Analysis of Carbon Nanotubes (CNT) as Interconnects for Future

VLSI Technology

Harish PetaIMI2013002

VLSI Technology

OVERVIEW

• Introduction• Carbon Nanotubes: Potential Solution• Analysis of Mixed Bundle CNTs• Comparison with Cu Interconnects• Summary• References

Introduction

• Cu has a higher M.P (1,357 K) than Al (933K), which gives Cu the advantage over aluminum in electromigration and stress migration as well.

• Device performance improves as gate length, gate dielectric thickness, and junction depth are scaled down.

• As the dimensions are reaching mean free path of Cu, the resistivity is increasing with– Enhanced grain and surface scattering– Larger interconnect length

ITRS Roadmap for Cu Resistivity

Carbon Nanotubes: Potential Solution

• CNTs can be thought of being made by rolling up a single atomic layer of Graphene sheet to form a seamless cylinder with length-to-diameter ratio of up to 132,000,000:1.

• Depending on the direction in which the CNTs are rolled up (Chirality), they demonstrate either metallic or semiconducting properties.

• High mechanical, thermal strength, high thermal conductivity and large current carrying capacity in the comparison with Cu interconnects.

Types of CNTs

1. Single Wall CNT (SWCNT)

2. Multi Wall CNT (MWCNT)

3. Mixed Bundle of CNTs

Analysis of Mixed Bundle CNTs

• Bundle CNTs has a very low resistance compared to high resistance (6.45 kΩ) of SWCNT.

• A dense CNT bundle local interconnect with ideal metal nanotube contacts has resistance much lower than that of a Cu interconnect of identical dimensions.

• For small lengths (L), especially for L < λ, the large contact resistance dominates the overall CNT resistance.

RLC Equivalent Circuit of CNT

Resistance of Mixed CNT-bundle

• The resistance of an MWCNT or an SWCNT is determined by two factors: the conducting channels per shell and the number of shells.

• All SWCNT consists of only one shell.• Number of shells in an MWCNT is determined by the outer

diameter and inner diameter of the tube:

where - van der Waals distance (= 0.34nm)• Number of conduction channel per shell is given by:

> 6nm= < 6nm

where a = 0.1836 /nm, b = 1.275, is the shell diameter and is the probability of the tube being metallic

• Any conducting channel provides either intrinsic resistance () or ohmic resistance () according to the CNT length ( l )

• Channel intrinsic resistance () is a constant and given by:

• Ohmic resistance () depends on the diameter of the shell and the tube length

where h is the Planck’s constant,q is the charge of an electron

• MFP of any shell depends on the diameter of that shell

where α is the total scattering rate, is the temperature, is the Fermi velocity of graphene

< = >

where is the diameter of the shell, is the tube lengthλ is the mean free path (MFP)

• Since the resistance of a single CNT (SWCNT or MWCNT) is very high, a bundle of CNTs should be used as interconnects

• Figure plots the variation in the resistance of a 200μm long mixed bundle of CNTs with variation in the average diameter of the tubes.

• The resistance of the bundle is inversely proportional to the density of CNTs in the bundle.

• It is clear that the diameter of the tubes and the tube density in a bundle can be optimized to yield the minimum bundle resistance.

Capacitance of Mixed CNT Bundle

• The CNT capacitance is produced from two sources – Electrostatic capacitance ()

– Quantum capacitance ()

where

Comparison with Cu Interconnects

• Local Interconnect Resistance (l ≤ λ) – CNTs in the bundle operate in the ballistic region and has a

high value of length independent intrinsic resistance associated with them

• Intermediate Length Resistance

• Global Interconnects Resistance

• Local Interconnect Capacitance

• Intermediate Interconnect Capacitance

• Global Interconnect Capacitance

Summary

• Analyzed the applicability of CNT bundles as interconnects of future VLSI circuits

• Bundles of CNTs have smaller resistances for Intermediate and Global interconnects but for Local interconnect, the CNT bundle resistance is higher than Cu

• Resistance of CNT bundle interconnects can be optimized by varying the average diameter of CNTs and the density of tubes in the bundle

• Capacitances of CNT bundles are marginally smaller for all the interconnects

References• [1] Yograj Singh Duksh, Brajesh Kumar Kaushik, Sankar Sarkar and Raghuvir

Singh, “Performance comparison of carbon nanotube, nickel silicide nanowire and copper VLSI interconnects. Perspectives and challenges ahead”, Journal of Engineering, Design and Technology Vol. 8 No. 3, 2010.

• [2] Tarun Parihar and Abhilasha Sharma, “A comparative study of Mixed CNT bundle with Copper for VLSI Interconnect at 32nm”, International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013.

• [3] Naushad Alam, A. K. Kureshi, Mohd. Hasan and T. Arslan, “Analysis of Carbon Nanotube Interconnects and their Comparison with Cu Interconnects”, IMPACT-2009.

• [4] Tafseer Alam, Rohit Dhiman, Rajeevan Chandel and Dhrub Solanki, “Mixed Carbon Nanotube Bundle: Capacitance Analysis and Comparison with Copper Interconnect”, PROCEEDINGS OF ICETECT 2011.

• [5] www.wikipedia.org• [6] www.semiwiki.com