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Sept. 27, 2004
Oxidation of Si
Why spend a whole lecture on oxidation of Si?
Ge has high µe, µh , Ge stable…
… but no oxide
GaAs has high µe and direct band…
… no oxide
Why SiO2?
SiO2 is stable down to 10-9 Torr, T > 900°C
SiO2 can be etched with HF which leaves Si unaffected
SiO2 is a diffusion barrier for B, P, As
SiO2 is good insulator, ρ > 1016 Ωcm, Eg = 8 eV!
O2
SiO2 has high dielectric breakdown field, 500 V/µm
SiO2
SiO2 growth on Si ⇒ clean Si / SiO2 interface
Si
because DSi through SiO2 << DOxy through SiO2
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Because DSi through SiO2 << DOxy through SiO2
SiO2 growth occurs at inside surface
Si + O2 → SiO2
or
dtOxide
1
O2
SiO2
dtOxide
Si
Si + 2H2O = SiO2 + 2H2
(faster growth,
more porous,
lower quality)
Unsaturated bond
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O2
SiO2
dtOxide
Si
Only when oxide is
patterned does it
cause problems
with planarity.
Extra free volume
in dangling bonds of
amorphous SiO2 =>
Implications different for field vs. patterned oxide.
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RCA cleaning station for removing organic
contaminants, Na+ and other ions as well as
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.
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Probably safe to say that
entire course of semiconductor industry would be
different without good SiO2 growth on Si wafer.
Device fabrication, especially MOS,
would be more difficult.
Depositing SiO2 or Al2O3 is not clean.
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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
SiO2 growth: the Deal-Grove model.
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SiOx growth
Deal-Grove model
model is similar
to CVD
SiO2but
growth occurs
with extra step
at Si / SiO2 interface
added:
oxygen
diffusion
through SiOx.
because
O2
of silicon oxidation
O2
SiO2
Si
D (SiO 2 ) >> D (SiO 2 )
Si
Growth Process limited by
dead
layer SiO
2
O2
1.
P(O2) = Pg ∝ Cg
Concentration C
g
Co
3. Adhesion of Cs(O2) at SiO2 surface C0
4. Diffusion O2 through SiO2
5. Chemical reaction rate
Cs
J1
2. Transport O2 to SiO2 surface across dead layer J1
Si
J2
J2
Ci
J3
x
J3
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Deal-Grove model of silicon oxidation
J1 = J2 = J3
Oxide growth rate
Ideal gas law:
O2
PgV = NkT
Concentration
Cg
P
N
= Cg = g
V
kT
J1
(Cgg "- C
(C
Css))
tdead layer
C "C
x ox
Turbulence =>
O
J2 = D 2 (SiO 2 ) C00 - Ci i
J1 = hg(Cg - Cs)
Diffusion (D cm2/s)
to J2 & Henry
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Ci
x
J3 = kiCi
rate constant
ki (cm/s)
Equate J2 & Henry to J3
" Ci = f n ( Pg ,hg ,H,DO 2 , x oxide ,k i )
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!
Co
J3
Henry’s law
Equate ideal!gas & J1
Si
Cs
J2
C0 = HPs = HkBTCs
JJ11 > D
dead
layer SiO
2
8
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Sept. 27, 2004
Deal-Grove model of silicon oxidation
dead
layer SiO
2
O2
J1 = J2 = J3
Concentration
Cg
" Ci = f n ( Pg ,hg ,H,DO 2 , x oxide ,k i )
J1
Cs
Co
J2
!
Ci =
HPg / ki
1
x
1
+ ox
+
h
DO2 k i
mass
transport
!
x
(ki = ks in text)
Diffusion Reaction
J3
J
J1
Ci
J3
hg
HkT
h=
Si
2
Slowest process controls concentration of oxygen at interface…
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Ci =
Limits:
HPg / ki
1
x
1
+ ox
+
O2
h
D
ki
Growth
mass
limited by: transport
diffusion
!
Diffusion
limited:
!
DO2/xox < ki, h,
Ci =
9
h=
hg
very large
HkT
reaction
Reaction-rate limited:
ki < h, DO2/xox
HPg DO2
k i x ox
Ci = HPg
!
Slower process controls concentration of oxygen at interface,
which in turn controls growth rate…
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τ is the time
corresponding to growth
of pre-existing oxide
Oxide growth rate
Rate of growth=
dx ox
J
Ck
= 3 = i i,
dt
n SiOx n SiOx
Ci =
( nSiO = # O2 molecules in oxide / cm3 )
dx ox
22
3
n!
SiO = 2.2 x 10 / cm , dry
4.4 x 1022 / cm3, H2O
x ox
"1
( $# h +
x0
!
x ox 1 %
+ 'dx ox =
D ki &
t
! dt
HPg
(n
0
SiO x
2
ox
x + Ax ox = B( t + " )
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HPg /n SiOx
1 x ox 1 rate depends on xoxide
+
+
h D ki
SiO2
!
Si
xo
"1 1 %
A = 2D$ + ' (length)
# h ki &
length 2
B = 2DH Pg n SiOx (
)
time
2
" = x 0 + Ax 0 B (time)
(
!
!
dt
=
HPg / ki
1
x
1
+ ox
+
h
DO2 k i
Si
t>0
)
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!
t≈0
11
!
x ox
"1 x
1%
( $# h + Dox + k '&dx ox =
i
x0
t
HPg
(n
0
"1 1%
A = 2D$$ + ''
# h ki &
B = 2DH Pg n SiOx
x ox + Ax ox = B( t + " )
"A + A 2 + 4B(t + # )
x ox =
!
2
!
Si
SiO x
2
!
SiO2
dt
!
Si
" = ( x + Ax 0 ) B
Rate constants A and B known experimentally;
both ∝ D = D0e-Ea/kT
xox
Thick oxide => parabolic rate constant, B
Thin oxide => linear rate constant, B/A
.Eq
2
2
x ox
<< Ax ox
"Quad
""
# x ox $
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!
!
B
(t + % )
A
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t
τ
.Eq
2
x ox
>> Ax ox "Quad
""
# x ox = B( t + $ )
!
t>0
2
0
Parabolic and linear growth rates
!
t≈0
xox
t
12
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How thick is thick, how thin is thin??
x 2ox + Ax ox = B( t + " )
x 2ox > Ax ox or x ox > A " thick
!
( wet oxidation is much faster than dry)
!
x ox > 0.165 µm,dry; > 0.226 µm,wet " thick
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!
( wet oxidation is much faster than dry)
DO 2 (SiO 2 )
DH2 O (SiO 2 )
<
700-1200ºC, 1 atm, 0.1 µm / hr
=> dry oxide, denser,
use for gate oxide.
!
750-1100°C, 25 atm , 1 µm / hr
=> wet oxide,
more porous, poorer diffusion barriers;
use for etch oxide, field oxide.
Dry O2 + 1-3% Cl; Cl is a metal getter ⇒ cleaner oxide.
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Exercise: calculate xOX grown for 1 hr. in dry oxidation at 1100 °C.
From table, A = 0.09 µm , B = 0.027 µm2 / hr, τ = 0.076 hr.
x ox =
"A + A 2 + 4B( t + # )
2
(0.1 - 1.0 µm / hr is typical)
= 0.14 µm
This is the oxide thickness grown over any thin native oxide present.
Now you calculate xox for steam oxidation at same time and temp.
!
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Why is wet oxidation faster?
SiO2/Si interface, local charges
O2
SiO2
Si
xox
cO2
Oxygen gradient exists in SiOx.
Oxide near the interface
is a sub oxide, SiOx, x < 2.
SiO, which is often
+ charged.
WHY?
SiO2
Electronegativity
Si
Si
eSi4+
O2O
SiO2
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Si
Si2+
O2-
O2-
O
O
SiO
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Si3+
eO2O
SiO+ + e16
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SiO2/Si interface and dry vs. wet oxidation
O2
SiO2
Which species
diffuse quickly?
Si
Large
O -,
Slow
xox
cO2
O,
small
H-,
SiO+
SiO2
SiO+
SiO2
cO2
e- .
H, H+, h+
fast
e- .
H+, h+
Gases unstable at
Outside
100oC,
dissociate at surface.
in oxide
O + O- +
O2
->
h+
2H2O -> O + O- + h+ +
n(H+, H, H-)
e- .
O-
What does dipole layer do to ions?
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SiO+
SiO2
cO2
O - + SiO+ -> SiO2
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Initial oxidation regime.
17
x 2ox + Ax ox = B( t + " )
Deal - Grove: at small xox,
x ox =
B
(t + " )
A
!
dx ox B
= = const.
dt
A
!
cOx
δx
!
O2
SiO2
Si
To explain this…
many models have been proposed.
It appears that SiO2 / Si interface is not sharp.
small xox
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Oxide grows not just at xox but also at
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x ox "
#x
2
18
!
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Sept. 27, 2004
Structure of SiO2
Quartzite
Si
Si
Si
Si
Si
Si
Si
Si
O
Si
Si
Si
Si
O
Si
O
O
bridging
oxygen
Si
disorder
Amorphous
fewer bridging O’s,
tetrahedral
some non-bridging.
network
Network modifiers B, P
replace Si
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Effects of Dopants on Oxidation of Si → SiO2
We will see segregation coefficient for crystal growth:
k=
max
c solid
max
c liquid
Related parameter
for segregation of impurity X on oxidation:
!
m=
generally < 1
c X (in Si)
c X (in SiO2)
Impurity concentration profiles depend on m, Dx in Si, Dx in SiO2 and growth rate
(not shown below):
m > 1 ( oxide rejects impurity,
X)
!
x
x
D (SiO 2 ) < D (Si)
J x (SiO 2 ) int = J x (Si)
SiO2
Si
Dx (SiO 2 ) > Dx (Si)
CX (0)
m < 1( oxide consumes X )
Dx (SiO 2 ) > Dx (Si)
SiO
Si
Dx (SiO 2 ) < Dx (Si)
2
CX (0)
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SiO2
Si
SiO2
Si
CX (0)
CX (0)
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Common dopants in Si enhance oxidation at higher concentration
boron
phosphorus
CP
Oxide thickness vs. wet oxidation time
For three different boron concentrations
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Linear, B/A, and parabolic, B, rate constants
vs. phosphorus concentration.
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Now, go grow
some glass!
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