Download - Section 4: Thermal Oxidation
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EE143 - Ali Javey
Section 4: Thermal Oxidation
Jaeger Chapter 3
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EE143 - Ali Javey
Properties of SiO2
Thermal SiO2 is amorphous.Weight Density = 2.20 gm/cm3
Molecular Density = 2.3E22 molecules/cm3
Crystalline SiO2 [Quartz] = 2.65 gm/cm3
SiO2
<Si>
(1) Excellent Electrical InsulatorResistivity > 1E20 ohm-cm Energy Gap ~ 9 eV
(2) High Breakdown Electric Field > 10MV/cm
(3) Stable and Reproducible Si/SiO2 Interface
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EE143 - Ali Javey
Properties of SiO2 (cont’d)
(4) Conformal oxide growth on exposed Si surface
Si Si
SiO2
ThermalOxidation
SiSi Si
SiO2
ThermalOxidation
(5) SiO2 is a good diffusion mask for common dopants
D Dsio si2 e.g. B, P, As, Sb.
SiO2
Si
*exceptions are Ga (a p-type dopant) and some
metals, e.g. Cu, Au
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EE143 - Ali Javey
SiO2
Si
HF dip
Si
(6) Very good etching selectivity between Si and SiO2.
Properties of SiO2 (cont’d)
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EE143 - Ali Javey
Thermal Oxidation of Silicon
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EE143 - Ali Javey
Thermal Oxidation Equipment
Horizontal Furnace
Vertical Furnace
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EE143 - Ali Javey
Gas Diffusion
Solid-state Diffusion
SiO2
Formation
Si-Substrate
SiO2
Oxidant Flow(O2 or H2O)
Gas FlowStagnant Layer
Kinetics of SiO2 growth
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EE143 - Ali Javey
1m Si oxidized 2.17 m SiO2
Si
Si
SiO21m2.17 m
Silicon consumption during oxidation
si
oxoxsi N
NXX
oxox Xcmatoms
cmmoleculesX 46.0
/105
/103.2322
322
molecular density of SiO2
atomic density of Si
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EE143 - Ali Javey
The Deal-Grove Model of Oxidation
CG
Cs
Co
Ci
X0x
stagnant layer
SiO2 Si
F1 F2 F3
gastransport flux
diffusion fluxthrough SiO2
reaction fluxat interface
NoteCs Co
NoteCs Co
F: oxygen flux – the number of oxygen molecules that crosses a plane of a certain area in a certain time
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EE143 - Ali Javey
The Deal-Grove Model of Oxidation (cont’d)CG
Cs
Co
Ci
X0x
stagnantlayer
SiO2 Si
F1 F2 F3
NoteCs Co
NoteCs Co
F h C CG G S1
x
CDF
2
ox
io
X
CCD
is CkF 3
Diffusivity [cm2/sec]
Mass transfer coefficient [cm/sec].
“Fick’s Law of Solid-state Diffusion”
Oxidation reaction rate constant
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EE143 - Ali Javey
re temperatuabsolute=T
J/K x101.38=constant sBoltzmann'=k
energy activationE
exp
23-
A
kT
EDD A
O
Diffusivity: the diffusion coefficient
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EE143 - Ali Javey
The Deal-Grove Model of Oxidation (cont’d)CG
Cs
Co
Ci
X0x
stagnantlayer
SiO2 Si
F1 F2 F3
NoteCs Co
NoteCs Co
• CS and Co are related by Henry’s Law
• CG is a controlled process variable (proportional to the input oxidant gas pressure)
Only Co and Ci are the 2 unknown variables which can be solved from the steady-state condition:
F1 = F2 =F3 ( 2 equations)
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EE143 - Ali Javey
The Deal-Grove Model of Oxidation (cont’d)CG
Cs
Co
Ci
X0x
stagnantlayer
SiO2 Si
F1 F2 F3
NoteCs Co
NoteCs Co
so PHC
sCkTH
partial pressure of oxidantat surface [in gaseous form].
Henry’sconstant
from ideal gas law PV= NkT
HkT
CC o
s
Henry’s Law
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EE143 – Vivek Subramanian
The Deal-Grove Model of Oxidation (cont’d)CG
Cs
Co
Ci
X0x
stagnantlayer
SiO2 Si
F1 F2 F3
NoteCs Co
NoteCs Co
)( GA CHkTC
Fh
HkTC CG
A o1 ( )
321 FFF
Define
Similarly, we can set up equations for F2 and F3
Using the steady-state condition:
We therefore can solve for Co and Ci
h
1 2
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EE143 - Ali Javey
The Deal-Grove Model of Oxidation (cont’d)We have:
At equilibrium: F1=F2=F3
Solving, we get:
ox
io
X
CCDF2 is CkF 3 )1 ( oA
G CCh
hF
CC
k
h
k X
D
iA
s s ox
1
D
XkCC oxs
io 1
D
Xk
h
k1
CkCkFFFF
oxss
Asis321
Where h=hg/HkT
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EE143 - Ali Javey
The Deal-Grove Model of Oxidation (cont’d)We can convert flux into growth thickness from:
dt
dX
N
F ox
1
Oxidant molecules/unit volume required to form a unit volume of SiO2.
SiO2 Si
F
Xox
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EE143 - Ali Javey
The Deal-Grove Model of Oxidation (cont’d)
1
2
)11
(2
N
DCB
hkDA
A
gs
B
AXX ii
2
Initial Condition: At t = 0 , Xox = Xi
)(2 tBAXX oxoxSolution
Note: hg >>ks for typical oxidation condition
SiO2
Si
SiO2
Si
xox
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EE143 - Ali Javey
Dry / Wet Oxidation
N cm1
22 32 3 10 . / for O2 as oxidant
Si O SiO 2 2
Si H O SiO H 2 22 2 2
N cm1
22 34 6 10 . / for H2O as oxidant
Note : “dry” and “wet” oxidation have different N1 factors
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EE143 - Ali Javey
Bdt
dxA
dt
dxX
tBAXX
oxoxox
xox
2
)(0
2
t
t
Xox
t
ox
ox
XA
B
dt
dx
2
Summary: Deal-Grove Model
Oxide Growth Rate slowsdown with increase of oxide thickness
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EE143 - Ali Javey
(Case 1) Large t [ large Xox ]
BtX ox
(Case 2) Small t [ Small Xox ]
tA
BX ox
Solution: Oxide Thickness Regimes
1
4
12 2
BA
tAX ox
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EE143 - Ali Javey
Thermal Oxidation on <100> Silicon
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EE143 - Ali Javey
Thermal Oxidation on <111> Silicon
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EE143 - Ali Javey
Thermal Oxidation Example
A <100> silicon wafer has a 2000-Å oxide on its surface
(a) How long did it take to grow this oxide at 1100o C in dry oxygen?
(b)The wafer is put back in the furnace in wet oxygen at 1000o C. How long will it take to grow an additional 3000 Å of oxide?
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EE143 - Ali Javey
Thermal Oxidation ExampleGraphical Solution
(a) According to Fig. 3.6, it would take 2.8 hr to grow 0.2 m oxide in dry oxygen at 1100o C.
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EE143 - Ali Javey
Thermal Oxidation ExampleGraphical Solution
(b) The total oxide thickness at the end of the oxidation would be 0.5 m which would require 1.5 hr to grow if there was no oxide on the surface to begin with. However, the wafer “thinks” it has already been in the furnace 0.4 hr. Thus the additional time needed to grow the 0.3 m oxide is 1.5-0.4 = 1.1 hr.
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EE143 - Ali Javey
Thermal Oxidation ExampleMathematical Solution
hrhr
hrm
m
hrm
mt
hr
hrmm
hrm
m
hr
m
A
B
hr
m
nmXhr
m
kTx
A
B
hr
m
kTxB i
70.2174.0169.0
2.0
0236.0
2.0=
174.0169.0
025.0
0236.0
025.0
169.0 and 0.0236=B K, 1373=TFor
25 00.2
exp1071.3 23.1
exp1072.7=
3.1, Table From (a)
2
2
2
2
2
62
2
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EE143 - Ali Javey
Thermal Oxidation ExampleMathematical Solution
hrhr
hrm
m
hrm
mt
hr
hrm
m
hrm
m
hr
m
A
B
hr
m
Xhr
m
kTx
A
B
hr
m
kTxB i
07.1398.0742.0
5.0
314.0
5.0=
398.0742.0
2.0
314.0
2.0
742.0 and 0.314=B K, 1273=TFor
0 05.2
exp1070.9 78.0
exp1086.3=
3.1, Table From (b)
2
2
2
2
2
72
2
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EE143 - Ali Javey
Effect of Xi on Wafer Topography
SiO2 SiO2 Xi
1 32
Si
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EE143 - Ali Javey
Effect of Xi on Wafer Topography
SiO2 SiO2 Xi
1 32
Si
less oxide grownless Si consumed
less oxide grownless Si consumed
more oxide grownmore Si consumed
more oxide grownmore Si consumed
32
1
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EE143 - Ali Javey
Factors Influencing Thermal Oxidation
– Temperature
– Ambient Type (Dry O2, Steam, HCl)
– Ambient Pressure– Substrate Crystallographic Orientation– Substrate Doping
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EE143 - Ali Javey
High Doping Concentration Effect
n+
nn+
n
Coefficients for dry oxidation at 900oC as function of surface Phosphorus concentration
SiO2
Dry oxidation, 900oC
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EE143 - Ali Javey
AmorphousSiO2
CrystallineSi
Transmission Electron Micrograph of Si/SiO2 Interface
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EE143 - Ali Javey
potassiumpotassium
sodiumsodium
Thermal Oxide Charges
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EE143 - Ali Javey
To minimize Interface Charges Qf and Qit
•Use inert gas ambient (Ar or N2) when cooling down at end of oxidation step
•A final annealing step at 400-450oC is performed with 10%H2+90%N2 ambient (“forming gas”) after the IC metallization step.
Oxide Quality Improvement
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EE143 - Ali Javey
• Introduction of halogen species during oxidation e.g. add ~1- 5% HCl or TCE (trichloroethylene) to O2
reduction in metallic contamination improved SiO2/Si interface properties
MClClM
Na+ or K+ in SiO2 are mobile!
SiO2
Cl2
SiNa+
K+
Oxidation with Chlorine-containing Gas
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EE143 - Ali Javey
222 ClOHOHCl
Effect of HCl on Oxidation Rate
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EE143 - Ali Javey
Local Oxidation of Si [LOCOS]
~100 A SiO2 (thermal) - pad oxideto release mechanical stress
between nitride and Si.Oxidation
Nitride Etch
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EE143 - Ali Javey
Local Oxidation of Silicon (LOCOS)Fully recessed process attempts
to minimize bird’s beakStandard process suffers for
significant bird’s beak
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EE143 - Ali Javey
SiO2 Si
C2
CB
C1CB (uniform)
x
conc.Si e. g. B, P, As, Sb.
Segregation Coefficient
m equilibrium dopant conc. in Si
equilibrium dopant conc. in SiO2
C
C1
2
Fixed ratio
(can be>1 or <1)
Dopant Redistribution during Thermal Oxidation
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EE143 - Ali Javey
Four Cases of Interest
(A) m < 1 and dopant diffuses slowly in SiO2
SiO2 SiC2
CB
C1
D e. g. B (m = 0.3)
flux loss through SiO2 surface not considered here.
B will be depleted near Si interface.
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EE143 - Ali Javey
Four Cases of Interest
(B) m > 1, slow diffusion in SiO2.
SiO2 Si
C2
CB
C1
e.g. P, As, Sb
dopant piling up near Si interfacefor P, As & Sb
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EE143 - Ali Javey
Four Cases of Interest
C1
(C) m < 1, fast diffusion in SiO2
SiO2 Si
C2 CB
e. g. B, oxidize with presence of H2
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EE143 - Ali Javey
Four Cases of Interest(D) m > 1, fast diffusion in SiO2
SiO2 Si
C2
CB
C1e. g. Ga (m=20)
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EE143 - Ali Javey
Polycrystalline Si Oxidation
poly-Si
grain boundaries (have lots of defects).
SiO2
roughnesswith Xox
fast slower
a
b
Overall growth rateis higher than single-crystal Si
SiO2
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EE143 - Ali Javey
(110)
(100)
(100)
Thinner oxideThickeroxide
(100)
(110)
Mechanical stress created by SiO2 volume expansion also affects oxide growth rate
Si cylinder
Topview
2-Dimensional oxidation effects