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D.L. Pulfrey, D.L. John, L.C. Castro
Department of Electrical and Computer EngineeringUniversity of British ColumbiaVancouver, B.C. V6T1Z4, Canada
Performance Predictions forPerformance Predictions forCarbon Nanotube Field-Effect TransistorsCarbon Nanotube Field-Effect Transistors
Single-Walled Carbon NanotubeSingle-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
Zig-zag (6,0)Zig-zag (6,0)
Armchair (3,3)Armchair (3,3)
d
aE CCg
2
• NANOSCALE -- no photolithography
•BANDGAP TUNABILITY -- 0.5-1.5eV
• METALS AND SEMICONDUCTORS -- all-carbon ICs
• BALLISTIC TRANSPORT -- 20-300nm
• STRONG COVALENT BONDING
-- strength and stability of graphite
-- no surface states (less scattering, compatibility with many insulators)
• HIGH THERMAL CONDUCTIVITY
-- almost as high as diamond (dense circuits)
• SELF-ASSEMBLY -- biological, recognition-based assembly
Compelling Properties of Carbon NanotubesCompelling Properties of Carbon Nanotubes
Self-assembly of DNA-templated CNFETsSelf-assembly of DNA-templated CNFETs K.Keren et al., Technion.
Self-assembly of DNA-templated CNFETsSelf-assembly of DNA-templated CNFETs K.Keren et al., Technion.
CLOSED COAXIAL NANOTUBE FET STRUCTURECLOSED 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 CONSTRICTIONMODE CONSTRICTIONandand
TRANSMISSIONTRANSMISSION
T
Interfacial G: even when transport is ballistic in CNT
155 S for M=2
CURRENT in 1-D SYSTEMSCURRENT 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(
The Landauer currentThe Landauer current
General non-equilibrium General non-equilibrium casecase
E
f(E)
EFS
0.5
E
f(E)
EFD
0.5
g(E)
E
1D DOS
Non-equilib f(E-EC,z)
Q(z,E)=qf(E-EC,z)g(E-EC,z)
)(
)(
,
,
,,
midzcs
midC
midCSGSmidC
VfT
TfQ
VVCQ
Solve:Solve:1. Self-consistent SP2. Compact model
Quantum-Quantum-mechanical mechanical treatmenttreatment
• Need full QM treatment to compute:
-- Q(z) within barrier regions
-- Q in evanescent states (MIGS)
-- resonance, coherence
-- S D tunneling.
Emid
Transmission Probability TTransmission Probability TSS Comparison Comparison
Emid
VGS=VDS=0.4 V
CM1CM2
SP
D.L. John et al., Nanotech04, March 2004
VGS=0.4V
CM1
CM2
SP
L.C. Castro et al., Nanotechnology, submitted.
Drain I-V ComparisonDrain I-V Comparison
I-V dependence on S,D I-V dependence on S,D workfunctionworkfunction
Negative barrier(p-type) device
Positive barrier (p-type) device
VGS = -0.4 V
nm/A5
D.L. John et al., Nanotech04, March 2004
nm/A4.0
15nm Intel
continuous2
)( :1D
)( :2D
),()()(
2
2
,2
0
Q
metalQ
CSeCS
CSQ
CE
mEg
mqC
mEg
dEqVEfEgqQV
VQC
Quantum Quantum CapacitanceCapacitance
gate
insulator
nanotube
Cins
CQ
source
- - + -- - + -
Q
"Quantum" Capacitance in "Quantum" Capacitance in CNCN
D.L. John et al., JAP, submitted.
VDS=0.2V
Band Band 11
Band 2Band 2
VDS=0
Transconductance: the Ultimate LimitTransconductance: the Ultimate Limit
)}(- )({)(4
)}(- )(){(2
2
DSCDCSinsQ
insCm
E DSDSee
qVEfEfCC
CET
h
qg
dEqVEfEfETMh
qI
C
E
f(E)
EFS
0.5
E
f(E)
EFD
0.5
EC
nm/S05
nm/S1
15nm Intel
CONCLUSIONSCONCLUSIONS
• CNs have excellent thermal and mechanical properties.
• CNFETs can be self-assembled via biological recognition.
• QMR is important in negative-barrier SB-CNFETs.
• High DC currents and transconductances are feasible.
• Capacitance is not quantized.
• CNFETs deserve serious study as molecular transistors.
