Oxidation of Si
Why spend a whole lecture on oxidation of Si?
Ge has high m
e
,m
h
,Ge stable… … but no oxide
GaAs has high m and direct band… … no oxide
e
Why SiO
2
SiO
2
is stable down to 10
-9
Torr,T > 900°C
SiO
2
can be etched with HF which leaves Si unaffected
SiO
2
is a diffusion barrier for B,P,As
SiO
2
is good insulator,r > 10
16
Wcm,E
g
= 8 eV!
O
2
SiO
2
has high dielectric breakdown field,500 V/mm
SiO
2
growth on Si fi clean Si / SiO
2
interface
because D
Si
through SiO
2
<< D
Oxy
through SiO
2
SiO
2
Si
dt
Oxide
Sept,19,2003 3.155J/6.152J 1
2
So SiO
2
growth occurs at inside surface
Si + O
2
SiO
2
or
Si + 2H
2
O = SiO
2
+ 2H
2
(faster growth,
more porous,
lower quality)
O
2
SiO
2
Si
dt
Oxide
Sept,19,2003 3.155J/6.152J
O
2
SiO
2
Si
dt
Oxide
in dangling bonds of
=>
Extra free volume
amorphous SiO
2
Implications different for field vs,patterned oxide,
Sept,19,2003
3.155J/6.152J
3
Cleaning station for removing organic
contaminants and native oxide (by HF-dip)
from Si wafers,
Oxidation furnaces for controlled growth of
oxide layer on Si,
1050 C and steam for field oxide,
Sept,19,2003 3.155J/6.152J 4
Probably safe to say that
entire course of semiconductor industry would be
different without SiO
2
.
Device fabrication,especially MOS,
more difficult,
Depositing SiO
2
or Al
2
O
3
is not clean,
Sept,19,2003 3.155J/6.152J 5
It’s no accident that the world leader in
Si chip technology,Intel,has been led
by the flamboyant Hungarian,Andy
Grove.
As a young researcher at Fairchild
Semiconductor,he wrote the book on
SiO
2
growth,the Deal-Grove model.
Sept,19,2003 3.155J/6.152J 6
Deal-Grove model of silicon oxidation
SiO
2
Si
O
2SiO
2
growth occurs
at Si / SiO
2
interface
because D
O
2
(SiO
2
) >> D
Si
(SiO
2
)
Growth Process limited by
O
2
1,P(O
2
) = P
g
μ C
g
2,Transport O
2
to SiO
2
surface across dead layer J
1
3,Adhesion of C
s
(O
2
) at SiO
2
surface C
0
4,Diffusion O
2
through SiO
2
J
2
Concentration
SiO
2
Si
C
g
C
s
C
o
C
i
dead
layer
J
1
J
2
J
3
x
5,Chemical reaction rate J
3
Sept,19,2003 3.155J/6.152J 7
C
g
J
2
C
0
- C
i
J
1
(C -C
s
)
N
V
Deal-Grove model of silicon oxidation
Oxide growth rate
Ideal gas law,
P
g
V = NkT
O
2
Concentration
= C =
g
C
0
= HP = Hk
B
TC
s s
(C
g
g
- C )
s
Henry’s law
> D
t
dead layer
SiO
2
Si
dead
layer
C
i
C
o
J
3
3
C
s
J
1
J
1
C
g
2
J
2
= J= J
C-C
0
J
1 g
(C
g
- C
s
)= h
Turbulence =>
2
= D
O
2
(
SiO
2
)
s
x
ox
x
J
3 i
C
i
= k
rate constant
Diffusion (D cm
2
/s)
P
g
kT
k
i
(cm/s)
Equate ideal gas + J
1
Equate J
2
+ Henry to J
3
Sept,19,2003
to J
2
+ Henry
3.155J/6.152J
fi C
i
= f
n
P
g
,h
g
,H,D
O
2
,x
oxide
,k
i
( )
8
Deal-Grove model of silicon oxidation
J
1
= J
2
= J
3
O
2
Concentration
fi C
i
= f
n
(
P
g
,h
g
,H,D
O
2
,x
oxide
,k
i
)
h
g
h =
x
SiO
2
Si
C
g
C
s
C
o
C
i
dead
layer
J
2
J
3
J
1
HkT
C
i
=
HP
g
/k
i
1
h
+
x
ox
D
O
2
+
1
k
i
mass (k
i
= k in text)
s
Diffusion
Reaction
transport
J
2
J
3
J
1
Slowest process controls concentration of oxygen at interface…
Sept,19,2003 3.155J/6.152J 9
2
Limits:
Growth
limited by,
C
i
=
HP
g
/k
i
1
h
+
x
ox
D
O
2
+
1
k
i
mass
transport
diffusion
reaction
Reaction-rate limited,
Diffusion limited,
k
i
< h
g
,D
O
2/x
ox
h
g
h = very large
HkT
C
i
=
HP
g
D
O
2/x
ox
< k
i
,h
g
,
C
i
=
g
D
O
2
k
i
x
ox
HP
Sept,19,2003
Slower process controls concentration of oxygen at interface,
which in turn controls growth rate…
Oxide growth rate
C
i
k
i
Rate of growth
=
dx
ox
=
J
3
=,
dt N N
HP
g
/k
i
C
i
=
1 x 1
+
ox
+
h D
O
2
k
i
( N = # O
2
molecules incorporated / cm
3
)
N = 2.2 x 10
22
/ cm
3
,dry
dx
ox
dt
=
HP
g
/N
1
h
+
x
ox
D
+
1
k
i
rate depends on x
oxide
4.4 x 10
22
/ cm
3
,H
2
O
x
ox
ê
1
t
o
SiO
2
ox
g
ú á
+
x
+
1
dx
ox
=
ú
HP
dt
Si
h D k
i
ˉ
N
x
0
0
t 0x
ê
11
x
ox
2
+ Ax
ox
= + t
( )
B t
A = 2D
á
+
(length)
h k
i
ˉ
Si
(
length
2
t > 0
B = 2DH P N )
g
time
2
t =
(
x
0
+ Ax
0
)
B (time)
Sept,19,2003 3.155J/6.152J 11
Sept,19,2003 3.155J/6.152J 12
Parabolic and linear growth rates
1
h
+
x
ox
D
+
1
k
i
ê
á
ˉ
x
0
x
ox
ú
dx
ox
=
HP
g
N
0
t
ú
dt
A = 2D
1
h
+
1
k
i
ê
á
á
ˉ
B = 2DH P
g
N
t = x
0
2
+ Ax
0
()
B
x
ox
2
+ Ax
ox
= Bt+ t
()
SiO
2
Si
t 0
Si
t >0
x
ox
=
-A + A
2
+ 4B(t + t)
2
Rate constants A and B known experimentally;
both μ D = D
0
e
-Ea/kT
t
x
ox
t
x
ox
2
>> Ax
ox
Quad,Eq
x
ox
= Bt+ t
()
Thick oxide => parabolic rate constant,B
x
ox
2
<< Ax
ox
2 Quad,Eq
x
ox
@
B
A
t + t
()
Thin oxide => linear rate constant,B/A
t
x
ox
( )wet oxidation is much faster than dry
D
O
2
SiO
2
( )
<
D
H
2
O
SiO
2
( )
700-1200oC,1 atm,0.1 mm / hr
750-1100°C,25 atm,1 mm / hr
fi dry oxide,denser,
=> wet oxide,
use for gate oxide.
more porous,poorer diffusion barriers;
use for etch oxide,field oxide.
Dry O
2
+ 1-3% Cl; Cl is a metal getter fi cleaner oxide,
Sept,19,2003 3.155J/6.152J 13
Exercise,calculate x
OX
grown for 1 hr,in dry oxidation at 1100 °C.
From table,A = 0.09 mm,B = 0.027 mm
2
/ hr,t = 0.076 hr,
-A +
(
A
2
+ 4Bt + t
)
(0.1 - 1.0 mm / hr is typical)
x = = 0.14 mm
ox
2
This is the oxide thickness grown over any thin native oxide present,
Now you calculate x
ox
for steam oxidation at same time and temp,
Sept,19,2003 3.155J/6.152J 14
SiO
2
/Si interface,local charges
O
2
SiO
2
Si
Oxide near the interface
is a sub oxide,SiO
x
,x < 2,
x
ox
C
O2
SiO
2
SiO,which is often
+ charged.
WHY?
Electronegativity
Si
Si Si
-
e
Si
2+
Si
3+
O
2-
Si
4+
e
-
O
2-
O
2-
O
2-
OO
SiO
2
SiO
-
SiO
+
+e
Sept,19,2003 3.155J/6.152J 15
SiO
2
/Si interface and dry vs,wet oxidation
O
2
SiO
2
Si
SiO
+
C
O2
x
ox
e
SiO
2
->
-
+ h
+
2H
2
-
+ h
+
+
in oxide
O + O
Gases unstable at 100
O -> O + O
-
.
Outside
O
2
n(H
+
,H,H
-
)
Which species
diffuse quickly?
Large small
-
O,H
-
,H,H
+
,h
+
Slow fast
o
C,dissociate at surface,
SiO
2
SiO
+
C
O2
-
e,
H
+
,h
+
SiO
2
SiO
+
C
O2
-
e,
O
-
O
- +
-> SiO
2
O,
+SiO
Sept,19,2003 3.155J/6.152J 16
2
x + Ax
Initial oxidation regime.
= B t + t
)(
O
2
x
ox
,
dx
ox
dt
=
B
A
=
To explain this…
It appears that SiO
2
/ Si interface is not sharp,
x
ox
=
B
A
t + t
( )
dx
SiO
2
Si
ox
ox
Deal - Grove,at small
con
many models proposed,
st,
small x
Oxide grows not just at x
ox
but also at x -
ox
ox
2
Sept,19,2003 3.155J/6.152J 17
3.155J/6.152J
Structure of SiO
2
Quartzite
Si
Si
O
Si Si Si
Si
bridging
O
Si Si Si
O
oxygen
Si
O
Si Si Si
Si
disorder
Amorphous
tetrahedral
fewer bridging O’s,
some non-bridging.
network
Network modifyers B,P
replace Si
Sept,19,2003 18
Effects of Dopants on Oxidation of Si? SiO
2
C
We will see segregation coefficient for crystal growth,k =
C
S
generally < 1
L
Related parameter
C
X
(in Si)
for segregation of impurity X on oxidation,
m =
C
X
(in SiO
2
)
Impurity concentration profiles depend on m,D
x
in Si,D
x
in SiO
2
and growth rate
(not shown below),
m > 1 ( oxide rejects impurity,X)
SiO
2
Si
x
D
x
(SiO
2
) < D
x
(Si)
D (SiO
2
) > D
x
(Si)
J (SiO
2
) = J (Si)
C
X
(0)
xx
int
C
X
(0)
SiO
2
Si
m < 1( oxide consumes X )
D
x
(SiO
2
) < D
x
(Si)
D
x
(SiO
2
) > D
x
(Si)
C
X
(0)
SiO
2
Si
C
X
(0)
Sept,19,2003 3.155J/6.152J
SiO
2
Si
19
Common dopants in Si enhance oxidation at higher concentration
Oxide thickness vs,wet oxidation time Linear,B/A,and parabolic,B,rate constants
For three different boron concentrations vs,phosphorus concentration,
Sept,19,2003 3.155J/6.152J 20