<s>
The	O
Deal	B-Algorithm
–	I-Algorithm
Grove	I-Algorithm
model	I-Algorithm
mathematically	O
describes	O
the	O
growth	O
of	O
an	O
oxide	O
layer	O
on	O
the	O
surface	O
of	O
a	O
material	O
.	O
</s>
<s>
In	O
particular	O
,	O
it	O
is	O
used	O
to	O
predict	O
and	O
interpret	O
thermal	B-Algorithm
oxidation	I-Algorithm
of	O
silicon	O
in	O
semiconductor	B-Architecture
device	I-Architecture
fabrication	I-Architecture
.	O
</s>
<s>
The	O
model	O
was	O
first	O
published	O
in	O
1965	O
by	O
Bruce	O
Deal	O
and	O
Andrew	O
Grove	O
of	O
Fairchild	O
Semiconductor	O
,	O
building	O
on	O
Mohamed	O
M	O
.	O
Atalla	O
's	O
work	O
on	O
silicon	O
surface	B-Application
passivation	I-Application
by	O
thermal	B-Algorithm
oxidation	I-Algorithm
at	O
Bell	O
Labs	O
in	O
the	O
late	O
1950s	O
.	O
</s>
<s>
This	O
served	O
as	O
a	O
step	O
in	O
the	O
development	O
of	O
CMOS	B-Device
devices	O
and	O
the	O
fabrication	B-Architecture
of	O
integrated	O
circuits	O
.	O
</s>
<s>
The	O
model	O
assumes	O
that	O
the	O
oxidation	B-Operating_System
reaction	O
occurs	O
at	O
the	O
interface	O
between	O
the	O
oxide	O
layer	O
and	O
the	O
substrate	O
material	O
,	O
rather	O
than	O
between	O
the	O
oxide	O
and	O
the	O
ambient	O
gas	O
.	O
</s>
<s>
Given	O
these	O
assumptions	O
,	O
the	O
flux	B-General_Concept
of	O
oxidant	O
through	O
each	O
of	O
the	O
three	O
phases	O
can	O
be	O
expressed	O
in	O
terms	O
of	O
concentrations	O
,	O
material	O
properties	O
,	O
and	O
temperature	O
.	O
</s>
<s>
By	O
setting	O
the	O
three	O
fluxes	B-General_Concept
equal	O
to	O
each	O
other	O
,	O
the	O
following	O
relations	O
can	O
be	O
derived	O
:	O
</s>
<s>
The	O
second	O
mode	O
gives	O
a	O
quadratic	O
growth	O
and	O
occurs	O
when	O
the	O
oxide	O
thickens	O
as	O
the	O
oxidation	B-Operating_System
time	O
increases	O
.	O
</s>
<s>
The	O
following	O
table	O
lists	O
the	O
values	O
of	O
the	O
four	O
parameters	O
for	O
single-crystal	O
silicon	O
under	O
conditions	O
typically	O
used	O
in	O
industry	O
(	O
low	O
doping	B-Algorithm
,	O
atmospheric	O
pressure	O
)	O
.	O
</s>
<s>
The	O
Deal	B-Algorithm
–	I-Algorithm
Grove	I-Algorithm
model	I-Algorithm
works	O
very	O
well	O
for	O
single-crystal	O
silicon	O
under	O
most	O
conditions	O
.	O
</s>
<s>
In	O
silicon	O
nanostructures	O
(	O
e.g.	O
,	O
silicon	B-Algorithm
nanowires	I-Algorithm
)	O
this	O
rapid	O
growth	O
is	O
generally	O
followed	O
by	O
diminishing	O
oxidation	B-Operating_System
kinetics	O
in	O
a	O
process	O
known	O
as	O
self-limiting	O
oxidation	B-Operating_System
,	O
necessitating	O
a	O
modification	O
of	O
the	O
Deal	B-Algorithm
–	I-Algorithm
Grove	I-Algorithm
model	I-Algorithm
.	O
</s>
<s>
If	O
the	O
oxide	O
grown	O
in	O
a	O
particular	O
oxidation	B-Operating_System
step	O
greatly	O
exceeds	O
25nm	O
,	O
a	O
simple	O
adjustment	O
accounts	O
for	O
the	O
aberrant	O
growth	O
rate	O
.	O
</s>
<s>
The	O
model	O
yields	O
accurate	O
results	O
for	O
thick	O
oxides	O
if	O
,	O
instead	O
of	O
assuming	O
zero	O
initial	O
thickness	O
(	O
or	O
any	O
initial	O
thickness	O
less	O
than	O
25nm	O
)	O
,	O
we	O
assume	O
that	O
25nm	O
of	O
oxide	O
exists	O
before	O
oxidation	B-Operating_System
begins	O
.	O
</s>
<s>
In	O
the	O
1980s	O
,	O
it	O
became	O
obvious	O
that	O
an	O
update	O
to	O
the	O
Deal-Grove	B-Algorithm
model	I-Algorithm
is	O
necessary	O
to	O
model	O
the	O
aforementioned	O
thin	O
oxides	O
(	O
self-limiting	O
cases	O
)	O
.	O
</s>
<s>
The	O
Massoud	O
model	O
is	O
analytical	O
and	O
based	O
on	O
parallel	O
oxidation	B-Operating_System
mechanisms	O
.	O
</s>
<s>
It	O
changes	O
the	O
parameters	O
of	O
the	O
Deal-Grove	B-Algorithm
model	I-Algorithm
to	O
better	O
model	O
the	O
initial	O
oxide	O
growth	O
with	O
the	O
addition	O
of	O
rate-enhancement	O
terms	O
.	O
</s>
<s>
The	O
Deal-Grove	B-Algorithm
model	I-Algorithm
also	O
fails	O
for	O
polycrystalline	O
silicon	O
(	O
"	O
poly-silicon	O
"	O
)	O
.	O
</s>
<s>
This	O
effect	O
may	O
be	O
neglected	O
in	O
many	O
cases	O
,	O
but	O
heavily	O
doped	B-Algorithm
silicon	I-Algorithm
oxidizes	O
significantly	O
faster	O
.	O
</s>
<s>
The	O
pressure	O
of	O
the	O
ambient	O
gas	O
also	O
affects	O
oxidation	B-Operating_System
rate	O
.	O
</s>
