Size and temperature effects on the resistance of copper and carbon nanotubes nano-interconnects

Chiariello, Andrea G.; Miano, G.; Maffucci, Antonio

doi:10.1109/epeps.2010.5642555

Cited by 25 publications

(18 citation statements)

References 10 publications

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“…where the production term q = J 2 r is the volumetric heat generated by Joule effect (J being the rms value of the current density), k is the thermal conductivity of the conductor, and L H is the thermal heating length. The latter may be expressed as [18] L H ¼ ffiffiffiffiffiffiffiffiffiffi ffi kA k ILD S r ; (15) being A as the conductor cross-section and S as a shape factor given by…”

Section: Coupled Thermal-electrical Modelmentioning

confidence: 99%

“…In the low frequency regime and assuming that the effects of the intershell tunneling between adjacent shells are not important, the electrical behavior of the CNT bundles is governed by the semi‐classical transport equation, based on Boltzmann equation . The TL model for CNT interconnects has been derived in by coupling Maxwell equations to this transport equation, assuming quasi‐TEM propagation. This circuital model is valid for low bias conditions (longitudinal electric field < 0.54 V/µm) and for frequencies up to hundreds of GHz .…”

Section: Modeling Nano‐interconnectsmentioning

confidence: 99%

“…Assuming steady‐state condition, the spatial distribution of temperature along an interconnect is governed by the heat equation

\frac{d^{2} T (x)}{d x^{2}} - \frac{T (x)}{L_{H}^{2}} = - \frac{q}{k},

where the production term q = J 2 ρ is the volumetric heat generated by Joule effect ( J being the rms value of the current density), k is the thermal conductivity of the conductor, and L H is the thermal heating length. The latter may be expressed as

L_{H} = \sqrt{\frac{k A}{k_{ILD} S}},

being A as the conductor cross‐section and S as a shape factor given by

S_{italictrace} = {([], \frac{1}{2} ln ((), \frac{W + d}{W}) + \frac{t_{ILD} - d / 2}{W + d})}^{- 1}, S_{italicvias} = \frac{2 π}{ln (4 t_{italicILD} / D)},

for a trace and for a via, respectively, (note that d is the trace separation). The simple electro‐thermal model adopted in this paper comes from coupling (14) to the circuit model described previously for the different types of interconnects.…”

Section: Modeling Nano‐interconnectsmentioning

confidence: 99%

“…Taking into account the typical values of rms currents predicted by ITRS at each level , and assuming metal #1 level to be at 378 K (see ), the distribution of temperature over the stack layer is computed by using the electro‐thermal model introduced in Section 2 and plotted in Figure . The thermal parameters for Cu and CNT are given in , whereas for GNRs, we assumed a thermal conductivity of 5000 w/m/K. As shown in Figure , in the Cu case, the temperature of layer #12 rises to about 550 K, whereas for the hybrid CNT realizations, layer #12 operates at 480 K.…”

Section: Effects Of Temperature Change On Electrical Performancementioning

confidence: 99%

“…Following the stream of what is performed in (, here, we develop a simple but effective model in the frame of the Transmission Line (TL) theory. In the low frequency regime and neglecting the intershell tunneling between adjacent CNTs or GNRs, the electrical behavior of the carbon interconnects is governed by the semi‐classical transport equation and by Maxwell equations .…”

Section: Introductionmentioning

confidence: 99%

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Temperature effects on electrical performance of carbon‐based nano‐interconnects at chip and package level

Chiariello

Maffucci

Miano

2013

Int J Numerical Modelling

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This paper investigates the electrical performance of innovative carbon-based nano-interconnects made by carbon nanotubes and graphene nanoribbons. The electronic transport in the carbon materials is modeled in the frame of the Transmission Line theory, where the classical per-unit-length circuital parameters are corrected by new terms arising from the quantistic nature of the transport. These parameters are related to the number of the conducting channels and the mean free path, which in turn, are expressed as functions of temperature and size. By coupling this model to the heat equation, a simple electro-thermal model is derived. Case-studies are carried out with reference to 22-nm technology node applications. Copyright ?????? 2013 John Wiley & Sons, Ltd. Copyright ?????? 2013 John Wiley & Sons, Ltd

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Section: Coupled Thermal-electrical Modelmentioning

confidence: 99%

Section: Modeling Nano‐interconnectsmentioning

confidence: 99%

“…Assuming steady‐state condition, the spatial distribution of temperature along an interconnect is governed by the heat equation

\frac{d^{2} T (x)}{d x^{2}} - \frac{T (x)}{L_{H}^{2}} = - \frac{q}{k},

L_{H} = \sqrt{\frac{k A}{k_{ILD} S}},

being A as the conductor cross‐section and S as a shape factor given by

S_{italictrace} = {([], \frac{1}{2} ln ((), \frac{W + d}{W}) + \frac{t_{ILD} - d / 2}{W + d})}^{- 1}, S_{italicvias} = \frac{2 π}{ln (4 t_{italicILD} / D)},

Section: Modeling Nano‐interconnectsmentioning

confidence: 99%

Section: Effects Of Temperature Change On Electrical Performancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Temperature effects on electrical performance of carbon‐based nano‐interconnects at chip and package level

Chiariello

Maffucci

Miano

2013

Int J Numerical Modelling

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Modeling a copper/carbon nanotube composite for applications in electronic packaging

Feng

Burkett

2015

Computational Materials Science

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High‐speed sub‐threshold operation of carbon nanotube interconnects

Sathyakam¹,

Mallick²,

Saxena³

2019

IET Circuits, Devices & Systems

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Sub-threshold voltage operated circuits are the future for ultra-low-power applications. These circuits are inherently slow due to the very small sub-threshold currents. Here, the authors propose two approaches for improving the speed of SWCNT bundle interconnects driven by CNTFET-based circuits under sub-threshold conditions. First, the authors modulate the channel length of the CNTFETs that are used in the driver circuits to increase sub-threshold output current. The output current is maximum when the channel length is optimised to 15 nm. Second, the authors design driver circuits made of CNTFET-based inverters and transmission gates for SWCNT bundle interconnects at sub-threshold voltages. The authors consider five different configurations of the driver and load circuits. SPICE simulations show that transmission gates play a vital role in driver circuits by reducing the propagation delay and increasing the switching speed at high frequencies. Finally, the authors perform temperature-dependent analysis of the best cases from the proposed circuits and show that the propagation delay and power dissipated by them increases drastically at increased temperatures up to 500 K. 2 CNTFET current model CNTFET is regarded as the most advanced device which has similarities of MOSFET but has an advantage of working in

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Size and temperature effects on the resistance of copper and carbon nanotubes nano-interconnects

Cited by 25 publications

References 10 publications

Temperature effects on electrical performance of carbon‐based nano‐interconnects at chip and package level

Temperature effects on electrical performance of carbon‐based nano‐interconnects at chip and package level

Modeling a copper/carbon nanotube composite for applications in electronic packaging

High‐speed sub‐threshold operation of carbon nanotube interconnects

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