Tailoring the thermal and electrical transport properties of graphene films by grain size engineering

Abstract

Understanding the influence of grain boundaries (GBs) on the electrical and thermal transport properties of graphene films is essentially important for electronic, optoelectronic and thermoelectric applications. Here we report a segregation-adsorption chemical vapour deposition method to grow well-stitched high-quality monolayer graphene films with a tunable uniform grain size from ∼200 nm to ∼1 μm, by using a Pt substrate with medium carbon solubility, which enables the determination of the scaling laws of thermal and electrical conductivities as a function of grain size. We found that the thermal conductivity of graphene films dramatically decreases with decreasing grain size by a small thermal boundary conductance of ∼3.8 × 10⁹ W m^-2 K^-1 , while the electrical conductivity slowly decreases with an extraordinarily small GB transport gap of ∼0.01 eV and resistivity of ∼0.3 kΩ μm. Moreover, the changes in both the thermal and electrical conductivities with grain size change are greater than those of typical semiconducting thermoelectric materials.

ARTICLE

Received 30 Jan 2016 | Accepted 5 Jan 2017 | Published 16 Feb 2017

Teng Ma1, Zhibo Liu1, Jinxiu Wen2, Yang Gao1, Xibiao Ren3, Huanjun Chen2, Chuanhong Jin3, Xiu-Liang Ma1, Ningsheng Xu2, Hui-Ming Cheng1 & Wencai Ren1

Understanding the inuence of grain boundaries (GBs) on the electrical and thermal transport properties of graphene lms is essentially important for electronic, optoelectronic and thermoelectric applications. Here we report a segregationadsorption chemical vapour deposition method to grow well-stitched high-quality monolayer graphene lms with a tunable uniform grain size from B200 nm to B1 mm, by using a Pt substrate with medium carbon solubility, which enables the determination of the scaling laws of thermal and electrical conductivities as a function of grain size. We found that the thermal conductivity of graphene lms dramatically decreases with decreasing grain size by a small thermal boundary conductance of B3.8 109 Wm 2 K 1, while the electrical conductivity slowly decreases

with an extraordinarily small GB transport gap of B0.01 eV and resistivity of B0.3 kO mm. Moreover, the changes in both the thermal and electrical conductivities with grain size change are greater than those of typical semiconducting thermoelectric materials.

DOI: 10.1038/ncomms14486 OPEN

Tailoring the thermal and electrical transport properties of graphene lms by grain size engineering

1 Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, China.

2 State Key Laboratory of Optoelectronic Materials and Technologies, Guangdong Province Key Laboratory of Display Material and Technology, School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, China. 3 State Key Laboratory of Silicon Materials, School of MaterialsScience and Engineering, Zhejiang University, Hangzhou 310027, China. Correspondence and requests for materials should be addressed to W.R. (email: mailto:[email protected]

Web End [email protected] ) or to H.-M.C. (email: mailto:[email protected]

Web End [email protected] ).

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Graphene has attracted increasing interest because of the extraordinary properties of its defect-free pristine form, such as the highest known carrier mobility, record

thermal conductivity and extremely high mechanical strength13. However, large-area graphene lms produced by scalable methods, such as chemical vapour deposition (CVD), usually have various defects, especially grain boundaries (GBs)413, forming a polycrystalline structure. Moreover, the GBs are formed randomly during CVD growth5,6,8,12,13. Therefore, in addition to studies of individual GBs, understanding the inuence of grain size on the overall electrical and thermal transport properties of graphene lms on a large scale is not only fundamental but also technologically important in order to tune their properties for electronic, optoelectronic and thermoelectric applications1224. These studies strongly depend on the controlled synthesis of graphene lms with tunable and uniform grain size that is smaller than the phonon and electron mean free paths (B a few hundreds of nanometres) because the contributions to electrical and thermal transports due to scattering from GBs are more signicant in this range.

From the point of view of crystal growth, it is equally difcult to reduce and increase nucleation density on metals by CVD to fabricate large-size single-crystal graphene and polycrystalline graphene with nano-sized grains, respectively, while keeping monolayer growth of graphene. For surface adsorption growth on the commonly used Cu with a low carbon solubility, a high-concentration carbon source and/or defective substrates have usually been used to obtain a high domain density, however, these conditions led to the formation of multi-layer graphene domains10,25,26. It is well known that the graphene lms segregated from Ni with a high carbon solubility are usually nonuniform multi-layers2729. As a result, the polycrystalline graphene lms prepared so far usually have a grain size ranging from B1 mm to B1 mm (refs 413), which is larger than the electron and phonon mean free paths (a few hundreds of nanometres)21, and/or have very broad grain size distributions5,6. This strongly hinders the experimental studies on the real inuence of grain size on the electrical and thermal transport properties of graphene lms.

It has been theoretically predicted that electrical transport in graphene could be markedly altered by electron scattering at GBs14,15. Consistent with these predictions, many experimental studies on individual GB have shown that GBs can greatly impede electronic transport, thus degrading the carrier mobility and electrical conductivity of graphene4,1013, although a few experiments have shown that perfect inter-grain connectivity at GBs retains the remarkable electrical conductance of graphene7,8. However, the electrical measurements on graphene lms have shown no strong correlation between the average grain size and the overall electron mobility5,9. The present studies on the inuence of GBs on the thermal transport of graphene have been mainly limited to theoretical works, and different calculation methods have led to contradictory conclusions. Some theoretical calculations20,22 have suggested that the thermal transport in polycrystalline graphene could be signicantly degraded when the grain size is smaller than a few hundred nanometres, while others suggested that all types of GBs have excellent thermal transport19. Experimentally, the inuences of the degree of disorders on the thermal and electrical conductivities have been investigated30 and recent thermal transport measurements on individual GB have shown that a single GB can signicantly decrease the thermal conductivity of graphene31. However, the inuence of grain size on the overall thermal conductivity of graphene lms remains unknown.

Here we have developed a segregationadsorption CVD (SACVD) method to achieve a great increase in the nucleation density of

graphene (by segregation) and monolayer growth (by surface adsorption) simultaneously, by using a Pt substrate with medium carbon solubility. As a result, we can easily grow well-stitched high-quality monolayer graphene lms with a tunable uniform grain size from B200 nm to B1 mm, which have never been achieved before by the present conventional CVD methods based on either surface adsorption413,27,32 or segregation mechanism2729. Using these materials, we determined the scaling laws of thermal and electrical conductivities of graphene lms as a function of grain size. It was found that the thermal conductivity of graphene lms dramatically decreases with decreasing grain size by a small thermal boundary conductance of B3.8 109 W m 2 K 1, while the electrical conductivity

slowly decreases with an extraordinarily small GB transport gap of B0.01 eV and GB resistivity of B0.3 kO mm. Moreover, both the thermal and electrical conductivities of graphene change more signicantly with grain size change than that of typical thermoelectric materials3335.

ResultsSACVD growth process. Figure 1a illustrates the fabrication process of polycrystalline graphene lms by SACVD. First, we used a relatively high ow rate of methane mixed with hydrogen to rapidly grow a monolayer dominate graphene lm on a Pt substrate by a surface growth mechanism (Fig. 1b, the rst step). During this process, some carbon atoms were dissolved in the Pt substrate (Supplementary Figs 1 and 2, and Supplementary Note 1) because of the medium carbon solubility of Pt (0.07 wt.%) (ref. 36), which is higher than Cu (0.008 wt.%) but lower than Ni (0.3 wt.%) at 1,000 C (ref. 27). Such medium carbon solubility allows that the growth behaviour of graphene can be tuned between surface adsorption and segregation. We then changed the atmosphere to pure argon to etch the graphene lm formed on the surface into the bulk (Fig. 1c, the second step). After this, we induced the segregation of the dissolved carbon atoms by reintroducing a trace of hydrogen (Supplementary Figs 15 and Supplementary Notes 1 and 2), and a large number of small graphene domains appeared (Fig. 1d, the third step, Supplementary Note 2). Finally, we introduced a low ow rate of methane to induce surface growth of the graphene domains to form continuous monolayer polycrystalline lms (Fig. 1e, Supplementary Fig. 6, the fourth step and Supplementary Note 3).

Interestingly, we can easily obtain a very high domain density that is suitable for growing monolayer graphene lms with a grain size smaller than 1 mm by this SACVD method (Fig. 2ad). The reaction temperature in the segregation process is the only factor that determines the domain density, and this is increased by decreasing the growth temperature (Fig. 2ad and Supplementary Fig. 4). With reaction temperatures of 900, 950, 1,000 and 1,040 C, monolayer graphene domains with respective densities of 9613, 186, 113 and 42 mm 2 were obtained (Fig. 2ad). The corresponding mean domain sizes are

B50 (Figs 1d and 2a), 100 (Fig. 2b), 200 (Fig. 2c) and 500 nm (Fig. 2d). Moreover, the domain density is entirely unrelated to the growth atmosphere, including the ow rates of hydrogen, argon and methane. In sharp contrast, such high-density monolayer graphene domains cannot be achieved by either surface adsorption growth on Cu10,2527 or segregation growth on Ni2729, as mentioned above. In our method, the use of Pt with medium carbon solubility allows the dissolution of a small amount of carbon, which is the key to obtaining a high-density monolayer of graphene domains by subsequent segregation.

Structural characterization. We used dark-eld transmission electron microscopy (TEM)5,6 to determine the grain size of the

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a b

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Figure 1 | SACVD growth of polycrystalline graphene lms with well-controlled grain sizes. (a) Schematic for the fabrication process of a polycrystalline graphene lm. (b) Scanning electron microscope (SEM) image of a graphene lm, mostly monolayer, grown on Pt with a mixture of hydrogen(700 standard-state cubic centimetre per minute, sccm) and methane (7 sccm) for 10 min. (c) SEM image of the Pt substrate in b after treating with pure argon (700 sccm) for 20 min, showing that the graphene lm has disappeared. (d) SEM image of the Pt substrate in c after treating with a trace of hydrogen (5 sccm) for 20 min, showing that many small graphene domains have appeared. (e) SEM image of a monolayer polycrystalline graphene lm formed from d by introducing a low ow rate of methane (0.1 sccm) for 1 h. The reaction temperature was all 900 C in above cases.

graphene lms formed from isolated domains with different densities. To do this, the graphene lms were rst transferred onto a TEM grid with 2 2 mm2 circular holes covered with amorphous

carbon. We then used different objective aperture lters to image the grains with different lattice orientations. Finally, the obtained multiple dark-eld images were coloured with different colours and overlaid to form a complete map of the lms, as shown in Fig. 2eh. It can be clearly seen that the graphene lms consist of high-quality grains with different orientations. TEM and Raman spectroscopy measurements show that all the grains are perfectly stitched together without any gaps (Supplementary Figs 711). We further performed aberration-corrected high-resolution TEM (HRTEM) measurements to obtain atomic-resolution structure information of the GBs. As shown in Fig. 2i,j and Supplementary Fig. 12, the GBs exhibit atomically sharp interface regions by chains of pentagons and heptagons embedded in the hexagonal lattice of graphene without overlapping, buckling and other defects. Note that a low ow rate ratio of methane to hydrogen was used during the surface adsorption growth process. The resulting slow growth rate facilitates the relaxation of metal-carbon system towards thermal equilibrium during growth, and consequently enables the perfect stitching of high-density graphene domains to form high-quality monolayer graphene lms (Supplementary Figs 7 and 8).

We obtained histograms of grain sizes by measuring more than 100 grains for each sample (Fig. 2kn). The mean grain sizes, dened as the square root of the grain area, are 1,01390, 72179, 47074 and 22473 nm. It is important to note that these sizes are much smaller than the typical grain size of the graphene lms reported so far (usually larger than 1 mm) (refs 413), and smaller than or similar to the electron and phonon mean free paths21. Moreover, graphene lms prepared under the same conditions show the same grain size distribution, that is, the process produces reproducible results. This highly reproducible synthesis of graphene lms with a uniform mean grain size, smaller than the electron and phonon mean free paths, and perfect stitching of the GBs, opens up the possibility of investigating the real inuence of grain size on the electrical and thermal transport in graphene.

Thermal transport measurements. Confocal micro-Raman spectroscopy is an efcient method for measuring the thermal conductivity of suspended graphene. Its value is extracted from the dependence of the Raman G or 2D peak frequency on the excitation laser power37,38. Here, we used the 2D peak shift to determine the graphene temperature because of its higher temperature sensitivity than the G peak39. Before thermal transport measurements, we rst characterized the transferred graphene lms on SiO2/Si holey substrates (circular holes: 5 mm in diameter, 290 nm in depth) to make sure that the suspended area is intact. The SEM image shows that most area of the substrate is covered by graphene without visible cracks (Fig. 3a). Figure 3c shows a 40 40 mm2 2D peak intensity map of a

graphene lm with the corresponding optical image shown in Fig. 3b. It can be clearly seen that most of the suspended graphene lms exhibits a uniform and much stronger 2D peak than the supporting area without the D peak (Fig. 3c and Supplementary Fig. 13), indicating that they are intact and have high quality. For thermal measurements, a 532 nm laser beam was focused on the centre of the suspended graphene lm to obtain the power coefcient or on the supported graphene on SiO2/Si to obtain the temperature coefcient, as reported by Balandin et al38. The thermal conductivity (k) of the graphene lms was calculated by k w(1/2hp)(dw/dP) 1, where dw is the shift of 2D peak

position due to the change of heating power dP on the sample, w is the 2D peak temperature coefcient, and h is the thickness of the graphene lm.

Figure 3d shows the Raman spectra of the graphene lms with B200 nm-size grains excited by lasers with different powers.

It is interesting to see that the D peak intensity and ID/IG

increase sharply while the G peak intensity decreases dramatically when the laser power is larger than 1.2 mW (Fig. 3d and Supplementary Fig. 14). The 2D peak upshifts and dramatically increases in intensity with the laser power until 1.2 mW (Fig. 3e,f). However, when further increasing the laser power, the 2D peak intensity decreases and the corresponding peak position changes randomly. Moreover, the intensities of 2D and G peak and ID/IG cannot recover their original values

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14486

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Figure 2 | Structural characterization of graphene domains and lms. (ad) SEM images of graphene domains obtained with a segregation temperature of 900, 950, 1,000 and 1,040 C, showing that the domain density decreases with segregation temperature. (eh) False-colour, dark-eld image overlays of the graphene lms formed by growth and stitching of the graphene domains in ad. Scale bars, 500 nm. (i,j) High-magnication HRTEM images of graphene lms with grain size of B200 and B700 nm, respectively. The pentagons (blue), heptagons (red) and hexagons (yellow) in the GBs are outlined.

All images were processed with an improved Wiener-ltering to remove the noises. Scale bars, 1 nm. (kn) Histograms of grain sizes of the graphene lms in eh, showing that the grain size is very uniform for each sample.

at the same laser power when the laser power was decreased (Fig. 3e and Supplementary Fig. 14). These phenomena indicate that the suspended graphene lms with small grains have been destroyed by the high-power laser. According to the 2D peak shift (13.8 cm 1) and the extracted temperature coefcient (0.039 cm 1 K 1), we estimated that the temperature at the GBs of the graphene lm with B200 nm grains reached 650 K when the laser power was 1.2 mW. Combined with the Raman spectra evolution, the physical origins of the D and G peak40 and the high activity of GB12,41, we suggest that this temperature jump results in the breaking of the graphene lm at GB due to strong thermal vibration42. In sharp contrast, the suspended graphene lms with B1 mm grains (no GBs across the suspended area) remained intact with a low D peak even when illuminated by a laser of 2.8 mW for 10 s (Supplementary Fig. 15). The above results give direct evidence that GBs greatly reduce the thermal conductivity of graphene.

Figure 4a shows the thermal conductivity of the polycrystalline graphene lms (k) as a function of grain size (lg). It is clear that the thermal conductivity increases exponentially from

B610 to B5,230 W m 1 K 1 when the grain size is increased

from B200 nm to B10 mm. In fact, the graphene lms with grain size larger than B5 mm (the size of the suspended area) all show a similar thermal conductivity of B5,200 W m 1 K 1 (thermal conductivity within the grain, kg), which is similar to the value reported for pristine graphene made by mechanical exfoliation38.

This conrms that our measurement method is appropriate and our SACVD grown samples have very high quality, which rules out the inuence of defects on the thermal conductivity and ensures that the thermal conductivity change is intrinsically related to GBs. On the basis of the kinetic theory of phonon transport21, the effective phonon mean free path is given by leff 1 l

phph

1 lg 1, where lphph denotes the phonon phonon scattering length and lg is the scattering length due to the boundaries (that is, grain size)18. Consistent with this, it is very interesting to note that the inverse of thermal conductivity (k 1) versus the inverse of grain size (lg 1) can be well t by k 1 kg 1 (lgG) 1, where kg is the thermal conductivity

within the grain (B5,200 W m 1 K 1) and G is the boundary conductance18. The extracted thermal boundary conductance is

B3.8 109 W m 2 K 1, which is consistent with the theo

retical value obtained using non-equilibrium Greens functions (38 109 W m 2 K 1) (ref. 20). The scaling law can be written

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Figure 3 | Thermal transport of graphene lms with B200 nm-sized grains. (a) SEM image of a polycrystalline graphene lm on a holeySiO2/Si substrate. Scale bar, 10 mm. (b) Optical image of a polycrystalline graphene lm transferred onto a holey SiO2/Si substrate. Scale bar, 10 mm.

(c) Raman map of the polycrystalline graphene lm shown in b, and the typical Raman spectra are shown in Supplementary Fig. 12. (d) Raman spectra of the polycrystalline graphene lm excited with different power lasers. (e,f) Intensity (e) and position (f) of the 2D peak as a function of laser power.

Raman shift (cm1)

as k 1 0.26 lg 1 0.19. As we know, the scattering of phonons

within the grains primarily determine the thermal conductivity of the polycrystalline graphene when the grains are large in size, while the contribution to thermal conductivity due to scattering from GBs becomes more signicant with decreasing grain size18. Using the above scaling law, we estimated that the critical size of grains below which the contribution from the GBs becomes comparable to the scattering from the grain is lg kg/GE1.4 mm.

Electrical transport measurements. To evaluate the inuence of GBs on electrical properties, we used a four-probe station to

measure the sheet resistances of the graphene lms with different grain sizes (Fig. 4c), and dozens of positions were measured for each sample (2 cm 2 cm). We t the data using modied

Arrhenius equation43 s s0 exp{ Ea/[RT(lg c)]} (Fig. 4d),

where s is the electrical conductivity of the polycrystalline graphene lms, s0 is the electrical conductivity within the grain, Ea is the GB transport gap (the energy that is needed to overcome for the charge carrier transmitting through the GB region), R is the universal gas constant, T is the absolute temperature, lg is the grain size and c is the correction value. The tting gives s0E2.85 106 S m 1 and EaE0.01 eV. Note that the

GB transport gap extracted here is dramatically smaller than the theoretically predicted value for asymmetric GBs (0.31.4 eV)

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[afii9846] = 2.85 exp[0.43/(Ig + 0.27)]

0 2 4 6 8 10 Ig (m)

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Figure 4 | Thermal and electrical transport of the graphene lms with different grain sizes. (a) Thermal conductivity as a function of grain size with a t (red curve). The error bars (standard error of the mean, s.e.m.) represent the thermal conductivity variation measured for the same sample. (b) The inverse of thermal conductivity as a function of the inverse of grain size with a t (red curve), showing a linear relationship. (c) Sheet resistance as a function of grain size with a t (red curve). (d) Electrical conductivity as a function of grain size with a t (red curve), showing an exponential relationship. The error bars (s.e.m.) in c and d represent the electrical conductivity variation measured for the same sample and the samples prepared with the same conditions.

(ref. 14). Using this scaling law, we found that the GBs begin to dominant the electrical conductivity of the poly-crystalline graphene lms only when the grain size is smaller than lgE0.8 mm. We also t the data using the equation Rs RsG rGB/lg (Supplementary Fig. 16)13, where Rs is

the sheet resistance of the polycrystalline graphene lms, RsG is the

sheet resistance within the grain, rGB is the GB resistivity and lg is

the grain size. The tting gives RsGE0.98 kO sq 1 and rGBE0.33 kO mm. It is worth noting that the GB resistivity extracted here is smaller than those reported previously, typically larger than 0.5 kO mm4,8,13,44, further conrming the perfect stitching of neighbouring grains in our graphene lms. Both the small GB transport gap and GB resistivity suggest the weak inuence of grain size on the electrical conductivity, which is in sharp contrast to thermal conductivity. As shown in Supplementary Fig. 17, when the mean grain size is increased from B200 nm to B1 mm (ve orders of magnitude increase), there is only a fourfold increase in electrical conductivity. The above results suggest that increasing grain size is not an efcient way to improve the electrical conductivity of graphene for transparent conductive electrode applications when the grain size is larger than 1 mm.

DiscussionTo further compare the inuence of GBs on the thermal/ electrical conductivity of graphene lms, we plotted (Fig. 5) the thermal/electrical conductivity change rate as a function of grain

size change rate (Dlg lg 1). Note that the thermal conductivity change rate (Dk k 1) increases linearly with grain size change rate (Fig. 5a), while electrical conductivity change rate (Ds s 1)

increases exponentially with grain size change rate (Fig. 5b). More importantly, the thermal conductivity change rate of graphene is dramatically larger than the electrical conductivity change rate (Fig. 5). According to the scaling law of thermal conductivity as a function of grain size shown above, the thermal conductivity of graphene lms with a grain size of 5 nm is extrapolated to be B19.2 W m 1 K 1, a B300 times decrease compared with pristine graphene. However, the electrical conductivity is extrapolated to be B5.9 105 S m 1 based on the modied Arrhenius

equation with better tting than the equation Rs RsG rGB/lg,

only a B10 times decrease compared with graphene with a millimetre grain size. Therefore, nano-crystallization should be an efcient way to tune the electrical and thermal conductivities of polycrystalline graphene lms for thermoelectric applications if graphene could be used in thermoelectric materials in the future as predicted45,46. Even for the graphene lms with a 1-nm grain size, both the thermal and electrical conductivities are much larger than those of amorphous carbon although its grain size is much smaller17, indicating that the disorder within grain plane may have much stronger inuence on the electrical and thermal properties of carbon materials.

We also compared the thermal/electrical conductivity change rate of graphene with those of some typical metals (Au, Ag, Cu and Al)4749 and semiconducting thermoelectric materials

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Figure 5 | Thermal/electrical conductivity change rate of graphene with grain size change rate. (a) Thermal conductivity change rate of grapheneas a function of grain size change rate with a t (blue curve), showing a linear relationship. (b) Electrical conductivity change rate of graphene as a function of grain size change rate with a t (blue curve), showing an exponential relationship. The thermal/electrical conductivity change rates of some typical metals (Au47, Al47, Ag48 and Cu49) and semiconducting thermoelectric materials (BiSbTe33, SrTe34 and BiTeSe35) are also shown in different colours for comparison.

(BiTeSe, SrTe and BiSbTe)3335. As shown in Fig. 5, the thermal conductivity change rate of graphene is much larger than those of all the compared materials, while the electrical conductivity change rate of graphene is larger than those of thermoelectric materials but smaller than those of metals. Moreover, the rates of change of electrical and thermal conductivity with grain size are almost the same for semiconducting thermoelectric materials. For instance, both the thermal and electrical conductivities of SrTe decrease by only 37% when its grain size is reduced by 99.8% of the pristine value (B500 times difference)34. In contrast, when the grain size of graphene is decreased by 90% (10 times difference), its thermal and electrical conductivities are reduced by 89% (10 times difference) and 48% (two times difference), respectively. These results further conrm that nano-crystallization should be an efcient way to improve the thermoelectric properties of graphene.

The GBs in graphene can be approximated as linear periodic arrays of dislocations12. The crystal momentum conservation has a crucial role in the transmission of charge carriers across these topological defects14. As reported previously14, these GBs can be classied into two classes according to the matching vectors (nL, mL) and (nR, mR) that belong to the left and right crystalline domains, respectively. If only one matching vector fullls the criterion (nm) 3q (q, integer), then the GB is of class-II type.

Otherwise it belongs to class-I. For class-II GB, there is signicant misalignment of the allowed momentumenergy manifolds corresponding to the two crystalline domains of graphene, which introduces a transport gap (usually 0.31.4 eV) that depends exclusively on the periodicity14,45. That is, class-II GB perfectly reects low-energy carriers. In contrast, class-I GB is highly transparent with respect to charge carriers14,45. Different from the strong dependence of charge carrier transport on GB type, the phonon transmission shows a weak dependence on GB type45. More importantly, both types of GBs greatly suppress the phonon transmission45. Therefore, the thermal conductivity change rate of graphene as a function of grain size is dramatically larger than the electrical conductivity change rate. However, the deep mechanisms and physical pictures need to be further studied in the future.

In conclusion, we report a SACVD method to grow well-stitched high-quality monolayer graphene lms with a tunable uniform grain size from B200 nm to B1 mm, by using a Pt substrate with medium carbon solubility. Using these

materials, we determined the scaling laws of the thermal and electrical conductivities of graphene lms as a function of grain size. It was found that the thermal conductivity of polycrystalline graphene lms dramatically decreases with decreasing grain size by a small thermal boundary conductance of B3.8 109 W m 2 K 1, while the electrical conductivity

slowly decreases with an extraordinarily small GB transport gap of B0.01 eV and GB resistivity of B0.3 kO mm. Moreover, the changes in both the thermal and electrical conductivities with grain size change are greater than those of typical semiconducting thermoelectric materials. These ndings provide valuable information for tuning the thermal and electrical properties of graphene for electronic, optoelectronic and thermo-electric applications through grain size engineering.

Methods

SACVD growth of polycrystalline graphene lms. A typical procedure for the SACVD growth of graphene lms with grain sizes o1 mm includes four steps: surface growth, etching, segregation and surface growth. Before growth, a piece of Pt foil (180 mm thick, 99.9 wt% metal basis, 20 mm 20 mm) was rinsed with

acetone and ethanol in sequence for 1 h each, loaded into a fused-silica tube (inner diameter: 22 mm), heated to a certain temperature under the protection of hydrogen, and then annealed for 10 min to remove any residual carbon or organic substances. The rst step: surface growth was started with the substrate being held for a certain time under a mixture of methane and hydrogen. In the second step the methane and hydrogen ows were turned off, and pure argon (700 sccm) was introduced to the system for 20 min to etch the graphene grown on the Pt inthe rst step into the bulk. In the third step, a small amount of hydrogen was introduced into the system to mix the argon ow, initiating segregation of the carbon to form small graphene domains on the Pt surface. In the fourth stepa low ow rate of methane (0.1 sccm) was introduced into the system while maintaining the hydrogen and argon ows, to cause surface growth of the graphene domains produced in step 3 to form a continuous polycrystalline lm. The detailed experimental conditions were given in the main text and Supplementary Information. Polycrystalline graphene lms with grain sizes larger than 1 mm were grown by conventional CVD as previously reported11.

Structural characterization. To investigate the structure of the graphene formed at different stages, the Pt foil was quickly pulled out of the high-temperature zone after SACVD growth. The furnace was then shut down and the methane ow was stopped after the furnace temperature had decreased to 600 C. Finally, the Pt foil was taken out and characterized by SEM (Nova NanoSEM 430, acceleration voltage of 5 kV). The small graphene domains and polycrystalline lms were transferred onto Si/SiO2 (290 nm) substrates using a improved bubbling transfer method11, in which the Poly(methyl methacrylate) (PMMA) used for transfer had a smaller molecular weight (600 kDa, 4 wt.% in ethyl lactate) and the acetone used for removing PMMA was heated at 50 C to enhance the solubilities, for

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14486

morphological and quality analysis by optical microscopy (Nikon LV100D) and Raman spectroscopy (JY HR800, 532 nm laser wavelength, 1 mm spot size, 1 s integration time, laser power below 2 mW). The polycrystalline lms were transferred to TEM grids by using a improved bubbling transfer method mentioned above for GB analysis by TEM (FEI Tecnai F20, 200 kV; FEI Tecnai T12, 120 kV; FEI Titan G2 equipped with an image-side spherical aberration corrector, 80300 kV).

Thermal and eletrical transport measurments. We used a Renishaw inVia micro-Raman spectroscopy system with a 532 nm laser as excitation source to measure the thermal conductivity of the graphene lms. A laser beam witha spot size of 1 mm was focused onto the samples through a 50 objective

(NA 0.8), and the integration time at each position was 10 s. The temperature

rise was determined from the shift of the Raman 2D peak. The sheet resistances of the graphene lms were measured by a four-probe method (RTS-9) atroom temperature. These two methods have been widely used in the literatures12,13,38,44,50. It is worth noting that the measured sheet resistance of the graphene on SiO2/Si substrate and thermal conductivity of the suspended graphene in our experiments show the similar values with those of graphene with similar grain size reported in the literatures44,50. Moreover, we also measured the thermal conductivity of the suspended mechanical exfoliated graphene lms, which gives a value of up to 5.7 103 W m 1 K 1, close to the reported value

(5.3 103 W m 1 K 1) (ref. 38). These comparison results give concrete

validations for our methodology.

Data availability. The data that support the ndings of this study are available from the corresponding author upon request.

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Acknowledgements

This work was supported by the Ministry of Science and Technology of China (No. 2016YFA0200101), National Science Foundation of China (Nos. 51325205, 51290273, 51521091, 51172240 and 51222202), and Chinese Academy of Sciences (Nos KGZDEW-303-1 and KGZD-EW-T06). This work partly used the resources of the Center of Electron Microscopy of Zhejiang University.

Author contributions

W.R. proposed the project. W.R. and H.M.C. supervised the project. W.R. and T.M. designed the experiments. T.M. performed the experiments. Z.L. performed TEM measurements under the supervision of X.M. J.W. performed thermal measurements under the supervision of H.C. and N.X. X.R. performed aberration-corrected HRTEM measurements under the supervision of C.J. W.R. and T.M. analysed the experimental data. W.R., T.M. and H.M.C. wrote the manuscript. All the authors discussed the results and commented on the manuscript.

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How to cite this article: Ma, T. et al. Tailoring the thermal and electrical transport properties of graphene lms by grain size engineering. Nat. Commun. 8, 14486doi: 10.1038/ncomms14486 (2017).

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