Thermal conductivity of Carbon NanotubesNavdeep Singh DhillonTheoretical overview of Thermal Conductivityin CNTsSome points I should make●Thermal conductivity = phonon + electron components●Ballistic transport behavior at small L and T (no scattering)●Quantization observed at low T●Studies help to elucidate the physics of thermal transport ●Phonon transport depends only on Radius●Electron transport also on Chirality1-D ballistic phonon system●Landauer energy fluxHotbathCold bathSVCNTPhonon modesPhonon energyPhonon groupvelocityPhonon distributionin the baths (BE)TransmissionprobabilityAnalytical formFrom wavevector to energy spaceAnalytical form for phononthermal conductivityLow energy phonon dispersoncurves for a (10,10) SWCNTAcoustic modesOptical modesTemperature dependence of phonon conductivityT --> 0 KT > 0 KQuantized value due to ACOUSTIC modesOptical modes come into playChirality independence of phonon transport●Optical mode energy gap depends on–radius R–Not on ChiralityElectonic contribution to thermal conductance●Electron (Fermi dist.)●Electron/Phonon statistics exactly similar at low T●Characteristic energy for electrons >> phonons●Phonon transport dominates at high TExperimental measurementof Thermal Conductivityin CNTsGreat Expectations●Theoretically predicted –1600-6000 W/mK●Experimentally measured–Individual SWCTs●3000 W/mK–Bundles●12-150 W/mK●Why the disparity?●Reasons–Models underestimate phonon scattering–Bundles might have flawed individual CNTs–Thermal contact resistance affects measurementsPhoto-Thermal measurement technique●High resolution measurement of thermal properties●Pulsed laser source focused on sample●Sample emits IR radiation●Model predicts properties of material based on phase lag and frequency dependence of emitted radiationMeasured values Vertically Aligned CNTsampleResistance predictions from modelTotal effective thermal resistance: 0.12 cm2 K/W (resolution of 0.01)Thermal interface resistance: 0.01 cm2 K/WCNT array Thermal Conductivity: 40.1 W/m KConclusions●Thermal resistance of CNTs vary over wide range●Significant dependence on CNT manufacturing techniques is observed●Application areas:–CNT thermal properties will affect performance of future nano-scale device–High conductivity CNT arrays could find use in IC cooling
View Full Document
Unlocking...