Probabilistic modelling of performance parameters of carbon nanotube transistors
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Probabilistic modelling of performance parameters of Carbon Nanotube transistors. Department of Electrical and Computer Engineering. By Yaman Sangar Amitesh Narayan Snehal Mhatre. Overview. Motivation Introduction CMOS v/s CNTFETs CNT Technology - Challenges

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Probabilistic modelling of performance parameters of Carbon Nanotube transistors

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Probabilistic modelling of performance parameters of carbon nanotube transistors

Probabilistic modelling of performance parameters of Carbon Nanotube transistors

Department of Electrical and Computer Engineering

By

Yaman Sangar

Amitesh Narayan

Snehal Mhatre


Overview

Overview

  • Motivation

  • Introduction

  • CMOS v/s CNTFETs

  • CNT Technology - Challenges

  • Probabilistic model of faults

  • Modelling performance parameters:

    • ION / IOFF tuning ratio

    • Gate delay

    • Noise Margin

  • Conclusion


Overview1

Overview

  • Motivation

  • Introduction

  • CMOS v/s CNTFETs

  • CNT Technology – Challenges

  • Probabilistic model of faults

  • Modelling performance parameters:

    • ION / IOFF tuning ratio

    • Gate delay

    • Noise Margin

  • Conclusion


Probabilistic modelling of performance parameters of carbon nanotube transistors

MOTIVATION: Why CNTFET?

  • Dennard Scaling might not last long

  • Increased performance by better algorithms?

  • More parallelism?

  • Alternatives to CMOS - FinFETs, Ge-nanowire FET, Si-nanowire FET, wrap-around gate MOS, graphene ribbon FET

  • What about an inherently faster and less power consuming device?

  • Yay CNTFET – faster with low power


Overview2

Overview

  • Motivation

  • Introduction

  • CMOS v/s CNTFETs

  • CNT Technology – Challenges

  • Probabilistic model of faults

  • Modelling performance parameters:

    • ION / IOFF tuning ratio

    • Gate delay

    • Noise Margin

  • Conclusion


Probabilistic modelling of performance parameters of carbon nanotube transistors

  • CNT is a tubular form of carbon with diameter as small as 1nm

  • CNT is configurationally equivalent to a 2-D graphene sheet rolled into a tube.

Carbon Nanotubes


Probabilistic modelling of performance parameters of carbon nanotube transistors

  • Single Walled CNT (SWNT)

  • Double Walled CNT (DWNT)

  • Multiple Walled CNT (MWNT)

  • Depending on Chiral angle:

  • Semiconducting CNT (s-CNT)

    • Metallic CNT (m-CNT)

Types of CNTs


Probabilistic modelling of performance parameters of carbon nanotube transistors

Properties of CNTs

  • Strong and very flexible molecular material

  • Electrical conductivity is 6 times that of copper

  • High current carrying capacity

  • Thermal conductivity is 15 times more than copper

  • Toxicity?


Probabilistic modelling of performance parameters of carbon nanotube transistors

CNTFET

  • How CNTs conduct?

  • Gate used to electrostatically induce carriers into tube

  • Ballistic Transport


Overview3

Overview

  • Motivation

  • Introduction

  • CMOS v/s CNTFETs

  • CNT Technology – Challenges

  • Probabilistic model of faults

  • Modelling performance parameters:

    • ION / IOFF tuning ratio

    • Gate delay

    • Noise Margin

  • Conclusion


Probabilistic modelling of performance parameters of carbon nanotube transistors

  • Simulation based Comparison between CMOS and CNT technology


Probabilistic modelling of performance parameters of carbon nanotube transistors

  • Simulation based Comparison between CMOS and CNT technology

Better delay


Probabilistic modelling of performance parameters of carbon nanotube transistors

  • Simulation based Comparison between CMOS and CNT technology

Better delay

At lower power!


Overview4

Overview

  • Motivation

  • Introduction

  • CMOS v/s CNTFETs

  • CNT Technology – Challenges

  • Probabilistic model of faults

  • Modelling performance parameters:

    • ION / IOFF tuning ratio

    • Gate delay

    • Noise Margin

  • Conclusion


Probabilistic modelling of performance parameters of carbon nanotube transistors

Major CNT specific variations

CNT density variation

Metallic CNT induced count variation

CNT diameter variation

CNT misalignment

CNT doping variation

  • Unavoidable process variations

  • Performance parameters affected

Challenges with CNT technology


Probabilistic modelling of performance parameters of carbon nanotube transistors

CNT diameter variation

CNT density variation

  • Current variation

  • Threshold voltage variation


Probabilistic modelling of performance parameters of carbon nanotube transistors

CNT doping variation

CNT Misalignment

  • Changes effective CNT length

  • Short between CNTs

  • Incorrect logic functionality

  • Reduction in drive current

  • May not lead to unipolar behavior


Probabilistic modelling of performance parameters of carbon nanotube transistors

Metallic CNT induced count variation

m-CNT

m-CNT

Current

s-CNT

s-CNT

  • Excessive leakage current

  • Increases power consumption

  • Changes gate delay

  • Inferior noise performance

  • Defective functionality

Vgs


Removal of m cntfets

Removal of m-CNTFETs

  • VMR Technique : A special layout called VMR structure consisting of inter-digitated electrodes at minimum metal pitch is fabricated. M-CNT electrical breakdown performed by applying high voltage all at once using VMR. M-CNTs are burnt out and unwanted sections of VMR are later removed.

  • Using Thermal and Fluidic Process: Preferential thermal desorption of the alkyls from the semiconducting nanotubes and further dissolution of m-CNTs in chloroform.

  • Chemical Etching: Diameter dependent etching technique which removes all m-CNTs below a cutoff diameter.


Overview5

Overview

  • Motivation

  • Introduction

  • CMOS v/s CNTFETs

  • CNT Technology – Challenges

  • Probabilistic model of faults

  • Modelling performance parameters:

    • ION / IOFF tuning ratio

    • Gate delay

    • Noise Margin

  • Conclusion


Probabilistic model of cnt count variation due to m cnts

Probabilistic model of CNT count variation due to m-CNTs

Probability of grown CNT count

  • ps= probability of s-CNT

  • pm= probability of m-CNT

  • ps = 1 - pm

  • Ngs= number of grown s-CNTs

  • Ngm= number of grown m-CNTs

  • N= total number of CNTs


Conditional probability after removal techniques

Conditional probability after removal techniques

  • Ns= number of surviving s-CNTs

  • Nm = number of surving m-CNTs

  • prs= conditional probability that a CNT is removed given that it is s-CNT

  • prm= conditional probability that a CNT is removed given that it is m-CNT

  • qrs= 1 - prs

  • qrm= 1 -prm


Overview6

Overview

  • Motivation

  • Introduction

  • CMOS v/s CNTFETs

  • CNT Technology – Challenges

  • Probabilistic model of faults

  • Modelling performance parameters:

    • ION / IOFF tuning ratio

    • Gate delay

    • Noise Margin

  • Conclusion


Probabilistic modelling of performance parameters of carbon nanotube transistors

  • ION / IOFF is indicator of transistor leakage

  • Improper ION / IOFF → slow output transition or low output swing

  • Target value of ION / IOFF = 104

Effect of CNT count variation on ION / IOFF tuning ratio


Probabilistic modelling of performance parameters of carbon nanotube transistors

Current of a single CNT

  • ICNT= ps Is+ pmIm

  • µ(ICNT) = psµ(Is)+ pmµ(Im)

  • ICNT=drive current of single CNT (type unknown)

  • Is =drive current of single s-CNT

  • Im= drive current of single m-CNT

  • ps= probability of s-CNT

  • pm= probability of m-CNT


Probabilistic modelling of performance parameters of carbon nanotube transistors

Ns= count of s-CNT

Nm= count of m-CNT

Is,on= s-CNT current, Vgs = Vds = Vdd

Is,off= s-CNT current, Vgs = 0 and Vds = Vdd

Im= m-CNT current, Vds = Vdd

ION / IOFF ratio of CNTFET


Probabilistic modelling of performance parameters of carbon nanotube transistors

ION / IOFF ratio of CNTFET

µ (Ns) = ps (1 - prs) N

µ (Nm) = pm(1 - prm) N


Probabilistic modelling of performance parameters of carbon nanotube transistors

Effect of various processing parameters on the ratio µ(ION) / µ(IOFF)

  • µ(ION) / µ(IOFF) is more sensitive to prm

  • µ(ION) / µ(IOFF) = 104 for prm > 1 – 10 -4 = 99.99 % for pm = 33.33%

1- prm


Overview7

Overview

  • Motivation

  • Introduction

  • CMOS v/s CNTFETs

  • CNT Technology – Challenges

  • Probabilistic model of faults

  • Modelling performance parameters:

    • ION / IOFF tuning ratio

    • Gate delay

    • Noise Margin

  • Conclusion


Probabilistic modelling of performance parameters of carbon nanotube transistors

Effect of CNT count variation on Gate delay


Probabilistic modelling of performance parameters of carbon nanotube transistors

= =


Probabilistic modelling of performance parameters of carbon nanotube transistors

Plot of v/s

= 0.3

N = 10

N = 20

N = 40

N = 30

N = 50


Probabilistic modelling of performance parameters of carbon nanotube transistors

Plot of v/s N

0.9

0.8

0.6

0.4

0.2

N


Overview8

Overview

  • Motivation

  • Introduction

  • CMOS v/s CNTFETs

  • CNT Technology – Challenges

  • Probabilistic model of faults

  • Modelling performance parameters:

    • ION / IOFF tuning ratio

    • Gate delay

    • Noise Margin

  • Conclusion


Probabilistic modelling of performance parameters of carbon nanotube transistors

Noise Margin of CNTFET


V il and v ih

VIL and VIH

pFET

  • Substituting= Vin, , and

  • =

  • Differentiating with respect to Vin and substituting -1

nFET


Probabilistic modelling of performance parameters of carbon nanotube transistors

VIL and VIH

For CMOS,

For CNTFET,

NML = VIL - 0

NMH = VDD – VIH


Overview9

Overview

  • Motivation

  • Introduction

  • CMOS v/s CNTFETs

  • CNT Technology – Challenges

  • Probabilistic model of faults

  • Modelling performance parameters:

    • ION / IOFF tuning ratio

    • Gate delay

    • Noise Margin

  • Conclusion


Conclusion

CONCLUSION

  • Modeled count variations and hence device current as a probabilistic function

  • Studied the affect of these faults on tuning ratio and gate delay

  • Inferred some design guidelines that could be used to judge the correctness of a process

  • Mathematically derived noise margin based on current equations – better noise margin than a CMOS


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