Optimization and Modeling of Photovoltaic Silicon ... Institute IISB, Erlangen (Germany)...
Transcript of Optimization and Modeling of Photovoltaic Silicon ... Institute IISB, Erlangen (Germany)...
Optimization and Modeling
of Photovoltaic Silicon
ISSCG 14 Dalian August 1 - 7, 2010
1
Crystallization Processes
Georg Müller
Jochen Friedrich
Fraunhofer Institute IISB, Erlangen (Germany)
Photovoltaic Power Generation by Solar Cells
3 important features:
(1) photovoltaic effect:
absorption of photons (h·ν) generates
electron-holes pairs in Si
(2) transport of electrons and holes by
1 kWatt
per m2
Solar cells
2
(2) transport of electrons and holes by
electric field of pn-junction to plus and
minus electrode
(3) crystal defects are causing a reduction
of the number and liftime of generated
electrons and holes by recombination,
i.e. crystal defects are reducing the
solar cell efficiency ηelectric power generated by solar cell
incident power of sunlight η =
Next goal : achievement of „grid parity“, i.e.
price (1 Watt)solar power = price (1 Watt)conventional power
Important Aspects of Economic PV Power Generation
3
Next goal : achievement of „grid parity“, i.e.
price (1 Watt)solar power = price (1 Watt)conventional power
Important Aspects of Economic Power Generation
How to reach this goal?
(1) Increase of solar cell efficiency
by improvement of Si material quality, i.e.
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by improvement of Si material quality, i.e.
decrease of deleterious crystal defects
(2) Reduction of expenses of crystallization processes, i.e.
- improvement of crystal yield
- reduced processing time (growth rate, cooling rate)
- reduced consumption of consumables (crucible, graphite, gases, power)
Next goal : achievement of „grid parity“, i.e.
price (1 Watt)solar power = price (1 Watt)conventional power
Important Aspects of Economic Power Generation
How to reach this goal?
(1) Increase of solar cell efficiency
by improvement of Si material quality, i.e.
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by improvement of Si material quality, i.e.
decrease of deleterious crystal defects
(2) Reduction of expenses of crystallization processes, i.e.
- improvement of crystal yield
- reduced processing time (growth rate, cooling rate)
- reduced consumption of consumables (crucible, graphite, gases, power)
� 1) Introduction
2) Solar Cell Performance and Silicon Crystal Properties
What kind of crystal defect and which concentration are
harmful for solar cells?
3) Crystallization Processes for Photovoltaic Silicon
Outline
6
3) Crystallization Processes for Photovoltaic Silicon
4) Modeling of Si-Crystallization
5) Optimization of Cz-Growth of PV Si
6) Optimization Directional Solidification
7) Conclusions
Acknowledgements
Crystal defects with relevance for solar Silicon
(1) point defects
dopants, metal impurity, O, N, C
(2) line defects (dislocations)
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(3) grain boundaries
(4) precipitates of impurities
metals, silicides, SiO2, Si3N4, SiC
Point defects: doping atoms
Problem: doping atoms: B (0.8), P (0.3), Ga (0.008), ... are non-uniformly
incorporated during crystallization due to segregation coefficient k < 1
problem for solar cell:
non-uniform resistivity of
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non-uniform resistivity of
wafers along growth
direction
Point defects: metal impurity
Metal impurity decrease solar cell efficiency due to minority carrier recombination
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Davis et al., 1982
Please consider
the requirement of
extreme purity
ppb = part per billion
Non-metal impurities
impurity source of contamination defect problem for solar cell
Oxygen O
- dissolution of SiO2-
crucible by Si melt
(Czochralski)
- oxide particles in
feedstock
- interstitial oxygen
- SiO2 precipitates
- degradation of ν by B-O
complex
- thermal donor
- decrease of electric
properties
CO and gaseous hydro-
carbons, e.g. from reactions
- SiC-precipitates cause
wire break during wire
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Carbon C
carbons, e.g. from reactions
of graphite (heaters) with
H2O
wire break during wire
sawing
- electrical shunts in solar
cell
Nitrogen N
dissolution of Si3N4 coating
by Si melt (directional
solidification)
Si3N4-precipitates act as
nuclei for SiC
precipitation
Non-metal impurities
impurity source of contamination defect problem for solar cell
Oxygen O
- dissolution of SiO2-
crucible by Si melt
(Czochralski)
- oxide particles in
feedstock
- interstitial oxygen
- SiO2 precipitates
- degradation of ν by B-O
complex
- thermal donor
- decrease of electric
properties
CO and hydro-carbons,
e.g. from reactions of
- SiC-precipitates cause
wire break during wire
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Carbon C
e.g. from reactions of
graphite (heaters) with H2O
wire break during wire
sawing
-electrical shunts
in solar cells
Nitrogen N
dissolution of Si3N4 coating
by Si melt (directional
solidification)
Si3N4-precipitates act as
nuclei for SiC
precipitation
Non-metal impurities
impurity source of contamination defect problem for solar cell
Oxygen O
- dissolution of SiO2-
crucible by Si melt
(Czochralski)
- oxide particles in
feedstock
- interstitial oxygen
- SiO2 precipitates
- degradation of ν by B-O
complex
- thermal donor
- decrease of electric
properties
CO and gaseous hydro-
carbons, e.g. from reactions
- SiC-precipitates cause
wire break during wire
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Carbon C
carbons, e.g. from reactions
of graphite (heaters) with
H2O
wire break during wire
sawing
- electrical shunts in solar
cell
Nitrogen N
dissolution of Si3N4 coating
by Si melt (directional
solidification)
Si3N4-precipitates act as
nuclei for SiC
precipitation
Crystal defects with relevance for PV Si
Solar-Silicium
1) point defects ����
2) dislocations (line defects) are reducing the lifetime τ of the minority carriers (electrons)
60° dislocation in Si
with electrically active dangling bonds
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Dislocations in multi-crystalline Si
are mostly decorated by metal atoms
corresponds disclocation density
Crystal defects with relevance for PV Si
1) point defects ����
2) line defects /dislocations����
3) grain boundaries
- typical multi-crystalline Silicon
- the impact of grain boundaries on the performance of solar cells depends on its
crystallographic orientation (coincidence lattice site parameter Σ)
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typical mc-waferIncreased resistivity at
certain grain boundaries
Häßler et al., 2000
Gettering effect of grain boundaries
Metal impurities and precipitates are accumulated in grain boundaries (GB)
(for thermodynamic reasons)
Increased lifetime of minority
carriers in the vicinity of grain
boundaries (GB)
15Martinuzzi et al., 2007 Buonassisi et al, 2006
Bauer, 2005
grain boundary
� 1) Introduction
� 2) Solar Cell Performance and Silicon Crystal Properties
3) Crystallization Processes for Photovoltaic Silicon
4) Modeling of Si-Crystallization
5) Optimization of Cz-Growth of PV Si
Outline
16
5) Optimization of Cz-Growth of PV Si
6) Optimization Directional Solidification
7) Conclusions
Acknowledgements
Processes for crystallization of PV Si
Si mono-crystals:
- no grain boundary
- no dislocations
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multi-
crystalline Si:
- many grain
boundaries
- dislocations
EPD103-106cm-2
Processes for crystallization of PV Si
Si mono-crystals:
- no grain boundary
- dislocation free
multi-
crystalline Si:
This lecturemono-crystalline Si
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crystalline Si:
- grain
boundaries
- dislocations
multi-crystalline Si
� 1) Introduction
� 2) Solar Cell Performance and Silicon Crystal Properties
� 3) Crystallization Processes for Photovoltaic Silicon
4) Modeling of Si-Crystallization
4.1 General Issues
Outline
19
4.2 Modeling of Temperature Distribution
4.3 Modeling of Defect Formation
5) Optimization of Cz-Growth of PV Si
6) Optimization Directional Solidification
7) Conclusions
Acknowledgements
Goal of modeling / simulation
Correlation of crystallization process conditions (parameters) and
properties of crystal or solar cell, resp.
material
properties
solar cell
performance
process
parametercrystallization
conditions
defect
formation
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efficiency
fill factor
4.2 global thermal model
temperature T
stress σvm
σvmT(x,y,z,t)
4.3 modeling of defect formation
geometry
heater powercrystal defects
impurity
grain boundary
carrier
lifetime
(i) pre-processing (ii) calculation mode (iii) post-processing
Important steps of modeling
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geometry
editing
(CAD drawing)
assignment of
materials
- generation of numerical grid
- parameter settings
- numerical solution of
governing equations
- visualisation of modeling
results
- comparison to experimental
results
4.2 Temperature distribution and growth rate
material
propertiessolar cell
performance
process
parametercrystallization
conditionsdefect
formation
σT(x,y,z,t)
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efficiency
fill factor
global thermal model: heat transfer by conduction, convection and radiation
boundary conditions: * T = Tm (crystal-melt interface): “free boundary problem”
* heat source = heaters
* heat sink = cooled container walls
temperature T
stress σvm
σvmT(x,y,z,t)
geometry
heater power
crystal defects
impurity
grain boundary
carrier
lifetime
Global 3-dimensional modeling
global 3-dimensional modeling and time-depending modeling are very expensive;
global 3-dimensional modeling needs parallel and high performance computing
Kuliev et al., J.Crystal Growth
303(2007) 236-240
23CGS/PVA (Germany)
Efficient simulation of geometry in 2 dimensions
2-dim Cartesian coordinates T (x,y)
typical for directional solidificationrotational symmetry T (r,z)
typical for Czochralski puller
heater
heater
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Further simplifications by omitting of power connections, flanges, lead-throughs, etc.
heater
heater
crucible
Simplification by “partial” models
Heat and mass transfer in the melt can be simulated by considering only the melt region
example: Cz-melt (3D) example: DS Silicon melt (3D)
25numerical grid
Velocity field in a 70x70x20 cm3 melt volume
Dropka et al. JCG (2010)
• forward simulation: {Pn} ⇒ T(x)
heater powers are given, like in experiments, problem is
mathematically well posed
• inverse simulation:
selection of N points {x1, ... xn}
where N temperatures {ϑ1, ... ϑN} are given
mathematical problem:P
Pn+2
Pn+1
ϑ1
ϑ2 ϑ3
Inverse modeling principle
CZ
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mathematical problem:
find the heating powers Pm so that T(xn)=ϑn for all n
(1≤n≤N)
This problem is mathematically ill-posed
strategy of solution within CrysMAS software
Pn
P1
P3
ϑϑϑϑ3
ϑϑϑϑ2
ϑϑϑϑ1P2
weak formulation regularization
DS
mathematical
formulation
of the physical +
chemical processes
by PDEs
with corresponding
boundary conditions
numerical treatment of PDEs
in computers
- discretization of the
linear equation systems
- solving of these
equations
1st verification
� model
experiments
� simulation of
model
experiments
Procedure for process optimization by modeling
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� check of physical models
� check of mathematical formulation
� check of numerical treatment
process
optimization
fit?no
yes
“Model Experiments” to analyze Si crystal growth
Model experiments provide extensive data for crystallization process, such as:
• temperature distribution within the crystallization furnace, the Si melt and the
Si crystal (or graphite “dummy crystal“)
• shape of the solid (crystal) – liquid (melt) interface
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• shape of the solid (crystal) – liquid (melt) interface
• position of the s–l interface, i.e. growth rate
Examples , see next viewgraphs
20
30
Axia
l positio
n in c
m
Profile 1m
oveable
th
erm
ocouple
heater
Model experiment with crystal dummy (graphite)
and axial movable thermo-couples in a DS furnace
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0
10
1340 1360 1380 1400 1420 1440 1460 1480 1500
Temperature in °C
Axia
l positio
n in c
mProfile 2
Profile 3
insulation
gra
phite
dum
my
In-situ temperatur measurement in the melt
during Cz growth
∅∅∅∅c = 360mm, ∅∅∅∅x= 200mm, ωωωωc: crucible rotation
ωωωωc = 2 rpm
ωωωωc = 5 rpm
results
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ωωωωc = 5 rpm
+ cusp field
40mT
ωωωωc = 5 rpm
+ vertical
field 128mT
ωωωωc = 5 rpm
Model experiment with thermocouples inside Si crystal
Temperature measurements Numerical simulation and
experimental data (symbols)
Si-Cz (∅∅∅∅crystal = 100 mm)Crystal
Thermo-
Shield
distance from m
elt surface in m
m300
•
without heat shield
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Thermo-
couples
Melt
distance from m
elt surface in m
m
temperature in °C
100
200
♦
♦
♦
♦♦
•
•
•
700 1100 1500
0
with heat shield
Shape of crystal (solid) – melt (liquid) interface
Comparison of measured and calculated results
Visualization of s-l interface by analysis of axial crystal section
DS with different growth rates:
2.2 cm/h
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0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
solidified length [ cm ]
growth rate [ cm/h ] simulation experiment
1.0 cm/h
0.2 cm/h
In-situ detection of interface position, i.e. growth rate
Dipping rods for in-situ detection
of interface position
Measurement of growth rate R
by interface dipping during DS of Si
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4.3 Modeling of defect formation
material
propertiessolar cell
performance
process
parametercrystallization
conditionsdefect
formation
σvmT(x,y,z,t)
34
efficiency
fill factortemperature T
stress σvm
Modeling of defect formation
geometry
heater power
crystal defects
impurity
grain boundary
carrier
lifetime
1. Step: temperature distribution in furnace, melt, crystal ����
2. Step: modeling of thermodynamics (Gibbs Free Enthalpy), steady calculation
3. Step: modeling of reaction kinetics, time-depending calculation
Example of defect modeling:
formation of SiC precipitates during DS of Si
(1) Thermal model
(a) boundary
conditions
(2) defect model
35Thermal model (1) provides temperatures
for defect model (2)
(b)
Convective
transport of
C in Si melt
(c)
Formation of
SiC if solubility
of C in Si melt
Is exceeded
Modeling of Carbon distribution in Si-crystal
and comparison to experimental results
Modelling of axial
Carbon concentration C
Variation of CO incorpo-
ration (pC) via melt surface
by variation of
pC = melt transfer coeff.
and interface shape
A=planar
B=slightly concave
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B=slightly concave
C=strongly concave
axial
Carbon concentration C
Measured (FTIR, symbols)
and calculated (curves)
for 3 different growth rates
R = 0.2,1,2.2 cm/hFor more details see Friedrich et al.
ICCG16 in Beijing next week
Formation
Of SiC
precipitates
Combination of simulation and experiment
Important: Only the combination of experiment and simulation is successful!
Special sensors are developed to analyze the
crystallization process:
- thermocouples
Special ”model-experiments” are providing important process data
which are needed to validate the simulation tools
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- thermocouples
- phase dipping rod
- gas detector
Modeling software
must be appropriate for
crystal growth problems and
validated by experiments
Production crystallizer
with thermocouple
� 1) Introduction
� 2) Solar Cell Performance and Silicon Crystal Properties
� 3) Crystallization Processes for Photovoltaic Silicon
� 4) Modeling of Si-Crystallization
5) Optimization of Cz-Growth of PV Si
Outline
38
5) Optimization of Cz-Growth of PV Si
6) Optimization Directional Solidification
7) Conclusions
Acknowledgements
Crystal pulling by the Czochralski (Cz) Method
pulling
mechanism
seed
crystal
1917
Czochralski
2010
heater
1950 (Si) Teal, Bühler
39
crystal
melt
crucible
heater
melt
© Siltronic
crystallization rate of metalsGe and Si single crystals (Ø=20 mm)
for first transistors
Si single crystals dislocation-free
Ø=300 mm (IT devices)
Ø=200 mm (solar cells)
Advantages of the Cz process for the growth of PV Silicon
• Si crystal grows without any contact to a container or crucible wall
• Cz process provides Si single crystals with low defect concentrations
(e.g. dislocation free) which result in high solar cell efficiencies
• Growing crystal can be observed in-situ by visual inspection
40
• Growing crystal can be observed in-situ by visual inspection
and eventually (partly) remelted if unwanted crystal defects are formed
• Cz crystal growth process of Si is based on a mature technology;
ready to use equipment is commercially available
Disadvantages and problems of the Cz process for PV Silicon
and strategies of optimization
Problem Optimization Goal Methods Examples
Next
Viewgraph
high O-content
dissolution SiO2 crucible
reduction of O-content • alternative crucible mat.
• steady magnetic field
• FZ process
a
expensive equipment and
process cost
reduction of production cost:
(crucible, gas flow,
electrical power,)
• technical improvements
(see literature) b
41
electrical power,)
process yield improvement of yield e.g. multiple Cz c
doping non-uniformity for n-
type (P)
improved uniformity recharging techniques
e.eg. continuous Cz d
cylindrical crystal shape square crystal cross section See invited talk of
Prof. Rudolph at ICCG16 e
strong turbulent melt power control of convective flow time-dependent magnetic
fields: TMF, RMF,
heater magnets
a
(a) Optimization goal: Reduction of O-content of Si-
monocrystals by MCz and FZ
conventional MCz:
magnetic field
by external magnet
advanced MCz:
magnetic field by
Internal heater magnet
Floating Zone (FZ):
crucible-free melt
42
magnet is outside of
growth chamber heater = magnet
Inside growth chamber
(see Rudolph ICCG 16)
FZ could replace Cz
(b) Optimization goal: Reduction of Cz production cost
Before (left)
reduction of heat loss
(i.e. electric power)
and reduction of Ar gas consumption
by improved heat shields and
after optimization (right):
43
by improved heat shields and
gas leading geometry
Su et al. J.Crystal Growth 312 (2010) 495-501
silicon
meltseed
polysilicon
rod or
chunks
(c) Optimization goal: Improvement of yield
per run multiple Czochralski
44
melting pulling removal recharging reseeding
repeat
Saves: crucible, heat-up and cool-down periods
(d) Optimization goal: improved uniformity of resistivity
conventional Cz:
segregation causes
nonuniformity of resistivity
improvement by
continuous Cz
45
(e) Optimization goal: square-shaped Si crystal cross section
as-grown Si-Cz crystal and wafer
46
Rudolph et al. (presentation at ICCG 16)
� 1) Introduction
� 2) Solar Cell Performance and Silicon Crystal Properties
� 3) Crystallization Processes for Photovoltaic Silicon
� 4) Modeling of Si-Crystallization
� 5) Optimization of Cz-Growth of PV Si
Outline
47
� 5) Optimization of Cz-Growth of PV Si
6) Optimization of Directional Solidification
7) Conclusions
Acknowledgements
Side heater
Melt
Top heateraxia
l P
ositio
n
t3Crucible
mc-crystal
Melts/l interface
Crystallization of PV Si by Directional Solidification (DS)
48
200020042006
Bottom heater
Temperature
t1
t2
Tm
mc-crystal mc-crystal
cooled
steel vessel
s/l interface
typical DS-grown mc-Si ingotsA.Müller 2006
Advantages of the Directional Solodification process of Si
(compared to Cz)
• The DS process is less complex as Cz; for example it needs (up to now)
no seeding and Dash necking procedure, no conical growth
• The bottom cooling results in a higher hydrodynamic stability with
less affinity to turbulent melt flow
• DS crystallizers are less expensive because no movements of crystal
and crucible are needed
49
and crucible are needed
• DS-grown ingots have well adjusted size with rectangular shape,
without any special diameter control
• Up scaling of DS is much easier than Cz;
charge size of 1000 kg is under development
• The thermal processing of a DS growth run can be fully automized
and well optimized by computer simulation
Disadvantages and problems of the Cz process for PV Silicon
and strategies of optimization
Problem Optimization Goal MethodsExamples
Next
Viewgrap
no visual inspection of
growth process
better process control • improved simulation
• In-situ phase boundary
detection
direct contact of crucible
wall
reduced contamination from
crucible wall
• improved crucib. coating
• alternative cruc. material
Formation of Si3N4 and SiC • reduced contamination • feedstock quality
50
Formation of Si3N4 and SiC
precipitates
• reduced contamination
with N and C
• improved convective
transport of N, C
in Si melt
• feedstock quality
• handling of materials
• improved stirring of melt a
high contents of metal
impurity
• reduced contamination
• reduction of metal content
inside grains
• purification of feedstock
• Intrinsic gettering by
grain boundaries
b1
high density of grain
boundaries and related
defects
growth of large grains use of seed crystal
b2
8
10
12
14
C concentration [ 1017 atoms/cm
3 ]
(a) Reduced incorporation of C and
avoiding of SiC precipitates by forced melt convection
unsufficient stirring of Si-melt
SiC precipitates
51
0
2
4
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
solidified length x / crystal length L
C concentration [ 10
process I
process II
Scheil equation (mixed and closed system)
enhanced stirring of Si-melt
For more details see Friedrich et al, at ICCG16, Beijing next week
(b) Optimization goals: intrinsic gettering, larger grains
Intrinsic gettering of metals by
diffusion into grain boundariesGrowth of large grains or
mono-crystals by seeding
phase boundary
52
Martinuzzi et al. 2007
Helmreich 1980Mapping of minority carrier lifetime τ in mc Si
GB = Grain Boundary, DZ = Denuded Zone
Vertical section through Si crystal
grown by DS with seed
phase boundary
seed crystal
7) Conclusions
• Crystal growth can contribute considerably to the fabrication
of low cost and efficient solar cells
by optimization of the crystallization processes
• Modeling is an indispensable tool
53
Thank you for your kind attention !