Letter pubs.acs.org/NanoLett
Hot Spot Dynamics in Carbon Nanotube Array Devices Michael Engel,† Mathias Steiner,*,†,‡ Jung-Woo T. Seo,§,∥ Mark C. Hersam,§,∥ and Phaedon Avouris† †
IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, United States IBM Research-Brazil, Rio de Janeiro, RJ 22290-240, Brazil § Department of Materials Science and Engineering and ∥Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States ‡
S Supporting Information *
ABSTRACT: We report on the dynamics of spatial temperature distributions in aligned semiconducting carbon nanotube array devices with submicrometer channel lengths. By using highresolution optical microscopy in combination with electrical transport measurements, we observe under steady state bias conditions the emergence of time-variable, local temperature maxima with dimensions below 300 nm, and temperatures above 400 K. On the basis of time domain cross-correlation analysis, we investigate how the intensity fluctuations of the thermal radiation patterns are correlated with the overall device current. The analysis reveals the interdependence of electrical current fluctuations and time-variable hot spot formation that limits the overall device performance and, ultimately, may cause device degradation. The findings have implications for the future development of carbon nanotube-based technologies. KEYWORDS: Carbon nanotubes, power dissipation, thermal imaging, nanoelectronics, nanooptics
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A schematic of the carbon nanotube array device and scanning electron microscope images of the device are shown in Figure 1a,b. The carbon nanotubes were separated by means of density gradient ultracentrifugation20,21 and have a semiconducting purity of ∼99% with a refined average diameter of 1.6 nm.22 Sandwiched between Al2O3 thin films, the carbon nanotubes have an average spacing of 20 nm and are aligned perpendicular to the metallic contacts made of Pd and Al, respectively. The devices function as pn-diodes with an internal electrostatic potential drop that results from the work function difference of the contact metals.13 Details regarding the device design and manufacturing are discussed in the Supporting Information. For optical measurements through the transparent device stack, we used an inverted optical microscope with an immersion objective (NA = 1.25) and a scanning stage that is equipped with electric probe needles for connecting the device with the external electronic measurement system. This way, the device can be raster-scanned with respect to the microscope objective for image formation. As indicated in Figure 1c, the optical setup is equipped with an avalanche photo diode (APD). The APD, which is synchronized with the scanning system, enables the detection of the integrated thermal radiation in the spectral range between about 500 and 1000 nm. Indeed, a series of thermal radiation spectra shown in Figure 1d reveals that the tail of the thermal radiation distribution emitted by the carbon nanotube array device
ecause of the combination of high current densities, switching speeds, and on−off current ratios, carbon nanotube film and array transistors are promising candidates for nanoelectronic technologies.1 Electrical power dissipation in carbon nanotube devices2 is, however, different from bulk semiconductors because of nonequilibrium phonon distributions3−5 and spatially nonuniform heat distributions.6−10 In nanotube devices at high bias, phonon scattering11 limits electrical transport, an effect that is expected to cause hot spot formation in nanotube array devices even when percolationtype transport becomes neglible. However, experimental demonstration of temperature distribution mapping in functioning carbon nanotube array devices with channel lengths equal to or smaller than the average nanotube length are not available yet. Herein, we measure and analyze temperature distributions in semiconducting carbon nanotube array devices with channel lengths ranging from 3 to 0.9 μm, which is of the order of the average nanotube length used to assemble the arrays by means of a solution-based process.12 Surprisingly, even for seemingly uniform array devices under steady state bias conditions, we observe that the temperature distributions of carbon nanotube array device are spatially nonuniform and exhibit strong fluctuations in time. We correlate the emitted thermal radiation intensity of various regions of interest across the entire device with the electrical device current as a function of time. On the basis of the specifics of the hot spots observed, we discuss the carrier scattering mechanisms that could have led to their formation. In view of previous studies on percolation-type devices,8,10 we find that electrical power dissipation in short-channel carbon nanotube array devices is a site-specific, dynamic process. © 2015 American Chemical Society
Received: January 6, 2015 Revised: February 6, 2015 Published: February 25, 2015 2127
DOI: 10.1021/acs.nanolett.5b00048 Nano Lett. 2015, 15, 2127−2131
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Nano Letters
conditions, we raster-scanned the carbon nanotube array device point-by-point from the underside and recorded the twodimensional distribution of the integrated thermal radiation intensity. The integrated thermal radiation intensity was then converted into temperature (for details, see Supporting Information), resulting in a two-dimensional temperature map of the functioning carbon nanotube array device. In Figure 2a, we plot two-dimensional temperature distributions of a carbon nanotube array device with a channel length of 3 μm, which is operated under steady-state bias conditions at four representative electrical power levels Pel = Vds·Ids. The gate electrode (ITO layer) is kept grounded to provide a constant gate potential. The corresponding cross sections through the T-distributions (along the white dashed lines in Figure 2a) are plotted in Figure 2b. The measurement at Pel = 0 μW serves as a reference, providing a baseline with an ambient temperature of T0 = 300 K. As Pel increases, we observed the formation of two main temperature maxima in the device channel that extend beyond the contacts. The maximum temperatures of the two spatially isolated radiation patterns (indicated by circles in Figure 2b) are plotted as a function of Pel in Figure 2c. The data is in agreement with a linear fit, as expected for Joule heating. Notably, while the spatial distribution of carbon nanotubes captured by electron microscopy in the device is seemingly homogeneous (see Figure 1b), the temperature distribution in the device is clearly not. This finding is supported by photocurrent microscopy studies probing local deformation of the electronic potentials revealing local heterogeneities related to variations in nanotube diameters, nanotube-metal contacts, and defects.13,14 We note that this information cannot be obtained by electron microscopy. If an electrical bias is applied, such heterogeneities can act as localized heat sources that introduce temperature gradients at various locations of the device. By increasing the bias voltage, we observed that the measured temperature distributions in the device exhibit
Figure 1. Carbon nanotube array device and measurement setup. (a) Schematic view of the carbon nanotube array device. (b) False color scanning electron microscope image of the carbon nanotube array device coated with an Al2O3 thin film. Scale bar, 200 nm. Inset: carbon nanotube array after evaporation-driven deposition on Al2O3. Scale bar, 400 nm. (c) Experimental setup consisting of an inverted optical microscope and a sample scanning stage that provides electrical interconnects to the device (not shown). During device operation, thermal radiation is recorded by means of an APD or a CCD. (d) Thermal emission spectra (symbols) measured from the device shown in panels a and b for various bias voltages. The solid lines represent fits to the experimental data based on Planck’s distribution, see Supporting Information.
overlaps with the spectral detection window of the APD. For a given bias voltage and by maintaining steady measurement
Figure 2. Temperature distributions in carbon nanotube array transistors. (a) Microscopic temperature maps for various electrical power levels of a device having a channel length of 3 μm. The positions of the metal contacts are indicated by blue dashed lines. Scale bar, 2 μm. (b) Cross sections through the temperature maps taken along the white dashed lines shown in (a). (c) Temperature dependence on injected electrical power taken at the local maxima positions as indicated in (b). Linear fits (lines) are in agreement with the experimental data (circles). (d) Microscopic temperature map of a device having a channel length of 1 μm at an electrical power level of 392 μW. The positions of the metal contacts are indicated by blue dashed lines. Scale bar, 2 μm. 2128
DOI: 10.1021/acs.nanolett.5b00048 Nano Lett. 2015, 15, 2127−2131
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Nano Letters
Figure 3. Dynamics of nanoscale hot spots in operating carbon nanotube array devices. (a) Microscope images exhibit thermal hot spots in the array at distinct locations labeled A−D at different times t = 0, 4, and 40 s during device operation under constant voltage bias, Vds = 10 V. For data analysis, various ROI (indicated by colored frames) representing an area of 0.625 × 1.25 micron2 are defined at sites A−D. Scale bar for all frames, 1 μm. (b) Time dependence of the thermal radiation intensity, which is plotted for the entire device (lower panel) as well as for the isolated regions of interest A−D as indicated in (a) (upper panel). (c) Cross-correlation coefficients obtained by correlating the measured thermal light intensity with the measured device current as a function of time for the entire device and for the respective ROIs defined as shown in a. The confidence level of 0.28 is indicated by a gray band.
temporal fluctuations. Fluctuations of the local temperature in the device that occur on the time scale of the raster scanning motion, that is 30 ms per pixel, reveal themselves by line formation along the scanning direction (up−down in Figure 2a,d) during image acquisition. The formation of local temperature maxima, as well as their their dynamical behavior, is more pronounced for devices with shorter channels. The transition from the percolation transport regime to the domain of direct transport occurs at a channel length of about 1 μm (see Figure 2d), which is the average length of carbon nanotubes in the sample solution. In Figure 2d, a carbon nanotube array device with a channel length of 1 μm exhibits a higher peak temperature of about 440 K along with much stronger thermal fluctuations. Data acquisition times for the thermal images shown in Figure 2 are of the order of minutes, thus precluding the extraction of information regarding the thermal distribution dynamics on a shorter time scale. In order to capture the time-variable hot spot formation as evidenced by the blinking signatures in Figure 2, we used a wide-field imaging method based on a Peltier-cooled chargecoupled device (CCD)-array (see schematic in Figure 1c). This approach enables monitoring of the spatial distribution of thermal radiation for the entire device with a time resolution that is limited by the frame rate of the camera (∼0.25 Hz in the present case). In Figure 3a, we plot images of a carbon nanotube array device with a channel length of 1 μm (position of metal contacts are indicated by white dashed lines) taken at various times t while the device is under high constant voltage bias, Vds = 10 V. We observed the signature of thermal hot spots through the detection of emitted thermal radiation at various locations of the device (see Figure 3a). While we were able to capture time-variable hot spots in our measurement, the background heat distribution was flat, which is due to the lower sensitivity of the CCD as compared to the APD measurements shown in Figure 2. For the purpose of data analysis, four
regions of interest (ROI) are defined across the device (labeled A−D in Figure 3a). The thermal radiation is integrated independently for the four ROIs and plotted as a function of time in the upper panel of Figure 3b. The thermal hot spot emission within the boundaries of the four ROIs varies strongly as a function of time while hot spots appear and disappear in the four ROIs at different t. The key question in view of electrical device performance is how the hot spot formation in the carbon nanotube array is related to the electrical drive current. On the basis of the previous discussion, we would expect a high degree of correlation between the device current and the thermal radiation intensity emitted by the device. For comparison, the electrical drive current of the device is plotted as a function of time in the lower panel of Figure 3b, together with the total integrated intensity emitted by the device. Indeed, on the same time scale the electrical current shows strong fluctuations on the order of σ(Ids)/⟨Ids⟩ ≈ 0.24, where σ(Ids) and ⟨Ids⟩ denote the standard deviation and mean of the electrical current, respectively. We attribute the general decrease in device current in Figure 3b to degradation and to a lesser extent to charge injection into the underlying oxide layer giving rise to an effective gate field. On the basis of device layout and CNT density, we estimate an average current of 2.5 μA per nanotube, which is well below what the current level single nanotube has shown to fail. Hence, device degradation or failure most likely originates from an uneven current distribution within the CNT array. In order to investigate the degree of correlation between electrical and optical signal in detail, we performed a crosscorrelation analysis in the time domain (for details, see Supporting Information). In Figure 3c, we plot the coefficients that quantify the degree of cross-correlation between the electrical drive current and the thermal radiation emitted by the hot spots. The analysis is performed for the entire carbon 2129
DOI: 10.1021/acs.nanolett.5b00048 Nano Lett. 2015, 15, 2127−2131
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Nano Letters nanotube array device as well as individually for each ROI. As a result, we found that the cross-correlation between optical and electrical signals is significant for time lags τ up to 50 s for the entire device and the ROI labeled D, decaying at about τ1/e ≈ 20 s (the 1/e-value is estimated with respect to the baseline defined by the confidence level at 0.28). In contrast, thermal radiation captured by the ROIs labeled A, B, and C exhibit a smaller degree of cross-correlation significant only for τ →0 s. This finding has important implications for the relation between global device current and local heat dissipation in the carbon nanotube array. As expected, the thermal radiation integrated over the entire device area is significantly correlated with the overall device current (see vertical lines in Figure 3c). However, the degree of cross-correlation for the individual hot spots (as represented by the different ROIs) varies largely. In other words, some of the hot spot emissions are strongly crosscorrelated with the overall device current while others are not. For example, the integrated intensities measured in ROIs A and D are very similar (∼15k (arb. units) in Figure 3b), while the associated cross-correlation coefficients differ by nearly a factor of 2 (see Figure 3c). The results of the cross-correlation analysis indicate that the electrical current densities vary strongly from tube to tube within the device. The specifics of charge carrier scattering leading to hot spot formation depends on the tube location within the array, as well as local contact conditions. In a microscopic conception, excess heat is produced by the different carrier scattering mechanisms operating simultaneously in current-carrying nanotubes. Among the physical processes, the ones that are mainly responsible for local heat generation in the array devices include carrier resistance at nanotube-metal contacts, carrier resistance at nanotube− nanotube contacts, carrier scattering with nanotube phonons, and defect-induced carrier scattering (see refs 15 and 16 and references therein). By inferring the dominant heat-generating scattering mechanism from the cross-correlation analysis and taking into consideration the different hot spot locations observed in the measurement, we argue that the hot spot in D could be caused mainly by intratube electron−phonon scattering or a nearby current carrying CNT (hot spot extends deep into the channel, away from contact with high correlation with device current) while for A and B the hot spots are likely from carrier scattering at the metal-nanotube contact (hot spots located directly at metal contact with low correlation with device current). Finally, the hot spot in C could result from defects or from a nanotube−nanotube contact within the device channel (hot spot located away from the metal contacts with low correlation with device current). Such assignments could be experimentally verified on the level of individual hot spots by applying near-field optical measurements techniques as shown in previous work14,17 or by improving the time resolution of the thermal emission measurements.18 In Figure 4a, we plot the spatial distribution of the crosscorrelation coefficient obtained for the emitted thermal radiation and the overall device current. The map is overlaid onto an optical microscopy image of the device that indicates the position of the contact leads. This demonstration enables us to quantitatively visualize the main results of the study, that is, the spatial extension of hot spots as well as the degree of correlation with the overall device current. In Figure 4b, we compare a cross section taken along the direction of the blue arrow indicated in the cross-correlation map and compare it with the cross section taken from the thermal image of the hot
Figure 4. Two-dimensional cross-correlation map of a carbon nanotube array device. (a) White-light transmission microscopy image of the carbon nanotube array device showing the position of the metal contacts (bright areas) overlaid with a two-dimensional map that is obtained by cross-correlating the measured thermal radiation distribution and the electrical drive current in the operating device. Scale bar, 2 μm. (b) Cross section (blue line) through the crosscorrelation map along the direction of the blue arrow depicted in (a). Also shown is a cross section through the thermal radiation distribution measured at the same device position (circles) together with a fit to a Gaussian model function (black line), revealing a hot spot diameter of 260 nm (full width at half-maximum).
spot. As a result, the spatial resolution in the cross-correlation image is on the order of the diameter of individual hot spots (260 nm), which is close to the optical resolution limit of the thermal imaging configuration used in this study. We estimate that the number of carbon nanotubes covering that area is about 15, which can be considered as the upper limit of the number of nanotubes required for the formation of the hot spots imaged in Figure 3. It should be noted, however, that the actual extension of a hot spot can be as small as the cross section of an individual carbon nanotube, which has a length scale 2 orders of magnitude smaller than the optical resolution. Because current-carrying carbon nanotubes can feature temperatures of several hundred degrees,5 the materials surrounding the nanotube (metals, dieelectrics) at a hot spot location are at risk of irreversible degradation. Eventually, the electrical power dissipation in a nanotube will lead to larger-scale damage and could eventually result in the breakdown of larger device areas.19 Indeed, this is confirmed by scanning electron microscope images that reveal current-induced modifications of the nanotubes, metals, and dielectrics in the device due to the hot spot formation, see Supporting Information Figure S1. While a microscopic model of electrical current fluctuations and dynamic temperature distributions in carbon nanotube array devices is beyond the scope of this paper, the experimental results suggest that inclusion of nanotube-metal contact resistance variations, hot phonon effects, and temperature-dependent nanotube-dielectric interfacial effects are needed to quantify the dynamics of heat dissipation in scaled carbon nanotube array devices. From an experimental perspective, both a higher temporal resolution and a higher 2130
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(9) Xie, X.; et al. Quantitative Thermal Imaging of Single-Walled Carbon Nanotube Devices by Scanning Joule Expansion Microscopy. ACS Nano 2012, 6 (11), 10267. (10) Behnam, A.; et al. High-Field Transport and Thermal Reliability of Sorted Carbon Nanotube Network Devices. ACS Nano 2013, 7 (1), 482. (11) Yao, Z.; Kane, C. L.; Dekker, C. High-Field Electrical Transport in Single-Wall Carbon Nanotubes. Phys. Rev. Lett. 2000, 84 (13), 2941. (12) Engel, M.; et al. Thin Film Nanotube Transistors Based on SelfAssembled, Aligned, Semiconducting Carbon Nanotube Arrays. ACS Nano 2008, 2 (12), 2445. (13) Engel, M.; Small, J. P.; Steiner, M.; Freitag, M.; Green, A. A.; Hersam, M. C.; Avouris, P. Spatially Resolved Electrostatic Potential and Photocurrent Generation in Carbon Nanotube Array Devices. ACS Nano 2012, 6 (8), 7303. (14) Rauhut, N.; Engel, M.; Steiner, M.; Krupke, R.; Avouris, P.; Hartschuh, A. Antenna-Enhanced Photocurrent Microscopy on SingleWalled Carbon Nanotubes at 30 nm Resolution. ACS Nano 2012, 6 (7), 6416. (15) Charlier, J.-C.; Blase, X.; Roche, S. Electronic and transport properties of nanotubes. Rev. Mod. Phys. 2007, 79 (2), 677. (16) Biercuk, M. J.; Ilani, S.; Marcus, C. M.; McEuen, P. L. In Carbon Nanotubes; Jorio, A, Dresselhaus, G., Dresselhaus, M. S., Eds.; Springer: Berlin, Heidelberg, 2008; Vol. 111, p 455. (17) Mauser, N.; Hartmann, N.; Hofamnn, M. S.; Janik, J.; Högele, A.; Hartschuh, A. Antenna-Enhanced Optoelectronic Probing of Carbon Nanotubes. Nano Lett. 2014, 14 (7), 3773. (18) Mori, T.; Yamauchi, Y.; Honda, S.; Maki, H. An Electrically Driven, Ultrahigh-Speed, on-Chip Light Emitter Based on Carbon Nanotubes. Nano Lett. 2014, 14 (6), 3277. (19) Shekhar, S.; Erementchouk, M.; Leuenberger, M. N.; Khondaker, S. I. Correlated electrical breakdown in arrays of high density aligned carbon nanotubes. Appl. Phys. Lett. 2011, 98 (24), 243121. (20) Arnold, M. S.; Green, A. A.; Hulvat, J. F.; Stupp, S. I.; Hersam, M. C. Sorting carbon nanotubes by electronic structure using density differentiation. Nat. Nanotechnol 2006, 1 (1), 60. (21) Hersam, M. C. Progress towards monodisperse single-walled carbon nanotubes. Nat. Nanotechnol. 2008, 3 (7), 387. (22) Seo, J.-W. T.; Yoder, N. L.; Shastry, T. A.; Humes, J. J.; Johns, J. E.; Green, A. A.; Hersam, M. C. Diameter Refinement of Semiconducting Arc Discharge Single-Walled Carbon Nanotubes via Density Gradient Ultracentrifugation. J. Phys. Chem. Lett. 2013, 4 (17), 2805.
spatial resolution would be highly desirable for detailed study of the physics of power dissipation and hot spot formation in carbon nanotube array devices. In summary, we have investigated hot spot formation in semiconducting carbon nanotube array devices. Local heterogeneities in the nanotube array cause spatially nonuniform heat distributions that exhibit dynamical behavior on the time scale of the resolution of our measurement system (milliseconds and seconds). The thermal radiation emitted by local hot spots is significantly correlated with the overall device current while the degree of correlation depends on the specific hot spot location. The local hot spot formation limits the overall device performance and can lead to irreversible device degradation. Research aimed at reducing device heterogeneities through advancements in nanotube separation, placement, and contacting will need to be complemented by a deeper physical understanding of electrical power dissipation in one-dimensional systems at the nanometer scale.
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ASSOCIATED CONTENT
S Supporting Information *
Additional information and figures. 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 We acknowledge the provision of high-quality dielectric layers by Damon Farmer and expert technical assistance by Bruce Ek (both IBM). Furthermore, we acknowledge discussion with V. Perebeinos (Skoltech), Ralph Krupke (KIT), and support by Claudius Feger and Shu-Jen Han (IBM). M.C.H. and J.T.S. acknowledge the National Science Foundation (DMR-1006391 and DMR-1121262).
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REFERENCES
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