Thermal and structural characterizations of individual single ......[*] Prof. L. Shi, M. T. Pettes...

FULLPAPER

www.afm-journal.dewww.MaterialsViews.com

3918

Thermal and Structural Characterizations of IndividualSingle-, Double-, and Multi-Walled Carbon Nanotubes

By Michael T. Pettes and Li Shi*

Thermal conductance measurements of individual single- (S), double- (D),

and multi- (M) walled (W) carbon nanotubes (CNTs) grown using thermal

chemical vapor deposition between two suspended microthermometers are

reported. The crystal structure of the measured CNT samples is characterized

in detail using transmission electron microscopy (TEM). The thermal

conductance, diameter, and chirality are all determined on the same

individual SWCNT. The thermal contact resistance per unit length is obtained

as 78–585mKW�1 for three as-grown 10–14 nm diameter MWCNTs on

rough Pt electrodes, and decreases by more than 2 times after the deposition

of amorphous platinum–carbon composites at the contacts. The obtained

intrinsic thermal conductivity of approximately 42–48, 178–336, and 269–

343Wm�1 K�1 at room-temperature for the three MWCNT samples

correlates well with TEM-observed defects spaced approximately 13, 20, and

29 nm apart, respectively; whereas the effective thermal conductivity is found

to be limited by the thermal contact resistance to be about 600Wm�1 K�1 at

room temperature for the as-grown DWCNT and SWCNT samples without

the contact deposition.

1. Introduction

The high electron mobility and thermal conductivity of carbonnanotubes (CNTs) have attracted interest in their potentialapplications as nanoelectronic devices[1] and thermal manage-ment solutions, such as thermal interface materials (TIMs).[2–7]

These potential applications have motivated fundamental investiga-tions of the transport properties of CNTs. Current reportedexperimental thermal conductivity values of individual single-walled(SW) andmulti-walled (MW) CNTs vary by one order of magnitude.In addition, some of the results of these measurements have beenattributed to unique thermal transport phenomena in lowdimensions. These prior measurements were conducted ondifferent samples by using different methods, each with its ownadvantages and limitations. Based on a suspended microther-mometer device[8–11] or a T-junction sensor[12] that required a

[*] Prof. L. Shi, M. T. PettesDepartment of Mechanical Engineering andthe Center for Nano and Molecular Science and TechnologyTexas Materials InstituteUniversity of Texas at AustinAustin, TX 78712 (USA)E-mail: [email protected]

DOI: 10.1002/adfm.200900932

� 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

complicated sample preparation process,direct thermal conductance measurementsof SWandMWCNTs of several micrometersin length were made with few assumptions,butwithanuncertainty in thethermalcontactresistance. The 3v method based on modu-latedelectricalheatingof thesamplewas lateremployed to obtain the thermal conductanceof a 1.4mm long MWCNT.[13] Becauseofmode-selective electron–phonon couplingand non-equilibrium phonon populations inSWCNTs of several micrometers in lengthand at bias voltage above the optical phononenergy of about 0.16 eV,[14] as revealeddirectly by Raman spectroscopy measure-ments,[15–17] the 3v and other self-electricalheatingmethods could not be applied readilyto SWCNTs.[18] To account for non-equili-brium transport in a current-carryingSWCNT, a coupled electron–phonon trans-portmodel was developed andused to obtainthe thermal conductance of a 2.6mm longSWCNT by fitting the current–voltage

characteristicswith several other parameters, including the couplingconstant between optical and acoustic phonons and contact thermalandelectrical resistances; this revealed that the thermal conductanceis inversely proportional to temperature above room temperature.[19]

Spatially resolved Raman spectroscopy was recently employed toprofile the temperature distribution along a current-carryingsuspended SWCNT, from which the thermal conductance of a2mm long SWCNT was attributed mainly to hot optical phononswhile that of a 5mm long SWCNT was attributed to equilibriumphonons and found to be proportional to temperature above roomtemperature.[20] In amore recent report,[21] Raman spectroscopywasused to measure the temperature and thermal conductance of over30mm long, current-carrying SW and MWCNTs, where localthermal equilibrium among different phonon branches wasestablished in the very long CNTs. In these Raman measurementsof thermal transport in CNTs,[20–22] the thermal contact resistancecould be determined from the obtained temperature profile.However, the temperature dependence of the thermal conductancehad not been obtained partly because the temperature resolution ofthe Raman measurements was 50–100K and the temperature riseused in the experiments usually exceeded 100K.[20–23]

In order to obtain the thermal conductivity from the measuredthermal conductance, the cross-sectionof theCNTsampleneeds tobe determined. In addition, the CNT thermal conductivity candepend on the number of shells, diameter, chirality, and structuraldefect concentrations. However, in many of the existing

Adv. Funct. Mater. 2009, 19, 3918–3925

FULLPAPER

www.MaterialsViews.comwww.afm-journal.de

Figure 1. a) Scanning electron microscopy (SEM) image of the suspended

microdevice for thermal conductance measurements of CNTs. b) SEM

image of the two central membranes of the microdevice. c) SEM and

d) TEM image of SWCNT sample S1 bridging the two membranes.

e) Diffraction pattern for S1 using a 350 nm coherent electron beam.

The two hexagons are added to highlight the f1010g layer lines from the top

and bottom of the nanotube. The diameter and chiral angle are determined

to be 2.33� 0.02 nm and 20.44� 0.28, respectively. f) Equatorial oscil-

lations (solid line) along EE0 in (e) and calculation (dashed line) for a

(22,12) SWCNT are in good agreement.

measurements, the crystal structure of the CNTs was notadequately characterized. Consequently, the obtained thermalconductivity valuesmayhave errors resulting from the uncertaintyin the CNT cross-section, and the structure–thermal propertyrelationship could not be established.

In two experiments,[10,12] transmission electron microscopy(TEM) was used to characterize the cross-section of individualMWCNTs assembled on a suspended microthermometer deviceor T-junction sensor for thermal measurement. In both experi-ments, the effective thermal conductivity of the MWCNTs wasfound to increase with decreasing diameters. In anotherexperiment conducted using the suspended microthermometerdevice, the measurement results were attributed to an increase ofthe intrinsic thermal conductivitywith the suspended length of theMWCNTs.[11] In these direct thermal conductancemeasurements,thermal contact resistance to the MWCNTs could not be obtainedas readily as inmicro-Raman thermometry-basedmethods. In twoearlier reports on thermal measurements of a MWCNT and aSWCNT using the suspended device,[8,9] it was suggested thatcontact resistance played a role. Thermal contact resistance waslater shown to account for the effective thermal conductivityobserved at low temperatures in a MWCNT[8], whose value waslower than that for graphite.[24] The presence of large thermalcontact resistance has recently been revealed via spatially resolvedtemperature measurements of optically and electrically heatedSWCNTs by using Raman and scanning thermal microscopy(SThM) measurements.[20,22,25]

The objectives of this work are to quantify the thermal contactresistance to CNTs, and to establish the structure–thermalproperty relationship by conducting thermal conductance andTEM measurements on the same individual SW, double-walled(DW), and MWCNTs directly grown between two suspendedmicrothermometers by thermal chemical vapor deposition (CVD).The thermal conductance, diameter, and chirality of one SWCNTare all characterized, and the thermal conductance of a DWCNT ismeasured. For three MWCNT samples, the thermal contactresistance is determined from thermal measurements before andafter deposition of platinum–carbon (Pt–C) composites at thecontacts. We find that thermal contact resistance limits thermaltransport in the as-grown CVD SW, DW, and MWCNT sampleswithout the contact deposition, and is still appreciable forMWCNTsamples after the contact deposition. The intrinsic thermalconductivity values determined for the three MWCNT samplescorrelate well with the different structural defect concentrationsobserved by TEM.

2. Results and Discussion

Thermal conductance measurements and TEM analysis wereconducted on the same individual CVD-grown CNTs betweenthe two suspended microthermometers of the measurementdevice (Fig. 1a and b),[26] which is described in the ExperimentalSection together with the CNT synthesis method.

2.1. Structure Characterization

TEM analysis was carried out after thermal conductancemeasurements, revealing that the CVD growth process yieldedSW, DW, and MWCNTs under identical growth conditions. In

Adv. Funct. Mater. 2009, 19, 3918–3925 � 2009 WILEY-VCH Verl

addition, the MWCNTs were observed to be produced by the tip-growth mechanism (Fig. S1, Supporting Information). It is likelythat a variation of the iron-ruthenium (Fe-Ru) catalyst thicknessand composition led to thenucleationof the threedifferent types of

ag GmbH & Co. KGaA, Weinheim 3919

FULLPAPER


Figure 2. a) SEM and b) TEM image of DWCNT sample D1.

Figure 3. a) SEM image of as-grown MWCNT sample M3. b) SEM image

of M3 after focused electron beam induced deposition of Pt–C at the

nanotube–membrane contacts; the suspended segment of M3 shifted and

a 180 nm section contacted the edge of the right membrane. c) One of the

TEM images taken along the nanotube sample M3 after Pt–C was depos-

ited at the contacts. These images reveal an axial structure defect con-

centration of about 50mm�1, corresponding to an effective grain size of

20 nm. d) High-resolution TEM image of M3 reveals a seven-shelled

multiwalled nanotube. e) Diffraction pattern for M3 obtained using a

350 nm coherent electron beam.

Table 1. CNT sample dimensions. di and do are the inner and outer CNTdiameters, respectively. L is the as-grown CNT suspended length. Lc,l andLc,r are left and right CNT-membrane contact lengths. MWCNT sample M1consists of three individual CNTs in parallel, labeled A, B, and C. N/A¼notavailable.

Sample # Shells di/do [nm] L [mm] Lc,l [mm] Lc,r [mm]

S1 1 2.34 4.31 N/A 2.10

S2 1 1.5 2.03 0.72 N/A

D1 2 2.1/2.7 4.02 0.40 0.64

M1 A 5 7.0/10.3 3.02 0.92 2.53

B 5 7.0/10.5 2.83 2.44 2.53

C 5 6.9/9.9 3.06 0.80 1.63

M2 5 6.8/9.9 1.95 2.14 0.40

M3 7 6.7/11.4 1.97 3.28 0.57

M4 11 6.6/14.0 3.31 2.29 5.63

3920

CNTs.We are unaware of other studies using the bimetallic Fe-Ruthin film catalyst and methane CVD growth method, which willrequire further studies to illuminate the critical phase transitionparameters for the growth regimes observed in thiswork. A total ofseven CNTsamples are reported in this work. These samples aredenoted as S1 and S2 for the two SWCNT samples, D1 for aDWCNTsample, and M1, M2, M3, and M4 for the four MWCNTsamples. SEM and TEM results are shown in Figure 1, 2 and 3 forS1, D1, andM3, respectively. Additional SEM and TEM results forS2, M1, M2, M3, and M4 are included in the SupportingInformation (Fig. S1–S8). The CNT dimensions are listed inTable 1, where the suspended and contact lengths were measuredby using SEM and the number of shells and the diameter weredetermined using TEM. Specifically, diameters were determinedby nanoarea electron diffraction (NAED)[27,28] for sample S1 andphase contrast TEM[29] for all others samples.

Except for samples S2 and D1, where the CNTs were brokenduring the TEM sample preparation procedure after thermalconductance measurements and the remaining suspendedsections were not long enough to obtain diffraction patterns,NAED patterns were obtained for each CNTsample of this work.TheNAEDpatternofS1 is shown inFigure1e.Thechiral angle anddiameter of S1 are determined to be 20.44� 0.28 and2.33� 0.02 nm, respectively, based on methods reported inliterature.[27,28] The best fit for both the diameter and chiral angleis (n,m)¼ (22, 12), which has a chiral angle and diameter of 20.368and 2.34 nm, respectively. The experimental intensity oscillationsalong the equatorial line in the NAED pattern for S1 are in goodagreementwith those calculated for a (22, 12) SWCNT, as shown inFigure 1f. The two closest alternatives are (21, 12) and (23, 13),which have diameters of 2.27 and 2.47 nm, respectively, and chiralangles of 21.058 and 20.898, respectively, outside of experimentalerror. Most importantly, the experimental intensity oscillationsalong the equatorial line for S1 do not agree with those calculatedfor the closest alternative chiralities (Fig. S7, SupportingInformation).

TEM analysis allowed for quantification of axial defects in theCNTs. Samples S1, S2, and D1 showed no observable defects. Onthe other hand, the defect concentration observed on the fourMWCNT samples appears to increase with the number of shells.MWCNTsamplesM1,M2,M3, andM4, consistingof5, 5, 7, and11shells, were observed to have about 35, 30, 50, and 77 dislocations,respectively, per micrometer length of the MWCNT. In otherwords, the average separation between two adjacent dislocations,La, is approximately 29, 33, 20, and13 nmforM1,M2,M3, andM4,

� 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Adv. Funct. Mater. 2009, 19, 3918–3925

FULLPAPER


Figure 4. As-measured effective thermal conductivity (k) versus tempera-

ture (T) for the two SWCNT, one DWCNT, and fourMWCNT samples in this

work. Filled symbols and unfilled symbols are results measured before and

respectively, and is equivalent to an effective grain size. Thediffraction patterns of M3 (Fig. 3e), M1, M2, and M4 (Fig. S6,Supporting Information) also show multiple equatorial lines thatvary by a few degrees from the average orientation, indicating thepresence of dislocations along the MWCNTs within the 350 nmcoherent electron beam.These results reveal thatMWCNTs grownby the thermal CVD method consist of more defects than thoseproduced by laser ablation[30] and arc-discharge processes.[31,32] Inrecent experiments, in situ environmental TEM observationduring CVD growth of CNTs by transition-metal catalyst particleshas shown that axial defects may be a result of dynamic reshapingof the catalyst particle during the growth process.[33,34] Furtherstudy of a large number of CVD MWCNT samples is required toverify the existence of the correlation between number of shellsand defect concentration, and to better understand the cause ofsuch correlation.

after Pt–C deposited at the contacts, respectively.

2.2. Thermal Conductance and Effective Thermal Conductivity

The thermal conductance of the as-grown CNTs was measuredusing the suspendedmicrothermometerdevicebasedonamethoddescribed previously[26] and discussed in detail in the SupportingInformation. The obtained total sample thermal conductance (Gs)results of the two SWCNT, one DWCNT, and four MWCNTsamples are shown in Fig. S11 in the Supporting Information.

The effective thermal conductivity k is obtained as k¼Gs L/AwhereA and L are the cross-sectional area and suspended length ofthe as-grown CNTsample, respectively. The cross-sectional area iscalculated in this work as

A �Xn

jpdjd ¼ npd d1 þ n� 1ð Þd½ � (1)

where n is the number of shells in the CNT, dj is the diameter ofthe j-th nanotube shell, and d¼ 3.35 A is the interplanar spacingof graphite. Equation 1 reduces to A¼pdd for SWCNT samplesand accounts for the cross-sectional area of each shell in DWCNTand MWCNT samples. In comparison, the definition A¼p(do

2–di2)/4, where do and di are the outer and inner diameters

of the CNT, respectively, can underestimate the cross-sectionalarea by up to 50% for the DWCNT. Both cross-sectional areadefinitions converge to within the measurement error for theMWCNT samples. The obtained effective thermal conductivityresults for the two SWCNT, one DWCNT, and four MWCNTsamples are shown in Figure 4.

Figure 5. Measured thermal resistance (Rs) versus temperature (T) for

three MWCNT samples before (filled symbols) and after (unfilled symbols)

Pt–C was deposited at the contacts.

2.3. Thermal Contact Resistance

For three MWCNT samples (M1, M3, and M4), the measuredthermal resistance was decreased by a factor of two after Pt–Cwasdeposited at the MWCNT–membrane contacts using focusedelectron beam induced deposition from an organometallicgaseous precursor,[35] as shown in Figure 5. Compared to thosetaken before the deposition (e.g., Fig. S4b and c, SupportingInformation), TEM images taken after the Pt–C deposition (e.g.,Fig. 3c and d) reveal some additional black dots on the MWCNT


surface, which are likely amorphous Pt–C with low thermalconductivity. Because these dots are small compared to theMWCNTcross-section anddonot forma continuous layer, they arenot expected to contribute to the reduction in the thermalresistance of the sample. In addition, the suspended lengths ofsampleM1andM4remained thesamebefore andafterdeposition;whereas a short (�180 nm) segment of the suspended section ofM3 was found to touch the side edge of one membrane after thedeposition (Fig. 3b and S8, Supporting Information). Hence, weattribute the large thermal resistance decrease to the decrease inthe thermal contact resistance. The result suggests that thermaltransport in the as-grown MWCNTs is limited by thermal contactresistance before the contact deposition.

We calculate the contact resistance using the fin heat transfermodel[24,36]

Rc;j �ffiffiffiffiffiffiffiffiffiffiffikNTA

R0c

stanh

Lc;jffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikNTAR0

c

p !" #�1

(2)

where Rc,j is the thermal contact resistance at each of the twoCNT–membrane contacts, Lc,j is the contact length, kNT is the


FULLPAPER


3922

intrinsic axial thermal conductivity of the CNT, and R0c is the

contact resistance between the CNT and the membrane per unitlength. It has been suggested that R0

c is dominated by theinterface thermal resistance between a CNT and the contactingmedium per unit length, R0

i,[24] which is proportional to the

contact width, b, and the phonon transmission coefficient, a1�2,across the interface from the CNT to the contacting surface.Hence, one expects that increasing contact area after the Pt–Cdeposition considerably reduces R0

c and the contact resistance.To evaluate the R0

c value after the Pt–C deposition, we analyzethe results from a recent work,[11] where the thermal resistances ofMWCNTs placed between two suspended microthermometerswere measured after each of several 0.5–1mm long Pt–C patternswas deposited in sequence to connect part of the suspendedMWCNTsegment with onemembrane. After each deposition, thesuspended lengthof theMWCNTswas decreased and the length ofone CNT–membrane contact (contact 1) was increased. Becausethe other contact (contact 2) was much shorter than contact 1 andwas covered by Pt–Cdeposition for only about 0.5–1mm in length,the thermal contact resistance of contact 2 is expected to be muchlarger than that of contact 1. The thermal resistance datameasuredafter oneor twomorePt–Cdepositions at contact 1 than at contact 2decreases approximately linearly with the decreasing suspendedlength. By extrapolating these thermal resistance data to zerosuspended MWCNT length, we obtain the thermal contactresistance to be in the range of (2.7–5.1)� 107 KW�1, which is54–88% of the measured total thermal resistance of the MWCNTsamples after all Pt–Cdepositionswere completed at contact 1. Theobtained contact resistance values arehigher than those thatwouldbe obtained for the case that the MWCNT thermal conductivityincreases with the suspended length.[11] By using Equation 2 to fitthe obtained contact resistance, we calculateR0

c in the range of 10–41mKW�1 for the four arc-grown MWCNT samples reported inRef. 11. We attribute the variation of the obtained R0

c values to thevariation of theouter diameter, do, of theMWCNTsamples from10to 33 nm. We use the obtained R0

c range to calculate the contactresistance, Rc,a, to be 19–37, 28–54, and 12–23% of the measuredtotal thermal resistance of our CVD samples after the Pt–Cdeposition, Rs,a, for sample M1, M3, and M4, respectively, whichhave diameters in the 10–14 nm range.

The contact resistance, Rc,b, of the as-grown MWCNT samplesbefore Pt–Cdeposition can be obtained based on the relationRs,b –Rs,a¼Rc,b – Rc,a – DL / (kNT A), where Rs,b is the total thermalresistance of the as-grown sample measured before the Pt–Cdeposition and DL is the difference in the suspended length. ForM1 and M4, DL¼ 0. For M3, poor thermal contact is expectedbetween the 180 nm segment in contact with the rough right-membrane edge compared to the segment covered by the Pt–Cdeposition. Ifwe ignore thermal contact between this segment andthe side edge, DL¼ 0. On the other hand, if we consider thermalcontact for this segment is the same as that covered by the Pt–Cdeposition, DL¼ –180 nm and the contact length increases by thesame amount. With these two limiting cases taken into accountforM3, the obtainedRc,b valueswould be 5.9–3.6, 4.2–2.5, and 6.8–4.1 times larger than the above-obtained Rc,a, for sample M1, M3,andM4, respectively. This comparison affirms the expectation thatthe increased contact area after the Pt–C deposition considerablyreduces the thermal contact resistance. Based on the obtained Rc,b

values, we further use Equation 2 to obtain the contact resistance

� 2009 WILEY-VCH Verlag GmbH & C

perunit lengthbefore thePt–Cdeposition,R0c,b, to be 201–258, 78–

125, and 439–585mKW�1, for M1, M3, and M4, respectively.We compare the obtained R0

c,b values with literature values. Inrecent work based on an electrical breakdown method,[37–40] thethermal contact resistance per unit length at the breakdowntemperature of about 900K was obtained as 2–6mKW�1 forindividual SWNCTs on SiO2 and sapphire, and 0.6mKW�1 for anindividual MWCNT on SiO2. The value obtained by aSThM measurement is 17–142mKW�1 for individual SWCNTson SiO2 and electrically heated to 380–540K.

[25] In addition, whenthe diffusive resistance component in the contact resistance istaken as much smaller than the interface resistance, the contactresistanceperunit length canbe calculated asR0

c�R00i b,whereR00

i

is the interface resistance per unit area and b is the contact width toa CNT. R00

i was recently measured to be 2� 10�8m2KW�1

between the graphite basal plane and a thin aluminum filmdepositedon top.[41] In addition,Ref. 24 canbe followed to calculateR00

i¼ 6.3� 10�9m2KW�1 near room temperature betweenplatinum and the graphite basal plane for the case of stronginterface bonding. The contact width due to van der Waals (vdW)force between a CNT and a perfectly smooth Pt surfacecan be calculated to be about 1 nm for a 10 nm diameterMWCNT,[24] yielding R0

c in the range of 7–22mKW�1 whenR00

i¼ 6.3� 10�9–2� 10�8m2KW�1 is used. On the other hand,the same b value would result in R0

c of 89mKW�1 if one uses theR00

i value of 8.3� 10�8m2KW�1 measured between a SWCNTand surfactant micelles.[42]

The R0c,b values obtained from our measurements are on the

same order of magnitude as that for CNT–micelles interface andthe upper limit of the SThMmeasurement results, but 1–3 ordersof magnitude higher than the other literature values. We note thatboth Rc,b and R0

c,b would be overestimated if R0c after Pt–C

deposition and Rc,a were overestimated in the above calculation.However, because the obtained Rc,a values are already 2.5–6.8 times smaller than the Rc,b values, the limiting case of Rc,a¼ 0only reducesRc,bby 17, 28, and15%andR0

c,bby 29, 45, and30% forM1, M3, and M4, respectively. Hence, we conclude that the R0

c,b

values for the three MWCNT samples are indeed considerablyhigher than the measurement values found from electricalbreakdown experiments and the theoretical values based onstrong interface bonding of a MWCNT to a smooth metal surface.

Several factors can lead to the high R0c,b values observed in this

work. First, the surface of the Pt electrodes became rather roughafter the high temperature CVD growth process, as shown in all ofthe SEM images of the Pt surface (e.g., Fig. 1c). The rough Ptsurface can reduce the contact area to be much smaller than thosefor smooth surfaces encountered in other experimental ortheoretical works. In addition, as shown in a recent calculation,[43]

R00i can increase by orders of magnitude for weak vdW bonding

compared to strong interface adhesion that is assumed for thecalculated R00

i¼ 6.3� 10�9m2KW�1 value between Pt and thegraphite basal plane.[24] Before the Pt–Cdeposition, our CVDCNTsampleswere only exposedbriefly to lowenergy (1.5 keV) electronsin a clean SEM chamber for acquiring an image of the sample.Detailed structure characterization was conducted after comple-tion of the thermalmeasurement of the as-grown samples.Hence,the interface adhesion energy could bemuch smaller for our clean,as-grown CNT samples than for CNT devices that have beenfabricated using lithography and metal deposition or exposed in

o. KGaA, Weinheim Adv. Funct. Mater. 2009, 19, 3918–3925

FULLPAPER


highenergy electronbeams ina contaminatedSEMchamber, suchas that used for Pt–C deposition. In addition to these two majorreasons, two additional factors can also lead to the large R0

c,b. Thefirst one is associated with the much lower temperatures in ourmeasurements than in the electrical breakdown experiments. Forgraphite, the specific heat (C) increases by about 2.5 times whenthe temperature is increased from 300 to 900K,[44] thus reducingR00

i by a similar factor because R00i is inversely proportional to C.

Moreover, the diffuse thermal resistance component to the contactresistance, R0

d, could be appreciable inMWCNTs because of weakintershell coupling.

The contact deposition was not applied to the SWCNT andDWCNT samples in this work as they did not survive the manysteps required by this experiment. For as-grown samples withoutPt–C deposition, the influence of contact resistance could be lessapparent in the smaller diameter SWCNTs and DWCNTs thanMWCNTs because of a smaller surface-to-cross-section ratio andweak intershell coupling in the MWCNTs, provided that theintrinsic thermal conductivity is not a strong function of diameteror number of shells. However, SWCNTsamples S1 and S2 couldalso have a high thermal contact resistance because of a very shortcontact length (�100 nm) on one contact, which could not bemeasured accurately with SEM. In fact, no electrical contact wasmade to the two SWCNT samples while �1MV electricalresistance was found for the DWCNT measured in this workand another likely SWCNTsample of higher thermal conductancemeasured in an earlier work.[9]

To evaluate the thermal contact resistance to the as-grown SWand DWCNTsamples, we followed Ref. 24 to calculate the contactwidth to be �0.3 nm between S1, S2, and D1 and a perfectlysmooth Pt surface in vdWcontact. Using R00

i in the range between2� 10�8–6.3� 10�9m2KW�1 for the strong interface bondingcase, we use Equation 2 to obtain a contact resistance of 10–25, 22–55, 15–31% of the measured total thermal resistance for the as-grown samples S1, S2, and D1, respectively. The actual contactresistance could be considerably higher because of the rough Ptsurface and weak vdW bonding. Hence, we conclude that theintrinsic thermal conductivity could be considerably higher thanthe effective thermal conductivity of about 600Wm�1 K�1

measured at room temperature for the SWCNT and DWCNTsamples.

2.4. Intrinsic Thermal Conductivity of MWCNT Samples

By eliminating the obtained contact resistance, Rc,a, frommeasured total resistance, Rs,a, after the Pt–C deposition, weobtain an intrinsic thermal conductivity kNTof 269–343, 178–336,and 42–48Wm�1 K�1 for sample M1, M3, and M4, respectively.These intrinsic thermal conductivity values have been used inEquation 2 for calculating theRc,a values in an iterative procedure.Although the obtained kNT increases with decreasing number ofshells, we attribute this trend to the observed increased defectconcentration instead of increased intershell scattering withnumber of shells.We calculate the phononmean free path, l, of theMWCNTs using the thermal conductivity expression from kinetictheory for the 2D case, k¼Cnl/2 whereC is the specific heat and nis thephonongroupvelocity.Using specificheat[44] andbasal planeDebye velocity[24] values forgraphite, thephononmean freepath in


M1, M3, and M4 is calculated from the intrinsic thermalconductivity values at 300K to be l¼ 23–30, 15–29, and 4 nm,respectively, which agree reasonably well with the effective grainsize La¼ 29, 20, and 13 nm determined by TEM analysis for M1,M3, and M4, respectively. Hence, the observed low thermalconductivity of the MWCNT can be attributed to phonon-defectscattering, with k increasing with effective grain size as can beexpected. The capability demonstrated here for correlatingthe intrinsic thermal conductivity of the CVD grown MWCNTwith the structural defect concentration allows us to explain theorder-of-magnitude lowerkof theCVDMWCNTs in thiswork thanthose measured for MWCNTs grown by arc-discharge.[8,10,12]

2.5. Electron Irradiation Effects

In addition, we observed the effects of electron irradiation damageon the thermal conductance.BeforePt–Cdepositionat thecontactsand after exposure of MWCNT samples M1 and M2 to 120 keVelectron irradiation during the TEM analysis, the thermalconductance of the two samples was again measured, and foundto be 21 and 39% lower than that measured before the TEManalysis, respectively, which is qualitatively expected as a result ofprimary knock-on damage.[45] Interestingly, it was found that thethermal conductance could be recovered to the original valuesprior to electron irradiation by passing about 7mA of electricalcurrent through MWCNT sample M1. With knowledge of thecontact resistance, intrinsic thermal conductivity, and electricalheating rate (�3.6mW), we calculate the maximum latticetemperature rise of M1 to be in the range of 650–850K. In thiscalculation, the thermal conductivity is assumed to be the same asthe measurement value at 300K, which could slightly under-estimate the actual temperature rise. Nevertheless, the obtainedtemperature range is on the order of the current-annealingtemperature used to achieve ultrahigh mobility in suspendedgraphene (600 K)[46] and that used to join SWCNTs in a Jouleheating/electromigration technique (600–1200K).[47] The rela-tively high temperature during current annealing is likelyresponsible for repairing the defect sites caused by the knock-on damage. In MWCNT sample M2, when more aggressivecurrent-annealing was attempted, the sample experiencedelectrical break-down at a current density of approximately6� 107 Acm�2 (�56mW electrical power). This current densityis an order of magnitude below those observed in high-quality SWCNTs[14] and MWCNTs.[48,49] Hence, it is likely thatdefects in the CVD MWCNTs localize heating and/or electro-migration processes, leading to structural failure of the CNT.[47]

3. Conclusions

This work reports combined thermal conductance and TEMcharacterizations of the same SW, DW, and MWCNTs, anddemonstrates the measurement of the thermal conductance,diameter, and chirality of the same SWCNTsample as well as thethermal conductance of a DWCNT. For four MWCNT samples,the observed defect concentration appears to increase with thenumber of walls. For a MWCNT sample, high-energy electronbeam irradiation was found to cause a 21–39% reduction of thethermal conductance, which was recovered after electrical current


FULLPAPER


3924

annealing of the sample. The thermal contact resistance per unitlength is obtained as 78–585mKW�1 for three as-grown 10–14 nm diameter CVD MWCNTs on rough Pt electrodes, anddecreases by more than 2 times after Pt–C is deposited at thecontacts. With the thermal contact resistance eliminated fromthe measured thermal resistance after the Pt–C deposition, theobtained intrinsic thermal conductivity in the range of 42–343Wm�1 K�1 of the MWCNT samples at room temperaturecorrelates well with the axial defect concentration determined byTEM. On the other hand, the large thermal contact resistancelimits the effective thermal conductivity to about 600Wm�1 K�1 atroom temperature for the as-grown CVD SW and DWCNTswithout the Pt�C deposition at the contacts. With further efforts,the intrinsic thermal conductivity of high-quality, high-thermalconductivity CNTs at different temperatures can potentially beobtained by exploring the recently developed four-probe thermalmeasurement method[50,51] based on the same suspendedmicrothermometer device used in this work.

4. Experimental

Microthermometer Device Fabrication: The thermal conductance mea-surements were conducted using a suspended device [26], which consistsof two adjacent low-stress silicon nitride (SiNx) membranes eachsuspended by six 420mm long SiNx beams. One 35 nm thick, 200 nmwide, and 350mm long serpentine Pt resistance thermometer (PRT) andtwo 1mm wide Pt electrodes are patterned on each membrane. Electronbeam lithography and a lift-off process was used to pattern a 10 A thick Fethin film covered by a 5 A thick Ru thin film on the Pt electrodes of the twomembranes in order to locally seed CNT growth via thermal CVD. Athrough-substrate hole was etched beneath the suspended membranes toallow for TEM characterization of the as-grown suspended CNTs.

Carbon Nanotube Synthesis: Carbon nanotubes were grown betweenthe two suspended membranes directly by catalytic decomposition ofhydrocarbon gas on the transitionmetal catalysts patterned only on the twomembranes [52]. The temperature of the growth furnace was ramped/cooled under hydrogen (200 cm3min�1, 99.999%) and CVD wasconducted at 900 8C and atmospheric pressure for 10min with methane(1000 cm3min�1, 99.999%) as the carbon feedstock, yielding clean CNTsbridging the two membranes of the suspended microthermometer device.A high-resolution scanning electron microscope (Zeiss Supra 40 VP) wasused to image each sample in this work and to ensure that no CNTs weregrown on the suspended measurement device except between the twocentral membranes.

Transmission Electron Microscopy: TEM analysis was carried out afterthermal conductance measurements using a FEI Tecnai G2 F20 X-Twin at120 kV accelerating voltage. NAED patterns of the CNT samples wereacquired using a 350 nm coherent electron beam and recorded on a charge-coupled device camera with a camera length of 33 cm and exposure timesgreater than 1min.

Pt–C Deposition at the Contacts: A 30 keV electron beam wasused to decompose the metal-organic precursor, trimethyl(methylcyclopentadienyl)platinum(IV), at the contacts of MWCNT samplesM1, M3, and M4 in a scanning electron microscope (FEI DB Strata 235).The suspended MWCNT segments were not imaged during or after thegaseous organometallic precursor entered the chamber. After Pt–Cdeposition and prior to thermal conductance measurements, the samplewas annealed in vacuum at 490 K for several hours to improve Pt–C density[53] prior to thermal conductance measurements.

Acknowledgements

This work is supported by the U.S. Department of Energy award DE-FG02-07ER46377 and the Graduate Research Fellowship Program and Thermal

� 2009 WILEY-VCH Verlag GmbH & C

Transport Processes Program of the National Science Foundation.Supporting Information is available online from Wiley InterScience orfrom the author.

Received: May 28, 2009

Revised: September 7, 2009

Published online: November 17, 2009

[1] P. Avouris, Z. H. Chen, V. Perebeinos, Nat. Nanotechnol. 2007, 2, 605.

[2] M. J. Biercuk, M. C. Llaguno, M. Radosavljevic, J. K. Hyun, A. T. Johnson,

J. E. Fischer, Appl. Phys. Lett. 2002, 80, 2767.

[3] H. Huang, C. H. Liu, Y. Wu, S. S. Fan, Adv. Mater. 2005, 17, 1652.

[4] J. Xu, T. S. Fisher, Int. J. Heat Mass Transf. 2006, 49, 1658.

[5] R. Prasher, Proc. IEEE 2006, 94, 1571.

[6] T. Tong, Y. Zhao, L. Delzeit, A. Kashani, M. Meyyappan, A. Majumdar, IEEE

Trans. Compon. Packaging Technol. 2007, 30, 92.

[7] M. A. Panzer, G. Zhang, D. Mann, X. Hu, E. Pop, H. Dai, K. E. Goodson,

J. Heat Transfer 2008, 130, 052401.

[8] P. Kim, L. Shi, A. Majumdar, P. L. McEuen, Phys. Rev. Lett. 2001, 87, 215502.

[9] C. H. Yu, L. Shi, Z. Yao, D. Y. Li, A. Majumdar, Nano Lett. 2005, 5, 1842.

[10] C. W. Chang, A. M. Fennimore, A. Afanasiev, D. Okawa, T. Ikuno, H. Garcia,

D. Y. Li, A. Majumdar, A. Zettl, Phys. Rev. Lett. 2006, 97, 085901.

[11] C. W. Chang, D. Okawa, H. Garcia, A. Majumdar, A. Zettl, Phys. Rev. Lett.

2008, 101, 075903.

[12] M. Fujii, X. Zhang, H. Q. Xie, H. Ago, K. Takahashi, T. Ikuta, H. Abe,

T. Shimizu, Phys. Rev. Lett. 2005, 95, 065502.

[13] T. Y. Choi, D. Poulikakos, J. Tharian, U. Sennhauser, Nano Lett. 2006, 6,

1589.

[14] Z. Yao, C. L. Kane, C. Dekker, Phys. Rev. Lett. 2000, 84, 2941.

[15] A. W. Bushmaker, V. V. Deshpande, M. W. Bockrath, S. B. Cronin, Nano

Lett. 2007, 7, 3618.

[16] M. Oron-Carl, R. Krupke, Phys. Rev. Lett. 2008, 100, 127401.

[17] M. Steiner, M. Freitag, V. Perebeinos, J. C. Tsang, J. P. Small, M. Kinoshita,

D. Yuan, J. Liu, P. Avouris, Nat. Nanotechnol. 2009, 4, 320.

[18] L. Shi, Appl. Phys. Lett. 2008, 92, 206103.

[19] E. Pop, D. Mann, Q. Wang, K. Goodson, H. J. Dai, Nano Lett. 2006, 6, 96.

[20] V. V. Deshpande, S. Hsieh, A. W. Bushmaker, M. Bockrath, S. B. Cronin,

Phys. Rev. Lett. 2009, 102, 105501.

[21] Q. W. Li, C. H. Liu, X. S. Wang, S. S. Fan,Nanotechnology 2009, 20, 145702.

[22] I. K. Hsu, R. Kumar, A. Bushmaker, S. B. Cronin, M. T. Pettes, L. Shi,

T. Brintlinger, M. S. Fuhrer, J. Cumings, Appl. Phys. Lett. 2008, 92, 063119.

[23] I. K. Hsu, M. T. Pettes, A. Bushmaker, M. Aykol, L. Shi, S. B. Cronin, Nano

Lett. 2009, 9, 590.

[24] R. Prasher, Phys. Rev. B 2008, 77, 075424.

[25] L. Shi, J. Zhou, P. Kim, A. Bachtold, A. Majumdar, P. L. McEuen, J. Appl.

Phys. 2009, 105, 104306.

[26] L. Shi, D. Y. Li, C. H. Yu, W. Y. Jang, D. Kim, Z. Yao, P. Kim, A. Majumdar,

J. Heat Transfer 2003, 125, 881.

[27] M. Gao, J. M. Zuo, R. D. Twesten, I. Petrov, L. A. Nagahara, R. Zhang, Appl.

Phys. Lett. 2003, 82, 2703.

[28] J. M. Zuo, T. Kim, A. Celik-Aktas, J. Tao, Z. Kristall. 2007, 222, 625.

[29] C. Qin, L. M. Peng, Phys. Rev. B. 2002, 65, 155431.

[30] T. W. Odom, J.-L. Huang, P. Kim, C. M. Lieber, Nature 1998, 391, 62.

[31] S. Iijima, Nature 1991, 354, 56.

[32] T. W. Ebbesen, P. M. Ajayan, Nature 1992, 358, 220.

[33] R. Sharma, P. Rez, M. M. J. Treacy, S. J. Stuart, J. Electron Microsc. 2005, 54,

231.

[34] S. Hofmann, R. Sharma, C. Ducati, G. Du, C. Mattevi, C. Cepek,

M. Cantoro, S. Pisana, A. Parvez, F. Cervantes-Sodi, A. C. Ferrari,

R. Dunin-Borkowski, S. Lizzit, L. Petaccia, A. Goldoni, J. Robertson, Nano

Lett. 2007, 7, 602.

[35] H. W. P. Koops, A. Kaya, M. Weber, J. Vac. Sci. Technol. B 1995, 13, 2400.

[36] C. H. Yu, S. Saha, J. H. Zhou, L. Shi, A. M. Cassell, B. A. Cruden, Q. Ngo,

J. Li, J. Heat Transfer 2006, 128, 234.

[37] H. Maune, H.-Y. Chiu, M. Bockrath, Appl. Phys. Lett. 2006, 89, 013109.

o. KGaA, Weinheim Adv. Funct. Mater. 2009, 19, 3918–3925

FULLPAPER


[38] E. Pop, D. A. Mann, K. E. Goodson, H. J. Dai, J. Appl. Phys. 2007, 101,

093710.

[39] H. Y. Chiu, V. V. Deshpande, H. W. C. Postma, C. N. Lau, C. Miko, L. Forro,

M. Bockrath, Phys. Rev. Lett. 2005, 95, 226101.

[40] A. Javey, J. Guo, M. Paulsson, Q. Wang, D. Mann, M. Lundstrom, H. Dai,

Phys. Rev. Lett. 2004, 92, 106804.

[41] A. J. Schmidt, X. Chen, G. Chen, Rev. Sci. Instrum. 2008, 79,

114902.

[42] S. T. Huxtable, D. G. Cahill, S. Shenogin, L. Xue, R. Ozisik, P. Barone,

M. Usrey, M. S. Strano, G. Siddons, M. Shim, P. Keblinski, Nat. Mater.

2003, 2, 731.

[43] R. Prasher, Appl. Phys. Lett. 2009, 94, 041905.

[44] Y. S. Touloukian, E. Y. Buyco, in: Thermophysical Properties of Matter, Vol. 5:

Specific Heat–Nonmetallic Solids, (Eds: Y. S. Touloukian, C. Y. Ho), IFI/

Plenum, New York 1970, pp. 9–14.


[45] J. C. Meyer, M. Paillet, G. S. Duesberg, S. Roth, Ultramicroscopy 2006, 106,

176.

[46] K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone,

P. Kim, H. L. Stormer, Solid State Commun. 2008, 146,351.

[47] C. Jin, K. Suenaga, S. Iijima, Nat. Nanotechnol. 2008, 3, 17.

[48] S. Frank, P. Poncharal, Z. L. Wang, W. A. de Heer, Science 1998, 280, 1744.

[49] P. G. Collins, M. S. Arnold, P. Avouris, Science 2001, 292, 706.

[50] A. Mavrokefalos, M. T. Pettes, F. Zhou, L. Shi, Rev. Sci. Instrum. 2007, 78,

034901.

[51] F. Zhou, J. Szczech, M. T. Pettes, A. L. Moore, S. Jin, L. Shi,Nano Lett. 2007,

7, 1649.

[52] X. Li, X. Tu, S. Zaric, K. Welsher, W. S. Seo, W. Zhao, H. Dai, J. Am. Chem.

Soc. 2007, 129, 15770.

[53] V. Gopal, V. R. Radmilovic, C. Daraio, S. Jin, P. D. Yang, E. A. Stach, Nano

Lett. 2004, 4, 2059.


1

Supporting Information for: (DOI: 10.1002/adfm.200900932)

Thermal and Structural Characterizations of Individual Single-, Double-, and Multi-Walled Carbon Nanotubes By Michael T. Pettes and Li Shi* [*] Prof. L. Shi, M. T. Pettes Department of Mechanical Engineering and the Center for Nano and Molecular Science and Technology, Texas Materials Institute, University of Texas at Austin, Austin, TX 78712 (USA) E-mail: [email protected] 1. Electron Microscopy Analysis of Carbon Nanotubes

Figure S1. TEM images of (a) MWCNT sample M1A and (b) M1C. Arrows indicate

bimetallic catalyst particles as evidence for tip-growth formation. Methane flow direction is

top to bottom with respect to the images, and no free-standing MWCNT was observed without

a catalyst particle at its tip.

Figure S2. (a) SEM and (b) TEM image of SWCNT sample S2.

2

Figure S3. (a) SEM image of as-grown MWCNT sample M1 that consists of 3 individual

MWCNTs, denoted as A, B, and C. (b) SEM of M1 after focused electron beam induced

deposition of Pt-C at the nanotube-membrane contacts. (c)-(d) TEM images of A, B and C

reveal that they are quintuple-walled nanotubes with an axial defect structure density of 35

μm-1, corresponding to an effective grain size of 29 nm. TEM images were taken before Pt-C

was deposited at the contacts.

3

Figure S4. (a) SEM and (b)-(c) TEM images of MWCNT sample M2 reveal a quintuple-

walled nanotube with an axial grain size of about 33 nm.

Figure S5. (a) SEM image of as-grown MWCNT sample M4. (b)-(c) SEM of M4 after

focused electron beam induced deposition of Pt-C at the nanotube-membrane contacts. (d)-(e)

TEM images of M4 reveal an 11-shelled MWCNT with an axial defect structure concentration

of 77 μm-1, corresponding to an effective grain size of 13 nm. TEM images were taken after

Pt-C was deposited at the contacts.

4

Figure S6. Diffraction patterns for (a) M1A, (b) M2, and (c) M4 obtained using a 350 nm

coherent electron beam. Diffraction patterns show multiple equatorial lines that vary by a few

degrees from the average orientation, a result of the probe size being an order of magnitude

larger than the grain size of the MWCNT. The diffraction pattern of M4 shows the weakest

intensity of 0}1{10 reflections compared with M1A and M2, further evidence of its relatively

lower crystalline quality.

Figure S7. Experimental intensity oscillations for S1 (blue line) along the equatorial line (EE'

in Fig. 1e, Manuscript) are in good agreement with those calculated for a (22, 12) SWCNT

(red line). Calculated intensity oscillations for the two closest alternative chiralities, (21, 12)

(black line) and (23, 13) (green line), do not fit the experimentally observed intensity profile.

5

Figure S8. (a) TEM image of MWCNT sample M3 after focused electron beam induced

deposition of Pt-C at the nanotube-membrane contacts and (b) high resolution TEM image

showing the 180 nm as-grown suspended section that has come in contact with the right

membrane edge.

2. Thermal Conductance Measurement

The thermal conductance of the as-grown CNTs was measured using a method described

previously.[1] During the measurement, the sample was placed into a cryostat under high

vacuum to eliminate heat transfer through the air. The schematic and thermal resistance circuit

for this measurement method is shown in Fig. S9. The two suspended membranes of the

measurement device are denoted as the heating membrane and the sensing membrane,

respectively. When a direct current, I, is supplied to the platinum resistance thermometer

(PRT) on the heating membrane, part of the Joule heat generated in the heating membrane is

conducted through the CNT to the sensing membrane. The temperature distribution on each

membrane was found to be uniform in a numerical simulation.[2] At different I values, the two

PRTs are used to measure the temperature rises on the heating and sensing membranes, ΔTh(I)

6

≡ Th(I) – T0 and ΔTs(I) ≡ Ts(I) – T0, respectively, where T0 is the substrate temperature. The

thermal resistance of the six beams supporting each membrane can be obtained as RB = (ΔTh +

ΔTs) / (Qh + Ql), where Qh is the Joule heat dissipation in the PRT on the heating membrane,

and Ql is half of the Joule heat dissipation in the two identical Pt leads supplying the current to

the heating PRT.[1] The total measured thermal resistance of the CNT sample is obtained as Rm

= (Th – Ts) / Q, where Q is obtained as Q = ΔTs / RB. With the use of a sensitive AC

measurement of the differential electrical resistances of the two PRTs, the measurement

method can achieve a sensitivity on the order of 0.1 nW K-1 in the measured thermal

conductance, Gm ≡ 1 / Rm. The maximum temperature rise (ΔTh,max) on the heating membrane

was between 10 and 20 K, so that the obtained Gm is the average value over the temperature

range between T0 and (T0 + ΔTh,max).

For this thermal conductance measurement, radiation loss from the heating membrane is

calculated to be below 3 % of Qh; whereas less than 5 % of Ql is lost via radiation from the

two Pt lead wires supplying the heating current. We note that RB of the supporting beams is

the fin thermal resistance that has accounted for the radiation loss from the circumference of

the beams in addition to heat conduction along the beams, with the radiation calculated to be

at least one order of magnitude smaller than the conduction. On the other hand, radiation heat

loss from the circumference of a CNT is calculated to be several orders of magnitude smaller

than heat conduction along the CNT.

Because of the small cross section, Gm of a SWCNT is often not much higher than the

background thermal conductance, Gbg, measured with the suspended device after the SWCNT

between the two membranes was broken (Fig. S10). Gbg is a result of parasitic heat transfer

between the two membranes via radiation or conduction by residual molecules in the

evacuated cryostat, and by heating of the substrate due to a finite substrate thermal resistance.

At 300 K, Gbg was measured to be about 0.3 nW K-1. At each temperature, the measured Gbg

7

value was subtracted from the as-measured thermal conductance, Gm, to obtain the sample

thermal conductance Gs ≡ 1 / Rs = 1 / (Rc + RNT), (Fig. S11) where Rc is the total contact

thermal resistance and RNT is the intrinsic thermal resistance of the CNT.

Figure S9. Schematic and thermal resistance circuit of the experimental method for thermal

resistance or conductance measurements of individual suspended CNTs.

8

Figure S10. Measured total thermal conductance (Gm) versus temperature (T) for the two

SWCNTs, one DWCNT and two MWCNT samples in this work. Also shown is the

background thermal conductance (Gbg) due to parasitic heat transfer between the two

membranes via radiation or conduction and by substrate heating. Filled symbols and unfilled

symbols are results measured before and after Pt-C deposition at the contacts, respectively.

Figure S11. Background corrected total thermal conductance (Gs) versus temperature (T) for

the two SWCNT, one DWCNT, and two MWCNT samples in this work. Filled symbols and

9

unfilled symbols are results measured before and after Pt-C deposition at the contacts,

respectively.

References

[1] L. Shi, D. Y. Li, C. H. Yu, W. Y. Jang, D. Kim, Z. Yao, P. Kim, A. Majumdar, J. Heat

Transfer 2003, 125, 881.

[2] C. H. Yu, S. Saha, J. H. Zhou, L. Shi, A. M. Cassell, B. A. Cruden, Q. Ngo, J. Li, J.

Heat Transfer 2006, 128, 234.

Thermal and structural characterizations of individual single ......[*] Prof. L. Shi, M. T. Pettes...

Documents

Transcript of Thermal and structural characterizations of individual single ......[*] Prof. L. Shi, M. T. Pettes...