An electrical method for the measurement of the thermal and electrical conductivity of reduced graphene oxide nanostructures

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2009 Nanotechnology 20 405704

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An electrical method for the measurement of the thermal and electrical conductivity of reduced graphene oxide nanostructures Timo Schwamb,Brian R Burg,Niklas C Schirmer and

Dimos Poulikakos

Laboratory of Thermodynamics in Emerging Technologies,Institute of Energy Technology,

Department of Mechanical and Process Engineering,ETH Zurich,CH-8092Zurich,

Switzerland

E-mail:dimos.poulikakos@ethz.ch

Received25June2009,infinal form28July2009

Published8September2009

Online at stacks.iop.org/Nano/20/405704

Abstract

This paper introduces an electrical four-point measurement method enabling thermal and

electrical conductivity measurements of nanoscale materials.The method was applied to

determine the thermal and electrical conductivity of reduced graphene oxideflakes.The

dielectrophoretically deposited samples exhibited thermal conductivities in the range of

0.14–2.87W m−1K−1and electrical conductivities in the range of

6.2×102–6.2×103 −1m−1.The measured properties of eachflake were found to be

dependent on the duration of the thermal reduction and are in this sense controllable.

(Somefigures in this article are in colour only in the electronic version)

1.Introduction

The emergence of engineered graphene and graphene oxide (GOx)structures into nanotechnology research has sparked related research activities worldwide[1–3].A widefield of possible application areas has been suggested so far, e.g.membrane materials for fuel cells[4],transparent electrodes[5],solar cells[6],transistors[3,7],molecular sensors[8]and composite materials[9].Essential for the development of applications and devices based on graphene and GOx is an accurate knowledge of their material properties. To date,results have been presented for the electrical properties of graphene and GOx[1,3,5,7,10–12]and the thermal properties of graphenefilms[13,14].A lack of knowledge exists on the thermal properties of GOxfilms.

In this work,measurements of the electrical conductivity σand thermal conductivityκof suspended,thermally reduced graphene oxide(RGOx)flakes,deposited by dielectrophoresis (DEP)are presented.The electrical measurements were performed in the four-contact configuration,which enables the determination of the intrinsic electrical sample resistance R. The employed method to measure the thermal conductivity differs from the electrical1ω-/3ω-methods[15–18]and is described in the following.2.Method description and experimental procedure 2.1.Measurement method

The measurement method is afive-step process based on the

assumptions of diffusive heat transport in the sample and Joule

heating causing electrical resistance variations.

(1)In thefirst step,the electrical current limit causing no

detectable Joule heating,I0,was determined by measuring

the intrinsic electrical resistance R as a function of the electrical current I.This limit is identified by the intrinsic electrical resistance R obeying R(I I0)=R0= constant.During the measurements the temperature inside

the vacuum chamber was kept at T=20◦C.

(2)In the second step,the sample was heated externally(not

electrically)by placing it in a temperature controlled oven,

to predefined temperatures.The temperature gradient of

the electrical resistance R was determined by applying

a current I0to the sample to avoid Joule heating as

mentioned above.The equation for R reads

R =

R(T=20◦C)−R0/T(=20◦C)−T20◦C

I0

.(1) In this equation,T(=20◦C)represents the temperature measurement points and R(T=20◦C)the corresponding

Figure1.Image(a)depicts a RGOxflake deposited across the electrode gap without touching the SiN substrate.The corresponding schematic diagram of the electrical configuration is displayed in inset(c).In(b)the RGOxflake bridges four parallel electrodes touching the substrate beneath it,which is schematically shown in inset(d).

measured electrical resistance.Since in this step the

sample was heated by the surrounding atmosphere and not

by Joule heating,it is crucial that the sample temperature

is in thermal equilibrium with the controlled temperature

of the surrounding atmosphere.This was achieved

by maintaining a long heating time and temperature

monitoring by a platinum(Pt)100resistance temperature

detector(RTD)unit,which was placed directly next to the

microchip.In order to assure a linear R(T)relationship,

the variation of the chamber temperature was restricted to

only5–10K.

(3)The known power input by Joule heating was linked to the

unknown temperature rise in the sample by measurements

which were performed solely by Joule heating of the

sample by an electrical current chosen to be greater than

I0.The atmosphere around the sample was kept at

constant temperature.The subsequent rise of the sample

temperature T was calculated by

T=[(R(I=I

0)−R0)/R ]T

atmosphere=const.

.(2)

(4)The one-dimensional heat conduction equation

−κd 2T s(x)

d x2

=I

2R

SL

,(3)

was solved for the unknown temperature of the sample T s(x)with constant temperature boundary conditions.The variable x points in the direction of the sample length L connecting the electrodes.The right-hand side of the heat conduction equation accounts for Joule heating and S represents the cross section of the sample.For the solution of the heat conduction equation it was assumed that the thermal conductivity is not a function of the temperature.This is a valid assumption for the small temperature rise caused by the heating and the chosen region(above the room temperature)for the temperature

measurement.Further,the temperature dependent Joule heating term,T s(x)R ,was not taken into account in equation(3).Neglecting this term was justified by calculating the temperature rise of the heat conduction equation with and without the temperature dependent Joule heating term.The comparison of both solutions resulted in an insignificant difference of∼1%between the two calculated temperature rises in the sample.

(5)In thefinal step,the thermal conductivity of the sample

was determined by substituting the measured temperature (from step three)for the maximum temperature T s(x=

0.5L)=T s,max in the parabolic temperature solution of

the heat conduction equation.This maximum temperature substitution was performed supported by the fact that the maximum temperature T s,max corresponds to the measured resistance of the sample,which was also supported by the results of the platinum reference measurements.

2.2.Experimental procedure

In order to perform measurements with RGOxflakes,GOx flakes were deposited onto MEMS(microelectro-mechanical systems)structures on a silicon-based microchip.This was achieved with a recently reported DEP technique[19,20]. The used GOxflakes were prepared by a modified Hummers method combining a long acid oxidation step with subsequent thorough purification for highly exfoliated and pure GOx dispersions[22].The employed microchip design,described in detail in[21],features four metal electrodes manufactured in pairs with an insulating silicon nitride(SiN)layer in between (figures1(a)and(c)),or aligned in-plane(figures1(b)and(d)). The four-point contacted GOxflakes(figures1(a)and(b))were reduced in a rapid thermal annealing device(J.I.P.Elec JetFirst 100)at450◦C in a N2environment.The time of thermal treatmentτwas varied between5and60min reducing the amount of oxygenated groups bound to the GOxflake[24].

Figure2.Measurement results of the platinum microwire and the RGOxflakes over the electrical current.Thefilled circles show the reference measurements with the Pt microwire(left).The results of the RGOx samples are represented by hollow circles for sample1 (left),hollow triangles for sample2(right)and hollow squares for sample3(right),respectively.

All measurements were performed in vacuum (<0.03mbar)and in thermal equilibrium.A chip carrier hold-ing the microchip itself and the Pt100RTD was placed inside a two-part chip mount,equipped with two integrated heating units including thermocouples.The heating units were used to control the temperature in the vacuum chamber around the microchip.The temperature of the microchip itself was mon-itored by the Pt100RTD.This RTD was placed directly next to the microchip with the sample,allowing the sample tem-perature to be monitored accurately during the measurements. Additionally,the mount served as a radiation shield and pro-vided the electrical contacts to the measurement devices.The measurement samples were connected to an electrical current source(Keithley6221),a lock-in amplifier(Stanford Research System SR850)and a data acquisition unit.In order to perform the measurements,an electrical current was passed through the sample and,at the same time,a reference signal was fed to the lock-in amplifier.The voltage drop across the sample was measured by the lock-in amplifier.The data acquisition and the temperature control were controlled and processed in a Lab-View environment.

3.Results and discussion

A platinum microwire(diameter:13μm,length: 3.69mm, purity:99.9%)served as the reference material for the applied measurement method.This microwire was electrically four-point contacted to platinum electrodes resulting in a suspended measurement section.The results of the Pt wire are illustrated infigures2and3asfilled circles.In the manner described above,I0was identified to be<1mA from the data presented infigure2.Above1mA,the electrical resistance of the wire increased due to Joule heating.The R0value corresponding to I0was found to be2.636 .Displaying the electrical resistance as a function of the temperature of the surrounding atmosphere(figure3,left graph),R was calculated by linear interpolation between the data points(filled circles).The temperature rise in the sample caused by Joule heating

was Figure3.Measurement results of the platinum microwire and the RGOxflakes over the temperature of the surrounding atmosphere. Thefilled circles show the reference measurements with a Pt microwire(left).The measurement results of the RGOx samples are represented by hollow circles for sample1(left),hollow triangles for sample2(right)and hollow squares for sample3(right), respectively.The temperature coefficient of the electrical resistance R was determined by a linear interpolation between the data points for each sample.

measured at I>I0and was compared to the analytical

solution of the1d heat conduction equation,in order to validate κagainst literature values.The accuracy of the proposed thermal conductivity measurement method depends on several

factors,namely,the accuracy of the electrical measurement, the choice of the boundary conditions for the calculation of the energy equation solution,the availability of information about the sample geometry,heat loss caused by radiation, and,for non-suspended samples,convection losses.For the platinum wire a thermal conductivity of66–67W m−1K−1 was measured.This yields an accuracy of∼10%,when taking a heat loss of6–7%due to radiation into account.The impact of all possible error sources on the preciseness of the GOx property measurements is discussed within the following section.

Figures2and3also present the measurement results

for the RGOxflakes indicated by hollow circles(sample1, left graphs),hollow triangles(sample2,right graphs)and hollow squares(sample3,right graphs).Figure2indicates that detectable Joule heating occurred at an electrical input current greater than100nA for samples2and3and greater than1μA for sample1,respectively.Figure3reports the RGOx resistance as a function of the surrounding atmosphere temperature.In order to elucidate the thermal and electrical conductivities of the RGOxflakes,the data plotted infigures2 and3were processed by the above explained method.I–V curves of samples1,2and3are displayed infigure4.The curves are plotted over the entire measurement range in which the thermal conductivity measurements were carried out.The first-order linearity of the I–V curves proves that the RGOx flakes exhibited no apparent non-linearities in the measurement range.Consequently,material effects can be excluded to be at the origin of the second-order deviations of the electrical sample resistance shown infigure2.This exclusion allows the attribution of the second-order deviations to Joule heating, confirming the basic assumption of the herein presented model.

Figure4.Current–voltage plots of the RGOx samples.The curves are byfirst order linear in the entire thermal conductivity measurement range.

The RGOx samples1and4were not suspended.The samples2and3were deposited suspended(not touching the substrate underneath).As investigated by Burg et al[19], the RGOxflakes deposited by the DEP method mentioned above consist of a few layers with a total thickness of5nm, i.e.approx.four layers[23].For the present study an additional height analysis of the deposited RGOx samples was conducted in an atomic force microscope(AFM).The results of the height analysis are depicted infigure5.The two upper images were both taken by the same scan over a multi-layered chip,such as presented infigure1(a),in the area around the deposited sample.The upper left image visualizes the deposited sample bridging the electrode gap by displaying a broad z-axis range between0and−250nm.Focusing on the electrode surface by a narrower z-axis range(upper right image),the surface roughness of the electrodes can be measured.An average surface roughness of3–5nm was estimated from the height curve recorded on the electrode surface.The height curve is shown in the lower image of figure5.The RGOxflake touching the electrodes at the scanned position cannot be distinguished in the height diagram from the surface roughness.Consequently,the height of the specimen was in the same range as the surface roughness.

The length of the samples was defined by the electrode gap.The gap width varied between0.5and3μm.

The RGOxflakes exhibited an electrical conductivityσ0at T=20◦C in the range of6.2×102–6.2×103 −1m−1,which is in good agreement with reported electrical conductivities of reduced GOx[5,7,10,26].

Analysing the data in table1,sample1exhibited an electrical conductivity which is an order of magnitude higher than that of samples2and3.This is explained by the longer thermal treatment of sample1[11,24].As a result of the thermal treatment and based on the results of Yang et al [24],the atomic ratio of carbon to oxygen increases from GOx to RGOx by a factor greater than2.Nevertheless,the electrical conductivities associated with pristine graphenefilms are several orders of magnitude higher[10,12

].Figure5.Atomic force microscope images of a deposited RGOx

flake.The scan allows the determination of the specimen height. Table1.Measured electrical and thermal properties of RGOx.It was observed that a longer thermal treatment timeτinduces higher electrical and thermal conductivities(σ0,κ).

Sampleκ(W mK−1)σ0( −1m−1)τ(min)R c(k )

1 2.876.22×10360120

20.876.21×10252

30.146.57×1025130

4—∼1.95×10320300

In order to estimate the influence of Joule heating at the contacts on the thermal conductivity measurements,

the electrical contact resistances R c were determined by

subtracting the measured four-point electrical resistance from

the measured two-point electrical resistance of the graphene oxideflakes,R c=(R2pt−R4pt)/2[25].Table1summarizes the results.The lowest electrical contact resistance of2k was

found to belong to sample2.The R c values of samples1and3 were120–130k .Sample4showed the highest R c of300k . The results revealed no relation between R c and the time of thermal treatment.The I–V curves shown infigure4are linear byfirst order,indicating the absence of Schottky barriers in the contacts.Due to the significantly larger thermal mass,the higher thermal conductivity of the electrodes compared to the samples and the absence of Schottky barriers,the influence of Joule heating in the electrical contacts was neglected.Thus, for the boundary conditions of the heat conduction equation the electrodes were modelled as infinite heat sinks,as mentioned earlier.

The thermal conductivity of sample1was the highest with κ=2.87W m−1K−1.Since sample1was not suspended,heat loss to the substrate has to be taken into account.An estimate according to[27]resulted in an uncertainty of0.85W m−1K−1 due to heat loss to the substrate.This large uncertainty underpins the need for suspended samples.The samples2 and3did not have heat losses from heat conduction to the substrate.These samples were not in contact with the substrate due to their suspended deposition.They yielded values inthe rangeκ=0.14–0.87W m−1K−1(table1).The thermal conductivity of sample4could not be measured.It showed an unstable behaviour which is possibly explained by low quality contacts between the electrodes and the RGOx.

Comparing the results presented herein to the thermal conductivity of pristine graphene,the still oxidized nature of the RGOxflakes,even after thermal reduction,is revealed.The oxidized chemical structure introduces lattice defects which hinder the thermal transport and promote diffusion effects. Hence,pristine graphene has a markedly higher thermal conductivity by a factor of103–104[13,14].

As discussed in[11,23]and[28],RGOx and GOx can be described as a quasi-2d amorphous carbon with sp3-similar, distorted C–C bonds.Thus,the thermal properties of other amorphous carbon materials serve as a benchmark for the results reported herein.Indeed,a study by Shamsa et al [29]reports that thermal conductivity values of diamond-like carbonfilms mainly constituted by sp3C–C bonds are in a comparable range to the RGOxflakes of the present study. 4.Conclusions

Concluding,a method which enables thermal and electrical conductivity measurements of diffusive nanoscale materials was presented and applied to the study of graphene oxide structures deposited dielectrophoretically between electrodes. The feasibility and expected accuracy of the method was pursued and tested against a platinum microwire reference sample.The thermal and electrical properties of few-layered, reduced graphene oxide were found to be related to their level of oxidation.

Acknowledgments

The experimental support of Julian Schneider,the technical support of Jovo Vidic,the support of the EMEZ and FIRST laboratory platforms of ETH,and thefinancial support of the ETH Research Commission are greatly acknowledged. References

[1]Geim A K and Novoselov K S2007Nat.Mater.6183–91

[2]Ruoff R2008Nat.Nanotechnol.310–1

[3]Novoselov K S,Geim A K,Morozov S V,Jiang D,Zhang Y,

Dubonos S V,Grigorieva I V and Firsov A A2004Science

306666–9

[4]Dikin D A,Stankovich S,Zimney E J,Piner R D,

Dommett G H B,Evmenenko G,Nguyen S T and Ruoff R S

2007Nature448457–60

[5]Becerril H A,Mao J,Liu Z,Stoltenberg R M,Bao Z and

Chen Y2008ACS Nano2463–70

[6]Wang X,Zhi L and M¨u llen K2008Nano Lett.8323–7

[7]Eda G,Fanchini G and Chhowalla M2008Nat.Nanotechnol.

3270–4

[8]Robinson J T,Perkins F K,Snow E S,Wei Z and Sheehan P E

2008Nano Lett.83137–40

[9]Stankovich S,Dikin D A,Dommett G H B,Kohlhaas K M,

Zimney E J,Stach E A,Piner R D,Nguyen S T and

Ruoff R S2006Nature442282–6

[10]Stankovich S,Dikin D A,Piner R D,Kohlhaas K A,

Kleinhammes A,Jia Y,Wu Y,Nguyen S T and Ruoff R S

2007Carbon451558–65

[11]Jung I,Dikin D A,Piner R D and Ruoff R S2008Nano Lett.

84283–7

[12]Tan Y W,Zhang Y,Bolotin K,Zhao Y,Adam S,Hwang E H,

Das Sarma S,Stormer H L and Kim P2007Phys.Rev.Lett.

99246803

[13]Balandin A A,Ghosh S,Bao W,Calizo I,Teweldebrhan D,

Miao F and Lau C N2008Nano Lett.02–7

[14]Ghosh S,Calizo I,Teweldebrhan D,Pokatilov E P,Nika D L,

Balandin A A,Bao W,Miao F and Lau C N2008Appl.

Phys.Lett.92151911

[15]Lu L,Yi W and Zhang D L2001Rev.Sci.Instrum.

722996–3003

[16]Choi T Y,Poulikakos D,Tharian J and Sennhauser U2005

Appl.Phys.Lett.87013108

[17]Choi T Y,Poulikakos D,Tharian J and Sennhauser U2006

Nano Lett.615–93

[18]Dames C and Chen G2005Rev.Sci.Instrum.76124902

[19]Burg B R,L¨u tolf F,Schneider J,Schirmer N C,

Schwamb T and Poulikakos D2009Appl.Phys.Lett.

94053110

[20]Schwamb T,Schirmer N C,Burg R B and Poulikakos D2008

Appl.Phys.Lett.93193104

[21]Schwamb T,Choi T Y,Schirmer N,Bieri N R,Burg B,

Tharian J,Sennhauser U and Poulikakos D2007Nano Lett.

73633–8

[22]Hummers W S Jr and Offeman R E1958J.Am.Chem.Soc.

801339

[23]Mkhoyan A K,Contryman A W,Silcox J,Stewart D A,Eda G,

Mattevi C,Miller S and Chhowalla M2009Nano Lett.

91058–63

[24]Yang D et al2009Carbon47145–52

[25]Schwamb T,Burg B,Schirmer N and Poulikakos D2008Appl.

Phys.Lett.92243106

[26]Gilje S,Han S,Wang M,Wang K L and Kaner R B2007Nano

Lett.73394–8

[27]Kuroda M A,Cangellaris A and Leburton J P2005Phys.Rev.

Lett.95

[28]Cai W et al2008Science3211815

[29]Shamsa M,Liu W L,Balandin A A,Casiraghi C,Milne W I

and Ferrari A C2006Appl.Phys.Lett.161921下载本文