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



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.

4


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)



Important Aspects of Economic Power Generation

How to reach this goal?

(1) Increase of solar cell efficiency


5


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


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)

7

(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

8

non-uniform resistivity of

wafers along growth

direction

Point defects: metal impurity

Metal impurity decrease solar cell efficiency due to minority carrier recombination

9

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

10

Carbon C


of graphite (heaters) with

H2O


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



Oxygen O


crucible by Si melt

(Czochralski)


feedstock


- SiO2 precipitates


complex

- thermal donor


properties

CO and hydro-carbons,

e.g. from reactions of



11

Carbon C

e.g. from reactions of

graphite (heaters) with H2O


sawing

-electrical shunts

in solar cells

Nitrogen N



solidification)


nuclei for SiC

precipitation



Oxygen O


crucible by Si melt

(Czochralski)


feedstock


- SiO2 precipitates


complex

- thermal donor


properties

CO and gaseous hydro-




12

Carbon C


of graphite (heaters) with

H2O


sawing

- electrical shunts in solar

cell

Nitrogen N



solidification)


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

13

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)

14

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




Outline

16



7) Conclusions

Acknowledgements

Processes for crystallization of PV Si

Si mono-crystals:

- no grain boundary

- no dislocations

17

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

18

crystalline Si:

- grain

boundaries

- dislocations

multi-crystalline Si

� 1) Introduction


� 3) Crystallization Processes for Photovoltaic Silicon


4.1 General Issues

Outline

19

4.2 Modeling of Temperature Distribution

4.3 Modeling of Defect Formation



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

20

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

21

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


conditionsdefect

formation

σT(x,y,z,t)

22

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

24

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

26

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

27

� 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

28

• 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

29

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

30

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

31

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

32

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

33

4.3 Modeling of defect formation

material

propertiessolar cell

performance

process


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

36

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

37

- 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



� 4) Modeling of Si-Crystallization


Outline

38



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



� 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 !

Optimization and Modeling of Photovoltaic Silicon ... Institute IISB, Erlangen (Germany)...

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Transcript of Optimization and Modeling of Photovoltaic Silicon ... Institute IISB, Erlangen (Germany)...