Ultrafast Growth of Uniform Multi-Layer Graphene Films Directly on Silicon Dioxide Substrates

To realize the applications of graphene in electronics, a large-scale, high-quality, and uniform graphene film should first be placed on the dielectric substrates. Challenges still remain with respect to the current methods for the synthesis graphene directly on the dielectric substrates via chemical vapor deposition, such as a low growth rate and poor quality. Herein, we present an ultrafast method for direct growth of uniform graphene on a silicon dioxide (SiO2/Si) substrate using methanol as the only carbon source. A 1 × 1 cm2 SiO2/Si substrate square was almost fully covered with graphene within 5 min, resulting in a record growth rate of ~33.6 µm/s. This outcome is attributed to the quick pyrolysis of methanol, with the help of trace copper atoms. The as-grown graphene exhibited a highly uniform thickness, with a sheet resistance of 0.9–1.2 kΩ/sq and a hole mobility of up to 115.4 cm2/V·s in air at room temperature. It would be quite suitable for transparent conductive electrodes in electrophoretic displays and may be interesting for related industrial applications.


Introduction
Graphene is considered to be promising for use in future electronics [1]. To achieve its usage in electrical devices, first, large-scale, high-quality, and uniform graphene film should be placed on the dielectric substrate. Until now, many methods have been developed to grow graphene on metal surfaces and then transfer it onto a dielectric substrate for electrical applications [2][3][4]. However, the transfer process inevitably damages the film by introducing contaminations, wrinkles, and cracks [5]. Recently, graphene was successfully grown on a dielectric surface using the chemical vapor deposition (CVD) method [6]. However, one of biggest barriers is the very long growth duration (e.g., 1-82 h) [6][7][8], which means a low growth rate and limited potential in commercialization. For industrial production, a new method with a fast growth rate that produces an acceptable quality graphene is a must, which means decreased costs and energy consumption, and increased compatibility. Nevertheless, this goal is not easy to achieve, since there is a lack of metallic catalysts on the substrates needed to effectively pyrolyze the carbon source [9][10][11][12]. Liu et al. first reported the direct growth of graphene on a silicon dioxide (SiO 2 /Si) (i.e., 1 × 1 cm 2 ) substrate without any metallic catalysts, which took 3 h to be fully covered [9]. In this condition, the carbon precursors were quite difficult to decompose and nucleate on the dielectric substrates. Furthermore, the plasma-enhanced CVD method has been employed

Direct Growth of Graphene on the SiO 2 /Si Substrate
The growth was carried out in a horizontal tube furnace, in a manner that was the same as our previous paper [21]. A 1 × 1 cm 2 SiO 2 /Si substrate was ultrasonically cleaned in acetone, isopropanol alcohol, and deionized water for 5 min each, and dried with pure nitrogen gas. Then it was loaded in the center of the horizontal tube furnace, above which a curved piece of Cu foil was suspended, as illustrated in Figure 1. The distance between the copper foil and the SiO 2 substrate was controlled to be below 100 µm to facilitate enough copper atoms travelling to the substrate after overcoming the gas flow and vacuum forces (Figure 1b) [10]. The tube was first pumped to 150 m Torr and maintained at the same pressure, while 10 sccm H 2 was applied before annealing. The tube was then heated to Nanomaterials 2019, 9,964 3 of 11 1020 • C at a rate of 15 • C/min. After 20 min of annealing, the H 2 was stopped. Then 10 sccm Argon (Ar) was used as carrier gas for methanol to introduce the methanol vapor into the tube. The flow rate of the methanol vapor was calculated to be~1.56 × 10 −6 mol/min. After a desired duration, the furnace was naturally cooled to room temperature while applying 10 sccm H 2 again. Nanomaterials 2019, 9, x FOR PEER REVIEW 3 of 12 1020 °C at a rate of 15 °C/min. After 20 min of annealing, the H2 was stopped. Then 10 sccm Argon (Ar) was used as carrier gas for methanol to introduce the methanol vapor into the tube. The flow rate of the methanol vapor was calculated to be ~1.56 × 10 −6 mol/min. After a desired duration, the furnace was naturally cooled to room temperature while applying 10 sccm H2 again.

Characterization
The as-grown graphene was characterized using optical microscopy (DM4500P, Leica, Germany), transmission electron microscopy (TEM, Tacnai-G2 F30, Philips-FEI Inc., Netherlands, accelerating voltage of 300 kV), Raman spectroscopy (LabRAM XploRA, HORIBA JY, France, incident power of ~1 mW, pumping wavelength of 532 nm), and atomic force microscopy (AFM, Dimension 5000, Bruker, Germany, tapping mode). The species that were used for the Raman, optical, and AFM tests were the as-grown graphene on the original SiO2/Si substrates without further annealing, unless addressed in other parts in this paper. The species used for TEM tests were from the transferred graphene on the copper grids.

Fabrication of Field Effect Transistors for Electrical Measurements
The electrical properties of the graphene were evaluated based on a field effect transistor (FET) configuration. The as-grown graphene film was first patterned into micro-ribbons. Then, Cr/Au metal contacts (10/50 nm) were fabricated onto the micro-ribbons via thermal evaporation to form the bottom-gate FETs. The channel length (L) and width (W) were measured to be ~27 µm and 70 µm, respectively. To obtain better contact, the devices were thermally annealed at 200 °C in an H2/Ar (10/90 sccm) atmosphere for 30 min. The electrical measurements were carried out in air at room temperature using a semiconductor analyser (Keithley 4200-SCS, Tektronix Inc., Beaverton, OR, USA). Figure 1a illustrates the process of direct growth of graphene on the SiO2/Si substrate. In brief, a piece of Cu foil was suspended on the SiO2/Si substrate (Figure 1b), which releases copper atoms at

Characterization
The as-grown graphene was characterized using optical microscopy (DM4500P, Leica, Germany), transmission electron microscopy (TEM, Tacnai-G2 F30, Philips-FEI Inc., Netherlands, accelerating voltage of 300 kV), Raman spectroscopy (LabRAM XploRA, HORIBA JY, France, incident power of 1 mW, pumping wavelength of 532 nm), and atomic force microscopy (AFM, Dimension 5000, Bruker, Germany, tapping mode). The species that were used for the Raman, optical, and AFM tests were the as-grown graphene on the original SiO 2 /Si substrates without further annealing, unless addressed in other parts in this paper. The species used for TEM tests were from the transferred graphene on the copper grids.

Fabrication of Field Effect Transistors for Electrical Measurements
The electrical properties of the graphene were evaluated based on a field effect transistor (FET) configuration. The as-grown graphene film was first patterned into micro-ribbons. Then, Cr/Au metal contacts (10/50 nm) were fabricated onto the micro-ribbons via thermal evaporation to form the bottom-gate FETs. The channel length (L) and width (W) were measured to be~27 µm and 70 µm, respectively. To obtain better contact, the devices were thermally annealed at 200 • C in an H 2 /Ar (10/90 sccm) atmosphere for 30 min. The electrical measurements were carried out in air at room temperature using a semiconductor analyser (Keithley 4200-SCS, Tektronix Inc., Beaverton, OR, USA). high temperatures during the growth process [10]. Methanol vapor was carried into the tube by Ar gas and transported through the tube during growth (arrows in Figure 1a). It worked as the carbon source, which was quickly decomposed with the presence of the catalytic copper atoms. The suspended Cu foil would prevent copper contaminations in both the graphene film and SiO 2 /Si substrates [10]. According to Oshima's findings, approximately 70% of alcohols would be pyrolyzed within 3 min at temperatures above 1000 • C [22]. This could be further accelerated in the presence of metallic catalysts [23]. The high temperature (i.e., 1020 • C) and presence of the trace of copper atoms in the experiments may have responded to our ultrafast growth process. After the exclusion of stable methane in a previous study, methanol was found to be a good candidate for the carbon source. It can be a source of carbon and hydrogen and act as an inhibitor to amorphous carbon formation [24]. The previous study confirmed that there was no amorphous carbon that was observed in the CVD synthesis process when using methanol as precursor. This is quite different from other hydrocarbons, such as methane [24].

Results and Discussion
The catalytic pyrolysis of methanol is expected to generate a complex mixture, including hydrogen (H 2 ), carbon monoxide (CO), carbon dioxide (CO 2 ), water and methane [23,24]. According to the thermodynamic equilibrium of the composition at high temperatures (e.g., >750 • C), the content of the main by-product, H 2 , is saturated at~68.5% [24,25]. The intermediate, CO 2 , will gradually reduce to CO and H 2 O due to the H 2 , leading to the final content of CO reaching up to~25.5%. The residual CO 2 and methane were below 5.5% and 0.5% in the composition, respectively, which was reasonably negligible in our experiment. Finally, the reaction of CO + H 2 →C + H 2 O occurred at our set temperature (i.e., 1020 • C) with the copper catalyst, thus leading to highly active deposition of carbon radicals [25]. After the catalytic decomposition in the presence of the evaporated copper, those carbon radicals were nucleated on the SiO 2 /Si substrate at the low energy locations and formed the carbon nuclei and domains as prolonging the duration of the process (Figure 1a). The effective catalytic pyrolysis of methanol generated a large quantity of carbon radicals, leading to the faster growth of graphene in comparison to the traditional methods [9][10][11][12]. In addition, the reduction of the H 2 in the feedback gas would reduce the etching at the edge of graphene domains, thereby increasing the growth rate further.
To reveal the effect of H 2 on this newly developed process, a series of graphene samples were synthesized using different H 2 concentrations. Figure 2a-d show a series of Raman spectra that were collected from random points on each graphene sample grown using different H 2 flow rates of 0, 20, 60, and 100 sccm. The peaks at~1610 cm −1 and~2700 cm −1 were assigned to the G band and 2D band, respectively, which confirmed the presence of graphitic carbon [26]. Compared with the exfoliated graphene on the SiO 2 /Si substrate, the shift of G and 2D bands could be attributed to the stress in the graphene plane during growth [24,27]. Another peak at~1350 cm −1 was assigned to the D band, which was activated by the defects via an inter-valley double-resonance process [27]. Generally, the intensity ratio of the D band over the G band (I D /I G ) revealed the degree of the defects and the in-plane crystallite size (L a ). The parameters that are derived from Raman spectra are accumulated in Figure 2e-g, which can be used to determine the influence of the H 2 gas. The value of I D /I G increased from 0.94 ± 0.30 to 1.79 ± 0.67 (Figure 2e) as the H 2 flow increased from 0 to 100 sccm, suggesting the degradation of the quality of the graphene [26,27]. This can be attributed to the increase of the etching effect at high H 2 concentrations, resulting in the formation of structural defects, vacancies, and fragments in-plane and at the edge of as-grown graphene [16,17,28]. The in-plane crystallite size of L a ((L a ) 2 = (1.8 ± 0.5) × 10 −9 × λ L 2 (I D /I G ) −1 ) [29] reduced from 12.26 ± 1.74 nm to 8.89 ± 1.26 nm, indicating less crystallinity at a larger H 2 flow. In addition, the ratio of the 2D band over the G band (I 2D /I G ) gradually decreased from 1.74 ± 0.43 to 1.01 ± 0.77 (Figure 2f). Previous results showed that the decreased value of I 2D /I G may be caused by the increasing layer number and/or degradation of the quality of graphene [25,30]. In our study, all the graphene samples had a constant layer number, which was confirmed by the slightly variable full width at half maximum (FWHM) of the 2D band (i.e., 51-55 cm −1 , as shown in Figure 2g) [26,30]. Therefore, the decrease of I 2D /I G could be attributed to the degradation of the graphene. Overall, the Raman results suggested that the presence of H 2 during the reaction would degenerate the as-grown graphene. According to the decomposition route of methanol, the by-product CO was reduced by the H 2 to generate the carbon nuclei. This is the main driving force of the graphene growth on the SiO 2 surface when using methanol as the only carbon source. Additionally, the exclusion of H 2 in the carrier gas may also have reduced the etching effect and boost the growth rate remarkably.
Nanomaterials 2019, 9, x FOR PEER REVIEW 5 of 12 methanol, the by-product CO was reduced by the H2 to generate the carbon nuclei. This is the main driving force of the graphene growth on the SiO2 surface when using methanol as the only carbon source. Additionally, the exclusion of H2 in the carrier gas may also have reduced the etching effect and boost the growth rate remarkably. Furthermore, we have investigated the morphological evolution of graphene film on the SiO2/Si substrate by varying the growth duration. The optical images of graphene films that were obtained by various growth durations (0.5-30 min) are shown in Figure 3. A large quantity of graphene flakes with an average size of 2-6.5 µm appeared in the first 0.5 min (Figure 3a). The enlarged optical image Furthermore, we have investigated the morphological evolution of graphene film on the SiO 2 /Si substrate by varying the growth duration. The optical images of graphene films that were obtained by various growth durations (0.5-30 min) are shown in Figure 3. A large quantity of graphene flakes with an average size of 2-6.5 µm appeared in the first 0.5 min (Figure 3a). The enlarged optical image (Figure 3a, inset) shows the approximately hexagonal shape of the graphene domain. Some flakes quickly extended the size to 20-36 µm in the following 2 min (Figure 3b, inset) and merged with adjacent ones within a further 2.5 min (Figure 3c). As the flakes grew in size, a large quantity of new nuclei was deposited on the uncovered area of the SiO 2 substrate, resulting in the limitation of further growth of the graphene flake. As a result, the numerous nuclei were responsible for our ultrafast growth rate. The substrate was almost fully covered by the graphene film within 5 min (Figure 3c), resulting in an average growth rate of~33.6 µm/s. To the best of our knowledge, this is the highest growth rate that has ever been reported for the direct growth of uniform graphene film on a SiO 2 /Si surface [9][10][11][12]15]. Further prolonging the growth duration, the graphene film tended to form a uniform film, considering the same reflection in the optical images (Figure 3d-h). Therefore, the thickness (analogous to layer number) of graphene remained unchanged after 5 min growth. This behavior is analogous to the growth of graphene film on Cu foils using alcohols in consideration of a continuous supply of the precursor and copper atoms [31].  (Figure 3b, inset) and merged with adjacent ones within a further 2.5 min (Figure 3c). As the flakes grew in size, a large quantity of new nuclei was deposited on the uncovered area of the SiO2 substrate, resulting in the limitation of further growth of the graphene flake. As a result, the numerous nuclei were responsible for our ultrafast growth rate. The substrate was almost fully covered by the graphene film within 5 min (Figure 3c), resulting in an average growth rate of ~33.6 µm/s. To the best of our knowledge, this is the highest growth rate that has ever been reported for the direct growth of uniform graphene film on a SiO2/Si surface [9][10][11][12]15]. Further prolonging the growth duration, the graphene film tended to form a uniform film, considering the same reflection in the optical images (Figure 3d-h). Therefore, the thickness (analogous to layer number) of graphene remained unchanged after 5 min growth. This behavior is analogous to the growth of graphene film on Cu foils using alcohols in consideration of a continuous supply of the precursor and copper atoms [31]. The systematical Raman measurements revealed the quality, layer number, and defects of graphene samples with different growth durations ( Figure 4). The values in Figure 4 are the statistical data (average with error) from five random spectra (points) of each graphene sample. The ID/IG increased a little at first and then uniformly decreased down to 0.94 ± 0.11 (Figure 4a), reflecting the constantly improved crystallization of the graphene film as the growth duration increased. This could be attributed to the restoration of the sp 2 -hybrid structure in-plane during the high temperature annealing process, which was also used to restore the graphene oxide [32]. Nevertheless, the value of ID/IG was still larger than that measured in graphene grown with a long duration or on the metals. This could be attributed to the lack of sufficient metallic catalysts to completely pyrolyze methanol in a short time, resulting in many structural defects in the graphene. The average ID/IG of the graphene samples that were grown with 30 min was much smaller than that measured in the reduced graphene oxide and some of the CVD-grown samples [33][34][35]. This indicates that the obtained graphene is more suitable for electronic applications than the reduced graphene oxide and some CVD-grown graphene [33][34][35]. Additionally, the improvement in quality was confirmed by the increase of I2D/IG from 0.1 ± 0.002 to 1.86 ± 0.24 (Figure 4b). Simultaneously, these values indicated a multilayer feature of the asgrown graphene, considering that it was usually above 2 in the single-layer graphene [27,30]. In addition, the FWHM(2D) fluctuated slightly at 55.3 ± 1.92 cm -1 (Figure 4c), which was similar to the The systematical Raman measurements revealed the quality, layer number, and defects of graphene samples with different growth durations ( Figure 4). The values in Figure 4 are the statistical data (average with error) from five random spectra (points) of each graphene sample. The I D /I G increased a little at first and then uniformly decreased down to 0.94 ± 0.11 (Figure 4a), reflecting the constantly improved crystallization of the graphene film as the growth duration increased. This could be attributed to the restoration of the sp 2 -hybrid structure in-plane during the high temperature annealing process, which was also used to restore the graphene oxide [32]. Nevertheless, the value of I D /I G was still larger than that measured in graphene grown with a long duration or on the metals. This could be attributed to the lack of sufficient metallic catalysts to completely pyrolyze methanol in a short time, resulting in many structural defects in the graphene. The average I D /I G of the graphene samples that were grown with 30 min was much smaller than that measured in the reduced graphene oxide and some of the CVD-grown samples [33][34][35]. This indicates that the obtained graphene is more suitable for electronic applications than the reduced graphene oxide and some CVD-grown graphene [33][34][35]. Additionally, the improvement in quality was confirmed by the increase of I 2D /I G from 0.1 ± 0.002 to 1.86 ± 0.24 (Figure 4b). Simultaneously, these values indicated a multilayer feature of the as-grown graphene, considering that it was usually above 2 in the single-layer graphene [27,30]. In addition, the FWHM(2D) fluctuated slightly at 55.3 ± 1.92 cm −1 (Figure 4c), which was similar to the previous Nanomaterials 2019, 9,964 7 of 11 results (56.2 ± 1.6 cm −1 ) in three-layer exfoliated graphene [27]. It was almost confirmed to be three layers of as-grown graphene [27]. Nanomaterials 2019, 9, x FOR PEER REVIEW 7 of 12 previous results (56.2 ± 1.6 cm -1 ) in three-layer exfoliated graphene [27]. It was almost confirmed to be three layers of as-grown graphene [27]. AFM and TEM measurements were performed to determine the layer feature of the graphene films. The thicknesses of the graphene film at the growth durations of 5~30 min were measured to be in the range of 1.5-2.0 nm (Figure 5a shows a thickness of 1.5 nm), which indicates a three-layer feature, considering the deviation in the AFM measurements [36]. Furthermore, the high-resolution TEM image at the back-folded edge (Figure 5b,c) of each graphene sample clearly shows a three-layer feature. A selected area electron diffraction (SAED) pattern has been applied to investigate the crystallographic pattern and orientation of the graphene. A typical SAED image (Figure 5d) shows two sets of hexagonal diffraction patterns, indicating that there is rotational stacking within the region measured [37]. The rotation of the diffraction pattern is determined by many features, such as intrinsic rotational stacking, back-folding of edges, and overlapping domains [37]. Herein, the rotation has been solely attributed to back-folding, considering that there were only two sets of patterns in the SAED images, indicating the single crystal feature of the selected areas [37]. The lattice constant was calculated to be 0.2468 nm from the SAED patterns (Figure 5d), which fit the graphene lattice of 0.247 nm [38].  AFM and TEM measurements were performed to determine the layer feature of the graphene films. The thicknesses of the graphene film at the growth durations of 5~30 min were measured to be in the range of 1.5-2.0 nm (Figure 5a shows a thickness of 1.5 nm), which indicates a three-layer feature, considering the deviation in the AFM measurements [36]. Furthermore, the high-resolution TEM image at the back-folded edge (Figure 5b,c) of each graphene sample clearly shows a three-layer feature. A selected area electron diffraction (SAED) pattern has been applied to investigate the crystallographic pattern and orientation of the graphene. A typical SAED image (Figure 5d) shows two sets of hexagonal diffraction patterns, indicating that there is rotational stacking within the region measured [37]. The rotation of the diffraction pattern is determined by many features, such as intrinsic rotational stacking, back-folding of edges, and overlapping domains [37]. Herein, the rotation has been solely attributed to back-folding, considering that there were only two sets of patterns in the SAED images, indicating the single crystal feature of the selected areas [37]. The lattice constant was calculated to be 0.2468 nm from the SAED patterns (Figure 5d), which fit the graphene lattice of 0.247 nm [38]. previous results (56.2 ± 1.6 cm -1 ) in three-layer exfoliated graphene [27]. It was almost confirmed to be three layers of as-grown graphene [27]. AFM and TEM measurements were performed to determine the layer feature of the graphene films. The thicknesses of the graphene film at the growth durations of 5~30 min were measured to be in the range of 1.5-2.0 nm (Figure 5a shows a thickness of 1.5 nm), which indicates a three-layer feature, considering the deviation in the AFM measurements [36]. Furthermore, the high-resolution TEM image at the back-folded edge (Figure 5b,c) of each graphene sample clearly shows a three-layer feature. A selected area electron diffraction (SAED) pattern has been applied to investigate the crystallographic pattern and orientation of the graphene. A typical SAED image (Figure 5d) shows two sets of hexagonal diffraction patterns, indicating that there is rotational stacking within the region measured [37]. The rotation of the diffraction pattern is determined by many features, such as intrinsic rotational stacking, back-folding of edges, and overlapping domains [37]. Herein, the rotation has been solely attributed to back-folding, considering that there were only two sets of patterns in the SAED images, indicating the single crystal feature of the selected areas [37]. The lattice constant was calculated to be 0.2468 nm from the SAED patterns (Figure 5d), which fit the graphene lattice of 0.247 nm [38]. To evaluate the electrical properties of the as-grown graphene, bottom-gated field effect transistors (FETs) were made. The inset image in Figure 6a shows the FET device's configuration, in which the graphene works as a channel material. Figure 6a shows a typical transfer property (current of source-drain vs voltage applied on the gate Ids-Vgs) of the FET devices. The Ids decreased uniformly with a positive shifting of the gate voltage and a neutrality point at approximately 30 V. It demonstrated a typical electrical feature of graphene that is measured in air at room temperature. In addition, the corresponding output curve (Ids-Vds, Figure 6b) showed decreasing Ids as the gate voltage increased. Both of characteristics indicated a heavy hole doping (p-type) feature in the graphene. The appearance of a strong p-type doping feature ( Figure 6) was possibly due to the adsorption of oxygen and water molecules, since there are a lots of oxygen-containing groups in the graphene plane [7,10]. The sheet resistances measured by the four-terminate devices were found to be in the range of 0.9-1.2 kΩ/sq, which is much smaller than some previous results [39][40][41][42][43][44][45] (Table 1), indicating the promised electrical conductivity. The carrier mobility was calculated according to the equation: µ = (∆I ds ·L/W)/(∆V gs ·V ds ·C ox ), where, C ox is the silica gate capacitance (1.15 × 10 −8 F/cm 2 for a gate oxide thickness of 300 nm). As a result, the hole and electron mobility were approximately 115.4 and 13.7 cm 2 /V·s, respectively, which are higher than those of graphene film grown on some dielectrics (Table 1) [21,[41][42][43], and also were comparable to those of the CVD-grown graphene on nickel [46,47] and copper films [48][49][50] (Table 1). In addition, the hole mobility has been improved at least five-fold compared to our previous results within the same growth duration [21]. Specifically, as-grown graphene films could be quite suitable for transparent conductive electrodes in electrophoretic displays, which require moderate conductivity and mobility. Further optimization parameters for growth should be investigated to improve the quality of graphene that is grown over a very short duration. To evaluate the electrical properties of the as-grown graphene, bottom-gated field effect transistors (FETs) were made. The inset image in Figure 6a shows the FET device's configuration, in which the graphene works as a channel material. Figure 6a shows a typical transfer property (current of source-drain vs voltage applied on the gate Ids-Vgs) of the FET devices. The Ids decreased uniformly with a positive shifting of the gate voltage and a neutrality point at approximately 30 V. It demonstrated a typical electrical feature of graphene that is measured in air at room temperature. In addition, the corresponding output curve (Ids-Vds, Figure 6b) showed decreasing Ids as the gate voltage increased. Both of characteristics indicated a heavy hole doping (p-type) feature in the graphene. The appearance of a strong p-type doping feature ( Figure 6) was possibly due to the adsorption of oxygen and water molecules, since there are a lots of oxygen-containing groups in the graphene plane [7,10]. The sheet resistances measured by the four-terminate devices were found to be in the range of 0.9-1.2 kΩ/sq, which is much smaller than some previous results [39][40][41][42][43][44][45] (Table 1), indicating the promised electrical conductivity. The carrier mobility was calculated according to the equation: μ = (ΔIds·L/W)/(ΔVgs·Vds·Cox), where, Cox is the silica gate capacitance (1.15 × 10 -8 F/cm 2 for a gate oxide thickness of 300 nm). As a result, the hole and electron mobility were approximately 115.4 and 13.7 cm 2 /V·s, respectively, which are higher than those of graphene film grown on some dielectrics (Table 1) [21,[41][42][43], and also were comparable to those of the CVD-grown graphene on nickel [46,47] and copper films [48][49][50] (Table 1). In addition, the hole mobility has been improved at least five-fold compared to our previous results within the same growth duration [21]. Specifically, as-grown graphene films could be quite suitable for transparent conductive electrodes in electrophoretic displays, which require moderate conductivity and mobility. Further optimization parameters for growth should be investigated to improve the quality of graphene that is grown over a very short duration.

Conclusions
In summary, we have presented an ultrafast method for the direct growth of uniform graphene film on a SiO 2 /Si substrate. The methanol precursor was rapidly catalytically decomposed once it was introduced into the tube, leading to the ultrafast nucleation and growth of the graphene and a record growth rate of~33.6 µm/s. Meanwhile, the exclusion of H 2 in the carrier gas reduced the etching of the as-grown graphene domains, thereby improving the crystallization of the graphene. As a result, the trilayer graphene film was of a good quality, with a sheet resistance of 0.9-1.2 kΩ/sq and hole mobility of up to 115.4 cm 2 /V·s in air at room temperature. These graphene films would be quite suitable for transparent conductive electrodes in the electrophoretic displays, which require moderate conductivity and mobility. Therefore, our method possesses a competitive advantage in related industrial applications.