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Ballistic Transport in Schottky-Barrier andMOSFET-like Carbon Nanotube Field EffectTransistors: Modeling, Simulation and AnalysisPresented by:

Protik DasExam Roll: 2240

Outline

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Carbon Nanotube Field Effect Transistor (CNTFET)

NEGF Formalism Results

Quantum Effects I-V Characteristics Scaling Effects

Objective

Analysis of ballistic transport in CNTFETs. Comparison of performance between

Schottky-Barrier & MOSFET-like CNTFETs.

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Carbon Nanotube (CNT)

Rolled up Graphene sheet

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A spinning Carbon Nanotube

CNT Types

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(a) zigzag type

(b) armchair type

Field Effect Transistor (FET)

The Field-Effect Transistor (FET) is a transistor that uses an electric field to control the conductivity of a channel in a semiconductor material.

A generic FET structure

Showed in figure.

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Keyword: Ballistic Transport

Ballistic Transport is the transport of electrons in a medium with negligible electrical resistivity due to scattering. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds.

Simply, Ballistic Transport is the transport of electrons in a channel considering no impurity or scatterer in the region.

Ballistic Transport can be considered when mean free path of an electron is greater than channel length. i. e., λ >> L

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Carbon Nanotube FET (CNTFET) A Carbon Nanotube Field Effect Transistor (CNTFET)

refers to a field effect transistor that utilizes a single carbon nanotube or an array of carbon nanotubes as the channel material.

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Why Carbon Nanotube?

Near ballistic transport Symmetric conduction/valence bands Direct bandgap Small size Confinement of charge inside the nanotube allows ideal

control of the electrostatics

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CNTFET Structures

Back Gated CNTFETs Top Gated CNTFETs Vertical CNTFETs

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Back Gated CNTFET

Top Gated CNTFET Vertical CNTFET

CNTFET Operation

Schottky-Barrier CNTFET Schottky-Barrier is formed between Source/Drain and channel Direct tunneling through the Schottky barrier at the source-

channel junction Barrier width is controlled by Gate voltage

MOSFET-like/Doped Contact CNTFET Heavily doped Source and Drain instead of metal Barrier height is controlled by gate voltage

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Schottky-Barrier CNTFET

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Doped Contact CNTFET

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NEGF Formalism Review

Retarded Green’s

function in matrix form,

Hamiltonian matrix

for the subbands,

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NEGF Formalism Review (contd.) Current,

Where T(E) is

the transmision

coefficient,

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NEGF Formalism Review (contd.)

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Self-consistantly solving NEGF & Poisson’s Equation

Device Structure & Parameters

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Channel length, Lch = 20nm

Source/Drain length, LSD = 30nm

Oxide Thickness, tOX = 2nm Dielectric Constant, k = 16 Source/Drain Doping, NSD = 1.5/nm CNT (13, 0) diameter, 1.01nm Bandgap 0.68eV

Results

Quantum Effects Quantum-Mechanical Interference Quantum Confinement Tunneling

I-V characteristics Effect of Gate Dielectric Constant Scaling Effects

Diameter Length Oxide Thickness

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Quantum Effects

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Quantum-Mechanical Interference Quantum Confinement

At VGS = 0.5V and VD=0.5V for doped contact CNTFET

Quantum Effects (contd.)

Tunneling in Channel Region of Schottky-Barrier CNTFET [1]

Current in Channel Region of Doped Contact CNTFET

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[1] J. Guo, “Carbon Nanotube Electronics: Modeling, Physics and Applications”

I-V Characteristics ID-VD Comparison

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Schottky-Barrier CNTFET Doped Contact CNTFET

Doped Contact CNTFET provides more current for same VGS.

5 uA15 uA

I-V Characteristics (contd.)

ID-VGS Comparison

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Schottky-Barrier CNTFET Doped Contact CNTFET

Effect of Gate Dielectric Constant

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Schottky-Barrier CNTFET Doped Contact CNTFET [Table]

Constant table

Higher Dielectric Constant provides more Drain Current

2.5 uA

7.5 uA

Effect of Gate Dielectric Constant (contd.)

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The conduction band profile of SB CNTFETat VG= 0.5V . The solid line is for k = 25 thedashed line for k = 8 and the dash-dot line for k= 1 [2][2] J. Guo, “Carbon Nanotube Electronics: Modeling, Physics and Applications”

Constant table

K = 3.9

K = 14

Scaling Effects: Diameter

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ID− VGS characteristics at VD= 0.5V for SB CNTFET. The solid line with circles is for d 1nm, the sold line is for d 1.3nm, ∼ ∼and the dashed line is for d 2nm [3]∼

ID− VGS characteristics at VD= 0.5V for doped contact CNTFET.

[3] J. Guo, “Carbon Nanotube Electronics: Modeling, Physics and Applications” [Table]

Lower diameter provides better ON/OFF ratio.

[Cause]

Scaling Effect: Channel Length

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Schottky-Barrier CNTFET Doped Contact CNTFET

[Table]

Channel Length have very negligible effect on Drain Current.

Scaling Effect: Length (contd.)

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Conduction band profile for doped contact CNTFET at (a) Lch= 30mn,(b) Lch = 15nm & (c) Lch = 5nm for VGS= 0.5V and VDS= 0.3V

Lch = 15nmLch = 30nm Lch = 5nm

Scaling Effect: Oxide Thickness

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Schottky-Barrier CNTFET Doped Contact CNTFET [Table]

Thinner oxide provides much more ON/OFF ratio for both types of CNTFETs.

Overview of Our Findings

Parameter Effect Comment

Dielectric Constant, k Higher k provides better electrostatic control

Doped Contact CNTFET gives better performance

Channel Diameter Lower diameter provides higher current

Doped Contact have higher ON/OFF ratio

Channel Length Channel length have negligible

effect on I-V

No mentionable advantage for length

Oxide Thickness Thinner oxide provides much higher ON/OFF ratio

Doped Contact CNTFET have higher ratio than SB

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One of our key findings: Thinner oxide provides much higher ON/OFF ratio but it also increases leakage current. So using thinner oxide of higher k ensures less leakage current & gives more electrostatic control over channel.

Conclusions

The ON/OFF current ratio improves with high-κ gate dielectric.

This improvement is relatively higher in doped contact devices.

Thinner oxide provides better electrostatic control and improves device performance for both type of contacts.

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Future Perspectives

Completion of the partial code we have developed.

Convert the devices characteristic into SPICE model for circuit design.

Including the effect of phonon scattering.

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Questions

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Thank You

Dielectric Constant Table [3]

Oxide Material Dielectric Constant, k

SiO2 3.9

Si3N4 8

HfO2 14

ZrO2 25

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[3] Robertson, J. "High dielectric constant oxides." The European Physical Journal Applied Physics 28.03 (2004): 265-291.

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Simulator Software Screenshot

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CNTFET Lab Cylindrical CNT MOSFET Simulator

Effect of Diameter

Bandgap,

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