Electro-thermal transport in metallic single-wall carbon nanotubes for interconnect applications

Pop, Eric; Mann, David J.; Reifenberg, John P.; Goodson, Kenneth E.; Dai, Hongjie

doi:10.1109/iedm.2005.1609321

Cited by 49 publications

(59 citation statements)

References 15 publications

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“…An analytic expression for the temperature profile T(x) along the SWNT can first be obtained if we make the simplifying assumption of uniform heat generation along the tube, p' ≈ I 2 (R-R C )/L where R is the total electrical resistance of the nanotube and R C is the combined electrical resistance of the two contacts. This is reasonable, given the relatively flat expected temperature profiles, especially in longer tubes [17,21] and yields:…”

Section: Joule Heating and Breakdown In Airmentioning

confidence: 97%

“…3 above. Using the finite-element model described in the later sections of this work we have found that the breakdown voltage of SWNTs shorter than 1 µm is consistent with a contact thermal resistance R C,Th ≈ 5 × 10 6 K/W [11,21], however more detailed future efforts must be made to investigate electro-thermal transport in such short metallic SWNTs. In addition, we note that when the electrical resistance of the contacts (R C ) is significant, the breakdown voltage in Eq.…”

Section: Joule Heating and Breakdown In Airmentioning

confidence: 99%

“…We note the current saturation close to 20 µA, and the subsequent breakdown of this tube when its suggests that all nanotubes longer than about 1 µm (the length range considered in this study) have relatively flat temperature profiles under Joule heating at high bias [21]. Nevertheless, our model relies on a complete discretization of all equations previously mentioned along the length of the nanotube, and the MFPs and temperature profile are computed at each point.…”

Section: Current-voltage Characteristicsmentioning

confidence: 99%

“…Figure 1 shows a schematic of the SWNT-on-substrate layout used in the experiments and the model presented here. The heat conduction equation along the length of a current-carrying SWNT, including heat generation from Joule self-heating and heat loss to the substrate is [21]:…”

Section: Joule Heating and Breakdown In Airmentioning

confidence: 99%

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Electrical and thermal transport in metallic single-wall carbon nanotubes on insulating substrates

Pop

Mann

Goodson

et al. 2007

Journal of Applied Physics

319

307

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We analyze transport in metallic single-wall carbon nanotubes (SWNTs) on insulating substrates over the bias range up to electrical breakdown in air. To account for Joule self-heating, a temperature-dependent Landauer model for electrical transport is coupled with the heat conduction equation along the nanotube.The electrical breakdown voltage of SWNTs in air is found to scale linearly with their length, approximately as 5 V/µm; we use this to deduce a thermal conductance between SWNT and substrate g ≈ 0.17 ± 0.03 WK -1 m -1 per tube length, which appears limited by the SWNT-substrate interface rather than the thermal properties of the substrate itself. We examine the phonon scattering mechanisms limiting electron transport, and find the strong temperature dependence of the optical phonon absorption rate to have a remarkable influence on the electrical resistance of micron-length nanotubes. Further analysis reveals that unlike in typical metals, electrons are responsible for less than 15% of the total thermal conductivity of metallic nanotubes around room temperature, and this contribution decreases at high bias or higher temperatures. For interconnect applications of metallic SWNTs, significant self-heating may be avoided if power densities are limited below 5 µW/µm, or if the SWNT-surrounding thermal interface is optimized.Contact: epop@stanfordalumni.org, hdai@stanford.edu 2

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Section: Joule Heating and Breakdown In Airmentioning

confidence: 97%

Section: Joule Heating and Breakdown In Airmentioning

confidence: 99%

Section: Current-voltage Characteristicsmentioning

confidence: 99%

Section: Joule Heating and Breakdown In Airmentioning

confidence: 99%

See 2 more Smart Citations

Electrical and thermal transport in metallic single-wall carbon nanotubes on insulating substrates

Pop

Mann

Goodson

et al. 2007

Journal of Applied Physics

319

307

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show abstract

“…This is much smaller than g ~ 100 mWK -1 m -1 estimated for tubes lying on solid SiO 2 substrates, 6 indicating little heat sinking by the gaseous molecules around the nanotube. The combined SWNT heat loss to the gas ambient and to radiation is estimated to be < 2 % of the power dissipation at all relevant temperatures.…”

mentioning

confidence: 84%

Thermally and Molecularly Stimulated Relaxation of Hot Phonons in Suspended Carbon Nanotubes

et al. 2006

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The high-bias electrical transport properties of suspended metallic single-walled carbon nanotubes (SWNTs) are investigated at various temperatures in vacuum, in various gases and when coated with molecular solids. It is revealed that non-equilibrium optical phonon effects in suspended nanotubes decrease as the ambient temperature increases. Gas molecules surrounding suspended SWNTs assist the relaxation of hot phonons and afford enhanced current flow along nanotubes. Molecular solids of carbon dioxide frozen onto suspended SWNTs quench the non-equilibrium phonon effect. The discovery of strong environmental effects on high current transport in nanotubes is important to high performance nanoelectronics applications of 1D nanowires in general.* E-mail: hdai@stanford.edu. 2The effect of environment on the electrical transport properties of small structures is an interesting topic with implications to a wide range of applications, from high performance nanoscale electronic devices and interconnects to nanosensors. Thus far, it has been largely unexplored how extrinsic factors affect high field electron transport in 1D nanostructures, and how to exploit them to tune and manipulate the high-current carrying abilities of 1D materials. As an extreme example, it has been shown recently 1 that freely suspended SWNTs in vacuum (in an isolated environment) display negative differential conductance (NDC) and drastically reduced current levels compared to nanotubes lying on solid substrates, 2,3 caused by substantial self-heating and scattering by non-equilibrium optical phonons (OPs) in the suspended isolated SWNTs. and always observed their hallmark negative differential conductance (NDC) behavior at high biases (Fig. 2a). 1 Interestingly, the I-V curves taken at different T 0 tend to converge in the high bias regime, and NDC appears less pronounced at higher T 0 (Fig. 2a). To understand the I-V data, we adopt and extend a recently introduced electro-thermal model for suspended SWNTs. 1 Briefly, the resistance of a SWNT under self-heating can be written aswhere R c is the contact resistance and where κ th is the SWNT thermal conductivity, p'= I 2 (R-R c )/L is the Joule heating per unit length, A=πdb is the cross-sectional area (b~0.34 nm: tube wall thickness) and g is the net heat loss by radiation and heat conduction per unit length. With κ th vs. T as fitting parameters, we solve Eqs. (1) and (2) iteratively until the temperature profile at each point along the SWNT converges within 0.1 K, while obtaining the best current fit with experimental data, at every bias. This temperature profile corresponds to AC phonons 4 (T ac ), which are the main heat carriers in the temperature range considered. 7 We capture the non-equilibrium OP effects in suspended SWNTs with an effective OP temperaturewhere the non-equilibrium phonon coefficient α > 0. The physical picture is that OP phonons emitted by hot electrons relax by decay into AC modes (T op to T ac ) that are subsequently carried out of the tube through the contacts (T ac to...

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Temperature dependant crosstalk analysis in coupled single‐walled carbon nanotube (SWCNT) bundle interconnects

Kumar

Sarkar

2014

Circuit Theory & Apps

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The temperature‐dependent, crosstalk‐induced, noise voltage waveform and its frequency spectrum, in capacitive coupled single‐walled carbon nanotube (SWCNT) bundle interconnects, at the far end of victim line, have been analyzed at 22‐nm technology node. A similar analysis is performed for copper interconnects and a comparison is made between the results of these two analyses. The SPICE simulation results reveal that at temperature variations ranging from 300 to 500 K, compared with conventional metal (copper) conductors, crosstalk noise voltage levels in CNT, at the far end of victim line, are significantly low. Simulated results further reveal that, with rise in interconnect temperatures, compared with copper interconnects, coupled interconnects of SWCNT bundle filter more noise frequency components. Based on these comparative results, an improved model for extracting inter‐bundle, real life, coupling capacitances between SWCNT bundles has been proposed. Copyright © 2014 John Wiley & Sons, Ltd.

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Electro-thermal transport in metallic single-wall carbon nanotubes for interconnect applications

Cited by 49 publications

References 15 publications

Electrical and thermal transport in metallic single-wall carbon nanotubes on insulating substrates

Electrical and thermal transport in metallic single-wall carbon nanotubes on insulating substrates

Thermally and Molecularly Stimulated Relaxation of Hot Phonons in Suspended Carbon Nanotubes

Temperature dependant crosstalk analysis in coupled single‐walled carbon nanotube (SWCNT) bundle interconnects

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