Atomistic Simulation of Carbon Nanotube FETs

1
Atomistic Simulation of Carbon Nanotube
FETs Using Non-Equilibrium Greens 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. Introduction
2. NEGF Formalism
3. Ballistic CNTFETs
4. Summary

2
Introduction carbon nanotubes
McEuen et al., IEEE Trans. Nanotech., 1 , 78,
2002.
(see also R. Saito, G. Dresselhaus, and M.S.
Dresselhaus, Physical Properties of Carbon
Nanotubes, Imperial College Press, London, 1998.)
3
Introduction device performance
VG0.2V
nanotube diameter 1.7 nm
-0.1 V
-0.4 V
-0.7 V
-1.0 V
-1.3 V
tube d 1.7 nm
( W 2d )
Javey, Guo, Farmer, Wang, Yenilmez, Gordon.
Lundstrom, and Dai, Nano Lett., 2004
4
Outline

1. Introduction
2. NEGF Formalism
3. Ballistic CNTFETs
4. Summary

5
Nonequilibrium Greens Function (NEGF)
Charge density (ballistic)
Current
Datta, Electronic Transport in Mesoscopic
Systems, Cambridge, 1995
6
Outline

1. Introduction
2. NEGF Formalism
3. Ballistic CNTFETs
4. Summary

7
CNTFETs real-space basis (ballistic)
SS
H
SD
(m, 0) CNT
Recursive algorithm for Gr O(m3N) Lake et al.,
JAP, 81, 7845, 1997
8
CNTFETs real-space results
2nd subband
interference
band gap
Confined states
9
CNTFETs mode-space approach (ballistic)
The qth mode
c
t
(m,0) CNT

• ?S (1,1) and ?D (N,N) analytically computed
• Computational cost O(N) real space O(m3N)

k
t
10
CNTFETs mode-space results
coaxial G
dCNT1nm
i
n
n
coaxial G
2 modes
2 modes
coaxial G VD0.4V
real space
real space
coaxial G
band profile (ON)
11
CNTFETs treatment of M/CNT contacts
M
band discontinuity
metallic tube band
Kienle et al, ab initio study of contacts in
progress
12
CNTFETs treatment of M/CNT contacts
Gate
Metal S
metal D
tunneling
VDVG0.4V
Charge transfer in unit cell Leonard et al.,
APL, 81, 4835, 2002
13
CNTFETs 3D Poisson solver
Method of moments
Electrostatic kernel
for 2 types of dielectrics available in
Jackson, Classical Electrodynamics, 1962
Neophytou, Guo, and Lundstrom, 3D
Electrostatics of CNTFETs, IWCE10
14
CNTFETs numerical techniques

• 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

given n
---
gt
U
given n
---
gt
U










scf
scf
Poisson
Poisson


Iterate
Iterate


until
until


self
-
self
-




consistent
consistent


given
U

---
gt n
given
U

---
gt n












scf
scf
transport equation
NEGF
Transport


15
CNTFETs theory vs. experiment
VD -0.3V
-0.2V
-0.1V
Javey, et al., Nano Letters, 4, 1319, 2004
G
?Bp0 dCNT 1.7nm RSRD1.7K?
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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