IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 1, JANUARY 2011 229
Inductance Properties of In Situ-Grown HorizontallyAligned Carbon Nanotubes
Minghui Sun, Zhiyong Xiao, Yang Chai, Yuan Li, and Philip C. H. Chan, Fellow, IEEE
Abstract—Kinetic inductance is an important property of car-bon nanotubes (CNTs) in high-frequency applications. However,disagreements exist in whether the kinetic inductance of CNTs ispresent in the diffusive transport regime. In this paper, we fab-ricated the horizontally aligned multiwalled nanotube (MWNT)arrays on silicon substrates and investigated the inductance prop-erties of the MWNT arrays with different lengths using directcurrent and radio frequency characterizations. The experimentalresults show that the electron transport in the CNT arrays is diffu-sive and that the value of the kinetic inductance is proportional tothe length of the CNT arrays. We have experimentally validatedthat the kinetic inductance theory is applicable to CNTs in thediffusive transport regime. This paper could quell the existingdisagreements about the kinetic inductance and provide insightsto the potential applications of CNTs as interconnects and on-chipinductors.
Index Terms—Carbon nanotube (CNT), diffusive transport,interconnect, kinetic inductance.
I. INTRODUCTION
A HIGHLY dense carbon nanotube (CNT) array has beenproposed for use as future very large scale integrated
interconnects [1], [2] and on-chip inductors [3], [4] due to itsexcellent electrical properties and high-frequency performance.Simulation [3] shows that the skin effect in the CNT array issignificantly reduced compared with the state-of-the-art copperinterconnect at tens of gigahertz frequency, which makes theCNT an attractive material for high-frequency applications.This unique property can be attributed to the presence of largekinetic inductance in the CNT [3].
As a 1-D material, the CNT has a large mean free path (MFP)on the order of micrometers theoretically. When the lengthof the CNT is longer than its MFP, the electron transport inthe CNT is diffusive, and the resistance of the CNT linearlyincreases with its length. Otherwise, the electron transport isballistic, and the resistance of the CNT becomes independent ofits length [5], [6]. The kinetic inductance represents the excesskinetic energy of electrons in the CNT. Theoretical studies[7]–[10] have predicted that the kinetic inductance of the CNT
Manuscript received July 8, 2010; revised September 12, 2010 andOctober 3, 2010; accepted October 5, 2010. Date of publication November 11,2010; date of current version December 27, 2010. This work was supportedby the Hong Kong Research Grant Council under Grant HKUST 611307. Thereview of this paper was arranged by Editor M. A. Reed.
The authors are with the Department of Electronic and Computer Engi-neering, The Hong Kong University of Science and Technology, Kowloon,Hong Kong (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TED.2010.2087023
is 8 nH/μm for each conducting channel [11], [12], which aremore than three orders of magnitude larger than the magneticinductance of the CNT (in picohenries per micrometer). WithN conducting channels in parallel, the kinetic inductance isdecreased to 8/N nH/μm. Thus, theoretically, the kinetic in-ductance of the CNT array is inversely proportional to the num-ber of CNTs in parallel. However, the relationship between thekinetic inductance and the length of the CNT remains contro-versial. Yamada et al. [8] attributed the large kinetic inductanceof the CNT to the ballistic transport without inelastic scatteringin the CNT. They held the view that the kinetic inductanceshould be absent when the length of the CNT was longer thanits MFP. Salahuddin et al. [13] and Li and Banerjee [9] held theview that the kinetic inductance theory was applicable to CNTsin both the ballistic and diffusive transport regimes because thelarge momentum relaxation time [14] in the CNT was the factorthat made the kinetic inductance significant; thus, the kineticinductance should be always proportional to the length ofthe CNT.
For the applications of CNTs as interconnects and on-chipinductors, the length of the CNT arrays could be much longerthan that of the MFP. To take advantage of the negligibleskin effect in CNTs, it is important to experimentally checkwhether the kinetic inductance is present in the diffusivetransport regime. There are a few reported works [15]–[22]on the characterization of the CNT kinetic inductance. Twoimportant works are summarized as follows: Zhang et al. [15]performed RF characterization to 15 single-walled nanotubes(SWNTs) with 1.65-nm average diameter and 1.5-μm length.They obtained the result of 10.4 nH/μm for each conductingchannel. Plombon et al. [16] conducted RF measurements on anisolated SWNT with 1.0 ± 0.1 nm diameter and 2-μm length.They obtained 78 nH/μm for each conducting channel, whichwas one order larger than the theoretical value of 8 nH/μm.Although these two works demonstrate the existence of thekinetic inductance, it is difficult to tell the electron transportregime in their CNT samples. The theoretical MFP of theCNT is proportional to the CNT diameter, and the proportionalcoefficient is on the order of thousands [23], [24]. However, in areal case, the coefficient is suppressed by impurities and defectsin the CNT and depends on the individual fabrication conditions[5], [6], [25]–[27]. Furthermore, these results were obtainedfrom CNT samples with low density. The limited drive currentin the CNT samples would induce a large impedance mismatch,which may hinder RF characterization at high frequency andcause inaccurate measurements.
Recently, we have developed a method to grow horizontaland dense multiwalled nanotube (MWNT) arrays on silicon
230 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 1, JANUARY 2011
Fig. 1. Schematic of the device fabrication process. (a). Deposit 3 μm LTO.(b) Deposit and pattern TiW layer. (c) Deposit Fe layer. (d) Grow CNTsby PECVD. (e) Planarize CNTs and insulate the substrate. (f) Form metalelectrodes by lift-off.
substrates [28], [29]. The highly dense nanotubes providemultiple transport pathways and large drive current and, fur-thermore, lead to smaller device-to-device variations due tostatistical averaging effects. As it has been highlighted in[30], the inductance of MWNT arrays has been experimentallyconfirmed to be proportional to its length and inversely pro-portional to the number of CNTs in parallel. In this paper, wenot only present a systematic method to investigate the kineticinductance properties of CNTs but also explore the relation-ship between the kinetic inductance and the electron transportmechanisms in CNTs. Our analysis could quell the existingdisagreements about the kinetic inductance theory and provideinsights to the potential applications of CNTs as interconnectsand on-chip inductors.
II. FABRICATION
The starting substrate was a high-resistivity (200–300 Ω · cm) N-type (100)-oriented silicon wafer. Thefabrication process is illustrated in Fig. 1 and briefly describedin the list that follows.
1) Deposit a 3-μm low-temperature oxide film on the siliconsubstrate to reduce the substrate loss and increase theaccuracy of RF characterization.
2) Deposit a 3-nm TiW film and perform photolithography.A H2O2 solution was used to etch the TiW layer.
3) Deposit a 1-nm Fe layer on the entire wafer as the catalystfor CNT growth.
4) Grow CNTs by plasma-enhanced chemical vapor deposi-tion at 850 ◦C with CH4, N2, and H2 as the feed gases.The CNTs only selectively grew on the areas where TiWwas removed, because TiW formed an alloy with Fe athigh temperature and deactivated the function of Fe asthe catalyst. The dimension of the active catalyst stripewas fixed at 10-μm length and 8-μm width.
5) Planarize the CNTs by soaking the entire wafer in anisopropanol (IPA) solution for 10 min and evaporate theIPA by placing the wafer in the fume hood for 2 h[29], [31]. After the evaporation process, the CNTs were
Fig. 2. TEM micrographs of the fabricated MWNTs.
Fig. 3. SEM micrographs of the CNT arrays after planarization. (a) and(c) with 100-nm scale bar. (b) With 10-μm scale bar.
firmly attached to the substrate and densified. Insulate thesubstrate by soaking the wafer in the 70 ◦C H2O2 solutionfor 30 min to remove the TiW layer and the Fe layer.
6) Deposit Ti/Au (15 nm/3000 nm) and pattern the metalelectrodes by lift-off. The Ti layer acts as the adhesionlayer between the CNTs and the Au layer. The back gateelectrode is not fabricated in this paper.
The CNTs grown in this process are MWNTs with 5- to10-nm diameters and two to five shells, and structural defectsexist in some of the tubes, as shown in the transmission electronmicroscopy (TEM) micrographs in Fig. 2. Scattering caused bythe defects would reduce the MFP and the conductivity of theCNTs [17], [32].
Fig. 3 shows the scanning electron microscopy (SEM) mi-crographs of CNT arrays after planarization. The CNT arrayhas very high site density [see Fig. 3(a)] and is attached to thesilicon substrate with excellent flatness [see Fig. 3(b)]. There-fore, only the top few layers of MWNTs in the CNT arrayscould form effective contact with metal pads. By counting thenumber of all the visible CNTs in different CNT arrays [seeFig. 3(c)], the density of CNTs per unit width is obtained as
SUN et al.: INDUCTANCE PROPERTIES OF In Situ-GROWN HORIZONTALLY ALIGNED CNTs 231
Fig. 4. (a) Device structure. (b) CNT array. (c) Open pad structure.
85−105 μm−1. For the CNT arrays fabricated on the same chip,due to the same process conditions, the site density is relativelystable.
The device structure in this paper is a coplanar waveguide(CPW) with a dense CNT array in the signal path, as shown inFig. 4(a). According to the work of Mann et al. [5], the bulklength of the CNTs under the metal appeared to be electricallyoff, and transport occurred from the metal to the CNTs atthe edges of the contact. Therefore, the effective length of theCNT arrays is approximately the same as the spacing of thesignal pads. Since the dimension of the active catalyst stripis constant, the number of fabricated CNTs is approximatelythe same in different devices. After the planarization process,the CNTs shrunk into dense arrays with width of 3−4 μmdue to the liquid densification effect [see Fig. 4(b)]. In ourmeasurements, sufficient samples were characterized for eachtype of device structures to obtain reasonable statistics. Tosimplify the analysis, the width variation was neglected, andthe number of conducting channels was considered as thesame in different CNT arrays. The variation in the numberof conducting channels was reflected as the error bars in thestatistical results. The corresponding open pad structures [seeFig. 4(c)] for parasitic deembedding were also fabricated.
III. SIMULATION
In order to gauge the importance of kinetic inductance, it isnecessary to calculate the fraction of the kinetic inductance inthe total effective inductance for the fabricated CNT arrays.
Although the CNTs are multiwalled, due to weak intershellcoupling, the inner shells have small impact on conduction[32], [33]. Therefore, only the outmost shells of the contactedMWNTs contribute to electrical conduction. Based on therandom chiralities, one third of the contacted shells of MWNTsare metallic [34]. The diameter of the CNTs was estimated asthe average value of 7.5 nm. The length and the width of thesimulated CNT array were 10 and 3.5 μm, respectively. Thekinetic inductance of the CNT array, i.e., LK , was calculatedusing the theoretical value of 8/N nH/μm. The number ofconducting channels N was estimated according to the modelproposed in Naeemi and Meindl [12]. The self- and mutualmagnetic inductances of the CNTs were calculated using themodels proposed in [35]. We calculated the total effectiveinductance of the CNT array, i.e., LTOT, using the partial-element equivalent-circuit formulation proposed in Nieuwoudtand Massoud [4] and Li and Banerjee [9].
The fraction of the kinetic inductance in the total inductanceof the CNT array, i.e., LK/LTOT, was simulated at differentCNT densities (85−105 μm−1), as shown in Fig. 5. The value
Fig. 5. Simulated fraction of the kinetic inductance LK/LTOT of a 10-μm-long and 3.5-μm-wide MWNT array at different MWNT densities.
Fig. 6. Differential resistance dV/dI of the CNT arrays with different effec-tive lengths lCNT.
of LK/LTOT is averaged to be 98.3%, which suggests that thekinetic inductance dominates the total effective inductance inour CNT arrays.
IV. CHARACTERIZATION
A. DC Characterization
DC characterization was performed on the three types ofdevice structures, of which the effective CNT lengths lCNT
were 10, 20, and 30 μm, respectively.Voltage was applied to the two signal pads of the CPW and
swept from −1 to 1 V. The current through the CNT arrays weremeasured in the dark at room temperature. Fig. 6 shows thedifferential resistance R = dV/dI of the MWNT arrays withdifferent lCNT. R consists of two parts, i.e., the CNT resistanceand the CNT–metal contact resistance. R is almost constant inthe entire voltage range, which indicates good linearity of theI–V curves and suggests good ohmic behavior of the MWNTsand stable contact resistance with the metal. R fluctuates a lot
232 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 1, JANUARY 2011
Fig. 7. Average DC resistance of the CNT arrays with different effectivelengths lCNT.
when V > 0.4 V, which gives us an upper limit of the RF powerlevel when performing RF characterization.
Three to ten samples of each type of device structures werecharacterized. The mean values of the DC resistance of the CNTarrays with different lCNT are plotted in Fig. 7. The data fit wellto the linear model, i.e.,
The distributed scattering resistance of the CNT arrays is90.0 Ω/μm with a variation of 8.4 Ω/μm. RDC linearlyincreases with lCNT, which indicates the diffusive electrontransport in the CNT arrays.
B. RF Characterization
RF characterization was performed using the ground–signal–ground probes and the Agilent E8361A vector networkanalyzer. Before the measurement, the two-port short–open–load–through calibration was performed on the impedance stan-dard substrate to establish the reference plane at the probe tipsand to compensate for the imperfections of the measurementsystem [36]. The S-parameters [37] of the CNT device struc-tures and the open pad structures were measured from 100 MHzto 40 GHz in the dark at room temperature. The output powerlevel was set at 2 dBm, which corresponded to a peak sinusoidalvoltage Vpeak of 0.4 V.
Fig. 8(a) shows the typical S11 and S21 magnitude curves ofa CNT device and its corresponding open pad structure. Theeffective length of the CNT array is 20 μm. The test structuresare all designed to be symmetric, which results in two symmet-ric S-parameters, i.e., S11 = S22 and S21 = S12. Because theinput impedance of the CNT device is much smaller than thatof the open pad structure, there are small signal reflection andlarge signal transmission in the CNT device. With the frequencyincreasing, the stronger capacitive coupling between the twosignal pads leads to the smaller input impedance and the smallersignal reflection in both structures. Thus, both the |S11| curvesdecrease with frequency, whereas both the |S21| curves increase
Fig. 8. (a) Measured S11 and S21 magnitudes of a device structure with a20-μm-long CNT array and the corresponding open pad structure. (b) LumpedLRC model for the CNT arrays. (c) Measured CNT impedance and fittingresults of the LRC model.
with frequency. At high frequency (> 25 GHz), the capacitivecoupling between the input and output metal pads dominatesthe input impedance, bringing the two |S21| curves close to eachother. Moreover, the noise and the parasitic effects are morenoticeable at high frequency.
To obtain the electrical properties of the CNT arrays, ageneral deembedding procedure [38], [39] was employed todeembed the pad parasitics from the overall device character-istics. The lumped LRC elements [15], [16], [20], [21] werechosen to model the electrical properties of the CNT arrays inthis paper, as shown in Fig. 8(b). RCNT is the resistance ofthe CNT array, and LTOT is the total inductance of the CNTarray. RC and CC are the contact resistance and the capacitancebetween the metal pad and the CNT array, respectively. Thevalue of each element was extracted by fitting the impedanceof the LRC model to the measured data using the Advanced
SUN et al.: INDUCTANCE PROPERTIES OF In Situ-GROWN HORIZONTALLY ALIGNED CNTs 233
TABLE IEXTRACTED VALUES OF PARAMETERS FOR A
20-μm-LONG MWNT ARRAY
Fig. 9. Average inductance of the CNT arrays with different effective lengthslCNT.
Design System design package [40]. Fig. 8(c) shows the fittingresults for a 20-μm-long CNT array. The model fits well to themeasured data up to 30 GHz. At frequency larger than 10 GHz,the presence of a positive phase of the CNT impedance is astrong evidence for the existence of LTOT [16]. The extractedvalues of elements are shown in Table I. LTOT = 2.2 nH wasextracted. We also measured the parasitic inductance of themetal pads, which was around 100 pH and negligible comparedwith LTOT of the CNT arrays.
RF characterization was carried out on the same devices asin DC characterization. Fig. 9 shows the mean value of LTOT
for different lCNT. LTOT could be well fitted to the linearmodel, i.e.,
To validate the presence and dominance of the kinetic in-ductance, we normalized LTOT to each conducting channeland compared it with the theoretical kinetic inductance of8 nH/μm. With the variations included, the MWNT diameteris 7.5 ± 2.5 nm, which corresponds to 0.884 ± 0.295 conduct-ing channels [12]. The width and density of the CNT arraysare 3.5 ± 0.5 μm and 95 ± 10 μm−1, respectively. Therefore,the number of conducting channels N was estimated to be322 ± 172, and the normalized LTOT per conducting channelwas 34.5 ± 19.5 nH/μm. Since some of the side-contactedCNTs have structural defects in the trunk and do not actuallycontribute to the electrical conduction, N is overestimated.Therefore, it is reasonable that the normalized LTOT is largerthan 8 nH/μm. Our experimental results validate the presenceof the kinetic inductance and support the dominance of thekinetic inductance in the total inductance of CNT arrays.
Combining the results of DC and RF characterization, weexperimentally validate that the kinetic inductance still existsin CNTs when the electron transport is in the diffusive regimeand that the value of the kinetic inductance is proportional to thelength of CNTs. Our experiment results support that the largemomentum relaxation time in CNTs is the factor that makes thekinetic inductance significant.
For potential applications of CNTs as interconnects and on-chip inductors, the fabrication of the horizontal CNT arrays isrequired, and highly dense CNTs are desirable to scale downthe total resistance and the kinetic inductance of CNT arrays.Our group has fabricated the horizontal and dense CNT arrays[28]–[30]. However, only a small fraction of the fabricatedCNTs could form effective contact with the electrodes. There-fore, the resistance and the kinetic inductance of CNT arraysare still too large for interconnect and inductor applications.How to form more effective contact between the metal and thehorizontal CNTs becomes the biggest challenge for the futureof CNTs as interconnects and inductors.
V. CONCLUSION
In this paper, we have investigated the inductance proper-ties of in situ-grown horizontally aligned MWNT arrays withdifferent lengths. We have experimentally validated that thekinetic inductance theory is applicable to CNTs in the diffusivetransport regime and that the value of the kinetic inductanceis proportional to the length of CNTs. This work assures thepotential advantage of CNT arrays, i.e., a negligible skin effectat high frequency, and provides good potential for the applica-tions of CNTs as VLSI interconnects and on-chip inductors.Continuing efforts will be needed to develop more effectivecontact between the metal and the horizontal CNT arrays thatcan further scale down the inductance and the resistance ofCNT arrays.
ACKNOWLEDGMENT
The authors would like to thank Prof. K. J. Chen andK. W. Chan of The Hong Kong University of Science andTechnology for the fruitful discussion and assistance in the RFmeasurements.
REFERENCES
[1] F. Kreupl, A. P. Graham, M. Liebau, G. S. Duesberg, R. Seidel, andE. Unger, “Carbon nanotubes for interconnect applications,” in IEDMTech. Dig., 2004, pp. 683–686.
[2] A. Naeemi, R. Sarvari, and J. D. Meindl, “Performance comparison be-tween carbon nanotube and copper interconnects for gigascale integration(GSI),” IEEE Electron Device Lett., vol. 26, no. 2, pp. 84–86, Feb. 2005.
[3] H. Li and K. Banerjee, “High-frequency effects in carbon nanotube in-terconnects and implications for on-chip inductor design,” in IEDM Tech.Dig., 2008, pp. 525–528.
[4] A. Nieuwoudt and Y. Massoud, “Predicting the performance of low-losson-chip inductors realized using carbon nanotube bundles,” IEEE Trans.Electron Devices, vol. 55, no. 1, pp. 298–312, Jan. 2008.
[5] D. Mann, A. Javey, J. Kong, Q. Wang, and H. Dai, “Ballistic transport inmetallic nanotubes with reliable Pd ohmic contacts,” Nano Lett., vol. 3,no. 11, pp. 1541–1544, Nov. 2003.
[6] J. Park, S. Rosenblatt, Y. Yaish, V. Sazonova, H. Ustunel, S. Braig,T. A. Arias, P. W. Brouwer, and P. L. McEuen, “Electron–phonon
234 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 1, JANUARY 2011
scattering in metallic single-walled carbon nanotubes,” Nano Lett., vol. 4,no. 3, pp. 517–520, 2004.
[7] P. Burke, “Luttinger liquid theory as a model of the gigahertz electricalproperties of carbon nanotubes,” IEEE Trans. Nanotechnol., vol. 1, no. 3,pp. 129–144, Sep. 2002.
[8] T. Yamada, F. R. Madriz, and C. Y. Yang, “Inductance in one-dimensionalnanostructures,” IEEE Trans. Electron Devices, vol. 56, no. 9, pp. 1834–1839, Sep. 2009.
[9] H. Li and K. Banerjee, “High-frequency analysis of carbon nanotubeinterconnects and implications for on-chip inductor design,” IEEE Trans.Electron Devices, vol. 56, no. 10, pp. 2202–2214, Oct. 2009.
[10] A. Maffucci, G. Miano, and F. Villone, “A new circuit model for car-bon nanotube interconnects with diameter-dependent parameters,” IEEETrans. Nanotechnol., vol. 8, no. 3, pp. 345–354, May 2009.
[11] H. J. Li, W. G. Lu, J. J. Li, X. D. Bai, and C. Z. Gu, “Multichannel ballistictransport in multiwall carbon nanotubes,” Phys. Rev. Lett., vol. 95, no. 8,p. 86 601, Aug. 2005.
[12] A. Naeemi and J. Meindl, “Compact physical models for multiwallcarbon-nanotube interconnects,” IEEE Electron Device Lett., vol. 27,no. 5, pp. 338–340, May 2006.
[13] S. Salahuddin, M. Lundstrom, and S. Datta, “Transport effects on signalpropagation in quantum wires,” IEEE Trans. Electron Devices, vol. 52,no. 8, pp. 1734–1742, Aug. 2005.
[14] N. W. Ashcroft and N. D. Mermin, Solid State Physics. Philadelphia,PA: Saunders, 1976.
[15] M. Zhang, X. Huo, P. C. H. Chan, Q. Liang, and Z. K. Tang, “Radio-frequency transmission properties of carbon nanotubes in a field-effecttransistor configuration,” IEEE Electron Device Lett., vol. 27, no. 8,pp. 668–670, Aug. 2006.
[16] J. J. Plombon, K. P. OBrien, F. Gstrein, and V. M. Dubin, “High-frequencyelectrical properties of individual and bundled carbon nanotubes,” Appl.Phys. Lett., vol. 90, no. 6, p. 063 106, Feb. 2007.
[17] G. F. Close and H. S. Wong, “Fabrication and characterization of carbonnanotube interconnects,” in IEDM Tech. Dig., 2007, pp. 203–206.
[18] S. C. Jun, X. M. H. Huang, S. Moon, H. J. Kim, J. Hone, Y. W. Jin, andJ. M. Kim, “Passive electrical properties of multi-walled carbon nanotubesup to 0.1 THz,” New J. Phys., vol. 9, p. 265, Aug. 2007.
[19] L. Gomez-Rojas, S. Bhattacharyya, E. Mendoza, D. C. Cox,J. M. Rosolen, and S. R. P. Silva, “RF response of single-walledcarbon nanotubes,” Nano Lett., vol. 7, no. 9, pp. 2672–2675, Sep. 2007.
[20] A. Tselev, M. Woodson, C. Qian, and J. Liu, “Microwave impedancespectroscopy of dense carbon nanotube bundles,” Nano Lett., vol. 8, no. 1,pp. 152–156, Jan. 2008.
[21] M. G. Kang, J. H. Lim, S. H. Hong, D. J. Lee, S. W. Hwang, D. Whang,J. S. Hwang, and D. Ahn, “Microwave characterization of a single wallcarbon nanotube bundle,” Jpn. J. Appl. Phys., vol. 47, no. 6, pp. 4965–4968, Jun. 2008.
[22] C. Rutherglen, D. Jain, and P. Burke, “rf resistance and inductance ofmassively parallel single walled carbon nanotubes: Direct, broadbandmeasurements and near perfect 50 Ω impedance matching,” Appl. Phys.Lett., vol. 93, no. 8, p. 083 119, Aug. 2008.
[23] C. T. White and T. N. Todorov, “Carbon nanotubes as long ballisticconductors,” Nature, vol. 393, pp. 240–242, May 1998.
[24] J. Jiang, J. Dong, H. T. Yang, and D. Y. Xing, “Universal expression forlocalization length in metallic carbon nanotubes,” Phys. Rev. B, Condens.Matter, vol. 64, no. 4, p. 045 409, Jul. 2001.
[25] P. J. de Pablo, C. Gómez-Navarro, J. Colchero, P. A. Serena,J. Gómez-Herrero, and A. M. Baró, “Nonlinear resistance versus lengthin single-walled carbon nanotubes,” Phys. Rev. Lett., vol. 88, no. 3,p. 036 804, Jan. 2002.
[26] C. Berger, Y. Yi, Z. L. Wang, and W. A. de Heer, “Multiwalled carbonnanotubes are ballistic conductors at room temperature,” Appl. Phys. A,Mater. Sci. Process., vol. 74, no. 3, pp. 363–365, Mar. 2002.
[27] P. Sundqvist, F. J. Garcia-Vidal, F. Flores, M. Moreno-Moreno,C. Gomez-Navarro, J. S. Bunch, and J. Gomez-Herrero, “Voltage andlength-dependent phase diagram of the electronic transport in carbonnanotubes,” Nano Lett., vol. 7, no. 9, pp. 2568–2573, Sep. 2007.
[28] Y. Chai, Z. Xiao, and P. C. H. Chan, “Electron-shading effect on thehorizontal aligned growth of carbon nanotubes,” Appl. Phys. Lett., vol. 94,no. 4, p. 043 116, Jan. 2009.
[29] Z. Xiao, Y. Chai, Y. Li, M. Sun, and P. C. H. Chan, “Integration ofhorizontal carbon nanotube devices on silicon substrate using liquid evap-oration,” in Proc. 60th Electron. Compon. Technol. Conf., Las Vegas, NV,Jun. 2010, pp. 943–947.
[30] M. Sun, Z. Xiao, Y. Chai, Y. Li, and P. C. H. Chan, “Inductance propertiesof silicon-in-grown horizontal carbon nanotubes,” in Proc. 60th Electron.Compon. Technol. Conf., Las Vegas, NV, Jun. 2010, pp. 1329–1334.
[31] Y. Hayamizu, T. Yamada, K. Mizuno, R. C. Davis, D. N. Futaba,M. Yumura, and K. Hata, “Integrated three-dimensional microelectro-mechanical devices from processable carbon nanotube wafers,” Nat. Nan-otechnol., vol. 3, no. 5, pp. 289–294, May 2008.
[32] S. Frank, P. Poncharal, Z. L. Wang, and W. A. de Heer, “Carbon nano-tube quantum resistors,” Science, vol. 280, no. 5370, pp. 1744–1746,Jun. 1998.
[33] A. Bachtold, C. Strunk, J. Salvetat, J. Bonard, L. Forro, T. Nussbaumer,and C. Schonenberger, “Aharonov-Bohm oscillations in carbon nano-tubes,” Nature, vol. 397, pp. 673–675, Feb. 1999.
[34] M. Dresselhaus, G. Dresselhaus, and P. Eklund, Science of Fullerenes andCarbon Nanotubes. San Diego, CA: Academic, 1996.
[35] A. Nieuwoudt and Y. Massoud, “Understanding the impact of inductancein carbon nanotube bundles for VLSI interconnect using scalable model-ing techniques,” IEEE Trans. Nanotechnol., vol. 5, no. 6, pp. 758–765,Nov. 2006.
[36] Network Analysis Basics—Applying Error Correction To Network An-alyzer Measurements (AN 1287-3), Agilent Technol. Inc., Santa Clara,CA, 2002.
[37] D. M. Pozar, Microwave Engineering. Hoboken, NJ: Wiley, 2005.[38] X. Huo, K. J. Chen, and P. C. H. Chan, “Silicon-based high- Q inductors
incorporating electroplated copper and low- K BCB dielectric,” IEEEElectron Device Lett., vol. 23, no. 9, pp. 520–522, Sep. 2002.
[39] P. Rice, T. M. Wallis, S. E. Russek, and P. Kabos, “Broadband electricalcharacterization of multiwalled carbon nanotubes and contacts,” NanoLett., vol. 7, no. 4, pp. 1086–1090, Apr. 2007.
Minghui Sun received the B.S. degree in microelec-tronics from Peking University, Beijing, China, in2008 and the M.S. degree in electronic and com-puter engineering from the Hong Kong Universityof Science and Technology, Kowloon, Hongkong,in 2010. Her M.S. study focused on the fabricationand the radio-frequency characterization of carbonnanotubes.
She is currently an Analog Design Engineer withthe Singapore design team of Texas Instruments.
Zhiyong Xiao received the B.S. degree and the M.S.degree in microelectronics from Peking University,Beijing, China, in 2000 and 2003, respectively, andthe Ph.D. degree in electrical engineering from theHong Kong University of Science and Technology(HKUST), Kowloon, Hongkong, in 2008. His Ph.D.study focused on the design, the modeling, the fabri-cation, and the characterization of the silicon-basedmicrofuel cells.
He worked as a Postdoctoral Research Associateon the integration of carbon nanotube components on
silicon chips with the Department of Electronic and Computer Engineering,HKUST, for two years. He is currently a Research Engineer for a light-emitting-diode company on process integration.
Yang Chai received the Ph.D. degree from theHong Kong University of Science and Technology,Kowloon, Hongkong, in 2009.
He is currently working on the fabrication ofcarbon-related materials and carbon-based devices,including the testing and the characterization of re-sulting prototypes.
SUN et al.: INDUCTANCE PROPERTIES OF In Situ-GROWN HORIZONTALLY ALIGNED CNTs 235
Yuan Li received the B.S. degree in microelectronicsfrom Peking University, Beijing, China, in 2008 andthe M.S. degree in electronic and computer engineer-ing from the Hong Kong University of Science andTechnology, Kowloon, Hongkong, in 2010. Her M.S.study focused on the fabrication and the integrationof carbon nanotube field-effect transistors on siliconsubstrate and the electrical characterization of thetransistors.
Philip C. H. Chan (SM’97–F’07) received the B.S.degree in electrical engineering from the Universityof California, Davis, in 1973 and the M.S. andPh.D. degrees in electrical engineering from theUniversity of Illinois at Urbana-Champaign (UIUC),Champaign, in 1975 and 1978, respectively.
He started his career as a Postdoctoral Fellow andAssistant Professor with the UIUC. He later joinedIntel Corporation in the US and was promoted as aSenior Project Manager. In 1991, he was a Readerand a Founding Member with the Hong Kong Uni-
versity of Science and Technology (HKUST), where he became the ChairProfessor of the Department of Electronic and Computer Engineering. SinceSeptember 2003, he has been the Dean of Engineering with HKUST. Hehas also served as the Director of the Microelectronics Fabrication Facility,HKUST, and has received a total research funding of HK$71.7 million since hejoined the university. He has also been a key player in the commercialization ofthe HKUST knowledge and technology. He is currently the Deputy Presidentand Provost of Hong Kong Polytechnic University, Kowloon, Hongkong. Hisresearch interests include very-large-scale-integration devices, circuits andsystems, microelectronics, electronic packaging, integrated sensors, semicon-ductor device, and material research.
Prof. Chan is a Fellow of Hong Kong Institution of Engineering (HKIE). InHong Kong, he has served on various Innovation and Technology Commissionand HKIE committees, and the Electronics Committee of the Industry andTrade Department Council. He has advised the government on the setup ofthe Hong Kong Applied Science and Technology Research Institute CompanyLtd., where he currently serves in its board and is Chair of the TechnologyCommittee. He has also served as a panel member on the Research GrantCouncil and the University Grants Committee’s Research Assessment Panel.He has an extensive network in the US and has facilitated the collaborationbetween the HKUST and many topnotch engineering schools in the U.S.,including the University of Pennsylvania, Cornell University, and the Universityof Southern California. He also holds honorary positions in various universitiesin the Chinese mainland. He is the recipient of the Electrical and ComputerEngineering Distinguished Alumni Award from the UIUC in 2010.
