Optimization and Modeling. of Photovoltaic Silicon. Crystallization Processes

Transcription

1 ISSCG 14 Dalian August 1-7, 2010 Optimization and Modeling of Photovoltaic Silicon Crystallization Processes Georg Müller Jochen Friedrich Fraunhofer Institute IISB, Erlangen (Germany) 1

2 Photovoltaic Power Generation by Solar Cells 1 kwatt per m 2 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 electric field of pn-junction to plus and minus electrode η= electric power generated by solar cell incident power of sunlight (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 η 2

3 Important Aspects of Economic PV Power Generation Next goal : achievement of grid parity, i.e. price (1 Watt) solar power = price (1 Watt) conventional power 3

4 Important Aspects of Economic Power Generation Next goal : achievement of grid parity, i.e. price (1 Watt) solar power = price (1 Watt) conventional power How to reach this goal? (1) Increase of solar cell efficiency 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) 4

5 Important Aspects of Economic Power Generation Next goal : achievement of grid parity, i.e. price (1 Watt) solar power = price (1 Watt) conventional power How to reach this goal? (1) Increase of solar cell efficiency 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) 5

6 Outline 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 4) Modeling of Si-Crystallization 5) Optimization of Cz-Growth of PV Si 6) Optimization Directional Solidification 7) Conclusions Acknowledgements 6

7 Crystal defects with relevance for solar Silicon (1) point defects dopants, metal impurity, O, N, C (2) line defects (dislocations) (3) grain boundaries (4) precipitates of impurities metals, silicides, SiO 2, Si 3 N 4, SiC 7

8 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 wafers along growth direction 8

9 Point defects: metal impurity Metal impurity decrease solar cell efficiency due to minority carrier recombination Please consider the requirement of extreme purity ppb = part per billion Davis et al.,

10 Non-metal impurities impurity source of contamination defect problem for solar cell Oxygen O Carbon C - dissolution of SiO 2 - crucible by Si melt (Czochralski) - oxide particles in feedstock CO and gaseous hydro- carbons, e.g. from reactions of graphite (heaters) with H 2 O - interstitial oxygen - SiO 2 precipitates - degradation of ν by B-O complex - thermal donor - decrease of electric properties - SiC-precipitates cause wire break during wire sawing - electrical shunts in solar cell Nitrogen N dissolution of Si 3 N 4 coating by Si melt (directional solidification) Si 3 N 4 -precipitates act as nuclei for SiC precipitation 10

11 Non-metal impurities impurity source of contamination defect problem for solar cell Oxygen O Carbon C - dissolution of SiO 2 - crucible by Si melt (Czochralski) - oxide particles in feedstock CO and hydro-carbons, e.g. from reactions of graphite (heaters) with H 2 O - interstitial oxygen - SiO 2 precipitates - degradation of ν by B-O complex - thermal donor - decrease of electric properties - SiC-precipitates cause wire break during wire sawing -electrical shunts in solar cells Nitrogen N dissolution of Si 3 N 4 coating by Si melt (directional solidification) Si 3 N 4 -precipitates act as nuclei for SiC precipitation 11

12 Non-metal impurities impurity source of contamination defect problem for solar cell Oxygen O Carbon C - dissolution of SiO 2 - crucible by Si melt (Czochralski) - oxide particles in feedstock CO and gaseous hydro- carbons, e.g. from reactions of graphite (heaters) with H 2 O - interstitial oxygen - SiO 2 precipitates - degradation of ν by B-O complex - thermal donor - decrease of electric properties - SiC-precipitates cause wire break during wire sawing - electrical shunts in solar cell Nitrogen N dissolution of Si 3 N 4 coating by Si melt (directional solidification) Si 3 N 4 -precipitates act as nuclei for SiC precipitation 12

13 Crystal defects with relevance for PV Si 1) point defects 2) dislocations (line defects) are reducing the lifetime τ of the minority carriers (electrons) Solar-Silicium 60 dislocation in Si with electrically active dangling bonds Dislocations in multi-crystalline Si are mostly decorated by metal atoms corresponds disclocation density 13

14 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) typical mc-wafer Häßler et al., 2000 Increased resistivity at certain grain boundaries 14

15 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) grain boundary Martinuzzi et al., 2007 Buonassisi et al, 2006 Bauer,

16 Outline 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 6) Optimization Directional Solidification 7) Conclusions Acknowledgements 16

17 Processes for crystallization of PV Si Si mono-crystals: - no grain boundary - no dislocations multicrystalline Si: - many grain boundaries - dislocations EPD cm -2 17

18 Processes for crystallization of PV Si This lecture mono-crystalline Si Si mono-crystals: - no grain boundary - dislocation free multi- crystalline Si: - grain multi-crystalline Si boundaries - dislocations 18

19 Outline 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 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 19

20 Goal of modeling / simulation Correlation of crystallization process conditions (parameters) and properties of crystal or solar cell, resp. process parameter crystallization conditions defect formation material properties solar cell performance T(x,y,z,t) σ vm geometry heater power temperature T stressσ vm crystal defects impurity grain boundary carrier lifetime efficiency fill factor 4.2 global thermal model 4.3 modeling of defect formation 20

21 Important steps of modeling (i) pre-processing (ii) calculation mode (iii) post-processing 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 21

22 4.2 Temperature distribution and growth rate process parameter crystallization conditions defect formation material properties solar cell performance T(x,y,z,t) σ vm geometry heater power temperature T stressσ vm crystal defects impurity grain boundary carrier lifetime efficiency fill factor global thermal model: heat transfer by conduction, convection and radiation boundary conditions: * T = T m (crystal-melt interface): free boundary problem * heat source = heaters * heat sink = cooled container walls 22

23 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) CGS/PVA (Germany) 23

24 Efficient simulation of geometry in 2 dimensions 2-dim Cartesian coordinates T (x,y) typical for directional solidification rotational symmetry T (r,z) typical for Czochralski puller heater heater crucible heater Further simplifications by omitting of power connections, flanges, lead-throughs, etc. 24

25 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) numerical grid Velocity field in a 70x70x20 cm 3 melt volume Dropka et al. JCG (2010) 25

26 Inverse modeling principle CZ P n+2 ϑ P 2 ϑ 3 n+1 ϑ 1 forward simulation: {P n } T(x) heater powers are given, like in experiments, problem is mathematically well posed inverse simulation: selection of N points {x 1,... x n } where N temperatures {ϑ 1,... ϑ N } are given DS P n P 1 mathematical problem: find the heating powers P m so that T(x n )=ϑ n for all n (1 n N) This problem is mathematically ill-posed strategy of solution within CrysMAS software P 2 ϑ 1 ϑ 3 ϑ2 weak formulation regularization P 3 26

27 Procedure for process optimization by modeling 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 check of physical models check of mathematical formulation no fit? check of numerical treatment yes process optimization 27

28 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 position of the s l interface, i.e. growth rate Examples, see next viewgraphs 28

29 Model experiment with crystal dummy (graphite) and axial movable thermo-couples in a DS furnace heater moveable thermocouple 30 Profile 1 graphite dummy Axial position in cm Profile 2 Profile 3 insulation Temperature in C 29

30 In-situ temperatur measurement in the melt during Cz growth results c = 360mm, x = 200mm, ω c : crucible rotation ω c = 2 rpm ω c = 5 rpm ω c = 5 rpm + cusp field 40mT ω c = 5 rpm + vertical field 128mT 30

31 Model experiment with thermocouples inside Si crystal Temperature measurements Crystal Numerical simulation and experimental data (symbols) Si-Cz ( crystal = 100 mm) Shield without heat shield Thermocouples Melt with heat shield distance from melt surface in mm temperature in C 31

32 Shape of crystal (solid) melt (liquid) interface Visualization of s-l interface by analysis of axial crystal section DS with different growth rates: Comparison of measured and calculated results 2.2 cm/h 1.0 cm/h cm/h growth rate [ cm/h ] simulation experiment solidified length [ cm ] 32

33 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

34 4.3 Modeling of defect formation process parameter crystallization conditions defect formation material properties solar cell performance T(x,y,z,t) σ vm geometry heater power temperature T stressσ vm crystal defects impurity grain boundary carrier lifetime efficiency fill factor Modeling of defect formation 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 34

35 Example of defect modeling: formation of SiC precipitates during DS of Si (1) Thermal model (2) defect model (a) boundary conditions (b) Convective transport of C in Si melt Thermal model (1) provides temperatures for defect model (2) (c) Formation of SiC if solubility of C in Si melt Is exceeded 35

36 Modeling of Carbon distribution in Si-crystal and comparison to experimental results Modelling of axial Carbon concentration C Variation of CO incorporation (p C ) via melt surface by variation of p C = melt transfer coeff. and interface shape A=planar B=slightly concave C=strongly concave Formation Of SiC precipitates axial Carbon concentration C Measured (FTIR, symbols) and calculated (curves) for 3 different growth rates R = 0.2,1,2.2 cm/h For more details see Friedrich et al. ICCG16 in Beijing next week 36

37 Combination of simulation and experiment Important: Only the combination of experiment and simulation is successful! Special model-experiments are providing important process data which are needed to validate the simulation tools Special sensors are developed to analyze the crystallization process: Production crystallizer with thermocouple - thermocouples - phase dipping rod - gas detector Modeling software must be appropriate for crystal growth problems and validated by experiments 37

38 Outline 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 6) Optimization Directional Solidification 7) Conclusions Acknowledgements 38

39 Crystal pulling by the Czochralski (Cz) Method 1917 Czochralski pulling mechanism 1950 (Si) Teal, Bühler 2010 seed crystal heater melt crucible melt Siltronic crystallization rate of metals Ge 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) 39

40 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 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 40

41 Disadvantages and problems of the Cz process for PV Silicon and strategies of optimization Problem Optimization Goal Methods high O-content dissolution SiO 2 crucible reduction of O-content alternative crucible mat. steady magnetic field FZ process expensive equipment and process cost reduction of production cost: (crucible, gas flow, electrical power,) technical improvements (see literature) b process yield improvement of yield e.g. multiple Cz c Examples Next Viewgraph a doping non-uniformity for n- type (P) improved uniformity recharging techniques e.eg. continuous Cz cylindrical crystal shape square crystal cross section See invited talk of Prof. Rudolph at ICCG16 strong turbulent melt power control of convective flow time-dependent magnetic fields: TMF, RMF, heater magnets d e a 41

42 (a) Optimization goal: Reduction of O-content of Simonocrystals 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 magnet is outside of growth chamber heater = magnet Inside growth chamber (see Rudolph ICCG 16) FZ could replace Cz 42

43 (b) Optimization goal: Reduction of Cz production cost Before (left) after optimization (right): reduction of heat loss (i.e. electric power) and reduction of Ar gas consumption by improved heat shields and gas leading geometry Su et al. J.Crystal Growth 312 (2010)

44 (c) Optimization goal: Improvement of yield per run multiple Czochralski silicon melt polysilicon rod or chunks seed melting pulling removal recharging reseeding repeat Saves: crucible, heat-up and cool-down periods 44

45 (d) Optimization goal: improved uniformity of resistivity conventional Cz: segregation causes nonuniformity of resistivity improvement by continuous Cz 45

46 (e) Optimization goal: square-shaped Si crystal cross section as-grown Si-Cz crystal and wafer Rudolph et al. (presentation at ICCG 16) 46

47 Outline 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 6) Optimization of Directional Solidification 7) Conclusions Acknowledgements 47

48 Crystallization of PV Si by Directional Solidification (DS) axial Position Top heater Side heater t 3 t 2 Melt mc-crystal Crucible s/l interface Melt mc-crystal T m t 1 Temperature Bottom heater cooled steel vessel typical DS-grown mc-si ingots A.Müller

49 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 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 49

50 Disadvantages and problems of the Cz process for PV Silicon and strategies of optimization Problem Optimization Goal Methods no visual inspection of growth process direct contact of crucible wall better process control reduced contamination from crucible wall improved simulation In-situ phase boundary detection improved crucib. coating alternative cruc. material Formation of Si 3 N 4 and SiC reduced contamination feedstock quality precipitates with N and C handling of materials improved convective improved stirring of melt transport of N, C in Si melt high contents of metal impurity high density of grain boundaries and related defects reduced contamination reduction of metal content inside grains growth of large grains purification of feedstock Intrinsic gettering by grain boundaries use of seed crystal Examples Next Viewgrap a b1 b2 50

51 (a) Reduced incorporation of C and avoiding of SiC precipitates by forced melt convection 14 C concentration [ atoms/cm 3 ] unsufficient stirring of Si-melt SiC precipitates For more details see Friedrich et al, at ICCG16, Beijing next week process I process II Scheil equation (mixed and closed system) enhanced stirring of Si-melt solidified length x / crystal length L 51

52 (b) Optimization goals: intrinsic gettering, larger grains Intrinsic gettering of metals by diffusion into grain boundaries Growth of large grains or mono-crystals by seeding phase boundary seed crystal Mapping of minority carrier lifetime τ in mc Si GB = Grain Boundary, DZ = Denuded Zone Martinuzzi et al Vertical section through Si crystal grown by DS with seed Helmreich

53 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 Thank you for your kind attention! 53