Carbon nanotubes (cnt) as interconnects for future

1. Analysis of Carbon Nanotubes (CNT)
as Interconnects for Future
VLSI Technology
Harish Peta
IMI2013002
VLSI Technology

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

3. 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

5. ITRS Roadmap for Cu Resistivity

6. 𝑅 = (𝜌𝑠𝑖𝑧𝑒 + 𝜌 𝑔𝑟𝑎𝑖𝑛)
𝑙
𝑤 𝐶𝑢ℎ 𝐶𝑢
𝐶𝑐 =
𝜀ℎ 𝐶𝑢 𝑙
(𝑑−𝑤 𝐶𝑢)

7. 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.

8. Types of CNTs
1. Single Wall CNT (SWCNT)

9. 2. Multi Wall CNT (MWCNT)

10. 3. Mixed Bundle of CNTs

11. 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.

12. RLC Equivalent Circuit of CNT

13. 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:
𝑵 𝒔𝒉𝒆𝒍𝒍 = 𝟏 + (𝑫 𝒐𝒖𝒕𝒆𝒓 − 𝑫𝒊𝒏𝒏𝒆𝒓)/𝟐𝜹
where 𝛿- van der Waals distance (𝛿= 0.34nm)
• Number of conduction channel per shell is given by:
𝑵 𝒄𝒉𝒂𝒏𝒏𝒆𝒍/𝒔𝒉𝒆𝒍𝒍 = (𝒂. 𝒅𝒊 + 𝒃)𝒑 𝒎 𝒅 > 6nm
= 𝟐. 𝒑 𝒎 𝒅< 6nm

14. where a = 0.1836 /nm, b = 1.275,
𝑑𝑖 is the shell diameter and
𝑝 𝑚 is the probability of the tube being metallic
• Any conducting channel provides either intrinsic resistance (𝑹𝒊) or
ohmic resistance (𝑹 𝒐) according to the CNT length ( l )
• Channel intrinsic resistance (𝑅𝑖) is a constant and given by:
𝑹𝒊 = 𝒉/𝟐𝒒 𝟐
• Ohmic resistance (𝑅 𝑜) depends on the diameter of the shell and the
tube length
𝑹 𝒐 =
𝒉
𝟐𝒒 𝟐 .
𝒍
𝝀
= 𝑹𝒊.
𝒍
𝝀
where h is the Planck’s constant,
q is the charge of an electron

15. • MFP of any shell depends on the diameter of that shell
𝝀 = (𝒗 𝑭. 𝒅𝒊/𝜶𝑻)
where α is the total scattering rate,
𝑇 is the temperature,
𝑣 𝐹 is the Fermi velocity of graphene
𝑹 𝒔𝒉𝒆𝒍𝒍 𝒅𝒊, 𝒍 = 𝑹𝒊 𝑵 𝒄𝒉𝒂𝒏𝒏𝒆𝒍/𝒔𝒉𝒆𝒍𝒍 𝒍 < 𝝀
= 𝑹 𝒐 𝑵 𝒄𝒉𝒂𝒏𝒏𝒆𝒍/𝒔𝒉𝒆𝒍𝒍 𝒍 > 𝝀
where 𝑑𝑖 is the diameter of the shell,
𝑙 is the tube length
λ is the mean free path (MFP)

16. • 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.

17. • 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.

18. Capacitance of Mixed CNT Bundle
• The CNT capacitance is produced from two sources
– Electrostatic capacitance (𝐶 𝐸)
𝑪 𝑬 =
𝟐𝝅
𝐥𝐧(
𝒚
𝒅
)
– Quantum capacitance (𝐶 𝑄)
𝑪 𝑸 =
𝟐𝒆 𝟐
𝒉𝒗 𝑭
where 𝑣 𝐹 = 𝐹𝑒𝑟𝑚𝑖 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑪 𝒃𝒖𝒏𝒅𝒍𝒆,𝒕𝒐𝒕𝒂𝒍 =
𝒊=𝟏
𝒏
(
𝑪 𝑬,𝒊. 𝑪 𝑸,𝒊
𝑪 𝑬,𝒊 + 𝑪 𝑸,𝒊
)

19. 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

20. • Intermediate Length Resistance

21. • Global Interconnects Resistance

22. • Local Interconnect Capacitance

23. • Intermediate Interconnect Capacitance

24. • Global Interconnect Capacitance

25. 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

26. 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