step coverage by ald films - theory and examples of ideal
TRANSCRIPT
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
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Har
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Har
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Uni
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Sum
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Har
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Uni
vers
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Ack
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Har
vard
Uni
vers
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