Kinetics of Silicon Oxidation in a
Rapid Thermal Processor
Asad M. Haider, Ph.D.
Texas Instruments
Dallas, Texas
USA
Presentation at the National Center of Physics
International Spring Week 2010
Islamabad
Pakistan
March 01, 2010
Asad M. Haider ; March 01, 2010 ; NCP
PRESENTATION OUTLINE
• Introduction and motivation to study Si oxidation
• Mechanism of Si oxidation
• Mathematical model for Si oxidation
• Hardware design of a Rapid Thermal Processor (RTP)
• Experimental data and the model parameter estimation
• Oxide quality
• Conclusions
Asad M. Haider ; March 01, 2010 ; NCP
INTRODUCTION: Importance of SiO2 in SC Industry
During semiconductor device manufacturing SiO2 is thermally grown to be used as a:
a)
b)
c)
d)
Gate oxide
Isolation oxide liner between devices (STI liner)
Masking element (for eg., during ion implantation)
Surface passivation (for eg., Pad oxide. A sacrificial layer for contamination control)
Gate
Source
Lg
Substrate
Please note the difference between “grown” SiO2 and “deposited” SiO2
This presentation is about thermally “grown” SiO2
Asad M. Haider ; March 01, 2010 ; NCP
Drain
Isolation
Isolation
Gate Oxide
MOTIVATION TO STUDY OXIDATION IN RTP
1. To indirectly measure across wafer temperature uniformity of a Rapid
Thermal Processor in > 900C range.
2. Understand the Si oxidation kinetics in a RTP chamber and measure
Deal-Grove oxidation model parameters for < 30nm thick oxides.
3. Understand the impact of various process parameters on SiO2 growth
in a RTP chamber.
4. Compare the oxide quality grown in a RTP with that grown in a
furnace.
Asad M. Haider ; March 01, 2010 ; NCP
OXIDATION OF SILICON
Si has great affinity for oxygen and is easily oxidized in a number of ways:
1. Chemical oxidation
Boil Si in HNO3,,for example.
2. Anodic oxidation
In an electrolytic bath use Si as an anode and a noble metal as a cathode.
3. Plasma oxidation
Uses ions of an oxidant species to grow oxide film.
4. Thermal oxidation
• Used exclusively in semiconductor device fabrication.
• Gives by far the best quality oxide.
• Typically done in a furnace.
• Two types of thermal oxides:
Si + O2 Î SiO2
Dry oxidation
Si + 2 H2O Î SiO2 + 2 H2
Wet Oxidation
• Dry oxidation: Slow, high density, good quality Î Thin gate oxides
• Wet oxidation: Fast, low density, poorer quality Î Thick mask/passivation
This study looks at kinetics of dry oxidation in a Rapid Thermal Processor.
Asad M. Haider ; March 01, 2010 ; NCP
MECHANISM OF Si OXIDATION
Question: Is it the Si atoms that diffuse through the oxide to react with O2 at the
oxide surface or is it the O2 that diffuses through the oxide to react with Si at the
Si/SiO2 interface?
Answer: For thermal oxidation, it has been established through radioactive tracer
studies that it is the O2 that diffuses through the oxide and reacts with Si at the
Si/SiO2 interface.
SiO2
Si
O2
Consequently, thermal oxidation always takes place on fresh Si surface rather than
the original surface that may have been exposed to ambient contaminants.
Next, we look at a detailed mathematical model for the oxidation of Si.
Asad M. Haider ; March 01, 2010 ; NCP
MATHEMATICAL MODEL FOR SILICON OXIDATION
Si + O2 Î SiO2
Dry Oxidation
Oxide
Gas
Silicon
δ
Cg
Cs
Co
Deal and Grove, J. Appl. Physics,
vol 36, p 3770, (1965)
Ci
N1
N2
N3
x
Cg ≡ Concentration of oxidant molecules in the bulk gas
Cs ≡ Concentration of oxidant molecules immediately adjacent to the oxide surface
Co ≡ Equilibrium concentration of oxidant molecules at the oxide surface
Ci ≡ Concentration of oxidant molecules at the Si/SiO2 interface
Note:
i) Cg > Cs due to depletion of the oxidant at the oxide surface
ii) Cs > Co due to solubility limits of the oxide
δ ≡ Oxide thickness at a given time
Ni ≡ Flux of oxidant molecules
Asad M. Haider ; March 01, 2010 ; NCP
MATHEMATICAL MODEL FOR SILICON OXIDATION – Contd.
Oxide
Gas
N1 = Oxidant flux from bulk gas to the oxide surface
N1 = km (Cg − Cs )
Cg
pg
(Eq. 1)
ps
δ
Cs
C*
Silicon
Co
N2 = Oxidant flux through the oxide
Ci
N1
r
dC
dC
N2 = −D
+ Cv = − D
dx
dx
D (Co − Ci )
δ
C* = Equilibrium conc in bulk oxide
(Eq. 2)
N 3 = kCi
(Eq. 3)
Henry’s law dictates that:
Co = Hps
Therefore, Eq. 1 becomes:
N1 =
N3
x
Integration across the oxide film gives:
N2 =
N2
km
(
C * − Co )
HRT
Asad M. Haider ; March 01, 2010 ; NCP
(Eq. 4)
and
C * = Hpg
MATHEMATICAL MODEL FOR SILICON OXIDATION – Contd.
Express Co and Ci in terms of measurable quantities.
At steady state: N1 = N2 = N3
This results in:
⎛ kδ ⎞
⎟
⎜1 +
D⎠
*
⎝
Co = C
⎛ kHRT kδ
⎜⎜1 +
+
km
D
⎝
Oxide
Gas
Cg
pg
ps
δ
Cs
C*
Silicon
Co
(Eq. 5)
⎞
⎟⎟
⎠
Ci
N1
N2
N3
x
1
Ci = C *
⎛ kHRT kδ ⎞
⎟⎟
⎜⎜1 +
+
km
D⎠
⎝
(Eq. 6)
C* = Equilibrium conc in bulk oxide
Case 1: Mass transfer controlled process:
Oxide growth rate depends only on how fast oxidant is supplied to the Si/SiO2 interface.
Hence, D << k ⇒ Ci ~ 0 and Co ~ C*
Case 2: Kinetics controlled process:
Oxide growth rate depends only on how fast the oxidant reacts at the Si/SiO2 interface.
Hence, D >> k ⇒
C*
Ci = Co =
⎛ kHRT
⎜⎜1 +
km
⎝
Asad M. Haider ; March 01, 2010 ; NCP
⎞
⎟⎟
⎠
MATHEMATICAL MODEL FOR SILICON OXIDATION – Contd.
Oxide Growth Rate:
Let Γ be the number of oxidant molecules per unit volume of the oxide film. Then,
kC *
d
(Γδ ) = N 3 = kCi =
dt
⎛ kHRT kδ ⎞
⎜⎜1 +
⎟⎟
+
k
D
m
⎝
⎠
(Eq. 7)
Integrating Eq. 7 with initial condition: At t = 0 ; δ = δi results in:
δ 2 + Aδ = B (t + E )
Where,
(Eq. 8)
⎛ 1 HRT ⎞
⎟⎟
A = 2 D ⎜⎜ +
km ⎠
⎝k
2DC *
B=
Γ
E=
δ i2 + Aδ i
B
A and B are the only two model parameters to be found experimentally.
Asad M. Haider ; March 01, 2010 ; NCP
MATHEMATICAL MODEL FOR SILICON OXIDATION – Contd.
Special Cases:
A. For very short times, δ is very small and the process is kinetics limited. In this regime Eq. 8 becomes:
δ=
B
(t + E )
A
(Eq. 9)
B. For very long times, δ is pretty thick and the process is diffusion limited. In this regime Eq. 8 becomes:
δ = Bt
(Eq. 10)
To find model parameters A and B requires collecting oxide thickness vs. time data.
Since A and B are in turn functions of temperature, oxide thickness data needs to be
collected at different temperatures in order to develop a general equation to predict oxide
thickness as a function of time and temperature, δ = δ(time, temperature)
But first, let us look at the hardware design of a RTP chamber.
Asad M. Haider ; March 01, 2010 ; NCP
DESIGN OF RTP (Rapid Thermal Processor)
Transfer chamber and chambers A and B.
Asad M. Haider ; March 01, 2010 ; NCP
DESIGN OF RTP – Contd.
Close-up of the reflector plate.
Pyrometers and lift pin holes visible.
View of an open RTP chamber.
Asad M. Haider ; March 01, 2010 ; NCP
Wafer Edge Ring and Support Cylinder Assembly Schematic
Asad M. Haider ; March 01, 2010 ; NCP
DESIGN OF RTP – Contd.
Assembled parts: SiC wafer edge ring sitting on top of the support cylinder around the reflector plate.
Asad M. Haider ; March 01, 2010 ; NCP
DESIGN OF RTP – Contd.
Reflector plate showing raised wafer lift pins.
Asad M. Haider ; March 01, 2010 ; NCP
RTP Centura Lamp Zones and Temperature Probe Locations
Asad M. Haider ; March 01, 2010 ; NCP
DESIGN OF RTP – Contd.
Close up of the RTP multi-zone lamp heater assembly capable of precision controlled
temperature ramp rates of >100C/s.
Asad M. Haider ; March 01, 2010 ; NCP
KEY PROCESS PARAMETERS AND THEIR
EFFECT ON OXIDATION KINETICS
Oxide Growth Rate vs. Pressure at 1050C
1.2
Oxide Growth Rate, A/s
1
0.8
0.6
0.4
0.2
0
0
100
200
300
400
500
Pressure, torr
Recall,
2DC * ; As P increases, C* increases
B=
Γ
Asad M. Haider ; March 01, 2010 ; NCP
600
700
800
900
SiO2 Growth Rate Vs. O2 Flow Rate
T = 1050C ; P = 780 torr
1.2
SiO2 Growth Rate, A/s
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
O2 Flow Rate, slm
All Si oxidation tests were conducted in O2 ambient at 5 slm at a chamber pressure of 780 torr
at various temperatures.
Asad M. Haider ; March 01, 2010 ; NCP
Arrhenius Plot for SiO2 Growth
P = 780 torr, O2 = 5 slm
0.6
0.4
ln (Rate), A/s
0.2
y = -13808x + 10.493
R2 = 0.9982
0
-0.2
E = 114.8 kJ/mole
-0.4
-0.6
-0.8
-1
0.00072 0.00073 0.00074 0.00075 0.00076 0.00077 0.00078 0.00079
0.0008
0.00081 0.00082 0.00083
1/Temp, 1/K
Next, estimate model constants A and B by doing a least squares fit of the
model to the experimentally collected Si oxidation data.
Asad M. Haider ; March 01, 2010 ; NCP
EXPERIMENTAL DATA AND CALCULATION
OF MODEL PARAMETERS
Oxide Growth at 1050C in RTP Reactor
200
180
Theory
Oxide Thickness, A
160
Measured
140
120
100
80
60
40
20
0
0
50
100
150
200
Oxidation Time, s
A = 40 °A
B = 131 °A2/s
Asad M. Haider ; March 01, 2010 ; NCP
250
300
350
EXPERIMENTAL DATA AND CALCULATION
OF MODEL PARAMETERS
Oxide Grow th at 1075C in RT P Reactor
250
Theory
Measured
Oxide Thickness, A
200
A = 55 °A
B = 188.5 °A2/s
150
100
50
0
0
50
100
150
200
250
300
350
Oxidation Time, s
Repeat these tests at multiple temperatures to get dependency of A and B on temperature.
Asad M. Haider ; March 01, 2010 ; NCP
Rate Constant A vs. Temperature
70
y = 0.4582x - 439.45
R 2 = 0.9971
60
A, Ang
50
40
30
20
10
0
950
975
1000
1025
1050
Tem p, C
Asad M. Haider ; March 01, 2010 ; NCP
1075
1100
1125
Parabolic Rate Constant B vs. Temperature
350
B, Ang^2/s
300
y = 0.0145x2 - 28.029x + 13567
R 2 = 0.9975
250
200
150
100
50
0
950
975
1000
1025
1050
Tem p, C
Asad M. Haider ; March 01, 2010 ; NCP
1075
1100
1125
Semi Empirical Model to Predict SiO2 Thickness Near
Atmospheric Pressures in RTP
δ 2 + Aδ = B (t + E )
A = 0.4582T − 439.45
B = 0.0145T 2 − 28.029T + 13567
E=
δ i2 + Aδ i
B
δ = Oxide thickness grown at any time
δi = Initial oxide thickness
t = Time
T = Temperature
Asad M. Haider ; March 01, 2010 ; NCP
OXIDE QUALITY
Best way to tell the quality of oxide is by measuring the charges in it.
SiO2
K+
Na+
SiOx
Si
+ + -
+
+
-
+
-
+
-
+
-
+
-
+
-
+
-
Mobile ionic charges
Oxide trapped charges
Fixed oxide charges
Interface trapped charges
Source:
• Mostly humans.
• Contaminated water
or if it is not fully
deionized.
Source:
• Exposure to radiation
environment.
• Hot electron effect in
short channel MOSFET
devices.
Source:
• Incomplete oxidation
Source:
• Mechanical damage in Si
wafer.
• Dangling Si bonds left unreacted after oxidation.
Effect:
Wreaks havoc on
transistor
characteristics.
Fix:
Use chlorine oxidation
– bubble O2 through
TCE. Be careful, too
much Cl will result in
“halogen pitting”.
Effect:
Interferes with electronic
activity.
Fix:
Typically not caused by
processing itself.
Asad M. Haider ; March 01, 2010 ; NCP
Effect:
Pushes VT in –ve direction
Fix:
At the end of oxidation
step purge the system
with N2 or Ar gas and then
drop the temperature.
Effect:
Trap and de-trap electrons
affecting MOS device
performance.
Fix:
Do a low temp (~450C)
anneal in H2 ambient post
oxidation.
SUMMARY AND CONCLUSIONS
• Deal and Grove model was successfully applied to oxidation of Si in a
RTP reactor for oxide thicknesses less than 30nm.
• Model parameters A and B were empirically found as a function of
temperature at 780 torr to obtain a generalized model capable of
accurately predicting dry Si oxidation rates between 975C and 1100C for
oxide thicknesses less than 30nm.
• Activation energy of dry Si oxidation in RTP was found to be 115
kJ/mole.
• Discussed various types of charges in SiO2 that determine the quality of
oxide and how to mitigate them.
Asad M. Haider ; March 01, 2010 ; NCP