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Carbon Nanotube Field-Effect Transistors: An Evaluation. D.L. Pulfrey, L.C. Castro, D.L. John. Department of Electrical and Computer Engineering University of British Columbia Vancouver, B.C. V6T1Z4, Canada [email protected] S.Iijima, Nature 354 (1991) 56.

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Carbon Nanotube Field-Effect Transistors: An Evaluation

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Carbon Nanotube Field-Effect Transistors:

An Evaluation

D.L. Pulfrey, L.C. Castro, D.L. John

Department of Electrical and Computer Engineering

University of British Columbia

Vancouver, B.C. V6T1Z4, Canada

[email protected]


S.Iijima, Nature 354 (1991) 56

Single-wall and multi-wall NANOTUBES

Compare: flaxen hair - 20,000 nm


CNT formation by catalytic CVD

2000nm

5m islands in PMMA

patterned by EBL

LPD of Fe/Mo/Al catalyst

Lift-off PMMA

No field

CVD from methane at 1000C

J.Kong et al., Nature, 395, 878, 1998

A. Ural et al., Appl. Phys. Lett., 81, 3464, 2002

Growth in field (1V/micron)


2p orbital, 1e-(-bonds)

Single-Walled Carbon Nanotube

Hybridized carbon atom  graphene monolayer  carbon nanotube


Structure (n,m):

(5,2) Tube

VECTOR NOTATION FOR NANOTUBES

Chiral tube

Adapted from Richard Martel


E-EF (eV) vs. k|| (1/nm)

Eg/2

(5,0) semiconducting

(5,5) metallic


Doping

  • Substitutional unlikely

  • Adsorbed possible

  • e.g., K, O

Tubes are naturally intrinsic

  • Interior possible


Phonons

  • Acoustic phonons (twistons) mfp  300 nm

  • Optical phonons

  • mfp  15 nm

Ballistic

transport

possible


Nanotube

Fabricated Carbon Nanotube FETs

  • Few prototypes

    • [Tans98]: 1st published device

    • [Wind02]: Top-gated CNFET

    • [Rosenblatt02]: Electrolyte-gated


CLOSED COAXIAL NANOTUBE FET STRUCTURE

chirality: (16,0)

radius: 0.62 nm

bandgap: 0.63 eV

length: 15 - 100 nm

oxide thickness: (RG-RT): 2 - 6 nm


E

kz

kx

kx

MODE CONSTRICTION

and

TRANSMISSION

Doubly degenerate lowest mode

T

CNT (few modes)

METAL (many modes)


Eb

Quantum Capacitance Limit

gate

Cins

insulator

CQ

nanotube

source


Quantum Capacitance and Sub-threshold Slope

High k dielectrics:

zirconia - 25

water - 80

70 mV/decade !

- Javey et al., Nature Materials, 1, 241, 2002


AMBIPOLAR CONDUCTION

Experimental data:

M. Radosavljevic et al.,

arXiv: cond-mat/0305570 v1

Vds= - 0.4V

Vgs=

-0.15

+0.05

+0.30


Minimize the OFF Current

S,D = 3.9 eV

Increasing G  3.0, 4.37 eV

G = 4.2 eV

Increasing S,D 

3.9, 4.2, 4.5 eV

ON/OFF 103


E

E

1D DOS

E

EFS

g(E)

EFD

0.5

f(E)

f(E)

0.5

General non-equilibrium case

Non-equilib f(E)

Q(z,E)=qf(E)g(E)

Solve Poisson iteratively


CURRENT in 1-D SYSTEMS


Quantized Conductance

In the low-temperature limit:

Interfacial G: even when transport is ballistic in CNT

155 S for M=2


Measured Conductance

G  0.4 Gmax

at 280K !!

A. Javey et al., Nature, 424, 654, 2003

  • No tunneling barriers

  • Low R contacts (Pd)


Drain Saturation Current

VGS

Eb

EF

If T=1

Get BJT behaviour!

Zero-height Schottky barrier


ON Current: Measured and Possible

CQ limit

S,D= 3.9eV

G = 4.37eV

80% of

QC limit!

Present world record

Javey et al., Nature, 424, 654, 2003


Predicted Drain Current

-ve

0

+ve

Vgs=Vds=0.4V

70mA/m !!


Transconductance

Low VDS: modulate for G

High VDS: modulate VGS for gm


Transconductance: Measured and Possible

CQ limit

S,D= 3.9eV

G = 4.37eV

80% of

QC limit!

Highest measured:

Rosenblatt et al.

Nano. Lett., 2, 869, 2002


CNFET Logic

A.Javey et al., Nature Materials, 1, 241, 2002

Gain=60

0,0

1st OR-gate


Recognition-based assembly

CNTs Functionalized with DNA

Williams, Veenhuizen, de la Torre, Eritja and Dekker Nature,420, 761, 2002.


Self-assembly of DNA-templated CNFETsK.Keren et al., Technion.


Self-assembly of DNA-templated CNFETsK.Keren et al., Technion.


CONCLUSIONS

  • Schottky barriers play a crucial role in determining the drain current.

  • Negative barrier devices enable:

    • control of ambipolarity,

    • high ON/OFF ratios,

    • near ultimate-limit S, G, ID, gm.

  • CNFETs can be self-assembled via biological recognition.

  • CNs have excellent thermal and mechanical properties.

  • CNFETs deserve serious study as molecular transistors.


Extra Slides


Compelling Properties of Carbon Nanotubes

  • Nanoscale

  • Bandgap tunability

  • Metals and semiconductors

  • Ballistic transport

  • Strong covalent bonding:

  • -- strength and stability of graphite

  • -- reduced electromigration (high current operation)

  • -- no surface states (less scattering, compatibility with many insulators)

  • High thermal conductivity

  • -- almost as high as diamond (dense circuits)

  • Let’s make transistors!


CHIRAL NANOTUBES

Armchair

Zig-Zag

Chiral

From: Dresselhaus, Dresselhaus & Eklund. 1996 Science of Fullerenes

and Carbon Nanotubes. San Diego, Academic Press. Adapted from Richard Martel.


Carbon Nanotube Properties

  • Graphene sheet 2D E(k//,k)

    • Quantization of transverse wavevectors

      k (along tube circumference)

       Nanotube 1D E(k//)

  • Nanotube 1D density-of-states derived from [E(k//)/k]-1

  • Get E(k//)vs. k(k//,k) from Tight-Binding Approximation


Density of States

k|| or kz


Tight Binding

David John, UBC

Wolfe et al., “Physical Properties of Semiconductors”


David John

Density of States

(5,0) tube

E(eV) vs. DOS (100/eV/nm)

E(eV) vs. k|| (1/nm)


Tuning the Bandgap

T. Odom et al., Nature, 391, 62, 1998

Eg < 0.1 eV for d > 7 nm

“zero bandgap” semiconductor


The Ideal Structure

nanotube

oxide

gate

Coaxial

Planar


CNT formation by catalytic CVD

5m islands in PMMA

patterned by EBL

1000nm

LPD of Fe/Mo/Al catalyst

300nm

Lift-off PMMA

CVD from methane at 1000C

2000nm

J.Kong et al., Nature, 395, 878, 1998


CNT formation by E-field assisted CVD

V applied between Mo electrodes.

CVD from catalytic islands.

No field

10V applied

A. Ural et al., Appl. Phys. Lett., 81, 3464, 2002


Nanotube

Bottom-gated Nanotube FETs

1st CNFET

S. Tans et al., Nature, 393, 49, 1998

Note very high ID

10mA/m

A. Javey et al., Nature, 424, 654, 2003


Phenomenological treatment of metal/nanotube contacts

Evidence of work function-dependence of I-V: A. Javey et al., Nature, 424, 654, 2003

Zero holebarrier


Schrödinger-Poisson Model

  • Need full QM treatment to compute:

  • -- Q(z) within positive barrier regions

  • -- Q in evanescent states (MIGS)

  • -- S  D tunneling

  • -- resonance, coherence


Schrödinger-Poisson Model

L.C. Castro,

D.L. John

S

CNT

D

Unbounded plane waves


Increasing the Drain Current

Vgs=Vds=0.4V

70mA/m !!


Array of vertically grown CNFETs

W.B. Choi et al., Appl. Phys. Lett., 79, 3696, 2001.

2x1011 CNTs/cm2 !!


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