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

pulfrey@ece.ubc.ca

S.Iijima, Nature 354 (1991) 56

Single-wall and multi-wall NANOTUBES

Compare: flaxen hair - 20,000 nm

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

CNT formation by catalytic CVD

5m islands in PMMApatterned by EBL

LPD of Fe/Mo/Al catalyst

Lift-off PMMA

CVD from methane at 1000C

2000nm

No field

Growth in field (1V/micron)A. Ural et al., Appl. Phys. Lett., 81, 3464, 2002

Single-Walled Carbon Nanotube

2p orbital, 1e-

(-bonds)

Hybridized carbon atom graphene monolayer carbon nanotube

Chiral tubeChiral tube

a2

a1

(5,2) Tube(5,2) Tube

Structure (n,m):Structure (n,m):

VECTOR NOTATION FOR NANOTUBESVECTOR NOTATION FOR NANOTUBES

Adapted from Richard Martel

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

(5,0) semiconducting (5,5) metallic

Eg/2

eV (nm)

80

2

d

.

d

aE CC

g

Doping

• Substitutional unlikely •Adsorbed possiblee.g., K, O

• Interior possibleTubes are naturally intrinsic

Phonons

• Acoustic phonons (twistons) mfp 300 nm

Ballistic

transport

possible

• Optical phonons

mfp 15 nm

Fabricated Carbon Nanotube FETs

• Few prototypes

– [Tans98]: 1st published device

– [Wind02]: Top-gated CNFET

– [Rosenblatt02]: Electrolyte-gated

Nanotube

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 nmq

VLV

qV

qVzRV

DDS

S

GGSG

),(

)0,(

),(

:ConditionsBoundary

kx

kx

kz

E

METAL (many modes)

CNT (few modes)

Doubly degenerate lowest mode

MODE CONSTRICTIONand

TRANSMISSION

T

gate

insulator

nanotube

Cins

CQ

Quantum Capacitance Limit

)/( qEd

dQC

b

zQ

Eb

source!CNFETs!in 1

1

Q

QCSGS

ins

QCSGS

CSGCGS

m

mdVdV

C

CdVdV

dVdVV

Quantum Capacitance and Sub-threshold Slope

High k dielectrics:zirconia - 25water - 80

mV/decade 60loglog

exp1010

QD

CSQ

D

GSCSsubT m

Id

dVm

Id

dVS

kT

qVI

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= - 0.4VVgs= -0.15+0.05+0.30

Minimize the OFF Current

G = 4.2 eVIncreasing S,D 3.9, 4.2, 4.5 eV

S,D = 3.9 eVIncreasing G 3.0, 4.37 eV

ON/OFF 103

General non-equilibrium case

E

f(E)

EFS

0.5

E

f(E)

EFD

0.5

g(E)

E

1D DOS

Non-equilib f(E)

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

Solve Poisson iteratively

CURRENT in 1-D SYSTEMS

E DSeeee

zz

z

E eSee

dEEfEfETh

qIII

dk

dE

hv

dE

dk

dE

dNEg

dEEvEgETEfEMqvqnI

)}(- )(){(4

)modes 2(

2

modes) 2 ng(consideri m.eV / states 2

)( DOS

)()()()()()1D()1D(

Quantized Conductance

E DSee dEEfEfETM

h

qI )}(- )(){(

2

In the low-temperature limit:

Mh

qG

T

qVdEEfEfE DSSDS

2

D

2

1 if

- )}(- )({

Interfacial G: even when transport is ballistic in CNT

155 S for M=2

Measured Conductance

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

• No tunneling barriers• Low R contacts (Pd)

G 0.4 Gmax

at 280K !!

Drain Saturation Current

E DSee dEEfEfETM

h

qI )}(- )(){(

2

bE

SMAX

SATeE SeSATe dEEfh

qIdEEfETM

h

qI )(

4 )()(

2,,

If T=1Get BJT behaviour!

VGS

Eb

EF

Zero-height Schottky barrier

Present world record

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

ON Current: Measured and Possible

S,D= 3.9eVG = 4.37eV

CQ limit

80% ofQC limit!

Predicted Drain Current

0 0.2 0.4 0.6 0.80

5

10

15

20

25

30

35

40

45

50Varying drain work function, gate: 4.2, Vgs=0.4

VDS

(V)

0 0.2 0.4 0.6 0.80

10

20

30

40

50

60

70

80

90Varying gate work function, D/S: 3.9, Vgs=0.4

VDS

(V)

4.54.23.9

4.54.23.9

Dra

in c

urre

nt ( A

)

Dra

in c

urre

nt ( A

)

-ve

0

+ve

-5 0 5 10 15 20 25-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

z [nm]

Ene

rgy

[eV

]

4.5 eV

4.2

3.9

Vgs=Vds=0.4V

70mA/m !!

Transconductance

!! 4

)/exp(14

1T and high At

)}(- )(){(2

2

12

h

qg

kTqVh

q

dV

dIg

V

dEEfEfETMh

qI

m

GSGS

em

DS

E DSee

Low VDS: modulate for G

High VDS: modulate VGS for gm

Transconductance: Measured and Possible

Highest measured:Rosenblatt et al.Nano. Lett., 2, 869, 2002

CQ limit

S,D= 3.9eVG = 4.37eV

80% ofQC limit!

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

Gain=60

1st OR-gate

0,0

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

CNTs Functionalized with DNA

Recognition-based assembly

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

Self-assembly of DNA-templated CNFETs K.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

• 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!

Compelling Properties of Carbon Nanotubes

From: Dresselhaus, Dresselhaus & Eklund. 1996 Science of Fullerenesand Carbon Nanotubes. San Diego, Academic Press. Adapted from Richard Martel.

Armchair

Zig-Zag

Chiral

CHIRAL NANOTUBES

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

bandeach for 21

)( )(2

1

2

eV / nm / states 1

eunit volumper )( DOS

spin)for (allowing states 2

2 are therein

space in volume2

occupies state One

22

CC

z

z

zz

z

EE

m

hEg

EEm

m

dE

dk

m

kE

dE

dk

dE

dNEg

dkL

dNdk

kL

k|| or kz

L

2

Tight Binding

rrrRr

Rk

dU

iEE

atomic

V

atomicR

RRatomic

)( )( )(

)exp(

*

David John, UBC

Wolfe et al., “Physical Properties of Semiconductors”

Density of States(5,0) tube David John

E(eV) vs. k|| (1/nm) E(eV) vs. DOS (100/eV/nm)

Tuning the Bandgap

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

eV 8.2 2

d

aE CC

g

Eg < 0.1 eV for d > 7 nm

“zero bandgap” semiconductor

nanotube

oxidegate

Planar Coaxial

The Ideal Structure

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

CNT formation by catalytic CVD

5m islands in PMMApatterned by EBL

LPD of Fe/Mo/Al catalyst

Lift-off PMMA

CVD from methane at 1000C

1000nm

300nm

2000nm

CNT formation by E-field assisted CVD

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

V applied between Mo electrodes.

CVD from catalytic islands.

No field

10V applied

Bottom-gated Nanotube FETsBottom-gated Nanotube FETs

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

Note very high ID

10mA/m

Nanotube

1st CNFET

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

Phenomenological treatment of metal/nanotube contacts

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

BngBp

CNTmBn

E

:pinning level-Fermi No

Zero hole barrier

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

-5 0 5 10 15 20 25-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

z [nm]

Ene

rgy

[eV

]

Schrödinger-Poisson ModelL.C. Castro, D.L. John

S DCNT

Unbounded plane waves

)()()(

2)(

:ILandauer and PDI equatingby J.m Find

),( :define Instead,

:ionnormalizat spatial doCannot

**

1-

2

*

Q(z,E)n(z,E)ETEfq

EI

zzi

m

qEI

Ezn

dz

SL

PD

z

Increasing the Drain Current

0 0.2 0.4 0.6 0.80

5

10

15

20

25

30

35

40

45

50Varying drain work function, gate: 4.2, Vgs=0.4

VDS

(V)

0 0.2 0.4 0.6 0.80

10

20

30

40

50

60

70

80

90Varying gate work function, D/S: 3.9, Vgs=0.4

VDS

(V)

4.54.23.9

4.54.23.9

Dra

in c

urre

nt ( A

)

Dra

in c

urre

nt ( A

)

-5 0 5 10 15 20 25-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

z [nm]

Ene

rgy

[eV

]

Varying gate work function: D/S=3.9, Vds=Vgs=0.4V

4.5

4.2

3.9

Vgs=Vds=0.4V

70mA/m !!

Array of vertically grown CNFETsW.B. Choi et al., Appl. Phys. Lett., 79, 3696, 2001.

2x1011 CNTs/cm2 !!