Scaling of the performance of
carbon nanotube transistors
S. Heinze1, M. Radosavljević2, J. Tersoff3, and Ph. Avouris3
1 Institute
of Applied Physics, University of Hamburg, Germany
2 Novel Device Group, Intel Corporation, Hillsboro, OR
3 IBM Research Division, TJ Watson Research Center, Yorktown Heights, NY
• Why carbon nanotube transistors?
• Evidence for Schottky barriers
• Carbon nanotube Schottky barrier transistors
• Gas adsorption versus doping
• Scaling of transistor performance
• New device designs & capabilities
• Conclusions
Carbon nanotube field-effect transistors
comparable with Si MOS-FETs
Nanotube FETs with top gates:
• turn-on gate voltage is about 1V
• favorable device characteristics
(all p-type)
Gate length (nm)
Gate oxide thickness (nm)
Vt (V)
ION (A/m)
(Vds = Vgs-Vt ~ -1V)
IOFF (nA/m)
Subthreshold slope (mV/dec)
T ransconductanceS/m)
(
260nm CNFET 50nm SOI MOSFET
260
15
~ 0.5
2100
50
1.5
~ -0.2
650
150
130
2321
9
70
650
S. J. Wind et al., Appl. Phys. Lett. 80, 3817 (2002).
Evidence for Schottky barriers:
scanned gate microscopy at contacts
map transport current as a function of moving, charged AFM tip
(a)
(b)
Vtip = -2V
current increase when gating the source junction
 barrier thinning.
M. Freitag et al., Appl. Phys. Lett. 79, 3326 (2001).
Evidence for Schottky barriers:
ambipolar conduction in SWNTs
Bottom gate CNFETs with Ti contacts annealed;
conversion from p-type to ambipolar conductance
R. Martel et al., PRL 87, 256805 (2001).
Evidence for Schottky barriers:
Influence of the contacts for CNFETs
Current [A]
10
10
10
10
10
10
10
-6
-500
-7
L=300nm
-8
tox=5nm
-9
-10
-11
-12
-13
Vd=-0.9V to -0.5V
0.2V steps
-2.0
-1.0
0.0
NT
1.0
-300
-200
0
0.0
-0.5
-1.0
-1.5
Drain Voltage [V]
Switching S & D changes:
Vs = 0 – Slope by factor of 2
– ON-state by factor of 5
Vd
Vg
Vg=-1.5V to 0V
0.5V steps
-100
Gate Voltage [V]
Vd Vs = 0
-400
Current [nA]
10
 not due to bulk,
it is a contact effect
M.Radosavljević et al.
Conventional vs. Schottky barrier FET
Conventional Transistor
p-type Characteristic
Schottky Barrier Transistor
dNT=1.4nm  Eg~0.6eV
ambipolar
Characteristic
Typical
SBs for
NTs ~ 0.3eV
Transmission through Schottky barrier
WKB approximation
+ single NT band:
T(E)*[F(E)-F(E-eVd)] (arb.units)
0.3
E (eV)
0.2
Conduction
Band
0.1
0.0
-0.1
0.0
0.2
0.4
0.6
0.8
Transmission (E)
Landauer-Büttiker
formula for current:
1.0
0
2
4
6
8
10
Distance from Contact (nm)
Self-consistent SB-transistor model
for needle-like contact
• Cylindrical gate at RGate
• Metal electrode of NT diameter
• Analytic electrostatic kernel G
• Test of approximations for 
Gate
NT
Metal
R
V( z )  Vgate   G ( z  z)  ( z)dz
4

Charge on the  ( z )  e f 
 F ( E ) g ( E  eV( z))dE
Electrostatic
potential:
nanotube:

Ec ( z )
 Solution by self-consistency cycle
Needle-like contact:
conductance vs. gate voltage
10
-4
50
hole
tunneling
10
10
10
10
-5
40
-6
30
-7
20
-8
10
-9
-1.0
-0.5
0.0
0.5
Gate Voltage (V)
Conductance (S)
Conductance (S)
10
electron
tunneling
0
1.0
Ideal sharp Metal-NT Contact
 turn-on voltage ~ Eg/2
Gate
Metal
NT
Carbon nanotube transistors
with planar gates
-4
Conductance
ElectrostaticModulation
Potential
Conductance (S)
10
Calculated NT-potential
-5
10
-6
10
-7
10
-8
10
-9
10
-20
-10
0
10
20
Top Gate Voltage (V)
• Solve a 2D boundary value problem  Vext(x)
• Local approximation for potential from NT charge
Influence of the contact geometry
Gate
Metal
NT
Scaled Characteristics
PRL 89, 106801 (2002)
Gas adsorption vs. doping:
Experimental observations
Gas Adsorption (O2)
Doping with Potassium
4
In Air
Increase of Potassium
Current (nA)
3
Annealed in Vacuum
Increase of O2
2
1
0
-15
-10
-5
0
5
Gate Voltage (V)
V. Derycke et al., APL 80, 2773 (2002).
10
15
Uniform doping:
Experiment vs. SB model
Doping with Potassium
Increase of Potassium
Gate
Metal
NT
Needle-Contact Model
Uniform doping of nanotube
Calculated
Doping Characteristics
n-doped at
510-4 e/atom
Gate
Metal
NT
Uniform doping of nanotube
Calculated
Doping Characteristics
n-doped at
110-3 e/atom
Gate
Metal
NT
Gas adsorption:
Experiment vs. SB model
Gas Adsorption (O2)
4
In Air
Current (nA)
3
Annealed in Vacuum
Increase of O2
2
1
0
-15
-10
-5
0
5
Gate Voltage (V)
10
15
Gate
Metal
NT
Needle-Contact Model
Gas adsorption:
Change in metal workfunction
Calculated Gas
Adsorption Characteristics
Metal workfunction
increased by 0.2eV
Gate
Metal
NT
How does the performance of
Schottky barrier CNFETs scale?
ultra-thin oxide CNFETs:
10
Current (A)
10
10
10
10
10
110 mV/dec
tox=2nm
-8
-9
130 mV/dec
tox=2nm
Scaling law with oxide thickness?
280 mV/dec
tox=20nm
-10
-11
-12
170 mV/dec
tox=5nm
-13
-1.5
-1.0
-0.5
0.0
0.5
1.0
Gate Voltage (V)
 Why is the thermal limit of
60 mV/decade not reached?
J. Appenzeller et al., PRL 89, 126801 (2002).
Turn-on vs oxide thickness for
bottom gate SB-CNFETs
Device geometry
 Vscale ~ sqrt(tox)
Analytic model for thin sheet contact
Gate
Source
tox
tox
Gate
Gate
Potential near the Edge:
z
Analytic model applied to
bottom gate SB-CNFETs
Single, empirical factor
for bottom gate devices
Scaling of turn-on performance of
CNFETs with oxide thickness
Analytic Model
Top Electrode
0.3
80
0.4
0.2
Height (nm)
120
40
Nanotube
Source
tox
0
Drain
0.9
Bottom Gate
0
100
200
300
400
Length (nm)
Largest improvements
by optimization of the
contact geometry
PRB 68, 235418 (2003)
Scaling of drain voltage for
ultra-thin oxide CNFETs?
Top Electrode Minimal
Current (OFF-current)
rises with lower oxide thickness
0.1
0.2
0.3
0.1
0.3
0.0
40
Source
-0.1
-5
0
0
0
0.4
Drain=0.5V
Nanotube
0.0
tox=30nm
tox=2nm
0.9
Gate=1V
5 Bottom
10 15 20
-0.3
100
Distance
from Contact200
(nm)
Source
80
0.2
Energy (eV)
Height (nm)
120
Energy (eV)
0.3
300
400
Length
(nm)
-0.6
Drain
• independent barriers –-0.9
Vdrain=+0.8V, V gate=+0.4V
one controlled by Vg, the other by Vd–Vg
-1.2
• identical (and
minimal)
hole/electron
Ultra-thin
oxide:
turn-on
0
100voltage
200 ~ Vd
300
400
current at Vg = Vd–Vg  Vd = 2V
Position
along Nanotube (nm)
g
Effect of drain voltage for
ultra-thin oxide CNFET
Bottom-gate: tox=2nm
 exponential increase of OFF current with Vd
Scaling of drain voltage:
model vs. experiment
tox=2nm
APL 83, 2435 (2003)
OFF state problem for transistor
 light emission device
Infrared light emission from a SWNT:
J. Misewich et al., Science 300, 783 (2003).
Asymmetric device design
to solve OFF state problem
Symmetric CNFET (tox=2nm)
 unfavorable OFF state
Asymmetric CNFET  low OFF current
& p- and n-type device for Vd<0 and Vd>0
APL 83, 5038 (2003)
Conclusions
CN Transistors competetive with Si MOSFETs, however:
• Transistor action in CNFETs due to Schottky barriers
 ambipolar transfer characteristic (I vs Vg)
• Nanoscale features of contacts are essential
• Gas adsorption modifies band line-up at the contact
• Scaling in turn-on regime with sqrt(tox)
• Scaling of drain voltage at ultra-thin oxides necessary
• New device physics: light emission device
• New device designs may be favorable