Step

Cov

erag

e by

ALD

Film

s:

Theo

ry a

nd E

xam

ples

of

Idea

l and

Non

-Idea

l Rea

ctio

ns

Roy

G. G

ordo

nHa

rvar

dUn

iver

sity

Harv

ard

Univ

ersit

yC

ambr

idge

, MA

Har

vard

Uni

vers

ity11

Step

Cov

erag

e in

Hol

es w

ith H

igh

Asp

ect R

atio

Step

cov

erag

e =

(b/a

) x10

0%

Ai

L/d

aA

spec

t rat

io =

L/d

ALD

i10

0%t

i

a ALD

can

giv

e10

0% st

ep c

over

age

even

inna

rrow

hol

es w

ith h

igh

aspe

ct ra

tio.

Ld

How

hig

h an

asp

ect r

atio

can

be

coat

ed?

Toda

y: T

heor

etic

al a

nd e

xper

imen

tal a

nsw

ers

b

Har

vard

Uni

vers

ity22

Theo

ryof

Step

Cov

erag

ein

ALD

Out

line

Theo

ryof

Step

Cov

erag

ein

ALD

assu

mpt

ions

fl

ft

form

ulas

for s

tep

cove

rage

Exam

ples

of I

deal

Rea

ctio

ns

Non

-idea

l cha

ract

eris

tics

of s

ome

ALD

reac

tions

thld

itith

erm

alde

com

posi

tion

plas

ma-

radi

cal r

ecom

bina

tion

adso

rptio

n of

reac

tant

s in

to fi

lmco

mpe

titiv

e ad

sorp

tion

of b

ypro

duct

s

Har

vard

Uni

vers

ity33

etch

ing

by re

acta

nts

or b

ypro

duct

s

Fast

Sel

f-Lim

iting

Sur

face

Rea

ctio

nsSi

mpl

ifyin

gas

sum

ptio

ns:

Sim

plify

ing

assu

mpt

ions

:

•Pre

curs

or m

olec

ules

reac

t with

pro

babi

lity

1on

each

colli

sion

with

the

surf

ace

until

allr

eact

ive

each

colli

sion

with

the

surf

ace

until

allr

eact

ive

site

s ar

e fil

led.

•Afte

r all

site

s ha

ve re

acte

d, a

dditi

onal

pre

curs

or

mol

ecul

es s

catte

r diff

usel

y fr

om th

e su

rfac

e.1

Prob

abili

tyf

ti

1

of re

actio

n 0

Har

vard

Uni

vers

ity44

Surf

ace

cove

rage10

0 %

Dep

ositi

on o

n Fl

at S

urfa

ces

Req

uire

men

ts fo

r Sat

urat

ion

of a

Sur

face

Rea

ctio

n:

1.M

inim

um n

umbe

r of

pre

curs

or m

olec

ules

(sto

ichi

omet

ry).

2M

inim

umnu

mbe

rof

colli

sion

swith

surf

ace

need

edto

bind

2.M

inim

umnu

mbe

rof

colli

sion

swith

surf

ace

need

edto

bind

this

num

ber o

f pre

curs

or m

olec

ules

to su

rfac

e (k

inet

ics)

.

Har

vard

Uni

vers

ity55

How

Man

y M

olec

ules

Sat

urat

e a

Flat

Sur

face

?

S =

area

den

sity

of p

recu

rsor

mol

ecul

es c

hem

isor

bed

per m

2 :X

-ray

refle

ctiv

ity(X

RR

):de

nsity

×thi

ckne

ssX

-ray

refle

ctiv

ity(X

RR

):de

nsity

×thi

ckne

ssR

uthe

rfor

d B

acks

catte

ring

(RB

S): i

nteg

ratio

n of

pea

k Q

uartz

Cry

stal

Mic

roba

lanc

e (Q

CM

)

For e

xam

ple,

ALD

of 0

.1 n

m/c

ycle

of H

fO2,

dens

ity 9

.23

g/cm

3 ,re

quire

s SH

f=

2.5×

1018

Hf a

tom

s/m

2 /cyc

leH

f

Har

vard

Uni

vers

ity66

Min

imum

Tim

e N

eede

d to

Sat

urat

e Fl

at S

urfa

ce

From

kin

etic

theo

ry, F

lux

J = P

(2m

kT)-1

/2

Min

imum

time

t=ar

eade

nsity

/flux

=S

/J=

S(2

mkT

)½/P

Min

imum

time

tar

eade

nsity

/flux

S/J

S(2

mkT

)/P

“Exp

osur

e” n

eede

d fo

r sat

urat

ion

= (P

t) =

S(2

mkT

)½

Har

vard

Uni

vers

ity77

Exam

ples

of F

ast S

elf-L

imiti

ng R

eact

ions

½(P

t) fla

t=

S(2

mkT

)½

prec

urso

rS

MT

(Pt)

prec

urso

rS

(101

8 m-2

)M

(am

u)T (K

)(P

t) fla

t(1

0-6

Torr

-sec

)

MA

l4

462

573

23

Me 3

Al

4.4

6257

32.

3

Hf(N

Me 2

) 42.

541

147

33.

1

W(N

Me 2

) 2(N

t Bu)

2

3.6

414

623

5.2

La((

i PrN

) 2C

Me)

32.

356

357

33.

7

Har

vard

Uni

vers

ity88

Dep

ositi

on in

Hig

h-A

spec

t Rat

io H

oles

Nho

le=

Add

ition

al p

recu

rsor

mol

ecul

es re

quire

d fo

r sur

face

are

a of

hol

e

(t) ho

le=

Add

ition

al ti

me

requ

ired

to sa

tura

te su

rfac

e ar

ea o

f hol

e

Fort

hefo

llow

ing

deriv

atio

nse

eR

oyG

Gor

don

Den

nis

Hau

sman

n

Har

vard

Uni

vers

ity99

Fort

hefo

llow

ing

deriv

atio

n,se

eR

oyG

.Gor

don,

Den

nis

Hau

sman

n,Es

ther

Kim

and

Jos

eph

Shep

ard,

Che

mic

al V

apor

Dep

ositi

on9,

73

(200

3)

How

Man

y M

olec

ules

for 1

00%

Ste

p C

over

age?

Nw

all=

num

ber o

f pre

curs

or m

olec

ules

nee

ded

to c

oat w

all

N=

SA

rea

=SA

=S

A4

LL

dN

wal

l=S

Are

a wal

l=

SAho

le=

SA

hole4

(def

ine

aspe

ct ra

tio =

a=

L/d

= le

ngth

/ di

amet

er)d

¼d2

Aho

le

Nw

all=

SA

hole4a

LIf

man

y m

ore

mol

ecul

es

than

Nar

eav

aila

ble

d

than

Nw

alla

reav

aila

ble,

then

P =

con

stan

t

Har

vard

Uni

vers

ity1010

Add

ition

al E

xpos

ure

is A

lso

Nee

ded

“Exp

osur

e” (i

n La

ngm

uirs

) = ti

me

(in m

icro

-sec

onds

)m

ultip

lied

bypr

ecur

sorp

artia

lpre

ssur

e(in

Torr

)pre

sent

mul

tiplie

dby

prec

urso

rpar

tialp

ress

ure

(inTo

rr)p

rese

ntat

the

open

end

of t

he h

ole.

Ifth

tti

ii

tith

thIf

the

prec

urso

r con

cent

ratio

n va

riesi

ntim

e,th

enth

eex

posu

re is

def

ined

by

t'

dt)'t(PEx

posu

re0

dt)t(PEx

posu

re

We

will

show

that

ace

rtai

nm

inim

umex

posu

reis

We

will

show

that

ace

rtai

nm

inim

umex

posu

reis

requ

ired

for

100%

step

cov

erag

e of

a h

ole.

Har

vard

Uni

vers

ity1111

How

Muc

h A

dditi

onal

Exp

osur

e is

Nee

ded?

Sinc

e ho

le d

iam

eter

(~nm

) <<

mea

n fr

ee p

ath

(~ 1

00

m),

flow

regi

me

in a

hol

e is

mol

ecul

ar (K

nuds

en d

iffus

ion)

The

unco

ated

low

er p

ortio

n of

a h

ole

acts

as a

n id

eal v

acuu

m p

ump:

Flux

at e

ntra

nce

to h

ole

= P(

2m

kT)-½

LFl

ux a

t thi

s poi

nt re

duce

d by

[1 +

(¾

/d

)]-1

(com

pare

tocr

yopu

mp

atth

een

dof

api

pe)

d

(com

pare

tocr

yopu

mp

atth

een

dof

api

pe)

thus

J(

) = P

(2m

kT)-1

/2[1

+ (¾

/d

)]-1

Har

vard

Uni

vers

ity1212

or

(P/

J) =

(2m

kT)1/

2[1

+(¾

/d

)]

Add

ition

al E

xpos

ure

to C

oat W

alls

of a

Hol

eH

ow m

uch

time

(dt)

is re

quire

d fo

r eno

ugh

mol

ecul

es to

diff

use

dow

n th

e co

ated

upp

er p

art o

f a h

ole

to c

oat a

n in

crem

enta

l dis

tanc

e (d

) of t

he h

ole?

4Sd(

mol

ecul

es)

Sd(A

wal

l)S

(d

dtra

nspo

rt ra

teJA

hole

J (¼

d2 )4S Jd

d=

==

dt =

Aho

let

P'

Expo

sure

t 0P

LJ

d)J/

P(d

)d/S4(p

L 0

0

d

d

Har

vard

Uni

vers

ity1313

Inte

grat

e to

Fin

d Ex

posu

re fo

r Coa

ting

Hol

e

2L 0

2/1w

alls

)d/

3()d/

4(d

mkT

2S

)tP(

22/1

22/1

)2/3(

4kT

2S

)d/L

)(2/3(

)d/L(4

mkT

2S A

sim

ilar c

alcu

latio

n fo

r coa

ting

the

botto

m

2 a)2/3(

a4m

kT2

S

gaf

ter t

he w

alls

are

com

plet

ely

coat

ed, g

ives

(Pt) b

otto

m=

S (2

mkT

)½[1

+ (3

/4)a

]

Add

to g

et th

e to

tal e

xpos

ure

for c

oatin

g bo

th b

otto

m &

wal

ls:

Har

vard

Uni

vers

ity1414

(Pt) t

otal

= S

(2m

kT)½

[1 +

(19/

4)a

+ (3

/2)a

2 ]

Expo

sure

Nee

ded

to C

over

a H

ole

(Pt)

=S

(2m

kT)½

[1+

(19/

4)a

+(3

/2)a

2 ](P

t) tot

al=

S(2

mkT

)½[1

+(1

9/4)

a+

(3/2

)a2 ]

For l

arge

asp

ect r

atio

a, t

he a

2te

rm d

omin

ates

Expo

sure

(Pt) t

otal

~ S

(2m

kT)½

(3/2

) a2

The

requ

ired

expo

sure

incr

ease

s as

the

squa

reof

the

aspe

ct ra

tio.

aspe

ctra

tioa

S-1/

2 (9

mkT

/2)-1

/4(e

xpos

ure)

1/2

aspe

ctra

tioa

~S-

1/2 (

9m

kT/2

)-1/4

(exp

osur

e)1/

2

whe

re S

= s

atur

atio

n de

nsity

(fro

m g

row

th p

er c

ycle

)m

= m

olec

ular

mas

s of

pre

curs

ork

= B

oltz

man

n’s

cons

tant

T=

tem

pera

ture

(K)

Har

vard

Uni

vers

ity1515

Tte

mpe

ratu

re(K

)P

t = e

xpos

ure

Min

imum

Exp

osur

e fo

r Con

form

al C

oatin

g

Si(P

t)S

(2kT

)½Si

nce

(Pt) f

lat=

S(2

mkT

)½w

e ca

n w

rite

the

expo

sure

as

(Pt) h

ole

= (P

t) fla

t{1

+ (1

9/4)

a +

(3/2

)a2 }

~ (P

t) fla

t(3

/2)a

2fo

r a >

> 1

1a

for

flat

for

expo

sure

3ho

lefo

rex

posu

re2

a2/1

whe

rea

=as

pect

ratio

=L/

dfo

raci

rcul

arho

le

flat

for

expo

sure

3

Har

vard

Uni

vers

ity1616

whe

rea

aspe

ctra

tioL/

dfo

raci

rcul

arho

le

Opt

ical

Mea

sure

men

t of S

tep

Cov

erag

e

Use

a te

st st

ruct

ure

with

ver

y hi

gh a

spec

t rat

io h

ole:

Fuse

d si

lica

capi

llary

tubi

ng w

ith 2

0 m

inne

r di

amet

er.

2 cm

leng

th g

ives

a h

ole

with

100

0:1

aspe

ct r

atio

.

Mea

nfr

eepa

that

200

o C0

2To

rris

400

m>>

20m

;M

ean

free

path

at20

0o C

,0.2

Torr

is40

0m

>>20

m;

tran

spor

t is b

y m

olec

ular

diff

usio

n as

in sm

alle

r fe

atur

es.

Imag

e in

terf

eren

ce p

atte

rn w

ith o

ptic

al m

icro

scop

e

Har

vard

Uni

vers

ity1717

ALD

of T

anta

lum

Oxi

de fr

om T

a(N

Me 2

) 5

Al

dih

hl

lkl

id

Rea

ctio

n: 2

Ta(

NM

e 2) 5

+ 5

H2O

Ta2O

5+

10

Me 2

NH

•Als

odo

ne w

ith o

ther

tant

alum

alk

ylam

ides

:(te

rt-b

utyl

imid

o)tri

s(di

ethy

lam

ido)

tant

alum

•Dep

ositi

on in

itiat

es im

med

iate

ly o

n hy

drox

ylat

ed su

rfac

es

•ALD

rate

:abo

ut0

07na

nom

eter

sper

cycl

e•A

LDra

te:a

bout

0.07

nano

met

ersp

ercy

cle

•Ide

al A

LD b

ehav

ior f

rom

150

to 2

50 o C

•Yie

ld n

ear 1

00%

Har

vard

Uni

vers

ity1818

Mea

sure

men

t of S

tep

Cov

erag

eA

LD T

a 2O

5co

atin

g 1

m th

ick

insi

de 2

0 m

tubi

ng

Dar

kin

terf

eren

ceba

nds

Ope

n en

d of

cap

illar

y

Dar

kin

terf

eren

ceba

nds

End

of c

oatin

gV

iew

ed in

mon

ochr

omat

ic g

reen

ligh

t

Out

erdi

amet

erO

uter

diam

eter

of c

apill

ary

Vie

wed

in w

hite

ligh

t

Har

vard

Uni

vers

ity1919

Mea

sure

men

t of S

tep

Cov

erag

eD

istr

ibut

ion

of A

LD T

a 2O

5co

atin

g th

ickn

ess

insi

de m

icro

-bor

e ca

pilla

ry tu

bing

1000

1200

)

600

800

1000

ess (nm

Tail

due

to s

ticki

ng

coef

ficie

nt <

100

%,

200

400

Thickne

51:1

aspe

ctra

tio

and

to n

arro

win

g of

dia

met

er fr

om

20m

to18

m0

010

2030

4050

6070

Dist

ance

(dia

met

ers)

51:1

aspe

ctra

tio20

mto

18m

Har

vard

Uni

vers

ity2020

Dist

ance

(dia

met

ers)

ALD

of M

etal

lic W

N

WB

ut NN

But

+ N

H3

WN

NM

e 2M

e 2N

Bis

(tert

-but

ylim

ido)

bis(

dim

ethy

lam

ido)

tung

sten

,vo

latil

e liq

uid

prec

urso

r

ALD

of a

mor

phou

s tu

ngst

en(II

I) ni

trid

e at

270

-380

o C

01

/l

t350

o C0.

1 nm

/cyc

le a

t350

o C

Har

vard

Uni

vers

ity2121

Step

Cov

erag

e of

WN T

opT

opU

nifo

rm c

over

age

in h

oles

with

43:1

aspe

ctra

tio33

nm

33 n

mw

ith43

:1as

pect

ratio

Expe

rimen

tal e

xpos

ure

2.1

x 10

-2To

rr-s

ec /

cycl

e32

nm

Bot

tom

32 n

m

Bot

tom

y

Theo

retic

alm

inim

umex

posu

re=

Theo

retic

alm

inim

umex

posu

re=

(5.2

x 1

0-6 )

x {1

+ (1

9/4)

43+

(3/2

)432

} = 1

.5x

10-2

Torr

-sec

Har

vard

Uni

vers

ity2222

2.1

>1.

5, s

o co

mpl

ete

step

cov

erag

e pr

edic

ted

and

obse

rved

Step

Cov

erag

e in

Hig

h A

spec

t Rat

io H

oles

AL

D W

N c

oatin

g 40

nm

thic

k in

side

fuse

d si

lica

capi

llary

tubi

ng w

ith 2

0 m

icro

n in

ner

diam

eter

py

g

Ope

n en

d E

nd o

f coa

ting,

210

diam

eter

sin

of tu

bing

210

diam

eter

sin

Har

vard

Uni

vers

ity2323

ALD

WN

Ste

p C

over

age

vs. E

xpos

ure

Asp

ect r

atio

= S

-1/2

(9m

kT/2

)-1/4

(ex

posu

re)1

/2

120

140

160

180

atio

6080100

120

spect Ra

02040

As

010

020

030

040

0

Squa

re R

oot o

f Exp

osur

e (L

angm

uirs

1/2 )

Har

vard

Uni

vers

ity2424

ALD

of A

l 2O3

from

TM

A a

nd w

ater

Com

pute

r sim

ulat

ions

of s

tep

cove

rage

for t

he A

LD re

actio

n

2 M

e 3A

l + 3

H2O

=>

Al 2O

3+

6 C

H4

carr

ied

out a

t Inf

ineo

n (n

ow Q

imon

da) a

gree

com

plet

ely

with

i

td

ithth

il

fl

expe

rimen

ts a

nd w

ithth

e si

mpl

efo

rmul

a:

(Pt) h

ole

= S(

2m

kT)½

x {1

+ (1

9/4)

a +

(3/2

)a2 }

=(2

.3x

10-6

Torr

-sec

)x{1

+(1

9/4)

a+

(3/2

)a2 }

Har

vard

Uni

vers

ity2525

(2.3

x10

Torr

sec)

x{1

+(1

9/4)

a+

(3/2

)a}

Step

Cov

erag

e of

ALD

SiO

2

Alu

min

um-c

atal

yzed

dep

ositi

on o

f SiO

2

from

tris

(tert

-but

oxy)

sila

nol

For h

igh

expo

sure

s of

the

sila

nol,

the

step

cove

rage

islim

ited

byth

est

epco

vera

geis

limite

dby

the

alum

inum

from

the

reac

tion

of M

e 3A

l.

For a

= 4

3, th

e M

e 3A

l exp

osur

e m

ust b

e >

(2.3

x 1

0-6

Torr

-sec

) x {1

+ (1

9/4)

43 +

Har

vard

Uni

vers

ity2626

(3/2

)432

} = 7

x 1

0-3

Torr

-sec

Part

ial S

tep

cove

rage

of A

LD S

iO2

For v

ery

smal

l Me 3

Al e

xpos

ures

,

610

5T

~6

x 10

-5To

rr-s

ec,

the

silic

a de

posi

tion

is c

onfin

ed

toju

stth

eto

pof

the

hole

sa

~3

toju

stth

eto

pof

the

hole

sa

~3

Expo

sure

(hol

e)/e

xpos

ure(

flat)

= 6x

10-5

/ 2.3

x10-

6=

26

1+ (1

9/4)

a +

(3/2

)a2

= 29

for

a =

3

Har

vard

Uni

vers

ity2727

ALD

of H

afni

um O

xide

from

Hf(N

Me 2

) 4

Al

dih

hh

fi

lkl

id

Rea

ctio

n: H

f(N

Me 2

) 4+

2 H

2OH

fO2

+ 4

Me 2

NH

•Als

odo

ne w

ith o

ther

hafn

ium

alk

yl a

mid

es:

Die

thyl

am

ide

(NEt

2) a

nd E

thyl

met

hyl a

mid

e (N

MeE

t)

•Dep

ositi

on in

itiat

es im

med

iate

ly o

n hy

drox

ylat

ed su

rfac

es

•ALD

rate

:abo

ut0

1na

nom

eter

sper

cycl

e•A

LDra

te:a

bout

0.1

nano

met

ersp

ercy

cle

•Ide

al A

LD b

ehav

ior f

rom

50

to 3

50 o C

•Yie

ld n

ear 1

00%

Har

vard

Uni

vers

ity2828

Step

Cov

erag

e of

HfO

2

Uni

form

cov

erag

e on

ly d

own

toas

pect

ratio

a=

32:1

toas

pect

ratio

a32

:1

Expe

rimen

tale

xpos

ure

coat

edEx

perim

enta

lexp

osur

e

4x

10-3

Torr

-sec

/ cy

cle

Theo

retic

al e

xpos

ure

=(3

x10

-6)x

{1+

(19/

4)32

+(3

/2)3

22}

=(3

x10

-6)x

{1+

(19/

4)32

+(3

/2)3

22}

=5

x 10

-3To

rr-s

ec

Har

vard

Uni

vers

ity2929

unco

ated

Step

Cov

erag

e of

ALD

HfO

2U

nifo

rm c

over

age

over

aspe

ct ra

tio a

=43

:1

top

Expe

rimen

tal e

xpos

ure

30x

10-3

Torr

-sec

/ cy

cle

Theo

retic

alm

inex

posu

reTh

eore

tical

min

.exp

osur

e

= (3

.6 x

10-

6 ) x

{1 +

(19/

4)43

+(3

/2)4

32}

botto

m(3

/2)4

3}

=11

x 10

-3To

rr-s

ec

Har

vard

Uni

vers

ity3030

30>

11, s

o co

mpl

ete

cove

rage

pred

icte

d an

d ob

serv

ed

Step

Cov

erag

e in

Hig

h A

spec

t Rat

io H

oles

AL

D H

fO2

coat

ing

80 n

m th

ick

insi

de fu

sed

silic

a ca

pilla

ry tu

bing

with

20

mic

ron

inne

r di

amet

erp

yg

Ope

n en

d ~

End

of c

oatin

g,of

tubi

ng81

dia

met

ers i

n

Pred

icte

d10

302

)tP(2

2/13

2/1i

tl

Har

vard

Uni

vers

ity3131

Pred

icte

das

pect

ratio

8010

1.33

1030

2)t

P(3)t

P(2a

6fla

t

erim

enta

lex

p

LaA

lO3

Film

57nm

thic

kby

ellip

som

eter

on fl

atsu

rface

ALD

of L

aAlO

3w

ith h

igh

expo

sure

sa

O3

5t

cby

eps

oet

eo

atsu

ace

60 n

m

60 n

m53

nm

54 n

m

50 n

m

54 n

m

53 n

m

54nm

54nm H

arva

rd U

nive

rsity

323242

:1 a

spec

t rat

io (i

nitia

lly)

Cap

illar

y Te

st fo

r Ver

y H

igh

Asp

ect R

atio

s

LaA

lO3

1930

μm

/ 20

m ID

= 9

7=

aspe

ct ra

tio

Ass

umin

g th

e sa

tura

ted

vapo

r pre

ssur

e in

the

bubb

ler,

the

expo

sure

to th

e La

pre

curs

or s

houl

d be

0.0

6To

rr-s

ecp

p

From

the

obse

rved

asp

ect r

atio

, the

La

expo

sure

sho

uld

be(

6)

{(

/)

(/

)2 }

=(3

.7 x

10-

6To

rr-s

ec) x

{1 +

(19/

4)97

+(3

/2)9

72}

=0.

054

Torr

-sec

Har

vard

Uni

vers

ity3333

Cap

illar

y Te

st fo

r Ver

y H

igh

Asp

ect R

atio

s

PrA

lO3

220 μm

Asp

ectR

atio

of11

obse

rved

Asp

ectR

atio

of11

obse

rved

Equi

libriu

m v

apor

pre

ssur

e =>

exp

osur

e of

0.0

16 T

orr-

sec

Expo

sure

ded

uced

from

the

step

cov

erag

e is

16

x sm

alle

r

the

Prva

pori

slim

ited

byth

eki

netic

sof

subl

imat

ion

Har

vard

Uni

vers

ity3434

the

Prva

pori

slim

ited

byth

eki

netic

sof

subl

imat

ion,

not b

y its

equ

ilibr

ium

vap

or p

ress

ure

Step

Cov

erag

e in

Non

-Circ

ular

Hol

es

Gen

eral

ize

to n

on-c

ircul

ar h

oles

:A

spec

t rat

io a

=(d

epth

) x (p

erim

eter

) / 4

(are

a)

For c

ircul

ar h

oles

:a

= L

(2r)

/ 4(

r2) =

L /

(2r)

= d

epth

/ w

idth

For t

renc

hes:

a=

L x

(2 x

leng

th) /

4 (w

idth

x le

ngth

) = d

epth

/ 2

(wid

th)

(g

)(

g)

p(

)

(Not

e th

at fo

r tre

nche

s, c

onve

ntio

nally

a=

dept

h / w

idth

)

Sam

e fo

rmul

a fo

r ste

p co

vera

ge if

this

gen

eral

ized

ais

use

d

4i

hh

hl

ihd

h/id

h

Har

vard

Uni

vers

ity3535

4 x

easi

er to

coa

t tre

nche

s th

anho

les

with

sam

e de

pth/

wid

th

Slow

Sel

f-Lim

iting

Sur

face

Rea

ctio

nsSi

mpl

ifyin

gas

sum

ptio

ns:

Sim

plify

ing

assu

mpt

ions

:

•Pre

curs

or m

olec

ules

reac

t with

low

pro

babi

lity

f<<

1on

each

colli

sion

with

the

surf

ace

until

all

f<<

1on

each

colli

sion

with

the

surf

ace

until

all

reac

tive

site

s ar

e fil

led.

•Afte

r all

site

s ha

ve re

acte

d, a

dditi

onal

pre

curs

or

mol

ecul

es s

catte

r diff

usel

y fr

om th

e su

rfac

e.f

Prob

abili

tyf

ti

f

of re

actio

n 0

Har

vard

Uni

vers

ity3636

Surf

ace

cove

rage10

0 %

Slow

Sel

f-Lim

iting

Sur

face

Rea

ctio

ns

the

slow

step

isco

mpl

etin

gth

esu

rfac

ere

actio

n,

Iff-1

>> {

1 +

(19/

4)a

+ (3

/2)a

2 }

the

slow

step

isco

mpl

etin

gth

esu

rfac

ere

actio

n,no

t diff

usio

n in

to th

e ho

le.

(Pt) h

ole

~ (P

t) fla

t=

S(2

mkT

)½/ f

An

expo

sure

that

sat

urat

es a

flat

sur

face

will

als

o co

at th

e in

side

of a

hol

e un

iform

ly.

Expo

sure

s le

ss th

an th

is v

alue

coa

t the

hol

e un

iform

ly,

but w

ith a

thin

ner t

han

satu

rate

d co

atin

g.

Har

vard

Uni

vers

ity3737

Exam

ples

of S

low

Sel

f-Lim

iting

Rea

ctio

ns½

(Pt) f

lat=

S(2

mkT

)½/f

film

SM

Tf

(Pt)

film

S(1

018 m

-2)

M(a

mu)

T (K)

f(P

t) fla

t(T

orr-

sec)

CN

146

643

310

61

Cu 3

N1

466

433

~10-

61

Cu

446

643

3~2

x10-

50.

15

Co

534

152

3~1

0-5

0.5

Har

vard

Uni

vers

ity3838

Step

Cov

erag

e of

Cu 3

NU

nifo

rm c

over

age

in h

oles

with

43:1

aspe

ctra

tiow

ith43

:1as

pect

ratio

Expe

rimen

tale

xpos

ure

Expe

rimen

tale

xpos

ure

1To

rr-s

ec /

cycl

e

(sam

eas

forf

lats

urfa

ces)

(sam

eas

forf

lats

urfa

ces)

min

imum

exp

osur

e fo

r diff

usio

n

=(1

x10

-6)x

{1+

(19/

4)43

+(3

/2)4

32}=

0.00

3To

rr-s

ec

Har

vard

Uni

vers

ity3939

(1x

10)x

{1(1

9/4)

43(3

/2)4

3}

0.00

3To

rrse

c

=> d

iffus

ion

time

is n

ot li

miti

ng; c

ompl

ete

step

cov

erag

e

Step

Cov

erag

e of

Cu

Uni

form

cov

erag

e in

hol

es

with

43:

1 as

pect

ratio

Expe

rimen

tal e

xpos

ure

0.2

Torr

-sec

/ cy

cle

(sam

e as

for f

lat s

urfa

ces)

min

imum

exp

osur

e fo

r diff

usio

n(3

106 )

{1+

(19/

4)43

+(3

/2)4

32}

=(3

x 1

0-6 )

x {1

+(1

9/4)

43+

(3/2

)432

}=

0.00

8To

rr-s

ec

Har

vard

Uni

vers

ity4040

diffu

sion

is n

ot li

miti

ng; c

ompl

ete

step

cov

erag

e

Step

Cov

erag

e of

Cob

alt

Co

depo

site

d in

side

qua

rtz

capi

llary

tube

, 20

m d

iam

eter

hol

e

Asp

ect R

atio

= 2

20:1

Expe

rimen

tale

xpos

ure

~0.

5To

rr-s

ecEx

perim

enta

lexp

osur

e0.

5To

rrse

c

min

imum

exp

osur

e fo

r diff

usio

n=

(5x

10-6

)x{1

+(1

9/4)

210

+(3

/2)2

102 }

=(5

x10

)x{1

+(1

9/4)

210

+(3

/2)2

10}

=0.

4To

rr-s

ec

Bot

hdi

ffusi

onan

dre

actio

nra

telim

itth

isco

atin

g

Har

vard

Uni

vers

ity4141

Bot

hdi

ffusi

onan

dre

actio

nra

telim

itth

isco

atin

g.N

on-u

nifo

rm th

ickn

ess

is e

xpec

ted.

Inco

mpl

ete

Step

Cov

erag

eTh

erm

al d

ecom

posi

tion

Mos

tmet

al-o

rgan

icpr

ecur

sors

deco

mpo

sew

hen

Mos

tmet

alor

gani

cpr

ecur

sors

deco

mpo

sew

hen

the

surf

ace

tem

pera

ture

is to

o hi

gh.

Me 3

Ala

tT>

350

Me 3

Ala

tT>

350

Hf(N

EtM

e)4

at T

> 2

80

La(a

md)

3at

T >

330

W(N

Me 2

) 2(N

tBu)

2at

T>

400

=> T

hick

er c

oatin

g ne

ar e

ntra

nces

to h

oles

W(N

Me 2

) 2(N

tBu)

2at

T>

400

Har

vard

Uni

vers

ity4242

g

Inco

mpl

ete

Step

Cov

erag

eR

ecom

bina

tion

of p

lasm

as -

atom

s an

d ra

dica

ls

Mos

t sur

face

s ca

taly

ze th

e re

com

bina

tion

of a

tom

s an

d ra

dica

ls in

to le

ss re

activ

e m

olec

ules

plas

ma-

activ

ated

ALD

reac

tions

hav

e th

icke

r coa

ting

near

en

tran

ces

to h

oles

.

H +

Me 3

Al =

> A

l 7

5 %

ste

p co

vera

ge in

5:1

asp

ect r

atio

H +

N +

TiC

l 4=>

TiN

18

% s

tep

cove

rage

in 2

0:1

aspe

ct ra

tio

Har

vard

Uni

vers

ity4343

Inco

mpl

ete

Step

Cov

erag

eR

ever

sibl

e ab

sorp

tion

of a

reac

tant

into

film

Exam

ple:

2 L

aL3

+ 3

H2O

=>

La 2

O3

+ 6

HL

H2O

isab

sorb

edin

toth

efil

mdu

ring

the

H2O

dose

.H

2Ois

abso

rbed

into

the

film

durin

gth

eH

2Odo

se.

The

H2O

des

orbs

reve

rsib

ly d

urin

g th

e pu

rge.

The

deso

rptio

n is

rapi

d w

hen

the

film

is th

in (<

10 n

m).

Des

orpt

ion

from

thic

k fil

ms

(>10

nm

) is

slow

(min

utes

).

=>C

VDre

actio

n=>

non-

conf

orm

alco

atin

gs

Har

vard

Uni

vers

ity4444

CVD

reac

tion

non

conf

orm

alco

atin

gs

Inco

mpl

ete

Step

Cov

erag

eC

ompe

titiv

e ad

sorp

tion

of b

ypro

duct

sTi

Cl

2H

OTi

O4

HC

lTi

Cl 4

+2

H2O

=>

TiO

2+

4H

Cl

HfC

l 4+

2 H

2O =

> H

fO2

+ 4

HC

l

HC

l com

pete

s fo

r ads

orpt

ion

site

s w

ith M

Cl 4.

HC

l diff

uses

fast

er th

an M

Cl 4,

so

HC

l rea

ches

th

e ad

sorp

tion

site

s de

eper

in th

e ho

le fi

rst.

=> th

inne

r film

dee

per i

nsid

e ho

le.

Har

vard

Uni

vers

ity4545

Inco

mpl

ete

Step

Cov

erag

eE

tchi

ng o

f film

by

bypr

oduc

ts

Dep

ositi

on:

2 N

bCl 5

+ 5

H2O

=>

Nb 2

O5

+ 1

0 H

Cl

Etch

ing:

Nb 2

O5

+ 6

HC

l =>

2 N

bOC

l 3+

3 H

2O

Nb

O+

3N

bCl

=>5

NbO

Cl

Nb 2

O5

+3

NbC

l 5=>

5N

bOC

l 3

>f

lti

=> n

on-c

onfo

rmal

coa

tings

Har

vard

Uni

vers

ity4646

Inco

mpl

ete

Step

Cov

erag

eA

erog

els

have

ext

rem

ely

high

asp

ect r

atio

s, >

105

but h

ard

to d

efin

e ex

actly

bec

ause

tort

uous

pat

hs

ALD

coa

ting

insi

de a

erog

els

is

Uni

form

for p

recu

rsor

s w

ith h

igh

vapo

r pre

ssur

e:W

F 6, M

e 3A

l, Et

2Zn

(P >

10

Torr

)6

32

Non

-uni

form

for p

recu

rsor

s w

ith lo

w v

apor

pre

ssur

e:R

u, P

t, C

u, F

e (P

< 1

Tor

r, so

exp

osur

e is

too

low

),

,,

(,

p)

S. O

. Kuc

heye

v, J

. Bie

ner,

T. F

. Bau

man

n, Y

. M. W

ang,

A. V

. Ham

za,

Har

vard

Uni

vers

ity4747

y,

,,

g,,

Z. L

i, D

. K. L

ee a

nd R

. G. G

ordo

n, L

angm

uir2

4, 9

43(2

008)

Har

vard

Uni

vers

ity4848

Sum

mar

y of

Ste

p C

over

age

Mod

el A

ssum

ptio

nsve

ry fa

st o

r ver

y sl

ow s

urfa

ce re

actio

nsdi

ffuse

scat

terin

gof

non

reac

ting

prec

urso

rsdi

ffuse

scat

terin

gof

non-

reac

ting

prec

urso

rs

Kin

etic

The

ory

of S

tep

Cov

erag

e in

Nar

row

Hol

es:

1/2

1/2

1/4

aspe

ct ra

tio a

~ (P

t)1/2S-

1/2 (

9m

kT/2

)-1/4

hole

for

expo

sure

22/1

1a

for

flat

for

expo

sure

3ho

lefo

rex

posu

re2

a

Agr

eem

ent w

ith c

ompu

ter s

imul

atio

ns

Har

vard

Uni

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ity4949

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ity5151

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vard

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vers

ity5252