Influence of gate capacitance on CNTFET performance using Monte Carlo simulation H. Cazin d'Honincthun, S. Retailleau, A. Bournel, P. Dollfus, J.P. Bourgoin*

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


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


Plan






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


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


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


Plan






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


Plan






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


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


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


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


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


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


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


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

Documents

Influence of gate capacitance on CNTFET performance using Monte Carlo simulation H. Cazin d'Honincthun, S. Retailleau, A. Bournel, P. Dollfus, J.P. Bourgoin*