Dev

ice

Sim

ulat

ion

for

Car

bon

Nan

otub

e El

ectr

onic

sJi

ng G

uo

Dep

artm

ent o

f EC

E, U

nive

rsity

of F

lorid

aG

aine

svill

e, F

L, 3

2611

1.In

trodu

ctio

n2.

NE

GF

form

alis

m3.

Sim

ulat

ion

App

roac

h4.

Dev

ice

Ana

lysi

s5.

Sum

mar

y

2

Ack

now

ledg

emen

ts

Theo

ry: M

ark

Lund

stro

m, S

upriy

o D

atta

(Pur

due)

Exp

erim

ent:

Hon

gjie

Dai

, Ali

Jave

y(S

tanf

ord)

3

)nm(

8.0d

eVE G

≈

()

()2 2

31

2kd

Ek

EG

+

±=

McE

uen,

Fuh

rer,

Par

k, IE

EE

Tra

ns. N

anot

ech.

, 1, 7

8, 2

002.

Car

bon

nano

tube

s

(see

als

o: R

. Sai

to, G

. Dre

ssel

haus

, and

M.S

. Dre

ssel

haus

, Phy

sica

l Pro

perti

es

of C

arbo

n N

anot

ubes

, Im

peria

l Col

lege

Pre

ss, L

ondo

n, 1

998.

)

4

Top-

dow

n an

d bo

ttom

-up

view

Gat

e

atom

istic

pZ

orbi

tals

Qua

ntum

app

roac

h-t

unne

ling

at M

/CN

T co

ntac

ts

-tun

nelin

g an

d in

terfe

renc

e in

th

e C

NT

Bot

tom

-up

view

Gat

e

Top-

dow

n vi

ew

DS

E

kmob

ility

Sem

icla

ssic

al a

ppro

ach

appl

icab

le o

nly

whe

n qu

antu

m

effe

cts

not i

mpo

rtant

5

gate

ele

ctro

de

sour

ceco

ntac

tV

= 0

Cha

lleng

es in

nano

scal

ede

vice

sim

ulat

ion:

1)de

scrip

tion

at a

n at

omis

tic le

vel

2)qu

antu

m d

escr

iptio

n of

ope

n sy

stem

s un

der b

ias

3)tre

atm

ent o

f ine

last

ic s

catte

ring

Qua

ntum

sim

ulat

ion

forN

anoe

lect

roni

cs

drai

nco

ntac

tV

> 0

Nan

osca

lede

vice

Our

app

roac

h: t

he G

reen

’s fu

nctio

n fo

rmal

ism

6

1.In

trodu

ctio

n2.

NE

GF

form

alis

m3.

Sim

ulat

ion

App

roac

h4.

Dev

ice

Ana

lysi

s5.

Sum

mar

y

Out

line

7

One

con

tact

γ

D(E

)

EF

])

()

([

0E

FE

NE

Ef

UE

DdtdN

−−

−=hγ

)(

)(

0FE

Ef

UE

DdE

N−

−= ∫

in-fl

ow:

0)

(f

UE

D−

hγ

out-f

low

:EN

hγ

Dat

ta, Q

uant

um T

rans

port

Ato

m to

Tra

nsis

tor,

Cam

brid

ge U

niv.

Pre

ss, 2

005

8

Two

cont

acts

])

([

])

([

22

11

EE

EN

fE

DN

fE

DdtdN

−+

−=

hh

γγ

in-fl

ow:

11

)(

fU

ED

−hγ

out-f

low

:EN

h1γin

-flow

:2

2)

(f

UE

D−

hγ

out-f

low

:EN

h2γ

D(E

)

γ 1γ 2

EF2

EF1

9

[]2

12

1

21

)(

2f

fU

ED

dEq

I−

+−

=∫

γγ

γγ

h

N=

dE ∫D(E

−U)

γ 1f 1

+γ 2f 2

γ 1+

γ 2

U=UL

+U0(N

−N0)

Two

cont

acts

N

U

U

N

“Poi

sson

”

“Tra

nspo

rt”

Rah

man

, Guo

, Dat

ta, L

unds

trom

, IE

EE

Tra

ns. E

lect

ron

Dev

., p.

189

7 ,2

003

D(E

)

γ 1γ 2

EF2

EF1

10

ε→

H[]

γ→

Γ[] Σ[]

G=ES

−H

−Σ

[]−1

N

[ρ

][H

]

[U]

[Σ1]

[Σ2]

[ΣS]

Mul

tiple

leve

ls

11

Non

equ

ilibriu

m G

reen

’s F

unct

ion

(NE

GF)

Gat

e

mol

ecul

e or

dev

ice

[H]

Σ 1Σ

2

Σ SD

Sf 1

f 2

G=EI

−H

−Σ 1

−Σ

2−

ΣS

[]−1

devi

ceco

ntac

tssc

atte

ring

I D=2q h

T(E)

∫f 1(E)−f 2(E)

()dE

[]

[] π

ρ2)

()

()

()

(2

21

1dE

Ef

EA

Ef

EA ∫

+=

+Γ

=G

G)

(A

2,12,1E

]G

GTrace[

)(

21

+Γ

Γ=

ET

Cha

rge

dens

ity (b

allis

tic)

Cur

rent

][

2,12,1

+1,

2Σ

−Σ

=Γ

i

12

1.In

trodu

ctio

n2.

NE

GF

form

alis

m3.

Sim

ulat

ion

App

roac

h4.

Dev

ice

Ana

lysi

s5.

Sum

mar

y

Out

line

13

Rea

l-spa

ce b

asis

(bal

listic

)

DS

Gat

e

atom

istic

(pZ

orbi

tals

)

c

t

H=

Σ D

ΣS

=∑

+

O

00

00

00

00

][

ττS

S

g

=∑

+]

[0

00

00

00

0

ττD

D

g

O

1]

[−

Σ−

Σ−

−=

DS

rH

EIG

Rec

ursi

ve a

lgor

ithm

for G

r : O

(m3 N

)La

ke e

t al.,

JA

P, 8

1, 7

845,

199

7

(m, 0

) CN

T

14

Rea

l-spa

ce re

sults

band

ga

p

inte

rfer

ence

2nd

subb

and

Con

fined

sta

tes

Gat

e

n+n+

i

15

Mod

e-sp

ace

appr

oach

(bal

listic

)

c

t

k

t

The qt

hm

ode

=

Nq

q

q

q

q

ub

bu

tt

ub

bu

HO

O

O3

2

1

cqk q

π2=

-Σ S

(1,1

) and

ΣD

(N,N

) an

alyt

ical

ly c

ompu

ted

-C

ompu

tatio

nal c

ost:

O(N

)re

al s

pace

O(m

3 N)

(m,0

) CN

T

16

Mod

e-sp

ace

resu

lts

n+n+

i

2 m

odes

real

spa

ce

Con

duct

ion

band

pro

file

(ON

)

coax

ial G

V

D=0

.4V

d CN

T~1n

mco

axia

l G

coax

ial G

2 m

odes

real

spa

ceco

axia

l G

Gat

e8n

m H

fO2

SiO

2

p++

Si

Pd

Pd

CN

T

17

Trea

tmen

t of M

/CN

T co

ntac

ts

M

CE VE

FE

tα0Bφ

met

allic

tube

ban

d

−≈

∑O

00

0αit

m

:0Bφ

band

dis

cont

inui

ty

18

Trea

tmen

t of M

/CN

T co

ntac

ts

Gat

e

VD=V

G=0

.4V

Cha

rge

trans

fer i

n un

it ce

ll: L

eona

rd e

t al.,

AP

L, 8

1, 4

835,

200

2

Met

alS

met

alD

tunn

elin

g

19

3D P

oiss

on s

olve

r

Gat

e8n

m H

fO2

SiO

2

p++

Si

PdPd

CN

TMet

hod

of m

omen

ts:

∫−

='

)'(

)'(

)(

rdr

rr

Kr

Vv

vv

vv

ρ

Elec

tros

tatic

ker

nel:

for 2

type

s of

die

lect

rics

avai

labl

e in

Ja

ckso

n, C

lass

ical

Ele

ctro

dyna

mic

s, 1

962

)'(

rr

Kv

v−

)'(

rr

Kv

v−

20

Num

eric

al te

chni

ques

give

n n:

---

> U

scf

“Poi

sson

”

give

n U s

cf:

--->

n

trans

port

equa

tion

Itera

teun

tilse

lf-co

nsis

tent

give

n n:

---

> U

scf

Poi

sson

give

n U s

cf:

--->

n

NE

GF

Tran

spor

t

Itera

teun

tilse

lf-co

nsis

tent

-N

on-li

near

Poi

sson

-R

ecur

sive

alg

orith

m fo

r

-G

auss

ian

quad

ratu

refo

r do

ing

inte

gral

-Pa

ralle

l diff

eren

t bia

s po

ints

-~2

0min

for f

ull I

-V o

f a 5

0-nm

C

NTF

ET

1]

[)

(−

∑−

∑−

−=

DS

HEI

EG

21

1.In

trodu

ctio

n2.

NE

GF

form

alis

m3.

Sim

ulat

ion

App

roac

h4.

Dev

ice

Ana

lysi

s5.

Sum

mar

y

Out

line

22

nano

tube

dia

met

er ~

1.7

nm

L ch

~50n

m

Gat

e8n

m H

fO2

SiO

2

p++

Si

PdPd

CN

T

Dev

ice

issu

es

1)C

an w

e m

odel

and

und

erst

and

I-V?

2)H

ow c

lose

to th

e ba

llist

ic li

mit?

3)W

hat i

s th

e ro

le o

f sca

tterin

g?

4)H

ow to

opt

imiz

eI O

N?

5)H

ow to

redu

ce I o

ff?

6)H

ow to

com

pare

to S

i MO

SFE

Ts?

Jave

y et

al,

Nan

o Le

tt., 2

004

23

Mod

elin

g I D

-VG

SB

hei

ght:

φ Bp=

0, d

CN

T~1

.7nm

RS=R

D~1

.7K

Ω

VD=

-0.3

V

expe

rimen

t-0

.2V

-0.1

Vth

eory

24

Two

kind

s of

tran

sist

ors

tunn

elin

gGS

VTE

n+n+

ior p

-

gate

sour

cedr

ain

met

alm

etal

ior p

-

gate

sour

cedr

ain

MO

SFE

TS

BFE

TC

arbo

n na

notu

bes

as S

chot

tky

barr

ier t

rans

isto

rsH

einz

eet

al,

PR

L, 8

9, 1

0680

1,20

02

25

Am

bipo

lar c

ondu

ctio

n (th

in o

xide

)

hole

con

duct

ion

at lo

w V

G

EFD

EFS

EC EV

EFD

EFS

EC

EV

elec

tron

cond

uctio

n at

hig

h V G

log

I D

VG

barri

er th

ickn

ess

set b

yt in

s (g

eom

etric

scr

eeni

ng)

φ bp=

0

26

t ox=

40 n

m

φ Bp=

0

EFS

EFD

EC

EV

opaq

ue b

arrie

r for

el

ectr

on tu

nnel

inng

barri

er th

ickn

ess

set b

yt in

s (g

eom

etric

scr

eeni

ng)

Thic

k ox

ide

Guo

, Dat

ta a

nd L

unds

trom

, IE

EE

Tra

ns. E

D, 5

1, 1

72,

2004

VD=-

0.4V

27

How

clo

se to

bal

listic

lim

it?

expe

rimen

tth

eory

(bal

listic

)

SB

hei

ght:

φ Bp=

0, d

CN

T~1

.7nm

, R

S=R

D~1

.7K

Ω

Del

iver

nea

r-ba

llist

ic D

C o

n-cu

rren

t

G

28

No

surfa

ce ro

ughn

ess

scat

terin

g in

CN

Ts

CN

Tgr

aphe

ne

Phon

on s

catte

ring

dom

inat

es in

CN

TsY

ao, K

ane,

and

Dek

keer

, Phy

s. R

ev. L

ett.,

84,

294

1, 2

000

29

Pho

non

scat

terin

g in

CN

TsE

kA

P

E

kO

P(in

tra.

)O

P (in

terv

alle

y)

AP

: lon

g m

fp(

~1

µm)

OP

: sho

rt m

fp(

~1

0nm

)

ωh

E

k

ωh

Par

k, R

osen

blat

t, Y

aish

et a

l.,N

ano

Lett.

, 4, 5

17

high

1λhigh2λ

Jave

y, G

uo, P

auls

son

et a

l., P

hys.

Rev

. Let

t., 9

2, 1

0680

4, 2

004

Ky/k

0(K

x=0)

30

Sm

all e

ffect

of O

P s

catte

ring

E

Pos

ition

, x

OP

/ZB

P e

mis

sion

E FS

E FD

eV16.0

~ωh

conf

irmed

by

a se

para

te M

onte

-Car

lo s

imul

atio

n

Del

iver

nea

r-ba

llist

ic D

C o

n-cu

rren

t

31

How

clo

se to

the

ballis

tic li

mit?

expe

rimen

t

balli

stic

, φbp

=0

balli

stic

, φbp

=-0.

3V

φB

p= 0

E FS

E FD

zero

SB

stil

l lim

its I D

E V

E FS

E FD

E V

nega

tive

φ Bp

Guo

and

Lun

dstro

m,

IEE

E T

ED

, 49,

1897

, 200

2 (s

ilico

n)

VG=-

0.4V

32

Impr

ovin

g I O

N:S

calin

g t in

s

8nm

HfO

2

4nm

HfO

2

8nm

HfO

2

4nm

HfO

2

E FS

E FD

barri

er th

ickn

ess

set b

yt in

s (g

eom

etric

scr

eeni

ng)

VG=-

0.4V

33

Red

uce

I offfo

r thi

n t in

s

d CN

T~1.

7nm

t in

s~8n

m

d CN

T~1.

0nm

t in

s~4n

mV

D=-

0.4V

Eg~

0.8e

V/d

(nm

)

EFS

EFD

elec

tron

leak

age

hole

leak

age

p∆

n∆

2~

~D

gp

neV

E−

∆∆

near

ly tr

ansp

aren

t

smal

l dC

NT

redu

ces

I min

34

Red

uce

I offus

ing

MO

SFE

T-lik

e st

ruct

ure

elec

tric

al S

/D d

opin

gA

ppen

zelle

ret a

l, P

RL,

200

4

chem

ical

S/D

dop

ing

Che

n et

al.,

IED

M T

ech

Dig

, 200

4

Jave

y et

al.,

Nan

o Le

tt., 2

005

gate

p+p+

I

o-h+

o-h+

Gat

e8n

m H

fO2

10nm

SiO

2

p++

Si, V

bot=

-2.5

V

PdPd

++

++

+

35

ambi

pola

r SB C

NTF

ETM

OSF

ET-li

ke C

NTF

ET

band

gap

elec

tron

leak

age

negl

igib

le

hole

leak

age

unip

olar

gp

E~

∆

Sup

pres

sed

ambi

pola

r con

duct

ion

Red

uce

I offus

ing

MO

SFE

T-lik

e st

ruct

ure

EFS

EFD

elec

tron

leak

age

hole

leak

age

p∆

n∆

2~

~D

gp

neV

E−

∆∆

EC EV

EFS

EFD

36

How

to c

ompa

re to

Si M

OS

FET?

source

drain

S

source

drain

Si C

hann

elW

Si M

OSF

ETs

CN

T ar

ray

FETs

Key

dev

ice

met

rics:

I ONI OFF

τ=C GV D

DI ON

37

τvs

. IO

N/I O

FFte

chni

que

log10ID

V DD

V Glo

g 10

(I ON

/ I O

FF)

τ

subt

hres

hold

τ=C GV D

DI ON

Con

trol o

f VT

shift

s th

e w

indo

w

38

Com

pare

to 9

0nm

Si M

OS

FETs

90nm

Si n

-MO

S d

ata

from

Ant

onia

dis

and

Nay

feh,

MIT

39

1.In

trodu

ctio

n2.

NE

GF

form

alis

m3.

Sim

ulat

ion

App

roac

h4.

Dev

ice

Ana

lysi

s5.

Sum

mar

y

Out

line

40

Sum

mar

y: S

imul

atio

n A

ppro

ach

Qua

ntum

Tra

nspo

rt (N

EGF

form

alis

m)

-Ato

mis

tic d

escr

iptio

n

-Non

-equ

ilibr

ium

tran

spor

t

-Ine

last

ic s

catte

ring

Thre

e di

men

sion

al E

lect

rost

atic

s

-Met

hod

of m

omen

ts

Com

puta

tiona

l tec

hniq

ues

-rec

ursi

ve a

lgor

ithm

-mod

e-sp

ace

appr

oach

-par

alle

l sim

ulat

ion

41

Sum

mar

y

1)I-V

can

be

mod

eled

and

exp

lain

ed.

2)Th

e C

NTF

ET

deliv

ers

near

-bal

listic

I ON

3)S

calin

g t in

san

d us

ing

high

-κim

prov

es I O

N

4)Th

in t i

nsre

sults

in a

mbi

ploa

rcon

duct

ion

5)U

sing

sm

all d

CN

Ttu

be o

r MO

SFE

T-lik

e st

ruct

ure

supp

ress

es a

mbi

pola

r con

duct

ion

6)Th

e C

NTF

ET

perfo

rman

ce is

pro

mis

ing

42

Out

look

:

Tran

sist

ors

-3D

ele

ctro

stat

ics

-pho

non

scat

terin

g

-Adv

ance

d tra

nsis

tor s

truct

ures

-AC

cha

ract

eris

tics

New

dev

ices

-CN

T op

toel

ectro

nic

devi

ces

-CN

T-ba

sed

nano

sens

ors