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Horizontally aligned carbon nanotube bundles forinterconnect application: diameter-dependent

contact resistance and mean free path

Mohan Lal

Yang Chai1, Zhiyong Xiao and Philip C H Chan

Nanotechnology 21 (2010)

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O utline

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W hat is Carbon Nanotube(CNT)

Allotrope of CarbonRolled up sheet of

graphene

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Resistance dependence of CNT on itsD iameter

Rlow =Ri + Rc if lb ap(1)Rlow =Ro + Rc if lb > ap(2)

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Abstract

Fabrication of horizontally aligned carbonnanotube (CNT) bundlesBy controlling the catalyst thickness, fabricated

CNT with different diametersMeasured the resistances of the CNTs as afunction of the length and the diameterD ependence of the contact resistance on CNT

diameter was extracted from the resistance plotsValidated the relationship between the diameterand the mean free path of the CNT.

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Fabrication of Horizontally aligned CNT

Started with p-type doped silicon substrate.5000 SiO2 layer wasgrown on the siliconsubstrate.The oxide patterns were formed byphotolithography and reactive ion etching.

5 nm Fe was then deposited by e-beamevaporation techniques as the catalyst for theCNT growth.Excessive catalyst was removed in an acetonelift-off leaving catalyst only in thephotolithography patterned area.Samples into P ECVD system to grow the CNTs.

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Fabrication of the deviceThe growth temperature is 850 C

W orking pressure is 8.5 Torr.

Methane is used as a carbon source

and hydrogen is used as carrier gas toavoid the over decomposition of methane.

The growth time duration is 2 minExtra insulation layer (Si O 2) layer wasgrown over substrate for electrical

measurements on

The two-terminal resistance teststructure was completed by ebeamevaporating Ti/Au electrodes on topof the horizontally aligned CNTbundles

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Site D ensityThe catalyst thickness of Fe catalystare 5, 3 and 1.2 nm, respectively.The size of nano-particles determinesthe diameter of the CNT. The thickercatalyst makes larger nano-particle.The CNT bundles from 5 nm thick

catalysts have larger diameter, in therange of 25 35 nm and 1.2 nm thickcatalysts, their diameter distributionis in the range of 5 7 nm.The catalyst thickness determines notonly the diameter of the CNT but alsothe site density of the CNT bundles.St = n 4 (d/2)3 /3,From this Site density of the CNTbundles per unit width to beproportional to t/d 2Experimentally: 5 nm : 12 m 1 3 nm : 45 m 1 1.2 nm : 103 m 1

5 nm

1.2 nm

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Resistance statistical studyThe CNT bundles from a 1.2 nmthick catalyst exhibit lowerresistance because of the higherdensity.The average resistance of thesingle CNT is 33.08 k 1500Assuming that the inner walls of the CNT does not contribute to theoverall conductanceStill much larger than theresistance of a 1 D quantum wire R0(13 k)

Probable reasons Imperfect contact between

CNT and metal

Phonon scattering in thediffusive region.

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Investigation

The resistance of a single CNT consists of three parts:1. Intrinsic quantum resistance R0 = h/(2e2 ) resulting from the carrier

scattering between a one-dimensional and three-dimensionalconductor,

2. Resistance in the diffusion region caused by phonon scatteringhL/(4e2 eff ), where L is the length and eff is the effective MFP of the CNT

3. Imperfect contact resistance( Rcontact )

Total resistance of a single CNT is described byR1 = 2Rcontact + R0(1 + L/ eff )/N(d)

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The intercept of the R L plot with the Y -axis is the sum of the i m perfect contact resistance and quantumresistanceRcontact = [Rintercept R0 /N(d)]/2.The extracted imperfect contactresistance between the CNTand Ti/Au electrode is alsodiameter-dependent, as shown

in figure 4(b). Thesmallerdiameter CNT has largercontact resistance because of the current crowding effect atthe smaller interface area.

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Conclusion

D emonstrated a technique to grow horizontally alignedCNT bundles using the P ECVD method.The relationship between resistance and catalyst thickness(diameter) was investigated.W e extracted the diameter-dependent contact resistancebetween the CNT and Ti/Au metal electrode.The relationship between the diameter and the MFP isexperimentally validated.The larger-diameter CNT from a thicker catalyst has smallercontact resistance and longer MFP, while its site density issmaller than the CNT from a thinner catalyst.These fundamental studies help to understand the CNTparameters for future interconnect applications.