Ultrahigh Currents in Dielectric-Coated Carbon Nanotube ProbesYuliya Lisunova,*,† Ivan Levkivskyi,‡ and Patrycja Paruch†

†DPMC-MaNEP, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland‡Department of Physics, Harvard University, Cambridge, Massachusetts 02138, United States

*S Supporting Information

ABSTRACT: Carbon nanotubes used as conductive atomicforce microscopy probes are expected to withstand extremelyhigh currents. However, in existing prototypes, significant self-heating results in rapid degradation of the nanotube probe.Here, we investigate an alternative probe design, fabricated bydielectric encapsulation of multiwalled carbon nanotubes,which can support unexpectedly high currents with extremestability. We show that the dielectric coating acts as a reservoirfor Joule heat removal, and as a chemical barrier against thermal oxidation, greatly enhancing transport properties. In contact withAu surfaces, these probes can carry currents of 0.12 mA at a power of 1.5 mW and show no measurable change in resistance atcurrent densities of 1012 A/m2 over a time scale of 103 s. Our observations are in good agreement with theoretical modeling andexact numerical calculations, demonstrating that the enhanced transport characteristics of such probes are governed by theirmore effective heat removal mechanisms.

KEYWORDS: Conductive-atomic force microscopy, carbon nanotube probes, transport properties, resistive heating

Conductive atomic force microscopy (C-AFM) is anindispensable technique for local electrical character-

ization of functional materials and holds great promise forfuture nanotechnology applications. High spatial resolutionconductive tips with improved reliability are especiallyimportant for detailed studies of advanced semiconductors,1−3

correlated oxide thin films,4−9 and energy storage devices10 oforganic and biological systems6,11,12 and for potentialintegration into a probe-based memory technology.13,14 Oneextremely appealing route toward extending the physical limitsof C-AFM is through the use of carbon nanotubes (CNT) asthe active probe elements,10,15−19 exploiting their outstandingmechanical and electrical properties.15,20

It is well-known that, when supported fully by a substrate,CNT can sustain enormous current densities,21−24 with nodetectable failure in the nanotube structure for time scales of upto two weeks at 1013 A/m2, with a dissipation power higherthan 100 mW (ref 25). Thus, multiwalled carbon nanotube(MWNT)-based probe tips would be expected to providereliable high current carrying capabilities, with reasonablerigidity and metallic-like electrical conduction.17,21,25 However,studies of high-field transport of MWNTs suspended betweenPt electrodes, equivalent to the geometry of a conductingprobe, reveal significant current-induced Joule heating limi-tations.17,26 Due to the reduced dimensionality for thermalconduction and much smaller contact area with the substrate inthis case, MWNT failure is already observed at current densitiesof 1010 A/m2, at a much lower power of 4 μW, and after merelya few seconds. In fact, the suspended CNTs are undamaged bypower dissipation only in the pW range.17 Improved thermalmanagement of such probes is therefore a key requirement, anddielectric encapsulation of the MWNTs, beyond simply

rigidification, could provide an additional avenue for effectiveheat dissipation.27,28

In this Letter, we report on in-depth transport and reliabilitystudies of such dielectric-coated MWNT probes of variouslengths and diameters. We demonstrate that dielectricencapsulation significantly improves MWNT transport charac-teristics, providing both an efficient thermal reservoir and aprotective chemical barrier preventing thermal oxidation, thusallowing extremely high current densities to pass through theprobe without failure. In contact with Au surfaces, such probescan carry currents as high as 0.12 mA, at a power of 1.5 mW.Time-dependent measurements show greatly enhanced cur-rent-carrying capability, with no indication of saturation orresistance change at a current of 65 μA and a power greaterthan 0.5 mW for a time scale of 100 s. Moreover, in contrast toprevious studies of MWNT transport, which report highlynonlinear current−voltage behavior with increasing conduc-tance for higher currents,21−24 we observe almost linearcurrent−voltage characteristics. To develop a clear picture ofthe role of dielectric coating in the high-field regime and tocompare it directly with our experimental results, we simulateand numerically evaluate the temperature distribution anddifferential conductance of the MWNT probes, considering thetemperature dependence of both their thermal and electricalconductivity. For both dielectric-encapsulated and bare MWNTprobes, we find a highly nonuniform temperature distribution,with significant heat concentration in the middle of the

Received: July 6, 2013Revised: August 13, 2013Published: August 26, 2013

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nanotube, leading to increased variation of the differentialconductance with increasing nanotube length. However, for theencapsulated probes the average temperature is lower, and thetemperature profile along the nanotube is more homogeneousat the same bias voltage, giving rise to quasi-linear transportcharacteristics.To fabricate the probes for our study, MWNTs were first

grown on commercial Si-based AFM tips (μMasch NSC18,∼3.5 N/m) by chemical vapor deposition,29 resulting in thinbundles or individual MWNTs at the tip apex, 10−20 nm indiameter, 1−10 μm long (see Supporting Information for moredetails). These as-grown MWNT tips were shortened to typicallengths of 300−800 nm by electrical etching at 15−20 V on asputtered Nb surface,29,30 improving their stiffness. Theresulting shortened tips were resistant enough to withstandthe mechanical and thermal stresses during subsequent electronbeam evaporation deposition of a thin insulating SiOx coating,at room temperature, at a rate of 0.01 nm/s. This very lowgrowth rate resulted in a uniform and homogeneous formationof a well-adhered SiOx layer on the MWNT tips. Finally,focused ion beam etching was used to expose the conductivecore of the MWNT/SiOx composite structure, as shown inFigure 1a, following ref 31. In total, electrical transport

properties of eight such tips were studied in contact with anAu-coated Si wafer. The C-AFM current−voltage (I−V)measurements were carried out in a commercial AFM(VEECO Dimension 3100 with Nanoscope V controller) instandard contact mode (150 nN). During dynamic measure-ments, the current was acquired while sweeping the voltagewith 2−20 mV steps at 500 steps per second, while for static

measurements, a fixed voltage was applied to the probes, andthe current was monitored over 10−100 s.Although varying in small details, the overall features of the

I−V characteristics were similar across all of the differentMWNT probes, as shown in Figure 1b. All of the probesshowed almost linear I−V characteristics and extremely highcurrent-carrying capabilities, with currents approaching 100 μAunder 10−12 V bias, giving typical resistance values in therange of 0.1−0.4 MΩ. At the highest observed current of 120μA, an order of magnitude higher than the maximum currentsof 10−12 μA reported for suspended single walled carbonnanotubes32,33 or for bare MWNT probes,17 our encapsulatedMWNTs showed no sign of I−V saturation or physicaldeterioration. In addition, during static measurements nodegradation of probe conductance was observed at currentdensities of 1012 A/m2 for a time scale of 100 s. In fact, the 100s stability tests showed rather a very slight increase in theconductance at increased bias voltage, which we attribute toimprovement of the thermal contact during measurement. Wenote further that, although small conductance fluctuations canbe seen in the higher-bias measurements of the specific probeshown in Figure 1c, these follow no particular trend and werenot observed in tests of other probes, even for extendedmeasurements of repeated 100 s voltage pulses for 103 s (seeSupporting Information). We note that dielectric encapsulationallows MWNTs to withstand these high power densities of0.45−1.5 mW at ambient conditions, without specialprocedures to minimize thermal oxidation by vacuum23,24 orby heat removal directly into the substrate beneath thenanotube.21,25

To further characterize the transport properties of theencapsulated MWNT probes, we also numerically evaluated theI−V derivatives, which show varying sign of the conductanceslope from one probe to another. For most probes, theminimum conductance of approximately 5 μS extrapolated tozero current (zero bias voltage) increases steeply withincreasing current, as shown by the green line in Figure 1d.Such behavior is commonly observed in individual MWNTsand can be associated with thermally activated tunnelling ofelectrons between MWNT shells.21−23 However, we alsoobserved deviation from this typical behavior in two of theeight probes, which showed instead a negative conductanceslope (red lines in Figure 1b,d), although with no additionaldifference in either size or contact resistance. We thereforeattribute these discrepancies to structural differences betweenthe MWNTs in the different probes, grown here by chemicalvapor deposition (see Supporting Information). Specifically, itis difficult to control growth at single nanotube level, whichmay result in a bundle MWNT probe,15,20 the presence ofsingle-walled nanotubes (SWNT), and high defect densitiescompared to arc-discharge-produced MWNTs.20,28 The pres-ence of SWNTs and defects would likewise influence thetransport properties of the probes24 and may play adetermining role in their failure.21 In this study, the majorityof the probes investigated showed robust transport propertieseven at the maximum voltage of 12 V attainable with our setup.However, two failed very abruptly in a single step at 60−70 μAand 9 V (see Supporting Information for more details), aneffect we attribute to internal failure initiated at defect siteswithin the MWNT. In addition, our data shows no electricalconductance quantisation, and no systematic dependence onprobe diameter or length in the measurement range, beyond alinear increase with A/L, where A is the cross section and L the

Figure 1. High-field electronic transport of dielectric-encapsulatedMWNT probes. (a) SEM image of a dielectric-coated MWNT probe,exposed at the tip apex by focused ion beam etching, allowingelectrical contact with the sample surface. The inset shows the MWNTtip prior to SiOx deposition. (b) Current−voltage (I−V) character-istics of the eight probes. (c) The time trace of the current I(t) for theprobe indicated in green in b, showing no measurable change inresistance at current densities of 1012 A/m2 over a time scale of 100 s.(d) Representative measurements of probe conductance (dI/dV) as afunction of current, where the green line represents typical electricalbehavior of the MWNT probes and red line the negative conductanceslope observed in two of the eight devices, calculated from the (I−V)curves, respectively. The color code corresponds to that in b.

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length of the MWNT probe, indicating that the transportthrough the MWNTs is diffusive. Interestingly, we also foundthat the electrical conductance increase for higher currents ismuch more pronounced for longer MWNT probes, which weexplain below.To interpret our experimental observations, and to under-

stand the underlying mechanisms leading to the superiorcurrent-carrying capabilites of the dielectric-encapsulatedMWNT probes, we considered a theoretical model of resistiveheating in a CNT probe geometry and numerically evaluatedthe electrical conductance in the high-field regime, using aquasi-1D approximation for the temperature and conductancedistribution in the stationary state (see Supporting Informationfor more details). The temperature distribution is a solution ofthe heat equation34

κ ρ∇ ∇ = ΘT T T jr r r r r( , ( )) ( ) ( ( )) ( )2(1)

where κ(T) is the thermal conductivity (κ(T) ∼ 50−300 W/mK) (previously reported35), ρ(T) the electrical resistivity(ρ(T) of the order of 0.3 × 10−5 Ω·m) (extracted from I−Vmeasurements), and Θ(r) = 1 inside the CNT, where Jouleheat is generated, and 0 elsewhere. We assume a diffusivetransport regime, with the electron scattering length muchsmaller than the nanotube length. Since little is known aboutthe temperature dependence of MWNT conductivity, weassume a linear behavior and determine the slope by fitting theexperimental data. The time τs at which the stationarydistribution is achieved can be estimated as the Joule heatdivided by the thermal capacitance of the probe, giving τs < 1 μsfor typical voltages used in our experiments. Thus, we neglecttime-dependent effects and focus on the stationary state. Sincethe diameter of the probe is much smaller than its length, thetemperature is almost constant across the CNT, while varyingsignificantly along its length, as shown in Figure 2. Under these

natural assumptions, we can separately solve the 3D heatequation34 in the Si probe base and in the Au substrate,stitching these solutions with the solution for the 1D heatequation in the CNT which joins them, integrated over thecross-section:

π κ π κ∂ + − ∂ =r T x r r T x I R T x[ ( ( )) ( ) ] ( ) ( ( ))x x02

c2

02

SiO2

x

(2)

where R is the resistance per unit length. The stitchingprocedure leads to the mixed Dirichlet−von-Neumannboundary conditions imposed by the 3D solution T(r) =

T(r0)r0/|r|. From the requirement for energy conservation, wefind the boundary conditions:

π κ π κ

π κ

+ − ∂ |

= −

=r T r r T x

r T T

[ ( (0)) ( ) ] ( )

2 ( (0) )

x x02

c2

02

SiO 0

c 0 Si

x

(3)

and

π κ π κ

π κ

+ − ∂ |

= −

=r T L r r T x

r T L T

[ ( ( )) ( ) ] ( )

2 ( ( ) )

x x L02

c2

02

SiO

0 0 Au

x

(4)

where T0 is the room temperature. Solving the nonlinear first-order differential equation, at a fixed current we obtain thetemperature along the probe, and the I−V characteristics via

∫π κ κ

= +

= + − + −

V I R xR T x x

IR T T r T L T r I

( d ( ( ))d )

2 [( (0) ) ( ( ) ) ]/

c

c 0 Si c 0 Au 0(5)

shown in Figure 3, together with the differential conductance.

Our resistive heating model takes into account thetemperature dependence of both the thermal conductivityand of the electrical conduction, neglected in previousstudies36,37 and demonstrates a highly nonuniform temperatureprofile along the nanotube, with a concentration of dissipativeresistive heating in its middle and effective heat sinking at thecontacts. Along the dielectric-encapsulated CNT, the averagetemperature is lower, and the temperature profile is morehomogeneous, since the higher effective radius of the probeincreases both its contact area with the sample and heat transferalong the probe. This effect results in more linear I−Vcharacteristics, confirmed by our experimental observations, asshown in Figure 3c. We also compared the curvature observed

Figure 2. Simulations of the resistive heating of dielectric-encapsulatedMWNT probes. (a) 3D temperature distribution in the probe: thetemperature varies strongly along the CNT but remains almostconstant in the transverse direction. (b) Cross-sectional temperaturedistribution at different currents, with the formation of a distinct hot-spot in the middle of the CNT at high currents.

Figure 3. Resistive heating of dielectric-encapsulated MWNT probes.(a) Simulated dependence of the maximum temperature of the hotspot for bare (red curve) and encapsulated (blue curve) MWNTs and(b) their corresponding I−V characteristics. (c) The differentialconductance vs current for bare and encapsulated MWNTs.Compared to bare MWNTs, the average temperature of theencapsulated probes is lower at the same bias voltage, giving rise tomore linear transport characteristics, which agree better with theexperimental data.

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in the I−V curves (calculated as a second derivative of bestfitting parabolic function) for our bare (see SupportingInformation) and encapsulated probes, and reported for bareMWNTs.22,23 Only a slight nonlinearity is found for theencapsulated probes, where small curvatures of 0.001−0.3 μA/V2 can be observed in the I−V curves, whereas for bareMWNTs, this value is of the order of 20 μA/V2.To further test our hypothesis that nonlinearity can be

explained by the resistive self-heating and consequent highlynonhomogeneous temperature distribution induced by thecurrent through the nanotube, we investigated the differentialconduction variation along the length of the MWNT probe at afixed current of 40 μA. Indeed, both the experimental andtheoretical results demonstrate a significant increase of thedifferential conductance variation for higher CNT length,where temperature distribution is more inhomogeneous, asshown in Figure 4.

Finally, we note that our observations of the electricalbreakdown dynamics of two of the MWNT probes strengthenthe primary conclusions of the model regarding the form of thenonuniform temperature distribution and presence of the hotspot in the middle of the CNT. In contrast to previous studiesin ambient conditions, which reported that individual MWNTssupported by a substrate failed in a series of sharp steps,associated with destruction of individual nanotube shells in theexposed MWNT,21 we observed very rapid electrical failure ofthe probe in a single-step process (see Supporting Informa-tion), comparable to the failure of bare MWNTs invacuum.21,23 Using SEM measurements, we further confirmedthat there were no observable changes of the exposed part ofthe MWNTs at the probe apex after electrical failure, suggestingthat electrical breakdown in the nanotube is not initiated by thethermal oxidation of the outer shell of the exposed MWNT butrather results from a decomposition reaction at the hot spot atin the middle of the nanotube.21,38 Thus, dissipative self-heating, pre-existing defects, and current-induced stress in thenanotube may initiate internal failure and electrical breakdownof the probe.Both our experimental and theoretical studies indicate that

dielectric encapsulation greatly improves transport character-istics of MWNT probes (acting as a reservoir for Joule heatremoval and as a chemical barrier against thermal oxidation),allowing them to withstand much higher power densities andreach their full current-carrying capabilities. Such encapsulated

MWNT probes should have the potential for significantprogress in memory devices and nanoscale C-AFM inves-tigations of functional materials.

■ ASSOCIATED CONTENT*S Supporting InformationSample preparation method, characterization methods, andadditional transport measurements and details of the theoreticalmodel. This material is available free of charge via the Internetat http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: yuliya.lisunova@unige.ch.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors thank P. Zubko for helpful discussions on resistiveheating, Ch. Caillier and J. Teyssier for help with Ramanspectroscopy measurements, and M. Lopes and S. Muller fortechnical support. This work was funded by the Swiss NationalScience Foundation through the NCCR MaNEP and DivisionII grant 200020-138198. Y.L. acknowledges the UniGE SubsideTremplin grant.

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Figure 4. Quantitative comparison of experimental and simulationresults. Differential conductance variation Δ(dI/dV) versus A/L (crosssection/length) of dielectric coated MWNT probes, at a fixed currentof 40 μA, confirming that the resistive heating model is numericallyconsistent with the experimental observations. The theoretical curve isplotted assuming 25 kΩ contact resistance.

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