Current-induced breakdown is investigated for carbon nanofibers (CNF) for potential interconnect applications. The measured maximum current density in the suspended CNF is inversely proportional to the nanofiber length and is independent of diameter. This relationship can be described with a heat transport model that takes into account Joule heating and heat diffusion along the CNF, assuming that breakdown occurs when and where the temperature reaches a threshold or critical value

Fabris, Drazen

Jameson, John R.

Kitsuki, Hirohiko

Suzuki, Makoto

Wilhite, Patrick

Yamada, Toshishige

Yang, Cary Y.

English

Scholar Commons - Santa Clara University

Santa Clara UniversityScholar CommonsElectrical Engineering School of Engineering4-28-2008Length dependence of current-induced breakdownin carbon nanofiber interconnectsHirohiko KitsukiToshishige YamadaSanta Clara University, tyamada@scu.eduDrazen FabrisSanta Clara University, dfabris@scu.eduJohn R. JamesonPatrick WilhiteSanta Clara University, pwilhite@scu.eduSee next page for additional authorsFollow this and additional works at: https://scholarcommons.scu.edu/elecCopyright © 2008 American Institute of Physics Publishing. Reprinted with permission.This Article is brought to you for free and open access by the School of Engineering at Scholar Commons. It has been accepted for inclusion inElectrical Engineering by an authorized administrator of Scholar Commons. For more information, please contact rscroggin@scu.edu.Recommended CitationH. Kitsuki, T. Yamada, D. Fabris, J.R. Jameson, P. Wilhite, M. Suzuki, and C.Y. Yang, “Length dependence of current-inducedbreakdown in carbon nanofiber interconnects,” Applied Physics Letters 92, 173110 (3 pp) (2008). https://doi.org/10.1063/1.2918839AuthorsHirohiko Kitsuki, Toshishige Yamada, Drazen Fabris, John R. Jameson, Patrick Wilhite, Makoto Suzuki, andCary Y. YangThis article is available at Scholar Commons: https://scholarcommons.scu.edu/elec/37Length dependence of current-induced breakdown in carbonnanofiber interconnectsHirohiko Kitsuki, Toshishige Yamada,a Drazen Fabris, John R. Jameson, Patrick Wilhite,Makoto Suzuki, and Cary Y. YangCenter for Nanostructures, Santa Clara University, Santa Clara, California 95053, USAReceived 14 March 2008; accepted 10 April 2008; published online 1 May 2008Current-induced breakdown is investigated for carbon nanofibers CNF for potential interconnectapplications. The measured maximum current density in the suspended CNF is inverselyproportional to the nanofiber length and is independent of diameter. This relationship can bedescribed with a heat transport model that takes into account Joule heating and heat diffusion alongthe CNF, assuming that breakdown occurs when and where the temperature reaches a threshold orcritical value. © 2008 American Institute of Physics. DOI: 10.1063/1.2918839Because of their high electrical and thermal conductivi-ties as well as current capacity, carbon nanotubes1 CNTsand carbon nanofibers2–5 CNFs are being investigated forhigh-performance device and interconnect applications.Breakdown phenomena have been observed under high-current stress conditions for CNTs6–12 and amorphous carbonnanowires.13 Breakdown mechanisms generally depend onthe detailed carbon nanostructures. For CNFs, recentstudies5,14,15 suggest current-induced CNF breakdown to beclosely related to Joule heating, and thermal coupling be-tween CNF and electrodes affects the maximum current den-sity Jmax of CNF devices and their breakdown. Meanwhile,current annealing has been reported to drastically reduce theoverall resistance and this may be attributed to significantlowering of the contact resistances in CNT devices.16–18Therefore, one can assume that once the contact resistancesare reduced, the reliability of CNF interconnects becomeslargely dependent on the nanofiber resistance. In this work,systematic characterization of CNFs under high-currentstress is performed to examine and to elucidate the CNFbreakdown phenomena.The CNF samples are grown using plasma-enhancedchemical vapor deposition19,20 with a Ni catalyst layer on aSi substrate. A 30-nm-thick Ti adhesion layer is used be-tween the 35-nm-thick Ni layer and Si, and a gas mixture ofNH3:C2H2 4:1 at 4 Torr is used for the reaction.21 A solu-tion of CNFs is drop-casted onto a substrate of prepatternedgold electrodes on an oxidized silicon wafer. The structureshown in Fig. 1a is a model of an on-chip interconnectconfiguration, where the CNF sidewall is in contact withthe electrodes.22 Constant-current stress or anneal is appliedin ambient Fig. 1b for 13 samples, ranging from100 to 200 nm in diameter and 1.5 to 6 m in length.The progression of constant-current stress cycles at180 s each is illustrated in Fig. 2a. At the end of eachcycle, I-V characteristics are obtained around V=0. Increas-ing the annealing current results in a gradual decrease in thedifferential resistance R at V=0 before the nanofiber breaksdown at 700 A Fig. 2b. Since R consists of bulk andcontact contributions, and the CNF consistently breaks nearthe middle away from the contacts, current annealing likelyreduces the contact resistances significantly, while break-down occurs due to Joule heating in the CNF bulk.Systematic analysis using scanning transmission electronmicroscopy STEM and in situ scanning electron micros-copy SEM measurements has revealed the creation of voidand defective graphitic layers in the CNF induced by currentstress.14 This analysis suggests that the CNF resistance justbefore breakdown drastically increases due to severe degra-dation of the nanofiber internal structure. The SEM image ofa CNF before current stress is shown in Fig. 3a. In allexperiments for suspended CNFs, we have confirmed thatbreakdown always occurs near the middle of the nanofiber asin Figs. 3b and 3c. This is consistent with diffusive heattransport in CNTs at high bias,10 suggesting the importanceof Joule heating15 in breakdown.To understand these experimental results, a one-dimensional 1D thermal transport model15,23 is used. Wedefine Tx as the difference between the local temperatureTx and the temperature at infinity. Tx is determinedfrom the balance among heat diffusion d2T /dx2, heat dis-sipation to the surroundings a2T, and heat generation dueto Joule heating f ind2Tdx2− a2T = − f . 1Here, f = I2 / A2, where I is the current, A is the cross-sectional area,  is the electrical conductivity, and  is theCNF thermal conductivity. Also, a2=w /A, where w is theeffective contact line width and  is the coupling coefficientfor heat transport to the CNF surroundings air andaThe author to whom correspondence should be addressed. Electronic mail:tyamada@scu.edu.FIG. 1. Setup for current-stressing experiments. a SEM image of a CNFsample suspended between gold electrodes at 75° tilted-angle view. High-resolution STEM images of CNFs can be seen in Ref. 14. b Schematic ofelectrical measurement.APPLIED PHYSICS LETTERS 92, 173110 20080003-6951/2008/9217/173110/3/$23.00 © 2008 American Institute of Physics92, 173110-1substrate. We impose T=0 at the two ends wherex=L /2 and x=0 is the midpoint. Thus, Tx= f /a21−coshax /coshaL /2 results, with the maximum at x=0.We assume that, in general, breakdown occurs when Treaches a threshold critical temperature Tmax, which is com-mon for all CNFs with any diameters or lengths, preparedusing the same growth process. Then, the maximum currentdensity Jmax can be expressed asJmax = Tmax − Tw/A1/21 − 1/coshaL/2−1/2. 2In the suspended case, heat dissipation is expected to benegligible, or aL1, yielding Jmax22Tmax−T /L.Figure 4a shows the experimental results dots forJmax versus 1 /L for 13 devices. The behavior is consistentwith current-induced breakdown in single-walled CNTs24 orgold nanowires fabricated using conventional lithographytechniques.25 The same behavior is predicted in our model inthe aL1 limit of Eq. 2. This excellent agreement con-firms that for a suspended CNF, heat dissipation to its sur-roundings is, in fact, small and heat diffusion along the CNFleads to the highest temperature in the middle of the nanofi-ber. Moreover, Jmax scales with 1 /L, which is consistent withthe peak current behavior of suspended single-walledCNTs.24From the fitted result of Jmax=5.39 /L in Fig. 4a, Tmax=1260 K. This is comparable to the CNF synthesis tempera-ture, estimated to be in the 1000 K range. Here, a CNF ther-mal conductivity of 12 W /m K26 and the maximum electri-cal conductivity from the present data are used. Having noradiative heat transfer and in the limit of no coupling withthe substrate, the temperature estimate is only an indicationof CNF durability and points to the need for systematic localtemperature measurement.Our previous work showed a Jmax	1 /L behavior,14based on the assumption that CNF was a long 1D thermalconductor with an exponential decay of temperature beyondthe CNF/electrode contacts. In the present work, the heatdissipation to the substrate is weak over the suspended dis-tance, while the nanofiber coupling with the electrodes isrelatively strong, where T=0 is assumed. The difference inboundary conditions leads to Jmax scaling with 1 /L as veri-fied by the present experimental results.FIG. 2. Resistance reduction of CNF device due to current annealing. aSchematic of successive current annealing cycles using stepwise incrementof stressing current. b Resistance of the CNF device at V=0 obtained aftereach annealing cycle. The inset shows the current-voltage behavior at theend of one of the anneal cycles.FIG. 3. a SEM images of a CNF suspended gold electrode before currentstressing. b CNF after breakdown top view and c at 75° tilted-angleview.FIG. 4. a Maximum current density as a function of reciprocal CNF lengthfor thirteen devices. The line shows a linear fit predicted by our heat trans-port model. b Resistance of CNF device as a function of annealing currentafter each annealing cycle for the same thirteen devices. The line approxi-mates the resistance just before breakdown.173110-2 Kitsuki et al. Appl. Phys. Lett. 92, 173110 2008Figure 4b shows a plot of R measured at the end ofeach current annealing cycle as a function of annealing cur-rent Ianneal for all 13 devices. We note that each CNF has adifferent diameter and length, with different contact proper-ties. For this reason, one can expect that well before break-down when Jmax is reached, R significantly deviates fromsample to sample partly due to large contact resistances, upto a factor of 20 in our case. However, after successive cur-rent annealing cycles as illustrated in Fig. 2a, R begins toconverge for Ianneal100 A, and the deviation from sampleto sample is reduced to less than a factor of 5.This result can be understood by assuming that the con-tact resistance is initially large and dominates R but is sig-nificantly reduced through repeating current annealing, andfor Ianneal100 A, the bulk CNF resistance dominates. Infact, during these later annealing cycles, long CNFs havealready broken down, as shown in Fig. 4a and the survivingCNFs are mostly short or less than 2.5 m. For smaller Land negligible contact resistance, the dominant source forresistance variation is the cross-sectional area A. Since theCNF diameter ranges from 100 to 200 nm, A varies up to afactor of 4 and R is also expected to vary accordingly, whichis consistent with the observed high-Ianneal behavior in Fig.4b.In Fig. 4b, for samples with Ianneal100 A, the resis-tance just before breakdown converges to R	1 / Ianneal, re-gardless of A and L values. Assuming an Ohmic behavior,we have R=L /A=JannealL / Ianneal, where  is the resistivity.In the final annealing cycle, JannealJmax. Since we have es-tablished that Jmax	1 /L, R	1 / Ianneal results, confirming theempirical findings in Fig. 4b.In conclusion, current-induced breakdown has been in-vestigated for suspended CNFs. With reduced contact resis-tance due to current annealing, a simple relationship betweenthe maximum current capacity and CNF length is obtainedexperimentally and successfully explained with a 1D heattransport model. This result suggests that breakdown occurswhen the local temperature reaches a geometry-independentvalue at the midpoint of the suspended nanofiber. The ob-served Jmax	1 /L behavior is consistent with metallic nano-wires, and the present study represents an important steptoward understanding the reliability of CNF for potential in-terconnect applications.We are grateful to J. Li and A. M. Cassell for their help-ful advice and to Hitachi High-Technologies America for itsassistance in electron microscopy. This work was supportedby the United States Army Space and Missile Defense Com-mand SMDC and carries Distribution Statement A, ap-proved for public release, distribution unlimited.1See, e.g., Carbon Nanotubes: Synthesis, Structure, Properties, and Appli-cations, edited by R. E. Smalley, M. S. Dresselhaus, G. Dresselhaus, andPh. Avouris Springer, Boston, 2001.2L. C. Qin, D. Zhou, A. R. Kraus, and D. M. Gruen, Appl. Phys. Lett. 72,3437 1998.3J. Li, Q. Ye, A. M. Cassell, H. T. Ng, R. 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Length dependence of current-induced breakdown in carbon nanofiber interconnects

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Length dependence of current-induced breakdown in carbon nanofiber interconnects

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