Chan et al. Nanoscale Research Letters 2014, 9:581http://www.nanoscalereslett.com/content/9/1/581

NANO EXPRESS Open Access

The deviation of growth model for transparentconductive grapheneShih-Hao Chan1, Jia-Wei Chen1, Hung-Pin Chen1, Hung-Sen Wei1, Meng-Chi Li1,3, Sheng-Hui Chen1, Cheng-Chung Lee1

and Chien-Cheng Kuo1,2*

Abstract

An approximate growth model was employed to predict the time required to grow a graphene film by chemicalvapor deposition (CVD). Monolayer graphene films were synthesized on Cu foil at various hydrogen flow rates from10 to 50 sccm. The sheet resistance of the graphene film was 310Ω/□ and the optical transmittance was 97.7%. TheRaman intensity ratio of the G-peak to the 2D peak of the graphene film was as high as ~4 when the hydrogenflow rate was 30 sccm. The fitting curve obtained by the deviation equation of growth model closely matches thedata. We believe that under the same conditions and with the same setup, the presented growth model can helpmanufacturers and academics to predict graphene growth time more accurately.

Keywords: Graphene; Transparent conductive electrode; Chemical vapor deposition

BackgroundGraphene, comprising two-dimensional monolayer ofsp2-bonded carbon atoms, has attracted substantial atten-tion for use in transparent conductive electrodes (TCE),owing to its chemical stability and high optical transmit-tance from the ultraviolet to the infrared regions. Gra-phene as a TCE has a wide range of applications, includingin solar cells, solid-state lighting, and detectors, owing tonot only its higher optical transmittance but also its morefavorable conductance [1-4] than those of traditional trans-parent conductive electrodes, such as indium tin oxide(ITO) and zinc oxide (ZnO) [5]. (Additionally, Further-more, or Moreover), ITO is an expensive material, andit is unstable in chemical solution and cannot be utilizedin a hydrogen-containing environment. ZnO-based thinfilm has also attracted interest for use in TCEs owing toits low cost, non-toxicity, and abundant constituent ele-ments [6]. However, the properties of ZnO-based thinfilms are not uniform or stable. The several ways to pro-duce graphene include mechanical exfoliation, grapheneoxide (GO), and chemical vapor deposition (CVD).Mechanical exfoliation can yield high-quality graphene

* Correspondence: cckuo@ncu.edu.tw1Department of Optics and Photonics/Thin Film Technology Center, NationalCentral University, 300 Chung-Da Rd, Chung-Li 32001, Taiwan2Graduate Institute of Energy Engineering/Thin Film Technology Center,National Central University, 300 Chung-Da Rd, Chung-Li 32001, TaiwanFull list of author information is available at the end of the article

© 2014 Chan et al.; licensee Springer. This is anAttribution License (http://creativecommons.orin any medium, provided the original work is p

from graphite but this method produces graphene overa small area of the order of only a few tens of microme-ters [4]. Graphene oxide can be formed by oxidizinggraphite flakes; this method can produce large quantitiesof graphene whose electrical properties are, however, af-fected by the functional groups and various defects in thegraphene [7]. Nevertheless, CVD is a promising methodfor growing high-quality graphene over a large area usingCu foils. Li et al. were the first to grow graphene over alarge area of the order of square centimeters on Cu foil byCVD using methane, and this method has become a stand-ard approach to forming graphene films in recent years [8].Four-layered graphene exhibits a sheet resistance of about350Ω/□, which represents a large step toward lower sheetresistance and a large increase in the range of grapheneapplications [9]. Additionally, various methods have beenproposed to optimize the properties of CVD graphene[10-14]. This work develops a simply derived graphenegrowth model to predict the growth time with varioushydrogen flow rates.

MethodsGraphene films were grown by chemical vapor deposition(APCVD) on 25-μm-thick Cu foils (99.8%, Alfa-Aesar,item no. 13382) in a 3-in. quartz tube furnace under at-mospheric pressure. Beforehand, electrochemical pol-ishing (50% H3PO4 in deionized water of 100 mL) was

Open Access article distributed under the terms of the Creative Commonsg/licenses/by/4.0), which permits unrestricted use, distribution, and reproductionroperly credited.

Figure 1 Surface profile of Cu foil and SEM images of graphene domains. Surface profile of Cu foil (a) before and (c) after electropolishing.(b) SEM image of morphology of graphene domains (c) before and (d) after electropolishing.

Figure 2 Calculation of graphene domain densities with varioushydrogen flow rates from 10 to 50 sccm.

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utilized to smooth out the foil, and a voltage from 2 to4 V was applied until the Cu foil glowed. Thereafter,the Cu foil was rinsed in a large amount of deionizedwater with sonication and then blow-dried with nitrogengas. The Cu foil was placed in the reaction chamber, theAr and H2 (1,000 and 2 sccm, respectively) gases were in-troduced into the chamber during temperature ramp-up.The Cu foil was annealed at 1,070°C for an hour. Then,0.3 sccm of methane (purity, 99.99%) was used as a sourceof carbon to grow the graphene. The H2 flow rate was var-ied from 10 to 50 sccm prior to observation of the morph-ology of the graphene domains and the nucleation density.Following the growth process, the as-grown graphene/Cufoil was removed from the heating zone for rapid cooling.Polymethyl methacrylate (PMMA) was spin-coated on theas-grown graphene/Cu foil as a supporting layer to pre-vent any cracking during the transfer process. The gra-phene grew on both sides of the Cu foil. The graphene atthe back of the foil was removed by floating on nitrideacid solution (30% in deionized water) for 10 s. The Cufoil was etched away overnight using an ammonium per-sulfate solution (0.1 M) and then rinsed three times in de-ionized water. The PMMA/graphene was placed on thesubstrate, and the PMMA was then dissolved in hot acet-one bath for 24 h. The residual PMMA was removed byannealing in air at 200°C for an hour and reduced to pris-tine graphene using an H2/Ar (7/20 sccm) mixture. The

morphology and the nucleation density of the graphenedomain were measured by scanning electron microscopy(SEM); The surface profile of Cu foils were measured byatomic force microscopy (AFM); the sheet resistance wasmeasured using a four-probe stage; the Raman shift of thegraphene was measured by Raman spectroscopy using alaser with a wavelength of 532 nm, the laser power at thefocused spot was 2 mW, and the numerical aperture valuewas 0.75 on the sample with an area of 1 μm2.

Figure 4 Growth model of graphene at various hydrogen flow rates and corresponding fitting curves. (a) 10, (b) 20, (c) 30, (d) 40, and(e) 50 sccm.

Figure 3 Results of growth model and SEM image. Results of growth model with growth time of (a) t1 and (b) t2. (c) SEM image ofhexagonal graphene domain with hydrogen flow rate of 30 sccm. (d) The deviation of growth model for graphene domain.

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Results and discussionThe number of graphene layers, the shape, and the nu-cleation density were significantly influenced by the sur-face roughness of Cu foil. Figure 1a,c presents AFMimages of the reduction of the rolling marks on the Cufoil by electropolishing. The domain density of grapheneclearly declined from Figure 1b-d, and the graphenemorphology became star-shaped under hydrogen at a1flow rate of 20 sccm. In the latter experiments, theelectropolishing of Cu foils were applied for growinggraphene films. To synthesize a larger graphene domain,experiments were conducted in which the hydrogenflow rate was increased from 10 to 50 sccm, and the

Figure 5 Optical transmittance and sheet resistance of graphene filmgraphene film obtained using various hydrogen flow rates from 10 to 50 sc

graphene domain density is calculated, as displayed inFigure 2. A previous investigation revealed that thehydrogen flow rate importantly affects the graphenegrowth mechanism, owing to the etch effect and its effecton the graphene domain density. The density of graphenenuclei is reduced as the hydrogen flow rate is increased.The hydrogen flow rate also affects the morphology ofgraphene. In this case, the graphene had a hexagonalshape when the hydrogen flow rate was 30 sccm, as shownin Figure 3c. A growth model to elucidate the rate ofgraphene domain growth was proposed. If the graphenedomain is circular, then this model allows the easy cal-culation of the difference between the graphene domain

. (a) Optical transmittance of graphene film. (b) Sheet resistance ofcm.

Figure 6 Raman spectrum of single-layer graphene film.

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sizes at two growth times. Figure 3 displays the deriv-ation of the growth model. Figure 3a,b schematically de-picts the growth of the graphene domains from growthtime t1 to t2. Figure 3d presents the growth model in de-tail, where L is the circumference of graphene domain;A is the mean area of the grown domains, and the r isthe average radius of the domains. Now, an area factoris sought such that

dA ¼ Ldr ð1ÞFor a carbon deposition rate v, the deposition rate of

carbon atoms at one direction is given by,

v ¼ drdt

ð2Þ

Combining Equations 1 and 2 yields simultaneousequations,

dA ¼ Lvdt

L ¼ 4πAð Þ12

(ð3Þ

Solving Equation 3 yields,

4πAð Þ−12dA ¼ vdt ð4Þ

12π

4πAð Þ12 ¼ vt ð5Þ

A ¼ π vtð Þ2 ð6ÞThe mean area A now becomes

A ¼ π vtð Þ2 ¼ 12d2Adt2

t2 ð7Þ

The A is a quadratic equation which means the gra-phene domains grown with an acceleration rate on the Cufoil. Equation 7 can be utilized to predict the coveragearea of graphene on the Cu foil under various hydrogenflow rates from 10 to 50 sccm, as displayed in Figure 4.The dashed line is the area of the Cu foil (1.1 cm2) andthe red spots represent the growth times of graphene thatyield the specified area, based on Equation 7. A red spotat the dashed line indicates that the graphene fully cov-ered the Cu foil. Figure 4 reveals that the graphene fullycovered the foil when the hydrogen flow rate was 10, 20,or 30. When the hydrogen flow rate exceeded 30 sccm,the graphene did not fully cover the Cu foil because of theetching effect and thermal equilibrium occurs on the edgeof graphene domains. Also, a fitting equation is obtainedfor the growth of graphene with different hydrogen flowrate, which is plotted as the blue curve. Based on the de-veloped growth model, we can adjust any coverage of gra-phene on the Cu foil which closely matches the fittingcurve; the growth model predicts the growth rate of gra-phene. As mentioned above, the graphene domain was

hexagonal when the hydrogen flow rate was 30 sccm. Thegraphene fully covered the Cu foil both according to thegrowth model and in the experiment. The graphene wastransferred onto a glass substrate to measure its transpar-ency, sheet resistance, and Raman shift. In Figure 5a, thegraphene film is placed on the glass substrate with a rela-tively high transmittance of about 97.7% at λ =550 nm.The attenuation coefficient (α =2.3%) was fitted usingBeer’s law; the value matches the theoretical value of 2.3%when the λ =550 nm [15]. The graphene films that weresynthesized using various hydrogen flow rates were alsotransferred to the substrate and their sheet resistance wasmeasured, as shown in Figure 5b. The lowest obtainedsheet resistance of graphene was 310Ω/□, which wasachieved when the hydrogen flow rate was 30 sccm, be-cause the smooth edge of the graphene domain reducedthe number of scattering centers which inhibited the car-rier transportation. The sheet resistance increased withthe hydrogen flow rate over 30 sccm because the graphenedid not fully cover the Cu foil, and because the largernumber of pores in the graphene increased the sheet re-sistance. Figure 6 shows the Raman spectrum of graphenefilm, in which the peaks are typical of a single-layer gra-phene, with a 2D/G ratio of as high as ~4 when thehydrogen flow rate was 30 sccm. The full width at halfmaximum (FWHM) was 23.5 cm−1, verifying the pres-ence of a single-layer graphene [8].

ConclusionsAn approximate growth model of the synthesis of gra-phene by APCVD was developed. When the hydrogenflow rate was 30 sccm, the transmittance as a functionof wavelength for single-layer graphene reached its max-imum of 97.7% at λ =550 nm. The 2D/G ratio and theFWHM indicated that the graphene comprised a singlelayer of high quality. The lowest obtained sheet resist-ance of a single layer of graphene was about 310Ω/□.

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The results of the experiments closely matched the fittingcurve. We believe that, under the same conditions andwith the same experimental setup, the proposed growthmodel can help manufacturers and academics predictthe growth time of graphene more accurately.

Competing interestsThe authors declare that they have no competing interests.

Authors’ contributionsSHC (Chan) designed the study and wrote the paper. JWC, HSW, MCL, andHBC analyzed the data. SHC (Chen), CCL, and CCK are advisors. All authorsread and approved the final manuscript.

AcknowledgmentsThe authors would like to thank the National Science Council of the Republicof China, Taiwan, for financially supporting this research under contractnos. NSC 102-2633-E-008-001, NSC 103-2623-E-008-001-ET, and MOST103-2221-E-008-101-MY2.

Author details1Department of Optics and Photonics/Thin Film Technology Center, NationalCentral University, 300 Chung-Da Rd, Chung-Li 32001, Taiwan. 2GraduateInstitute of Energy Engineering/Thin Film Technology Center, NationalCentral University, 300 Chung-Da Rd, Chung-Li 32001, Taiwan. 3OpticalSciences Center/Thin Film Technology Center, National Central University,300 Chung-Da Rd, Chung-Li 32001, Taiwan.

Received: 1 September 2014 Accepted: 11 October 2014Published: 20 October 2014

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doi:10.1186/1556-276X-9-581Cite this article as: Chan et al.: The deviation of growth model fortransparent conductive graphene. Nanoscale Research Letters 2014 9:581.

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