Atomistic Simulation of Carbon Nanotube FETsUsing Non-Equilibrium Green’s Function Formalism
Jing Guo1, Supriyo Datta2, M P Anantram3, and Mark Lundstrom2 1Department of ECE, University of Florida, Gainesville, FL
2School of ECE, Purdue University, West Lafayette, IN 3NASA Ames Research Center, Moffett Field, CA
1. Introduction2. NEGF Formalism3. Ballistic CNTFETs4. Summary
2
)nm(8.0 deVEG
22312
kdE
kE G
McEuen et al., IEEE Trans. Nanotech., 1 , 78, 2002.
Introduction: carbon nanotubes
(see also: R. Saito, G. Dresselhaus, and M.S. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, London, 1998.)
3
-25
-20
-15
-10
-5
I DS (A
)-0.4 -0.3 -0.2 -0.1 0.0
VDS (V)
Introduction: device performance
Javey, Guo, Farmer, Wang, Yenilmez, Gordon. Lundstrom, and Dai, Nano Lett., 2004
BD GG
mAION /000,3
tube d ~1.7 nm
( W = 2d )
-0.1 V
-0.4 V
-0.7 V
-1.0 V
-1.3 V
VG=0.2Vnanotube diameter ~1.7 nm
Lch ~50nm
Gate
8nm HfO2
SiO2
p++ Si
PdPd CNT
4
1. Introduction2. NEGF Formalism3. Ballistic CNTFETs4. Summary
Outline
5
Nonequilibrium Green’s Function (NEGF)
Gate
molecule or device[H]
S
DSf1 f2
G EI H S 1
device contacts scattering
Datta, Electronic Transport in Mesoscopic Systems, Cambridge, 1995
ID 2q
hT (E) f1(E) f2(E) dE
dEEfEDEfEDN )()()()( 2211
GG2
1)( 2,12,1 ED
]GGTrace[)( 21ET
Charge density (ballistic)
Current
][2,12,1
i
6
1. Introduction2. NEGF Formalism3. Ballistic CNTFETs4. Summary
Outline
7
CNTFETs: real-space basis (ballistic)
DS
Gate
atomistic (pZ orbitals )
c
t
H=
ΣD
ΣS
000
000
00][ S
S
g
][00
000
000
D
D
g
1][ DSr HEIG
Recursive algorithm for Gr: O(m3N)
Lake et al., JAP, 81, 7845, 1997
(m, 0) CNT
8
CNTFETs: real-space results
band gap
interference2nd subband
Confined states
Gate
n+ n+i
9
CNTFETs: mode-space approach (ballistic)
c
t
k
t
The qth mode
Nq
q
q
q
q
ub
b
ut
tub
bu
H
3
2
1
c
qkq
2 S (1,1) and D (N,N)
analytically computed
- Computational cost: O(N)real space O(m3N)
(m,0) CNT
10
CNTFETs: mode-space results
n+ n+i
2 modes
real space
band profile (ON)
coaxial G VD=0.4V
dCNT~1nmcoaxial G
coaxial G
2 modes
real spacecoaxial G
Gate 8nm HfO2
SiO2
p++ Si
PdPd CNT
11
CNTFETs: treatment of M/CNT contacts
M
CE
VE
FE
t
0B
metallic tube band
00
0it
m
:0B band discontinuity
Kienle et al, ab initio study of contacts in progress
12
CNTFETs: treatment of M/CNT contacts
Gate
VD=VG=0.4V
Charge transfer in unit cell: Leonard et al., APL, 81, 4835, 2002
MetalS
metalD
tunneling
13
CNTFETs: 3D Poisson solver
Gate
8nm HfO2
SiO2
p++ Si
PdPd CNT
Method of moments:
')'()'()( rdrrrKrV
Electrostatic kernel:
for 2 types of dielectrics available in Jackson, Classical Electrodynamics, 1962
)'( rrK
)'( rrK
Neophytou, Guo, and Lundstrom, 3D Electrostatics of CNTFETs, IWCE10
14
CNTFETs: numerical techniques
given n: --- > U scf
“Poisson”
given U scf : --- > n
transport equation
Iterate until self -
consistent
given n: --- > U scf
Poisson
given U scf : --- > n
NEGF Transport
Iterate until self -
consistent
- Non-linear Poisson
- Recursive algorithm for
- Gaussian quadrature for doing integral
- Parallel different bias points
- ~20min for full I-V of a 50-nm CNTFET
1][)( DSHEIEG
15
CNTFETs: theory vs. experiment
G
Bp=0
dCNT ~1.7nm
RS=RD~1.7K
VD= -0.3V
-0.2V
-0.1Vexperimenttheory
Gate
8nm HfO2
10 nm SiO2
p++ Si
PdPd CNT
Javey, et al., Nano Letters, 4, 1319, 2004
16
Summary
A simulator for ballistic CNTFETs is developed
- atomistic treatment of the CNT- 3D electrostatics- phenomenological treatment of M/CNT contacts- efficient numerical techniques
Theory is calibrated to experiment
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