Influence of gate capacitance on CNTFET performance using Monte Carlo simulation H. Cazin...

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

Influence of gate capacitance on CNTFET performance using Monte Carlo simulation H. Cazin...

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