ee143 f2010 lecture 6 thermal oxidation of siee143/fa10/lectures/lec_06.pdf · thermal oxidation of...
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Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
1
Thermal Oxidation of Si• General Properties of SiO2
• Applications of thermal SiO2
• Deal-Grove Model of Oxidation
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>
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
2
Thermal SiO2 Properties(1) Excellent Electrical Insulator
Resistivity > 1E20 ohm-cm Energy Gap ~ 9 eV
(2) High Breakdown Electric Field> 10MV/cm
(3) Stable and Reproducible Si/SiO2 Interface
(4) Conformal oxide growth on exposed Si surface
Si Si
SiO2
ThermalOxidation
SiSi Si
SiO2
ThermalOxidation
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
3
(5) SiO2 is a good diffusion mask for common dopants
D Dsio si2 e.g. B, P, As, Sb.
(6) Very good etching selectivity between Si and SiO2.
SiO2
Si
SiO2
Si
HF dip
*exceptions are Ga(a p-type dopant) and somemetals, e.g. Cu, Au
*exceptions are Ga(a p-type dopant) and somemetals, e.g. Cu, Au
Thermal SiO2 Properties – cont.
Si
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
4
Steam generationfor wet oxidation
ThermalOxidationEquipment
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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Volume change due to thermal oxidation
Molecular Density of SiO2 = 2.3E22 molecules / cm3
Atomic Density of Si = 5.0E22 atoms / cm3
Volume of SiO2 = 2.16 Volume of Si consumed
Mechanical stress will be generated with confined oxidation
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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1 m Si oxidized 2.17 m SiO2
One-dimensional planar oxide growth
Suggested exercise:
Si1 m diameterSi sphere
SiO21.3 mdiameterSiO2 sphere
completelyoxidized
SiSi
SiO21 m2.17 m
•Roughly half of oxide grownis under original Si surface
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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Thickness of Si consumed (planar oxidation)
si
oxoxsi NNXX
oxox XcmatomscmmoleculesX 46.0
/105/103.2
322
322
XsiSiSi
SiO2
originalsurface
Xox
molecular density of SiO2
atomic density of Si
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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Kinetics of SiO2 Growth
Gas Diffusion
Solid-stateDiffusion
SiO2Formation
Si-Substrate
SiO2
Oxidant Flow(O2 or H2O)
Gas FlowStagnant Layer
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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Deal-Grove Model
CGCs
Co
Ci
X0x
stagnantlayer
SiO2 Si
F1 F2 F3
gastransportflux
diffusionflux
through SiO2
reactionflux
at interface
NoteCs Co
NoteCs Co
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
10
F h C CG G S1
xCDF
2
ox
io
XCCD
isCkF 3
Diffusivity [cm2/sec]
Mass transfer coefficient [cm/sec].
“Fick’s Law of Solid-state Diffusion”
Surface reaction rate constant [cm/sec]Comment: The derivation used in Jaeger textbook assumes F1 is large (not a rate-limiting factor for growth rate).Hence, the algebra looks simpler. However, the lecture notes derivation includes gas transport effect and can bedirectly applied to the CVD growth rate model which will be discussed in later weeks.
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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• CS and Co are related by Henry’s Law
• CG is a controlled process variable (proportional to theinput oxidant gas pressure)
Only Co and Ci are the 2 unknown variableswhich can be solved from the steady-state condition:
F1 = F2 =F3 ( 2 equations)
Only Co and Ci are the 2 unknown variableswhich can be solved from the steady-state condition:
F1 = F2 =F3 ( 2 equations)
How to solve the oxidant concentrations?
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
12
so PHC
sCkTH
partial pressure of oxidantat surface [in gaseous form].Henry’s
constant
from ideal gas law PV= NkT
HkTCC o
s
Derivation of Oxidation Growth Rate
Henry’s Law
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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)( GA CHkTC
F hHkT
C CGA o1 ( )
321 FFF
Define
Using the steady-state condition:
2 equations to solve the2 unknowns: Co & Ci
2 equations to solve the2 unknowns: Co & Ci
1 2
h
This is a controlprocess variable.For a given oxidantpressure, CA is known.
F1 can be re-written as:
Derivation of Oxidation Growth Rate – cont.
Conservationof mass flux
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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C Ckh
k XD
iA
s s ox
1
DXkCC oxs
io 1
DXk
hk1
CkCkFFFFoxss
Asis321
Therefore
Derivation of Oxidation Growth Rate – cont.
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
15
Now, convert Flux F into Oxide Thickness Growth Rate
dtdXNF ox
1
Oxidant molecules/unit volume requiredto form a unit volume of SiO2.
SiO2 Si
F
X ox
Therefore, we have the oxide growth rate eqn:
DXk
hk
CkdtdXN
oxss
Asox
11
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
16
1
2
)11(2
NDCB
hkDA
A
s
BAXX ii
2
Initial Condition: At t = 0 , Xox = Xi
)(2 tBAXX oxoxSolution
Note: h >>ks for typicaloxidation condition
SiO2
Si
SiO2
Si
xox
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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Note : “dry” and “wet” oxidation have differentN1 factors
N cm122 32 3 10 . / for O2 as oxidant
Si O SiO 2 2
Si H O SiO H 2 22 2 2
N cm122 34 6 10 . / for H2O as oxidant
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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BdtdxA
dtdxX
tBAXX
oxoxox
xox
2
)(02
Summary of Deal-Grove Model
t
t
Xox
t
ox
ox
XAB
dtdx
2 Oxide Growth Rate slows
down with increase of oxidethickness
Oxide Growth Rate slowsdown with increase of oxide
thickness
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
19
X A tA
Box
2
14
12
(Case 1) Large t [ large Xox ]
BtXox
(Case 2) Small t [ Small Xox ]
tABX ox
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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Deal-Grove Model Parameters
DNCDB A 1
2 kTQ
eD
(1)
(2)1
A
s
NC
)k
1h1(
1AB
Q = activation energyfor diffusion
For thermal oxidation of Si, h is typically >> ksB/A is ks (i.e. F1 is rarely the rate-limiting step)For thermal oxidation of Si, h is typically >> ks
B/A is ks (i.e. F1 is rarely the rate-limiting step)
kTQ
s
'
ek
Q’ = activation energyfor interface reaction
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
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B = Parabolic ConstantB/A = Linear Constant
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
22
Oxidation Charts
The charts arebased on
Xi = 0 !
The charts arebased on
Xi = 0 !
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
23
Two Ways to Calculate Oxide ThicknessGrown by Thermal Oxidation
E.g.
SiO2
Si4000Axi=
1100oC33min
steam
SiO2
Si
xox
Method 1: Find B & B/A from Charts
Solve )(2 tBAXX oxox
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
24
Method 2: Use Oxidation Charts
The charts arebased on
Xi =0 !
The charts arebased on
Xi =0 !
min244000 AX i at 1100oC from chart
Total effective oxidation timemin57min)3324( if start with 0iX
Xox T3
T2
T16500oA
4000oA
24 33 57
time(min)0
Two Ways to Calculate Oxide ThicknessGrown by Thermal Oxidation
Professor N. Cheung, U.C. Berkeley
Lecture 6EE143 F2010
25
SiO2
Si
4000oA
SiO2
Si
4000oA
SiO2
Si
4000oAxiCVDOxide
(1) Grown at 1000oC, 5hrs
(2) Grown at 1100oC, 24min
(3) CVD Oxide
For same Xi,is the same for all three
cases shown here
For same Xi,is the same for all three
cases shown here