Transcript No Slide Title

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]
Single-wall and multi-wall NANOTUBES
S.Iijima, Nature 354 (1991) 56
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)
Single-Walled Carbon Nanotube
Hybridized carbon atom  graphene monolayer  carbon nanotube
2p orbital, 1e(-bonds)
VECTOR NOTATION FOR NANOTUBES
Chiral tube
a1
a2
Adapted from Richard Martel
Structure (n,m):
(5,2) Tube
E-EF (eV) vs. k|| (1/nm)
Eg/2
(5,0) semiconducting
(5,5) metallic
2aCC
0.8
Eg 

eV
d
d (nm)
Doping
• Substitutional unlikely
• Interior possible
•Adsorbed possible
e.g., K, O
Tubes are naturally
intrinsic
Phonons
• Acoustic phonons
(twistons) mfp  300 nm
• Optical phonons
mfp  15 nm
Ballistic
transport
possible
Fabricated Carbon Nanotube FETs
Nanotube
• Few prototypes
– [Tans98]: 1st published device
– [Wind02]: Top-gated CNFET
– [Rosenblatt02]: Electrolyte-gated
CLOSED COAXIAL NANOTUBE FET STRUCTURE
chirality: (16,0)
BoundaryConditions:
radius: 0.62 nm
V ( RG , z )  VGS 
bandgap: 0.63 eV
length: 15 - 100 nm
oxide thickness: (RG-RT): 2 - 6 nm
V (  ,0)  
G
q
S
q
V (  , L)  VDS 
D
q
MODE CONSTRICTION
and
TRANSMISSION
E
Doubly
degenerate
lowest mode
T
kz
kx
CNT (few modes)
kx
METAL (many modes)
Quantum Capacitance Limit
gate
Cins
CQ
VGS  dVGC  dVCS
insulator
nanotube
dVGS
dVGS
CQ

 dVCS 1 
 Cins
 dVCS mQ



mQ  1 in CNFET s!!
source
dQz
CQ 
d (  Eb / q )
Eb
Quantum Capacitance and Sub-threshold Slope
I subT
qVCS
 exp
kT
mQ dVCS
dVGS
S

 60mQ mV/decade
d log10 I D d log10 I D
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
G = 4.2 eV
Increasing S,D 
3.9, 4.2, 4.5 eV
S,D = 3.9 eV
Increasing G  3.0, 4.37 eV
ON/OFF 103
General non-equilibrium case
E
E
1D DOS
E
EFS
g(E)
0.5
EFD
f(E)
Non-equilib f(E)
f(E)
Q(z,E)=qf(E)g(E)
Solve Poisson iteratively
0.5
CURRENT in 1-D SYSTEMS
I e (1D)  qn(1D)v  q  M e ( E ) f S ( E )Te ( E ) g ( E )v( E ) dE
E
dN 2 dkz
DOS  g ( E ) 

states/ m.eV (considering 2 modes)
dE  dE
2 dE
vz 
h dkz
I e (2 modes)  I e  I e 
4q
Te ( E ){ f S ( E ) - f D ( E )} dE

h E
Quantized Conductance
2q
Ie 
M  Te ( E ){ f S ( E ) - f D ( E )} dE
E
h
In the low-temperature limit:
 {f
E
S
( E ) - f D ( E )} dE   S -  D  qVDS
 if T  1
2q 2
G
M
h
Interfacial G: even when transport is ballistic in CNT
155 S for M=2
Measured Conductance
G  0.4 Gmax
A. Javey et al., Nature, 424, 654, 2003
at 280K !!
• No tunneling barriers
• Low R contacts (Pd)
Drain Saturation Current
2q
Ie 
M  Te ( E ){ f S ( E ) - f D ( E )} dE
E
h
I e , SAT
2q

M  Te ( E ) f S ( E ) dE
E
h

 I eMAX
, SAT
4q
f S ( E )dE

h Eb
VGS 
EF
Eb
Zero-height
Schottky barrier
If T=1
Get BJT behaviour!
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
Varying drain work function, gate: 4.2, Vgs=0.4
Varying gate work function, D/S: 3.9, Vgs=0.4
50
90
4.5
4.2
3.9
45
0.4
-ve
40
4.5 eV
0.2
70
4.2
0
35
3.9
Drain current (A)
60
-0.2
30
25
Energy [eV]
Drain current (A)
4.5
4.2
3.9
80
0
20
50
-0.4
40
-0.6
30
15
-0.8
10
-1
+ve
5
0
0
0.2
0.4
VDS (V)
0.6
0.8
-1.2
-1.4
-5
20
10
0
Vgs=Vds=0.4V
0
00.2
0.4 5
VDS (V)
0.6
10 0.8
z [nm]
70mA/m !!
15
20
2
Transconductance
2q
Ie 
M  Te ( E ){ f S ( E ) - f D ( E )} dE
E
h
At high VDS and T  1
dIe
4q 2
1
1  exp(qVGS / kT )
gm 

dVGS
h
4q 2
gm 
!!
h
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
CNTs Functionalized with DNA
Recognition-based assembly
Williams, Veenhuizen, de la Torre, Eritja and Dekker Nature, 420, 761, 2002.
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
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
2
L
k|| or kz
One stateoccupies
2
volumein k z space
L
in dkz thereare dN  2
DOS  g ( E ) 
L
dkz states(allowingfor spin)
2
dN
1 dkz
per unit volume 
states/ nm / eV
dE
 dE
dkz m
2k 2
1
E


2m
dE  2m( E  EC )
 g (E) 
1
h
2m
E  EC
for each band
Tight Binding
David John, UBC
Wolfe et al., “Physical
Properties of
Semiconductors”
E  E atomic    R exp(ik  R)
R
*
 R    atomic
(r  R) U (r)  atomic (r)dr
V
Density of States
(5,0) tube
E(eV) vs. k|| (1/nm)
David John
E(eV) vs. DOS (100/eV/nm)
Tuning the Bandgap
T. Odom et al.,
Nature, 391, 62,
1998
2aCC
Eg 
d
  2.8 eV
Eg < 0.1 eV for d > 7 nm
“zero bandgap” semiconductor
The Ideal Structure
nanotube
oxide
gate
Planar
Coaxial
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.
A. Ural et al., Appl. Phys. Lett., 81, 3464, 2002
No field
10V applied
Bottom-gated Nanotube FETs
Nanotube
1st CNFET
S. Tans et al., Nature, 393, 49, 1998
A. Javey et al., Nature, 424, 654, 2003
Note very high ID
10mA/m
Phenomenological treatment of metal/nanotube contacts
No Fermi- levelpinning:  Bn   m   CNT
 Bp  E g   Bn
Evidence of work function-dependence of I-V:
A. Javey et al., Nature, 424, 654, 2003
Zero hole
barrier
Schrödinger-Poisson Model
• Need full QM treatment to compute:
-- Q(z) within positive barrier regions
-- Q in evanescent states (MIGS)
0.6
-- S  D tunneling
0.4
-- resonance, coherence
Energy [eV]
0.2
0
-0.2
-0.4
-0.6
-0.8
-5
0
5
10
z [nm]
15
20
25
Schrödinger-Poisson Model
L.C. Castro,
D.L. John
S
CNT
D
Unbounded plane waves
Cannotdo spatialnormalization :
*

 dz
z
Instead,define :
Find  J.m
-1
n( z , E )   
2
by equating PDI and Landauer I :
*

q   
*   
I PD ( E ) 
i 
  

2m  z 
 z 
q
I L (E) 
f S ( E )T ( E )

 n(z,E)  Q(z,E)
Increasing the Drain Current
: 4.2, Vgs=0.4
6
Varying gate work function, D/S: 3.9, Vgs=0.4
90
Varying gate work function: D/S=3.9, Vds=Vgs=0.4V
4.5
4.2
3.9
80
0.2
70
0
4.5
-0.2
4.2
-0.4
3.9
50
Energy [eV]
Drain current (A)
60
40
-0.6
-0.8
30
-1
20
-1.2
Vgs=Vds=0.4V
10
-1.4
-5
0.8
0
0
5
10
15
z [nm]
0
0.2
0.4
0.6
0.8
VDS (V)
70mA/m !!
20
25
Array of vertically grown CNFETs
W.B. Choi et al., Appl. Phys. Lett., 79, 3696, 2001.
2x1011 CNTs/cm2 !!