Delay and Power analysis of carbon nanotube interconnects

for VLSI Application

Author’s Name :

Mayank Kumar Rai ,Love Gupta ,S.SarkarPresented By: Love GuptaDept. of Electronics &

Instrumentation

INDEX1. Introduction

2. Dimensions of interconnect

3. Materials for Interconnect

4. Drawbacks of Copper

5. SWCNT – Introduction & Advantages

6. R,L,C calculation

7. Simulation of Results

8. Conclusion

9. References

INTRODUCTION

1. The interconnect has become a critical determiner of circuit performance in the deep sub-micron regime.

2. As the technology size is decreasing

the length of global interconnections

is increasing , which increases the

delay.15 20 25 30 35 40 45

Technology Node (nm)

Del

ay (s

econ

ds)

Global Interconnect (length=1mm)

Local Interconnect

Nominal Gate Delay

10-12

10-11

10-10

10-9

10-8

10-7

Traditional delay trends

K. Banerjee, et al., AMC, 2005

The wire linking transistors together is called interconnect

ρ= resistivity (m)

R = sheet resistance ( /)

l lR Rt w w

DIMENSIONS OF INTERCONNECT

Pitch = w + s Aspect ratio:

AR = t/w

Methods For Improving Propagation Delay

• By inserting buffers to drive large capacitive loads

• But single buffer is not a good solution , so a number of buffers need to be inserted at regular intervals of distance in interconnect , which are termed as repeaters.

Uniform minimum sized

Optimum sized

Tapered cascaded buffers

Repeater can be of different types

MATERIALSAluminum and copper are the two conductive materials currently used for on chip interconnections.

The main limitations of the aluminum-based process is its higher resistivity, compared to copper. The manufacturing difficulties related to Cu interconnections make it a more expensive than Al based interconnections, but this extra cost can be compensated by better performance.

DRAWBACKS OF COPPER

Increasing resistivity due to :

• The presence of highly resistive

diffusion barrier layer

• Surface scattering

• Enhanced grain boundary scattering.

What is a Carbon Nanotube?What is a Carbon Nanotube?What is a Carbon Nanotube?What is a Carbon Nanotube?CNT is a tubular form of carbon with diameter as small as 1nm.Length: few nm to microns.

CNT is configurationally equivalent to a two dimensional graphene sheet rolled into a tube.

• Single Wall CNT (SWCNT) Only one shell Diameter ranging from 0.4nm to 4nm

• Multiple Wall CNT (MWCNT)

Types of CNTs :

Having several concentric shells and diameterranging from several nanometers to tens of nanometers.

http://www.nature.com

ADVANTAGES OF SWCNT

CNTs exhibit extraordinary strength and unique electrical properties, and are efficient conductors of heat and have large current carrying capacity.

CNT Cu

Max current density (A/cm2)

>1x109

Wei, et al., APL, 2001

~1x107

Thermal conductivity (W/mK)

5800Hone, et al., Phys. Rev. B,

1999

385

Mean free path (nm)@ room temp

>1000McEuen, et al., Trans.

Nano., 2002

40

CNTs have long MFPs (of the order of several micrometers) Which provide low resistivity and possible ballistic transport in short length interconnects.

EQUIVALENT CIRCUIT MODEL FOR AN ISOLATED SWCNT

• RF=h/4e2 ~6.45K

• RCNT=(h/4e2)L/L0 Diffusive transport (L>> L0)

Total resistance of CNTs a) Fundamental one-dimensional system

(cnt) contact resistance,b) scattering resistance andc) imperfect metal nano tube contact

resistance

Ballistic transport (L<L0)Where L0 is the MFP

EC )/ln(/2 dy=

CAPACITANCE: a) Electrostatic capacitance (CE ) b) quantum capacitance (CQ )

, CQ=2e2/h~100aF/um~30aF/um

dyln

2

fveh22

LM= Lk=

fv 8x105m/s

a CNT has four conducting channels so the effective quantum capacitance resulting from four parallel capacitances CQ is given by 4 .

= 16nH/m

=

Total Inductance :1. Magnetic Inductance2. Kinetic Inductance

• Resistance of a CNT-Bundle

R bundle=R isolated/n CNT

Capacitance of a CNT-bundle

Where is 4 times of CQ.

iQC

Inductance of CNT-bundle L< L0CNT with L bundle=(LM+Lk/4)/nCNT and (b) L>> L0CNT with L bundle=LM/nCNT.

Bundle of SWCNTs

Delay of Copper and CNT at global and intermediate lengths(Tech:32nm)

Spice Simulation Results

Voltage-scaled repeaters for long interconnections

We use repeaters to reduce delay, but they increases the power dissipation in VLSI circuits ,so by using voltage scaled repeaters we can considerably reduce power dissipation.

Voltage scaling

Power vs Vdd (Tech:32nm)

At local level Cu Interconnect gives better performances than a bundle of SWCNT.

Where as a bundle of SWCNT has better efficiency at intermediate level and Global level.

Where as, power decreases with lower value of Vdd and increases with increase in number of repeaters due to higher value of capacitance. For better performance power supply should be balance, with voltage scaled repeaters.

Conclusion

REFERENCES[1] W. Steinhogl, G. Schindler, G. Steinlesberger, M. Traving, and M. Engelhardt, “Comprehensive study of the resistivity of copper wires with lateral dimensions of 100nm and smaller,” Journal of Applied Physics, vol. 97,pp. 5186-5189, 2005.[2] P. L. McEuen, M. S. Fuhrer, and H. K. Park, “Single-walled carbon nanotube electronics,” IEEE Trans. Nanotechnology, vol. 1, pp. 78-85, 2002.[3] F. Kreupl, et al., “Carbon Nanotubes in Interconnect Applications,” Microelectronic Engineering, vol.64 pp. 399-408, 2002.[4] J. Li, et al., "Bottom-up Approach for Carbon Nanotube Interconnects," Applied Physics Letters, Vol. 82, pp. 2491-2493, April 2003.[5] A. Thess, et al., “Crystalline Ropes of Metallic Carbon Nanotubes”, Science, Vol. 273, pp. 483-487, 1996.[6] J. Li, et al., "Carbon Nanotube Interconnects: A Process Solution", IEEE Intl. Interconnect Tech. Conf. pp. 271-272, 2003.[7] M. Nihei, et al., “Carbon Nanotube Vias for Future LSI Interconnects,”IEEE Intl Interconnect Tech Conf , pp.251-253, 2004.[8] P. J. Burke, “Luttinger Liquid Theory as a Model of the Gigahertz Electrical Properties of Carbon Nanotubes”, IEEE Trans. Nanotechnology, Vol. 1, pp.129-144, 2002.[9] P. L. McEuen, et al., “Single-Walled Carbon Nanotube Electronics,” IEEE Trans. Nanotechnology, Vol. 1, pp. 78-85, 2002.[10] N. Srivastava and K. Banerjee, “Performance analysis of carbon nanotube interconnects for VLSI applications,” IEEE/ACM Intl. Conf. on ICCAD , pp. 383-390, 2005.

THANK YOU

Ballistic transport (L<L0) Diffusive transport (L>> L0)

MODELPDISTRIBUTED MODEL

Different types of repeaters