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C. Chuang, M. Mineharu, N. Matsumoto, M. Matsunaga, C.-W. Liu, B.-Y. Wu, Gil-Ho Kim, L.-H. Lin, Y. Ochiai, [K. Watanabe](https://orcid.org/0000-0003-3701-8119), [T. Taniguchi](https://orcid.org/0000-0002-1467-3105), C.-T. Liang, N. Aoki

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[Hot Carriers in CVD-Grown Graphene Device with a Top h-BN Layer](https://mdr.nims.go.jp/datasets/c852ae1e-0f27-4102-a12e-e9a012bdb8c5)

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Research ArticleHot Carriers in CVD-Grown Graphene Devicewith a Top h-BN LayerC. Chuang ,1,2 M. Mineharu,1 N. Matsumoto,1 M. Matsunaga,1 C.-W. Liu,3B.-Y. Wu,3 Gil-Ho Kim,4 L.-H. Lin,5 Y. Ochiai,1 K. Watanabe,6 T. Taniguchi,6C.-T. Liang ,3 and N. Aoki 11Department of Materials Science, Chiba University, Chiba 263-8522, Japan2Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan3Graduate Institute of Applied Physics, National Taiwan University, Taipei 10617, Taiwan4School of Electronic and Electrical Engineering, Sungkyunkwan University, Suwon 16419, Republic of Korea5Department of Electrophysics, National Chiayi University, Chiayi 600, Taiwan6Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, JapanCorrespondence should be addressed to C.-T. Liang; ctliang@phys.ntu.edu.tw and N. Aoki; n-aoki@faculty.chiba-u.jpReceived 18 January 2018; Accepted 20 March 2018; Published 14 May 2018Academic Editor: Stefano BellucciCopyright © 2018 C. Chuang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.We investigate the energy relaxation of hot carriers in a CVD-grown graphene device with a top h-BN layer by driving the devicesinto the nonequilibrium regime. By using the magnetic field dependent conductance fluctuations of our graphene device as aself-thermometer, we can determine the effective carrier temperature 𝑇e at various driving currents 𝐼 while keeping the latticetemperature 𝑇L fixed. Interestingly, it is found that 𝑇e is proportional to I, indicating little electron-phonon scattering in our device.Furthermore the average rate of energy loss per carrier 𝑃e is proportional to (𝑇e2 − 𝑇L2), suggesting the heat diffusion rather thanacoustic phonon processes in our system. The long energy relaxation times due to the weak electron-phonon coupling in CVDgraphene capped with h-BN layer as well as in exfoliated multilayer graphene can find applications in hot carrier graphene-baseddevices.1. IntroductionRecently, researchers in the graphene community are muchinterested in hot carriers in graphene-based systems sincethey determine the performance of high-power and high-frequency electronics, thermal management of electronicdevices, optoelectronic devices, the quantumHall metrology,and bolometric detectors [1–6]. Most of the hot carriergraphene devices in the high carrier density limit (the Bloch-Gruneisen temperature (𝑇BG) > the lattice temperature (𝑇L))show the dominant cooling power from a weak coupling ofcarriers to acoustic phonon processes [7–10], which is repre-sented by a heat flow power law equation P = Σ(𝑇𝛿e −𝑇𝛿L ) [11],where 𝛿 = 4 is a characteristic exponent, 𝑇e is the carrier tem-perature, 𝑇L is the lattice temperature, and Σ is the couplingconstant. Furthermore, disordered-enhanced properties inhot carrier graphene devices revealed the supercollisioncooling processes, where 𝛿 = 3 [12–14]. Recently, hexagonalBoron Nitride (h-BN) bottom substrate can be a great heatdrained material for disordered graphene so as to extremelyreduce the carrier-phonon scattering via Wiedemann-Franzlaw heat diffusion, which is 𝛿 = 2 [15–17]. However, the car-riers of energy relaxation in such h-BN/disordered graphenesystems with less substrate phonon interactions following theWiedemann-Franz law heat diffusion are rarely studied. Akey parameter for discussing the cooling process is the energyrelaxation time (𝜏𝜖), the characteristic time when the thermalenergy is lost by the carriers [18–20].To date, CVD-grown graphene appears to be a goodcandidate for large-scale graphene-based applications. How-ever, as such a system may not be air stable, it is highlydesirable to cap the CVD graphene with an inert layer soHindawiJournal of NanomaterialsVolume 2018, Article ID 5174103, 7 pageshttps://doi.org/10.1155/2018/5174103http://orcid.org/0000-0002-7677-8121http://orcid.org/0000-0003-4435-5949http://orcid.org/0000-0001-9203-6040https://doi.org/10.1155/2018/51741032 Journal of NanomaterialsTransfer h-BN on the etchingprotected bychemical resistdepositionsh-BN h-BNOxygen Plasma etching CVDCVD GSiO2/SiSiO2/SiCr/Au5/50 nm Cr/AuCF4 plasmaCVD G/SiO2/Si chipG/SiO2/Si chip(a)10 Ｇ(b)Figure 1: (a) Schematic fabrication diagram of a top h-BN/CVD graphene device. (b) The top h-BN/CVD graphene device (sample A) witha scale bar of 10 𝜇m.as to experimentally realize stable, large-scale, and scalabledevices. To this end, we have prepared CVD graphene witha top h-BN layer and studied the hot carrier effects insuch a device. In this report, we studied the conductancefluctuations and hot carrier effects using a largemeasurementcurrent (I) so as to raise the effective 𝑇e above 𝑇L on h-BN/CVDgraphene andmultilayer exfoliated graphene due totheir disordered properties. Based on the self-thermometerlinear properties between 𝑇e and 𝐼 due to Wiedemann-Franz law heat diffusion, we can investigate energy relaxationcooling processes under high carrier density limit (𝑇BG > 𝑇L)between the h-BN/CVD graphene and multilayer exfoliatedgraphene for future graphene-based applications. By deter-mining 𝜏𝜖 from 𝑇e and input power 𝑃e, we can find that𝜏𝜖 of the CVD graphene with a top h-BN layer is almosttwo orders of magnitude longer than those in exfoliatedpristine monolayer/bilayer graphene. Such a result may findapplications in hot carrier graphene-based transistors as aresult of the weak electron-phonon coupling.2. Experimental Section2.1. Preparation of the Samples. As shown in the schematicdiagram in Figure 1(a), we used the scotch tape method tomechanically exfoliate high purity and homogenous h-BNcrystals synthesized by high pressure techniques [21] andtransferred them by Gel-Pak polymer using the viscoelasticeffect [22] on commercial chemical vapor deposition (CVD)graphene/285 nm SiO2/Si substrate [23]. The CVD grapheneregion outside h-BN sheet was etched by oxygen plasma so asto confine to our CVD graphene region under the h-BN sheet.CF4 gas was used to etch h-BN sheet protected by photoresistfor 8 terminals and Cr/Au metal depositions as shown inFigure 1(b).2.2. Electrical Measurements. An ac driving current fromlock-in amplifiers passed into the source and drain contactsthrough the graphene devices for Hall-bar measurements.The magnetoresistance was measured in a He3 cryostatequipped with a superconducting magnet.3. Results and DiscussionFigure 2(a) shows the longitudinal resistivity 𝜌𝑥𝑥 as a functionof magnetic field with fixed current I = 20 nA at differenttemperatures that are equivalent to 𝑇L. The conductancefluctuations are observed, and they decrease as 𝑇L increasefrom 𝑇L = 0.32 to 50K, which are typical properties indisordered mesoscopic graphene [24–27]. Figure 2(a) insetshows the correspondingHall resistivity at𝑇L = 0.32 K, whichcan calculate the carrier density 𝑛A = 3.5 × 1012 cm−2 fromthe Hall slope and Hall mobility 𝜇 = 2092 cm2/Vs fromcarrier density and zero field resistivity. Figure 2(b) shows theresults of 𝜌𝑥𝑥 at various driving currents 𝐼 from I = 20 nAto 30000 nA at a fixed 𝑇L of 0.32 K, which reveals similarconductance fluctuation characteristics by current heating inthe nonequilibrium regime due to the hot carrier effects indisordered two-dimensional systems [18, 28–31].By using a conductance fluctuations-based thermometerbetween 𝜌𝑥𝑥 (I) and 𝜌𝑥𝑥 (T), we are able to reveal the clearconductance variations for lattice temperature and currentdependence between B = 0.5 and 3 T by subtracting a smoothbackground that avoids the zero field weak localization peakand high field Shubnikov-de Haas-like oscillations as shownin Figures 3(a) and 3(b) [13]. Hence, we determine theroot mean square (RMS) conductance fluctuation (𝛿𝑔rms, inunits of e2/h) for every 𝛿𝑔rms (𝑇L) and 𝛿𝑔rms (I) data setas a common graph (see Supporting Information (availableJournal of Nanomaterials 3Sample AT = 0.32 ＋1.01.52.02.53.0 xx(kΩ)1 2 3 4 5 6 7 8 90B (４)−0.2−0.10.00.10.2 xy(kΩ)−0.5 0.0 0.5 1.0−1.0B (４)1.96K1.29 K0.32K10 K7.5 K5K30K19 K15 K 50K(a)Sample AT = 0.32 ＋1 2 3 4 5 6 7 8 90B (４)0.51.01.52.02.53.03.5 xx(kΩ)5000 nA10000 nA20000 nA30000 nA2000 nA3000 nA1000 nA700 nA300 nA500 nA200 nA100 nA70nA20 nA30nA50nA(b)Figure 2: (a) Magnetoresistivity 𝜌𝑥𝑥 (B) at various 𝑇L for sample A. The inset shows the Hall resistivity 𝜌𝑥𝑦 (B) at 𝑇L = 0.32 K. (b)Magnetoresistivity 𝜌𝑥𝑥 (B) at various driving currents 𝐼 at fixed 𝑇L = 0.32 K for sample A.Sample AI = 20 Ｈ！−0.2−0.10.00.10.20.30.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.00.6B (４)1.96K1.29 K0.32K10 K7.5 K5K30K19 K15 K 50Kg(？2 /Ｂ)(a)Sample AT = 0.32 ＋−0.2−0.10.00.10.20.30.40.50.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.00.6B (４)70nA20 nA30nA50nA 300 nA500 nA200 nA100 nA2000 nA3000 nA1000 nA700 nA 5000 nA10000 nA20000 nA30000 nAg(？2 /Ｂ)(b)Figure 3: (a) Conductance fluctuations in sample A as a function of magnetic field at various lattice temperatures with fixed I = 20 nA. (b)Conductance fluctuations in sample A as a function of magnetic field at various driving currents for 𝑇L = 0.32 K.here)) by averaging conductance fluctuations over the rangeof 𝐵 so as to assign an effective 𝑇e to the driving currentas shown in Figure 4(a) [13, 18]. Interestingly, 𝑇e shows alinear dependence on 𝐼. According to the seminal work doneby Baker and coworkers about the energy transfer betweencarriers and the lattice [31], the following relation can befound:𝑇e ∝ 𝐼𝛼, (1)where 𝛼 = 2/(p + 2) and 𝑝 is the exponent for the inelasticscattering rate 𝜏in−1 ∝ 𝑇𝑝. Therefore, Figure 4(a) showsthat 𝑇e (I) of our sample A follows (1) with 𝑝 ≈ 0 and𝛼 ≈ 1, which suggested little carrier-phonon scatteringin two-dimensional material heterostructure systems [26].Furthermore, one would be interested in whether the heatdissipation was transferred by another mechanism ratherthan carrier-phonon scattering. Under the low-temperaturelimit (𝑇L < 𝑇BG), 𝑇BG = 2ℎ𝑠𝑘F/𝑘B, where 𝑠 is the sound4 Journal of NanomaterialsSample A−10010203040506070Te(K)5000 10000 15000 200000I (nA)(a)Sample ATL = 0.32 ＋0.05.0 × 1091.0 × 10101.5 × 10102.0 × 1010Pe(eV/s)0 500 1000 1500 2000 2500 3000 3500 4000−500Te2 − TL2 (K2)(b)Figure 4: (a) Effective 𝑇e versus driving current 𝐼 in sample A. (b) 𝑃e as a function of (𝑇e2 − 𝑇L2) for sample A and at 𝑇L = 0.32 K.velocity and 𝑘F is the Fermi radius. For graphene systems (s= 2.1 × 104ms−1), 𝑇BG ∼ 54n1/2 K ≅ 93.4 K with the carrierdensity 𝑛 = 3.5 in units of 1012 cm−2 in sample A [13, 32].Theenergy loss (𝑃e), the average rate of energy loss per carrier, isusually expressed to the carrier and lattice temperatures as𝑃e = 𝐴 (𝑇𝛽e − 𝑇𝛽L ) , (2)with a constant 𝐴 and a characteristic exponent 𝛽. In generalgraphene systems, 𝛽 ≈ 3 suggests the supercollision coolingmechanism in disordered systems [13, 18, 33] and 𝛽 ≈4 suggests the two-dimensional acoustic phonon coolingprocesses in clean systems [34, 35]. Particularly, 𝛽 ≈ 2,the heat diffusion described by the Wiedemann-Franz law,was found in graphene on bottom h-BN substrate systems,where bottom h-BN substrate acts as a thermal conductionlayer, effectively reducing the electron-phonon coupling [14–16]. Such interesting bottom h-BN substrate underneathgraphene can change graphene heat transport mechanismfrom electron-phonon interactions (𝛽 ≈ 3 ∼ 4) toheat diffusion (𝛽 ≈ 2). One might be interested in whatheat transport mechanism will be in encapsulated graphenebetween bottom insulating SiO2 and top h-BN sheet as oursample A rather than traditional graphene on h-BN substrate[14–16]. Based on the work of Baker et al. [31], 𝛽 = p +2, which suggested 𝛽 in sample A should be close to 2since the linear relation between 𝑇e and 𝐼 is p≈ 0 (1 = 𝛼 =2/(p + 2)). Apparently, our results in sample A are highlyconsistent with this speculation for 𝛽 ≈ 2 as shown inFigure 4(b), where 𝑃e = 𝐼2𝑅𝑥𝑥/𝑛𝑊𝐿 (𝑊 and 𝐿 are the widthand length of our sample A, resp.). Interestingly, the heattransfer mechanism in our sample A with top h-BN sheeton graphene/SiO2 was dominated by heat diffusion (𝛽 ≈ 2),which is the same as traditional graphene/h-BN substratedevices [14–16]. Such interesting results suggest that the toph-BN sheet coupled with graphene is strong heat transfermedium in comparison with other coupled materials, likeSiO2 or air. Also, such structures in the top h-BN sheet ongraphene not only protected graphene without air molecularadsorbing doping [2–36], but also screened graphene fromelectrostatic force [37, 38], a great advancement for graphene-based devices.In order to further discuss the linear relation between𝑇e and 𝐼 that indicates little carrier-phonon scattering inour sample A, we fabricate multilayer exfoliated graphene(sample B) that showed the same linear relation between𝑇e and 𝐼 by zero field resistance as a thermometer andconductance fluctuations due to its disordered property asin our previous reports [23–26]. Again, we are able tomeasure the conductance fluctuations for temperature andcurrent dependence as shown in Figure 5(a) and inset [13].Consequently, we found the linear relation between 𝑇e and𝐼 by utilizing 𝛿𝑔rms (𝑇L) and 𝛿𝑔rms (I) as a thermometerfor determining 𝑇e (see Supporting Information) [13] asshown in the inset of Figure 5(b), which suggested p≈ 0and 𝛽 ≈ 2. Under the low-temperature limit (𝑇L < 𝑇BG),𝑇BG ∼ 54𝑛1/2 K ≅ 188.6 K with the carrier density 𝑛 =12.2 in units of 1012 cm−2 in sample B [13, 32]. Consistently,𝑃e is proportional to (𝑇2e − 𝑇2L) in sample B as shown inFigure 5(b), which belonged to Wiedemann-Franz law heatdiffusion and corresponded to the transport situation for littlecarrier-phonon scattering for 𝛼 ≈ 1 [7, 26]. Interestingly, themultilayer exfoliated graphene (sample B) has the same heattransfer mechanism (𝛽 ≈ 2) as the h-BN/graphene (sampleA) systems [14–16].Although the heat transfer mechanism of multilayerexfoliated graphene is the same as h-BN/CVD graphene forheat diffusion (𝛽 ≈ 2), the energy relaxation time can describethis cooling process about the typical time on which energyis lost from carriers [39, 40]. Therefore, the energy relaxationtime can be expressed by𝑃e =𝑘B (𝑇e − 𝑇L)𝜏𝜖. (3)Figure 6 compares the energy relaxation time 𝜏𝜖 betweenthe h-BN/CVD graphene (sample A) and the multilayerJournal of Nanomaterials 5Sample B0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.00.6B (４)−0.10.00.10.20.3g(？2 /Ｂ)20 nA10 nA30nA300 nA200 nA100 nA3000 nA7000 nA1000 nA10000 nA0.81.01.21.41.61.82.02.22.42.62.83.00.6B (４)−0.10.00.10.2g(？2 /Ｂ)1.1 K0.7 K0.28 K3.1 K2 K1.5 K11 K7 K5 K30 K20 K15 K(a)0 1000 2000 3000 4000 5000Sample BTL = 0.32 ＋Te2 − TL2 (K2)0.02.0 × 1084.0 × 1086.0 × 1088.0 × 108Pe(eV/s)010203040506070Te(K)0400060008000200010000I (nA)(b)Figure 5: (a) Conductance fluctuations in sample B as a function of magnetic field at various 𝑇L with fixed I = 20 nA. The inset showsconductance fluctuations in sample B as a function of magnetic field with various driving currents at fixed 𝑇L = 0.32 K. (b) 𝑃e as a function of(𝑇e2 − 𝑇L2) for sample B and at 𝑇L = 0.32 K. The inset shows effective 𝑇e versus driving current 𝐼 in sample B.Multi-layer grapheneH-BN/CVD graphene1/T1 10 1000.1Te (K)100101102103104105 (ns)Figure 6: (a) Comparison of 𝜏𝜖 (𝑇e) versus 𝑇e on a log-log scalefor sample A (h-BN/CVD graphene) and sample B (multilayergraphene).exfoliated graphene (sample B). Interestingly, we could obvi-ously find that 𝜏𝜖 of h-BN/CVD graphene (sample A) isabout two orders of magnitude faster than that of multilayergraphene (sample B). Both of these two samples are thesame n-type of carrier density and far from the Dirac point,which cannot be ascribed to the fast energy relaxation of hotcarriers near the Dirac point of graphene [18]. These resultssuggest that the carrier-phonon scattering is absent in themultilayer graphene and the h-BN/graphene. The extremelylong energy relaxation times in both devices (at least twoorders of magnitudes longer than those in pristine exfoliatedgraphene [27, 28] and graphene on SiC [30, 34]) can beadvantageous for applications in graphene-based hot carriertransistors [41] since carriers can maintain their high kineticenergy (and hence the high effective temperature) with arelatively low driving current.4. ConclusionWe have studied conductance fluctuations and hot carriereffects caused by current heating on h-BN/CVD grapheneand multilayer graphene as a self-thermometer. It has beenshown that 𝑇e (𝑃e) is linearly proportional to I (𝑇e2 − 𝑇L2)in both of the disordered graphene devices, suggesting thelittle electron-phonon scattering and heat diffusion due toWiedemann-Franz law.The extremely long energy relaxationtime may find applications in graphene-based hot carrierdevices. Such a resultmay be useful for othermaterial systems[42, 43].Data AvailabilityThe data used to support the findings of this study areavailable from the corresponding author upon requestConflicts of InterestThe authors declare that they have no conflicts of interest.AcknowledgmentsAs an International Research Fellow of the Japan Society forthe Promotion of Science (JSPS), C. Chuang acknowledges6 Journal of Nanomaterialsa JSPS Postdoctoral Fellowship and the MOST and Instituteof Atomic and Molecular Sciences, Academia Sinica, for apostdoctoral fellowship under the Contract no. MOST 106-2811-M-001-164. C.-T. Liang would like to acknowledge theMinistry of Science and Technology (MOST), Taiwan, forfinancial support (Grant no. MOST 105-2119-M-002-048-MY3). N. Aoki acknowledges funding from JSPS KAKENHI(Grant no. 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