МММ / 04_lecture5
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Oxide growth rate
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HPg / ki |
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Rate of growth = |
dxox |
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J3 |
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Ciki |
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Ci |
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1 |
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xox |
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1 |
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dt |
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N |
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N |
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h |
+ DO2 |
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+ ki |
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( N = # O2 molecules incorporated / cm3 ) |
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dx |
ox |
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HPg / N |
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N = 2.2 x 1022 / cm3, dry |
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rate depends on xoxide |
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1 |
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xox |
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4.4 x 1022 / cm3, H O |
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dt |
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h |
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D |
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ki |
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xox 1 |
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x |
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1 ˆ |
t |
HPg |
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SiO2 |
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ox |
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+ |
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˜dxox = |
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dt |
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Si |
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x0 h |
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D |
ki ↓ |
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N |
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x |
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0 |
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o |
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t 0 |
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A = 2D |
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(length) |
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2 |
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Axox = B(t + τ ) |
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˜ |
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h |
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ki ↓ |
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x ox |
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length |
2 |
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Si |
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B = 2DH P |
N |
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t > 0 |
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g |
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time |
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τ = (x02 + Ax0 )
B (time)
Sept. 19, 2003 |
3.155J/6.152J |
11 |
xox |
1 |
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xox |
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t |
HPg |
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+ |
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D |
k |
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ox |
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N |
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x0 |
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i |
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x2 + Axox = B(t + τ )
ox
xox = −A + 
A2 + 4B(t + τ )
2
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SiO2 |
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Si |
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t 0 |
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A = 2D |
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ki |
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h |
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B = 2DH Pg |
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t > 0 |
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τ = (x02 + Ax0 )
B
Rate constants A and B known experimentally; both D = D0e-Ea/kT
Parabolic and linear growth rates |
xox |
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Thick oxide => parabolic rate constant, B |
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>> Axox |
Quad .Eq |
= B(t + τ) |
xox |
xox |
t
τ
Thin oxide => linear rate constant, B/A |
xox |
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2 |
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Quad .Eq |
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B |
(t + τ ) |
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xox |
<< Axox |
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xox |
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A |
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t |
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Sept. 19, 2003 |
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3.155J/6.152J |
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12 |
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DO2 (SiO2 ) <
700-1200ºC, 1 atm, 0.1 μm / hr fi dry oxide, denser,
use for gate oxide.
DH2 O (SiO 2)
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 fi cleaner oxide.
Sept. 19, 2003 |
3.155J/6.152J |
13 |
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.
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−A + A2 + 4B(t + τ ) |
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(0.1 - 1.0 μm / hr is typical) |
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xox = |
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= 0.14 |
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2 |
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This is the oxide thickness grown over any thin native oxide present.
Now you calculate xox for steam oxidation at same time and temp.
Sept. 19, 2003 |
3.155J/6.152J |
14 |
SiO2 |
Si |
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O2 |
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SiO2/Si interface, local charges
Oxide near the interface is a sub oxide, SiOx, x < 2.
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xox |
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C |
O2 |
SiO2 |
SiO, which is often |
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+ charged. |
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WHY? |
Electronegativity |
Si |
e- |
Si |
Si |
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2+ |
e- |
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Si |
Si3+ |
O2- |
Si4+ |
O2- |
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O2- |
O2- |
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O |
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O |
O |
O |
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SiO2 |
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SiO |
SiO+ + e- |
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Sept. 19, 2003 |
3.155J/6.152J |
15 |
SiO2/Si interface and dry vs. wet oxidation
SiO2 |
Si |
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O2 |
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Which species diffuse quickly?
Large small
O -, O, H-, H, H+, h+
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xox |
C |
O2 |
SiO2 |
SiO+ |
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e-.
Gases unstable at 100oC, dissociate at surface.
Outside |
in oxide |
O2 |
-> O + O- + h+ |
2H2O -> O + O- + h+ + |
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n(H+, H, H-) |
Slow |
fast |
CO2 SiO2 |
SiO+ |
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e-. |
H+, h+ |
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CO2 SiO2 SiO+
e-.
O-
O - + SiO+ -> SiO2
Sept. 19, 2003 |
3.155J/6.152J |
16 |
Initial oxidation regime. |
x ox |
+ Axox = B(t + τ ) |
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Deal - Grove: at small xox,
B
xox = A (t + τ )
dxox = B = const. dt A
SiO2 |
Si |
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O2 |
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To explain this… many models proposed.
It appears that SiO2 / Si interface is not sharp.
Oxide grows not just at xox but also at |
xox |
− δx |
small xox |
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2 |
Sept. 19, 2003 |
3.155J/6.152J |
17 |
Structure of SiO2
Si
Si 
Si 
Si
Si 
Si 
Si
Si 
Si 
Si
Amorphous tetrahedral network
Quartzite
Si 
O 
Si
bridging
O O
oxygen
Si 
O 
Si
disorder
fewer bridging O’s, some non-bridging.
Network modifyers B, P replace Si
Sept. 19, 2003 |
3.155J/6.152J |
18 |
Effects of Dopants on Oxidation of Si SiO2
We will see segregation coefficient for crystal growth: |
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CS |
generally < 1 |
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k = |
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CL |
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Related parameter |
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m = |
CX |
(in Si) |
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for segregation of impurity X on oxidation: |
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CX |
(in SiO2) |
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Impurity concentration profiles depend on m, Dx in Si, Dx in SiO2 and growth rate
(not shown below):
m > 1 ( oxide rejects impurity, X)
Dx (SiO 2) < Dx (Si)
Jx (SiO 2) int = Jx (Si)
SiO2 |
Si |
CX (0) |
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Dx (SiO 2) > Dx (Si) |
SiO2 |
Si |
CX (0) |
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m < 1( oxide consumes X ) |
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Dx (SiO 2) < Dx (Si) |
Si |
Dx (SiO 2) > Dx (Si) |
SiO2 |
Si |
SiO2 |
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CX (0) |
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CX (0) |
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Sept. 19, 2003 |
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3.155J/6.152J |
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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 |