Imaging dissipation and hot spots in carbon nanotube network transistorsDavid Estrada1 and Eric Pop1,2,a�
1Department of Electrical and Computer Engineering, Micro and Nanotechnology Laboratory,University of Illinois, Urbana-Champaign, Illinois 61801, USA2Beckman Institute, University of Illinois, Urbana-Champaign, Illinois 61801, USA
�Received 8 October 2010; accepted 7 January 2011; published online 14 February 2011�
Random networks of single-walled carbon nanotubes�CNTs� are of interest for integrated circuits and displaydrivers1 on flexible or transparent substrates, particularlywhere they could exceed the performance of organic oramorphous thin-film transistors �TFTs�. Such TFTs are oftenplaced on low thermal conductivity substrates like glass orplastics, leading to self-heating effects and reducedreliability,2 topics not yet explored in carbon nanotube net-work �CNN� transistors. An additional concern with CNNs isthat performance and reliability may be limited by highelectrical3 and thermal4–7 intertube junction resistances. ForCNNs, this could result in large temperature increases �hotspots� at the CNT junctions, which greatly exceed the aver-age temperature of the device.
In this study, we use infrared �IR� thermal imaging8 andelectrical breakdown thermometry9 to investigate power dis-sipation in CNNs. We show that under voltage stress, devicesfail with a minimal rise in average temperature. Further-more, we find that power dissipation can be localized at “hotspots” in the CNN, which can be detrimental to TFT appli-cations. We also introduce a model to extract the averagethermal resistance between CNNs and the substrate �RC�, aswell as the CNT junction thermal resistance �RJ�. Our resultsindicate that the latter is the key limiting factor in CNNperformance, dissipation, and reliability.
The CNN devices in this work are networks of single-walled CNTs fabricated on SiO2�90 nm� /Si substrates, asoutlined in the supplementary information10 and shown in
Fig. 1. All IR thermometry is performed at a backgroundtemperature T0=70 °C for optimum IR microscopesensitivity.8 The highly n-doped Si acts as a back gate, set toVG�−15 V here, such that both metallic and semiconduct-ing CNTs are “on.” We acquire IR images at increasingsource-drain bias �VSD� and, surprisingly, we find that theimaged channel temperature increases very little, even nearthe device breakdown. For instance, the maximum tempera-ture rise imaged10 in the high density11 �HD� CNN shown inFig. 1 is �T�108 °C at a power P= IDVSD=25 mW. More-over, the temperature in the channel is nonuniform, with dis-tinct hot spots, which depend on the local CNN densityvariations and the CNT percolative pathways.
Lower density �LD� CNNs �Fig. 2�a�� do not provide asstrong an IR thermal signal,10 but facilitate analysis as thenumber of CNT junctions can be examined and counted byscanning electron microscopy �SEM�,11 as shown below. Themeasured power versus voltage of LD and HD CNNs up tobreakdown �BD� are shown in Fig. 2�b�. For both, we note asharp and irreversible drop, corresponding to PBD�6.7 and30 mW for the LD and HD devices, respectively. This sig-nals a catastrophic break of the CNN, also noted when theLD device cannot be recovered on a subsequent sweep�dashed line in Fig. 2�b��. In addition, the breakdown loca-tion of the film from Fig. 2�c� bears the imprint of the hotspot formation in the overlaid image of Fig. 2�d�.
We now focus on the LD device to understand how PBDcorresponds to TBD and the temperature measured by IR mi-
FIG. 1. �Color online� �a� Schematicof the CNN device and experimentalsetup. �b� SEM of high density �HD�CNN �W /L�25 /10 �m� before IRimaging and CNT breakdown. �c�Temperature of the device in �b� mea-sured at P�25 mW, in air, with T0
=70 °C �Ref. 10�. The nonuniformtemperature profile is indicative ofpercolative transport in such CNNs.
croscopy. In general, the power and temperature rise of adevice are related through its thermal resistance,12 here TBD−T0= PBDRTH at breakdown. We develop a thermal resis-tance model, as shown in Fig. 3�a�, and we assume the well-known TBD=600 °C for CNTs in air,9 recalling that T0=70 °C. To simplify the analysis, we assume uniform powerdissipation across the CNN, although this is not strictly thecase due to the percolative transport, as well as the imagedtemperature profile �Fig. 2�d��. However, as we will show,this allows us to determine a quantitative upper bound on theCNT junction resistance, RJ.
We note that power is dissipated both at the CNT junc-tions and along the length of the CNTs in contact withSiO2.13 This requires knowledge of the junction area fill fac-tor ��J� with respect to the CNN area �AC�. To determine �J,we first extract the area fill factor of the network ��C� byanalyzing SEM images. The images are imported to a matrixform in MATLAB �Ref. 14� and a threshold contrast is chosento designate areas occupied by CNTs,10 as shown in Fig.3�b�. The proportion of matrix elements with values abovethreshold is �0.72, which is a significant overestimate ofthe true areal coverage ��C� as CNT diameters appear muchlarger under SEM, 30� �d��80 nm. Choosing �d��50 nm, we estimate the total length of CNTs in the net-work, LC�7.2 mm, from �C= �d�LC /A, where the devicearea is A=WL. The actual area of the CNN is AC�dLC�14.4 �m2, with a true device area fill factor �C�0.03,where d�2 nm is the real CNT diameter averaged fromatomic force microscopy analysis. �We return to the effect ofvariability introduced by the SEM analysis below.�
We estimate the total CNT-CNT junction area asAJ tot�AJ�nJA�, where AJ is the average area of a CNT junc-tion and nJ is the junction density per device area A. We notethat the junction area depends on the angle of intersection ���of CNTs in the random network, i.e., AJ=d2 /sin���. Here, weagain use image analysis software14 to determine averagevalues for nJ, AJ, and �, as shown by histograms in Fig. 3�c�.We find AJ=4.69�0.93 nm2, �=98�28°, and nJ�26 �m−2. Thus, the density of junctions in the network�J=AJ tot /AC=0.0042, which completes the inputs needed forthe thermal model in Fig. 3�a�. We note that, in general,3 nJwill be proportional to CNN density and inversely propor-tional with CNT segment lengths13 between junctions.Therefore, when modeling other devices, it is important tocarefully estimate nJ for the particular CNN.
To find the total thermal resistance12 of the CNN,we include the Si substrate thermal resistance RSi=1 / �2Si A1/2�, the SiO2 thermal resistance Rox= tox / �oxAC�,and the CNT-SiO2 thermal boundary resistance of the net-work RC=1 / �gLC�. Here, tox=90 nm, ox�1.4 W m−1 K−1,Si�100 W m−1 K−1, and g�0.3 W K−1 m−1 for CNTswith a diameter of �2 nm near breakdown.9 This givesRSi=223.6 K W−1, Rox=4.46�103 K W−1, and RC=462.9 K W−1, respectively.
We can now calculate the temperature rise at theSiO2–Si interface, �TSi=TSi−T0= PBDRSi�1.5 K. This isa good match with the temperature measured by IR
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FIG. 2. �Color online� �a� SEM image of the LD device �W /L�50 /10 �m�. �b� Measured power vs voltage up to breakdown of the LDdevice from �a� and HD device from �c�. In both cases, large drops in powermark breaking of the CNN. The dashed line shows a second sweep of theLD device, taken after the first test was stopped at VSD=30 V break. Smallarrows indicate sweep directions. �c� SEM image of the HD device fromFig. 1�b� after breakdown. �d� Measured temperature just before breakdown,at P=25 mW from Fig. 1�c�, overlaid onto the SEM from �c�. The circledbreakdown location bears the imprint of the adjacent hot spot. Although thebreakdown occurs too fast to be imaged by the IR camera, we suspect thatthe initial CNN break occurred at the upper hot spot, leading to a reroutingof the current pathways to cause the subsequent full break.
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FIG. 3. �Color online� �a� Thermal resistance model used to evaluate CNN dissipation and estimate the temperature differences, including from CNTjunctions. �b� Processed SEM image of part of the LD device �from Fig. 2�a�� used for analysis of the total CNN length �LC�, area �AC�, and junction density�nJ�. Highlighted portions of the SEM are magnified and the number of CNT junctions �dots� is counted to obtain averages. �c� Histogram of the average CNTjunction area AJ and �inset� angle of intersection �.
073102-2 D. Estrada and E. Pop Appl. Phys. Lett. 98, 073102 �2011�
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
imaging for this device, considering that most of the IR sig-nal originates from the top of the heated Si substrate.8,10 Thetemperature drop across SiO2 is �Tox=Tox−TSi= PBDRox�29.9 K, and the temperature drop across the CNT-SiO2interface is15 �TC=TC−Tox= �1−�J /2�PBDRC� PBDRC
=3.1 K. Thus, the average temperature of theCNN without considering the effect of the junctions ismerely TC�104.5 °C, much smaller than the breakdowntemperature of CNTs in air, TBD�600 °C. This remains thecase even when variability of the CNT-SiO2 thermalcoupling9 �g� and that of the apparent diameter in SEM �d�are taken into account. In other words, considering g=0.3�0.2 W K−1 m−1 and 30� �d��80 nm in our analy-sis leads to a range TC�90–135 °C.
We suggest that the “missing” temperature difference isdue to highly localized hot spots associated with the CNTjunctions, which cannot be directly visualized by the IR ther-mometry. This is consistent with the emerging picture ofCNT junctions being points of high electrical3 and thermal4–7
resistance. Consequently, we can extract the thermal resis-tance of all CNT junctions �RJ tot� in the network acting inparallel,15
RJ tot =TBD − TC
1/2�JPBD=
TBD − �TC − �Tox − �TSi − T0
1/2�JPBD, �1�
which is bound between 2.1�107 and 5.9�107 K W−1
when allowing for uncertainty in g and �d� as above. RJ tot isseveral orders of magnitude greater than any other thermalresistance in the network and remains dominant even if theSiO2 were replaced with a substrate ten times less thermallyconducting �e.g., plastics�. If substrates with much higherthermal conductivity than SiO2 are used �e.g., sapphire�, theCNN junction thermal resistance will be even more of a lim-iting factor for dissipation and reliability.
We now estimate the thermal resistance of a single CNTjunction as RJ�RJ tot�nJA��4.4�1011 K W−1, equivalentto a thermal conductance GJ�2.27 pW K−1. We note it islikely that not all counted CNT junctions conduct currentdespite our effort to deliberately gate �turn on� the semicon-ducting CNTs. Thus, our estimate of CNT junction thermalresistance �conductance� represents an upper �lower� limit.Furthermore, accounting for the variability in CNT-SiO2coupling and �d� from SEM analysis, we can place boundson our estimate, RJ��2.7–7.6��1011 K W−1 �GJ
�1.3–3.6 pW K−1�. The RJ obtained here is in good agree-ment with experimental results for bulk single-walledCNTs,6 �3.3�1011 K W−1, and is one order of magnitudegreater than measurements of intersecting multi-walledCNTs,7 as would be expected. Our average CNT junctionthermal resistance normalized by the average contact areafrom Fig. 3�c� is rJ�2.1�10−6 m2 K W−1. This is one orderof magnitude greater than �10−7 m2 K W−1 predicted bymolecular dynamics simulations for overlapping �10,10�CNTs with 3.4 Å separation,4,6 perhaps due to idealized con-ditions in the simulation or imperfection in the experiments.
To further understand the large apparent thermal resis-tance at the CNT junctions, we note that this is not only afunction of the small overlap area AJ but also of the averageCNT separation and van der Waals interaction.4,6 In the har-monic approximation, the spring constant between pairs ofatoms is K=72 / �21/3�2� from a simplified Lennard-Jones
6-12 potential,16 where is related to the depth of the poten-tial well and � is a length parameter. Using typicalparameters,9,17 we find KC-C�KC-ox /2, i.e., the CNT-CNTthermal coupling is weaker than the CNT-SiO2 thermal cou-pling per pair of atoms. This simple analysis does not ac-count for the exact shape of the CNTs9,17 or the role of SiO2surface roughness,9 and thus further work must considerthese effects to investigate the relatively “high” experimen-tally observed thermal resistance at single-walled CNT junc-tions.
In conclusion, we directly imaged power dissipation inCNN transistors using IR microscopy. We found that localhot spots in power dissipation detected by IR correlate withthe subsequent breakdown of the network mapped by SEM.Nevertheless, these hot spots do not account for the CNNbreakdown at relatively low average temperatures,�180 °C. Instead, our analysis suggests that CNN break-down occurs at highly resistive CNT-CNT junctions, allow-ing us to extract the junction thermal resistance RJ�4.4�1011 K W−1 �conductance of 2.27 pW K−1�. These find-ings suggest that transport, dissipation, and reliability ofCNNs are limited by the CNT junctions rather than extrinsicfactors such as low substrate thermal conductivity.
We acknowledge the support from NSF Grant CAREERECCS 0954423, the NRI through the Nano-CEMMS Center,the Micron Technology Foundation, and the NDSEG Fellow-ship. We are indebted to A. Liao, J. D. Wood, and Z.-Y. Ongfor helpful discussions and technical support.
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11We label networks as HD if they are too dense to image individual CNTsby SEM. HD devices also carry much higher current density �Fig. 2�b��,here �10 times than LD devices �note the two times difference in width�.
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