Documents

223

Description
Thermal Transport in Suspended and Supported Monolayer Graphene Grown by Chemical Vapor Deposition Weiwei Cai, † Arden L. Moore, † Yanwu Zhu, Xuesong Li, Shanshan Chen, Li Shi,* and Rodney S. Ruoff* Department of Mechanical Engineering and Texas Materials Institute, University of Texas at Austin, Austin, Texas 78712 ABSTRACT Graphene monolayer has been grown by chemical vapor deposition on copper and then suspended over a hole. By measuring the laser heating and monitoring the Raman G peak, we
Categories
Published
of 7
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
  Thermal Transport in Suspended andSupported Monolayer Graphene Grown byChemical Vapor Deposition Weiwei Cai, † Arden L. Moore, † Yanwu Zhu, Xuesong Li, Shanshan Chen, Li Shi,* andRodney S. Ruoff* DepartmentofMechanicalEngineeringandTexasMaterialsInstitute,UniversityofTexasatAustin,Austin,Texas78712 ABSTRACT  Graphene monolayer has been grown by chemical vapor deposition on copper and then suspended over a hole. Bymeasuring the laser heating and monitoring the Raman G peak, we obtain room-temperature thermal conductivity and interfaceconductanceof(370 + 650/ - 320)W/mKand(28 + 16/ - 9.2)MW/m 2 Kforthesupportedgraphene.Thethermalconductivityofthesuspended graphene exceeds (2500 + 1100/ - 1050) W/m K near 350 K and becomes (1400 + 500/ - 480) W/m K at about 500 K. KEYWORDS  Thermal conductivity, thermal interface resistance, graphene, Raman, measurement S incegraphenewasexfoliatedfromgraphitein2004, 1 the two-dimensional monatomic sheet has attractedincreased interest for both fundamental studies andapplications in high-speed electronic devices, sensors,memory, and spintronic devices among others. 2 Because itisdifficulttoutilizemechanicallyexfoliated,smallgrapheneflakesformassproductionoffunctionaldevices,therehavebeen intense efforts to develop methods for synthesis of large-area,high-qualitygraphene,includingthermaldecom-position from SiC or chemical vapor deposition (CVD) on athin film transition metal catalyst such as Ni or Cu. 3 - 6 Electrontransportmeasurementshavefoundthatthechargemobility of as-synthesized graphene depends on the grainsize. For graphene grown by CVD on Cu, the mobility canreach about 4050 cm 2 V - 1 s - 1 , 6 which is about 4 timessmaller than the highest value of about 15000 cm 2 V - 1 s - 1 found in mechanically exfoliated graphene supported onSiO 2  at room temperature. 1,7 - 9 On the other hand, thethermalconductivityremainsunknownfortheselarge-areaCVDgraphene,whichcanbescaledupforthermalmanage-ment applications more readily than exfoliated grapheneflake.Althoughelectrontransportingraphenehasbeenstudiedextensively and graphene is predicted to have very highthermal conductivity near room temperature, 10 - 13 therehave been only limited experimental data in the literatureon phonon transport in graphene because of experimentalchallenges. In a recent experiment based on micro-Ramanspectroscopy, a thermal conductivity value of about 5000W/m K was found for a ∼ 20  µ m long monolayer grapheneflake with a  ∼ 3  µ m long suspended segment obtained bymicromechanical exfoliation of graphite. 14 This value isabout two times higher than values found in diamond andgraphite in the basal plane. 15 This measurement method isbased on the dependence of the Raman G peak frequencyon the temperature of the flake heated by the Ramanlaser. 14,16 Anopticalabsorptionof  ∼ 6%perpassofthelaserbeamwasdeterminedbasedonanopticalabsorptionmodelinconjunctionwithacalibrationwithgraphite.Thisnumberis considerably higher than the 2.3% value obtained froman optical transmission measurement of monolayergraphene. 17 While the discrepancy could be attributed tosamplecontaminationanddifferentabsorptioncoefficientsat different wavelengths, 11 it is desirable to measure theoptical absorption directly. In addition, heat loss from thegraphenetotheSiO 2 substrateatthetwoendsofthetrenchwasneglectedforthismeasurementandthethickergraphiteregionwasassumedtobeaperfectheatsink.Consequently,the thermal conductivity of the monolayer segment sup-ported on SiO 2  was assumed to be the same as that of thesuspended segment. However, a recent experiment showsthatthethermalconductivityofgraphenesupportedonSiO 2 could be considerably lower than values for the suspendedgraphene due to phonon leakage across the graphene - substrate interface. 18 Hence, it is necessary to re-evaluatethe thermal contact of the supported graphene segment tobetter understand the intrinsic thermal conductivity of suspended graphene.In this letter, we report a different approach based onmicro-Raman spectroscopy for the measurement of thethermal conductivity of large-area, monolayer graphenegrownbyCVDoncopper 6 andsubsequentlysuspendedovera circular hole. The obtained room-temperature thermalconductivity and thermal interface conductance for thesupported area of the CVD graphene are comparable to the *To whom correspondence should be addressed. E-mail: (RSR) r.ruoff@mail.utexas.edu; (LS) lishi@mail.utexas.edu. † These authors contributed equally to this work. Received for review: 12/18/2009Published on Web: 04/20/2010 pubs.acs.org/NanoLett  © 2010 American Chemical Society  1645  DOI: 10.1021/nl9041966 |  Nano Lett.  2010,  10  , 1645–1651  recentlyreportedvaluesformechanicallyexfoliatedgrapheneon SiO 2 . The thermal conductivity of the suspended regionof the CVD graphene is higher than the reported values forgraphiteatnearroomtemperatureand500K,respectively.Thesampleusedinthethermalmeasurementwaslarge-areahigh-qualitymonolayergraphenegrownon25  µ mthickCu foils using a CVD method that we demonstrated re-cently. 6 Thesurfaceofthegraphene-on-Cuwascoatedwithpoly(methylmethacrylate)(PMMA)followedbycuring.Afterthe Cu substrate was dissolved in an Fe(NO 3 ) 3  solution (1M/L), the PMMA-graphene was lifted up from the solutionand transferred to the Au-coated surface of a 300 nm thick,0.5 × 0.5 mm 2 , low-stress silicon nitride (SiN x ) membranesupportedonacircular3 × 3mm 2 siliconframe. 19 TheSiN x membraneconsistsofa100 × 100arrayof3.8  µ mdiameterholes at a pitch of 10  µ m between holes. The thermalconductivity of SiN x  is about ∼ 5 W/m K and rather low. Toincrease the thermal conductance of the membrane thatservesasaheatsinkforthismeasurement,a ∼ 500nmthickAu film was evaporated on the SiN x  surface prior to thegraphene transfer. After the transfer, the PMMA was re-moved in acetone. Figure 1a shows a schematic diagram of theobtainedgraphenesuspendedoverathroughholeintheAu-coated SiN x  support. The SEM image in Figure 1b showsagrapheneflakethatcoversholesintheAu/SiN x membrane.Some cracks can be observed in some areas of the flake.The quality and the number of (stacked) layers of thegraphene films were determined by micro-Raman spectros-copy. 6 Figure 1c shows a 25  ×  25  µ m 2 Raman mappingimage of the G peak intensity of the graphene on SiN x support. The Raman image clearly shows the existence of suspended graphene on the holes. On some holes, the filmis broken or wrinkled. We have chosen graphene areaswithout such visible defects for the thermal measurement.AsshowninFigure1d,e,thetypicalRamanspectraobtainedfrom the chosen suspended graphene do not contain the DBand associated with defects 6 and indicate high-qualitymonolayer graphene. In comparison, the relatively highbackground level in the Raman spectrum of the supportedgraphene comes from the Au coating on the SiN x  support.During the thermal measurement, a 532 nm laser beamisfocusedusinganobjectivelensoneitherthecenterofthesuspended graphene or the area of the graphene supportedontheAu/SiN x membrane.Inthisconfiguration,theheatfluxvector is along the radial direction away from the center of thegraphenesoastomatchtheradialsymmetryofthelaserbeam. The optical transmission through the suspendedgraphene is measured using a semiconductor laser powermeter (Newport, Model 1918-c) placed under the SiN x  sup-port,asillustratedinFigure1a.Thelaserbeamsizeismuchsmaller than the diameter of the holes, as discussed below.Because it has been reported that the reflection by thegraphene flake is less than 0.1% and is negligible, 17 thepower( Q )absorbedbythesuspendedgrapheneisobtainedasthedifferencebetweenthepowertransmittedthroughanemptyhole(  P empty )andthattransmittedthroughagrapheneflake (  P graphene ), that is,  Q )  P empty -  P graphene . The obtainedoptical absorption of 3.3 ( 1.1% at 532 nm wavelength iscomparable to the 2.3% value reported for 550 nm wave-length in the literature. 17 At the same incident laser power,theabsorbedlaserpowerbythesupportedgrapheneistakenas twice of that measured on the suspended graphenebecause of the reflection from the Au surface.The temperature rise in the optically heated graphenecauses red-shift of the  G  peak because of bond softening. Ithas been shown that the red shift of the Raman G peak of graphenelinearlydependsonthesampletemperature. 20 Tocalibrate the relationship between the Raman shift and thetemperaturerise,weobtainedRamanspectraofthegraphenesamplewhenthesamplewasplacedonaheatingstagewithits temperature measured by a thermocouple. On the basisof 12 measurements on both supported and suspendedgraphene areas, two of which are shown in the inset of Figure 2, the Raman G peak down shifts with increasingstage temperature at a rate of (4.05 ( 0.2) × 10 - 2 cm - 1 /K.We estimate that stress caused by thermal expansion mis-match resulted in Raman shift one order of magnitudesmaller than this measurement value. Hence, this value isused to determine the graphene temperature from the Gpeak position when the graphene is heated by the Ramanlaser at different powers and the stage is kept at ambienttemperature. Figure 2 shows the relationship between themeasured graphene temperature rise and the absorbedpower when the laser beam is focused on either the sup-ported graphene or the center of the suspended graphenewiththeuseofthe100 × and50 × objectives.ThemeasuredRamanshiftismuchsmallerwhenthelaserbeamisfocused FIGURE 1. (a) Schematic of the experimental setup for graphenethermal conductivity measurement. (b) The scanning electronmicroscopy image and (c) micro-Raman G peak map of the sus-pendedgrapheneontheAu-coatedSiN x porousmembrane.Ramanspectra of suspended graphene (d) and graphene on the Au-coatedSiN x support(e)showtheGpeakand2Dpeakfeaturescharacteristicof monolayer graphene.  © 2010 American Chemical Society  1646  DOI: 10.1021/nl9041966 |  Nano Lett.  2010,  10  , 1645-–1651  on the supported graphene than at the center of the sus-pendedgraphenebecauseheattransferfromthesupportedgraphenetotheAusupportresultsinlowertemperatureriseinthesupportedgraphenethaninthesuspendedgraphene.The thermal measurement requires a careful determina-tion of the radius of the laser beam spot ( r 0 ), which isobtained by performing a micro-Raman scan across asmooth cleaved edge of a Si substrate. Figure 3a,b shows ascanning electron microscopy image of the Si edge and a 1  µ m × 3  µ mmicro-Ramanimageintegratedfromthe490to550 cm - 1 frequency range of the Si peak obtained with the100 × objective. Au film of about 200 nm in thickness wasevaporated on the side of the freshly cleaved Si edge toeliminate the Raman signal from the cleaved edge. The Sipeak is much higher than the Au background, which is notincludedintheintegratedintensityoftheSipeak.Here,themeasured intensity (  I  ) of the silicon peak at  ∼ 520 cm - 1 isproportional to the total laser power incident on the siliconwafer. Figure 3c shows the measured  I   as a function of thedistance( x )ofthelaserbeamfromthecleavededge.Insteadof the more complicated Airy pattern, a Gaussian functionexp( - x 2 / r 02 ) can be used to fit the slope d  I  /d x  to obtain thebeam size  r 0 . This procedure yields  r 0 ) 0.17 and 0.28  µ mfor the 100 × and 50 × objectives. These  r 0  values are closeto the calculated values of 0.19 and 0.24  µ m using  r 0  )  λ / π  NA,whereNAisthenumericalaperturevalueof0.9and0.75 for the 100 × and 50 × objectives, respectively.We calculate that direct laser heating of the Au filmproduces a negligible rise in the film temperature. 21 Hence,the temperature rise measured with the laser beam on thesupported graphene is caused by optical absorption by thesupportedgraphene.Forthesupportedgraphene,substrateinteraction can reduce the mean free paths of phonons ingraphene, especially the long-wavelength phonons, to besmaller than the laser beam size. 18 In this case, diffusivephonon transport in the supported graphene makes it pos-sible to obtain the temperature ( T  ) distribution from thefollowingheatdiffusionequationinthecylindricalcoordinatewhere T  a istheambienttemperature, r istheradialpositionmeasured from the center of the laser beam,  t  ) 0.335 nmis the graphene thickness,  κ s  is the thermal conductivity of the supported graphene, which can be different from thethermal conductivity ( κ ) of the suspended graphene, and  g is the total interface thermal conductance per unit areabetween the graphene and the Au-covered support as wellas the surrounding air molecules. In eq 1,  q˙ ′′′  is the volu-metric optical heating and given aswhere  q  0 ′′  is the peak absorbed laser power per unit area atthecenterofthebeamspot.Thetotalabsorbedlaserpower Q  is thenWith the use of   θ  ≡  ( T   -  T  a ) and  z   )  (  g / κ s t  ) 1/2 r , eq 1becomes a nonhomogeneous Bessel’s equation FIGURE 2. The G peak shift (left axis) and temperature (right axis)measured on the supported graphene and at the center of thesuspendedgraphenewiththe100 × and50 × objectivesasafunctionof the absorbed laser power when the stage temperature is kept at room temperature. The inset shows that the red shift of the RamanG peak measured with low laser power on both supported andsuspended graphene as a function of the stage temperature.FIGURE 3. (a) The scanning electron microscopy image and (b) 3  µ m × 1  µ m micro-Raman map across a Au-coated sharp Si edge. (c)The Raman intensity (blue) and extracted profile of the laser beam(black) as a function of the beam position. 1 r dd r ( r  d T  d r )  -  g κ s t  ( T   -  T  a )  +  q˙ ′′′ κ s )  0 (1) q˙ ′′′  ) q  0 ′′ t   exp ( - r 2 r 02 )  (2) Q  )  ∫ 0 ∞ q  0 ′′  exp ( - r 2 r 02 ) 2 π  r  d r  )  q  0 ′′ π  r 02 (3) ∂ 2 θ ∂  z  2  +  1  z  ∂ θ ∂  z   -  θ  ) - q  0 ′′  g  exp ( -  z  2  z  02 )  (4)  © 2010 American Chemical Society  1647  DOI: 10.1021/nl9041966 |  Nano Lett.  2010,  10  , 1645-–1651  The solution to eq 4 is given as 22 wherethetwohomogeneoussolutions  I  0 (  z  )and  K 0 (  z  )arethezero-ordermodifiedBesselfunctionsofthefirstandsecondkind, respectively. The particular solution is obtained usingthe variation of parameters method as 22 where  I  1 (  z  ) and  K 1 (  z  ) are the first-order modified Besselfunctions of the first and second kind, respectively. Theboundary conditions (d θ )/(d  z  )|  z  ) 0 ) 0 and  θ (  z  f ∞ ) ) 0 yield C  2 ) 0 and  C  1 )- lim  z  f ∞  ( θ p (  z  ))/(  I  0 (  z  )), which approaches aconstant value for large  z  .The temperature rise in the graphene measured by theRaman laser beam isWe define the measured thermal resistance as  R m ≡ θ m / Q . On the basis of eqs 3 and 7Figure 2 shows approximately linear  θ m  and  Q  relationsfor the supported graphene, the slopes of which yield  R m valuesof(2.37 ( 0.81) × 10 5 ,and(1.05 ( 0.37) × 10 5 K/W,respectively, for the 100 ×  and 50 ×  objective lens. Theuncertainties in the  R m  values include both the calibrationor bias errors of   θ m  and  Q  and the random uncertainty infive measurements of the  θ m  versus  Q  slopes. Only therandomuncertaintiesneedtobepropagatedintothatoftheratio between the two  R m  values with the two objectives. 23 This ratio is determined to be 2.26 ( 0.23. On the basis of eq 8, this ratio only depends on the  g / κ s  ratio and can beused to determine  g / κ s  uniquely. The  κ s  and  g  values arefurther determined from the  R m  value measured with oneoftheobjectivelens.Theprocedureyields κ s of(370 + 650/ - 320) W/m K and  g  of (28  +  16/ - 9.2) MW/m 2 K. The  κ s value is comparable to the room-temperature thermal con-ductivity range of 479 - 680 W/m K recently measured forexfoliatedgraphenesupportedonSiO 2 . 18 The  g valueisalsocomparable to the reported thermal interface conductancevalues of   ∼ 50 and 83 MW/m 2 K between graphite andevaporated Al and for graphene embedded in SiO 2 , 24,25 respectively, and much larger than the interface thermalconductance between the graphene and surrounding airmolecules. 26 When the laser beam is focused on the center of thesuspended graphene, the measured thermal resistancebecomeswhere  R g ≡ ( T  m - T  1 )/ Q isdefinedastheequivalentthermalresistanceofthesuspendedgrapheneherealthoughthermalresistanceisusuallynotusedforregionsofheatgeneration,  R c ≡ ( T  1 - T  a )/ Q  is the contact thermal resistance betweenthe supported graphene and the membrane, and  T  1  is thetemperature at the edge of the suspended graphene. Be-cause the 1.9  µ m hole radius (  R ) is much larger than thebeamsize r 0 valuesof0.17and0.28  µ m,theopticalheatingterm q˙ ′′′ ineq1canbeneglectedforthesupportedgrapheneregion of   r  >  R . With  q˙ ′′′ ) 0, the temperature distributionfor r >  R isgivenbythehomogeneoussolutioncomponentsof eq 5. 27 With the use of the boundary conditions  θ (  z  f ∞ ) ) 0 and  Q (1 - exp( -  R 2 /r 02 )) )- 2 π   Rt  κ s ( ∂ T  / ∂ r )|  R , we obtainthe temperature distribution in the supported area of thegraphene aswhere  z   R  is the value of   z   at  r  )  R.  The thermal contactresistance is obtained asWiththeabove-obtained κ s and  g values,  R c ≈ (4.4 + 8.4/ - 2.0) × 10 4 K/W. θ (  z  )  )  C  1  I  0 (  z  )  +  C  2  K 0 (  z  )  +  θ p (  z  ) (5) θ p (  z  )  )  I  0 (  z  ) ∫  K 0 (  z  ) q  0 ′′  g  exp ( -  z  2  z  02 ) -  I  0 (  z  )  K 1 (  z  )  -  K 0 (  z  )  I  1 (  z  )  × d  z   -  K 0 (  z  ) ∫  I  0 (  z  ) q  0 ′′  g  exp ( -  z  2  z  02 ) -  I  0 (  z  )  K 1 (  z  )  -  K 0 (  z  )  I  1 (  z  ) d  z   (6) θ m  ) ∫ 0 ∞ θ ( r ) exp ( - r 2 r 02 ) r  d r ∫ 0 ∞ exp ( - r 2 r 02 ) r  d r (7)  R m  ) ∫ 0 ∞ ( -  I  0 (  z  )lim  z  f ∞ θ p (  z  )  I  0 (  z  )  +  θ p (  z  ) )  exp ( - r 2 r 02 ) r  d r ∫ 0 ∞ exp ( - r 2 r 02 ) r dr ∫ 0 ∞ q  0 ′′  exp ( - r 2 r 02 ) 2 π  r  d r (8)  R m  )  R g  +  R c  (9) θ (  z  )  ) Q ( 1  -  exp ( -  R 2 / r 02 )) 2 π   R √  gt  κ s  K 0 (  z  )  K 1 (  z  R  ), for  r  g  R (10)  R c  ) θ (  z  R  ) Q ( 1  -  exp ( -  R 2 / r 02 )) )  12 π   R √  gt  κ s  K 0 (  z  R  )  K 1 (  z  R  )(11)  © 2010 American Chemical Society  1648  DOI: 10.1021/nl9041966 |  Nano Lett.  2010,  10  , 1645-–1651
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks
SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...

Sign Now!

We are very appreciated for your Prompt Action!

x