1.
Use of computer modeling for optimization of
Cz Si growth: strategy and examples
animated visualization of unsteady effects
is not available in this edition of the presentation
STR Group
www.str-soft.com
2009
2.
Prehistory of STR:
1984: Start of the MOCVD modeling activities
at Ioffe Institute, St. Petersburg, Russia;
1993-96: Group for modeling of crystal growth and epitaxy
at University of Erlangen-Nuernberg, Germany;
History of R&D in STR on crystal growth from the melt:
1998: First cooperation project on Cz Si growth
2000: First cooperation project on encapsulated GaAs and InP growth
2001: Start of the development of CGSim package
2002: First cooperation project on Cz growth of oxides
2003: First cooperation project on Ge growth from the melt
2004: First industrial customers of CGSim package
2005: First cooperation projects on DS Si and Kyropoulos sapphire growth
2006: First cooperation projects on YAG and GGG (garnet) growth by Cz
3.
STR Today:
modeling of crystal growth, epitaxy, and devices
- STR Group, HQ and R&D, St.Petersburg, Russia
- STR Inc., Richmond VA, USA
- STR GmbH, Erlangen, Germany
- More than 30 scientists and software engineers in STR,
local representatives in China, Korea, Taiwan and Japan.
Software & consulting services :
- Czochralski, LEC, and Bridgman crystal growth from the melt: CGSim
- Polysilicon deposition by Siemens process: PolySim
- PVT bulk crystal growth of SiC, AlN, GaN: Virtual Reactor
- Modeling of epitaxy, MOVPE of Nitrides and III-Vs: CVDSim
- Modeling of opto- and electronic devices: SimuLED, FETIS, BESST, SELES
4.
Content
Introduction
- Description of Computer Model
- Verification Results
- Strategy of Cz Si Growth Optimization
- Cz Growth with diameter of 400 mm for electronics
5.
INTRODUCTION
There are 3 basic techniques for silicon
crystal growth from melt.
DSS (Casting, multicrystal)
Czochralski m. (monocrystal)
A.T. Kuliev, N.V. Durnev, V.V. Kalaev,
Y. Shiraishi et al., J. of Crystal
J. of Crystal Growth (2007) 236-240
Growth 229 (2001) p.17
6.
What is computer modeling?
Computer modeling is a comprehensive reconstruction or reproduction of
crystal growth process by a computer. Numerical model is used for
technology optimization to lower operation costs.
Advantages of computer modeling in comparison to experimental work:
- fast and low cost (from few minutes to several days; only special software
and computer are required)
- provide information in all points of a furnace, including data which are
impossible to measure quantitatively (temperature gradients, thermal stresses,
crystallization behavior, fluid dynamics, species transport)
-practically, no extra cost for changes of furnace design and growth parameters
(several minutes of the work of the user): fast and efficient technology
development
7.
Published CGSim successful stories
- Development of perfect 300 mm silicon crystal growth by the Czochralski technique in
Siltronic AG, Germany
- Optimization of impurity transport during EFG growth of dodecagonally shaped silicon
tubes of 0.5 m diameter in SCHOTT Solar GmbH, Germany
-Reduction of the macrodislocation generation probability in 3 times and 30% increase of
the pulling speed during 200 mm Si Cz growth for solar cells in JSC PCMP, Russia
-First technology for 300 mm sapphire growth by the Kyropoulos technique and reduction
of dislocation density in Monocrystal Inc., Russia
- Komatsu Metals Co., Japan (now a part of SUMCO) uses CGSim for optimization of large
scale Cz Si growth for electronics
8.
Content
Introduction
- Description of Computer Model
- Verification Results
- Strategy of Cz Si Growth Optimization
- Cz Growth with diameter of 400 mm for electronics
9.
Navier-Stokes equations, heat transfer, electric current,
scalar transport
p0 m
∂ρ r
or ρ = f (T )
ρ=
+ ∇ ⋅ (ρ u) = 0
(1)
Rg T
∂t
r
∂( ρ u ) r r r
+ (u ⋅ ∇) ρ u = −∇p + ∇ ⋅τ + ( ρ − ρ 0 ) g + j × B + S u
(2)
∂t
⎛ ∂ui ∂u j ⎞ 2 r
⎜ ⎟ − µ eff δ ij ∇ ⋅ u
τ ij = µ eff ⎜ +
∂x j ∂xi ⎟ 3
⎝ ⎠
∂ (ρ c p T )
+ ∇ ⋅ (ρ c p u T ) = ∇ ⋅ (λ eff ∇ T ) + S T
r
(3)
∂t
( )
( ) j = σ − ∇Φ + u × B
∆Φ = B ⋅ ∇ × u
(4)
Electric potential equation
∂ ( ρϕ i )
( )
r
+ ∇ ⋅ ( ρ u ϕ i ) = ∇ ⋅ ρ Dϕ i eff ∇ ϕ i + S ϕ i scalar
(5)
∂t
10.
Original approach for turbulence modeling: combined
LES/RANS
⎡⎛ ν t ⎞ ∂k ⎤ σm 2 σm 2 k
∂ .
dk
⎢⎜ν ⎟
⎟ ∂x ⎥ + 2ν t S − ε − ρ B k ⋅ exp(−0.025 ρ B ε )
= + 2
⎜ σk ⎠ j ⎥
dt ∂x j ⎢⎝
⎣ ⎦
3
ε = max(ε ), Ck 2
,ε
RANS LES
Cε = 0.75
ε ∆ = 3 ∆ x∆ y∆ z ,
=ε
LES
,
∆
3
k2 ky
−3
ε l = κCµ 4 y,
= Fε = f (Re y ), Re y =
RANS
,
ν
l ⋅ Fε
⎧
lt = min ⎨l ⋅ Fε , ∆ ⎫
ν t = C µ f µ lt k Cε ⎬
⎭
⎩
Wolfshtein model, 1969:
⎛ Re y ⎞
⎛ Re y ⎞
f µ = 1 − exp⎜ − ⎟,
Fε = 1 − exp⎜ −
⎜ A ⎟, Aε = 5.1 Aµ = 10.0
⎟ ⎜ A⎟
⎝ ε⎠ ⎝ µ⎠
N.G. Ivanov, A.B. Korsakov, E.M. Smirnov, K.V. Khodosevitch, V.V. Kalaev, Yu.N. Makarov,
E. Dornberger, J. Virbulis, W. von Ammon, J. Crystal Growth, 250/1-2 (2003) pp. 183-188
11.
Specific boundary conditions
(i) fixing velocity on solid rr 15 m/s
in the gas
u = Uw
walls and inlet boundaries: 0.015 m/s
in the melt
(ii) coupling of stresses along
gas/liquid interfaces: W [m/s]
0.2
r r 0.15
(u )1 = ( u ) 2
0.1
0.05
0
-0.05
-0.1
∂ uτ i ∂ uτ i ∂σ
-0.15
-0.2
( µ eff )1 = ( µ eff )2 + gradτ i (T )
∂n ∂n ∂T
∂T ∂T
(iii) heat transfer along the case of
(λ )1 = (λ )2
solid/solid interfaces, ∂n ∂n opaque blocks
liquid/liquid and
(T )1 = ( T ) 2 + ∆Tgap
liquid/solid interfaces :
(iv) along opaque/transparent interface radiative heat transfer is accounted for:
∂T ∂T
(λ ) opaque = (λ ) transparent + σ b ε rad Tw4 − Qrad
in
∂n ∂n
12.
Strategy of coupled 2D/3D approach
2D global HT model produces thermal boundary conditions for 3D/2D flow computations
⎛ ∂T ⎞ = Tmelting
T
and ⎜ λ
in
⎟
Q melt / crystal
rad
⎝ ∂n ⎠ gas
2D model of global heat transport
T [K]
1600
1400
1200
1000
40 0
800
500
600
600
400
argon
1300
crystal
1500
1700
melt
λeff melt
crucible
3D unsteady model
heater
⎛ ∂T ⎞ ⎛ ∂T ⎞
graphite
1700
λ + Qrad = ⎜ λ ⎟ + σεTwall
in 4
⎜ ⎟
1600
⎝ ∂n ⎠3 D ⎝ ∂n ⎠ gas
insulation
CZ growth of 400 mm Si crystal:
V.V. Kalaev et al., J. Crystal Growth, 250/1-2 (2003) p.203
Y. Shiraishi et al., J. of Crystal
V.V. Kalaev et al., Mat. Sci. in Semiconductor Processing, 5/4-5 (2003) p.369
Growth 229 (2001) p.17
13.
Study of crystal growth using 2D models
Temperature analysis coupled
450 mm Cz Si growth
with melt and gas flow
(animated visualization)
Temperature Flow
Velocity
Crystallization front animation
Global heat transfer simulation coupled to melt and gas convection is a powerful tool for day-by-day
engineering calculations to improve hot zone design and growth parameters.
14.
Study of melt flow structure and crystallization using 2D
models
450 mm Cz Si growth
animated visualization
Temperature Flow
Velocity
In large scale crystal growth, the effect of melt convection on crystallization front formation is significant.
Melt convection features often govern defects dynamics and macro-dislocation generation in the crystal.
15.
Analysis of unsteady features of crystal cooling
Crystal cooling at 450 mm Cz Si growth (animated visualization)
Temperature
Temperature gradient in the
crystal
Si charge meltdown and crystal cooling are optimized using 2D unsteady modeling. This helps to speed up
melting and cooling stages and to prevent beginning of melt crystallization from the gas/melt interface.
16.
Content
Introduction
- Description of Computer Model
- Verification Results
- Strategy of Cz Si Growth Optimization
- Cz Growth with diameter of 400 mm for electronics
17.
Temperature measurements in a Cz furnace
1400 calculation
Temperature [ C ]
experiment
0
1200
1000
800
0 100 200 300
Crystal Length [ mm ]
a)
calc. ins/ins
exp. ins/ins
calc. ins/graph
2000
Temperature [ 0C ]
exp. ins/graph
1750
1500
1250
1000
0 100 200 300 400
b) Insulation Length [ mm ]
calc. upper
exp. upper
2000
Tempearture [ 0C ]
calc. lower
1800 exp. lower
1600
1400
1200
1000
25 50 75 100
Insulation Length [ mm ]
c)
(b) (c)
(a)
The furnace geometry and experimental data are published in J. Crystal Growth 180 (1997) pp. 461-
467. The predicted temperature distribution (b) is compared to the experimental data (c) obtained in the
points shown in (a). The comparison shows that CGSim can adequately predict temperature distribution
in the industrial growth setup and inside the growing silicon crystal if material properties are well known.
18.
Temperature measurements in the melt
T [K]
no magnetic field (animated visualization)
1750
experimental data
1745
90 grad
1740
3D computation
1735
2D computation
1730
1725
1720
1715
1710
1705
0 grad
1700
1695
1690
0 grad
1685
0 20 40 60 80
T [K]
1750
cusp magnetic field (animated visualization)
1745
experimental data
1740
3D computaion
2D computation
1735
1730
1725
1720
1715
1710
1705
1700
Angle from the axis of rotation [grad]
1695
1690
1685
0 20 40 60 80
The measurements by thermocouples along the melt/crucible interface are published in
Microelectronic Engineering 56 (2001) 83–88. 3D calculations with CGSim predicts the
experimental distributions quantitatively.
19.
Temperature measurements in the melt by an optical sensor
10 0
T [K]
power s pectral dens ity
experiment
1700 calculations
10 -1
1695
-2
10
1690
experiment
s imulations
10 -3 -3
1685
10 -2 10 -1 10 0
0 20 40 60 80 10
frequency [ Hz ]
Time [s ]
Power spectral density of temperature
Temperature fluctuations in the melt, 1
fluctuations.
cm lower the free surface.
Growth parameters: The crystal diameter is 100 mm. The crucible/crystal rotations are 5/(-20) rpm. Argon flow
rate and pressure are 750 slh and 30 mbar. The average crystallization rate is 2 mm/min.
The experimental data are taken from the following paper: Mat. Sci. and Eng. B73 (2000) p.130.
CGSim predicted the average amplitude and spectral characteristics of the temperature fluctuations in the
melt near the triple point.
20.
3D Unsteady Calculations of the Crystallization Front
Geometry
animated visualization
∂T
⎛ ∂T ⎞
nx
⎜ λcrys crys − λmelt melt ⎟
Vcrys =
ρ crys ∆H ⎜ ∂n ⎟
∂n
⎝ ⎠
= Vcrys − Vcrys
relative *
Vcrys
∆X = Vcrys * TimeStep
relative
The experiments provided in Siltronic AG are published in:
[1] Mat. Sci. in Semiconductor Processing 5/4-5, 2003, p.369-373;
[2] J. Crystal Growth 250/1-2, 2003, p.203-208.
[3] J. Crystal Growth, 266/1-3 ,2004, pp. 20 - 27
The crystal diameter is 100 mm The crystal diameter is 300 mm
Computation, H=240mm
20
Computation, H=300mm
Experiment, H=240mm
Experiment, H=300mm
40
Computation, H=300mm
Interface deflection, [mm]
Computation, H=700mm
Experiment, H=300mm 35
15 Experiment, H=700mm
Interface deflection, [mm]
30
25
10
20
15
5 10
5
0 0
0 50 100 0 100 200 300
Radial position, [mm]
Radial position, [mm]
21.
Content
Introduction
- Description of Computer Model
- Verification Results
- Strategy of Cz Si Growth Optimization
- Cz Growth with diameter of 400 mm for electronics
22.
Increasing the crystallization (pulling) rate
- by modifications of the heat shields and other elements surrounding
the crystal
- changes in the crystal and crucible rotation rate
- optimization of the crucible position with respect to the heaters
- changes in the crucible design
General idea:
One needs to increase the heat flux (temperature gradient) in the crystal and
to decrease the heat flux in the melt. But it is necessary to avoid (i) crystal
twisting, (ii) macrodislocations, and (iii) melt supercooling.
23.
Effect of the heat shield modifications
Initial heat shield Optimization of HSh shape and composition
design up to +50% increase of pulling rate
Modifications of heat shield design can be efficiently used to increase crystal growth rate
24.
Reducing the heater power
- to find weak points in the insulation design by
analyzing the heat flux vectors and integral heat
fluxes along surfaces
- to improve insulations and repeat the analysis
by computer model
Usually, only 8-25% of the total
heater power is used for the
maintenance of the temperature in
the melt !
25.
Content
Introduction
- Description of Computer Model
- Verification Results
- Strategy of Cz Si Growth Optimization
- Cz Growth with diameter of 400 mm for electronics
26.
Growth of Cz Si crystals the with
diameter of 400 mm for electronics:
effect of DC magnetic fields on the
melt and crystallization front
27.
II.II. 3D Unsteady Parametric Analysis of
400 mm Si Crystal MCz Growth
Ωcrystal = 10 rpm T [K]
1600
1400
Ωcrucible = -5 rpm
1200
1000
400
800
500
600
600
400
Vg = 0.45 mm/min argon
1300
crystal
1500
1700
P = 10 mbar
melt
crucible
heater
Flow rate is 5200 slh graphite
1700
1600
insulation
Case 1: without MF
2D – 3D
Case 2: with cusp MF of 30 mT
model cusp MF
Case 3: with horizontal MF of 30 mT
Case 4: with horizontal MF of 300 mT
Case 5: with horizontal MF of 300 mT and
with the reduced argon flow rate of 520 slh
horizontal MF
Y. Shiraishi et al., J. of Crystal Growth 229 (2001) p.17
N. Machida et al., J. of Crystal Growth 186 (1998) p.362
K. Takano et al., Mat. Sci. and Eng. B73 (2000) p.30
28.
Modeling Results for Case 1: without MF
all plots here are animated to visualize unsteady effects
2 cm/s
T [K]
1716
1711
1706
1701
1696
1691
1686
velocity and temperature evolution time-averaged velocity and temperature
T ' [K]
2.6
0.8
2.2
1.8
0.6
1.4
1
0.6
0.2
time-averaged temperature fluctuation
2 2
k [m /s ]
0.002
0.0016
0.0004
0.0012
2
00 0.0008
0 .0
0.0004
0
evolution of the crystallization rate
time-averaged turbulence kinetic energy
29.
Modeling Results for Case 2: with Cusp MF of 30 mT
all plots here are animated to visualize unsteady effects
2 cm/s
T [K]
1716
1711
1706
1701
1696
1691
1686
time-averaged velocity and temperature
velocity and temperature evolution
T ' [K]
0.4
2.6
2.2
0.2
1.8
1.4
1
0.6
0.2
time-averaged temperature fluctuation
2 2
k [m /s ]
0.002
0.0004 0.0016
002 0.0012
0.0
0.0008
0.0004
0
evolution of the crystallization rate
time-averaged turbulence kinetic energy
30.
Modeling Rresults for Case 3: with Horizontal MF of 30 mT
all plots here are animated to visualize unsteady effects
2 cm/s
T [K]
1716
1711
1706
1701
1696
1691
r
r 1686
B
B
time-averaged velocity and temperature
velocity and temperature evolution
T ' [K]
2.6
2.2
0.4 6
0.
1.8
1.4
1
0.6
0.2
time-averaged temperature fluctuation
2 2
k [m /s ]
0.0002
0.002
0.0016
0.0012
0.0008
0.0004
0
evolution of the crystallization rate
time-averaged turbulence kinetic energy
31.
Modeling Results for Case 4: with Horizontal MF of 300 mT
all plots here are animated to visualize unsteady effects
r r
B B
velocity and temperature evolution
r
evolution of the velocity and
B
temperature over the melt free surface
velocity and temperature evolution
k [m2/s2]
0.002
0.0016
0.0012
0.0008
0.0004
0
time-averaged turbulence kinetic energy
evolution of the crystallization rate
32.
Modeling results for Case 4: with horizontal MF of 300 mT
all plots here are animated to visualize unsteady effects
r
Oxygen transport
B crystal
3
XSiO[at/cm ]
The results are obtained using a coupled
gas model of oxygen transport in the melt and
3.2E+15
3E+15
region SiO in the gas. It has been found that SiO
2.8E+15
2.6E+15
distribution in the gas is extremely
2.4E+15
2.2E+15
asymmetric due to the horizontal MF, and
2E+15
melt
1.8E+15
there is significant oxygen concentration
1.6E+15
gradient over the melt/crystal interface.
1.4E+15
1.2E+15
1E+15
8E+14
evolution of oxygen concentration
Evolution of SiO concentration in argon
r over the crystallization front:
B and oxygen content in the melt
3
crystal
Xoxygen[at/cm ]
1.6E+18
1.5E+18
gas
1.4E+18
1.3E+18
region
1.2E+18
1.1E+18
1E+18
9E+17
r
8E+17
7E+17
melt B
6E+17
5E+17
4E+17
33.
Results for Case 5: Horizontal MF of 300 mT and with the
Reduced Argon Flow Rate of 520 slh
r
r B
B
velocity and temperature evolution
r
B
evolution of the velocity and
temperature over the melt free surface
velocity and temperature evolution
The strong decrease of the argon flow rate has
resulted in a radical change of the flow structure
and melt/crystal interface geometry
K. Kakimoto and H. Ozoe, J. of Crystal Growth
212 (2000) p.429
evolution of the crystallization rate
all plots here are animated to visualize unsteady effects
34.
Time-Averaged Temperature Distributions over the Melt Free
Surface and in Vertical Cross Sections for Cases 3, 4, and 5
r
B
20 cm/s 40 cm/s 40 cm/s
T [K] T [K] T [K]
1712
1702
1710 1702
1700
1708 1700
1698
1706 1698
1696
1704 1696
1694
1702 1694
1692
1700 1692
1690
1698 1690
1688
1696 1688
1686
1694 1686
1692
1690
1688
case 4
case 3 case 5
r r
B B
2 cm/s
T [K]
1716
1711
1706
1701
1696
1691
1686
35.
Comparison of the Computed Crystallization Front
Geometries and V/G Distributions
no MF
no MF
Cusp DC MF, 30 mT
Cusp DC MF, 30 mT
Horizontal DC MF, 30 mT
Horizontal DC MF, 30 mT
V/G parameter [cm /Kmin]
Interface deflection [mm]
Horizontal DC MF, 300 mT
Horizontal DC MF, 300 mT
Horizontal DC MF, 300 mT; weak Gas Flow
Horizontal DC MF, 300 mT; weak Gas Flow -03
2.5x10
20
2
10
-03
2.0x10
0
-03
1.5x10
-10
-03
1.0x10
-20
-100 0 100
-100 0 100
Radial position [mm]
Radial position [mm]
V. V. Voronkov, J. Crystal Growth, 59 (1982) p.625
R.A. Brown et al., Journal of Crystal Growth 225 (2001) p.97
M. Kulkarni, Ind. Eng. Chem. Res. 2005, 44, p.6246
36.
I.VI. Defect incorporation and recombination
Initial defect kinetics:
dCm
= ∇ ⋅(Dm∇Cm) + 4πar (D + Dv ) exp(− ∆G )(C Cve − C Cv ) m=v, i : interstitial and
i kT ie i
dt vacancy respectively.
Initial defect equilibrium concentration and diffusion coefficient
m⎞
0 exp⎜ − H m ⎟
⎛
0 exp⎜ − H m − SmT
⎛ ⎞
Dm = Dm
⎟
Cme = C ⎜
kT ⎟
⎜ ⎟
m ⎜ ⎟
kT
⎜ ⎟ ⎝ ⎠
⎝ ⎠
Formation energy: Hv=2.48+2.33e-4*T (eV); Hi=3.46+3.08e-4*T (eV)
Sv=(-3.7+3.53e-3*T)k (eV/K); Si=(1.4+3.85e-3*T)*k (eV/K)
Concentration coefficient: Cv0=4.97*1022 (cm-3); Ci0=2.97*1023 (cm-3)
Migration energy: Hv=0.457 (eV); Hi=0.937 (eV)
Diffusion coefficient: Dv0=1.3*10-3 (cm2/s); Di0=0.242 (cm2/s)
This values set has taken from [1] T. Sinno, et al., J. Electrochem. Soc. 145-1 302
(1998)
Boundary conditions:
melt/crystal interface – equilibrium concentration; side crystal surface – zero
flux; top crystal surface – extrapolation from the inner crystal part.
37.
2D calculation of defect incorporation and recombination
(crystal diameter is 300 mm)
Interface Interface
computed with a computed using a
2D approximation 3D approximation The effect of melt
turbulent flow on
Cv - Ci [cm-3]
the formation of
the crystallization
2.1E+14
1.8E+14
front is much
1.4E+14
more significant
1.1E+14
7.8E+13
for 300 mm
4.5E+13
crystal growth.
1.2E+13
-2.1E+13
-5.4E+13
-8.7E+13
2D 3D
Technological parameters. Crystal height is 300 mm, pulling rate is 0.7 mm/min,
cruciblecrystal rotation are 6-12 rpm, Ar flowratepressure are 1000 slh 15 mbar.
38.
Defect clusterization
Free energy gain for void and oxygen precipitate, volume and surface terms:
⎛ ⎞
⎜C ⎟
G (n ) = − nf + λ ⋅ n 2 / 3 = − nkT ⋅ 4π R 2
V ⎟ +σ
⋅ ln ⎜ eq
V V V V
⎜C ⎟
⎜ ⎟
⎝V ⎠ ⎛V ⎞
⎜ ⎟
1 ⎜ SiO2
⎛ ⎞
−1⎟
⎜C ⎟ γ= ⎜
⎛ ⎞
2 / 3 = −γnkT ⋅ ln⎜ V ⎟ − nkT ⋅ ln⎜ Co ⎟ + σ ⋅ 4πR2 ⎟
G (n) = −nf + λ ⋅ n 2⎜ V
⎜ eq ⎟
⎜ C eq ⎟
⎟
Si
P PP P
⎜C ⎜ ⎟
⎟
⎝o⎠
⎜ ⎟
⎝V⎠ ⎝ ⎠
Interstitial injection mechanism of stress energy relaxation for oxygen precipitate
is neglected, assuming high Frenkel pair formation energy and high vacancy flux.
∂H m Evolution of point defect size distribution function
= − ∂ ⎛ Jm ⎞
⎜ ⎟
∂t ∂R ⎝ ⎠ describes using Fokker-Planck equation
⋅ ∂ ⎡(g m (R) + d m (R))H m ⎤
1 m=V,P: voids and
J m = ⎡ gm (R) − dm (R)⎤ H m −
8πR2 ρm ∂R ⎣
⎢ ⎥
⎢ ⎥ oxygen precipitate
⎣ ⎦ ⎦
respectively
gm(R) and dm(R) are point defect growth and dissolution rate respectively.
The initial defect loss equation takes into account the formation of new nucleus,
precipitating to existing point defects and binding vacancy (V02) formation.
This model based on the assumptions introduced in [1] V. V. Voronkov, R. Falster, J. Cryst. Growth
204, p.462 (1999) and [2] T. Sinno, R. Brown, J. Electrochem. Soc. 146 -6, p.2300 (1999)
39.
Radial distribution of point defect density and average size
6
4.0x10 9
4x10
2D interface
2D interface
3D interface
3D interface
-3
-3
Void density, cm
Particle density, cm
9
3x10
6
3.5x10
9
2x10
6
3.0x10
9
1x10
6
2.5x10 0
0 1 2 3 4 5 0 1 2 3 4 5
7
Radial position, cm Radial position, cm
60
Oxygen precipitate average size, nm
55
Void average size, nm
6
50
5
45
2D interface
40 2D interface
3D interface 4
3D interface
35
3
30
0 1 2 3 4 5
0 1 2 3 4 5
Radial position, cm Radial position, cm
Technological parameters: Crystal diameter is 100 mm. Crystal height is 300 mm, pulling rate is 2
mm/min, cruciblecrystal rotation are 5-20 rpm, Ar flowratepressure are 675 slh 25 mbar.
This values correlate well with data presented in [1] T. Sinno et al., Mat. Sci. Eng. 28 p.149 (2000)
40.
Summary on modeling of Cz single Si growth
We have presented a combined 2D-3D model of Cz Si growth. The model
considers melt and gas convection, heat transfer by radiation and conduction,
calculations of crystallization front shape, oxygen transport in the melt and SiO
transport in the gas, including deposition, and defects dynamics.
2D unsteady modeling of melt down and cooling stages provides information on
crucible and melt temperature evolution, thermal gradients in the cooled crystal
and freezing of the melt remainders
Multiple verification examples show high predictive capability of CGSim
software. Good correspondence between results of computations and
experimental data is obtained for temperature distributions, thermal fluctuations
in the melt, crystallization front shape, oxygen transport
Using CGSim software it is possible to make considerable optimization of hot
zone design for Cz Si growth and: increase the pulling rate, to decrease
probability of twisting phenomena, to decrease probability of macrodislocation
generation, to decrease power consumptions, to reduce operation time including
meltdown and cooling stages, etc.
Thank you for a great slide presentation.
May I have the file of this presentation. Would you please tell how I can download it?
http://www.linkedin.com/in/alexgalyukov
http://www.str-soft.com/products/CGSim/