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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
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 !!
