Electrothermal Transport in Carbon NanostructuresQuoc Ngo1, Toshishige Yamada1'2, Kris Gleason1, Makoto Suzuki1, Hirohiko Kitsuki1, Alan M. Cassell2,
and Cary Y. Yang"Center for Nanostructures, Santa Clara University, 500 El Camino Real, Santa Clara, California 950502Center for Advanced Aerospace Materials and Devices, NASA Ames Research Center, M/S 229-1
Moffett Field, California 94035*Phone: (408) 554-6814 Email: cyanggscu.edu
1. Introduction and Motivation density of 5.7 x 105 A/cm2, and the second at 2.0 x 106A/cm2. Both annealing steps are performed for one minute
Heat generation in carbon nanofibers (CNF) has raised under vacuum. The annealing is shown to reduce the overallconcerns regarding reliability in these structures under high- low-bias resistance. A typical I-V set of annealingcurrent conditions. This work addresses the interplay experiments is shown in Figure 2. For this CNF, the initialbetween electron transport and resulting Joule heating in resistance is 46 kQ, then reduced to 32 kQ after one anneal,CNFs. The model relates current to power dissipation and finally reduced to 11 kQ after the second annealing step.leading to temperature rise in the structure, thus elucidating A third anneal is performed to ensure that the lowestthe relationship between thermal and electrical properties in resistance has been achieved in the structure, and confirmscarbon nanostructures. the final resistance of 11 kQ. The reduction in resistance
Thermal properties of one-dimensional structures such as can be attributed to local heating due to higher electroncarbon nanotubes and carbon nanofibers (CNF) have temperature, resulting in re-arrangement of atoms at thegenerated concerns regarding reliability of these structures contact-metal interface. This structural change at theunder high-current conditions [1]. This work aims to model interface causes a reduction in the tunneling barrier, hence athe effect of heat generation on the I-V characteristics of lower resistance junction approaching ohmic behavior isCNFs. Our tunneling contact model accurately describes observed.electrical characteristics and helps elucidate Joule heating atthe contacts in a metal-CNF-metal system shown in Figure 1I(a). Experimental studies of carbon nanostructures to datehave primarily focused on electrical properties. For on-chip Ainterconnect applications in integrated circuits, bothelectrical and thermal properties must be considered whenevaluating the reliability of carbon-based devices underhigh-current stress. While modeling studies of thermaleffects on electrical characteristics have been reported [2],correlation between these two properties has not beeninvestigated in detail. Annealing effects due to Joule heatingare observed at the contact interface in our study, resulting in (b)a significant contact resistance reduction. In this work, +electrothermal modeling of carbon nanofiber-metal contactsystems is presented, with specific focus on heat generationat the CNF-metal interface. F 4
_p 1
2. Experimental Results + VL +VR
Vertically aligned carbon nanofibers are deposited on a Sisubstrate using existing plasma-enhanced chemical vapordeposition methods [3]. Following fabrication of the free-standing structures, the CNFs are suspended in an isopropyl Figure 1 (a) Experimental configuration for current-alcohol solution, and drop-cast onto the substrate, which is iu Joule hea tin.b Two-diode model of Au-CNF-an oxidized silicon wafer with pre-patterned gold electrodes. Au system as tunnel junctions at the contacts.Through the optimization of the drop-casting method,multiple sets of electrode pairs are bridged by a single CNF,as seen in Figure 1. I-V characteristics at low bias (-1 to 1V) are initially measured followed by current-inducedannealing. Low bias is used to ensure that no annealing istaking place during the initial voltage sweep. A two-stepanneal process is performed, one by applying a current
<5050 | Anneal #2 The data from Figure 2 allow us to test the model against0 . ! t ^+ totOpoooOOO .............$.-----ourexperimentalsystem. The only parameter varied
A- O9O,1 -0.5 0 0.5 between the three test cases is d, the width of the barrier.C: Ca) ....P.. rr t After each successive anneal, the barrier width should
decrease, resulting in an increase in current for the same0) °50 voltage. Using this model and the barrier width as an
adjustable parameter, we obtain a comparison between-100 measurement and model, as given in Figure 3. We deduce
that the barrier width does indeed decrease with successive-150 anneals, from 5.5 A for pre-anneal to 4.1 A for anneal #2,
-1oa0.50 0.5 1 most likely due to a physical change at the CNF-metalVoltage [V] interface. The model (solid lines in Figure 3) fits very well
with the measured data under all three conditions simply byFigure 2. Experimental current-voltage characteristics varying the barrier width parameter. What this data alsobefore and after current-induced annealing in the Au- reveals is that the heat generated at the contacts is decreasingCNF-Au system. Inset: Corresponding differential as we anneal out the contact defects. In addition, since noconductance plots. Scale for conductance and voltage other parameters are being varied during this experiment,plots are mS and V, respectively, and the sample is kept under vacuum during the entire
annealing and measurement process, we can conclude that3. Model details the change in electrical characteristics can be attributed to
The transport mechanism across a side-contacted metal- Joule heating at the contact and the resultant reduction in thecarbon junction is explained in Reference [4] as tunneling vacuum barrier width.across an energy barrier created by the finite separation The observed structural change can be modeled based on
between the gold electrode and carbon nanostructure. Such the above tunneling model for single-junction CNT-metala separation is considered due to the atomic scale surface systems [9,10]. Our structure is metal-CNF-metal, thusroughness of the gold electrodes [5] and is estimated to be a forming a double junction or a two-diode circuit as depictedfew Angstroms through the analysis of carbon nanotube in Fig. 1 (b). By knowing the single diode characteristics,Schottky barrier modulation [6] in conjunction with we can deduce the left and right voltages, VL and VR,experiments in the presence of oxygen [7]. Understanding respectively, for a given current. Comparison withthe tunnel-junction nature of the contact, we can initially measured data reveals the I-V characteristics of a singlevisualize the CNF-metal interface as two metals separated diode, and its effect upon annealing. We assume that theby a thin barrier brought about by a Van der Waals annealing changes only the barrier width at the metal contactinteraction between the two dissimilar materials. The junctions, which is consistent with experimental data.closed-form expression used to describe this junction was Figure 3 compares the model with the measured data forderived from the tunneling current density equation three different annealing stages. The increased current drivepresented in [8], originally used to analyze resonant corresponding to a reduction in contact resistance can clearlytunneling diodes. be seen in this device as a direct consequence of Joule
heating at the contacts. By modeling each contact as a
qh2k2 separate junction (with different voltages, one forward andJ= q dE|(E- 2 )dk2 [f(E,EF,T)-f(E,E -qV,T)] the other reverse) in which electrons must tunnel to
contribute to transport, we can also estimate the power
Here, Tt is the tunneling probability often given by the WKB generated at the contacts. The calculation of powerapproximation, f is the Fermi distribution function at T with dissipated in each contact is shown in Figure 4. Athe Fermi level EF, E is the total electron energy, and k is a noticeable difference in power dissipation is observed in themomentum component parallel to the interface. We reverse-biased right junction after the second anneal. Thisintegrate over the wave vector and energy domains where corresponds to the reduction in the barrier width of the righttunneling occurs. We assume that the temperature is low contact barrier, causing a higher voltage drop in the leftenough such that the difference of the Fermi functions can junction; and hence higher power dissipation in the leftbe approximated by a boxcar function having a finite value junction for the same current. Our model and measurementsbetween BF-qV and EF. BY adapting equation (1) uighave shown that annealing decreases the physical separationsimplifications to account for a finite temperature, we arrive btenteCFadtemtleetoe h oeat an analytical expression for metal-insulator-metal dissipation results shown here further support this finding.tunneling current density as follows.
156
4. Conclusion
9 9 In this work, the effect of heat generation at CNF-goldC : \ electrodes is examined. Through modeling, simulation, and
measurement, we have demonstrated that significant heat10-5 ~ =generation in a single CNF device bridging two gold
a): X9 / , \electrodes happens at the CNF-gold electrode interface.
This phenomenon can be described quantitatively by metal-
OS Annea. insulator-metal tunneling theory. Our model shows that theio-6 - 01Successive Anneals barrier width is modulated by annealing (through Joule
heating) the entire test structure, including the CNF-goldcontacts. More desirable electrical characteristics areobserved after high current density is passed through the
-1 -0.5 0 0.5 1 contact interfaces and CNF, resulting in a resistance of 11Voltage [V] kQ in the best case. Using measured parameters and the
barrier width as the single adjustable parameter, the model isFigure 3. Comparison of measured and modeled current- able to predict accurately I-V characteristics of the annealedvoltage characteristics for all three annealing conditions. CNF structure. Power dissipation as calculated from the I-VThe decrease in resistance from 46 kW to 11 kW can data reveals asymmetry of the two contacts as a result ofclearly be seen for this sample. Joule heating. Additional modeling work and measurements
are in progress to predict breakdown effects of CNFs in lightof Joule heating in these quasi-one-dimensional systems.
20Prior to Anneal References
Anneal #215 +A 2 [1] B. Bourlon, D. C. Giaftli, B. Placais, J. M. Berrior,
C. Miko, L. Forro, and A. Bachtold, "GeometricaleL .. *+dependence of high-bias current in multiwalled
*L ¢.++ [2] L. Dong, S. Youkey, J. Bush, J. Jiao, V. M. Dubin,5- * +and R. V. Chebiam, "Effects of local Joule heating
(a) +++on the reduction of contact resistance between(a) Left contact carbon nanotubes and metal electrodes," J Appi.
O 10 20 30 40 50 60 Phys., vol. 101, pp. 024320, 2007.Current [gA] [3] B. A. Cruden, A. M. Cassell, Q. Ye, and M.
20 Meyyappan, "Reactor design considerations in the*Prior to AnnealAnneal #1 * * hot filament/direct current plasma synthesis ofAnneal #2 carbon nanofibers," J Appl. Phys., vol. 94, pp.
15 4070-4078, 2003.[4] J. Tersoff, "Contact resistance of carbon
nanotubes," Appl. Phys. Lett., vol. 74, pp. 2122-a) 10- 2124, 1999.0 [5] G. Mills, M. S. Gordon, and H. Meiu, "Oxygenn. adsorption of Au clusters and a rough Au (111)
5- surface: The role of surface flatness, electronconfinement, excess electrons and band gap," J.
(b) Right contact Phys. Chem., vol. 118, pp. 4198-4205, 2003.0 10 20 30 40 50 60 [6] T. Yamada, "Modeling of carbon nanotube
Current [4A] Schottky barrier modulation under oxidizingconditions," Phys. Rev. B: Condensed Matter, vol.
Figure 4. Calculated power dissipation due to Joule 69, pp. 125408-1 to 125408-7, 2004.heating in the (a) left and (b) right contacts prior to and [7] V. Derycke, R. Martel, J. Appenzeller, and P.following anneal #1 and #2. Avouris, "Carbon nanotube inter- and
[8] L. L. Chang, P. J. Stiles, and L. Esaki, "Electrontunneling between a metal and semiconductor:Characteristics of Al-A1203-SnTe and GeTejunctions," J. Appl. Phys., vol. 38, pp. 4440-4445,1967.
[9] T. Yamada, "Modeling of electronic transport inscanning tunneling microscope tip-carbon nanotubesystems," Appl. Phys. Lett., vol. 78, pp. 1739-1741,2001.
[10] Q. Ngo, D. Petranovic, S. Krishnan, A. M. Cassell,Q. Yi, J. Li, M. Meyyappan, and C. Y. Yang,"Electron transport through metal-multiwall carbonnanotube interfaces," IEEE Trans. Nanotech., vol.3, pp. 311-317, 2004.
