zone around the graphene island, if the carbon precursor flux is not too small. Therefore, hexagonal graphene islands were frequently observed in experiments for CVD growth of graphene on liquid


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Cu substrates18, 39. However, if the carbon precursor flux is extremely small, star-like and fractal graphene islands can also be formed on liquid Cu surface21. From above discussions, we propose the following strategy for synthesizing high quality largesized graphene islands. During the nucleation stage, a very low carbon precursor concentration is needed to reduce the nucleation density. After nucleation, high flux of carbon precursor and its fast diffusion are required to facilitate the fast growth of graphene island and to prevent the formation of depletion zone. Besides, during the growth process, graphene nucleation on the bare surface of the substrate should be suppressed. CONCLUSION We, for the first time, revealed that the ratio between the size of the depletion zone of carbon precursors around the graphene island to the diameter of the graphene island (L/D) determines the island shape evolution during its CVD growth process, by using PFM simulations. Under high L/D, the graphene island shows a regular hexagonal shape, due to the uniform carbon precursor concentration around the graphene island. With the decrease of L/D, the graphene island would evolve to star-like shape and then hexagonal shape with very rough edges and dense branches, where the distance between neighboring branches is comparable to the size of the depletion zone. The synergistic effect of three important experimental parameters (i) carbon precursor flux, (ii) concentration of carbon precursor on substrate surface and (iii) diffusion of carbon precursor on the size of depletion zone is also systematically investigated. High equilibrium carbon precursor concentration favors the formation of the depletion zone, while high carbon precursor flux and diffusion would compensate for this effect, which is well consistent with a variety of experimental


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observations. The deep insights into the shape evolution of graphene islands during CVD growth provide important guidelines for synthesizing high-quality large-sized graphene islands.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]; [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENT The authors acknowledge support from the Institute for Basic Science (IBS‐R019‐D1) of South Korea and the Innovation and Technology Fund of Hong Kong SAR (GHP/034/12SZ).


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TOC

Figure TOC: The morphology of CVD grown graphene island is governed by the ratio of the length of depletion zone in the precursor concentration distribution map to the diameter of the graphene island.


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Morphology Evolution of Graphene during Chemical Vapor Deposition

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