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Influence of gate capacitance on CNTFET
performance using Monte Carlo
simulationH. Cazin d'Honincthun,
S. Retailleau, A. Bournel, P. Dollfus, J.P. Bourgoin*
UPS
Institut d'Electronique Fondamentale (IEF) UMR 8622 – CNRS-Université Paris Sud 11, Orsay, France
*Laboratoire d’électronique moléculaire, CEA/DSM/DRECAM/SPEC, CEA Saclay, France
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Plan
Carbon nanotubes: high potential material
Carbon nanotubes: Model for calculations (Monte Carlo)
Evaluation of Mean Free Path
Carbon nanotube field effect transistor simulation
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Potentialities of Carbon nanotubes
Charge transport and confinement
Charge transport is quasi-ballistic: few interactions
Charge confinement (1D): good control of electrostatics
Band structure « quasi » symmetric
Transport properties identical for electron and hole (same m*)
Carbon nanotubes can be either metallic as well as semi-conducting
All-nanotube-based electronic is possible
No dangling bonds
Possibility to use High K material for oxide
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Plan
Carbon nanotubes: high potential material
Carbon nanotubes: Model for calculations (Monte Carlo)
Evaluation of Mean Free Path
Carbon nanotube field effect transistor simulation
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Particle Monte-Carlo method
, ,f r k t
Carrier trajectories: Succession of free flight and scattering events
Study of carrier transport in this work: solving the Boltzmann equation by the
Monte Carlo method
1ft
2ftelectron
)(00
tk
F
)(101 f
ttk
)(2102 ff
tttk
Statistical solution :by Monte Carlo method
• assembly of individual particles
• 1 particle
• N particles allow us to reconstruct
),,( tkrf
)(),( tktr
scattering rates i k - time of free flights tf
- type of scattering i- effect of scattering (E, )(Monte Carlo algorithm)
random selection ofrandom selection of
r k
collisions
f F fv f f
t t
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Band structure and phonons
0
1
2
3
-3 109 -2 109 -1 109 0 1 109 2 109 3 109
Ene
rgy
(eV
)
Wave Vector (m-1)
E12
EG /2subbands 1
subbands 2
subbands 3
Energy dispersion calculated by:• Tight-binding• Zone-folding
Phonon dispersion curves calculated by zone folding method
Analytical approximation of dispersion curves [Pennington, Phys. Rev. B 68, 045426 (2003)]
Longitudinal acoustic and optical modes
are considered as dominant like in graphene
Analytical approximation of the three first subbands
Analytical approximation of the three first subbands
Approximation
+ RBM phonon (ERBM ≈ Cst./dt)
[M. Machon et al., Phys. Rev. B 71, 035416, (2005)]
Ex: Tube index n=19, ERBM=19 meV
2 2
12
m mzp p p p p
p
kE E E E
m
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Scattering Events Calculation
Scattering rates : 1st order Perturbation Theory by deformation potential model
with: Daco = 9 eV [L. Yang, M.P. Anantram et al. Phys. Rev. B 60, 13874 (1999) ]
DRBM = 0.65eV/cm (for n = 19) [M. Machon et al., PRB 71, 035416 (2005)]
Intrasubband acoustic scattering Elastic process
Intersubband transition Inelastic process
intravalley scattering from subband 1 intervalley scattering from subband 1
( )E
n = 19
1011
1012
1013
1014
0 0.2 0.4 0.6 0.8 1 1.2
Sca
tter
ing
rate
s (s
-1)
Energy(eV)
1-1
1-2 ab A
1-2 em A
1-3 ab A
1-3 em A1-2 em O 1-3 em O
1-1 em rbm
1010
1011
1012
1013
1014
1015
0 0.2 0.4 0.6 0.8 1 1.2
Scat
teri
ng r
ates
(s-1
)
Energy (eV)
1-1 em A
1-1 em O1-2 em A
1-2 em O1-3 em A
1-3 em O
1- 2 ab A
1-3 ab O
1-3 ab A
1- 2 ab O
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Plan
Carbon nanotubes: high potential material
Carbon nanotubes: Model for calculations (Monte Carlo)
Evaluation of Mean Free Path
Carbon nanotube field effect transistor simulation
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Mean Free Path
10
100
1000
104
1 10 100
n = 22n = 34n = 58
Electric Field (kV/cm)
Ele
ctro
n m
ean
free
pat
h (n
m)
Inelastic inter-valley acoustic and optical
Elastic acoustic intra-subband
The mean free path depends on diameter and electric field : lMFP=100-600 nm for elastic scattering lMFP=1000-20 nm for inelastic scatteringAgreement with experimental works (L. field:300-500 nm H. Field: 10-100nm)
Potential of quasi-ballistic transport in the low-field regimePotential of quasi-ballistic transport in the low-field regime
Simulation in steady-state regime
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Plan
Carbon nanotubes: high potential material
Carbon nanotubes: Model for calculations (Monte Carlo)
Evaluation of Mean Free Path
Carbon nanotube field effect transistor simulation
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
The modelled transistor
Coaxially gated carbon nanotube transistor with heavily-doped source drain extensions CNTFET
Characteristics:
• Zigzag tube (19,0) - dt = 1.5nm – EG = 0.55eV
• Cylindrically gated
• Ohmics Contacts (heavily n-doped)
• Intrinsic channel
• High K gate insulator HfO2 ( EOT = 16, 1.4, 0.4, 0.1 nm - COX = 72, 210, 560,1060 pF/m )
Lc = 100 nmL = 20 nm
et = 0.18 nm dt = 1.5 nm
EOT (nm)Oxide : HfO2S D
ND=5.108/m
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Conduction band
First subband energy profile
Weak field in the channel due to strong electrostatic gate control
-0.4
-0.3
-0.2
-0.1
0
0.1
0 20 40 60 80 100 120 140
Firs
t Sub
band
Ene
rgy
(eV
)
Position along source-drain axis (nm)
VDS = 0.4 V
COX = 1056 pF/mCOX = 72 pF/m
VGS = 0.15 V
VGS = 0.25 V
VGS = 0.4 V
Weak field in the channel quasi ballistic transportWeak field in the channel quasi ballistic transport
10
100
1000
104
1 10 100
n = 22n = 34n = 58
Electric Field (kV/cm)E
lect
ron
mea
n fr
ee p
ath
(nm
)
Zone boundary and optical
Acoustic elastic
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Capacitive effects
GGS
dQC
dVDetermination of CG for low VDS:
2
ln
o rOX
ox dt
dt
Ce r
r
≈ CG tends towards 4pF/cm
Evolution of Cox and CG as a function of 1/EOT
Reminder :1 1 1
G ox QC C C
CG leads towards CQ for Cox >> CQ
0
20
40
60
80
100
120
0 0.5 1 1.5 2 2.5
Cox
CG (V
DS = 0.05 V)
Cap
acit
ance
(aF
)
1/EOT (nm-1)
For Cox >> CQ quantum capacitance limitFor Cox >> CQ quantum capacitance limit
Weak Field 1D low density of states Channel potential is fixed
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
ID-VGS Characteristics
10-3
10-2
10-1
100
101
102
0
10
20
30
40
50
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
210 pF/m528 pF/m1060 pF/m
Dra
in C
urre
nt, I
D (
µA
) Drain C
urrent, ID (µA
)
Gate Voltage, VGS
(V)
COX
=
Expected result : ID increases with oxide capacitance Cox
but limited enhancement for high COX values
Expected result : ID increases with oxide capacitance Cox
but limited enhancement for high COX values
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Evaluation of Ballistic Transport
Unstrained Si. DG-MOSFET vs c-CNTFET
CNTFET : 70% of ballistic electrons at the drain end for Lch = 100nm
Unstrained Si DG : 50% of ballistic electrons pour Lch = 15 nm
CNTFET : 70% of ballistic electrons at the drain end for Lch = 100nm
Unstrained Si DG : 50% of ballistic electrons pour Lch = 15 nm
1
10
100
0 2 4 6 8 10 12
Lc = 50 nm
Lc = 25 nm
15 nm
CNTFET : Lch = 100 nm
Number of scattering events
Fra
ctio
n of
ele
ctro
ns (
%)
Si DG-MOSFET
VGS = VDS = 0.4V
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
ID-VDS characteristics
ION ≈ 10 – 30 µA. ION/ IOFF ≈ 5104– 5105ION ≈ 10 – 30 µA. ION/ IOFF ≈ 5104– 5105
COX (pF/m)
/EOT(nm)
210/1.4
560/0.4
1060/0.1
Expe.*1.5
S (mV/dec) 70 65 60 70
ION (µA) 24 40 44 5
gm (µS) 32 62 100 20
High values of S and gm are obtained
Acceptable agreement with experiments
High values of S and gm are obtained
Acceptable agreement with experiments
0
10
20
30
40
50
0 0.1 0.2 0.3 0.4 0.5 0.6
Dra
in C
urre
nt I
D (
µA
)
VDS (V)
Cox = 1060 pF/m
Cox = 210 pF/mVGS = 0.4 VVGS = 0.3 V
Device parameters extracted from simulation (Ioff=0.1nA)
* H. Dai, Nano Letter, vol.5, 345, (2005) : L=80nm, EOT=1.5nm
VDD = 0.4V
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
ION/IOFF ratio (VDD)
0 100
1 105
2 105
3 105
4 105
5 105
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
I ON
/IO
FF
ratio
Power Supply, VDD (V)
EOT = 0.1 nm CNTLch = 100 nm
EOT = 1.4 nm
GAA SiEOT = 1.2 nm
Lch = 19 nm
Lch = 15 nmexperiment*
Ioff=0.1nA
* H. Dai, Nano Letter, vol.5, 345, (2005) : L=80nm, EOT=1.5nm
Performances CNT for LC=100nm and VDD<0.4V
Performances Si for LC=15nm and VDD>0.7V
Performances CNT for LC=100nm and VDD<0.4V
Performances Si for LC=15nm and VDD>0.7V
Hugues Cazin d’Honincthun – URSI - 20/03/2007 UPS
Conclusion
This Monte Carlo simulation of a CNTFET shows excellent performances:
• Excellent electrostatic gate control (quantum capacitance regime)
• High fraction of ballistic electrons in the transistor channel
• High performances at relatively low power supply