Ultrahigh Currents in Dielectric-Coated Carbon Nanotube Probes

Aug 26, 2013 - DPMC-MaNEP, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland. ‡ Department of Physics, Harvard University, ...
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Ultrahigh Currents in Dielectric-Coated Carbon Nanotube Probes Yuliya 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 atomic force microscopy probes are expected to withstand extremely high currents. However, in existing prototypes, significant selfheating results in rapid degradation of the nanotube probe. Here, we investigate an alternative probe design, fabricated by dielectric encapsulation of multiwalled carbon nanotubes, which can support unexpectedly high currents with extreme stability. We show that the dielectric coating acts as a reservoir for Joule heat removal, and as a chemical barrier against thermal oxidation, greatly enhancing transport properties. In contact with Au surfaces, these probes can carry currents of 0.12 mA at a power of 1.5 mW and show no measurable change in resistance at current densities of 1012 A/m2 over a time scale of 103 s. Our observations are in good agreement with theoretical modeling and exact numerical calculations, demonstrating that the enhanced transport characteristics of such probes are governed by their more effective heat removal mechanisms. KEYWORDS: Conductive-atomic force microscopy, carbon nanotube probes, transport properties, resistive heating

C

rigidification, could provide an additional avenue for effective heat dissipation.27,28 In this Letter, we report on in-depth transport and reliability studies of such dielectric-coated MWNT probes of various lengths and diameters. We demonstrate that dielectric encapsulation significantly improves MWNT transport characteristics, providing both an efficient thermal reservoir and a protective chemical barrier preventing thermal oxidation, thus allowing extremely high current densities to pass through the probe without failure. In contact with Au surfaces, such probes can carry currents as high as 0.12 mA, at a power of 1.5 mW. Time-dependent measurements show greatly enhanced current-carrying capability, with no indication of saturation or resistance change at a current of 65 μA and a power greater than 0.5 mW for a time scale of 100 s. Moreover, in contrast to previous studies of MWNT transport, which report highly nonlinear current−voltage behavior with increasing conductance for higher currents,21−24 we observe almost linear current−voltage characteristics. To develop a clear picture of the role of dielectric coating in the high-field regime and to compare it directly with our experimental results, we simulate and numerically evaluate the temperature distribution and differential conductance of the MWNT probes, considering the temperature dependence of both their thermal and electrical conductivity. For both dielectric-encapsulated and bare MWNT probes, we find a highly nonuniform temperature distribution, with significant heat concentration in the middle of the

onductive atomic force microscopy (C-AFM) is an indispensable technique for local electrical characterization of functional materials and holds great promise for future nanotechnology applications. High spatial resolution conductive tips with improved reliability are especially important for detailed studies of advanced semiconductors,1−3 correlated oxide thin films,4−9 and energy storage devices10 of organic and biological systems6,11,12 and for potential integration into a probe-based memory technology.13,14 One extremely appealing route toward extending the physical limits of C-AFM is through the use of carbon nanotubes (CNT) as the active probe elements,10,15−19 exploiting their outstanding mechanical 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 no detectable failure in the nanotube structure for time scales of up to two weeks at 1013 A/m2, with a dissipation power higher than 100 mW (ref 25). Thus, multiwalled carbon nanotube (MWNT)-based probe tips would be expected to provide reliable high current carrying capabilities, with reasonable rigidity and metallic-like electrical conduction.17,21,25 However, studies of high-field transport of MWNTs suspended between Pt electrodes, equivalent to the geometry of a conducting probe, reveal significant current-induced Joule heating limitations.17,26 Due to the reduced dimensionality for thermal conduction and much smaller contact area with the substrate in this case, MWNT failure is already observed at current densities of 1010 A/m2, at a much lower power of 4 μW, and after merely a few seconds. In fact, the suspended CNTs are undamaged by power dissipation only in the pW range.17 Improved thermal management of such probes is therefore a key requirement, and dielectric encapsulation of the MWNTs, beyond simply © 2013 American Chemical Society

Received: July 6, 2013 Revised: August 13, 2013 Published: August 26, 2013 4527

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measurements, a fixed voltage was applied to the probes, and the 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 different MWNT probes, as shown in Figure 1b. All of the probes showed almost linear I−V characteristics and extremely high current-carrying capabilities, with currents approaching 100 μA under 10−12 V bias, giving typical resistance values in the range of 0.1−0.4 MΩ. At the highest observed current of 120 μA, an order of magnitude higher than the maximum currents of 10−12 μA reported for suspended single walled carbon nanotubes32,33 or for bare MWNT probes,17 our encapsulated MWNTs showed no sign of I−V saturation or physical deterioration. In addition, during static measurements no degradation of probe conductance was observed at current densities of 1012 A/m2 for a time scale of 100 s. In fact, the 100 s stability tests showed rather a very slight increase in the conductance at increased bias voltage, which we attribute to improvement of the thermal contact during measurement. We note further that, although small conductance fluctuations can be seen in the higher-bias measurements of the specific probe shown in Figure 1c, these follow no particular trend and were not observed in tests of other probes, even for extended measurements of repeated 100 s voltage pulses for 103 s (see Supporting Information). We note that dielectric encapsulation allows MWNTs to withstand these high power densities of 0.45−1.5 mW at ambient conditions, without special procedures to minimize thermal oxidation by vacuum23,24 or by heat removal directly into the substrate beneath the nanotube.21,25 To further characterize the transport properties of the encapsulated MWNT probes, we also numerically evaluated the I−V derivatives, which show varying sign of the conductance slope from one probe to another. For most probes, the minimum conductance of approximately 5 μS extrapolated to zero current (zero bias voltage) increases steeply with increasing current, as shown by the green line in Figure 1d. Such behavior is commonly observed in individual MWNTs and can be associated with thermally activated tunnelling of electrons between MWNT shells.21−23 However, we also observed deviation from this typical behavior in two of the eight probes, which showed instead a negative conductance slope (red lines in Figure 1b,d), although with no additional difference in either size or contact resistance. We therefore attribute these discrepancies to structural differences between the MWNTs in the different probes, grown here by chemical vapor deposition (see Supporting Information). Specifically, it is difficult to control growth at single nanotube level, which may result in a bundle MWNT probe,15,20 the presence of single-walled nanotubes (SWNT), and high defect densities compared to arc-discharge-produced MWNTs.20,28 The presence of SWNTs and defects would likewise influence the transport properties of the probes24 and may play a determining role in their failure.21 In this study, the majority of the probes investigated showed robust transport properties even at the maximum voltage of 12 V attainable with our setup. However, two failed very abruptly in a single step at 60−70 μA and 9 V (see Supporting Information for more details), an effect we attribute to internal failure initiated at defect sites within the MWNT. In addition, our data shows no electrical conductance quantisation, and no systematic dependence on probe diameter or length in the measurement range, beyond a linear increase with A/L, where A is the cross section and L the

nanotube, leading to increased variation of the differential conductance with increasing nanotube length. However, for the encapsulated probes the average temperature is lower, and the temperature profile along the nanotube is more homogeneous at the same bias voltage, giving rise to quasi-linear transport characteristics. 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 thin bundles or individual MWNTs at the tip apex, 10−20 nm in diameter, 1−10 μm long (see Supporting Information for more details). These as-grown MWNT tips were shortened to typical lengths of 300−800 nm by electrical etching at 15−20 V on a sputtered Nb surface,29,30 improving their stiffness. The resulting shortened tips were resistant enough to withstand the mechanical and thermal stresses during subsequent electron beam evaporation deposition of a thin insulating SiOx coating, at room temperature, at a rate of 0.01 nm/s. This very low growth rate resulted in a uniform and homogeneous formation of a well-adhered SiOx layer on the MWNT tips. Finally, focused ion beam etching was used to expose the conductive core of the MWNT/SiOx composite structure, as shown in Figure 1a, following ref 31. In total, electrical transport

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

properties of eight such tips were studied in contact with an Au-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) in standard contact mode (150 nN). During dynamic measurements, the current was acquired while sweeping the voltage with 2−20 mV steps at 500 steps per second, while for static 4528

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

length of the MWNT probe, indicating that the transport through the MWNTs is diffusive. Interestingly, we also found that the electrical conductance increase for higher currents is much more pronounced for longer MWNT probes, which we explain below. To interpret our experimental observations, and to understand the underlying mechanisms leading to the superior current-carrying capabilites of the dielectric-encapsulated MWNT probes, we considered a theoretical model of resistive heating in a CNT probe geometry and numerically evaluated the electrical conductance in the high-field regime, using a quasi-1D approximation for the temperature and conductance distribution in the stationary state (see Supporting Information for more details). The temperature distribution is a solution of the heat equation34 ∇⃗κ(r, T (r))∇⃗T (r) = ρ(T (r))j 2 Θ(r)

[πr02κ(T (0)) + π (rc2 − r02)κSiOx]∂xT (x)|x = 0 = 2πrc(T (0) − T0)κSi

(3)

and [πr02κ(T (L)) + π (rc2 − r02)κSiOx]∂xT (x)|x = L = 2πr0(T (L) − T0)κAu

(4)

where T0 is the room temperature. Solving the nonlinear firstorder differential equation, at a fixed current we obtain the temperature along the probe, and the I−V characteristics via V = I (R c +

(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−V measurements), and Θ(r) = 1 inside the CNT, where Joule heat is generated, and 0 elsewhere. We assume a diffusive transport regime, with the electron scattering length much smaller than the nanotube length. Since little is known about the temperature dependence of MWNT conductivity, we assume a linear behavior and determine the slope by fitting the experimental data. The time τs at which the stationary distribution is achieved can be estimated as the Joule heat divided by the thermal capacitance of the probe, giving τs < 1 μs for typical voltages used in our experiments. Thus, we neglect time-dependent effects and focus on the stationary state. Since the diameter of the probe is much smaller than its length, the temperature is almost constant across the CNT, while varying significantly along its length, as shown in Figure 2. Under these

∫ dxR(T(x))dx)

= IR c + 2π[(T (0) − T0)κSirc + (T (L) − T0)κAur0]/I (5)

shown in Figure 3, together with the differential conductance.

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

Figure 2. Simulations of the resistive heating of dielectric-encapsulated MWNT probes. (a) 3D temperature distribution in the probe: the temperature varies strongly along the CNT but remains almost constant in the transverse direction. (b) Cross-sectional temperature distribution at different currents, with the formation of a distinct hotspot in the middle of the CNT at high currents.

Our resistive heating model takes into account the temperature dependence of both the thermal conductivity and of the electrical conduction, neglected in previous studies36,37 and demonstrates a highly nonuniform temperature profile along the nanotube, with a concentration of dissipative resistive heating in its middle and effective heat sinking at the contacts. Along the dielectric-encapsulated CNT, the average temperature is lower, and the temperature profile is more homogeneous, since the higher effective radius of the probe increases both its contact area with the sample and heat transfer along the probe. This effect results in more linear I−V characteristics, confirmed by our experimental observations, as shown in Figure 3c. We also compared the curvature observed

natural assumptions, we can separately solve the 3D heat equation34 in the Si probe base and in the Au substrate, stitching these solutions with the solution for the 1D heat equation in the CNT which joins them, integrated over the cross-section: ∂x[πr02κ(T (x)) + π (rc2 − r02)κSiOx]∂xT (x) = I 2R(T (x)) (2)

where R is the resistance per unit length. The stitching procedure leads to the mixed Dirichlet−von-Neumann boundary conditions imposed by the 3D solution T(r) = 4529

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in the I−V curves (calculated as a second derivative of best fitting parabolic function) for our bare (see Supporting Information) and encapsulated probes, and reported for bare MWNTs.22,23 Only a slight nonlinearity is found for the encapsulated probes, where small curvatures of 0.001−0.3 μA/ V2 can be observed in the I−V curves, whereas for bare MWNTs, 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 highly nonhomogeneous temperature distribution induced by the current through the nanotube, we investigated the differential conduction variation along the length of the MWNT probe at a fixed current of 40 μA. Indeed, both the experimental and theoretical results demonstrate a significant increase of the differential conductance variation for higher CNT length, where temperature distribution is more inhomogeneous, as shown in Figure 4.

MWNT probes should have the potential for significant progress in memory devices and nanoscale C-AFM investigations of functional materials.

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ASSOCIATED CONTENT

S Supporting Information *

Sample preparation method, characterization methods, and additional transport measurements and details of the theoretical model. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank P. Zubko for helpful discussions on resistive heating, Ch. Caillier and J. Teyssier for help with Raman spectroscopy measurements, and M. Lopes and S. Muller for technical support. This work was funded by the Swiss National Science Foundation through the NCCR MaNEP and Division II grant 200020-138198. Y.L. acknowledges the UniGE Subside Tremplin grant.

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REFERENCES

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Figure 4. Quantitative comparison of experimental and simulation results. Differential conductance variation Δ(dI/dV) versus A/L (cross section/length) of dielectric coated MWNT probes, at a fixed current of 40 μA, confirming that the resistive heating model is numerically consistent with the experimental observations. The theoretical curve is plotted assuming 25 kΩ contact resistance.

Finally, we note that our observations of the electrical breakdown dynamics of two of the MWNT probes strengthen the primary conclusions of the model regarding the form of the nonuniform temperature distribution and presence of the hot spot in the middle of the CNT. In contrast to previous studies in ambient conditions, which reported that individual MWNTs supported by a substrate failed in a series of sharp steps, associated with destruction of individual nanotube shells in the exposed MWNT,21 we observed very rapid electrical failure of the probe in a single-step process (see Supporting Information), comparable to the failure of bare MWNTs in vacuum.21,23 Using SEM measurements, we further confirmed that there were no observable changes of the exposed part of the MWNTs at the probe apex after electrical failure, suggesting that electrical breakdown in the nanotube is not initiated by the thermal oxidation of the outer shell of the exposed MWNT but rather results from a decomposition reaction at the hot spot at in the middle of the nanotube.21,38 Thus, dissipative selfheating, pre-existing defects, and current-induced stress in the nanotube may initiate internal failure and electrical breakdown of the probe. Both our experimental and theoretical studies indicate that dielectric encapsulation greatly improves transport characteristics of MWNT probes (acting as a reservoir for Joule heat removal and as a chemical barrier against thermal oxidation), allowing them to withstand much higher power densities and reach their full current-carrying capabilities. Such encapsulated 4530

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