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The results of systematic numerical studies of graphene flakes growth in low-temperature arc discharge plasmas are presented. Diffusion-based growth model was developed, verified using the previously published experiments, and used to investigate the principal effects of the process parameters such as plasma density, electron temperature, surface temperature and time of growth on the size and structure of the plasma-grown graphene flakes. It was demonstrated that the higher growth temperatures result in larger graphene flakes reaching 5 μm, and simultaneously, lead to much lower density of the carbon atoms adsorbed on the flake surface. The low density of the carbon adatoms reduces the probability of the additional graphene layer nucleation on surface of growing flake, thus eventually resulting in the synthesis of the most valuable single-layered graphenes.

Single- and few-layered graphene flakes demonstrate exceptional mechanical [

Plasma-based techniques are the recently developed methods capable of producing the nanoscaled materials with quite different properties [

The growth process and hence the properties of the prepared graphene flakes significantly depend on the plasma and growth parameters (plasma density, electron energy, surface temperature etc.). Numerous experimental works were conducted and the results are published, but a comprehensive picture of the graphene growth still remains unclear, despite of the many applied efforts. Here we present the results of numerical studies of the

graphene flake growth in arc plasmas, conducted to mainly determine the general effect of the plasma parameters on the graphene growth behavior and specifically, to find the process parameters which directly affect the growth rates and nucleation conditions, with an ultimate view to better understand the processes leading to the transition from the formation of single-layer graphenes to few-layered flakes. We use here a relatively simple diffusion-based model which is not time-consuming, as compared with the molecular dynamics or Monte-Carlo techniques, but still is capable to reveal the main characteristics and parameters.

The main processes taken into account are illustrated in _{c} on graphene surface in plasma is:

where _{i} is the ion mass;

_{s} is the graphene flake surface temperature, _{a} is the energy of carbon adatom evaporation.

The diffusion flux from the flake side to edges _{1} one can obtain:

where ɛ_{d} is the surface diffusion activation energy. Finally we obtain:

Equation (4) is required for the two aims, namely 1) to find the diffusion flux from the flake side to the external edges _{c} calculated from (1), the graphene growth rate can be estimated as:

where λ is the mean (effective) graphene lattice period which was calculated from the mean surface density of graphene being 3.82 × 10^{15} cm^{−2} [_{s} is equal to the gas temperature T_{g}.

The task becomes more complicated after the nucleation of a second flake on the surface of a single-layered graphene. In this case the growth rate of the second layer is described by

where r_{2} is the second flake radius,

The plasma parameters and growth conditions used for the simulations are typical for the arc-based process effective for graphene and carbon nanotube growth [_{d} and carbon evaporation energy ɛ_{a} strongly influence the growth process. Direct measurement of these values is a hard task, thus we used the results of ab initio calculations [_{a} energy and have verified the most important diffusion activation energy ɛ_{d} by our previous experimental works [^{−1}) in arc plasma and inter-electrode gap of several mm.

Figures 2(a)-(d) represent the calculated dependencies of the carbon adatom density on the surface of growing graphene flake and single-layered flake size on the growth time with electron temperature (0.5 to 1.1 eV), surface temperature and temperature profile as parameters, for the lowest considered plasma density of 10^{20} m^{−3}.

Comparing the graphs in ^{−3} of monolayer density) for the case of a constant temperature 1300 K (

The time dependencies of the single-layer flake sizes are presented in

Hence, one can derive that the process at the high constant temperature features at least two significant advantages, namely 1) larger graphene flake size and even more important, 2) very low density of adatom on the surface of growing graphene which results in the formation of single-layered flakes.

Similar dependencies are shown in Figures 2(e)-(h) for the higher plasma density of 3 × 10^{20} m^{−3}. In this case the graphene flakes reach 6 μm for the constant temperature case and 3.5 μm for the growth temperatures descending to 1000 K. The influence of the plasma electron energy is not so strong at this higher plasma density. The adatom density on graphenes grown at the constant temperatures still remains low (8 × 10^{−3} mL), thus demonstrating the possibility to grow large (6 μm) single-layered flakes. It could be also mentioned that the adatom density demonstrate saturation with time, i.e. the flake could grow further in the single-layer mode.

Importantly, the conclusion about better growth under the constant temperature conditions was confirmed with numerous experiments with the magnetic-enhanced arc setups, where the permanent magnet was used to focus plasma and elevate the electron temperature. Indeed, higher yield and better quality of the deposit was obtained in the magnetic-enhanced arc discharges.

In _{s} = 1000 K. In this case the increase of the plasma density is not efficient. It can indeed ensure larger flake size (1.6 μm for the plasma density of 2 × 10^{20} m^{−3} versus 1.0 μm for 1 × 10^{20} m^{−3}) but at the expense of very high adatom density on the graphene surface (reaching 1, i.e. complete coverage of the graphene surface with adatom), which unavoidable resulted in the nucleation of new layer. Hence, it is impossible to grow relatively large (up to several μm) graphene flakes at low temperatures. Indeed, low plasma densities could sustain the growth in the single-player mode

(i.e., at low adatom density), but the size of the graphene flake in this case does not exceed 1 μm; when higher plasma density is used, the adatom density significantly increases and unavoidably leads to the transition to multi-layer graphene which is not favorable. The reasons for this are low diffusion fluxes to the graphene edges which promote the flake growth; on the other hand, low evaporation leads to the fast accumulation of the adatoms and hence, nucleation of new layers. The increase of the electron energy in plasma cannot help in this case, since it does not influence the diffusion and the graphene growth rates. Based on these results one can conclude that the low-temperature growth is not favorable and the low growth rates cannot be compensated by higher plasma density without compromising the graphene quality due to the transition to the multi-layered growth mode.

Moreover the calculations for elevated surface temperature of 1200 K and much higher plasma densities (5^{20} m^{−3}) are presented in ^{20} m^{−3} and 14 μm for 20 × 10^{20} m^{−3}) graphenes at the relatively low adatom density on the graphene surface (not exceeding 0.06 mL for 5 × 10^{20} m^{−3} and 0.25 mL for 20 × 10^{20} m^{−3}). Despite a very high plasma density, these relatively low adatom densities definitely ensure the graphene growth in the single-layer mode, since the formation of new graphene layers is impossible at such conditions. The apparent reasons for this are significantly enhanced surface diffusion rate at higher temperatures (since the surface diffusion exponentially depends on the temperature) and higher evaporation from the surface which prevents the accumulation of the excessive adatoms which could cause nucleation of a new layer. Much higher atom fluxes from the dense (20 × 10^{20} m^{−3}) plasma lead to the strong diffusion to the graphene edges where adatoms incorporate in the graphene structure. We can also note that the influence of the electron energy ɛ_{e} on the graphene size is low (since the Bohm velocity does not influence the diffusion), but the adatom density strongly depends on ɛ_{e} and hence could be efficiently controlled by changing, i.e., discharge voltage or using magnetic field to enhance ionization and electron energy. Another important fact is the apparent saturation of the adatom densities in both (5 × 10^{20} m^{−3} and 20 × 10^{20} m^{−3}) cases, which means that the further growth is possible in the single-layer mode by extending the growth zone; in this case the measures should be taken to maintain the plasma and graphene flake temperatures at the higher enough level, to avoid the situation shown in

To better characterize growth of graphenes in plasma, we have calculated the dependencies of the single-layer flake size on electron temperature in plasma, with the plasma density and surface temperature as parameters (

growth mode. The surface temperature appears to be an important parameter for the growth control, as seen in

Importantly, graphene flake growth rates do not demonstrate significant saturation with time, except of the situation when the surface temperature drops off abruptly (

We have demonstrated that the plasma parameters such as gas temperature, plasma density and electron energy could be efficiently used for maintaining the graphene growth to relatively large (up to 10 μm) sizes in the single layer mode. High growth rates and large flakes could be synthesized in plasma of 5 × 10^{20} m^{−3} to 20 × 10^{20} m^{−3} density, but the graphene surface temperature should be at least 200 to 1300 K to avoid accumulation of the excessive adatoms on graphene surface and hence, avoid the nucleation of new layers which causes transition to the undesired multilayer growth mode. The further works should study in detail the process and kinetics of the layers formation, and to find the optimum conditions for the production of the defect-free graphene flakes.

I. L. acknowledges the support from the School of Chemistry, Physics and Mechanical Engineering, Science and Engineering Faculty, Queensland University of Technology. This work was partially supported by Slovenian Research Agency (ARRS), project L2-6769. Work at GWU was sponsored in part by the GW Institute for Nanotechnology.

Igor Levchenko,Uroš Cvelbar,Michael Keidar, (2016) Graphene Flakes in Arc Plasma: Conditions for the Fast Single-Layer Growth. Graphene,05,81-89. doi: 10.4236/graphene.2016.52009