Subscriber access provided by University of Newcastle, Australia
Communication
In-plane thermal conductivity of polycrystalline CVD graphene with controlled grain sizes Woomin Lee, Kenneth David Kihm, Honggoo Kim, Seungha Shin, Changhyuk Lee, Jae-Sung Park, Sosan Cheon, Ohmyoung Kwon, Gyumin Lim, and Woorim Lee Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b05269 • Publication Date (Web): 02 Mar 2017 Downloaded from http://pubs.acs.org on March 3, 2017
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Nano Letters is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
In-plane thermal conductivity of polycrystalline CVD graphene with controlled grain sizes Woomin Leea, Kenneth David Kihm*a,c, Hong Goo Kima, Seungha Shinc, Changhyuk Leea, Jae Sung Parka, Sosan Cheona, Oh Myoung Kwonb, Gyumin Lima, and Woorim Leea a
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea, Department of Mechanical Engineering, Korea University, Seoul 136-713, Korea, c Mechanical, Aerospace, and Biomedical Engineering, the University of Tennessee, Knoxville *
[email protected] b
ABSTRACT: Manipulation of the CVD graphene synthesis conditions, such as operating P, T, heating/cooling time intervals, and precursor gas concentration ratios (CH4:H2), allowed for synthesis of polycrystalline single-layered graphene with controlled grain sizes. The graphene samples were then suspended on 8-µm diameter patterned holes on a silicon-nitride (Si3N4) substrate, and the in-plane thermal conductivities k(T), for 320K < T < 510K, were measured to be 2660-1230, 1890-1020, and 680-340 W/mK for average grain sizes of 4.1, 2.2 and 0.5 µm, respectively, using an opto-thermal Raman technique. Fitting of these data by a simple linear chain model of polycrystalline thermal transport determined k = 5500-1980 W/mK for single-crystal graphene, for the same temperature range above; thus, significant reduction of k was achieved when the grain size was decreased from infinite down to 0.5 m. Furthermore, detailed elaborations were performed to assess the measurement reliability of k by addressing the hole-edge boundary condition, and the air-convection/radiation losses from the graphene surface. KEYWORDS: graphene, CVD, grain size effect, thermal conductivity electron beam irradiation.11 On the other hand, the grain size variation is expected to enable more effective thermal transport control by including the grain boundary scattering effect in addition to size confinements. A number of theoretical studies evidenced the potential merit of grain size variation for thermal transport control; non-equilibrium Green’s function theory showed the reduction of thermal conductivity by decreasing grain sizes for supported graphene, 12 theoretical characterization of phonon transport in polycrystalline graphene found the thermal conductivity to increase with the grain size,13 and molecular dynamics simulations for the thermal transport behavior were performed to study the effect of grain size on the thermal conductivity of polycrystalline graphene.14 However, in our extensive search of literature, no study has been published that experimentally probed the grain size effect on thermal conductivity of polycrystalline graphene. In our experiment, the grain size of the CVD graphene has been effectively controlled by carefully adjusting the CVD conditions for operating pressure, temperature, time intervals for different progress steps, and the precursor gas ratios of CH4:H2 (SISection 1.1). In-plane thermal conductivity of suspended graphene layers has been determined from correlations of the Raman signal peak shifts with the laser heating spot temperature changes, using the 514 nm Raman micro spectroscopy system (Renishaw inVia-reflex model with a 100x 0.75 NA objective). The main focus is to correlate the in-plane thermal conductivity with controlled grain sizes of suspended CVD graphene. Our experimental findings are also supplemented by elaborating a linear chain model of polycrystalline thermal transport (SI-Section 5). Heat transport in defect-free single-crystalline graphene (Fig. 1a) is inherently governed by phonon-phonon scattering and
The lattice vibration of graphene accounts for the majority of heat conduction while the electric carrier contribution is negligibly small because of the near-zero charge carrier density for heat transport in pristine graphene.1,2 Thus, polycrystalline CVD graphene holds the potential for improving thermoelectric conversion efficiency (electric power factor/thermal conductivity, the so-called figure of merit ZT) by creating fine grains and independently lowering its thermal conductivity, which attributes to the enhanced boundary phonon scattering. Feasibility of independent lowering of thermal conductivity was also demonstrated for the case of a nanomesh-patterned semiconductor thin film, where its bulk-like electrical conductivity was preserved.3 Also, phonons with longer mean free paths (775 nm)4 tend to be more length scale-dependent than electron carriers with relatively shorter mean free paths (10-100 nm)5, and thus, when the grain size is reduced, a larger decrease in thermal transport can be expected than that in electrical transport. A combination of grain size control and other means, such as creating more favorable band structures, can possibly enhance the figure of merit - for instance, incorporating heavy adatoms and nanopores on graphene to suggest maximum ZT of 36 or employing edge-disordered zigzag graphene nanoribbons to devise a higher ZT.7 The effect of confined phonon mean free paths on graphene thermal conductivity has been examined by different groups; suspended graphene strips of various sizes (300 nm – 9 µm) showed strong length-dependence of their thermal conductivities,8 the hole-size dependence of thermal conductivity was experimentally examined for suspended graphene on the holes,9 the effect of surface wrinkles of graphene on thermal conductivity was studied using microRaman,10 and more recently, the effect of surface defects was investigated by inducing them on suspended graphene using
1 ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 8
broadenings of the full width at half maximum(FWHM).27 For the three samples with 𝑙𝐺 = 4.1, 2.2, and 0.5 µm, the measured optical absorption ranges from 2.95 to 3.17 %, showing no apparent correlation with the grain size, but falls within the known range of absorption of single-layer CVD graphene.9,10,28,29
should be limited by the dominant length scale of the phonon mean free path.15 In contrast, polycrystalline growth of CVD graphene (Fig. 1b) hinders the in-plane thermal transport due to additional phonon scattering associated with the grain boundaries (GBs). Increased GB concentration with smaller grains provides more frequent phonon scatterings and further deterioration of heat transfer. During the initial growth stage of graphene, both lower synthesis temperatures and higher methane flow rates allow denser nucleation of carbon atoms (Fig. 1c);16-19 thus proper combination of these conditions can create CVD graphene specimens with variable grain sizes as summarized in Table 1. Each of the synthesis recipes for both 4.1 ㎛ and 2.2 ㎛ grains consists of double steps: (1) the initial low CH4:H2 ratio reduces the initial nucleation density to allow the grain islands to grow slowly into relatively larger grains and (2) the higher CH4:H2 ratio of step 2 provides a sufficient amount of hydrocarbon radicals for full coverage beyond the island boundaries. (See more details in SI-Section 1.1). Note that the three images of Fig. 1c were taken at the prematurely grown CVD stage only to visibly confirm the different nucleation densities under different synthesis conditions. Once fully grown, the grain boundaries are optically invisible, but mild dry annealing (MDA)20 allows for visibility (Fig. 1d), owing to the fact that oxygen molecules readily penetrate the defects of grain boundaries (GBs) to oxidize the Cu substrate beneath along the grain boundaries.21 The digitally enhanced contrast further clarifies the grain boundaries (Fig. 1e) and the proper image analysis provides both the grain size distributions and their average values (Fig. 1f). The average grain size is given by the area-equivalent diameter that is defined as 𝑙𝐺 = √4𝐴/𝜋𝑛 where A is the total graphene area and n is the total number of grains (SI-Section 1.2). The graphene samples were then transferred via the PMMA (poly-methyl methacrylate) spin-coating/etching process22 onto the 8 m hole patterns that were made by micro-electro mechanical systems (MEMS) process including the deep reactive-ion etching (DRIE) and wet etching of a silicon-nitride (Si3N4) substrate (Figs. 2a & b). A thin Au (0.1 m)/Cr (10 nm) layer was sputtered on the substrate to increase the contact conductance of the suspended graphene layer. The hole diameter (D) was selected to be an order-of-magnitude larger than the typically known mean-free path 𝑝 ~ 775 nm for acoustic phonons at room temperature (Kn = D/2 𝑝 ~ 5.2),4 ensuring that the hole size is sufficiently large that the incident Gaussian laser heat absorbed at the center region of the suspended graphene can be assumed to transfer to the hole edge almost entirely by diffusion (Fig. 2c). Also, the selected hole size is at least twice larger than the largest grain sizes of tested grain samples so that the grain size and boundary effects can be properly included in k measurements. The distinctive G peak and 2D peak of the Raman spectra, together with their peak ratio of I(2D)/I(G) ~ 3.0 (Fig. 2a), depict the typical footprint23,24 of single-layer graphene (SLG).25 Also, a more pronounced D peak is observed with decreasing grain size showing higher I(D)/I(G) (Fig. 2d), which is consistent with expectations of more defects or atomic irregularities in association with smaller grain sizes.26. For increasing defect density for smaller grains, the 2D peaks also show significant
Fig. 1 (a) The phonon-phonon scattering is dominant for heat spreading in singlecrystal graphene. (b) There are additional GB scattering in polycrystalline graphene. (c) SEM images of different nucleation densities in the initial growth state depending on the synthesis temperature and pressure. (d) The optical images of the graphene with different grain sizes using MDA. (e) The images of clear GBs after digital image processing. (f) The distribution histograms of grain sizes. Table 1. CVD operation matrix for polycrystalline graphene synthesis with different grain sizes.
Average grain size (m) CVD synthesis temperature (C) CVD synthesis pressure (Torr) Cursor gas volume flow rate ratio for CH4:H2 Cursor gas flow duration (min)
2 ACS Paragon Plus Environment
0.5
2.2
4.1
800
900
1000
Step 1
Step 2
Step 1
Step 2
0.37
1.08
0.19
0.30
200 :100
80:5
200 :100
30:5
60:5
25
20
10
10
5
1.09
Page 3 of 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
determines the radial profiles of the temperature as a function of the in-plane thermal conductivity k together with other known geometrical variables as follows:
k
Q ln( R / r0 ) 2 t (Tm T0 )
(1)
where the measured temperature Tm at the laser spot area is determined from the 2D peak shift of Raman spectra. The Au/Cr contact layer temperature To is set equal to the ambient temperature (this assumption will be validated later and also in SI-Section 4) and α ~ 1.099 represents an integral function of r0 and R.28,31 The measured in-plane thermal conductivities of graphene (Fig. 3) show its grain size (𝑙𝐺 )- and temperature-dependence for the range of average grain sizes from 500 nm to 10 µm. Each data point represents an average of 10 individual opto-thermal Raman measurements. The single data point (◇) represents the thermal conductivity of exfoliat ed graphene with supposedly infinite or very large grain size.31 Considering the ballistic behavior of phonon inside grains and boundary scattering, the single-crystalline bulk graphene conductivities are estimated by extrapolation/fitting of the our experimental data as shown by the curve (SI-Section5), which are comparable, within our experimental uncertainty ranges, with previous reports of both theoretical and experimental findings.4,12,31,32 The discrepancy of this measured k value from the ideal limit of calculations is possibly due to the edge effect associated with the relatively smaller dimension (3 µm) of the rectangular geometry of their suspended graphene on the trench of the same width. The high thermal conductivity of
(514 nm)
Fig. 2 (a) The schematic and Raman spectra of graphene sheets suspended on the 8 m hole. (b) Schematic of suspended graphene on the hole pattern that was made by microelectro mechanical systems (MEMS) process including the deep reactive-ion etching (DRIE) and wet etching of a silicon-nitride (Si3N4) substrate. (c) Schematic illustration of the suspended graphene on a hole of radius R=4 µm and supported thereafter. (d) The ratio of Raman D peak to G peak versus the full width at half maximum (FWHM) of 2D peak. These multiple data points were measured at random area in the same samples for each grain size.
The in-plane thermal conductivity k of suspended graphene is measured from the temperature-dependent 2D peak shift in the Raman spectra (SI-Section 1.3), also known as the optothermal Raman technique.30 When the Raman laser beam of nominal radius ro is incident on the hole-suspended graphene of radius R and thickness t (the inset schematic of Fig. 2d), the absorbed laser heating amount Q is given by the incident laser power multiplied by the graphene absorption. Assuming negligibly small convection from the graphene surface to air (this assumption will be further assessed later and also in SISection 3), the axi-symmetric heat conduction equation
Fig. 3 The thermal conductivity as a function of the measured temperature for the suspended graphene on the hole of 8 m in air with grain sizes of 0.5, 2.2 and 4.1
m. The “◇” symbol represents the thermal conductivity of exfoliated graphene [31]. The thermal conductivities of “” were measured for the suspended graphene on the hole of 9.7 m in air and the thermal conductivities of “+” were measured for the suspended graphene on the hole of 8 m in vacuum condition [9].
3 ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
the graphene with the large grains of average size 10 µm can be attributed to the inclusive contributions from thermal conductance associated with the long-wavelength phonons (also with long p) inside the grain as well as their relatively good transmittance across the grain boundaries. The air convection heat loss slightly overestimates the measured conductivity in air (the “” symbols) than the measured conductivity in vacuum (the “+” symbols) as the heat loss is accounted for in the optothermal Raman process via enhanced thermal transport. For the graphene with smaller grain sizes of both 4.1 µm and 2.2 µm, the phonon dispersive range is reduced because of the smaller sizes, which in turn limits the long-wavelength phonon contributions and ultimately results in lowered conductivities. When the grain size is further reduced to 500 nm, below the phonon mean-free path of graphene (~775 nm), a more substantial reduction of thermal conductivity is observed down to approximately 1/5 of that for 4.1 µm grains. In the case of supported graphene on a SiO2 substrate, the non-equilibrium Green’s function (NEGF) analysis also demonstrated that the inplane thermal conductivity is subjected to a more distinctive decrease when the grain size approaches that of the phonon mean free path.12 The thermal conductivity of graphene decreases with increasing temperature, attributing at least partially to the enhanced phonon-phonon Umklapp scattering at higher temperature.2,33 This negative temperature dependence, however, gradually diminishes as the grain size decreases: k ~ T -1.95, T -1.38, T -1.30, and T -0.80 for 𝑙 = 10, 4.1, 2.2, and 0.5 µm, 𝐺 respectively. (The power law for temperature dependence is obtained by fitting the measured average conductivities, and the coefficients of determination (R2) are 0.953, 0.952, and 0.733, for grain sizes of 4.1, 2.2, and 0.5 μm, respectively.) Umklapp scattering and grain boundary scattering are regarded as two major scattering mechanisms of thermal carriers (i.e. phonons) in polycrystalline graphene. While the Umklapp scattering has strong temperature dependency due to increasing phonon populations at higher temperatures, grain boundary scattering depends on grain boundary density or grain sizes in addition to temperature.34 Theoretical analysis based on harmonic approximation demonstrates increasing boundary conductance with temperature as more phonons contribute to thermal transport.15 (This positive temperature dependency can be reduced by including anharmonic effects as in SI-Section 5.) Therefore, the negative temperature dependence of thermal conductivity is weakened by increasing the boundary scattering dominance in smaller-grain polycrystalline graphene. The overall measurement uncertainties for k are estimated by the so-called “root-sum-square” method35 and the resulting relative uncertainties 𝑈𝑘 /𝑘 range about ±22% for graphene samples with 4.1 µm grains, ±16% to ±24% for 2.2 µm grains, and ±15% to ±28% for 0.5 µm grains, all for the tested temperature range from 320K to 510K (SI-Section 2). The solid curve shows maximum k values calculated for infinitely large grains or ideal single-crystal graphene using the simple linear chain model (SI-Section 5). Thermal transport inside grains and across grain boundaries also depends on the grain crystallographic orientation36; thus, if the aspect ratio or
Page 4 of 8
crystallographic orientation of grains can be controlled, further reduction or enhancement of thermal conductivity can be achieved. However, the random orientations of grains in the CVD graphene mostly average out this effect to be insignificant. Despite the earlier finding of a minor correction requirement for the air convection loss for the case of graphene sample with relatively large 10-µm grain size,9 the air convection loss effect on k is re-examined for the graphene samples with the present smaller grain sizes. In lieu of using Eq. (1), the full energy balance equation that governs the heat transfer of the suspended graphene under the air convection loss was numerically solved (SI-Section 3), using the previously estimated air convection coefficient of h = 2.9 + 5.1/-2.9 x 104 W/m2K.9 For the two grain sizes of 4.1 and 2.2 µm, the discrepancies associated with the convection heat loss span up to 20% (Fig. 4a & b), which are fairly within the k measurement uncertainty ranges (±16% ~ ±24%). For the graphene samples with the smallest 0.5 µm grains (Fig. 4c), the relative deviations appear greater due to the substantially lowered k, while the deviation magnitudes are actually smaller compared with the previous two cases with bigger grains. Additionally, these k discrepancies may be exaggerated due to the excessively large uncertainties of the available h value, which presents a wide range from 0 to 8.0 x 104 W/m2K.12 Despite these uncertainties, the convection air loss effect turns out to be nontrivial for smaller grain size cases. However, since our study is focused on the lowered thermal conductivity due to the reduced grain sizes and its relative comparison, the degree of persistent overestimation of k when neglecting the air convection loss does not substantially affect the main discussions. The radiative heat losses, on the other hand, turned out to be quite negligible for all tested cases. The radiation heat transfer coefficient is given by ℎ𝑟𝑎𝑑 = 𝜀𝜎(𝑇 + 𝑇𝑜 )(𝑇 2 + 𝑇𝑜2 ), where σ is the Stefan-Boltzmann constant (5.670 × 10−8 Wm−2K−4) and the emissivity = 1.0, assuming a blackbody emission. For the upper limit temperature of 550K, the maximum ℎ𝑟𝑎𝑑 is estimated to be 18.92 W/m2K, which is quite negligible compared with the estimated convection heat transfer coefficient h = 2.9 x 104 W/m2K. Numerical solutions of the full heat transfer governing equations (SI-Section 4), accounting for the possible heat losses along the supported graphene as well as through the substrate - so-called parasitic thermal resistors, show that the discrepancy between the calculated hole-edge temperature and the ambient temperature To is less than 1K for the all tested cases (Table 2). This validates the aforementioned assumption in that the hole-edge temperature is equal to the ambient temperature To within 0.34% accuracy and that the heat leakage through the supported graphene/substrate is negligibly small. Furthermore, the corresponding errors in k due to the edge temperature discrepancies (maximum 0.34%) spans to 0.41%, and these error bounds are substantially narrower than the kmeasurement uncertainty, which ranges from ±15% up to ±28%.
4 ACS Paragon Plus Environment
Page 5 of 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
Table 2. The hole edge temperature variations from the environmental temperature (To = 300 K) and corresponding errors in thermal conductivity k for the three tested grain sizes at two different temperatures
Tgraphene = 300 K
Tgraphene = 500 K
Grain size (㎛)
THole edge (K)
k-error (%)
THole edge (K)
k-error (%)
4.1
300.08
0.41
300.76
0.24
2.2
300.16
0.29
300.69
0.18
0.5
300.96
0.19
300.21
0.02
Due to a large relaxation time mismatch between different energy carriers and tightly focused laser spots smaller than the thermalization length, local nonequilibrium (NE) between different phonon polarizations is expected inside the laser spot.37,38 While the most prominent 2D peak shifts were used in determining our temperature data T2D, the next prominent G peak shifts have now been additionally examined to assess any discrepancies between TG and T2D (Table 3). The slightly higher TG compared with T2D for the tested laser power range of 3.5 to 4.5 mW shows that the phonon system is not fully thermalized to an equilibrium. This can be attributed to the fact that population of high energy LA and TA phonons influences the G peak shift, while the 2D peak shift is affected by near Brillouin zone center phonons with lower energies.39 The temperature discrepancies between TG and T2D, ranging from 2.63 % to 8.47 % for the tested laser power range, are within the relatively large Raman measurement uncertainties ranging from ±15 % up to ±28 %. This supports that the NE effect possibly increases the overall measurement uncertainties, however, we believe that this does not contradict our main findings of the grain size effects on thermal conductivity of graphene. In summary, the thermal conductivities of polycrystalline CVD graphene with different grain sizes were probed to investigate the grain boundary effect on thermal transport. By controlling the methane flow rate as well as synthesis temperature and pressure, we created graphene with average grain sizes of 4.1, 2.2, and 0.5 m, and measured their thermal
Table 3. Temperature discrepancies between TG and T2D for the tested laser power range of 3.5 to 4.5 mW
Fig. 4 Comparison of thermal conductivities (k) with (open mark with a dash) and without convection effect (solid) in CVD polycrystalline graphene with a grain size of (a) 4.1 μm, (b) 2.2 μm, and (c) 0.5 μm.
Incident Laser Power
TG
T2D
(mW)
(K)
(K)
(TG – T2D)/ T2D
3.5
409.8 18.3
399.3 12.6
2.63%
4.0
436.5 21.7
417.6 14.1
4.53%
4.5
482.6 28.5
444.9 18.2
8.47%
5 ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 6 of 8
4. Ghosh, S.; Calizo, I.; Teweldebrhan, D.; Pokatilov, E.; Nika, D.; Balandin, A.; Bao, W.; Miao, F.; Lau, C. Applied Physics Letters 2008, 92, (15), 151911. 5. Tse, W.-K.; Hwang, E.; Sarma, S. D. Applied Physics Letters 2008, 93, (2), 023128. 6. Chang, P.-H.; Bahramy, M. S.; Nagaosa, N.; Nikolic, B. K. Nano Lett 2014, 14, (7), 3779-3784. 7. Sevinçli, H.; Cuniberti, G. Phys. Rev. B 2010, 81, (11), 113401. 8. Xu, X.; Pereira, L. F.; Wang, Y.; Wu, J.; Zhang, K.; Zhao, X.; Bae, S.; Bui, C. T.; Xie, R.; Thong, J. T. Nat. Commun. 2014, 5. 9. Chen, S.; Moore, A. L.; Cai, W.; Suk, J. W.; An, J.; Mishra, C.; Amos, C.; Magnuson, C. W.; Kang, J.; Shi, L., Ruoff, R. S. Acs Nano 2010, 5, (1), 321-328. 10. Chen, S.; Li, Q.; Zhang, Q.; Qu, Y.; Ji, H.; Ruoff, R. S.; Cai, W. Nanotechnology 2012, 23, (36), 365701. 11. Malekpour, H.; Ramnani, P.; Srinivasan, S.; Balasubramanian, G.; Nika, D. L.; Mulchandani, A.; Lake, R. K.; Balandin, A. A. Nanoscale 2016, 8, (30), 14608-14616. 12. Serov, A. Y.; Ong, Z.-Y.; Pop, E. Applied Physics Letters 2013, 102, (3), 033104. 13. Wang, Y.; Song, Z.; Xu, Z. Journal of Materials Research 2014, 29, (03), 362-372. 14. Wu, P.; Quek, S.; Sha, Z.; Dong, Z.; Liu, X.; Zhang, G.; Pei, Q.; Zhang, Y. J Appl Phys 2014, 116, (20), 204303. 15. Pop, E.; Varshney, V.; Roy, A. K. MRS Bull. 2012, 37, (12), 12731281. 16. Lewis, A. M.; Derby, B.; Kinloch, I. A. Acs Nano 2013, 7, (4), 31043117. 17. Li, X.; Magnuson, C. W.; Venugopal, A.; An, J.; Suk, J. W.; Han, B.; Borysiak, M.; Cai, W.; Velamakanni, A.; Zhu, Y. Nano Lett 2010, 10, (11), 4328-4334. 18. Eres, G.; Regmi, M.; Rouleau, C. M.; Chen, J.; Ivanov, I. N.; Puretzky, A. A.; Geohegan, D. B. Acs Nano 2014, 8, (6), 5657-5669. 19. Celebi, K.; Cole, M.; Teo, K.; Park, H. Electrochem. Solid-State Lett. 2011, 15, (1), K1-K4. 20. Lai, S.; Jang, S. K.; Song, Y. J.; Lee, S. Applied Physics Letters 2014, 104, (4), 043101. 21. Larciprete, R.; Ulstrup, S.; Lacovig, P.; Dalmiglio, M.; Bianchi, M.; Mazzola, F.; Hornekær, L.; Orlando, F.; Baraldi, A.; Hofmann, P. Acs Nano 2012, 6, (11), 9551-9558. 22. Li, X.; Zhu, Y.; Cai, W.; Borysiak, M.; Han, B.; Chen, D.; Piner, R. D.; Colombo, L.; Ruoff, R. S. Nano Lett 2009, 9, (12), 4359-4363. 23. Ferrari, A. C.; Basko, D. M. Nat Nanotechnol 2013, 8, (4), 235-246. 24. Berciaud, S.; Ryu, S.; Brus, L. E.; Heinz, T. F. Nano Lett 2008, 9, (1), 346-352. 25. Ferrari, A. C. Solid state communications 2007, 143, (1), 47-57. 26. Cançado, L. G.; Jorio, A.; Ferreira, E. M.; Stavale, F.; Achete, C.; Capaz, R.; Moutinho, M.; Lombardo, A.; Kulmala, T.; Ferrari, A. Nano Lett 2011, 11, (8), 3190-3196. 27. Eckmann, A.; Felten, A.; Mishchenko, A.; Britnell, L.; Krupke, R.; Novoselov, K. S.; Casiraghi, C. Nano Lett 2012, 12, (8), 3925-3930. 28. Cai, W.; Moore, A. L.; Zhu, Y.; Li, X.; Chen, S.; Shi, L.; Ruoff, R. S. Nano Lett 2010, 10, (5), 1645-1651. 29. Chen, S.; Wu, Q.; Mishra, C.; Kang, J.; Zhang, H.; Cho, K.; Cai, W.; Balandin, A. A.; Ruoff, R. S. Nat Mater 2012, 11, (3), 203-207. 30. Balandin, A. A. Nat Mater 2011, 10, (8), 569-581. 31. Balandin, A. A.; Ghosh, S.; Bao, W.; Calizo, I.; Teweldebrhan, D.; Miao, F.; Lau, C. N. Nano Lett 2008, 8, (3), 902-907. 32. Nika, D. L.; Pokatilov, E. P.; Balandin, A. A. Phys. Status Solidi B 2011, 248, (11), 2609-2614. 33. Cahill, D. G.; Braun, P. V.; Chen, G.; Clarke, D. R.; Fan, S.; Goodson, K. E.; Keblinski, P.; King, W. P.; Mahan, G. D.; Majumdar, A. Appl. Phys. Rev. 2014, 1, (1), 011305.
conductivities k (2660-1230, 1890-1020, and 680-340 W/mK, respectively, but all for 320K < T < 510K) by the opto-thermal Raman technique. The data reliabilities of Raman-measured k were elaborated and the effects of the hole-edge boundary condition and air-convection/radiation heat loss were quantitatively assessed; minor effect (~0.4%) by the hole-edge boundary condition, and up to 20% of additional heat loss by the air-convection/radiation.
ASSOCIATED CONTENT Electronic Supplementary Information (SI)-Sections 1. Methods, 2. The measurement uncertainty of k, 3. The effect of the air convection losses on k measurements, 4. The effect of the holeedge temperature boundary condition on k measurements, 5. Theoretical analysis using measured k, Figures S1, S2, S3, and S4, and Equations S1 - S8.
AUTHOR INFORAMTION Corresponding Author *E-mail:
[email protected] Author Contributions W.M.L. and K.D.K. carried out experiments including graphene synthesis, transfer and Raman measurements, and wrote this paper. H.G.K. contributed to fabricating polycrystalline CVD graphene samples and, together with J.S.P., developed the opto-thermal Raman system and conducted measurements. S.S. and C.L. performed the theoretical modelling studies and also wrote the corresponding section of the manuscript. G.L. fabricated the Si3N4 substrate with the hole pattern. O.M.K., S.C. and W.R.L. advised on experimental layouts and had discussions to elaborate the experimental results. Notes The authors declare no competing financial interests.
ACKNOWLEDGEMENTS This research was primarily supported by the Nano-Material Technology Development Program (R2011-003-2009) and NRF2013R1A1A2060720 through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning, and was also partially supported by the Magnavox Professorship fund (R0-1137-3164) from the University of Tennessee.
REFERENCES 1. Yigen, S.; Champagne, A. Nano Lett 2013, 14, (1), 289-293. 2. Nika, D.; Pokatilov, E.; Askerov, A.; Balandin, A. Phys. Rev. B 2009, 79, (15), 155413. 3. Yu, J.-K.; Mitrovic, S.; Tham, D.; Varghese, J.; Heath, J. R. Nat Nanotechnol 2010, 5, (10), 718-721.
6 ACS Paragon Plus Environment
Page 7 of 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
34. Kaviany, M., Heat transfer physics. Cambridge University Press: 2014. 35. Moffat, R. J. Experimental thermal and fluid science 1988, 1, (1), 3-17. 36. Aksamija, Z.; Knezevic, I. Applied Physics Letters 2011, 98, (14), 141919. 37. Vallabhaneni, A. K.; Singh, D.; Bao, H.; Murthy, J.; Ruan, X. Phys. Rev. B 2016, 93, (12), 125432. 38. Sullivan, S.; Vallabhaneni, A.; Kholmanov, I.; Ruan, X.; Murthy, J.; Shi, L. Nano Lett. 2007 (in press, DOI: 10.1021/acs.nanolett.7b00110) 39. Bonini, N.; Lazzeri, M.; Marzari, N.; Mauri, F. Phys Rev Lett 2007, 99, (17), 176802.
7 ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
A graphic for the Table of Contents
8 ACS Paragon Plus Environment
Page 8 of 8
