Zone-Melting Recrystallization for Crystalline Silicon Thin-Film Solar Cells

Dissertation

zur Erlangung des akademischen Grades des Doktors der Naturwissenschaften (Dr. rer. nat.) an der Universität Konstanz Fachbereich Physik

vorgelegt von

THOMAS KIELIBA

Fraunhofer Institut für Solare Energiesysteme Freiburg

2006

Kieliba, Thomas: Zone-Melting Recrystallization for Crystalline Silicon Thin-Film Solar Cells [Elektronische Ressource] / Thomas Kieliba. – Konstanz, Univ., Diss., 2006 Zugl. – Berlin : dissertation.de – Verlag im Internet GmbH, 2006 ISBN 3-86624-196-8

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Dissertation der Universität Konstanz Tag der mündlichen Prüfung: 22.09.2006 Referenten: Priv. Doz. Dr. Gerhard Willeke Prof. Dr. Ulrich Rüdiger

ii v3.4b (doc: 2006-11-06)

Acknowledgements

I would like to thank my advisor PD Dr. Gerhard Willeke for the faith in my abilities and the continuous support of my work. He allowed me great freedom in this research. I am very grateful to Prof. Dr. Ulrich Rüdiger for acting as a second reviewer and an examiner. The Fraunhofer ISE provided an excellent environment for creative work. Quite a lot of people contributed to this very comfortable working atmosphere, and there are too many to mention all individually. I am especially grateful to Dr. Stefan Reber for many stimulating discussions, including the consideration of industrial applications, and his helpful comments on the final draft. I very much appreciate the valuable input of Dr. Achim Eyer on crystal growing techniques and equipment design. I am extremely grateful to Dr. Wilhelm Warta for many helpful discussions on defects, their characterization, and on the appropriate communication of scientific results. The chapters on dislocation modeling and characterization profited very much from his con- structive input. I would like to thank Dr. Albert Hurrle for many inspiring discussions that often helped me get back on track. I am very appreciative of the help I received from the department staff in solar cell processing and characterization. Norbert Schillinger and Fridolin Haas are thanked for construction of the ZMR furnace that withstood many torturous experiments. Mira Kwiatkowska, Harald Lautenschlager, Toni Leimenstoll, and Christian Schetter kindly prepared solar cells on numerous, sometimes exotic, substrates. Many thanks to Elisabeth Schäffer for uncounted measurements, her helping hand whenever needed and the good humor she spread. Daniel M. Spinner is thanked for his perfect support regarding all computer software and hardware issues. I would like to thank all my colleagues who have contributed to this work in different ways. The following people deserve special mentioning: I would like to thank Stephan Riepe for many fruitful discussions on defects and their appropriate modeling, and also for MFCA measurements. I am very appreciative of

iii iv ACKNOWLEDGEMENTS

Dr. Stefan Peters from the Fraunhofer ISE »outpost« in Gelsenkirchen for a wealth of discussions on photovoltaics and everything under the sun. He was always a very welcome guest in the Rennweg apartment. I would like to thank Dominik Huljić for many contributions, inspiring discussions, and the great time we spent together. I am grateful to Dr. Sandra Bau for the good teamwork in silicon film preparation and many useful discussions. Further, I am indebted to Johannes Pohl whose studies contributed a lot to this work, and to Stefan Janz who took over the operation of the ZMR lab. Transferring the responsibilities over to him was a pleasure, and I know they are in good hands, which has helped me to concentrate on this thesis. Much of the research was conducted in conjunction with national and international projects. I appreciate the valuable contribution and helpful discussions of all partners involved. Along side the »official« projects some fruitful collabo- rations developed. I would like to thank Christian Schmiga from ISFH, Hameln/Emmerthal for hydrogen passivation of numerous samples. I am indebted to Dr. Melanie Nerding from the University of Erlangen-Nürnberg for TEM and EBSD characterization, and for helpful discussions. Thanks are also due to Dr. Gaute Stokkan from NTNU, Trondheim for the work on dislocation density measurements. I appreciate the funding of this work by the scholarship program of the German Federal Environmental Foundation (Deutsche Bundesstiftung Umwelt) and I would especially like to thank Dr. Maximilian Hempel for his support. I am very grateful to Nicole Kuepper for proofreading the English text and her incredibly fast response with helpful corrections from »Down Under«. Finally, I would like to express my deepest gratitude to my parents for their continuous support, and to my sister and my brothers for their support at all times.

Abstract

Thin-film solar cells from crystalline silicon combine advantages from silicon wafer based technology with thin-film features. On one hand, the use of a supporting substrate minimizes the consumption of highly pure silicon and enables integrated interconnection of the individual solar cells within a module. On the other hand, these solar cells profit from the established silicon technology and the abundance of quartz sand as a raw material. The thin-film solar cell technology investigated in this work belongs to the so-called »high temperature approaches«. On a low-cost substrate, an intermediate barrier layer is deposited. Then a thin silicon film is applied on top by chemical vapor deposition (CVD) and afterwards transferred into a large grained structure by zone-melting recrystallization (ZMR). The recrystallized film acts as a »seed« for subsequent epitaxial growth, again by silicon CVD. The final silicon thin film has a thickness of 20–30 µm. For silicon thin-film formation, ZMR is a key technology. This process largely determines film quality since defects, such as dislocations or grain boundaries, are replicated by the subsequent epitaxial growth. The ZMR method yields large grains with sizes comparable to those in multicrystalline silicon wafers grown by directional solidification. However, an inevitable feature of ZMR is the creation of low angle grain boundaries within the grains, so-called subgrain boundaries (SGBs). These subgrain boundaries induce stripes with high dislocation density in the epitaxial silicon layer. Therefore, they are especially harmful for the solar cell device. The analyzed films showed that dislocation density and therefore electronic material quality in subgrain boundary regions is related to the run of the subgrain boundaries relative to the ZMR scan direction. For equally spaced subgrain boundaries running parallel to the scan direction, their effect was found to be smallest. Investigations by optical and electron microscopy support an earlier theory, which explained subgrain boundary formation by tilting of subgrains and polygonization of dislocations. For the ZMR process, the effect of different material and process parameters on film quality has been investigated. These include the substrate type, the sili-

v vi ABSTRACT con film thickness, the scan speed and the type of capping used to prevent agglomeration of molten silicon. Regarding the capping type, a ∼0.15 µm thick rapid thermal oxide (RTO), which was grown inside the ZMR reactor, has been compared to a standard

2 µm thick SiO2 layer deposited by plasma enhanced CVD. For 8 µm thick silicon films, the thin thermal oxide was found to yield better film quality and solar cell performance. Scan speed is the most crucial parameter for costs of the ZMR process. An automated process control based on image analysis of the molten zone has been developed, which allows high-speed ZMR. On model substrates, the dependence of dislocation density and solar cell performance on scan speed has been studied for values between 10 mm min−1 and 100 mm min−1. The minimum value is similar to the pull speed for common silicon ribbon materials, such as Edge- defined Film-fed Growth (EFG) or String-Ribbon, and yielded comparable crystal quality. For a higher scan speed compromises regarding crystal quality and solar cell performance have to be made. For solar cells prepared without bulk hydrogenation, the tenfold increase of scan speed from 10 mm min−1 to 100 mm min−1 resulted in a relative decrease in solar cell conversion efficiency of approximately 35%. The choice of substrate material and its preparation have a major effect on quality of the ZMR films. For the investigated materials (Si3N4, SiSiC and

ZrSiO4 ceramics, SSP ribbons) three key issues have been identified, which currently lead to a drawback in solar cell performance compared to devices fabricated on »model« substrates. (i) Thermal expansion has to match very precisely with silicon. The maximum tolerable difference in length is estimated to be below 1 ‰. (ii) The stability of the intermediate layer is crucial for successful ZMR processing. Irregularities observed in situ during ZMR processing could often be traced back to a damaged intermediate layer. (iii) The substrate’s thermal conductivity significantly affects the thermal gradient at the solidification interface. Therefore, inhomogeneous thermal properties, e.g., caused by varying substrate thicknesses, hinder the growth of high quality ZMR films. For the investigated technology, dislocations induced by subgrain boundaries in the ZMR seed film are the main defects limiting solar cell performance. To obtain a more detailed understanding, an analytical model for the dependence of

ABSTRACT vii effective diffusion length on dislocation density has been developed. For this purpose the model published by Donolato [J. Appl. Phys. 84, 2656 (1998)] has been extended regarding the following features: (i) The use of the »quantum efficiency effective diffusion length«. This quantity is compatible with the usual diffusion length extraction from quantum efficiency data and is more adequate for the typical operation conditions of a solar cell than the quantity introduced in the original work. (ii) The appropriate description of thin devices with a finite thickness and a finite back surface recombination velocity. Since the associated boundary value problem does not allow a straightforward analytical solution, an approximate expression has been derived, which was validated by numerical simulations. The model has been applied to the characterization of thin-film solar cell devices using the techniques of etch pit density (EPD) mapping and spectrally resolved light beam induced current (SR-LBIC). For EPD measurements a special setup has been developed, which is based on an automated microscope and digital image analysis. This system is capable of producing EPD maps with tens of thousands of data points. To correlate EPD and SR-LBIC diffusion length data, the Gaussian profile of the LBIC beam has to be considered. Fur- ther, charge carriers can diffuse from the point of generation into neighboring areas (which might have different dislocation densities). Both effects were taken into account by convolving the EPD map with a filter kernel that contains information on LBIC profile and diffusion parameters. The result is an effective dislocation density (EDD) map. At the investigated structures, these EDD maps correlated well with SR-LBIC diffusion length maps. For a quantitative analysis, the extended version of Donolato’s model was locally fitted to EDD and effective diffusion length data. The determined normalized recombination strength values are in the range of 0.006 to 0.016, and are comparable to values measured on conventional multicrystalline silicon solar cells. In addition, the model has been applied to open circuit voltage data measured on samples with different dislocation densities. For these devices a strong decrease of open circuit voltage with increasing dislocation density was found. With the consideration of space charge region recombination, the experimental data could be modeled very well. However, in order to obtain satisfactory fitting results, it had to be assumed that the region of high recombination is much wider viii ABSTRACT than the »effective space charge region width« calculated from the electrical field strength. This finding is in accordance with results reported for solar cells from fine-grained Si thin films. The objective of the investigations described above has been the optimization of thin-film solar cell performance through the improvement of silicon thin-film quality. In parallel, the aim of device enhancement was approached by improvement of the solar cell process. Light trapping by front surface texturization, use of a lowly doped, passivated emitter, bulk hydrogen defect passivation, and a double-layer antireflection coating significantly increased device performance. Combining all these methods, the initial conversion efficiency could nearly be doubled. The best solar cell on a »model« substrate with a ∼31 µm thick active silicon film achieved a conversion efficiency of 13.5 %, with Voc = 610 mV, Jsc = 30.9 mA cm−2, and FF = 71.7 %.

Deutsche Zusammenfassung

Dünnschichtsolarzellen aus kristallenem Silicium kombinieren Vorteile der Silicium-Wafer-Technologie mit der Dünnschichttechnik. Zum einen wird durch die Verwendung eines tragenden Substrates der Bedarf an hochreinem Silicium minimiert und es kann eine integrierte Verbindung der einzelnen Solarzellen innerhalb des Moduls realisiert werden. Zum anderen profitieren diese Solar- zellen von der etablierten Siliciumtechnologie und von der unbegrenzten Roh- stoff-Verfügbarkeit in Form von Quarzsand. Die Dünnschichttechnologie, die in dieser Arbeit untersucht wird, gehört zu den sogenannten »Hochtemperaturansätzen«. Auf einem kostengünstigen Sub- strat wird eine Zwischenschicht aufgebracht. Danach wird hierauf ein dünner Silicium-Film mittels Gasphasenabscheidung (chemical vapor deposition, CVD) abgeschieden und anschließend durch Zonenschmelz-Rekristallisation (zone- melting recrystallization, ZMR) in eine großkörnige Struktur überführt. Der rekristallisierte Film dient als »Keimschicht« für eine nachfolgende eptiaktische Verdickung, die ebenfalls mittels Silicium-CVD erfolgt. Der fertige Silicium- Film hat eine Dicke von 20–30 µm. Für die Herstellung des Silicium-Films ist das ZMR-Verfahren eine Schlüs- seltechnologie. Dieser Schritt bestimmt die Filmqualität, da Defekte wie Verset- zungen oder Korngrenzen durch das nachfolgende eptiaktische Wachstum über- nommen werden. Die Korngröße in ZMR-Filmen ist mit der in multikristallinen Wafern vergleichbar, die durch gerichtete Erstarrung hergestellt werden. Nicht vermeidbar ist beim ZMR-Prozess jedoch die Entstehung von Kleinwinkelkorn- grenzen innerhalb der Körner, sogenannte Subkorngrenzen (subgrain boundaries, SGB). Diese Subkorngrenzen führen zu streifenförmigen Bereichen mit hoher Versetzungsdichte in der Epitaxie-Schicht und beinträchtigen die Leistung der Solarzellen. Die analysierten Filme zeigten, dass die Versetzungsdichte und damit die elektronische Materialqualität in den Subkorngrenzen-Bereichen mit dem Verlauf der Subkorngrenzen relativ zur Ziehrichtung beim ZMR-Prozess zusammenhängt. Am wenigsten schädlich sind Subkorngrenzen, die äquidistant und parallel zur Ziehrichtung verlaufen. Untersuchungen mittels optischer Mik-

ix x DEUTSCHE ZUSAMMENFASSUNG roskopie und Elektronenmikroskopie bestätigen eine frühere Theorie, nach der die Entstehung der SGB durch das Verkippen von Sub-Körnern und anschlie- ßender Polygonisierung erklärt wird. Für den ZMR-Prozess wurde der Einfluss verschiedener Material- und Pro- zessparameter auf die Schicht-Qualität untersucht. Hierzu gehören der Sub- strattyp, die Schichtdicke des Silicium-Films, die Ziehgeschwindigkeit und die Art der Capping-Schicht, die ein Zusammenziehen des flüssigen Siliciums ver- hindert. Bezüglich der Capping-Schicht wurde ein 0,15 µm dickes thermisches Oxid, das innerhalb des ZMR-Reaktors gewachsen wurde, mit einer 2 µm dicken

Standard SiO2-Schicht verglichen, die durch plasmaunterstützte CVD abgeschieden wurde. Für 8 µm dicke Keimschichten wurden mit dem dünnen thermischen Oxid bessere Ergebnisse hinsichtlich Filmqualität und Solarzellen- leistung erreicht als mit der Standard-Capping-Schicht. Die Ziehgeschwindigkeit ist essentiell für die Kosten des ZMR-Prozesses. Durch die Entwicklung einer automatisierten Prozesssteuerung, die auf Bild- analyse der Schmelzzone basiert, konnten ZMR-Prozesse mit hoher Geschwin- digkeit realisiert werden. Auf Modell-Substraten wurde untersucht wie Verset- zungsdichte und Solarzellenleistung von der Ziehgeschwindigkeit abhängen. Diese wurde im Bereich zwischen 10 mm min−1 und 100 mm min−1 variiert. Die kleinste Geschwindigkeit entspricht in etwa der Ziehgeschwindigkeit mit der Silicium-Bandmaterialien wie EFG (Edge-defined Film-fed Growth) oder String Ribbon hergestellt werden. In diesem Fall ist auch die kristallographische Qua- lität mit der von Bandmaterialien vergleichbar. Bei höheren Ziehgeschwindig- keiten müssen Kompromisse hinsichtlich Schichtqualität und Solarzellenleistung gemacht werden. Bei einer Verzehnfachung der Ziehgeschwindigkeit von 10 mm min−1 auf 100 mm min−1 reduzierte sich der Wirkungsgrad um 35 % relativ – bei Verwendung eines Solarzellenprozesses ohne Wasserstoffpassivie- rung. Das Substratmaterial und seine Vorbereitung haben einen deutlichen Einfluss auf die Qualität der ZMR Silicium-Filme. Für die untersuchten Materialien

(Si3N4-, SiSiC- und ZrSiO4-Keramiken, SSP-Bänder) wurden drei Hauptpunkte identifiziert, die momentan zu einer Reduktion der Solarzellenleistung im Ver- gleich zu Zellen auf Modell-Substraten führen. (i) Die thermische Ausdehnung

DEUTSCHE ZUSAMMENFASSUNG xi des Substrats muss sehr genau an die von Silicium angepasst sein. Aus den Messergebnissen lässt sich abschätzen, dass die maximal zulässige Längendif- ferenz 1 ‰ nicht überschreiten darf. (ii) Für den ZMR-Prozess ist eine ausrei- chende Stabilität der Zwischenschicht unerlässlich. Unregelmäßigkeiten, die während des ZMR-Prozesses in situ beobachtet wurden, ließen sich häufig auf eine beschädigte Zwischenschicht zurückführen. (iii) Die Wärmeleitfähigkeit des Substrates beeinflusst wesentlich den Temperaturgradienten an der Kristalli- sationsfront. Daher führen inhomogene thermischen Eigenschaften, z.B. durch variierende Substratstärke, zu Schichten minderer Qualität. Bei der untersuchten Technologie wird die Solarzellenleistung primär durch Versetzungen begrenzt, die durch Subkorngrenzen in der ZMR-Keimschicht verursacht werden. Für ein detaillierteres Verständnis wurde ein analytisches Modell für die Abhängigkeit der effektiven Diffusionslänge von der Verset- zungsdichte entwickelt. Hierzu wurde das Modell von Donolato [J. Appl. Phys. 84, 2656 (1998)] erweitert: (i) Es wurde für die Verwendung der »Quanteneffi- zienz-Effektiven-Diffusionslänge« angepasst. Diese Größe ist mit dem übli- cherweise aus der internen Quanteneffizient extrahierten Wert kompatibel, und passt besser zum typischen Betriebszustand einer Solarzelle als die »effektive Diffusionslänge«, die in der Originalarbeit verwendet wird. (ii) Das Modell wurde für die adäquate Beschreibung einer dünnen Solarzelle mit endlicher Dicke und endlicher Oberflächenrekombinationsgeschwindigkeit an der Rück- seite erweitert. Das zugehörige Randwertproblem ist nicht analytisch lösbar. Daher wurde eine Nährungslösung entwickelt und durch numerische Simulatio- nen validiert. Das Modell wurde zur Charakterisierung der gefertigten Dünnschichtsolar- zellen verwendet. Hierzu wurde die Ätzgrubendichte (etch pit density, EPD) bestimmt und die effektive Diffusionslänge mittels SR-LBIC (spectrally resolved light beam induced current) gemessen. Für die EPD-Messung wurde ein spezielles System entwickelt, das auf einem automatisierten Mikroskop und digitaler Bildanalyse basiert. Mit diesem System können EPD-Topographien aus einigen 10 000 Datenpunkten erzeugt werden. Um EPD- und SR-LBIC Daten miteinander zu korrelieren, muss das Gaußförmige Profil des LBIC-Lichtstrahls berücksichtigt werden. Außerdem können Ladungsträger vom Punkt der Gene- ration in benachbarte Bereiche (mit unterschiedlicher Versetzungsdichte) dif- xii DEUTSCHE ZUSAMMENFASSUNG fundieren. Beide Effekte wurden berücksichtigt, indem die EPD-Topographie mit einem Filterkern gefaltet wurde, der das LBIC-Profil und die Diffusions- funktion enthält. Das Resultat ist eine Topographie der effektiven Versetzungs- dichte (effective dislocation density, EDD). Für die untersuchten Silicium- Schichten korrelieren diese EDD-Topographien gut mit den SR-LBIC Diffusi- onslängentopographien. Für eine quantitative Analyse wurde die erweiterte Version des Donolato- Modells lokal an EDD- und Diffusionslängendaten angepasst. Die berechneten Werte für die normalisierte Rekombinationsstärke liegen im Bereich 0,006 bis 0,016 und sind damit mit den Werten vergleichbar, die an herkömmlichen multikristallinen Solarzellen gemessen wurden. Zusätzlich wurde das Modell auf Messdaten der offenen Klemmenspannungen angewendet, die an Proben mit unterschiedlicher Versetzungsdichte bestimmt wurden. Es zeigte sich, dass die offene Klemmenspannung mit Zunahme der Versetzungsdichte stark abnimmt. Die gemessenen Daten konnten sehr gut modelliert werden wenn die Rekombi- nation in der Raumladungszone berücksichtigt wird. Eine zufriedenstellende Kurvenanpassung gelang jedoch nur dann, wenn angenommen wird, dass die hoch rekombinationsaktive Region breiter als die »effektive Breite der Raumla- dungszone« ist, die sich aus der stärke des elektrischen Feldes ergibt. Diese Beo- bachtung passt zu Ergebnissen, die für Solarzellen aus feinkristallinen Silicium- Filmen berichtet wurden. Das Ziel der oben beschriebenen Untersuchungen war die Verbesserung des Solarzellen-Wirkungsgrads durch Optimierung der Silicium-Filmqualität. Parallel hierzu wurde in dieser Arbeit das Ziel der Wirkungsgradsteigerung durch eine Verbesserung des Solarzellenprozesses angegangen. Durch verbesserten »Lichteinfang« (light trapping) mittels Oberflächentextu- rierung, Verwendung eines niedrig dotierten, passivierten Emitters, Volumen- Wasserstoffpassivierung und Einsatz einer doppellagigen Antireflexbeschich- tung konnte der Wirkungsgrad der Solarzellen deutlich gesteigert werden. Durch Kombination aller genannten Methoden wurde der ursprüngliche Wirkungsgrad der Solarzellen fast verdoppelt. Die beste Solarzelle auf einem Modell-Substrat und einem ∼31 µm dicken aktiven Silicium-Film erreichte einen Wirkungsgrad −2 von 13,5 %, mit Voc = 610 mV, Jsc = 30,9 mA cm und FF = 71,7 %.

Contents

Acknowledgements iii

Abstract v

Deutsche Zusammenfassung ix

List of Tables xvii

List of Figures xix

1 Introduction 1

Thesis Outline ...... 2

2 Thin-Film Solar Cell Concepts and Silicon Growth Methods 5

2.1 Silicon Ribbon and Thin-Film Solar Cell Technologies ...... 5 2.1.1 Thin-Film Solar Cells from Crystalline Silicon...... 7

2.2 Silicon Growth Methods...... 8 2.2.1 Vertical versus Horizontal Ribbon Growth ...... 10

2.3 Summary ...... 12

3 Crystalline Silicon Thin-Film Solar Cell Technology 13

3.1 Solar Cell Structure and Fabrication Process ...... 13

3.2 Substrate...... 14 3.2.1 Material Requirements...... 14 3.2.2 Low-Cost and »Model« Substrates...... 17

3.3 Intermediate Layer...... 20 3.3.1 Light Trapping ...... 21

3.4 Silicon Chemical Vapor Deposition (CVD)...... 23

3.5 Zone-Melting Recrystallization ...... 25 3.5.1 Introduction...... 25 3.5.2 Interface Morphology, Subgrain Boundaries, and Texture ...... 26 xiii xiv CONTENTS

3.5.3 ZMR 100 System ...... 31 3.5.4 Capping Oxide ...... 35 3.5.5 ZMR Process...... 38

3.6 Solar Cell Process ...... 39

3.7 Summary and Outlook ...... 41

4 Silicon Solar Cell Device Physics 43

4.1 Recombination and Generation ...... 43 4.1.1 Recombination ...... 43 4.1.2 Generation...... 45

4.2 Basic Equations...... 46

4.3 p-n Junction...... 47 4.3.1 Two-Diode Model...... 51

4.4 Charge Collection Probability ...... 52 4.4.1 Charge Collection Probability and Reciprocity Theorem ...... 52 4.4.2 Charge Collection in Solar Cells of Finite Thickness ...... 55

4.5 Collection and Quantum Efficiency ...... 61

4.6 Summary ...... 63

5 Effective Diffusion Length and Effect of Dislocations 65

5.1 Introduction...... 65

5.2 Review on Definitions of Effective Diffusion Length ...... 66 5.2.1 Quantum Efficiency Effective Diffusion Length ...... 66 5.2.2 Collection Effective Diffusion Length ...... 68 5.2.3 Current-Voltage Effective Diffusion Length...... 70 5.2.4 Donolato’s Definition of Effective Diffusion Length ...... 71

5.3 Effective Diffusion Length for Textured Cells...... 74

5.4 Effect of Dislocations on Effective Diffusion Length...... 75 5.4.1 Donolato’s Model for a Semi-Infinite Specimen...... 76 5.4.2 Model for a Specimen of Finite Thickness...... 86

5.5 Summary ...... 91

CONTENTS xv

6 Characterization Methods 93

6.1 Dark and Illuminated I-V Characteristics ...... 93

6.2 Spectral Response and Quantum Efficiency...... 94 6.2.1 Error Analysis for Evaluation of Effective Diffusion Length by Linear Fitting...... 95

6.3 Spectrally Resolved Light Beam Induced Current ...... 98 6.3.1 Error Analysis for Evaluation of Effective Diffusion Length by SR-LBIC ...... 100

6.4 Modulated Free Carrier Absorption...... 103

6.5 Etch Pit Density Mapping...... 106 6.5.1 Hardware Setup...... 106 6.5.2 Image Analysis...... 107 6.5.3 Testing on Different Multicrystalline Silicon Materials...... 112 6.5.4 Correlation of Effective Diffusion Length and Etch Pit Density . 118

6.6 Summary ...... 122

7 Optimization of Silicon Film Quality 125

7.1 Microstructure and Origin of Defects...... 125 7.1.1 ZMR Growth Morphologies ...... 125 7.1.2 Correlation between Defects in ZMR Film and Epitaxial Layer.. 127 7.1.3 Microscopic Analysis...... 130

7.2 Effect of the Capping Layer...... 134 7.2.1 Film Properties...... 135 7.2.2 Solar Cell Results...... 137

7.3 Effect of Scan Speed and Seed Film Thickness ...... 138 7.3.1 Crystallization Front Morphology and Film Properties ...... 139 7.3.2 Solar Cell Results...... 144

7.4 Effect of Substrate...... 146 7.4.1 Thermal Expansion ...... 147 7.4.2 Surface Roughness and Intermediate Layer Stability...... 149 7.4.3 Thermal Properties...... 152

xvi CONTENTS

7.4.4 Summary on Substrate Investigations...... 153

7.5 Dependence of Effective Diffusion Length on Dislocation Density.....154 7.5.1 Discussion on Recombination Strength Results...... 157

7.6 Dependence of Open Circuit Voltage on Dislocation Density...... 159

7.7 Summary and Outlook ...... 164

8 Solar Cell Device Optimization 167

8.1 Emitter Passivation ...... 167

8.2 Surface Texturization...... 169

8.3 Bulk Hydrogen Passsivation...... 170

8.4 Optimized Solar Cell Process ...... 172

8.5 Transfer to Industrial Processes...... 173

8.6 Summary and Outlook ...... 175

Appendix A Symbols, Acronyms, and Constants 177

A.1 List of Symbols...... 177

A.2 Physical Constants ...... 182

A.3 List of Acronyms ...... 182

Appendix B Silicon Material Properties 185

B.1 Selected Properties...... 185

B.2 Mobilities ...... 185

B.3 Band-Gap Narrowing...... 186

Appendix C Thermal Oxidation 187

Appendix D Effective Diffusion Length Evaluation by Nonlinear Fit 189

References 191

Publications 219

List of Tables

2.1 Cost breakdown of Si photovoltaic modules. 6

2.2 Characteristics of common Si growth methods. 9

3.1 Overview on investigated substrate materials. 19

3.2 Overview on employed intermediate barrier layers. 21

3.3 Characteristic CVD Si film parameters. 24

3.4 Characteristics of different ZMR film growth methods. 30

5.1 Comparison of different definitions of effective diffusion length. 74

5.2 Dependence of effective diffusion length on dislocation density for a semiconductor of finite thickness and infinite surface recombination velocity at the back. 88

5.3 Limits of the functions Leff,D(ρd) and Leff,IQE(ρd) in the case ρd → 0 for a specimen of thickness W. 90

6.1 Wavelengths and corresponding absorption lengths of the laser diodes installed in the SR-LBIC system. 100

6.2 Estimation of effective surface recombination velocity at the p-p+ low- high junction. 101

6.3 Parameters measured at each detected object. 110

6.4 Example for definition of object classes. 111

7.1 Overview on investigated combinations of seed film thickness, capping type, and scan speed. 139

7.2 Parameters of the best thin-film solar cells fabricated on ceramic and SSP ribbon substrates. 154

7.3 Sensitivity of the fit parameters L0 and Γd on Leff,l. 156

7.4 Recombination strength data found in literature. 158

xvii xviii LIST OF TABLES

7.5 Technological parameters of analyzed samples together with measured values of dislocation density and effective diffusion length. 160

8.1 Dimensional and electrical parameters of the best thin-film solar cell fabricated with ZMR and Si-CVD technology. 173

8.2 First results of thin-film solar cell arrays fabricated from ZMR films on insulating substrates. 175

B.1 Coefficients at T = 300 K used in the mobility model. 185

B.2 Coefficients used in the band-gap narrowing model. 186

List of Figures

2.1 Principles of vertical and horizontal ribbon growth. 11

3.1 Schematic cross-sectional view of the investigated thin-film solar cell. 13

3.2 Process sequence for thin-film solar cell fabrication. 14

3.3 Linear thermal expansion coefficient of Si. 17

3.4 Different options for light trapping. 22

3.5 Principle of zone-melting recrystallization (ZMR). 25

3.6 Subgrain boundaries in a ZMR Si film and scheme of crystallization front morphology. 27

3.7 Schematic reactor setup of the ZMR 100 system. 32

3.8 Closed-loop control implemented in the ZMR 100 system. 34

3.9 Upper heater power and width of the molten zone for an automatically controlled ZMR process. 35

3.10 Thickness dependence of RTO on oxidation time and temperature. 37

3.11 Typical ZMR process including the growth of a RTO capping oxide. 39

4.1 Schematic device structure of the investigated thin-film solar cell. 48

4.2 Electron and hole carrier concentrations across the forward biased p-n junction in the dark. 49

4.3 Charge collection probability for a BSF solar cell. 58

4.4 Parametric plots for graphical evaluation of effective surface recombination velocity at a low-high junction. 60

4.5 Net photon flows in the investigated thin-film structure. 62

5.1 Groups of IQE−1 vs. α−1 curves which yield the same effective diffusion length. 67

5.2 Plot of inverse quantum efficiency versus absorption length for a typical c-Si thin-film solar cell. 69

xix xx LIST OF FIGURES

5.3 Charge collection probability function for a semi-infinite specimen and a specimen of finite thickness. 73

5.4 Schematic device structures used for the Donolato model. 77

5.5 Integrands ΛD and ΛIQE as a function of the variable t. 83

5.6 Dependence of effective diffusion length on dislocation density for the semi-infinite specimen. 84

5.7 Plots of IQE−1 vs. α−1 using Donolato’s model for the effect of dislocations. 85

5.8 Dependence of effective diffusion length on dislocation density for a specimen of finite thickness. 89

6.1 Maximum relative error made when determining Leff,IQE by a linear fit (α−1 = 5 µm, 6 µm, 7 µm, 8 µm, 9 µm, and 10 µm). 96

6.2 Maximum relative error made when determining Leff,IQE by a linear fit (α−1 = 7.7 µm, 10.8 µm, and 15.4 µm). 97

6.3. Schematic setup of the SR-LBIC system at Fraunhofer ISE. 99

6.4 Comparison of effective diffusion length maps obtained by linear fitting and by fitting with the exact function. 102

6.5 Schematic setup of the MFCA system at Fraunhofer ISE. 104

6.6 MFCA lifetime map of a sample with an unsuitable surface. 105

6.7 Typical surface of a ZMR Si seed film after epitaxial thickening. 105

6.8 Setup for automated etch pit density (EPD) mapping. 107

6.9 Illustration of object detection and classification. 108

6.10 Schematic object detection and analysis process. 109

6.11 Classification of objects based on measured parameters. 111

6.12 EPD map measured on an epitaxially thickened ZMR Si seed film. 112

6.13 EPD and grain boundary map measured on a small grained area of a standard mc-Si wafer. 113

6.14 EPD and grain boundary map measured on a typical EFG wafer. 115

LIST OF FIGURES xxi

6.15 Representative optical micrographs from an EFG wafer. 115

6.16 EPD and grain boundary map measured on a typical RGS wafer. 116

6.17 Representative optical micrograph from a RGS wafer. 117

6.18 Post-processing of etch pit density (EPD) data. 120

6.19 Filter kernel used for post-processing of EPD data. 121

7.1 Crystallization front morphologies observed in situ during ZMR processing. 126

7.2 Cross-sectional optical micrograph of an epitaxially thickened ZMR seed film. 128

7.3 Optical surface micrograph of an epitaxially thickened ZMR seed film. 128

7.4 Correlation between grain structure and texture measured by EBSD. 129

7.5 Beveled section of an epitaxially thickened ZMR seed film. 131

7.6 Details of the beveled section shown in Fig. 7.5. 132

7.7 Model for low angle grain boundary development by Baumgart and Phillipps. 133

7.8 TEM surface-sectional image of a subgrain boundary. 134

7.9 TEM cross-sectional image. 134

7.10 Optical surface micrographs of ZMR Si seed films grown with 150 nm RTO capping oxide. 136

7.11 Solar cell parameters of devices from ZMR seed films grown with different capping types. 138

7.12 In situ images of molten zone and crystallization front morphology during ZMR. 140

7.13 Typical grain structure of ZMR Si films using different combinations of film thickness and scan speed. 141

7.14 Comparison of EPD with minority carrier lifetime measured by MFCA.142

7.15 Dependence of EPD and minority carrier lifetime on ZMR scan speed. 143

7.16 Dependence of solar cell parameters on ZMR scan speed. 145

xxii LIST OF FIGURES

7.17 Dependence of saturation current densities J01 and J02 on ZMR scan speed. 146

7.18 Cracked Si film on a RBSN ceramic substrate. 147

7.19 Linear thermal expansion of different ceramic compositions. 148

7.20 Grinded surface and cross section of a ZrSiO4 substrate. 150

7.21 Agglomeration of liquid Si during ZMR processing due to a damaged intermediate layer. 150

7.22 Correlation between ZMR growth morphology and grain structure for a Si film on a SSP substrate. 151

7.23 Cross section of a ZMR seed film on a SSP substrate with a damaged intermediate barrier layer. 151

7.24 Molten zone with inhomogeneous width on SSP substrate. 153

7.25 EPD map with recombination strength values. 155

7.26 Correlation of EPD and effective diffusion length data. 155

7.27 EPD map and recombination strength values. 157

7.28 Dependence of effective diffusion length and open circuit voltage on dislocation density. 161

8.1 Comparison of open circuit voltage and conversion efficiency for solar cells with 80 Ω/sq and passivated 100 Ω/sq emitter. 168

8.2 Comparison of external quantum efficiency for solar cells with an 80 Ω/sq and a passivated 100 Ω/sq emitter. 169

8.3 Internal quantum efficiency and total reflectance for a thin-film solar cell with planar surface and for an equivalent device with textured surface. 170

8.4 Improvement of solar cell parameters due to bulk hydrogen passivation.171

8.5 Improvement of solar cell parameters through different process steps on a typical device. 172

1 Introduction Since 1999, solar cell production (measured in Mega-Watt peak output) has been growing on average by around 40% per year [1]. The price for photovoltaic (PV) modules exhibited a learning curve with a 20 % decrease with each doubling of production capacity [2]. Despite this very successful development, further cost reductions are needed for PV to be competitive with other electric energy sources, not only in off-grid but also in grid-connected systems. Today’s photovoltaic modules mainly incorporate crystalline silicon (c-Si) wafer based solar cells. During the last years, the percentage of c-Si based modules has been steadily increasing, and in 2005, these modules accounted for more than 93% of the annual production [1]. However, on the side of Si raw material the above-mentioned price decrease could not be realized. To the contrary, the price of Si feedstock has more than doubled during the last decade [3]. The current discrepancy between Si demand and supply led to a further price increase [4]. In the area of c-Si solar cell research and development, therefore the main goal is to reduce the costs of Si material per unit power output, i.e., costs per Watt peak. Three main directions are pursued: (i) saving of raw material, e.g., by using thinner wafers, thin films, or light concentrating optics, (ii) increase of solar cell conversion efficiency, and (iii) use of less pure and therefore cheaper Si raw material. So far, the most effective options have been (i) and (ii), partly in combination, while option (iii) has not yet yielded a breakthrough. Whereas the above options provide cost reduction potential for the near future, in parallel new materials and solar cell concepts are investigated. Examples are dye sensitized, organic, and so-called »third generation« solar cells. For general overviews on near future and long-term options see, e.g., Refs. [5–8]. So far, solar cell concepts with conversion efficiency below 10% could not carry through. Since many system costs are area related, costs savings on the solar cell side are often compensated if conversion efficiency is low. The objective of this work therefore is the development of a c-Si solar cell technology

1 2 INTRODUCTION with conversion efficiency similar to today’s industrially manufactured multi- 1 crystalline Si (mc-Si) solar cells, but with about /10 of the high purity Si consumption only. This thesis is structured as follows:

THESIS OUTLINE In Chapter 2, different concepts for thin-film solar cells are briefly reviewed, and the characteristics of the approach pursued in this work are discussed. The second part of this chapter is devoted to Si crystal growth methods. The zone- melting recrystallization (ZMR) technique employed in this work has much in common with sheet or ribbon growth methods. An overview on these Si growth methods is given and a classification is provided. Chapter 3 provides a summary on process steps and technologies used to fabricate the thin-film solar cells investigated in this work. Special emphasis is put on the ZMR technique. This step largely determines crystallographic film quality and therefore the performance of the finished solar cells. Development of an in situ process observation and an automated process control are important contributions to Si film optimization. Chapter 4 is devoted to the physics of solar cell devices. The basic equations governing carrier transport are reviewed and the ideal diode current-voltage characteristic is derived. The notation of charge collection probability is introduced. As an example, it is applied to the computation of effective recombination velocity at a low-high junction, implementing a so-called »back surface field«. Chapter 5 starts with a discussion on different definitions of effective diffusion length. The model by Donolato describing the effect of dislocations on effective diffusion length is reviewed, and it is modified and extended for the purpose of this work. This includes the description of thin devices with finite recombination velocity at the rear and the use of the »quantum efficiency effective diffusion length«. In Chapter 6, main characterization techniques are presented, which are employed in the subsequent investigations. Requirements for effective diffusion length evaluation from quantum efficiency data are discussed with regard to thin films. For spatially resolved measurement of dislocation density a new setup for

Thesis Outline 3 etch pit density (EPD) mapping is presented. The system is tested on different multicrystalline materials. Experimental results on Si thin-film optimization are presented in Chapter 7. On one hand, these investigations are directed to the understanding of the mechanism of defect generation. On the other hand, the effect of different external material and process parameters on film quality is studied. These investigations include capping type, Si film thickness, scan speed, and substrate material. The correlation between dislocation density and effective diffusion length is examined on a quantitative level, using the theoretical model and the measurement techniques developed in Chapters 5 and 6. The investigations discussed in Chapter 8 are based on a different approach. For a given Si thin-film quality, technology and solar cell process modifications are examined that are suitable to improve solar cell performance. These include light trapping through front surface texturization, use of a lowly doped passivated emitter, bulk hydrogen defect passivation, and antireflection coating. Improvement through each of these steps on solar cell performance is quantified. The chapter closes with an outlook on process transfer to industrial manufacturing methods.

2 Thin-Film Solar Cell Concepts and Silicon Growth Methods

This chapter is divided into two parts. The first part is devoted to alternatives to bulk Si wafer technology. After a short review of options currently under investigation, the concept of crystalline Si thin-film solar cells is introduced. It combines several features of standard Si wafer technology with thin-film approaches. For the concrete concept pursued in this work, Si film growth by zone-melting recrystallization (ZMR) is a key technology. This technology has much in common with standard methods for ingot and ribbon growth. Therefore, in the second part of this chapter, characteristics of different crystal growth methods are reviewed and a classification of the ZMR method is given.

2.1 SILICON RIBBON AND THIN-FILM SOLAR CELL TECHNOLOGIES The costs of Si wafers make up to about one-half of the total costs of a photovoltaic module. Since manufacturers usually do not publish their internal cost structures such data are mainly based on public studies. However, these studies also include input from wafer, cell, module, and equipment manufacturers. Table 2.1 summarizes the cost distributions based on two such studies and the data of one manufacturer. For the assumed scenarios calculated wafer costs are between 35 % and 55 % of total module costs. The above analysis has led to the search for alternatives to sliced wafers. In the 1980s, numerous technologies for ribbon or sheet materials were invented [9–11]. Compared to wire sawn wafers, only about half of the Si is needed, since kerf loss is omitted. However, defect density, inner stress, and surface flatness are still behind conventional wafer products. So far, only two of the ribbon technologies have been commercialized, Edge-defined Film-fed Growth (EFG) by SCHOTT Solar and String Ribbon by Evergreen Solar.

5 6 THIN-FILM SOLAR CELL CONCEPTS AND SILICON GROWTH METHODS

Table 2.1 Cost breakdown of Si photovoltaic modules due to diverse studies.

Cost breakdown Module Source Costs Wafer Cell Module Reference

Scenario [€/Wp] (crystal, wafering)

Siemens Solar Industries* 50 % 20 % 30 % [12]

(30 %, 20 %) MUSIC FM Project 0.91 55 % 12 % 33 % [13] mc-Si, screen printed contacts (31 %, 24 %) 500 MWp plant MUSIC FM Project 1.25 66 % 9 % 25 % [13] Cz-Si, screen printed contacts (49 %, 17 %) 500 MWp plant A. D. Little cost study 2.12 39 % 21 % 40 % [14] mc-Si, 10 MWp plant A. D. Little cost study 2.45 41 % 19 % 40 % [14] Cz-Si, 10 MWp plant * now SolarWorld Industries

At the same time, large efforts were taken to increase the efficiency of amorphous Si (a-Si) thin-film solar cells. As a general characteristic of thin-film solar cells, the absorber layer is reduced to a physically necessary minimum, while a substrate or superstrate provides for the mechanical support. However, conversion efficiency of a-Si solar cells could not cope with their crystalline ancestors, and therefore the technology could not meet the initial expectations concerning cost reduction. A review on a-Si thin-film solar cell technology is given in Ref. [15]. In the last years, new thin-film solar cell concepts have been developed that combine microcrystalline Si (µc-Si) with a-Si layers. These so-called »micro- morph« solar cells enable solar energy conversion of different spectral ranges within a single device. Overviews on these concepts are found in Refs. [16, 17]. Another thin-film solar cell route is based on chalkopyrides semiconductors such as cadmium telluride (CdTe) or copper indium (gallium) diselenide (CIS/CIGS). So far, these technologies are fabricated in relatively small quantities and in 2004, they did not contribute to more than 1.5 % of the worldwide solar cell production [18]. Major disadvantages, which are controversially dis-

2.1 Silicon Ribbon and Thin-Film Solar Cell Technologies 7 cussed, are the abundance of raw materials and the toxicity that necessitates a controlled recycling. A review on chalkopyride thin-film technologies is given in Ref. [19]. Other technologies are still a long way from commercialization or they are being developed for special applications. Examples are »third generation« concepts, solar cells with concentrating optics or GaAs solar cells.

2.1.1 Thin-Film Solar Cells from Crystalline Silicon In the last decade a number of new thin-film technologies based on crystalline Si have been developed. Although crystalline Si is an indirect semiconductor, the disadvantage of weak light absorption for long wavelength can largely be compensated by intelligent light trapping structures. It has been shown theoretically and experimentally that efficient c-Si solar cells can be realized with an absorber thickness being just 1% to 10% of today’s ∼270 µm thick bulk wafers [20–23]. Based on Si deposition temperature, c-Si thin-film solar cell concepts are often categorized into »low« and »high temperature approaches«. Another classification is based on the substrate type. In the following sections short intro- ductions to these concepts are given. Detailed overviews on c-Si thin-film solar cell technologies are provided by Shi and Green [24], Catchpole and McCann et al. [25, 26], and Bergmann and Werner [27, 28].

Low Temperature Concepts Usually, c-Si thin-film solar cell technologies classified as »low temperature concepts« allow for the use of (high temperature stable) glass as a substrate. These substrates are available at relatively low costs and are routinely fabricated in large areas. A major disadvantage of these concepts is a rather low Si deposition rate, since – in the kinetically controlled regime – this rate is proportional to the exponential of –T−1, where T is the deposition temperature. In addition, grain size of the deposited Si films is rather small. Grain enlargement is restricted to methods with low thermal budget such as laser recrystallization, electron beam recrystallization or solid phase crystallization (SPC). SPC requires annealing of

8 THIN-FILM SOLAR CELL CONCEPTS AND SILICON GROWTH METHODS the Si film for several hours at a temperature below the substrate’s melting point.

High Temperature Concepts The use of substrates, which are stable at high temperatures, allows for high deposition rates. For deposition temperatures around 1000°C, rates of several microns per minute can be achieved. Further, recrystallization processes may be applied for grain enlargement. These concepts therefore have the potential to reach much higher conversion efficiencies than low temperature concepts. Reviews on high temperature concepts are found in Refs. [29–31]. The thin-film solar cell concept investigated in this work follows the high temperature route.

Transfer Techniques These techniques combine elements of the low and high temperature concepts. For Si deposition a high-temperature stable substrate is employed. Usually a c-Si substrate is used and the crystal structure of this substrate is taken over by epitaxial growth, yielding very high crystal quality. For solar cell processing the Si layer is then transferred to a cheap glass or plastic substrate or superstrate. Due to the high crystal quality, conversion efficiencies demonstrated are close to values reached with bulk multicrystalline or monocrystalline Si solar cells. However, scaling of the transfer process to industrial manufacturing technologies is a major challenge [28]. A review on transfer processes is given in Ref. [32].

2.2 SILICON GROWTH METHODS Recrystallization by ZMR is a key process for the thin-film concept investigated in this work. Crystallographic quality of the thin film is largely determined by this process. In the following sections, a review is given on common Si growth methods employed for photovoltaics. Connections of the ZMR technique to sheet and ribbon growth methods are discussed. Table 2.2 gives an overview of the main Si growth methods currently used to grow Si wafers for photovoltaic applications. The properties listed focus on growth parameters and crystallographic quality. Discussions of other aspects, such as temperature gradient and impurity concentration, are found elsewhere (see, e.g., Refs. [33, 34]).

2.2 Silicon Growth Methods 9

Table 2.2 Characteristics of common growth methods used to fabricate Si wafers for photovoltaic applications.1

Method* Vert./ Pull Through- Energy Disloc. Grain Production Record horiz. speed put# use† density width efficiency efficiency‡ -2 mode [mm min−1] [m² h−1] [kWh m−2 [cm ] [mm] [%] [%] ]

FZ v 2–4 3.7–7.5 36 none ∞ 18 24.7 [37] [37, 38] [34] [37] [39] Cz v 0.6–1.2 1.7–3.5 21–48 none ∞ 16–17 24.5 [37, 38] [37, 38] [34] [40, 41] (MCz) [39] DS v 0.1–0.6 4.6–28 9–17 104–106 1–50 14–15 20.3 [34, 37, 38] [37, 38] [33, 34] [40] [42] EMC v 1.5–2.0 17–23 12 105–106 > 1 14–14.5 [37, 38, 43] [37, 38] [43] [43] EFG v 15–20 0.9–1.2 20 105–107 1–10 ∼14 18.2 [34] [37, 38] [33, 44] [35] [45] [46] String v 10–20 0.1–0.2 55 104–106 1–10 13.0–13.5 17.9 Ribbon [33] [37] [47] [35] [48] [46] Silicon- h 3100 39 n.a. 104–105 0.1–0.5 10 16.6 Film [49] [33] [35, 50] [50] [51] RGS h 1000–6000 12–75 n.a. 105–108 0.1–0.5 laboratory 12.8 [37, 38, 52] [53] [35] stage [54] ∗ FZ: Float Zone, Cz: Czochralski, DS: Directional Solidification, EMC: Electromagnetic Casting, EFG: Edge-defined Film-fed Growth, RGS: Ribbon Growth on Substrate # Calculated from pull speed with the following assumptions. FZ, Cz, DS, EMC: 0.5 mm thickness for wafer plus kerf loss; FZ: 125 mm wafer; Cz: 156 mm wafer; DS: 16 columns 156 × 156 mm2; EMC: 4 columns 156 × 156 mm; EFG: octagon, 125 mm face width; String Ribbon: two ribbon furnace, 100 mm width; Silicon-Film: 210 mm width; RGS: 156 mm width. † Only the energy for the growth itself is included. ‡ Cell size either 1 cm2 or 4 cm2.

The growth methods given in Table 2.2 can be divided into methods for ingot growth (FZ, Cz, DS) and for sheet or ribbon growth (EFG, String Ribbon, Silicon-Film™, RGS). Another major classification is into vertical and horizontal growth methods. Growth rate, grain size, and defect density are closely related to the employed method. The technological differences between the two modes are discussed in the subsequent section.

1 Pilot production of another ribbon material under development for several decades, Dendritic Web, was terminated by EBARA solar in 2003 [35]. With the bankruptcy of

10THIN-FILM SOLAR CELL CONCEPTS AND SILICON GROWTH METHODS

Still, growth rate alone does not determine throughput. As an example, the evolvement of the growth interface in a DS furnace by 0.5 mm will yield 16 wafers of 156 × 156 mm2 size, assuming a 68 × 68 cm2 crucible. For the same output two EFG octagons of 195 mm length and 125 mm face width would have to be grown. Therefore, as a rule of thumb, ribbon growth methods generally require a growth rate that is at least ten times faster than ingot growth in order to be competitive. Another important aspect when comparing ingot with ribbon/sheet growth methods is the number of furnaces needed to realize a certain capacity [33, 48]. For ribbon/sheet growth a large number of furnaces are required. Therefore, a simple design is necessary in order to avoid exorbitant investment costs.

2.2.1 Vertical versus Horizontal Ribbon Growth For vertical ribbon growth (Fig. 2.1a), as well as for ingot growth, the pulling direction is perpendicular to the growth interface. Consequently, pull and growth speed, i.e., the speed at which the crystallization interface evolves, are of the same magnitude. Vertically grown ribbons exhibit long and wide grains with sizes comparable to material grown by directional solidification. However, crystal quality is very sensitive to pull speed. If in ribbon techniques the growth rate exceeds several centimeters per minute very high dislocation densities are found, attributed to thermal stress [33]. For horizontal ribbon growth (Fig. 2.1b), pulling and growth direction are decoupled. Pull speed vp and growth speed vi are related by vi = vp cos θ, where θ denotes the angle between the substrate plane and the growth interface. If the temperature distribution is chosen to yield a very small angle θ, high growth rates can be achieved. To realize this condition, crystallization heat predominantly has to be transferred down into the supporting substrate and not into the already crystallized ribbon. Therefore, during horizontal growth new grains are continuously initiated by nucleation at the substrate’s surface, in contrast to vertical growth where the existing grains are enlarged by epitaxial growth. For horizontal growth, grain length is approximately identical to film thickness and

AstroPower and the selling of major assets to General Electric [36], also pilot production of Silicon Film™ has been stopped.

2.2 Silicon Growth Methods 11

vi = -vp

Ribbon

vi Melt v Meniscus θ Ribbon p Melt Substrate

(a) (b) Figure 2.1 Principles of (a) vertical and (b) horizontal ribbon growth (after Ref. [35]). vp denotes the pull speed, vi the interface or crystal growth speed. therefore anisotropic crystal growth cannot result in significant grain enlargement. The ZMR method investigated in this work (principle and technical details of this technique are discussed in Section 3.5) combines several advantages from both the vertical and the horizontal ribbon growth methods: • The use of a substrate enables the processing of thin Si films, while for nonsubstrate assisted techniques (such as EFG) a significant reduction in film thickness is difficult [35]. • The vertical growth mode results in grains with sizes comparable to mc-Si material grown by directional solidification. However, these advantages are also connected with some inherent limitations: • The substrate has to fulfill high requirements concerning mechanical, chemical, and thermal properties. • The coupling of pull speed and growth rate also connects pull speed and defect density. The testing of suitable substrates and investigations on the connection between ZMR pull speed and defect density therefore are important topics of this work.

12THIN-FILM SOLAR CELL CONCEPTS AND SILICON GROWTH METHODS

2.3 SUMMARY For today’s dominating solar cell technology, costs for c-Si wafers make up to about one-half of total module costs. One approach to decrease the costs per unit power output (Watt peak) is to decrease the contribution of Si material costs. Historically this approach has been addressed through the development of Si ribbons, which save the kerf loss of wire-sawn wafers, and through thin-film technologies, which use a supporting substrate or superstrate and reduce the thickness of the active layer to a necessary minimum. The solar cell concept investigated in this work has features of both technologies. On one hand, it belongs to the group of thin-film solar cells and mechanical support is by a substrate. On the other hand, the ZMR technology employed for Si film formation has much in common with ribbon or sheet growth methods. The common Si growth methods employed for photovoltaics can be divided into vertical and horizontal growth methods. They significantly differ regarding growth rate, grain size and defect density. Due to fundamental physical principles, optimum performance concerning all three criteria cannot be achieved at the same time. The ZMR technique belongs to the vertical growth method. The finding of suitable substrates and knowledge of the connection between scan speed and defect density are important requirements for the successful application of the ZMR technology. Therefore, investigations into these topics are important parts of this work.

3 Crystalline Silicon Thin-Film Solar Cell Technology

This chapter describes the thin-film solar cell structure investigated in this work. The following sections discuss the function, material requirements, and fabrication process of the individual components. Device fabrication can be divided into three main steps: (i) substrate production, (ii) Si thin-film formation, and (iii) solar cell processing. For the second step zone-melting recrystallization (ZMR) is a key technology. This process largely determines crystallographic and electronic quality of the Si thin-film. Therefore, ZMR optimization is a main topic of this work.

3.1 SOLAR CELL STRUCTURE AND FABRICATION PROCESS Figure 3.1 schematically sketches the thin-film solar cell structure fabricated for the investigations in this work. The active Si thin-film is supported by a 200 µm to 1000 µm thick ceramic or Si ribbon substrate. To prevent diffusion of impurities from the substrate into the active region, the substrate is covered with an intermediate barrier layer. This intermediate layer also serves a function as a back reflector. The totally 20 µm to 35 µm thick active Si thin-film consists of an n-type emitter region, and a p-type and p+-type base region. The change in doping concentration implements a so-called back surface field (BSF) and decreases recombination of minority charge carriers (see Sec. 4.4.2). A textured

Antireflection coating Base contact Emitter contact n Emitter Figure 3.1 Schematic cross- p Base (17–30 µm) p+ Base (3–10 µm) sectional view of the investigated thin-film solar cell device. For Intermediate barrier layer this test structure the base Substrate (200–1000 µm) metallization is located in a trench around the 10 × 10 mm2 active cell area. 13 14 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY

1. SUBSTRATE PROCESSING 3. SOLAR CELL PROCESSING

Substrate fabrication Alkaline surface texturing

Substrate conditioning (cleaning) Emitter diffusion, PSG removal

Intermediate barrier layer deposition Emitter passivation

Bulk hydrogen passivation 2. SI THIN-FILM FORMATION Emitter metallization Si film deposition Base metallization Capping oxide deposition Bulk hydrogen passivation Zone-melting recrystallization AR coating deposition Removal of capping oxide

Epitaxial seed film thickening optional step

Figure 3.2 Process sequence for thin-film solar cell fabrication. surface reduces reflection at the front surface and – in combination with the intermediate layer – implements a light trapping structure. Reflection losses at the front surface are further reduced by a double layer antireflection coating. For the test structures used in this work, the emitter is contacted in a standard way while the base metallization is formed in a trench around the active cell area.2 The fabrication steps for this device can be divided into three main groups (Fig. 3.2): (1) substrate processing, (2) Si thin-film formation, and (3) solar cell processing. The following sections focus on the individual components and process steps.

3.2 SUBSTRATE

3.2.1 Material Requirements The high-temperature concept pursued in this work enables high Si deposition rates, grain enlargement by recrystallization and low defect epitaxial growth.

2 More elaborate structures that are compatible with industrial manufacturing are discussed in Section 8.5.

3.2 Substrate 15

However, the necessary temperature stability restricts the choice of potential substrate materials. The following requirements have to be satisfied: Low Costs. The cost of the substrate plus the active Si thin-film must be sub- stantially lower than that of standard multicrystalline wafers; otherwise, the concept would not be cost effective. Cost calculations conclude that the upper limit for the costs of the substrate plus the costs for formation of the Si-layer is in the range of 50 € m−2 to 70 € m−2, assuming a conversion efficiency around 12 % [31]. For high volume production substrate costs of 20 € m-2 to 50 € m-2 have been projected [31, 55]3. If ceramics are chosen as substrate material, the ability to produce it by tape casting4 is a prerequisite since other forming techniques, such as hot pressing, are rather cost-intensive. Mechanical and Chemical Stability. A basic requirement on the substrate is its mechanical stability throughout all high-temperature processes. The mechanical requirements are determined by processes like screen printing and lamination [30]. As to chemical stability, the substrate material has to be inert to any interaction with liquid silicon during zone-melting recrystallization (ZMR). Diffusion of harmful impurities from the substrate into the active Si film is also not tolerable. In both cases, the use of an intermediate barrier layer may lower these requirements (Sec. 3.3). As a last point, the substrate has to withstand different chemicals used for solar cell processing. Replacing standard wet processing by dry processing can make this issue less critical [58]. Flatness and Thickness Uniformity. For ZMR to be successful substrate flatness is necessary to keep the focal line in a fixed plane. The maximum acceptable bow is in the range of 0.5 mm to 1.0 mm for a 150 × 150 mm2 wafer. Substrates with a bow exceeding this value would not only be problematic for ZMR but could not be processed with today’s standard solar cell manufacturing equipment. Thickness uniformity is important at various processes, and again especially for ZMR, where uniformity is a prerequisite for achieving homogeneous temperatures and therefore stable recrystallization.

3 Pursuing a similar concept AstroPower Inc. (now taken over by GE Energy) calculated with 9$ m-1 for substrate costs [56]. 4 For details on this technique see, e.g., Ref. [57], p. 41ff.

16 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY

Small Surface Roughness. Small surface roughness is necessary to ensure the formation of a closed film during Si deposition and recrystallization. As a rule of thumb, the maximum roughness should be less than one third of the seed film thickness (Ref. [59], p. 96). The requirement on small surface roughness also implies a low open porosity. Matched Thermal Expansion Coefficient (TEC). During Si deposition, the substrate is heated up to around 1200°C, and during recrystallization to even more than 1400°C locally. The substrate’s thermal expansion has to match that of Si in order to avoid the formation of cracks in the cooling phase after high- temperature processing. The change in length of a substance due to a temperature change is described by the coefficient of linear thermal expansion, which is defined by 1 dl α(T) = . (3.1) l dT

If the length at temperature T0 is l0, then the length at temperature T is given by

T  l(T) = l0 exp α(T )dT  . (3.2) ∫  T0 

For the case where α is independent of temperature, this equation reduces to

l(T ) = l0 exp[α 0 (T − T0 )]. (3.3) Expanding the exponential function and truncating the series after the second term leads to l = l [1+ α (T − T )], (3.4) 0 T0 ,T 0 where α is the mean thermal expansion coefficient commonly listed in litera- T0 ,T ture with the temperature range given by indices T0 and T [60]. Often the temperature dependent coefficient α(T) can well be approximated by a polynomial expression [61]

−2 α(T ) = a0 + a1T + a2T . (3.5)

Figure 3.3a shows the temperature dependent coefficient α(T) of Si. We note that the experimental data can be very well approximated by Eq. (3.5). The

3.2 Substrate 17

5.0 0.6

4.5 based on 0.5 [%]

-6 -1 0 α = 4.07 x 10 K 4.0 270,1600 K] l / l

-6 0.4 3.5 ∆ [10

α 0.3 3.0 0.2 TEC TEC 2.5 based on α (T) Eperimental data fit Polynomial fit α (T) 2.0 fit 0.1

1.5 length Change in 0.0 300 600 900 1200 1500 300 600 900 1200 1500 Temperature [K] Temperature [K] (a) (b) Figure 3.3 (a) Linear thermal expansion coefficient of Si in dependence of temperature and its approximation by a polynomial fit (Eq. (3.5)). The fit range is −6 −1 260 K to 1600 K and the fit parameters are a0 = 3.90 × 10 K , a1 = −10 −2 4.78 × 10 K , and a2 = 0.125 K. (b) Resulting relative change in length ∆l/l0 (solid line). For comparison, the change in length using the average coefficient α is given (dashed line). Experimental data from Ref. [62]. resulting change in length is displayed in Figure 3.3b. Further, the graph resulting from the exact relationship by Eq. (3.2) is compared to the graph obtained from Eq. (3.4) based on the average coefficient α . For the large temperature T0 ,T range of interest, a significant deviation between the exact function and its approximation is found. Another thermal property worth mentioning is the material’s thermoshock resistance, which must be compatible with the heat up and cool down ramps applied during the high-temperature processes.

3.2.2 Low-Cost and »Model« Substrates For this work, two different types of substrates were used. On one hand, Si ribbon and ceramic materials with low cost potential were tested. On the other hand, standard mono- and multicrystalline Si wafers were employed as »model« substrates for Si thin-film optimization.

Examined materials belonging to the first group were silicon nitride (Si3N4) ceramics, zirconium silicate (ZrSiO4) ceramics, silicon infiltrated silicon carbide

18 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY

(SiSiC) ceramics, and silicon sheets from powder (SSP) ribbons (Table 3.1). To a large extent, these investigations were carried out within the framework of several national and European research projects. Substrate materials investigated in other works include graphite [58, 63], aluminum oxide based ceramics (such as Al2O3 [64] or Mullite [65, 66]), and SiAlON [67, 68]. Silicon nitride ceramics were produced by two different methods: sintering of silicon nitride powder (sintered silicon nitride, SSN) and reaction bonding through nitridation (reaction bonded silicon nitride, RBSN). A benefit of SSN material is its higher material density compared to that of RBSN (see, e.g., Ref. [57], p. 215 ff). However, for the possible application as a thin-film solar cell substrate RBSN material is preferred since forming may be done by cost effective tape casting. Both silicon nitride materials are characterized by a thermal expansion coefficient slightly smaller than that of Si and a very good thermal shock resistance. SSN and warm pressed RBSN materials were produced by Ceramic for Industries (CFI), Rödental, Germany5. Tape cast RBSN ceramics were produced by the Energy research Centre of the Netherlands (ECN).

Zirconium silicate (ZrSiO4) occurs in the form of the natural mineral zircon and is mined as sands. This raw material is especially well suited to meet the cost goals. Due to their white color, the zirconium silicate substrates may act as a back reflector. Three different kinds of ZrSiO4 substrates were prepared for this investigation: (i) a composition made of fine grained ZrSiO4 powder

(d50 = 0.8 µm) and a methylphenyl silicone binder, (ii) one from the same powder but with the addition of 5% metallurgical Si, and (iii) one from a less fine- grained powder (d50 = 2.5 µm) and a PVC/glycerin binder. Samples from composition (ii) form a closed SiO2 surface coating during sintering due to the free Si. All samples were formed by uniaxial pressing, but type (iii) is also compatible with tape casting. All ZrSiO4 substrates were prepared by the Fraunhofer Institute for Ceramic Technologies and Sintered Materials IKTS, Dresden, Germany. Silicon carbide (SiC) is one of the most important nonoxide ceramics. It is characterized by a high-temperature stability and good thermal conductivity. Filling the pores of the ceramic matrix with liquid Si yields a very dense mate-

5 Now H.C. Stark Ceramics.

3.2 Substrate 19

Table 3.1 Overview on investigated substrate materials with low-cost potential.

Material Fabrication by Variations

Silicon nitride Sintering (SSN) Si/SiN ratio (Si3N4) ceramics Warm pressing and (in case of RBSN), reaction bonding (RBSN) different additives Tape casting and reaction bonding (RBSN) Zirconium silicate Uniaxially pressing and Compositions from pure (ZrSiO4) ceramics sintering in air ZrSiO4 and from ZrSiO4 plus Si, different binders Silicon infiltrated silicon Reaction bonding carbide (SiSiC) ceramics Silicon sheets from Ribbon growth Different growth ambients powder (SSP) ribbons rial without open pores, referred to as SiSiC. Basic information on these ceramics can be found, e.g., in Ref. [57], p. 210ff. The investigated SiSiC samples were fabricated by H.C. Stark Ceramics (Selb, Germany)6. While SiSiC ceramics are usually manufactured by hot pressing, an alternative more economic process has been developed for PV purposes [69]. This process relies on tape casting and reaction bonding. However, in contrast to SiSiC, this material contains open pores. The Silicon Sheets from Powder (SSP) ribbon growth process was developed by Fraunhofer ISE and Siemens AG [70, 71]. Originally, it featured a surface melting as well as a zone-melting step. Later the process was modified to yield substrates for thin-film solar cells, employing surface melting only [72]. Techni- cal details of the current setup are found in Ref. [73]. Improvements concerning flatness were recently made by changing the growth ambient [74]. This modified process yields a carbon and oxygen containing surface layer. Substrates made of SSP ribbons had a thickness around 600 µm and were used without any mechanical or chemical leveling of the surface. All ceramic and SSP ribbon substrates mentioned above have been especially developed for use in crystalline Si thin-film solar cells. Substrate compositions

6 Former Technical Ceramic (TeCe).

20 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY and fabrication methods are still being investigated, and they could therefore not be fabricated with the same reproducibility as that of routinely manufactured products. In addition, the available quantity of such substrates was not sufficient for Si thin-film optimization. For this reason, oxidized standard Cz-Si and mc-Si were used as »model« substrates for ZMR and solar cell optimization. Mainly 650–700 µm thick Cz-Si semiconductor industry monitor wafers were used for this purpose. In addition, wire-sawn and damaged etched mc-Si wafer were employed, with a thickness of either 300–350 µm or 700–800 µm.

3.3 INTERMEDIATE LAYER Low costs and chemical purity of the substrate material cannot usually be achieved simultaneously. Especially harmful are metals, which are present in free form, while those bound in the form of oxides are less detrimental [75]. However, the required purity cannot normally be achieved without an intermediate barrier layer.

Silicon oxide (SiO2) and silicon nitride (SiNx) layers deposited by plasma enhanced chemical vapor deposition (PECVD) or spin on coating (SOC) have proven to be effective diffusion barriers [76–78]. For the case of PECVD layers it has been shown that SiNx is a more effective barrier than SiO2 [77]. All ceramic substrates used in this work were generally coated with a stack of

1 µm SiO2, 0.1 µm SiNx, and 1 µm SiO2. The combination oxide/nitride/oxide is also referred to as an ONO stack. These layers were deposited by PECVD at

350°C from SiH4 and N2O precursors. Before intermediate layer deposition the substrates were wet chemically cleaned in HCl and subsequently annealed at around 1200°C for at least 15 min. Optionally, a second cleaning step in HNO3 was applied after annealing. On the mc-Si and Cz-Si wafer model substrates, an intermediate layer is not necessary for barrier purposes. Here the intermediate layer assures the same lateral Si film growth as on coated ceramic substrates. Furthermore, it provides electrical separation of the active Si thin-film from the substrate. On multicrystalline Si wafers and SSP substrates the intermediate layer consisted of 2 µm

SiO2 deposited by PECVD. On monocrystalline wafers, 1 µm of SiO2 was grown by thermal oxidation.

3.3 Intermediate Layer 21

Table 3.2 Overview on employed intermediate barrier layers.

Substrate Intermediate barrier layer Deposition technique

Ceramic ONO stack PECVD (1 µm SiO2, 0.1 µm SiNx, 1 µm SiO2)

SSP ribbon In situ coating or 2 µm SiO2 Thermal growth or PECVD

mc-Si wafers 2 µm SiO2 PECVD

Cz-Si wafers 1 µm SiO2 Thermal oxidation

An overview of the employed intermediate barrier layers is given in Table 3.2. Besides the barrier properties, an intermediate layer can serve two other purposes: Firstly, it may be a functional part of an advanced contacting scheme such as an integrated series interconnection. Secondly, the intermediate layer can act as a back reflector and be part of a light trapping structure.

3.3.1 Light Trapping Since crystalline Si is an indirect semiconductor, light trapping is a key feature in high efficiency thin-film solar cells. Without light path enhancement, it is not possible to profit from the advantages of thin cells compared to thick cells, i.e., the potential for a high open circuit voltage with reduced requirements regarding material quality. Indeed, companies with low-temperature c-Si thin- film solar cell concepts close to commercialization, such as Kaneka [79] and CSG Solar7 [23, 80], have been putting a lot of emphasis on light trapping technology. Using an analytical approach, Goetzberger demonstrated that the combination of a planar surface with an ideal diffuse reflector (Fig. 3.4a) provides a very effective light trapping structure [20]. The key of this concept is the Lambertian reflector – defined as a reflector with uniform radiance (brightness) in all directions, regardless of the angle of incidence. Using such a reflector, only a small fraction of scattered rays can escape at the front surface while all rays with an angle θ greater than the critical angle θc experience total reflection. In the wavelength region between 800 nm and 1200 nm, the critical angle θc is in the

7 Former Pacific Solar Ltd.

22 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY

θc Si Si θc Si Si IL IL IL IL

(a) (b) (c) (d) Figure 3.4 Different options for light trapping. The change in refraction at the interface of Si and the intermediate layer (IL) results in total reflection for rays

with an angle greater than θc. (a) Diffuse back reflector. (b) Structured front and planar back side. (c) Front and back side both structured. (Note: in reality this is a three dimensional pyramidal structure). (d) Structured surface and diffuse back side. range from 15.7° to 16.5° for Si and air, and in the range from 23.4° to 24.5° for 8 Si and SiO2. Yablonovitch and Cody have calculated a maximum light path 2 enhancement of 4 n21 for such a randomizing structure, where n21 is the ratio of the refractive index of Si to the one of the adjacent material [21, 82]. For Si and air the enhancement factor has a value of around 50. Numerical simulations show that even with more elaborate structures it is difficult to exceed the performance of the ideal diffuse reflector described above [83, 84]. However, in practice, this ideal Lambertian behavior cannot fully be achieved [85] and more realistic simulations of diffuse reflection use the Phong model [84, 86]. The numerical investigations cited above show that for practical realization the most efficient structures are one with pyramids on both sides (Fig. 3.4c) or one with a pyramidal structured surface in combination with a diffuse back reflector (Fig. 3.4d). Slightly less efficient is a combination of pyramidal structured front side and planar back reflector (Fig. 3.4b). The structure used in this work corresponds to Figure 3.4b for the case of Cz- Si model substrates. Damage etched mc-Si wafers and ceramic substrates provide some roughness, and the structure corresponds to an intermediate state between Figure 3.4b and Figure 3.4d. Since ZMR yields grains that are preferentially 〈100〉 oriented (see Sec. 3.5.2), texturing of the Si surface is easily possible by anisotropic etching. Often the 〈100〉 direction is slightly tilted relative to

8 Calculated from the data given in Ref. [81].

3.4 Silicon Chemical Vapor Deposition (CVD) 23 the surface normal. If the tilting angle is not too high, this geometry should improve light trapping efficiency [87].

3.4 SILICON CHEMICAL VAPOR DEPOSITION (CVD) Si thin-film formation, as employed in this work, involves two Si deposition steps (Fig. 3.2). The first deposition is on an amorphous specimen and yields a microcrystalline structure. After zone-melting recrystallization (ZMR), this film acts as a seed for further epitaxial growth. For both, seed film deposition and epitaxial thickening, the technique of atmospheric pressure chemical vapor deposition (APCVD) was applied. A trichlorosilane (SiHCl3, TCS) precursor was used as the Si source, and p-type doping was achieved by adding diborane

(B2H6) gas. For general information on (AP)CVD see, e.g., Refs. [88, 89]. Depositions were carried out in two different systems: (i) a commercial barrel type reactor at the Institut für Mikroelektronik Stuttgart (IMS Chips), and (ii) a laboratory type tube reactor at Fraunhofer ISE. The reactor at IMS Chips is a commercial barrel system, which fulfills the high requirements of microelectronics regarding thickness and doping uniformity. Depositions on Cz-Si wafers, used for ZMR optimization, were carried out in this system. In addition, this system was used for depositions on SSP ribbon substrates. The reactor developed at Fraunhofer ISE was especially designed for the needs of photovoltaics. In CVD reactors developed for microelectronics the stringent quality requirements are bought at the cost of relatively low chemical yield, but this parameter is crucial for a cost effective application in photovoltaics. The Fraunhofer ISE system therefore was constructed for high deposition rates and high chemical yield [90]. Rates > 5 µm min−1 and a chemical yield > 30 %, which – for the Cl/H ratio used – is close to the thermodynamic limit in equilibrium conditions, have been demonstrated [91]. However, thickness uniformity in the current setup is not satisfactory yet, and it has stimulated the development of a system where the substrate moves during deposition [92]. All depositions on ceramic substrates and partly on mc-Si wafers were performed in the Fraunhofer ISE system.

24 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY

Table 3.3 Characteristic CVD Si film parameters.

Process Description Method Temp. Thickness Doping conc. [°C] [µm] [cm−3]

Seed film S-I APCVD ~950 5−10* (3 ± 1) × 1018 FhG ISE Seed film 2 µm LPCVD n.a. 0.5 ± 0.05 undoped S-IIa IMS Chips plus APCVD 1100 1.5 ± 0.5 (1 ± 0.3) × 1019 Seed film 8 µm LPCVD n.a. 0.5 ± 0.05 undoped S-IIb IMS Chips plus APCVD 1100 7.5 ± 1 (1 ± 0.3) × 1019 Epitaxial layer E-I APCVD ~1170 20−30 (4 ± 2) × 1016 FhG ISE Epitaxial layer E-II APCVD 1100 (8 ± 1) × 1016 IMS Chips 30 ± 3

* on ceramics 5–15 µm

Table 3.3 summarizes the main technological parameters of the employed CVD Si films. For thin films prepared at Fraunhofer ISE, film thickness was determined by weighting the samples before and after Si deposition. Doping concentrations were measured by spreading resistance profiling (SRP). For films prepared at IMS Chips, Table 3.3 reproduces the institute’s specifications. Seed films prepared at IMS Chips consisted of two layers. Firstly, 0.5 µm of undoped poly-Si was deposited by LPCVD, then the film was thickened by 1.5 µm or 7.5 µm by APCVD, yielding a totally 2 µm or 8 µm thick film. The two-step process was chosen to assure growth of a closed layer even for the 2 µm thin films. Before thickening the recrystallized Si seed film, the surface was conditioned by removal of a thin Si layer. For epitaxial depositions at Fraunhofer ISE this was done by a CP1339 etch. For depositions at IMS Chips the seed film was first treated by the RCA cleaning process10. Then in situ etching was performed in the CVD reactor at 1180°C before deposition, removing ~0.3 µm of Si.

9 Polishing solution of HF (50%), CH3COOH and HNO3 in the ratio 1:3:3 [93]. 10 Cleaning procedure developed by RCA Corp. It basically consists of a organic removal in a 5:1:1 H2O:H2O2:NH4OH solution, oxide strip in a diluted 50:1 H2O:HF solution, and removal of ionic and heavy metal atomic contaminants in a solution of 6:1:1 H2O:H2O2:HCl [94].

3.5 Zone-Melting Recrystallization 25

3.5 ZONE-MELTING RECRYSTALLIZATION

3.5.1 Introduction Typically, the crystallite or »grain« size of Si films deposited on foreign substrates by high-temperature CVD is in the micron range. So far, using conventional solar cell processes with p-n structure, the maximum conversion efficiency obtained on such thin films has been below 6 % [66, 95, 96]. Through solid or liquid phase recrystallization, grain size can be increased by several orders of magnitude, allowing much higher solar cell conversion efficiencies to be reached. In this work zone-melting recrystallization (ZMR) is employed for grain enlargement. The principle of this technique is shown in Figure 3.5, where halogen lamps are used as heat sources. Common to all ZMR methods is the creation of a small molten zone that is scanned across the thin film. As the molten zone moves, at the initial starting point the melt cools below the melting point and heterogeneous nucleation starts. Stable crystallites develop and act as seeds for further growth. Due to the anisotropic crystal growth speed (see, e.g., Ref. [97]) grains with a particular crystal direction soon prevail. This kind of geometric selection is well known from the Bridgman technique [98], one of the preferred methods for multicrystalline ingot growth in photovoltaics [53]. Grains grown by ZMR reach up to several millimeters in width and several centimeters in length. Referring to the classification given in Section 2.2.1, the ZMR technique belongs to the vertical growth methods.

Linear lamp Elliptical reflector

Molten zone

µc mc Si film Substrate Scan Sample support Figure 3.5 Principle of zone- melting recrystallization (ZMR) using linear halogen lamp heaters. Lower heater

26 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY

A pioneer of ZMR was Leitz who, in 1950, patented a technique for growing single-crystal films of luminescent materials [99]. In the 1960s, ZMR was investigated for the growth of low-melting point semiconductors such as Ge or InSb [100]. At this time initial experiments with Si failed, but interest in ZMR was renewed in the 1980s when technologies were investigated for the production of silicon on insulator (SOI) films. Such films were desirable for high-speed integrated CMOS11 circuits realized with small structures, little capacitance, and the avoidance of parasitic transistors, as well as for high-power devices built up on insulators. A comprehensive review on activities and results during this period is given by Givargizov [101]. An overview with focus on modeling is provided by Miaoulis et al. [102]. For use in SOI technology, ZMR wafers could not carry through in the face of other technologies such as SIMOX (separation by implantation of oxygen) or wafer bonding. However, several research groups examined the ZMR technique for an application in photovoltaics. Especially worth mentioning in this field is the work of a group at Mitsubishi Electric Corp. [103]. Following the high-temperature route using strip and lamp heater ZMR, this group reported remarkable conversion efficiencies of 16.45% for a 1 × 1 cm2 [104], and of 16% for a 10 × 10 cm2 thin-film solar cell [105]. AstroPower Inc. pursued a thin-film solar cell concept similar to the one investigated in this work. It also involved an APCVD and a ZMR step [106]. In the last decade, progress in ZMR technology has mainly been made in two fields: (i) process control and (ii) numerical modeling. Both were enabled by the advances of computer technology and resulted in new equipment designs. Ref- erences regarding these developments are given in Section 3.5.2 and 3.5.3, respectively.

3.5.2 Interface Morphology, Subgrain Boundaries, and Texture When ZMR grown thin films are preferentially etched (e.g., with a Secco12 solution) they typically exhibit a defect structure as shown in Figure 3.6a. The defects visible as dark lines are low angle grain boundaries. They run nearly

11 Complementary metal oxide semiconductors. 12 Mixture of HF (48%) and K2Cr2O7 (0.15 molar solution) in the ratio 2:1 [107].

3.5 Zone-Melting Recrystallization 27

Supercooled region

solid

Scan Wsc liquid λsgb 〈100〉 Subgrain boundaries {111} -Planes

AB (a) (b)

Figure 3.6 (a) Subgrain boundaries in a ZMR Si film revealed by etching and optical microscopy [111]. (b) Scheme of crystallization front morphology and subgrain boundary formation. For faceted, cellular growth there is a direct

relationship between subgrain boundary spacing λsgb and the depth of the supercooled region Wsc. parallel to the scan direction and most of the time they are regularly spaced. Other typical features are the development of new boundaries and the coales- cence in a Y-shape connection. Since these boundaries are found within a single grain, they are called subgrain boundaries (SGB), or for short subboundaries. Their origin has been the subject of various experimental and theoretical studies [108–114]. A historical overview with detailed discussion on the different models is given in the above-mentioned book of Givargizov (Ref. [101] p. 168ff). Important progress in the understanding of subgrain boundary formation was made with the analysis of crystallization front morphology. First hints were obtained by quenching experiments [109, 112]. The structure resulting from very rapid cooling was interpreted as an instant image of the crystallization front. Not a planar, but faceted morphology was found, as sketched in Figure 3.6b. Further knowledge was gained from in situ observations using CCD cameras. These techniques were first developed for laser [115, 116] and electron beam ZMR [117]. Later they were also implemented for strip [113] and lamp heater sources [118]. Unlike the quenching results, in situ observations additionally yielded information on temporal development and stability of the crystallization front. In situ observation is also the base for advanced process control, as discussed in Section 3.5.3.

28 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY

Today, it is generally agreed upon that subgrain boundary formation and the particular crystallization front morphology are caused by an instability of the solid-liquid interface due to supercooling. Leamy et al. [119] and Lemons et al. [120] attributed subgrain boundary formation to constitutional supercooling, i.e., supercooling due to segregation of impurities ahead of the crystallization front. This mechanism is well known to be responsible for microcellular morphologies in other growth techniques, such as the Czochralski method [121, 122]. However, nonplanar morphologies have also been observed for stationary heating where constitutional supercooling is not present. By careful microscopic in situ observations, Im and co-workers verified the development of nonplanar solidification front morphologies for stationary strip heater ZMR [113]. Im et al. attributed the observed morphologies to a »radiative« supercooling. In this model, supercooling is explained by the difference in reflectivity between solid and liquid phase. The reflactance of liquid Si [Rl(0.6 µm) = 0.7] is much higher 13 than that of solid Si [Rs(0.6 µm) = 0.3] . Therefore, in the liquid state it absorbs less radiation than in the solid state. The effect is a supercooling of the liquid Si and a superheating of the solid Si near the solid-liquid interface. Such phenomena had been described before for laser melting experiments. Bösch and Lemons [125] reported the coexistence of solid and liquid Si in a lamella structure, a phenomena subsequently theoretically analyzed by Jackson and Kurtze [126]. Grigoropoulos et al. extended the stability analysis from the stationary case to that of a moving (laser) heat source [127]. Although constitutional and radiative supercooling are caused by different processes, both lead to the same effect and result in a fundamental relationship between the temperature gradient at the solid-liquid interface and the depth of the supercooled region. This connection is explained with reference to Figure 3.6b. Assuming an initially planar solid-liquid interface, this interface is located at line A. The supercooled region extends up to line B with a depth Wsc. This

13 Reflactance values for liquid Si calculated from refractive index and extinction coefficient at λ = 0.6 µm given in Ref. [123]. For solid Si and wavelengths ≥ 0.6 µm the extinction coefficient is negligible [81]. A more detailed analysis additionally has to take into account the corresponding emissivity values. They differ from the former ones since temperatures of Si film and lamp filament are not the same [124].

3.5 Zone-Melting Recrystallization 29 configuration is highly unstable. Small perturbations can cause the development of protrusions that extend up to the front given by line B. This way, the solid-liquid interface may self-adjust into a form that is more stable. For the cellular structure shown in Figure 3.6b, within the supercooled region, close to the solidification front (line A) most of the Si, on average, is solid while at the opposite site (line B) most of the Si is liquid. The experimentally observed maximum distance between tips and inner corners of the growth cells is a measure for the depth of the supercooled region Wsc. The question of interface morphology and stability has been addressed in several theoretical studies. Computations conducted in the 1980s [126–128] were based on the pioneering works of Mullins and Sekerka on morphological instability [129]. The idea of their linear stability analysis is to apply a sinusoidal perturbation – in the case of ZMR perpendicular to the scan direction – and then investigate the reaction of the system. This way, sets of material and process parameters can be identified that yield either stable or unstable growth. Advances in computer technology have enabled the simulation of the growth of microcellular structures in two or three dimensions. Using phase-field models, the evolvement of a patterned solidification front could successfully be simulated [130, 131]. While results qualitatively match well with experimental observations, further improvements are necessary to quantitatively correlate input parameters with experimental process conditions [130]. In both cases, constitutional or radiative supercooling, the depth of the supercooled region depends on the temperature gradient at the solid-liquid interface. The smaller the gradient, the deeper the supercooled region. With an increase in temperature, a transition of interface morphology has been observed from dendritic, to cellular14, to planar [113, 132]. For the faceted cellular interface as shown in Figure 3.6b, there is a direct relation between subgrain boundary spacing λsgb and depth of the supercooled region Wsc. This configuration yields the lowest defect density, which is confirmed by experimental results [102, 132, 133]. Films grown with a dendritic or planar interface are much more defective.

14 The nomenclature for this growth morphology is not consistent. Some authors distinguish between cellular and faceted growth (e.g., see Ref. [118]). Here we follow the naming in Ref. [101], where cellular is the main category, divided into the sub-categories of rounded and faceted cellular growth.

30 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY

Table 3.4 Characteristics of different ZMR film growth methods.

Heat source: Electron beam Laser Graphite stripe Incoherent lamp

Temp. gradient High High Low Low Grain size µm–mm µm–mm mm–cm mm–cm Defect density High High Medium Medium Substrate requirements Medium Medium High High Film contamination Oxygen Oxygen Carbon, Oxygen oxygen Investment costs Very high High Low Low

The last fact seems to contradict the results of stability analysis. However, it may be that the observed »planar« interface on a microscopic scale is still associated with a supercooled region and that the »real« planar interface can never be reached with common heat sources due to the high thermal conductivity of the Si film. The choice of heat source significantly affects the temperature gradient and therefore the film quality (Table 3.4). Strip or lamp heater sources produce much lower temperature gradients than laser or electron beam heat sources. This explains why lamp or strip heater ZMR produces better crystallographic quality than laser or electron beam ZMR [134]. Another aspect discussed in Table 3.4 is common impurities. During ZMR processing the Si film is typically confined between two SiO2 layers: (i) an insolating SiO2 intermediate layer and (ii) a SiO2 or SiO2/SiN capping layer to prevent agglomeration of molten Si (»balling-up effect«, see Sec. 3.5.4). There- fore, oxygen concentrations up to the solubility limit are found in recrystallized films [110, 135]. For strip heater ZMR an additional source of contamination is the graphite stripe. It has been made responsible for high carbon concentrations [108].

Texture As discussed before, the most stable ZMR growth and the lowest defect density is observed for cellular interface morphologies. In the case of faceted cells (as shown in Fig. 3.6b), the interface is composed of {111} planes, which for Si are the slowest growing faces. Both, scan direction and surface normal are then

3.5 Zone-Melting Recrystallization 31 in a 〈100〉 direction. The phenomenon of preferred orientation of the crystallites in a polycrystalline solid is referred to as texture. Experimental investigations showed that the percentage of 〈100〉 oriented grains depends on Si film thickness and scan speed [109]. It was determined that the critical thickness below which the 〈100〉 orientation dominates ranges between 2 µm and 5 µm [115, 136]. Biegelsen et al. have explained the preferential orientation based on the anisotropic interfacial free energy between crystalline Si and SiO2 [137]. They argue that at the initial stage of the crystallization process, where solid and liquid phase co-exist, those crystallites with minimum interfacial free energy prevail. According to their model, for the

Si–SiO2 interface these are the {100} planes, while there is no significant orientation dependence of interfacial free energy for the Sisolid–Siliquid interface. The 〈100〉 texture is especially useful for the implementation of a light-trapping structure since it allows an easy to apply surface texturization by anisotropic etching (see Sec. 3.6).

3.5.3 ZMR 100 System

Mechanical Setup The zone-melting recrystallization system used in this work was developed at Fraunhofer ISE in the framework of the author’s diploma thesis [138]. Since then the ZMR 100 system has continuously been improved. Figure 3.7 schematically shows the reactor setup. This reactor is mounted in a closed housing, which additionally contains the drive, the electric power supply, the control units for motor and lamps, and the gas supply system (not shown in Fig. 3.7). The ZMR 100 reactor is heated by linear tungsten halogen lamps. Generally, in strip and lamp heater ZMR the sample has to be preheated in order to reach the melting point of Si (Tm = 1414°C [139]). Preheating is also advantageous from the requirement of low temperature gradients. The ZMR 100 lower heater consists of an array of 15 linear tungsten halogen lamps with 4.5 kW power at 380 V each. It produces a heated area of approximately 24 × 28 cm2. The upper heater is made up of an elliptical reflector with a single linear tungsten halogen lamp positioned in the first focal line. The employed 2 kW lamp has a small coil diameter (1.5 mm) and can be adjusted by micrometer screws.

32 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY

Lamp house with elliptical reflector CCD camera Focused lamp Sample on quartz plate

Quartz tube (stationary)

Lamp array Ar, O2 Movable furnace 5–500 mm/min Figure 3.7 Schematic reactor setup of the ZMR 100 system.

The second focal line is positioned to lie within the Si film plane. All walls of the reactor are water-cooled and the inner sides are covered with a special highly reflective silver-coated foil. The reactor chamber is made of a rectangular quartz tube with the sample placed on a solid quartz plate15. During the recrystallization process, tube and sample stay fixed while the complete reactor moves. The simultaneous movement of upper and lower heater results in a steady temperature field at the location of the molten zone. Sufficient temperature homogeneity can be realized with less effort than in setups with movable upper heater and fixed lower heater (e.g., see Ref. [141]). Movement is by means of a spindle drive and a gear-less motor. Except for loading and unloading, the ends of the tube are closed by doors (not shown in Fig. 3.7). Integrated gas inlets and outlets allow a controlled atmosphere during processing, with Ar, O2, and N2 as available gases.

Process Control Above, the connection between temperature gradient, growth morphology, and defect density has been discussed in detail. Consequently, the precise control of the temperature gradient at the crystallization front is of immense importance for growth of high quality ZMR thin films.

15 This system is very flexible regarding sample size. However, it requires a complete contact to ensure homogeneous temperature. This may be prevented by an alternative support using quartz pins as common in rapid thermal processing (RTP) equipment [140].

3.5 Zone-Melting Recrystallization 33

Unfortunately, the value of the temperature gradient cannot easily be determined by direct measurements. However, the good visibility of molten Si, due to the change in reflectivity, can be utilized for an indirect measurement. The width of the molten zone is connected to the thermal gradient at the crystallization front as demonstrated by Robinson and Miaoulis using numerical modeling [124]. For a fixed preheating temperature, the smaller the molten zone, the lower the thermal gradient. This result is consistent with experimental observations of the crystallization front morphology [132, 142]. Therefore, image analysis can be used to detect the width of the molten zone and to implement a ZMR process control. Wong and Miaoulis were the first to report such a control for the recrystallization of Ga films [143]. Ga has the advantage of melting at a low temperature (29.8°C [144]), enabling a comparatively simple experimental setup. Their system implemented two control parameters: (i) crystallization front position and (ii) crystallization front pattern. The second task was implemented by performing a fast Fourier transform at a line scan across the patterned interface. A successful control of the crystallization front position was demonstrated. However, the system suffered from unstable lightning conditions, and the interface location oscillated 0.2 mm around the target value of 1.2 mm (±17% relative) due to a relatively long sampling time of 3 seconds. Kawama and co-workers at Mitsubishi Electric Corp. implemented a process control for ZMR of Si films, employing a CCD camera with a subsequent commercial width analyzer [145]. Their experiments confirmed that the width of the molten zone is a practical parameter to use for the control of crystallization front morphology. For a target value of 1.6 mm the authors were able to keep the width of the molten zone constant within 0.1 mm (±6% relative). Generally, they claim to achieve an accuracy of ±10% [141]. An advanced ZMR process control for the ZMR 100 system has been developed originally by the author [138]. The system is based on in situ observations of the molten zone and image analysis. Image acquisition is done by two minia- ture CCD cameras, providing an overview as well as a microscopic detail image. Both cameras are installed in the upper lamp house (only one of them shown in Fig. 3.7) and are protected by metal coated filters with very low transmission (∼0.01%).

34 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY

CCD camera

Focused lamp

Molten zone Image processing

Sample

x Guard wafer PID controller 50 Thyristors m m

Figure 3.8 Closed-loop control implemented in the ZMR 100 system.

For process control a special software application named ZMRPRO has been developed. This application analyzes the width of the molten zone and controls the power of the focused lamp upper heater by a closed-loop feedback (Fig. 3.8). The ZMRPRO software runs on a standard Microsoft Windows PC and features real time display and analysis of the images from the CCD camera, a software PID controller, and interfaces for the heaters and the drive. It manages process recipes and logs all relevant data into an ODBC compatible database. The sampling rate in the ZMRPRO software is variable and self-adjusts for optimum performance. On a state of the art computer with no limit by processor performance or other computation intensive tasks, the sampling rate is equal to the camera’s frame rate of 24 images per second. The PID controller has been tuned with the closed-loop (ultimate gain) and the open-loop (step test) proce- dures developed by Ziegler and Nichols [146–148]. While the closed-loop method is more accurate, it cancels out for high scan speed. For standard substrates the automatic control is able to keep the width of the molten zone within a range of ±5% from the desired value. Successful ZMR process control has been demonstrated even for scan speeds exceeding 300 mm min−1. At such speed, manual control would cancel out. Figure 3.9 shows data recorded during an automatically controlled ZMR process of a 50 mm long sample. The actual width of the molten zone only deviates slightly from the desired value of 1.0 mm. Noticeably, the upper heater power is

3.5 Zone-Melting Recrystallization 35

3.5

65 3.0

2.5

60 2.0

1.5

55 1.0 Molten zone width [mm] Upper heater power [a.u.] 0.5

0 1020304050 Molten zone position [mm] Figure 3.9 Upper heater power (focused lamp) and width of the molten zone as a function of the zone position for an automatically controlled ZMR process. The thick gray line indicates the desired value, the lower thin line the actual width. The PID controller adjusts the lamp power (upper thin line) to minimize the difference between desired and actual width. significantly lower in the center than at the start (x = 0 mm)16 and the end position (x = 50 mm). This finding can be explained by an effect well known from rapid thermal processing (RTP): Wafers homogeneously irradiated from top or bottom are colder at the edges than at the center due to radiation losses at the unheated sides. This effect is often diminished by the use of so-called »guard rings«, which artificially extend the wafer area [149]. Analogously, in the ZMR 100 reactor »guard stripe« wafers are placed parallel to the sample (Fig. 3.8). Without guard wafers the width of the molten zone would decrease at the wafer edges, yielding a cigar like form.

3.5.4 Capping Oxide Before ZMR processing, the Si film usually has to be coated by a so-called »capping layer«. Such capping is inevitable in the common case of an underlying SiO2 intermediate layer. The very poor wetting behavior of molten Si on

SiO2 is evident in a contact angle of ∼87° [150]. Therefore, on uncoated films

16 The x coordinate refers to the x axis sketched in Figure 3.8.

36 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY the molten Si agglomerates into droplets due to the high surface tension. This behavior is referred to as balling-up effect.

Usually, SiO2 films deposited by LPCVD or PECVD are applied as a capping layer. Several authors noted a much more stable process with an additional thin

SiN layer on top of the SiO2 [109]. This result has been attributed to the diffusion of nitrogen into the Si–SiO2 interface, which improves wetting [151]. For SiN deposition, sputtering is a preferred method.

The standard capping used in this work was a 2 µm thick SiO2 layer deposited by PECVD.

Rapid Thermal Oxide As an alternative, a rapid thermal oxide (RTO) was tested as a capping layer.17 It was directly grown in the ZMR reactor, saving deposition in an extra machine. However, with the requirement of manageable process time, such an oxide has to be much thinner than one applied by deposition techniques such as PECVD. Still, successful ZMR processing without balling-up could be demonstrated with a mere ∼50 nm thin RTO capping. As a basic step, the dependence of oxide thickness on time and temperature has been determined. Tabulated data are usually given for temperatures up to ∼1200°C only [153], while in the employed ZMR reactor much higher process temperatures, up to the melting point of Si, are possible. Oxidation experiments were done on Cz-Si wafers from which the native oxide was removed by an HF dip shortly before processing. Heater power settings were translated into temperature on the basis of calibration measurements made with a thermocouple equipped Si wafer. Figure 3.10 shows the oxide thickness measured by ellipsometry. For each data point drawn with an error bar, thickness was measured on three identically processed samples. At each sample, an average thickness was determined from measurements taken at nine positions. For the temperature range of interest, crystal orientation – contrary to low temperatures – should have no significant effect [153, 154].

17 These experiments were largely performed by J. Pohl as part of his thesis for the admission to secondary school teaching (see Ref. [152]).

3.5 Zone-Melting Recrystallization 37

160 300 100% vol. O 100% vol. O 2 140 2 250 Fit 120 E = (2.06 ± 0.47) eV a,l E = (0.95 ± 0.21) eV 200 100 a,p A = (0.0096 ± 0.027) nm 150 80 B = (0.3 ± 2.0) x 1012 60 100 40 50 Oxide Thickness d [nm] Thickness Oxide d [nm] Thickness Oxide 20 20% vol. O 2 0 0 0 102030405060 0 0 0 0 0 0 0 0 0 0 0 0 8 9 0 1 2 3 1 1 1 1 Time t [min] Temperature T [°C] (a) (b)

Figure 3.10 Thickness dependence of RTO oxides grown in the ZMR system. (a) Oxide thickness versus time for an oxidation temperature of 1350°C. (b) Oxide thickness versus temperature for an oxidation time of 15 min.

The experimental data (Fig. 3.10) can be fitted well with the theoretical model of the oxidation process outlined in Appendix C. The time dependent data (Fig. 3.10a) show a nearly ideal parabolic behavior, as expected for »long« oxidation times. For the first data point, recorded after 1 min oxidation time, the thickness is already 25 nm. Therefore, at this stage the process can be assumed to be already diffusion-limited. The plotted curve does not exactly cross the origin (0,0) since some additionally oxide grew during heat up and cool down phases, with 20 s duration each. The temperature dependent data (Fig. 3.10b) were fitted by Eq. (C.6) yielding the activation Energies Ea,l and Ea,p as fit parameters. The values obtained for the linear rate case Ea,l = (2.1 ± 0.5) eV and for the parabolic rate case Ea,p = (1.0

± 0.2) eV are well in accordance with data found in literature (Ea,l = 2.0 eV and

Ea,p = 1.24 eV [155]). In addition to the process conducted in a pure oxygen atmosphere, temperature dependent data were recorded for the case of 20% by volume oxygen and 80% by volume argon. From Eq. (C.4) oxide thickness is expected to be

1 5 = 0,447K of the value for pure oxygen. Indeed, by scaling the best-fit

38 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY function by the factor 1 5 , the experimental data were reproduced perfectly (Fig. 3.10b).

3.5.5 ZMR Process The sequence of a typical ZMR process is shown in Figure 3.11. It consists of the following main steps: 0. The sample is centered relative to the lower heater by moving the furnace forward by one-half of the sample’s length. 1. The power of the lower heater is increased linearly. Typical ramps are about −1 15 Ks . 2. Optionally, the capping oxide is directly grown in the ZMR reactor, as discussed above. In this case, the process is conducted in pure oxygen. The power setting of 65%, corresponds to a temperature of approximately 1350°C, for a Si substrate. 3. The temperature of the lower heater is linearly ramped up to approximately 1200°C (corresponding to a power setting in the range of 50% to 55%). A settling time of typically 30 s ensures that sample and heater get close to equilibrium conditions. 4. The furnace is moved backward to the start position (focal line at position x = 0 in Fig. 3.8). Then the power of the upper heater is increased until a small stripe of Si is molten. Next, the molten zone scans across the sample by moving the furnace with a typical speed of a few centimeters per minute. In automatic mode, the PID closed-loop controller adjusts the upper heater power to keep the width of the molten zone constant. For processes including oxidation (step 2) this step is also performed in a pure oxygen atmosphere. For standard processes an argon atmosphere is used with 5% by volume oxygen. Without the addition of oxygen, damage of the capping layer by deoxidation [156] has been observed. 5. Having reached the end position (focal line at position x = 50 mm in Fig. 3.8), the upper heater power is decreased. Then, again, the furnace is centered relative to the lower heater and the sample is cooled down by linearly decreasing the power of the lower heater.

3.6 Solar Cell Process 39

l) n o (optiona llizati ing ramp up a at g e n yst h i xidation ttl ecr Pre O Se R . 1. 2. 3 4. 5. Cool down 60 40 lower heater upper heater 20 Power [%]Power

100 80 60 40 20 0 Position [mm] Position 100

process 10 without step 2 5 :Ar Ratio [%] Ratio :Ar

2 0 100 200 900 1000 1100 1200 1300 1400 1500 O Time [s]

Figure 3.11 Typical ZMR process including the growth of a RTO capping oxide.

After ZMR processing, the capping oxide was removed by hydrofluoric acid (HF). For Si films with thickness > 5 µm an additional short CP133 etch was applied to reveal the grain structure.

3.6 SOLAR CELL PROCESS Principally, the stack of substrate, intermediate layer and Si thin-film can be processed analogues to conventional bulk Si wafers. This technology has been introduced as a »wafer equivalent concept« [157]. The main difference for the structure employed in this work is the requirement to contact both, emitter and base, at the front side. For Si thin-film characterization and optimization, small test solar cells, of 1 cm2 area, were fabricated. Design goals for the employed structure were simplicity and process stability. Therefore, the grid was defined by photolithogra-

40 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY phy and metallization was done by evaporation. Optional processes applied were remote plasma hydrogen passivation, front side texturization, emitter oxidation, and double layer antireflection coating. The basic steps for solar cell processing are given in Figure 3.2. For structured surfaces the Si film was treated by an aqueous solution of potassium hydroxide (KOH) and isopropyl alcohol, following an RCA cleaning. This texturization process makes use of the preferred 〈100〉 orientation of ZMR thin films (see Sec. 3.5.2) and yields a random pyramid structure.

The solar cell emitter was diffused in a tube furnace from a POCl3 source. As standard, a sheet resistivity of 80 Ω/sq was targeted. The applied process yields a typical junction depth of ~0.3 µm and a phosphorous surface concentration of ~1020 cm−3. After diffusion, the resulting phosphosilicate glass (PSG) was removed in hydrofluoric acid (HF). In an optional step, the emitter was passivated after diffusion by growing a ∼10 nm thick thermal oxide. In this case, the targeted sheet resistivity was 100 Ω/sq. For textured solar cells the thin passivation oxide has a positive side effect: it prevents metal precipitation during galvanic contact thickening, which is a result of strong electric fields at the peaks of uncoated random pyramids. On some samples, bulk defect hydrogen passivation was carried out at this stage. Such a step has proven to increase solar cell performance significantly on nearly all multicrystalline Si materials [23, 34, 158–163]. While bulk passivation through hydrogen rich SiNx layers is state of the art in industrial processing, passivation in a remote plasma hydrogen passivation (RPHP) is better compatible with the test structures fabricated in this work. However, both methods have proven to yield similar improvements regarding carrier lifetime [164]. Remote plasma hydrogen passivation was carried out at the Institut für Solarenergieforschung Hameln/Emmerthal (ISFH). A scheme of the reactor setup is given in Ref. [162]. Two options were tested: (i) bulk passivation before metallization and (ii) after metallization. The advantage of option (i) is the pos- sibility to use higher temperatures. As a disadvantage, some hydrogen may out- diffuse during contact sintering. In preliminary experiments, no significant difference between both methods was found. Process temperature was 400°C for option (i) and 350°C for option (ii). In both cases, process time was 30 min.

3.7 Summary and Outlook 41

Fabrication of the emitter grid involved the following steps: photolithographical definition of the emitter grid structure, evaporation of 30 nm Ti, 30 nm Pd and 100 nm Ag, photoresist lift-off, and electroplating by 10 µm Ag. Then the final cell area was defined by a photolithographical mask and the emitter was removed around this area, forming a trench by reactive ion etching (RIE) (see also Fig. 3.1). Next, another photolithographical step defined the area of the base contact within the trench. Here the evaporated Al formed a »frame type« contact. After removal of the photoresist, contacts were sintered in forming gas

(20:1 N2:H2). An optional step at this stage involved passivating the solar cell bulk by RPHP (see discussion above).

Finally, a double layer antireflection coating (ARC) of 58 nm TiO2 and

105 nm MgF2 was deposited. This step was omitted on solar cells fabricated for studying ZMR film growth parameters.

3.7 SUMMARY AND OUTLOOK Fabrication of the Si thin-film solar cell device investigated in this work can be divided into three main steps: (1) substrate processing, (2) Si film formation, and (3) solar cells processing. Basic requirements for the substrate are: low costs, mechanical and chemical stability, flatness and thickness uniformity, small surface roughness, and matching of the thermal expansion coefficient (TEC) to that of Si. The last requirement is of special importance. Therefore, fundamental relationships have been reviewed, including the definitions of the temperature dependent coefficient α(T) and the mean thermal expansion coefficient α . T0 ,T Si film formation involves the technologies of chemical vapor deposition (CVD) and zone-melting recrystallization (ZMR). Firstly, a seed film is created by CVD and subsequent ZMR processing. Then this seed film is thickened by a second, epitaxial, CVD process. For this concept ZMR is a key technology since any defects in the seed film propagate into the epitaxial layer. In this chapter a short review on ZMR has been given, including a historical background and a summary of major technological developments. Grain size in ZMR thin films is comparable to standard mc-Si material grown by directional solidification. However, typically low angle grain boundaries are

42 CRYSTALLINE SILICON THIN-FILM SOLAR CELL TECHNOLOGY found within the grains – so-called subgrain boundaries (SGB). In situ observations have shown a close connection between crystallization front morphology and defect structure. The temperature gradient at the crystallization front is the major parameter that affects film growth and film quality. A ZMR system with advanced process control has been developed by the author. Image analysis is used to control the width of the molten zone and therefore temperature gradients. The closed-loop controller keeps the width of the molten zone constant within 5% and enables high-speed ZMR. Further, the implemented software tracks all relevant process data. Based on the same concept, a much larger ZMR system for samples up to 400 mm width was build by Fraunhofer ISE in the framework of the national PRISMA research project [165]. Process control is done by the same software application, but with an extended interface enabling the use of standard programmable controllers as employed in industrial manufacturing equipment. ZMR processing requires the use of a so-called capping layer in order to prevent agglomeration of molten Si (»balling up« effect). As an alternative to SiO2 layers grown by PECVD, a rapid thermal oxide (RTO) capping has been successfully tested. The RTO was directly grown in the ZMR system. The measured dependence of oxide thickness on time and temperature was found to fit very well to theoretical curves. Si thin films fabricated by ZMR and CVD can be processed into solar cells in a similar way to bulk crystalline wafers. The main difference for the structure employed in this work is the requirement to contact both, emitter and base, at the front side. For material characterization and process optimization, small test solar cells were fabricated. This process has been developed with the goals of simplicity, stability, and reproducibility. Optional steps can be introduced to explore the performance potential.

4 Silicon Solar Cell Device Physics

This chapter gives an overview of the basic phenomena involved in solar cell operation: carrier generation, recombination, and transport by field and diffusion forces. The fundamental definitions and equations are reviewed and the classic ideal diode equation is derived. The notation of charge collection probability is introduced. Together with the reciprocity theorem of charge collection, it enables an elegant solution of different problems. As an example, the effective recombination velocity at a low-high junction is derived. In the solar cell structure investigated, this kind of junction implements a so-called back surface field (BSF).

4.1 RECOMBINATION AND GENERATION

4.1.1 Recombination If a semiconductor is exposed to light or if carriers are injected by applying an external voltage, the thermal equilibrium condition is disturbed. In such a case, processes exist which act to restore these conditions. Intrinsic recombination mechanisms are the emission of a photon and the Auger process. These processes cannot be avoided by their nature. For Si solar cells Auger recombination is the dominating intrinsic process. Extrinsic recombination is caused by defect levels located in the band-gap. Shockley, Read, and Hall have provided the theory for the description of recombination by a single trapping level [166, 167] and derived the basic expressions (see, e.g., p. 35 in Ref. [168]). For the Si thin-film solar cells investigated in this work, recombination via defect states is the carrier lifetime limiting process. These states are provided by crystal imperfections such as grain boundaries and dislocations, by impurities, and by insufficiently passivated surfaces.

43 44 SILICON SOLAR CELL DEVICE PHYSICS

Under low injection conditions, i.e., the excess concentration of electrons

∆n = n − n0 is much smaller than the equilibrium concentration n0 (∆n << n0), the 18 recombination rate of electrons as minority carriers Un is linear in the concentration ∆n. The equivalent relationship holds for holes as minority carriers with excess concentration ∆p = p − p0. The proportionality constants τn and

τp define the low injection minority carrier lifetimes in n-type and p-type material. n − n ∆n τ = 0 = n U U n n (4.1) p − p0 ∆p τ p = = . U p U p

The definition of minority carrier lifetime, τn or τp by Eqs. (4.1), is generally maintained even if the linear relation between recombination rate, Un or Up, and excess concentration, ∆n or ∆p, does not hold anymore, i.e., τn = τn(∆n) and

τp = τp(∆p), respectively [169]. A surface represents a severe disturbance of the periodic crystal structure and introduces states within the band-gap. Principally it can be treated analogous to extrinsic bulk recombination and a surface recombination velocity (SRV) can be defined by U S = s , (4.2) ∆ns where Us is the surface recombination rate and ∆ns is the excess minority carrier concentration at the surface. However surface charges in general bend the bands and create a space charge region (SCR) that extends from the surface at z = 0 to z = Wscr,s. Therefore, the notation of an effective surface recombination velocity can be introduced by considering the excess carrier concentration ∆nW at the edge of the space charge region z = Wscr,s. The corresponding recombination rate UW then takes into

18 The index n denotes that the variable refers to electrons as minority carriers and is an abbreviation of np. Electrons as majority carriers are denoted by nn. Holes as minority and majority carriers are denoted by p and pp, respectively.

4.1 Recombination and Generation 45 account all recombination within the volume between the surface and the space charge region edge [z < Wscr,s] (Ref. [59], p. 40).

UW Seff = (4.3) ∆nW Generally, bending of the bands results in an injection dependence of recombination rate and surface recombination velocity. Dividing the surface recombination velocity S by the diffusion constant D yields the reduced surface recombination velocity s defined as S s = . (4.4) D The dimension of s is inverse to the dimension of the bulk recombination parameter diffusion length, which will be introduced in Section 4.3. In the thin-film solar cell structure investigated in this work, recombination at the rear is reduced by a so-called back surface field (BSF). The effect is achieved by lowering the minority carrier concentration [171]. In the concrete structure, the BSF is implemented by a low-high junction (see Sec. 4.4.2).

4.1.2 Generation The annihilation of photons in the absorption process is described by dE (z) p,λ = −α(λ)E (z) , (4.5) dz p,λ where Ep,λ is the spectral photon flux at position z. The absorption coefficient α(λ) describes the probability that a photon of wavelength λ is absorbed within a unit length. If each absorbed photon generates one electron-hole pair19, the spectral generation rate Gλ must be equal to the change in photon flux, i.e.,

Gλ (z) = −α(λ)Ep,λ (z). (4.6)

Assuming homogeneous optical properties, integration of Eq. (4.5) yields an exponential decay of the photon flux. Therefore,

19 Photons may also be absorbed by processes like free carrier absorption (see Ref. [170], p. 59, for a more general treatment).

46 SILICON SOLAR CELL DEVICE PHYSICS

Gλ (z) = Ep,λ (0)α(λ)exp[−α(λ) z], (4.7) where Ep,λ(0) is the incident spectral photon flux at z = 0. The normalized generation rate g is obtained by applying the condition

W ∫ g(λ, z)dz ≡1. (4.8) 0 For a specimen of thickness W where the light is not subject to internal reflection the normalized generation rate g is given by α(λ) g(λ, z) = exp[]−α(λ) z . (4.9) 1− exp[−α(λ)W ]

4.2 BASIC EQUATIONS Five basic equations describe the behavior of charge carriers in a semiconductor. The Poisson equation relates the static electric field E to the space charge density ρ ρ ∆φ = −∇E = − , (4.10) ε 0ε s where φ is the electrostatic potential, ε0 is the permittivity in vacuum and εs is the relative permittivity of the semiconductor. The electron current density Jn and the hole current density Jp are given by

J = q(µ nE + D ∇n) n n n (4.11) J p = q(µ p pE − Dp∇p) .

They consist of a drift component caused by the electric field E and a diffusion component caused by the gradients of the carrier concentrations n and p. q is the elementary charge, µn and µp are the mobilities of electrons and holes, respectively, Dn and Dp are the corresponding diffusion constants. The continuity equations connect the temporal change in carrier concentration, the divergence of the current density, the generation rate G, and the recombination rate U

4.3 p-n Junction 47

∂n 1 = G −U + ∇J ∂t n n q n (4.12) ∂p 1 = G −U − ∇J . ∂t p p q p

Under low injection conditions the recombination rates Un and Up are given by Eqs. (4.1). Substitution of these expressions into Eqs. (4.12) yields the transport equations ∂n = G −U + µ n∇E + µ E∇n + D ∇2n ∂t n n n n n (4.13) ∂p = G −U − µ p∇E − µ E∇p + D ∇2 p . ∂t p p p p p Eqs. (4.10) and (4.13) form a set of coupled nonlinear differential equations for which it is not possible to find general analytical solutions. However, special solutions can be derived for particular boundary conditions.

4.3 p-n JUNCTION The solar cells examined in this work are essentially very large p-n junction diodes. For this device Shockley has derived the well-known ideal current- voltage characteristics [172]. Not all of the assumptions made are fulfilled in a real solar cell. However, the theory serves well as a basis for more elaborate models and is suited to describe individual features of a solar cell. The derivation of the Shockley equation is given in many textbooks (see, e.g., Refs. [168, 173]). Some of the main results are reviewed below since they are used in the subsequent sections. The analysis is based on the approximation that the p-n junction can be divided into two types of regions. In quasineutral regions, the space charge density is assumed to be zero, while in the depletion region the carrier concentrations are assumed to be small, and the only contribution to the space charge density comes from the ionized dopants. The change between the depletion regions and the quasineutral region is assumed to be abrupt. The following is restricted to a one-dimensional analysis. The semiconductor is assumed to extend indefinitely into the x and x directions with homogeneous properties. The p-n junction plane is perpendicular to the z axis (see Fig. 4.1).

48 SILICON SOLAR CELL DEVICE PHYSICS

y x z

Area A

We Emitter n

Wscr Space charge region W W1 Base p Wb W2 Base p+ (BSF) Figure 4.1 Schematic device structure

Wsub Substrate with barrier layer of the thin-film solar cell investigated in this work.

At equilibrium conditions the minority carrier concentrations p0 in the n-type region and n0 in the p-type region are given by Boltzmann relations

 qVbi  p0 = p p0 exp−   kBT  (4.14)  qVbi  n0 = nn0 exp−  ,  kBT  where pp0 and nn0 are the majority carrier equilibrium concentrations in the p- type and n-type material, respectively. Vbi is the built-in potential, kB is the Boltzmann constant, and T is the absolute temperature. The drift and the diffusion term contributing to the carrier current density in Eq. (4.11) are large and opposing, and balance at zero bias. The net current flow is therefore the difference between two large terms. This leads to the approximation that expressions similar to Eqs. (4.14) still hold when carriers are injected by an external applied voltage V and the additional current is small compared to the two other terms.

The voltage V is then added to −Vbi in Eqs. (4.14), and at the edges −zn and zp of the space charge region the minority carrier concentrations are (Fig. 4.2)

 qV  p(−zn ) = p0 exp   kBT  (4.15)  qV  n(z p ) = n0 exp  .  kBT 

4.3 p-n Junction 49

space charge n-type region p-type

p = NA

n = ND

p0 exp(qV / kBT)

n0 exp(qV/ kBT) log (carrier concentration) p(z)

p 0 n(z) Figure 4.2 Electron and hole n carrier concentrations across the W W W 0 n scr b forward biased p-n junction in the -z z n 0 p z dark (after Ref. [174]).

The approximation above is equivalent to the introduction of separate quasi- Fermi levels for electrons and holes (p. 340 in Ref. [170]). In this concept the electron and hole current densities are proportional to the gradients of the electron and hole quasi-Fermi levels. Eqs. (4.15) constitute boundary conditions that allow one to find separate solutions in the depletion and the quasineutral regions. We will now derive the solution in the p-type quasineutral region. If the concentration of minority carriers in this region is small compared to the concentration of the majority carriers, the minority carriers must flow predominantly by diffusion (see, e.g., p. 70 in Ref. [173]). Under low injection conditions, the recombination rates are given by Eqs. (4.1) and the transport equation (4.13) reduces to

2 n − n0 Dn ∇ n − = Gn . (4.16) τ n

In the dark case (Gn ≡ 0) Eq. (4.16) is a homogeneous equation with general solution

 z   z  ∆n = n − n0 = Aexp−  + Bexp  , (4.17)  Ln   Ln 

50 SILICON SOLAR CELL DEVICE PHYSICS where the diffusion length Ln is defined by

Ln ≡ Dnτ n . (4.18)

If the quasineutral regions extend indefinitely the boundary condition

lim n = n0 (4.19) z→∞ applies and yields B = 0. The constant A is then determined by boundary condition (4.15), which gives

  qV    z   p  A = n0 exp  −1exp  . (4.20)   kBT    Ln  To obtain the current densities across the junction, the gradients of the carrier concentrations at the edges of the space charge region zp and −zn have to be evaluated. For the p-side we find

d n(z) qD n   qV   J = qn D = n 0 exp  −1 . (4.21) n z=z 0 n     p dz L k T z=z p n   B  

The expression for Jp at −zn on the n-side is equivalent. Assuming that the currents through the depletion region are constant (i.e., no generation or recombination occurs in this region), the total current density is given by

  qV  J (V ) = J n + J p = J 0 exp −1 (4.22) z=z p z=−z   n   kBT  with the saturation current density

qDp p0 qDnn0 J 0 = J 0,E + J 0,B = + . (4.23) Lp Ln

Eq. (4.22) is the well-known current-voltage characteristics of the ideal diode in the dark. To obtain the current-voltage characteristic under illumination the inhomogeneous transport equation (4.16) has to be solved. If the recombination rates are linear in the excess carrier density, a superposition principle holds (see, e.g., Ref. [59], p. 53 or Ref. [174], p. 46). In this case, the total excess carrier density is the sum of the carrier densities obtained from voltage injection in the dark and

4.3 p-n Junction 51 from photogeneration. Therefore, the total current is found to be the sum of the currents by voltage excitation only and by light excitation only. Assuming spatially homogeneous generation – an assumption that is not valid for normal operating conditions – the ideal current-voltage curve is then just shifted by the light generated current density JL, i.e.,

  qV  J (V ) = J 0 exp −1 − J L . (4.24)   kBT  For a more general form of the generation rate G the solution to Eq. (4.16) is more complex. The charge collection probability and the reciprocity theorem, which are introduced in Section 4.4.1, allow an elegant solution for arbitrary generation rates.

4.3.1 Two-Diode Model In real solar cells, depletion region recombination may represent a substantial loss mechanism. Sah, Noyce, and Shockley have extended the ideal diode theory and derived analytical expressions for the recombination current in the depletion region Jrg [175]. The terms involved can be simplified with the assumption of single-level, uniformly distributed defect states, located at the intrinsic Fermi level, and the supposition of equal lifetimes, mobilities, and densities for both minority carrier types. In this case, the maximum recombination rate under forward bias can be approximated by (e.g., see Ref. [176], p. 119)

+ ni   qV   U max ≅ exp  −1 . (4.25) 2τ 0   2kBT   Contrary to the case of reverse bias, the forward bias recombination rate is spatially not constant. The recombination rate U+ falls exponentially with distance + on either side of its maximum Umax with a characteristic length of kBT/qEmax, where Emax is the maximum field strength. Assuming a linear potential variation across the junction this field strength is given by Emax = 2(Vbi − V)/Wscr, where

Vbi is the built-in potential and Wscr is the width of the space charge region. The total recombination current is proportional to the integral over the recombination

52 SILICON SOLAR CELL DEVICE PHYSICS rate U+. This integration may be approximated by a multiplication of the maxi- + 20 mum recombination rate Umax and an effective thickness Weff that reads

kBT kBT Wscr Weff = 2 = . (4.26) qEmax q Vbi −V The recombination current under forward bias then is

qW n   qV   J + (V ) q U + dz eff i exp  1 rg = ∫ max =    −  , (4.27) W 2τ 0   2kBT   eff 14243 J02 A large number of real solar cell I-V curves can be well described by the so- called »two-diode model«. In this model emitter and base region, and depletion region are considered by two individual diodes with their own I-V characteristics and saturation current densities J01 and J02, respectively. Further, ohmic resistors model a series resistance Rs and a parallel (or shunt) resistance Rp. The combined I-V characteristics read [177]

q[V −J (V )R ] q[V −J (V )R ]  s   s  V − J(V )R  n1kBT   n2kBT  s J (V ) = J 01 e −1 + J 02 e −1 + − J L ,(4.28) R     p where the parameters n1 and n2 are called ideality factors. For the derivation given above [Eq. (4.24) and Eq. (4.27)], they have values of 1 and 2, respectively. The result n2 = 2 is obtained with the approximations involved in the derivation sketched above. However, for more realistic calculations values different from 2 are found [175, 178, 179]. Therefore, n1 and n2 are often taken as variable parameters, allowing modeling a wide range of actual solar cell devices.

4.4 CHARGE COLLECTION PROBABILITY

4.4.1 Charge Collection Probability and Reciprocity Theorem The charge collection probability21 ϕ(r) is defined as the probability that a minority carrier, which is light-generated at position r, is collected by the

20 In reality the field falls slower than exp(−qEmaxz) near z = 0. To account for this effect, Weff has to be multiplied by the additional factor π/2 [175].

4.4 Charge Collection Probability 53 junction [180]. If Jgen is the current density resulting from generation at the position r, then ϕ(r) is equal to the fraction Jsc of this current density that is collected at the junction under short circuit conditions J ϕ(r) = sc . (4.29) J gen (r)

The notation of charge collection probability is especially useful in connection with the reciprocity theorem found by Donolato [181]. This theorem states that »The current collected by a p-n junction in presence of a unit point charge generation of carriers at a point P is the same (apart from the dimensions) as the excess minority-carrier density at P due to a unit density of carriers at the junction edge«. An independent proof of the theorem without the restriction of uniform doping was given by Markvart [183]. Misiakos and Linholm [184], Donolato [185], and Green [182] have extended the theorem for the case of arbitrary geometry, nonhomogeneous semiconductor properties (such as energy gap, mobilities etc.), and electric drift fields. Rau and Brendel have shown that the theorem is also valid for particles obeying Fermi statistics [186]. Their generalized formulation states that the charge collection probability at any point is proportional to the relative shift of the minority carrier Fermi-level at this point caused by a voltage applied at the junction. The reciprocity theorem simplifies the analytical calculation of quantum efficiency but is also helpful for numerical calculations since the carrier transport equation once solved in its homogeneous form can be combined with different generation profiles. This can be useful for the simulation of spatially nonhomogeneous solar cells. Below a short outline on the connection between the excess carrier density problem and the collection probability problem is given. Common characterization techniques, such as SR, LBIC, or EBIC22, measure the current under short circuit conditions that results from a particular generation function. To model this current analytically we could proceed as follows.

21 By some authors the quantity ϕ is also referred to as (spatial) charge collection efficiency (see, e.g., Ref. [59]). 22 SR – spectral response, LBIC – light beam induced current, EBIC – electron beam induced current. These techniques are introduced in Chapter 6.

54 SILICON SOLAR CELL DEVICE PHYSICS

Firstly, we would solve the carrier transport equation (4.16) for a point generation function (i.e., a δ-distribution) using the appropriate boundary conditions: At the junction surface Sjct the excess carrier ∆n density must vanish and the boundary condition is

∆n(r) = 0 . (4.30) r∈S jct

All other surfaces Si (i = 1,…,N) are characterized by (reduced) recombination velocities si and the boundary conditions are

∂∆n(r) = −si ∆n(r) , (4.31) ∂ni r∈Si where the differentiation is in the directions of the normals ni outward to the surfaces Si. Taking Dirac’s delta distribution δ(r−r') as the generation function, the solution to this special inhomogeneity is the Green’s function G(r,r'), where r' is the location of generation. Next, we could find the carrier density for an arbitrary generation function G by integrating the product of the generation function G and the Green’s function G with respect to r'. Finally, we would obtain the short circuit current density by evaluating the normal gradient of the (excess) carrier density at the junction surface Sjct, as was done in the one-dimensional case by Eq. (4.21). If we are interested in the collection probability ϕ(r), we do not perform the second step, but we evaluate the current for the point generation function and normalize it through Eq. (4.29). Donolato’s finding is that the solution ϕ(r) can be obtained in a single step if the homogeneous version of the transport equation (4.16), i.e.,

2 1 Dn∇ ϕ(r) − ϕ(r) = 0, (4.32) τ n is solved with the inhomogeneous boundary condition at the junction

ϕ(r) =1, (4.33) r∈S jct

4.4 Charge Collection Probability 55 while keeping the boundary conditions by Eqs. (4.31) for the other surfaces. The problem described by Eqs. (4.32), (4.33), and (4.31) is exactly that of finding the excess carrier density under carrier injection at the junction by a forward bias. Once the collection probability ϕ is known, the current density for an arbitrary generation function G is easily obtained by integration of ϕ weighted by G. From a physical point of view, the treatment of the carrier transport problem in terms of charge collection probability ϕ and generation G in separate steps corresponds to a split into electronic and optical device properties.

4.4.2 Charge Collection in Solar Cells of Finite Thickness In Section 4.3 the minority carrier density in the p-type base region was calculated assuming a semi-infinite extent. However, for most real solar cells this approximation is not applicable, and it is especially inappropriate for thin- film solar cells. As an example, the charge collection probability in the solar cell’s base shall be derived for the case of finite base thickness. The result is needed in the subsequent sections. Again spatially homogeneous material properties are assumed and the problem is treated in one dimension. The base thickness is denoted by

Wb and the origin of the z coordinate is now taken at the p-side edge of the space charge region (the position labeled zp in Fig. 4.2). The general solution to Eq. (4.32) is the same as the one to Eq. (4.17)23 with ∆n just replaced by ϕ , i.e.,

 z   z  ϕ(z) = Aexp−  + B exp  . (4.34)  L   L 

At the junction plane (z = 0) where ideal collection properties are assumed, the boundary condition is given by Eq. (4.33), which in the one-dimensional case reads ϕ(0) = 1. This condition yields

A = 1− B . (4.35)

23 All the following analysis is restricted to the p-type base region of a p-n device where electrons are minority carriers. The index denoting the carrier type (like n in Ln) is therefore omitted.

56 SILICON SOLAR CELL DEVICE PHYSICS

The back surface is characterized by the reduced surface recombination velocity s and boundary condition (4.31) applies. Translated to charge collection

probability this condition here reads ∂zϕ(z)|z = Wb = −sϕ(Wb), where ∂z denotes the partial derivative with respect to z. The constant B is then determined to 1− L s B = . (4.36) 1− Ls + (1+ Ls)exp(2Wb /L)

Inserting Eqs. (4.35) and (4.36) into Eq. (4.34) and simplification of the expression yields the final expression

cosh[(W − z)/L] + L ssinh[(W − z)/L] ϕ(z) = b b . (4.37) cosh(Wb /L) + L ssinh(Wb /L) In the limiting case of infinite surface recombination velocity at the back

(s → ∞) the second boundary condition has to be replaced by ϕ(Wb) = 0 and Eq. (4.37) reduces to sinh[(W − z)/L] ϕ(z) = b . (4.38) sinh(Wb /L) This function describes the charge collection probability in the base of a semiconductor with an ohmic back contact.

Effective Recombination Velocity at Low-High Junction In the solar cell structure investigated, surface recombination at the rear is reduced by a back surface field (BSF), implemented through a low-high junction. Godlewski et al. have derived an analytical expression for the effective surface recombination velocity at the interface of the differently doped layers [187]. In the subsequent section an alternative derivation of their formula is given. With the notation of charge collection probability and use of the reciprocity theorem it can be obtained in a short and elegant way. In addition, the effect of band-gap narrowing is taken into account. In a solar cell with two differently doped base regions as sketched in Fig. 4.1, the solutions of the transport equation have to be matched at the interface. Assuming that no recombination and generation is present at the junction’s space charge region, the current density across the junction has to be constant.

4.4 Charge Collection Probability 57

This condition yields the boundary condition qD1∂zn1 = qD2∂zn2 at z = W1. Here, n1 and n2 are the minority carrier densities, and D1 and D2 are the corresponding diffusion constants in regions 1 and 2, respectively. The equivalent boundary condition in terms of charge collection probability, requires the consideration of different carrier densities due to the difference in doping level. Due to the reciprocity theorem, the excess carrier density has to be normalized to the excess carrier density at the junction edge. Taking this condition into account, the boundary condition for ϕ reads

∂ϕ ∂ϕ qD n 1 = qD n 2 , (4.39) 1 01 ∂z 2 02 ∂z z=W1 z=W1 where n01 and n02 are the equilibrium carrier concentrations in regions 1 and 2, respectively. Further, the charge collection probability has to be continuous at the interface location z = W1, i.e., ϕ1(W1) = ϕ2(W1). The boundary conditions at the junction and at the rear (s2 = S2/D2) are the same as for the problem treated before. The solution for region 1 is found to be the same as for Eq. (4.37) with

Wb replaced by W1, L by L1, and s by S 1 n 1 s L + tanh(W / L ) s = 1 = D 02 2 2 2 2 . (4.40) 1 D D 2 n L 1 + s L tanh(W / L ) 1 1 12301 1242442 42 43442 42 fdop fgeom

Here, L2 denotes the bulk diffusion length in the highly doped region 2. The form of Eq. (4.40) suggests the interpretation of s1 as effective surface recombination velocity at the rear of region 1. For the following graphical evaluation Eq. (4.40) is split up into two products. The first factor fdop depends on the ratio of doping levels, while the second factor fgeom depends on the geometry and the surface recombination velocity at the rear of layer 2. In the highly doped layer 2, as well as in the emitter, band-gap narrowing significantly affects carrier densities. This fact can be taken into account by intro- ducing an effective intrinsic carrier concentration (Ref. [168], p. 143)

 ∆E  2 2  g  ni,eff = ni exp  , (4.41)  kBT 

58 SILICON SOLAR CELL DEVICE PHYSICS

Region 1 Region 2 ϕ

W1 W2 1.0 N = 7 x 1016 cm-3 19 -3 A 1 x 10 cm 0.8 S L = 30 µm 1 0.6 1 W = ∞ L = 10 µm 2 0.4

0.2 Charge collection probability probability collection Charge S = 106 cm s-1 2 0.0 0 10203040 Distance from junction z [µm]

Figure 4.3 Charge collection probability ϕ for a BSF solar cell (solid line). The

boundary conditions at the low-high junction located at z = W1 yield an effective 2 −1 surface recombination velocity S1 = 5 × 10 cm s . For comparison, the collection probability for a semi-infinite solar cell with the same bulk diffusion length L1 as those in region 1 of the BSF solar cell is plotted (dashed line).

where ∆Eg is the relative change in the band-gap energy due to band-gap narrowing. The ratio n02/n01 in Eq. (4.40) is then given by

n n2 N N  ∆E − ∆E  02 = i,eff A,1 = A,1 exp g1 g2  , (4.42) 2   n01 NA,2 ni,eff NA,2  kBT  where NA,1 and NA,2 are the acceptor doping concentrations in regions 1 and 2, respectively. For example, in Figure 4.3 the collection probability ϕ is plotted for a two layer BSF solar cell. The parameters are typical for the thin-film solar cell structure investigated in this work. The effective surface recombination velocity

S1 at the low high junction is proportional to the change in slope at the interface of regions 1 and 2. For comparison, the collection probability is plotted for a solar cell with infinite base thickness (»semi-infinite« structure) and bulk diffusion length identical to the diffusion length L1 in region 1. The comparison verifies that the thin cell with low back surface recombination velocity S1 can yield a higher current (obtained by an integration of ϕ ; see Sec. 4.5) and a higher open

4.4 Charge Collection Probability 59 circuit voltage (proportional to the inverse of the slope of ϕ at z = 0) than the thick cell. Still, for the model data, collection in the thin device is limited by the bulk diffusion length L1, which determines the curvature of ϕ in region 1, and not by the effective surface recombination velocity S1.

In Figure 4.4 the two factors fgeom and fdop composing the right side of Eq. (4.40) are displayed as two-dimensional parametric plots. These allow a graphical evaluation of the effective surface recombination velocity S1. In the plot of fdop band-gap narrowing was considered by the model and the parameters given in Appendix B.3 [Eq. (B.3) and Table B.2]. The diffusion coefficient D2 in fdop was obtained from the doping concentration NA,2 employing the mobility model provided in Appendix B.2 [Eq. (B.1) and Table B.1].

Whether the geometric factor fgeom is affected by the recombination velocity s2 or not, depends on the ratio of thickness W2 and bulk diffusion length L2, as can be seen in Figures 4.4a–c. In the case L2 > W2 (above the bottom left to top right diagonal) region 2 is called »transparent«. For this situation, fgeom increases with decreasing W2 if L2 > 1/s2, and fgeom decreases with decreasing W2 if L2 > 1/s2. In the case L2 < W2 (below the bottom left to top right diagonal), fgeom only depends on L2, but not on the thickness W2.

In the investigated solar cell structure, the thickness W2 is required to be larger than 1 µm. Otherwise the lateral conductivity in the highly doped region 2 would not be sufficient. Assuming L2 ≥ 1 µm, the geometric factor is likely to be in the range of 0.25 to 1.0.

The doping ratio factor fdop covers a much broader range, as can be seen in

Figure 4.4d. For values of NA,1 and NA,2 that are relevant for the practice, fdop can vary by about three orders of magnitude. An upper limit of NA,2 is given by the maximum amount of impurities that can be incorporated in the lattice in electrically active form. A further effect, which would have to be considered in a deeper analysis, is the increasing Auger recombination with an increasing doping level NA,2, yielding a decrease in the diffusion length L2. In conclusion, for the investigated solar cell structure the effective surface recombination velocity at the low-high junction is primarily determined by the ratio of doping levels. Geometrical parameters, i.e., thickness, have only a minor contribution.

60 SILICON SOLAR CELL DEVICE PHYSICS

f f geom geom 10 10 0.26 s = 20 µm-1 s = 2 µm-1 2 0.26 2 [µm]

2 6 -1 5 -1 (S = 10 cm s ) 0.41 (S = 10 cm s ) 2 [µm] 2 0.41 2 0.66 0.66 1.0 1 1 1.0 1.7 1.7 1/s 2.7 2 4.3 2.7 4.3 6.9 Diffusion length L length Diffusion 6.9 0.1 0.1 L length Diffusion 0.1 1 10 0.1 1 10 Thickness W [µm] Thickness W [µm] 2 2 (a) (b)

f f geom ] dop 20 10 -3 10 -1 0.16 7.1E1 cm s-1

s = 0.2 µm [cm 1/s 2 2 4 -1 (S = 10 cm s ) 0.26 A,2 [µm] 2 2 0.41 1019 1.9E2 0.66 5E2 1 1.0 1.3E3 18 3.6E3 1.7 10 2.7 9.5E3 4.3 2.5E4 6.9 0.1 17

Diffusion length L length Diffusion 10 0.1 1 10 1015 1016 1017 -3 Thickness W [µm] N concentration Doping Doping concentration N [cm ] 2 A,1

(c) (d) Figure 4.4 Parametric plots for graphical evaluation of effective surface recombination velocity S1 at a low-high junction. (a)–(c) geometric factor fgeom for different values of s2 (the surface recombination velocity at the rear of the highly doped region 2). For conversion of s2 to S2 = s2 D2 a fixed diffusion constant D2 = 2 −1 5 cm s was assumed. Actually, D2 depends on the doping concentration NA,2, a parameter incorporated into fdop. (d) doping ratio factor fdop. The effective surface recombination velocity S1 is obtained by multiplying one value for fgeom with one for fdop.

4.5 Collection and Quantum Efficiency 61

4.5 COLLECTION AND QUANTUM EFFICIENCY The charge collection probability ϕ(r) purely depends on electronic properties of a semiconductor device. Although the knowledge of this parameter would be desirable, it is not directly accessible by common measurement techniques. Methods such as SR, LBIC, or EBIC (see Chapter 6) measure the current density collected under short circuit conditions Jsc for light generation with known spectral distribution. Two properties, which can be determined from a wavelength dependent measurement of short circuit current, are collection efficiency 24 ηc and internal quantum efficiency IQE.

The collection efficiency ηc is defined as the probability that a photon of wavelength λ that got absorbed by creation of an electron-hole pair contributes one electron to the short circuit current. The collection efficiency is connected to the normalized generation rate g (Sec. 4.1.2) and the charge collection probability ϕ by

W ( ) g( , z) (z)dz ηc λ = ∫ λ ϕ , (4.43) 0 where W is the thickness of the device. For a semiconductor with homogeneous optical properties and no internal light reflection, the normalized generation rate g is given by Eq (4.9). If the charge collection probability is a three-dimensional function, the one-dimensional projection ϕ(z) can be obtained by 1 ϕ(z) = ∫∫ϕ(x, y, z)dxdy , (4.44) A yx where A is the area of the unit cell. This unit cell may be the whole solar cell or a symmetry element in a periodic array. Insertion of Eq. (4.44) into Eq. (4.43) then yields the average collection efficiency for this unit cell.

24 In this work a distinction is made between collection efficiency and internal quantum efficiency (see definitions). Often both properties are defined identically and therefore are taken as synonyms.

62 SILICON SOLAR CELL DEVICE PHYSICS

Φp,λ Φp,λ,R+E

Junction Active Si film

Figure 4.5 Net photon flows. The number of photons

Φp,λ,B absorbed in the active Si film is given by Φp,λ Φp,λ,T + Φp,λ,B − Φp,λ,R+E − Φp,λ,T. If each of these absorbed photons creates one electron-hole pair, the collection Substrate efficiency ηc(λ) is the fraction of these photons which contributes a carrier collected at the junction.

Figure 4.5 shows a simplified scheme of photon flows in the investigated thin-film solar cell device. Experimental determination of collection efficiency

ηc in this structure would not only require the measurements of the incident

(spectral) photon flow Φp,λ, and the flow of reflected photons and of photons escaping at the surface Φp,λ,R+E, but also the flow of transmitted photons at the back Φp,λ,T and the flow of photons entering at the back Φp,λ,B (e.g., by reflection of photons at the substrate’s rear side). Further, parasitic optical absorption would have to be taken into account, e.g., absorption by antireflection coatings or by free carriers. In the concrete structure, none of these properties are accessible with manageable effort. In conclusion, the definition of internal quantum efficiency (IQE) used in this work is based on a pragmatic ground. We define the IQE as the probability that a photon entering the solar cell from the illuminated side contributes one electron to the short circuit current. This definition is compatible with common IQE determination by spectral response and reflectance measurements (see Section 6.2). The way the IQE is defined here, it is connected to the charge collection 25 efficiency by ηc [188]

25 Carrier absorption and collection are assumed to be independent of each other [189]. This is not necessarily the case, e.g., for long wavelength (λ > 1130 nm) free carrier absorption enhances the absorption coefficient [190].

4.6 Summary 63

f IQE = abs η , (4.45) 1− R c where fabs is the fraction of photons absorbed and R is the sum of hemispherical reflectance and escape at the front surface. IQE and ηc are identical if fabs = 1 − R. This situation is given in a solar cell where no parasitic absorption occurs and where no light leaves or enters at the rear side, e.g., through use of an ideal reflector. Assuming the absence of parasitic absorption, the approximation fabs ≅ 1 − R is generally valid in the short wavelength range were the vast number of photons are absorbed before reaching the back (in Fig 4.5, Φp,λ,T and Φp,λ,B can then be considered as zero). For a solar cell with homogeneous optical properties and no internal reflection, the IQE is connected to the spectral generation rate Gλ, given by Eq. (4.7), and to the charge collection probability ϕ by

W G (z) IQE(λ) = ∫ λ ϕ(z)dz , (4.46) 0 Ep,λ (0) where Ep,λ is the incident spectral photon flux. Note that the normalization used here is different from the normalization of g. For a solar cell where light is transmitted through the cell’s back we have

W G (z) W ∫ λ dz <∫ g(λ, z)dz =1, (4.47) 0 Ep,λ (0) 0 and IQE(λ) < ηc(λ). For solar cells of infinite thickness (W → ∞) both normalization methods yield the same generation rate, i.e., Gλ/Ep,λ = g. The IQE provides depth dependent information on the solar cell and can be used to extract recombination parameters (see Chapter 5).

4.6 SUMMARY Carrier generation and recombination are essential phenomena involved in the operation of a solar cell device. In this chapter the basic definitions and equations have been summarized, which are needed in subsequent chapters. Furthermore, a review has been given on the basic equations describing carrier transport in a semiconductor. Applying several simplifying approximations,

64 SILICON SOLAR CELL DEVICE PHYSICS an analytical solution to the carrier transport problem can be found know as the ideal diode I-V characteristics. The behavior of an actual solar cell may deviate significantly from these characteristics. Therefore, more elaborate models have also been introduced. Among others, in real devices space charge region recombination has to be considered. Next, the notation of charge collection probability has been introduced. In conjunction with the reciprocity theorem for charge collection, it allows an elegant solution to numerous problems. This reciprocity theorem relates two important operating condition of a semiconductor device: (i) the collection of carriers, e.g., light generated, at the p-n junction under short circuit conditions, and (ii) the injection of carriers by an external applied voltage. As an application, the effective recombination velocity at a low-high junction has been derived. In the investigated thin-film solar cell structure, such a junction implements a so-called back surface field (BSF). For typical parameters two-dimensional plots were computed that allow a graphical evaluation of the effective surface recombination velocity at the low-high junction in the concrete structure. Lastly, the properties of collection efficiency and internal quantum efficiency (IQE) have been defined. In this work, a distinction between the two properties is made since the pure electronic property of collection efficiency can hardly be obtained by common measurement methods while the definition of IQE is compatible with standard characterization methods.

5 Effective Diffusion Length and Effect of Dislocations

From a practical point of view carrier recombination at different entities is often described by an effective diffusion length. For example, the notation may be used to take into account the recombination activity of surfaces, grain boundaries and dislocations, and to describe locally differing material properties by a single parameter. In the first part of this section different definitions of »effective diffusion length« are reviewed. In 1998, Donolato presented an analytical model describing the effect of dislocation density on minority carrier effective diffusion length. However, the special definition of an »effective diffusion length« used by Donolato is not compatible to that usually employed when analyzing quantum efficiency data and it does not refer to the typical operation conditions of a solar cell. Therefore, Donolato’s model is modified consistently using the quantum efficiency effective diffusion length. While Donolato’s original analysis was derived for a »semi-infinite« specimen, the objective in this work is the appropriate description of thin devices, such as crystalline Si thin-film solar cells with back surface field. Therefore, the model is extended accordingly. Since the associated boundary value problem does not allow a straightforward analytical solution an approximate expression is derived, which is validated by numerical simulations.

5.1 INTRODUCTION For p-n Si solar cells, the minority carrier lifetime or diffusion length is the most important electronic material parameter. From the viewpoint of the device, the charge collection probability can be regarded as the electronic property that determines performance. Bulk and surface recombination can affect the collection probability in a similar way. Therefore, most measurement techniques do 65 66 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS not allow a unique access of both recombination parameters. This fact leads to the introduction of an effective diffusion length. Sometimes a separation of bulk and surface recombination parameters is actually not even wanted. For example, the knowledge of an effective diffusion length for homogeneously distributed dislocations can be more useful for solar cell design than would be the knowledge of the exact recombination parameters at each dislocation. In the subsequent sections, different definitions of effective diffusion length are reviewed. The common idea of these definitions is to compare a particular parameter for an arbitrary specimen with that of a semi-infinite reference specimen with homogeneous diffusion length.

5.2 REVIEW ON DEFINITIONS OF EFFECTIVE DIFFUSION LENGTH

5.2.1 Quantum Efficiency Effective Diffusion Length For a homogeneous semi-infinite solar cell (W → ∞) with base diffusion length L the collection probability in the base is given by the exponentially decaying function ϕ(z) = exp(−z/L). This function is a special case of Eq. (4.34), with A = 1 and B = 0. If the, ideal collecting, junction is located at z = 0 and the emitter and the space charge region are assumed to have no spatial extend, Eq. (4.46) yields a linear relationship between the inverse quantum efficiency IQE−1 and the inverse of the absorption length α−1 1 1 = +1. (5.1) IQE(λ) α(λ) L

For finite widths of emitter We and space charge region Wscr this formula still −1 holds for absorption lengths α > We + Wscr. This relationship is the starting point for diffusion length extraction from quantum or collection efficiency data [191]. Note that the linear relationship between IQE−1 and α−1 is a result of the special, exponentially decaying collection probability function, which applies to solar cells with infinite base thickness. However, real devices do not extend infinitely and often material properties are not homogeneous, as is generally the case for multicrystalline solar cells. Still, in many cases the projection of the three-dimensional charge collection

5.2 Review on Definitions of Effective Diffusion Length 67

2.0 -1 15.7 µm -1 W = 30 µm, s = 0.0005 µm W = 30 µm, s = ∞ 15 µm 1.8 14.5 µm W = ∞ 51.4 µm 1.6 L = 15 µm eff,IQE 27 µm 1.4 L = 23.3 µm

1.2

Inverse quantum efficiency IQE L = 27 µm eff,IQE 1.0 02468101214 -1 Absorption length α [µm]

Figure 5.1 Two groups of IQE−1 vs. α−1 curves that yield the same effective diffu-

sion lengths, Leff,IQE = 15 µm and Leff,IQE = 27 µm, respectively. In the semi- infinite case (solid line) the relationship is linear, while for finite thickness the plots are curved (dashed and dotted lines). The curvature depends on the ratio of bulk diffusion length L and base thickness W, and is biggest for the largest L/W value. The plots were calculated from Eqs. (4.37) and (4.46). probability ϕ(r) on the z coordinate can be well approximated by the one- dimensional function

ϕ(z) = exp(−z / Leff ). (5.2) A prerequisite for this approximation to be valid is a bulk diffusion length L smaller than the device thickness W. For the collection probability given by Eq. (4.34), this is the case if A >> B. If Eq. (5.2) describes the actual collection efficiency well, then function Eq. (5.1) holds with L replaced by Leff. With the con- straint L << W Dugas and Qualid have defined an effective diffusion length by −1 −1 the slope 1/Leff of a linear fit to the IQE vs. α graph in the regime We << −1 α << W, where We is the emitter thickness [192]. In many of today’s crystalline Si solar cells, the bulk diffusion length exceeds the cell thickness. In this case, the linear relationship by Eq. (5.1) does not hold anymore and the IQE−1 vs. α−1 graph is curved (Fig. 5.1). The larger the ratio

68 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS

L/W, the larger the curvature. Therefore, Eq. (5.1) is not suitable for a general definition of an effective diffusion length. Such a definition has to use a fixed absorption length at which the slope of the IQE−1 vs. α−1 curve is evaluated. This is taken into account in the following definition of quantum efficiency effective diffusion length as given by Brendel (Ref. [59], p. 55).26

−1 −1 1 dηc dIQE = −1 ≅ −1 . (5.3) L dα dα −1 eff,IQE α −1=0 α =0

While the evaluation at α−1 = 0 is advantageous from theoretical considerations – as shown below – a drawback from a practical point of view is that for real solar cells the slope of the IQE−1 vs. α−1 curve at α−1 = 0 is dominated by the emitter (see inset in Fig. 5.2). The computation of the base effective diffusion length Leff,IQE as defined by Eq. (5.3) therefore requires an extrapolating fit to the −1 −1 –1 –1 IQE vs. α curve from the region We < α < W to the point α = 0. Spiegel et al. have proposed the use of a quadratic fit to evaluate Leff,IQE [193]. However, the fit range has to be restricted to α−1 < W/4. Further, in this range the condition α−1 < L must be fulfilled, limiting the applicability of their model. With similar computational effort and without these restrictions the exact analytical function given by Eqs. (4.37) and (4.46) can be fitted, as pointed out by Isenberg et al. [194].

5.2.2 Collection Effective Diffusion Length For solar cells with bulk diffusion length exceeding the device thickness, plots of inverse quantum efficiency IQE−1 versus absorption length α−1 usually show a second linear regime for photons with energy near the band-gap (Fig. 5.2). In this regime the absorption length α−1 is much larger than the cell thickness W and the photogeneration rate can be considered as spatially homogeneous. In accordance with Brendel (Ref. [59], p. 55) we name the quantity Leff,c defined by

26 −1 ηc and IQE are equal if fabs = 1−R [see (4.45)]. At α = 0, the optical properties of the device’s rear side do not have any affect on the internal quantum efficiency. Therefore the condition fabs = 1−R is satisfied if parasitic absorption is absent.

5.2 Review on Definitions of Effective Diffusion Length 69

3.0 -1 Slope 1/L = 1/340 µm eff,c 2.5

2.0 Slope 1.3 1/L = 1/39 µm eff,IQE 1.2 1.5 1.1

1.0 Inverse quantum efficiency IQE efficiency quantum Inverse 1.0 024681012 0 100 200 300 400 500 -1 Absorption length α [µm]

Figure 5.2 Plot of inverse quantum efficiency IQE−1 versus absorption length α−1, for a typical c-Si thin-film solar cell as investigated in this work. The effective diffusion lengths Leff,IQE and Leff,c are determined from fits to the data in the two – to a first approximation – linear regimes.

1 dIQE−1 = (5.4) L dα −1 eff,c α −1=∞ collection effective diffusion length, where the index (α−1 = ∞) indicates the evaluation at large absorption length [59]. In the case of homogeneous generation, the internal quantum efficiency depends less on electronic than on internal optical properties.27 Basore has developed an analytical model that allows one to assess the internal optical properties of a solar cell from the quantity Leff,c [188].

Using a linear approximation, Leff,c is connected to the collection efficiency for near band-gap wavelength ηc,∞ by

Leff,c = fopt Wηc,∞ , (5.5)

27 In this definition the quantity IQE has to be used. In the case of large absorption length, ηc −1 (and thus ηc ) is constant. Note that the generation rate in the function IQE is normalized to the incident spectral photon flux [Eqs. (4.46) and (4.7)] while the generation rate in the function ηc is completely independent from any optical properties [Eqs. (4.43) and (4.8)].

70 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS where W is the device thickness and fopt is a function that solely depends on the optical properties of the solar cell.

5.2.3 Current-Voltage Effective Diffusion Length

As can be seen from Eq. (4.23) the saturation current density J0,B is proportional to the inverse of the diffusion length Ln. The derivation of this formula was based on the decay of the minority carrier excess concentration in the base quasineutral region assuming infinite extend. An effective diffusion length for an arbitrary specimen can be defined by taking the semi-infinite specimen as reference and comparing the saturation currents. Starting from the charge collection probability ϕ, the minority carrier density at high reverse bias in the dark is n0(1-ϕ) [195]. For an arbitrary specimen the saturation current is then given by

dϕ(x, y, z) , (5.6) I0,B = qn0 Dn ∫∫ dxdy yx dz z=0 where x and y integrations are over the (unit) cell’s junction plane with area A. For a semi-infinite reference specimen with same area A and spatially homogeneous diffusion length Leff the charge collection probability is given by Eq. (5.2), and Eq. (5.6) yields

qDnn0 A I0,B,ref = . (5.7) Leff

An effective diffusion length Leff,J0 can be defined as the value of Leff for which the saturation current of the semi-infinite reference specimen I0,B,ref [Eq.

(5.7)] is equal to that of the arbitrary specimen I0,B given by Eq. (5.6). Therefore, qD n A L = n 0 . (5.8) eff,J0 I0,B

The saturation current J01 = J0,E + J0,B can be determined from the second linear regime in a semi-logarithmic plot of the dark I-V curve. Brendel therefore

names the property Leff,J0 current-voltage effective diffusion length (Ref. [59], p. 56). However, in practice the determination of an effective diffusion length from the dark I-V curve is less accurate than from IQE data. Therefore it is useful to note that the quantum efficiency effective diffusion length Leff,IQE as defined Eq.

5.2 Review on Definitions of Effective Diffusion Length 71

(5.3) is identical to Leff,J0 [188]. On the base of the charge collection reciprocity

theorem, Brendel and Rau have proven that the equality Leff,IQE ≡ Leff,J0 also holds for material with inhomogeneous diffusion constant and carrier lifetime [196]. If potential fluctuations are taken into account, this relation still holds locally,

while for the global electronic properties Leff,IQE > Leff,J0.

As an example, the effective diffusion length Leff,J0 is derived for the important case of a solar cell with homogeneous bulk diffusion length L, finite base thickness Wb, and finite back surface recombination velocity s. The charge collection probability for this case was derived in Section 4.4.2. Substitution of Eq. (4.37) into Eq. (5.6) and the use of definition (5.8) yields the often cited relation (see, e.g., Ref. [177], p. 89) L L = , (5.9) eff,J0 fgeom with the geometry factor

Lscosh(Wb /L) + sinh(Wb /L) fgeom = . (5.10) cosh(Wb /L) + Lssinh(Wb /L)

5.2.4 Donolato’s Definition of Effective Diffusion Length In his analytical models for the effect of dislocations [197, 198] and grain boundaries [195], Donolato has used a special definition of an »effective diffusion length«, which is based on the comparison of the short circuit current under homogeneous generation conditions. If minority carriers are generated with homogeneous rate G within a unit cell of volume Vc, the current collected at the junction is

I qG (r)dV . (5.11) sc = ∫ϕ Vc

This equation is a direct consequence from the definition of ϕ(r) by Eq. (4.29). For a semi-infinite reference specimen with same cell dimensions, and with spatially homogeneous diffusion length Leff, the charge collection probability is given by Eq. (5.2), and Eq. (5.11) yields

Isc,ref = q AG Leff , (5.12)

72 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS where A is the area of the unit cell’s junction.

Donolato now defines the effective diffusion length Leff,D as the value of Leff for which the current density of the semi-infinite reference specimen Isc,ref [Eq.

(5.12)] is equal to that of the arbitrary specimen Isc given by Eq. (5.11). There- fore, 1 L = ϕ(r)dV . (5.13) eff,D A ∫ Vc The connection between charge collection probability and effective diffusion length is visualized in Figure 5.3.

Both, the current-voltage effective diffusion length Leff,J0 (being equal to

Leff,IQE) and Donolato’s effective diffusion length Leff,D are based on the comparison of a particular quantity (I0,B and Isc respectively) with the corresponding quantity of a semi-infinite reference specimen with spatially homogeneous diffusion length Leff. The collection probability of this reference is given by Eq.

(5.2). As a consequence, for an arbitrary collection probability ϕ(r), Leff,IQE and

Leff,D are similar if ϕ(r) can be well approximated by the one-dimensional function exp(−z/Leff). However, for a specimen of finite thickness Leff,D generally differs from Leff,IQE. Since Donolato’s definition is based on an integration over the 28 cell’s volume the maximum value of Leff,D directly depends on the thickness W. As an example, two extreme cases shall be considered: (i) For ideal collection properties ϕ(z) ≡ 1, corresponding to L → ∞ and s = 0. In this case, Eq. (5.13) yields Leff,D = W. (ii) For L → ∞, but infinite recombination velocity at the back (s → ∞) we have ϕ = 1 − Wz, i.e., ϕ is given by the line through the points (0,1) and (W,0) (see Fig. 5.3). In this case, Leff,D = ½ W (see also Table 5.3). From practical and physical points of view there are some disadvantages in

Donolato’s definition of effective diffusion length: (i) Leff,D is not compatible with standard measurement methods that rely on the slope of IQE−1 vs. α−1

curves, (ii) Leff,D differs from the effective diffusion length Leff,J0 that determines the solar cell’s open circuit voltage, and (iii) most importantly, homogeneous generation does not correspond to the typical operation conditions of a solar cell.

28 For the reference specimen the z integration range is retained at {0,∞}.

5.2 Review on Definitions of Effective Diffusion Length 73

1.0 ϕ -1 0.8 (iii) W = 30 µm; s = 0.005 µm

0.6

0.4 (i) W = ∞

0.2 (ii) W = 30 µm; s = ∞ Charge collection probability probability collection Charge

0.0  01020L30 40 eff,IQE Distance from junction z [µm] Figure 5.3 Charge collection probability function ϕ(z) for (i) a semi-infinite specimen, (ii) a specimen with thickness W = 30 µm and infinite surface recombination velocity s, and (iii) a specimen with finite thickness W = 30 µm and finite reduced surface recombination velocity s = 0.005 µm−1. The quantum efficiency

effective diffusion length Leff,IQE is given by the inverse of the slope of ϕ at z = 0, and has the value 22.8 µm in all three cases. The effective diffusion length as de-

fined by Donolato Leff,D is equal to the integral over ϕ. For case (i) Leff,D has the same value as Leff,IQE, by definition. In the cases (ii) and (iii) Leff,D differs from Leff,IQE. The curves were calculated with a bulk diffusion length L0 = 30 µm.

Photons with near band-gap energy contribute to a very small portion of total irradiated energy only.

Connection between Leff,c and Leff,D For spatially homogeneous generation, the normalized generation rate g [Eq. (4.8)] must be equal to 1/W. Insertion into Eq. (4.43), use of Eq. (4.44), and comparison with Eq. (5.13) yields 1 η = L . (5.14) c,∞ W eff,D Referring to Eq. (5.5) it is easily seen that the collection efficiency effective diffusion length Leff,c and Donolato’s effective diffusion length Leff,D are related by

74 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS

Table 5.1 Comparison of different definitions of effective diffusion length. They all relate a particular quantity for an arbitrary specimen to the equivalent quantity of semi-infinite reference specimen with homogeneous diffusion Leff and collection probability ϕ(z) = exp(−z/Leff).

Quantum efficiency Current-voltage Donolato’s Collection effective effective effective efficiency effective diffusion length diffusion length diffusion length diffusion length

Symbol L L L eff,IQE Leff,J0 eff,D eff,c

Quantity dη −1 I0,B Isc for Isc for compared c homogeneous homogeneous dα −1 with α −1 =0 generation generation reference (without int. refl.) (incl. int. refl.) Relation to 1 ∂ϕ 1 ∂ϕ L ∝ ϕ(r)dV L ∝ f ϕ(r)dV collection ∝ ∝ eff,D ∫ eff,c opt∫ Leff,IQE ∂z z=0 Leff,J ∂z z=0 V V efficiency ϕ 0 c c Connection Leff,IQE ≡ Leff,J0 Leff,c ≡ fopt Leff,D

Leff,c = fopt Leff,D (5.15) and differ only by the function fopt, which describes the internal optical properties of the device. Evaluation of Leff,D/W by inserting Eq. (4.37) into Eq. (5.13) indeed yields the explicit formula for ηc given by Basore for near band-gap wavelengths [188]. Table 5.1 summarizes the main aspects of the different definitions of effective diffusion length. As a conclusion from the discussion above, the subsequent work builds up on the quantum efficiency effective diffusion length Leff,IQE.

5.3 EFFECTIVE DIFFUSION LENGTH FOR TEXTURED CELLS In order to determine the diffusion length from IQE data on a surface textured cell, the oblique light path has to be taken into account. In this case, α has to be replaced by α/cosθ in the generation function given by Eq. (4.7). For a ray entering the semiconductor normal to the surface, θ is the angle between the surface normal and the direction of the refracted ray inside the semiconductor. For the special case of a semi-infinite specimen and ϕ(z) = exp(−z/L), the internal quantum efficiency is given by

5.4 Effect of Dislocations on Effective Diffusion Length 75

∞ α z z ∞ z cosθ ∞ cosθ α − − α − (α + ) IQE = ∫e cosθ e L dz = ∫e cosθ L dz = α ∫e−z′α e L dz′, cosθ 0 cosθ 0 0 where z′ = z/cosθ. This is the same equation as for the planar case with L replaced by L/cosθ. Therefore, when determining diffusion length from a IQE−1 vs. α−1 plot, the inverse slope has to be multiplied by cosθ:

Ltext = Lcos θ . (5.16)

For chemically textured 〈100〉 oriented Si θ is 41.8° for λ ≈ 900 nm [188], yielding cos θ = 0.745.

5.4 EFFECT OF DISLOCATIONS ON EFFECTIVE DIFFUSION LENGTH In the investigated Si thin films, dislocations are the dominating defects that limit device performance. The theoretical basis for a quantitative description of dislocation recombination activity is developed in the subsequent sections. Different models have been proposed to describe the effect of dislocations on minority carrier effective lifetime or diffusion length [199–201]. The model developed by Donolato [197, 198] starts from a geometric description that is much closer to the physical reality than most of the models developed before. The predicted dependence of effective diffusion length on dislocation density matches well to experimental data and has been used to evaluate dislocation recombination strength values on Si solar cells [202-205]. Donolato analyzed the effect of dislocations from the viewpoint of charge collection at a p-n junction of a semi-infinite dislocation-containing specimen. However, it was found [198] that the predicted dependence of effective diffusion length (or carrier lifetime) on dislocation density is very close to the description of van Opdorp et al. [200], who analyzed an infinite semiconductor while modeling the dislocations in a similar way. Riepe et al. published an analysis based on similar assumptions as those made by van Opdorp et al. [206]. Numerical data show a close connection between the three models [207]. For a set of given recombination parameters, the curves of effective diffusion length (or lifetime) versus dislocation density are very similar. The following sections first review the original derivation of Donolato’s model. Then modifications and extensions are discussed that adapt the model to

76 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS the needs in this work: (i) The discussion before showed that the consistent use of the quantum efficiency effective diffusion length is advantageous. The standard methods to determine effective diffusion length from quantum efficiency and spatially resolved light beam induced current (SR-LBIC) data rely on this definition. (ii) The films analyzed in this work incorporate a highly doped BSF region to decrease recombination at the rear. Neither Donolato’s derivation for a semi-infinite specimen nor the extension for a specimen of finite thickness and infinite surface recombination velocity at the back (ohmic contact) provide an appropriate description. Therefore, a modeling for specimen of finite thickness and finite recombination velocity at the back is needed.

5.4.1 Donolato’s Model for a Semi-Infinite Specimen

Geometric Model The basic geometric arrangement for Donolato’s model is a neutral semiconductor half space (z > 0) where the surface plane (z = 0) coincides with the edge of the p-n junction (Fig. 5.4a). Dislocations are assumed as a hexagonal array of straight dislocation lines perpendicular to the surface with spacing d (Figs. 5.4b and c). Because of the periodicity of the arrangement, the carrier transport problem can be restricted to one unit cell. Approximating the hexagonal unit cell by a cylindrical cell with radius a, the problem can be treated in cylindrical coordinates. Dislocation distance d and unit cell radius a are then related by 1/2 2 2 3 /2 d = πa , and the dislocation density ρd is connected to a by 1 ρ = . (5.17) d π a2

The dislocation is described as a recombination line, characterized by a line recombination velocity γd. Donolato defines this quantity as the ratio between the incoming flux of minority carriers per unit length and excess carrier density. In closer analogy to the definition of the surface recombination velocity S by Eq.

(4.2), γd can equally be defined as the ratio between a line recombination rate and the excess carrier density, where the line recombination rate is given by the number of recombination events per unit length and unit time.

5.4 Effect of Dislocations on Effective Diffusion Length 77

d a

y x z (b) 2 ε

a z = 0 junction W

dislocation core recombination velocity s

(a) (c) (d) Figure 5.4 Schematic device structures used for the Donolato model: (a) Semi- infinite specimen with homogeneous material properties. (b) Top view on dislocation array and approximation of the hexagonal unit cell by a cylinder. (c) Semi- infinite specimen with dislocation core and unit cell. (d) Dislocated specimen of finite thickness and finite surface recombination velocity at the rear.

In Donolato’s model, γd is assumed to be constant. However, like at grain boundaries or coated surfaces, an injection dependence of recombination at dislocations has been observed by EBIC measurements [208–210]. The microscopic mechanisms are still unclear and many observations can be explained by both, the charge-controlled model by Wilshaw et al. [208] and the common Shockley-Read-Hall model, as shown by Kittler and Seifert [210]. Treating the parameter γd as constant, the analysis strictly applies to low injection conditions only.

The quantity γd is also called recombination strength [211] and has the same dimension as the diffusion constant D. Dividing γd by D, the dimensionless parameter normalized recombination strength is obtained γ Γ = d . (5.18) d D

78 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS

Differential Equation and Boundary-Value Problem The carrier transport problem is described by the differential equation (4.32), which in cylindrical coordinates reads

1 ∂  ∂ϕ  ∂ 2ϕ 1 r  + 2 − 2 ϕ = 0 , (5.19) r ∂r  ∂r  ∂z L0 where L0 is interpreted as the minority carrier diffusion length in the semiconductor without dislocations. At the collecting plane (z = 0) ϕ must fulfill boundary condition (4.33), i.e., ϕ(r,0) = 1, (5.20) while in the limit z → ∞ the boundary condition is limϕ(r, z) = 0 . (5.21) z→∞

For symmetry reasons the radial gradient of ϕ must vanish at the cylinder’s surface (r = a), yielding the boundary condition

∂ϕ = 0. (5.22) ∂r r=a According to the reciprocity theorem, the boundary condition at the dislocation line is the same that would apply to the excess carrier problem. Eq. (4.31) adapted to the line geometry reads [198]

 ∂ϕ  lim2π r  = Γdϕ(0, z) . (5.23) r→0 ∂r  A solution that satisfies differential Eq. (5.19) with boundary conditions

(5.20) and (5.21) is exp(−z/L0). Donolato therefore uses the ansatz

ϕ(r, z) = exp(−z / L0 ) − u(r, z) , (5.24) where the first term represents the collection probability in the dislocation-free material and u is interpreted as the reduction of this probability due to the dislocations. Using the Fourier sine transform of u

∞ u~(r,k) = ∫ u(r, z)sin(k z) dz (5.25) 0

5.4 Effect of Dislocations on Effective Diffusion Length 79

Eq. (5.19) can then be transformed into the ordinary differential equation

1 ∂  ∂u~  r  − µ 2u~ = 0, (5.26) r ∂r  ∂r  where

2 1 µ = k + 2 . (5.27) L0

The general solution to Eq. (5.26) is a linear combination of modified Bessel functions of order zero, I0 and K0 [212] ~ u = AI 0 (µr) + BK 0 (µr) . (5.28) The constants A and B are determined by the Fourier sine transforms of the boundary conditions (5.22) and (5.23), respectively. A difficulty arises with the transformed form of (5.23) because K0(µr) is singular for r → 0. Donolato circumvents this problem by replacing ũ(0,k) by the average value of ũ(r,k) over a small circle with radius ε around r = 0. From a physical point of view this approximation can be interpreted as attributing a finite cross section ε to the dislocation line (see Figs. 5.4c). The way ε is introduced leads to the supposition that the final result should not be very sensitive to the parameter ε. Indeed, Donolato has shown for numerical data that a variation of ε by one order of magnitude results only in a slight change in the Leff vs. ρd curve [198]. Performing the averaging around r = 0 and considering the boundary conditions, the final expression for ũ is Γ k K (µr) + [K (µa) I (µa)]I (µr) u~(r,k) = d 0 1 1 0 , (5.29) 2π 2 Γ µ 1+ d H (µε, µa) π where

1 − µεK1(µε) I1(µε )K1(µa) H (µε,µa) = 2 2 + , (5.30) µ ε µε I1(µ a) and I1 and K1 are modified Bessel functions of order one. The collection probability ϕ can finally be obtained by substituting Eqs. (5.29) and (5.30) into the inverse Fourier sine transform

80 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS

2 ∞ u(r, z) = ∫ u~(r,k)sin(k z) dk (5.31) π 0 and then substituting the resulting function into Eq. (5.24).

Effective Diffusion Length According to Donolato’s Definition The dependence of effective diffusion length, according to Donolato’s definition, on dislocation density ρd is obtained by substituting the expression for the charge collection probability ϕ [given by Eqs. (5.24), and (5.29) to (5.31)] into the definition of Leff,D by Eq. (5.13). The volume integration involved can be carried out analytically and the final expression is

2 ∞ 1 dk L = L − ρ Γ . (5.32) eff,D 0 d d ∫ 4 π µ Γd 0 1+ H (µε,µa) π

Effective Diffusion Length According to the Quantum Efficiency Definition In order to modify Donolato’s model for use with the quantum efficiency

effective diffusion length Leff,IQE, the identity Leff,IQE ≡ Leff,J0 can be used. The

right hand side (Leff,J0) is evaluated by definition (5.8) and Eq. (5.6). Using the 2 relationship A = πa = 1/ρd for the junction area of the unit cell A, the average saturation current density I0,B/A is given by

I a ∂ϕ 0,B I qD n 2 rdr = ρd 0,B = −ρd n 0 ∫ π . (5.33) A 0 ∂z z=0

In the above equation ϕ has to be substituted by Eq. (5.24), and Eqs. (5.29) to (5.31). The differentiation with respect to z and the integration over the volume (i.e., r and z) can be performed analytically. However, this is not possible for the wave vector k and yields

I qD n 2 ∞ k 2 dk 0B = n 0 + ρ qD n Γ . (5.34) d n 0 d ∫ 4 A L π µ Γd 0 0 1+ H (µε,µa) π Through definition (5.8), the final expression obtained is

5.4 Effect of Dislocations on Effective Diffusion Length 81

1 1 2 ∞ k 2 dk = + ρ Γ . (5.35) d d ∫ 4 L L π µ Γd eff,IQE 0 0 1+ H (µε,µa) π

Comparing this expression with the one for Leff,D [Eq. (5.32)], the following difference in structure is noticeable: While in Eq. (5.32) the effective diffusion length Leff,D is obtained by subtracting a dislocation term from the diffusion length in the dislocation-free sample L0, in Eq. (5.35) the inverse effective diffu- −1 −1 sion length Leff,IQE is the sum of the inverse diffusion length L0 and the dislocation term. This finding becomes clear when recalling the definition of current- voltage effective diffusion length [Eq. (5.8)]. The effective diffusion length

Leff,IQE is proportional to the inverse of the total recombination current, which equals the recombination current in the device without dislocations, plus the dislocation induced recombination current. This behavior is similar to a situation analyzed by Sinton, who discussed the averaging of effective lifetime in a multicrystalline wafer with highly conductive emitter and grains exhibiting different bulk lifetimes [213].

Approximate Form

In order to fit the functions Leff,D(ρd) or Leff,IQE(ρd) to experimental data, the forms given by Eqs. (5.32) and (5.35), respectively, are not very convenient. The numerical evaluation of the integral is time consuming since at each interpolation node several Bessel functions have to be evaluated. Therefore, a closed form approximation is desirable. Donolato has derived such an expression for

Leff,D given by Eq. (5.32) [198]. In the next paragraphs the derivation of the closed form approximation of Leff,D(ρd) by Donolato is reviewed, and in parallel similar considerations are applied for a closed form approximation of Leff,IQE(ρd).

Exchanging the integration variable from k to t = kL0, Eq. (5.32) can be written

∞ 2 3 1 dt L = L − ρ Γ L eff,D 0 d d 0 ∫ 4 Γ 1−νε K (ν ε ) I (ν ε )K (ν a) π 0 ν d 1 1 1 1 + 2 2 + π ν ε ν ε I1(ν a) (5.36) ∞ 2 3 L − L (t)dt , = 0 ρdΓd 0 ∫ Λ D π 0

82 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS

2 1/2 where ν = (1 + t ) ,ε = ε/L0, anda = a/L0. The value of the integrand ΛD(t) is dominated by the first term 1/ν4, which for large t varies with t as 1/t4 (Fig. 5.5). Application of the same transformation to Eq. (5.35) yields

1 1 2 ∞ t 2 dk = + ρ Γ L d d 0 ∫ 4 Γ 1−νε K (ν ε ) I (ν ε )K (ν a) Leff,IQE L0 π 0 ν d 1 1 1 1 + 2 2 + π ν ε ν ε I1(ν a) (5.37) 1 2 ∞ + L (t)dt . = ρdΓd 0 ∫ Λ IQE L0 π 0

2 In this case, the first term in the integrand ΛIQE(t) varies for large t as 1/t .

Therefore, ΛIQE(t) decays much slower than in the former case (Fig. 5.5). Note that the functions in Figure 5.5 are plotted on a logarithmic scale for the abscissa and therefore the areas below the curves are not proportional to the integral values. To allow the use of common small argument approximations for the modified Bessel functions [212] the conditionsεν << 1 andaν << 1 have to be satisfied.

Assuming ε = 0.01 µm and L0 > 100 µm the first condition is fulfilled if t << 10000. As can be taken from Figure 5.5, the major contribution to the integral, for typical dislocation density values, is in the range t < 3 (ΛD) and t < 30 29 (ΛIQE), respectively. This justifies the use of the following approximations, valid for smallεν

1−ν ε K (ν ε ) 1  ν ε  1 1 ≅ − ln − C + 2 2     ν ε 2  2  2   (5.38) I (ν ε ) 1 1 ≅ , ν ε 2 where C is Euler’s gamma constant, with numerical value ≈ 0.577 216.

The second conditionaν << 1 involves the dislocation density ρd. Making the 5 −2 same assumptions concerning ε and L0 as above and taking ρd = 10 cm , the 8 −2 requirement to fulfillaν << 1 is t << 6. For ρd = 10 cm it is t << 180. Consult-

29 The discussion here does not consider the dependence on the recombination strength Γd.

However, for small t the denominator in ΛIQE(t) and ΛD(t) is controlled by the second term.

Therefore Γd essentially just scales the integrands ΛIQE(t) and ΛD(t).

5.4 Effect of Dislocations on Effective Diffusion Length 83

0.6 Λ D 6 -2 Λ ρ = 10 cm IQE d ε = 0.01 µm Λ 0.4 L = 100 µm 0 Γ = 0.005 d

7 -2 Integrand 0.2 10 cm 106 cm-2

107 cm-2

0.0 0.1 1 10 100 Integration variable t

Figure 5.5 Integrands ΛD (dashed line) and ΛIQE (solid line) as a function of the variable t, plotted on a logarithmic scale. The integration of these terms is needed for the calculation of Leff,D and Leff,IQE by Eqs. (5.36) and (5.37), respectively.

ing again Figure 5.5 we note that the major contribution of ΛD is below these limits. However, for ΛIQE the condition aν << 1 is only valid in the case of a very high dislocation density. If the »high dislocation density condition« is applicable, the following approximation is justified

K1 (ν a) ν a  2 ≅ ln  + 2 2 . (5.39) I1 (ν a)  2  ν a Substituting Eqs. (5.38) and (5.39) into Eq. (5.36) and performing the integration yields the final approximate expression

−1/ 2      1 ρdΓd  Leff ≅  +  . (5.40) 2 Γ 1 L0 d   1+ − ln(ε πρd ) − C +   2π  2 By insertion of Eqs. (5.38) and (5.39) into (5.37) instead, exactly the same expression as above is obtained as an approximation to Leff,IQE.

For example, in Figure 5.6 the modeled dependence of Leff on ρd is plotted using typical device data. The function Leff(ρd) has been calculated (i) based on

84 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS

100 5x108 6x108 6.4 [µm]

eff 6.2 80 6.0 97.8 5.8 97.6 60 97.4 97.2

40 5 105 1.2x10

L 20 eff,IQE Leff,D L Effective diffusion length L Effective diffusion eff,approx 0 104 105 106 107 108 109 -2 Dislocation density ρ [cm ] d Figure 5.6 Dependence of effective diffusion length on dislocation density for the

semi-infinite specimen. Compared are the exact functions Leff,D(ρd) by Eq. (5.32),

Leff,IQE(ρd) by Eq. (5.35), and the approximate form by Eq. (5.40). For numerical evaluation of the exact expressions the upper integration limit was set to 1000/L0. (Fixed parameters: ε = 0.01 µm, L0 = 100 µm, and Γd = 0.005.)

Donolato’s definition of effective diffusion length [Eq. (5.32)], (ii) the quantum efficiency effective diffusion length [Eq. (5.35)], and (iii) the approximate form given by Eq. (5.40). The only slight difference between the three curves is visible in the region of very high dislocation density. In this region Leff,IQE(ρd) differs marginally from Leff,D(ρd) and the approximate form Leff(ρd). Two reasons might be responsible: firstly, from the approximations involved it is clear that

Leff(ρd) does not approximate Leff,IQE(ρd) as well as it does Leff,D(ρd). Secondly, the difference may also be caused by the numerical integration of the »exact« formulas. Recalling the discussion on definitions of effective diffusion length the following conclusions can be drawn for the semi-infinite specimen. By definition,

Leff,D and Leff,IQE are identical for the special charge collection probability function ϕ(z) = exp(−z/Leff). Therefore, if for an arbitrary charge collection probability function ϕ(r), Leff,D and Leff,IQE yield similar values, it can be assumed that the

5.4 Effect of Dislocations on Effective Diffusion Length 85

-1 IQE 25 Fit A Fit B 8 -2 ρ = 10 cm 0.01–0.05 µm 10 –100 µm 20 d ρd Leff Leff,IQE Leff Leff,D [cm−2] [µm] [µm] [µm] [µm] 15 0 100.0 100.0 100.0 100.0 10 106 104 83.23 83.22 83.62 83.63 5 106 13.74 13.72 13.89 13.89 104 8 1 0 10 1.254 1.253 1.265 1.265 0 20406080100 -1 α [µm] Fixed parameters: ε = 0.01 µm, L0 = 100 µm, Γd = 1 (a) (b)

Figure 5.7 (a) Plots of IQE−1 vs. α−1 using Donolato’s model for the effect of dislocations. (b) Comparison of numerical data for Leff obtained from linear fits to the plots in Fig (a) (fit A with fitting range α−1 = 0.01 µm to 0.05 µm, fit B −1 with fitting range α = 10 µm to 100 µm), and calculation of Leff,D and Leff,IQE by Eq. (5.32) and Eq. (5.35), respectively. The fits were not forced to go through (0,1). z dependence of the actual (three-dimensional) function ϕ(r) can be approximated well by the one-dimensional function ϕ(z) = exp(−z/Leff).

The finding above is supported by the data shown in Figure 5.7, in which Leff values from linear fits to the IQE−1 vs. α−1 curve are compared to results by Eqs. (5.32) and (5.35). On one hand, the function IQE−1(α−1) was evaluated at dis- −1 crete absorption length values αi using Eqs. (4.46), (4.7), and the expressions for the collection efficiency provided by Eqs. (5.24), and (5.29) to (5.31)30. −1 −1 Then, Leff was determined from a fit to the data points IQE (αi ). In case A, Leff −1 −1 −1 was evaluated based on data points at α1 = 0.01 µm, α2 = 0.02 µm, …, α5 = −1 −1 0.05 µm. In case B, Leff was evaluated based on data points at α1 = 10 µm, α2 −1 = 20 µm, …, α10 = 100 µm. On the other hand, Leff,D(ρd) and Leff,IQE(ρd) were computed by Eqs. (5.32) and (5.35), respectively.

Although the four Leff values for each ρd are quite similar, it is instructive to take a closer look at the small differences after the decimal point. For case A the

30 The resulting formula is also found in [197].

86 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS fit result is practically identical to the values of Leff,IQE, while for case B the fit results are closer to the values of Leff,D. This finding makes sense when recalling −1 −1 −1 that Leff,IQE is defined by the slope of the function ηc (α ) at α = 0 and Leff,D −1 −1 by the slope of ηc (α ) for homogeneous generation (usually corresponding to large α−1). A rough dimension criterion to divide between the two regimes is the 8 −2 diameter of the unit cell – e.g., 0.56 µm for ρd = 10 cm and 56 µm for ρd = 104 cm−2, respectively. If we assume that the dislocation line only enhances recombination in a low volume fraction, we can conclude that the radial variation in collection probability is small compared to the one in the z direction. This explains why both evaluation methods lead to similar results and the collection probability can well be approximated by ϕ(z) = exp(−z/Leff). For practical purposes, the deviations found in the case of the semi-infinite specimen are not relevant. Experimental data can be fitted well by both functions, Leff,D(ρd) and Leff,IQE(ρd). The situation is different for the case of finite thickness as will be shown below.

5.4.2 Model for a Specimen of Finite Thickness For actual devices, such as p-n junction crystalline Si solar cells, the semi- infinite model is an adequate approximation as long as the bulk diffusion length is much smaller than the base thickness. However, in most of today’s solar cells the bulk diffusion length exceeds the cell thickness, and this is also true for the investigated Si thin-film solar cells. Although Donolato has extended his analysis for the case of finite thickness and infinite back surface recombination velocity [198], again, these conditions do not fit our objectives since the investigated devices incorporate a BSF structure to decrease recombination at the rear. In the next section, a short review of Donolato’s solution to the problem with infinite surface recombination velocity is given. Then an extension of the model is presented, which was developed for devices with a finite thickness and a finite back surface recombination velocity.

Model for Infinite Surface Recombination Velocity For the problem of finite thickness and infinite surface recombination velocity at the rear, the problem to be solved is the same as that of Section 5.4.1, but with boundary condition (5.21) replaced by ϕ(W) = 0. The collection probability in

5.4 Effect of Dislocations on Effective Diffusion Length 87 the dislocation-free sample is then given by Eq. (4.38) and the Fourier expansion is in terms of discrete modes with wave vectors kn = nπ/h. Therefore, an infinite series instead of an integral is involved and the final expression reads

 W  4 ∞ 1 1 L = L tanh  − ρ Γ , n odd , (5.41) eff,D 0   d d ∑ 4 2L W µ Γd  0  n=1 n 1+ H (µ ε,µ a) π n n

2 2 1/2 where µn = (kn + 1/L0) [198].

Model for Finite Back Surface Recombination Velocity For the problem of finite thickness and finite surface recombination velocity at the rear (Fig. 5.4d), the appropriate boundary condition at z = W is given by Eq. (4.31), which for the concrete geometry is written

dϕ(r, z) = −sϕ(r,W ) . (5.42) dz z=W With this condition an approach equivalent to Eq. (5.24), which enables the transformation of the partial differential equation into an ordinary differential equation, is not possible. The solution in the z direction is no longer independent from the radial solution. To evaluate the left hand side of Eq. (5.42), the knowledge of the radial function ϕ (r,W) would be necessary. Instead of finding an exact solution to the boundary value problem, it is shown below that a good approximation is possible if the problem is split up into two steps: (i) calculation of the collection probability for the case of a dislocated semi-infinite specimen yielding a one dimensional projection of the charge collection probability function on the z axis ϕ (z), and (ii) »cutting off« the specimen at finite thickness by applying the appropriate boundary condition. A hint for the validity of the approximation involved in step (i) was given in the section before. The similarity of Leff,D(ρd) and Leff,IQE(ρd), as well as the line- arity of the IQE−1 vs. α−1 curves (Fig. 5.7) indicates that the charge collection probability ϕ (r,z) in the dislocated semi-infinite specimen is well described by the one-dimensional exponential decay ϕ (z) = exp(−z/Leff). Furthermore, physical arguments can be given for the »two-step approach«. Typical dislocation densities in multicrystalline Si range from 104 cm−2 to

88 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS

Table 5.2 Dependence of effective diffusion length Leff,D on dislocation density for a semiconductor of finite thickness and infinite surface recombination velocity at the back. For model A the values were calculated by the exact formula (5.41) while for model B the »two-step approach« described in the text was used. For numerical evaluation in model A [Eq. (5.41)] the sum was computed for 1000 terms, while in model B [Eq. (5.32)] the upper integration limit was set to

10000/L0. (Fixed parameters: W = 30 µm, ε = 0.01 µm, and L0 = 100 µm.)

−2 Γd ρd [cm ] Leff,D [µm]

Model A Model B

0.001 104 14.8884 14.8884 108 13.8744 13.8744 1012 0.3162 0.3162 1 104 14.8380 14.8412 108 1.2649 1.2649 1012 0.0102 0.0113

108 cm−2, corresponding to average dislocation distances d ranging from 100 µm to 1 µm. For very high recombination strength (Γd = 1) the effective diffusion length is in the same range as the average dislocation distance, as can be taken from the numbers tabulated in Figure 5.7b. However, typical Γd values are much lower ranging between 0.1 and 0.001. Therefore, the effective diffusion length exceeds the average dislocation distance. For example, L0 = 100 µm, Γd = 0.01, 6 −2 and ρd = 10 cm yield Leff = 71 µm, while the corresponding dislocation distance is 11 µm. This finding is reasonable since the small cross section of a dislocation should affect carrier transport much less than a recombination-enhanc- ing surface. From the viewpoint of the device, the above consideration justifies to model the dislocated material with homogeneous recombination properties.31 Practically the »two-step approach« is performed by (i) calculating the bulk effective diffusion length Leff,b(ρd) for the semi-infinite specimen containing dislocations by Eq. (5.32), (5.35), or (5.40) and (ii) inserting Leff,b(ρd) and the

31 The treatment here assumes that the back surface recombination velocity is independent from number and recombination strength of the dislocations. For high dislocation densities this assumption may not be valid [214].

5.4 Effect of Dislocations on Effective Diffusion Length 89

s = 0.005 µm-1 120 , W = 60 µm [µm]

eff L eff,IQE W = ∞ 100

60 s = ∞

-1 40 s = 0.005 µm

s = ∞ L 20 eff,D Effective diffusion length L 0 104 105 106 107 108 109 -2 Dislocation density ρ [cm ] d

Figure 5.8 Dependence of effective diffusion length Leff on dislocation density ρd for a specimen of finite thickness W. The functions based on Donolato’s definition of effective diffusion length Leff,D (dashed lines) are different from those based on the quantum efficiency definition of effective diffusion length Leff,IQE (solid lines). For comparison, the dependence is shown for the semi-infinite specimen (dotted line). In this case, Leff,D and Leff,IQE are (approximately) equal. (Fixed parameters: ε = 0.01 µm, L0 = 100 µm, and Γd = 0.005.)

back surface recombination velocity s into Eq. (4.37), yielding ϕ (ρd, z). Finally,

ϕ (ρd, z) is used to obtain Leff,D by Eq. (5.13) or Leff,IQE = Leff,J0 by Eq. (5.6) and

Eq. (5.8). The latter steps to calculate Leff,IQE are equivalent to the insertion of

Leff,b(ρd) and s into Eqs. (5.10) and (5.9). The »two-step approach« was tested for a specimen of finite thickness and infinite surface recombination velocity, where the analytical solution is known [Eq. (5.41)]. Table 5.2 presents computed data for parameters covering a broad range of dislocation density and recombination strength values. For numerical evaluation of Eq. (5.41) (model A) the sum was computed for 1000 terms, while for Eq. (5.32) (model B) the upper integration limit was set to 10000/L0. It was only in the case of an untypically high recombination strength Γd = 1 that mar- ginal differences were found. Consequently all computations for a specimen of finite thickness were performed by the »two-step approach«. The first step,

90 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS computation of Leff,b in the semi-infinite specimen, can be executed very fast if the approximate form by Eq. (5.40) is used.

Comparison of Leff,D and Leff,IQE for Finite Thickness

While for the semi-infinite specimen the functions Leff,D(ρd) and Leff,IQE(ρd) practically yield the same result (Fig. 5.6), the situation is completely different for the case of finite thickness. Figure 5.8 shows that Leff,D(ρd) and Leff,IQE(ρd) approach different limits for ρd → 0. Table 5.3 summarizes these limits for

ρd → 0, considering several extreme combinations of surface recombination velocity s and diffusion length L0. The discussion above could lead to the idea that the case of finite thickness might alternatively be approached by replacing the parameter L0 in the equations for the semi-infinite case [Eqs. (5.32), (5.35), or (5.40)] with an effective diffusion length L0,eff, which already includes the effect of the surface [205]. How- ever, Figure 5.9 shows that this approach would lead to inconsistent results.

Pairs of L0 and s, chosen to yield the same effective diffusion length in the dislocation-free specimen L0,eff (= Leff,IQE in the limit ρd → 0), result in different curves Leff,IQE(ρd) in the dislocated specimen. In a specimen with large bulk diffusion length L0 and high surface recombination velocity at the rear s, the charge collection efficiency, to a first approximation, decreases linearly with distance while in a specimen with small L0 and low s the charge collection efficiency drops quickly, but still has a significant value near the rear side [see, e.g., Fig.

Table 5.3 Limits of the functions Leff,D(ρd) and Leff,IQE(ρd) in the case ρd → 0 for a specimen of thickness W.

s L0 Leff,D Leff,IQE

W ∞ ∞ W 2 W (W s + 2) 1 Finite ∞ W + 2(W s +1) s

 W   W      0 Finite L0 tanh  L0 coth   2L0   L0  0 ∞ W ∞

5.5 Summary 91

-1 L (ρ → 0) = 30 µm L [µm] s [µm ] eff d 0 30 25 0.001 [µm]

eff 38 0.1 25 98 1

20 0.002 15 0.01 10 Γ = 0.05 5 Effective diffusion lengthL 0 105 106 107 108 109 1010 -2 Dislocation density ρ [cm ] d

Figure 5.9. Dependence of the function Leff(ρd) on the recombination parameters L0 and s for a specimen of thickness W. The combinations of L0 and s are chosen to yield the same (quantum efficiency) effective diffusion length Leff,IQE in the dislocation-free material (ρd → 0). (Fixed parameters: ε = 0.01 µm and W = 30 µm.)

5.3]. Therefore, in the latter case, a higher portion of carriers that are generated near the rear side contribute to the current. These charge carriers are more affected by dislocations than those that are generated near the junction. In conclusion, for fixed L0,eff, a specimen with small L0 and low s is more sensitive to dislocations than one with high L0 and high s. The net effect is similar to a change in the recombination parameter Γd. Therefore, not all three recombination parameters, L0, s, and Γd can be fitted simultaneously.

5.5 SUMMARY The concept of an effective diffusion length can be used to describe recombination at different sites in a semiconductor specimen (bulk, surface, etc.) by a single parameter. It is also useful to describe inhomogeneous materials such as multicrystalline Si wafers containing dislocations and grain boundaries. In the first part of this chapter different definitions of an »effective diffusion length« have been reviewed. All of these definitions compare the value of a particular

92 EFFECTIVE DIFFUSION LENGTH AND EFFECT OF DISLOCATIONS quantity in an arbitrary specimen to the corresponding value in a semi-infinite reference specimen. For the quantum efficiency effective diffusion length, this is the inverse IQE at absorption length α−1 = 0, for the current-voltage effective diffusion length it is the base saturation current density, for the effective diffusion length as defined by Donolato it is the short circuit current density, and for the collection efficiency effective diffusion length it is the slope of the inverse IQE in the limit α−1 → ∞. For the effect of dislocations on effective diffusion length, Donolato has presented an analytical model. However, the definition of »effective diffusion length« he introduced in the original work is not useful concerning (i) compatibility with common measurement methods and (ii) representation of the actual operational state of a solar cell. Donolato’s model therefore has been modified to be compatible with the »quantum efficiency effective diffusion length«. It has been shown that for a semi-infinite specimen it is not of importance whether Donolato’s or the quantum efficiency definition of effective diffusion length is used. However, for specimen of finite thickness both definitions yield very different results. Furthermore, Donolato’s model has been extended for the application to a thin specimen with a finite recombination velocity at the rear side. Since the associated boundary value problem does not allow a straightforward analytical solution, an approximate expression was derived and the method was validated by numerical computations using typical device data.

6 Characterization Methods The theory presented in the preceding chapter qualitatively correlates dislocation density with minority carrier lifetime. To apply this theory to experimental data, spatially resolved measurement techniques are necessary since most multicrystalline silicon materials are characterized by inhomogeneous defect distributions and inhomogeneous electronic properties. For lifetime measurements, in this chapter the methods of spectrally resolved light beam induced current (LBIC) and modulated free carrier absorption (MFCA) are examined. For spatially resolved measurements of dislocation density a system for automated etch pit density (EPD) mapping has been developed. It is build up on an automated microscope and digital image analysis. Meas- urements on a wide variety of materials are presented and strategies for material specific optimization are discussed.

6.1 DARK AND ILLUMINATED I-V CHARACTERISTICS The I-V curve measured under illumination provides the solar cell output

parameters open circuit voltage Voc and short circuit current density Jsc, as well

as voltage Vmp and current density Jmp at the point of maximum power generation. These parameters yield the fill factor FF defined by J V FF = mp mp , (6.1) JscVoc and the conversion efficiency

J V J V η = mp mp = FF sc oc , (6.2) E E where E is the solar irradiance. Standard measurement conditions regarding spectrum and cell temperature have been defined to make parameters comparable (see, e.g., Ref. [173], p. 98). All solar cell parameters in the subsequent

93 94 CHARACTERIZATION METHODS chapters refer to the AM 1.5 global spectrum with 1000 W m−2 irradiance and 25°C temperature. Further information can be obtained when the I-V curve is additionally measured in the dark. A fit of the two-diode model [Eq. (4.28)] to the acquired data yields these parameters: parallel resistance Rp, series resistance Rs, saturation current density of emitter and base J02, and saturation current density of space charge region J01. The ideality factors n1 and n2 can also be used as variable parameters. If the superposition principle (see Sec. 4.3.1) holds, the saturation current density J0 = J01 + J02 in the dark is the same as the one under illumination. The illuminated saturation current density determines open circuit voltage Voc. For the ideal diode case the dependence of Voc on J0 is easily seen by setting J = 0 in

Eq. (4.22) and solving for V. The open circuit voltage Voc is then obtained as

kBT  J L  kBT  J L  Voc = ln +1 ≈ ln  . (6.3) q  J 0  q  J 0 

In the two-diode model [Eq. (4.28)] a general analytical solution for Voc cannot be found. However, a (lengthy) analytical expression can be derived for the special case Rp = ∞.

6.2 SPECTRAL RESPONSE AND QUANTUM EFFICIENCY Light absorption in a semiconductor is a function of wavelength. Therefore, the measurement of wavelength dependent short circuit current allows the extraction of depth dependent device properties.

The spectral response SR is defined as the ratio of short circuit density Jsc to irradiance of monochromatic light E(λ) J (λ) SR(λ) = sc . (6.4) E(λ)

The external quantum efficiency (EQE) is obtained if the short circuit current density is not related to the incident energy but to the number of incident photons. The EQE is defined as the number of collected carriers under short circuit conditions, relative to the number of photons illuminating the cell. Equivalently, the EQE is given by the ratio of short circuit current density Jsc to incident light

6.2 Spectral Response and Quantum Efficiency 95 current density. The latter one is provided by the product of elementary charge q and photon flux Ep(λ). Thus, EQE and SR are related by J (λ) J (λ) hc hc EQE(λ) = sc = sc = SR(λ) . (6.5) qEp (λ) qE(λ) λ qλ

From the EQE the internal quantum efficiency (IQE), defined in Section 4.5, is calculated by EQE(λ) IQE(λ) = . (6.6) 1− R(λ) where R is the hemispherical reflectance.32 For spectral response measurements a grating monochromator was used. The light spot was set to a diameter between 6 mm and 8 mm. This spot covers a relatively large fraction of the 1 × 1 cm2 test solar cells. However, if material quality is very inhomogeneous, spot position may affect the measurement results. For SR measurements the samples were illuminated with a bias light of approximately 1 sun intensity. The hemispherical reflectance was measured using a spectrophotometer with integrating sphere (Ulbricht sphere).

6.2.1 Error Analysis for Evaluation of Effective Diffusion Length by Linear Fitting Analysis of the slope of the IQE−1 vs. α−1 curve is one of the preferred methods to determine the effective diffusion length of finished solar cells. This is −1 commonly done by applying a linear fit to the data in the range of We << α <<

Wb, where We and Wb are the emitter and the base thickness, respectively. How- ever, the linear approximation is valid in the case L < Wb only, where L denotes the bulk diffusion length (see Sec. 5.2.1). In many actual solar cells, this condition is not satisfied. This is regularly the case in well-designed thin-film solar

32 Relation (6.6) is valid if IQE and charge collection efficiency ηc are related by Eq. (4.45). If the IQE is defined to be identical to the collection efficiency ηc, Eq. (6.6) has to be replaced by IQE = EQE/(1−R−T), where T is the hemispherical transmittance at the back of the active cell region [59]. Conditions that have to be fulfilled in this case are: (i) no parasitic absorption occurs and (ii) no light enters at the back of the active region. As discussed in Sec. 4.5, this definition is not practical for the investigated thin-film solar cell structure.

96 CHARACTERIZATION METHODS

1 1 106 106 W = 30 µm 20% 0 b 0 105 105 2% W = 30 µm -1 4 4 b -1 10% 10 ] 10 -1 20% 10% -2 3 3 2% -2 30% 10 10 20% 40% 30% -3 2 2 -3 log(s µm) log(s µm) log(s 50% 10 s [cm S 10 40% -4 -4 60% 101 101 -5 -5 1 20406080100 120406080100 L [µm] L [µm] (a) (b)

Figure 6.1 Maximum relative error made when determining the quantum effi- −1 ciency effective diffusion length Leff,IQE approximately by a linear fit to the IQE −1 vs. α curve. The solar cell has a width Wb = 30 µm, the fitted data points were obtained by evaluating the function IQE−1(α−1) at α−1 = 5 µm, 6 µm, 7 µm, 8 µm, 9 µm, and 10 µm. (a) Results of linear fits with variable offset. (b) Results of linear fits through (0,1). cells. In the following, a quantitative analysis is given for the systematic error that is made when staying with the linear fit. The solar cell was modeled as a simple device of finite thickness and finite surface recombination velocity at the rear side. Furthermore, emitter and space charge region were assumed to have no spatial extend, and internal reflection was omitted. For this structure the charge collection probability ϕ is given by Eq. (4.37). From ϕ the IQE was calculated by Eq. (4.46) using the generation function by Eq. (4.7). In Figures 6.1 and 6.2 results are plotted for bulk diffusion length L and reduced surface recombination velocity s = S/D as variable parameters, and fixed −1 base thickness Wb = 30 µm. For conversion between s (in µm ) and S (in cm s−1) a diffusion constant D of 20 cm2 s−1 was assumed. The difference between Figures 6.1 and 6.2 are the values of α−1 for which the function IQE−1(α−1) was evaluated. In Figure 6.1 the values for the absorption length α−1 range from 5 µm to 10 µm with regular 1 µm spacing, while in Figure 6.2 the values α−1 = 7.7 µm, 10.8 µm, and 15.4 µm were used. The latter values corre-

6.2 Spectral Response and Quantum Efficiency 97

1 1 106 106 W = 30 µm 30% 0 W = 30 µm 5 5 b 0 2% b 10 10 -1 10% 4 4 2% -1 40% 10 ] 10 20% -1 10% -2 30% 50% 3 3 20% -2 10 10 30% 60% -3 2 2 40% -3 log(s µm) log(s µm) log(s 10 s [cm S 10 50% -4 -4 101 101 -5 -5 1 20406080100 120406080100 L [µm] L [µm] (a) (b)

Figure 6.2 Results for the same problem as in Fig. 6.1, but with data points evaluated for α−1 = 7.7 µm, 10.8 µm, and 15.4 µm. (a) Results of linear fits with variable offset. (b) Results of linear fits through (0,1). spond to the absorption lengths of the laser diodes in the SR-LBIC system used in this work (see Sec. 6.3). In both cases, the linear fit was performed with variable offset (Figs. 6.1a and 6.2a) as well as with fixed offset (Figs. 6.1b and 6.2b), i.e., the line was forced to go through the point (0,1). The graphs show that the systematic error is low, as long as the bulk diffusion length L does not exceed the base thickness Wb and the reduced surface recom- −1 −1 bination velocity is smaller than s = 0.01 µm (S = 2000 cm s ). If L > Wb the error significantly increases with increasing bulk diffusion length L. In this case, the IQE−1 vs. α−1 curve is no longer a straight line (see Fig. 5.1). As a result the −1 −1 slope evaluated at α > 0 is larger than at α = 0, and the obtained value Leff is smaller than Leff,IQE. The larger the ratio L/Wb, the larger the curvature, and therefore the larger the error.

While for L < Wb recombination at the back surface only plays a minor role, it significantly affects the result if L > Wb. The error is expected to be smallest for s = 1/L since in this case, the collection probability ϕ(z) by Eq. (4.37) reduces to ϕ(z) = exp(−z/L). This is the same collection probability found for the semi- infinite specimen (Sec. 5.2.1). Still, the IQEs in the finite and semi-infinite case are different since the integration range differs. This is why in a solar cell of

98 CHARACTERIZATION METHODS finite thickness the function IQE−1(α−1) is never linear and the error made through the linear approximation never vanishes. Comparing Figure 6.1a with Figure 6.1b, and Figure 6.2a with Figure 6.2b, it is found that the fixed offset case yields a smaller error than the variable offset case. In practice, this must not necessarily be true. For example, an error in the reflection measurement results in a shift of the IQE−1 vs. α−1 curve. Forcing the fit function through the point (0,1) then yields a faulty slope. In both cases, the relative error in Figure 6.2 is larger than in Figure 6.1. This yields the conclusion that the current SR-LBIC setup at Fraunhofer ISE could be improved by using additional laser sources and through the optimization of employed wavelengths. Anyway, the above considerations do not take into account measurement errors. In reality, each data point has to be attributed a measurement uncertainty. Generally, the error increases with decreasing absorption length range considered in the fit. A high recombination rate in the emitter may further complicate proper fitting.

6.3 SPECTRALLY RESOLVED LIGHT BEAM INDUCED CURRENT Multicrystalline materials are commonly characterized by inhomogeneous material and electronic properties. Therefore, spatially resolved measurement techniques are a key technique for the understanding of many effects. The light beam induced current (LBIC) technique allows analyzing finished solar cells in a nondestructive way. The measurement of finished cells is an advantage since many steps in the solar cell process affect diffusion length, and the operational state at LBIC measurements is comparable to the designed working state of a solar cell. The measurement principle behind the LBIC technique is the determination of short circuit current for local light generation through a white light or monochromatic beam. By scanning the beam across the sample, a map of short circuit current is obtained. Most LBIC systems use a monochromatic light source. If in addition the incident photon flux Ep(λ) is known, the method is principally a special version of the EQE measurement discussed in Section 6.2 with light generation restricted to a small spot. With simultaneous measurements of reflectance R the internal quantum efficiency IQE(λ) can be calculated by Eq. (6.6).

6.3 Spectrally Resolved Light Beam Induced Current 99

f 1 Glass fiber

Reference cell f3 IR Optics y V mounted x Isc on X-Y stage V f4

Solar cell IV converters Computer f5

Diode lasers with modulation frequencies f1..f5 Figure 6.3. Schematic setup of the SR-LBIC system at Fraunhofer ISE (after [215]).

Further information can be obtained using different monochromatic wavelengths λi. This way, several points IQE(λi) of the quantum efficiency curve are obtained. This technique is referred to as spectrally resolved light beam induced current (SR-LBIC). A schematic drawing of the SR-LBIC system used in this work is shown in Figure 6.3. Light beam generation is by five laser diodes. Their wavelengths and the corresponding absorption lengths are summarized in Table 6.1. The laser beam full width at half maximum33 is approximately 50 µm. The measurement is conducted without bias light and a local injection level between 1 and 3 suns. In the current setup, for IQE evaluation only the direct reflectance is measured. Therefore, it is not suitable for textured solar cells. The thin-film solar cells analyzed in this work often are not completely planar, yielding a potential error in IQE computation. For finished solar cells with antireflection coating, this effect is less severe than for uncoated devices. As a general remark, it has to be pointed out that a single IQE value measured in a LBIC system must be attributed a greater error than a value from a large area IQE system. One reason

33 The definitions of beam widths given in literature are not uniform. Besides the definition of full width at half maximum (FWHM) the width is often given at 1/e = 0.606… of the intensity maximum. Assuming a Gauss shaped intensity distribution the width then corresponds to two times the standard deviation σ. Another common definition takes the with at 1/e2 = 0.135… of the intensity maximum, corresponding to 4σ in the case of a Gauss distribution.

100 CHARACTERIZATION METHODS

Table 6.1 Wavelengths and corresponding absorption lengths of the laser diodes installed in the SR-LBIC system shown in Fig. 6.3. The absorption lengths are linear interpolations of the data given in Ref. [219].

Source no. Wavelength [nm] Absorption length [µm]

1 750 7.7 2 790 10.8 3 830 15.5 4 863 21.6 5 905 34.7 is the very small currents involved. Technical details of the system at Fraunhofer ISE are found in Refs. [215] and [216]. General information on the LBIC technique is given in Refs. [217] and [218].

6.3.1 Error Analysis for Evaluation of Effective Diffusion Length by SR-LBIC The systematic error in effective diffusion length evaluation by linear fitting is also important for SR-LBIC. For analysis of SR-LBIC data the error discussed in Section 6.2.1 may be even more important than for large area IQE data. This is the case when the conditions for linear approximation are satisfied globally but not locally. For example, in inhomogeneous material the condition L < Wb might be true for a large area IQE measurement, but locally the bulk diffusion length L may exceed the base thickness Wb. For SR-LBIC measurements on typical thin-film solar cells, diffusion length maps were calculated (i) by linear fit of the IQE−1(α−1) data, and (ii) by nonlinear fit based on the charge collection probability function by Eq. (4.37). The explicit fit function used is given in Appendix D. Fixed parameters in the fit function were the thickness of the p-doped base region W1 and the effective surface recombination velocity s1 at the low-high junction between p and p+ region.

The value of s1 was estimated using Eqs. (4.40) and (4.42). In the calculations band-gap narrowing was considered by the model given in Appendix B.3. Diffu- sion coefficients were derived from doping concentrations using the mobility model given in Appendix B.2. Doping data were taken from SRP measurements

6.3 Spectrally Resolved Light Beam Induced Current 101

Table 6.2 Estimation of effective surface recombination velocity s1 = S1/D1 at the p-p+ low-high junction of the solar cell analyzed in Fig. 6.4.

Doping Thickn. Recombination Effective SRV

NA,1 (p) NA,2 (p+) W2 (p+) Leff,2 S2 s1 S1 [cm−3] [cm−3] [µm] [µm] [cm s−1] [µm−1] [cm s−1]

Lower limit 2 × 1016 3 × 1018 4 10 1 × 105 0.002 600 Presumed 4 × 1016 3 × 1018 4 8 1 × 105 0.007 1500 Upper limit 6 × 1016 2 × 1018 3 3 1 × 106 0.02 4000

(Table 3.3) and thickness values were determined by optical microscopy at beveled samples. For the solar cell analyzed in Figure 6.4 the input data are shown in Table 6.2. −1 From these a reduced effective surface recombination velocity s1 = 0.007 µm −1 is calculated (corresponding to S1 = 1500 cm s ). In addition, upper and lower limits for s1 were estimated, taking into account measurement errors for each property. In the sensitivity analysis, the value of W1 was set fixed to 27 µm, as it is known with comparatively high accuracy. Strictly, an error also would have to be attributed to this dimension. For the diffusion length maps in Figure 6.4 a visible difference between the two fit methods is found. The map from the nonlinear fit (Fig. 6.4b) shows significantly higher maximum diffusion length values than the map from the linear fit (Fig. 6.4a). This behavior is also evident in the corresponding histograms shown in Figure 6.4c. The upper histogram has an asymmetric form and on the right side of the maximum it falls to zero within a relatively short distance. This behavior is typical for thin-film solar cells with a diffusion length equal to or larger than cell thickness. This behavior is obvious when recalling the results illustrated in Figures 6.1 and 6.2. The larger the bulk diffusion length, the larger the difference between the value Leff,IQE according to the definition and its approximation by the fit. The lower histogram in Figure 6.4c additionally examines the sensitivity on the surface recombination velocity s1. Comparing the histograms for s1 = 0.002 −1 −1 µm and s1 = 0.007 µm , only a moderate difference is found. However, for −1 s1 = 0.02 µm the distribution is significantly shifted. There is an especially

102 CHARACTERIZATION METHODS

Figure 6.4 (a) Leff map obtained Linear fit −1 with additional point (0,1) by linear fits to the values (αi , −1 2 IQEi ). The point (0,1) is included as an additional data 1 point. (b) Leff map from the same data fitted with the exact func- Counts1000 / tion. (c) Histograms of the data shown in parts (a) and (b). Be-

2 sides the presumed recombina- -1 -1 −1 s = 0.002 µm s = 0.02 µm tion velocity s1 = 0.007 µm 1 1 (gray columns), histograms are −1 1 shown for s1 = 0.002 µm −1 (dashed line) and s1 = 0.02 µm s = 0.007 µm-1 Counts / 1000 (solid line). The data included in the histograms are taken from 0 20406080the areas of interest marked by Effective diffusion length L [µm] eff frames in parts (a) and (b). (c) large peak for effective diffusion length values between 75 µm and 77 µm. On −1 one hand, the surface recombination velocity of s1 = 0.02 µm limits the effective diffusion length to 77 µm. On the other hand, to exceed the value 75 µm, the bulk diffusion length must be larger than 231 µm. Such a distribution is very unlikely. This is a strong hint that the true surface recombination velocity is −1 smaller than s1 = 0.02 µm .

For the investigated solar cells, the analysis above showed that Leff values determined by linear fitting to SR-LBIC data must be attributed a significant

6.4 Modulated Free Carrier Absorption 103 error. Therefore, for the correlation of effective diffusion length with dislocation density (Section 6.5.4) SR-LBIC data were fitted with the exact nonlinear function. Further, the discussion showed that for multicrystalline materials, the analysis of SR-LBIC effective diffusion length maps could provide more information on back surface recombination velocity than large area IQE measurements. This is the case if locally effective diffusion length exceeds solar cell thickness.

6.4 MODULATED FREE CARRIER ABSORPTION A major advantage of carrier lifetime measurement of finished solar cells is its relevance for device operation. At the same time, it is disadvantageous from the viewpoint of necessary preparational effort. Therefore, for carrier lifetime measurements on unprocessed Si thin films the technique of modulated free carrier absorption (MFCA) was used. The MFCA method has been proposed by Sanii et al. [220]. It is based on the absorption of infrared light by light-generated free carriers. The technique does not require any contacting of the sample and it is nondestructive. Carrier lifetime maps can be generated by scanning the injecting beam. A schema of the setup implemented at Fraunhofer ISE is shown in Figure 6.5. Generation of free carriers in the Si sample is by means of a 780 nm GaAlAs laser diode, modulated in amplitude with a sine function. The area in which carriers are light generated is at the same time illuminated by infrared light from a 1550 nm InGaAs laser. At this wavelength, photon energy is smaller than the band-gap and photons are essentially absorbed by free carrier absorption. The intensity of infrared light transmitted through the sample increases with decrease in carrier density. With sinusoidal modulation of carrier injection, the transmitted signal has the same frequency but the phase is shifted. From this phase shift carrier lifetime can be calculated. It is detected by a lock-in amplifier and yields a differential lifetime. More on technical details of the system can be found in Refs. [221, 222]. For local correlation between dislocation density and minority carrier lifetime a good lateral resolution is required. For the MFCA technique this resolution is determined by the diameter of the detection spot and the step size of the x-y stage. The minimum full width at half maximum value realized for the spot

104 CHARACTERIZATION METHODS

Bias light

InGaAs detector Lens InGaAs laser 1550 nm

Low pass filter Sample mounted on X-Y stage Sine generator

Glass fiber GaAlAs Power laser diode 780 nm supply Amplifier

Lock-in amplifier Signal Reference signal Figure 6.5 Schematic setup of the MFCA system at Fraunhofer ISE (after Ref. [222]). diameter was approximately 60 µm. Samples were either scanned with 25 µm or 50 µm step size. The smaller value of 25 µm is already well below the spot diameter. Therefore, resolution is only slightly better than for the 50 µm step size. To diminish the effect of surface recombination, all samples were coated with a hydrogen rich PECVD SiNx layer before MFCA measurement. The employed

SiNx has proven to yield a very low effective surface recombination velocity – on p-type FZ-Si wafers a value of 4–6 cm s−1 was demonstrated [223]. The quality of MFCA measurement data was found to be strongly dependent on the sample’s surface topography. Films of high crystallographic quality are usually characterized by parallel running subgrain boundaries and a smooth surface after epitaxial thickening. On such films MFCA measurements yielded reliable lifetime data. For an example, see Figure 7.14. In contrast to this, films of low crystallographic quality regularly exhibit an uneven surface. In this case, the film’s optical properties are not suitable for MFCA (Fig. 6.6). Figure 6.7 clearly shows the connection between crystallographic film quality and surface topography. For the grain on the left, typical variations in height are around one micron. Opposed to this, width and height of

6.4 Modulated Free Carrier Absorption 105

Figure 6.6 MFCA lifetime map of a sample with an unsuitable surface. In the hatched areas the surface is characterized by a relief-like topography and refraction of the detection beam results in incorrect measurement data. the »ridges« in the right images are in the range of 30 µm to 60 µm, dimensions which are similar to the diameter of the detection beam. Therefore, refraction can alter the beam geometry and the points of carrier generation and detection may not coincide anymore. In conclusion, for the examined set of parameters, the MFCA technique turned out to be suitable for epitaxially thickened thin films fabricated with ZMR scan speed ≤ 50 mm min−1 and seed film thickness ≥ 8 µm only. The surface of films recrystallized at higher scan speed or using thinner seed layers was too uneven for reliable measurements. Comparing MFCA lifetime data with values obtained by IQE measurements and PC1D modeling, the absolute values are too high. This deviation may be due

Figure 6.7 Typical surface of a ZMR Si seed film after epitaxial thickening. The left and the right image are enlarged details of the one in the middle. The grain on the left exhibits parallel running subgrain boundaries and a smooth surface, while the one on the right is characterized by irregular running subgrain boundaries and a relief-like topography.

106 CHARACTERIZATION METHODS to the differential measurement method. The negative effect of differential measuring is strengthened by the fact that (i) no bias light was used and (ii) beam energy density was maximized to yield a detectable signal even at low quality material. Therefore, injection level varied within a broad range and carrier trapping may significantly affect measurement results. However, the MFCA technique could provide a good qualitative correlation between carrier lifetime and dislocation density (see Fig. 7.14).

6.5 ETCH PIT DENSITY MAPPING In the preceding sections, two measurement techniques to map carrier lifetime have been presented. SR-LBIC for diffusion length determination at finished solar cells and MFCA for lifetime measurements of unprocessed films. Still, a method for spatially resolved measurement of dislocation density is necessary to correlate local carrier lifetime with local dislocation density, and to apply the theory derived in Chapter 4. In this work a setup for automated etch pit density (EPD) mapping has been implemented and algorithms for data analysis have been developed. The following sections describe the EPD mapping hardware and software setup. To test the capabilities of the newly developed system, different multicrystalline materials were analyzed. Last but not least, post- processing for correlation of carrier lifetime and etch pit density data is discussed.

6.5.1 Hardware Setup Figure 6.8 shows the EPD mapping system developed in this work. It is build around a ZEISS Axiotron optical microscope with autofocus and a Märzhäuser motorized x-y stage. Image acquisition is by means of a Roper Scientific CCD camera and frame grabber board. A PC running Media Cybernetics’ IMAGE-PRO PLUS analysis software controls all components. The computerized analysis of many thousand images requires an automatic focus control. Within the employed software, this can be achieved by analyzing local contrast and controlling the microscope’s z axis. However, this solution turned out to be very time consuming, even on a state of the art computer. The use of an integrated laser controlled system resulted in increased speed and reli- ability.

6.5 Etch Pit Density Mapping 107

CCD camera

Computer Microscope Sample Microscope controller (AF) X-Y stage Stage controller Figure 6.8 Setup for automated etch pit density (EPD) mapping implemented in this work.

The x-y stage has a travel distance of 100 mm, both, in the x and y direction. Its resolution is 0.1 µm and the reproducibility is better than 1 µm. The communication between stage controller and PC is through a RS232 interface. The digital camera works with a 1392 × 1040 pixel CCD sensor with 4.65 × 4.65 µm2 pixel size. Using a lens with 50× magnification the camera captures an area of approximately 98 × 130 µm2. This geometrical arrangement results in a theoretical resolution of 0.09 µm, while the actual resolution is determined by diffraction and the quality of the optics. To reveal crystallographic defects, the samples were mechanically polished and treated with a Secco etch [107]. Typical etching times were in the range of 15 s to 20 s and resulted in etch pits diameters of 0.4 µm to 0.7 µm.

6.5.2 Image Analysis All routines for image analysis and hardware control were implemented as macro scripts for the IMAGE-PRO PLUS software. The script syntax is VISUAL BASIC compatible.

Coordinate System Local correlation of carrier lifetime with EPD data requires the same coordinate system for both maps. Although affine transformations (translation, rotation, scaling) may be used to convert from one coordinate system into the other, these transformations cause interpolation errors. While the need for translational and rotational transformations can only be avoided by very precise mechanical

108 CHARACTERIZATION METHODS

Figure 6.9 Illustration of object detection and classification on a typical ZMR Si film thickened by epitaxy. Each 50 × 50 µm2 cell of the grid defines one AOI (area of interest) for which a separate EPD value is calculated. adjustment, scaling is not necessary if both measurement setups scan the sample with the same step size. To achieve flexible step sizes a »virtual grid« has been implemented. With this concept there is no restriction to tile the measured area into frames with size dictated by the camera frame (e.g., 98 µm × 130 µm in the concrete case). The size of a single cell in the virtual grid is independent from the camera frame. This principle is visualized in Figure 6.9. The black lines define a grid with rectangular 50 × 50 µm2 cells.34 For each cell a separate EPD value is calculated, represented as one data point in the final EPD map. The size of a single cell has to be determined by a weighting up of resolution and statistical accuracy. The smaller the cell size the better the resolution but the worse the statistical accuracy. The same is true vice versa. The optimum cell size depends on average EPD as well as homogeneity. Therefore, its optimization is material dependent.

34 In the notation of the EPD software the 100 × 100 µm2 area is called »virtual frame« and a single 50 × 50 µm2 cell is referred to as AOI (area of interest).

6.5 Etch Pit Density Mapping 109

Object Detection and Analysis The object detection process is sketched in Figure 6.10. Firstly, the image is reduced to a binary image. The threshold value separating between dark fore- ground objects (etch pits and grooves) and the light background is either set manually or automatically calculated on histogram data. In the latter case, the routine acquires several sample images and determines an average threshold value. Next, a pre-filtering routine drops all objects with area below a specified

Image

Segmentation Binary image

Pre-filtering (min. area) Objects

Measurement

Min. diameter filter Cluster Classification Single

Cluster analysis Avg. single area

Cluster Estimated number of singles Filtering Class 1 Number of singles

Classification Cluster Class 2 Class 2 Estimated umber of singles

Classification Cluster Class 3

Classification Cluster Class 4 Class 4 Estimated number of singles ...

... Total num. of singles EPD = AOI area Figure 6.10 Schematic object detection and analysis process. After segmentation and pre-filtering numerous object properties are measured (area, roundness, hole ratio, etc.). Based on their area all objects are either identified as »single« or »cluster« objects. For each cluster object the number of singles that make up the cluster is estimated. Then cluster objects are classified and filtered by morphological attributes. The final EPD value is calculated by summing the total number of singles and dividing by the AOI area.

110 CHARACTERIZATION METHODS

Measurement Definition

Area Area of object excluding area of holes

Hole ratio/ Area / (Area + Area of holes)

35 2 Roundness (Perimeter) (4π × Area) / / Table 6.3 Parameters Aspect ratio Ratio between major and minor axis of the measured at each ellipse with same area and first to second detected object. degree moments [224] limit. This saves computing time since advanced measurements can be restricted to the remaining objects. Then for each object several geometrical parameters are measured (Table 6.3). After that, objects are either identified as »single« or »cluster«. The cluster analysis routine first calculates the average area of all objects. Then objects with area smaller than two times the average area are assigned the attribute single while all other objects are assigned the attribute cluster [225]. This algorithm works very well as long as the examined area contains more single than cluster objects. To avoid incorrect object classification in the case of very few single objects, the routine automatically checks whether the calculated average single area makes sense. If this is not the case the cluster analysis routine uses an average single area from the grid cells analyzed before. For each cluster object the number of singles that make up the cluster is estimated and stored as an additional attribute.

Object Classification Not all objects identified as cluster objects are etch pit clusters, i.e., collec- tions of dislocations with spacing of neighboring dislocations smaller than typical etch pit diameter. Other objects which may be identified as clusters include grain boundaries and preparational artifacts such as scratches, holes, dust, etc. The next task therefore is to exclude these objects from the final count. This is done by classification of cluster objects according to their morphology and subsequent filtering. For cluster classification the four measurement parameters

35 Other literature and software uses the parameter form factor, which is just the inverse of the parameter roundness.

6.5 Etch Pit Density Mapping 111

Table 6.4 Example for definition of object classes. The exact parameters depend on the specific sample type and preparation (e.g., etching time).

Class Area Hole Ratio Roundness Aspect Ratio

Single etch pits π × (avg. diameter)2 1 Approx. 1 Approx. 1 Small clusters Medium ≤ 1 Medium 1 to medium Large clusters Large < 1 Large 1 to large Grain boundaries Medium 1 Large Large (in case of non- touching objects) listed in Table 6.3 are used.36 An example of possible class definitions is given in Table 6.4. Abstractly, each class represents a subspace in the four-dimensional space spanned by the four measurement parameters. Care is taken to avoid the counting of a single object in more than one class (Fig. 6.11b). The classification process can be compared to the sizing of sand or gravel by shaking through a

(c)

(b) Class 4

Class 3 Class 5

(a) Class 2 max. Count included in total Parameter 2 Parameter Class 1 number of etch pits min. Count discarded

min. max. Parameter 1 Figure 6.11 Classification of objects. (a) Each class is a subspace in the space spanned by all possible measurement values. (b) Overlapping classes: to avoid multiple counting the object is assigned to the class with a lower index (class 2 in this example). (c) Classes can be subtracted by defining a »dummy« class, which is discarded in the total count.

36 These measurements are a subset of the 54 possible measurement types available in IMAGE- PRO PLUS.

112 CHARACTERIZATION METHODS series of progressively larger sieves. Particles that do already fall through one of the small sieves do not have the chance to get into one of the larger grain size fractions. This concept allows a very flexible object classification. Through definition of »dummy« classes, objects with certain properties can explicitly be excluded from the count (Fig. 6.11c). Generally, for each class it can be selected separately, whether its objects should be included in the final count or not (filtering process in Fig. 6.10). Object classification is visualized in real time as shown in Figure 6.9, helping to optimize filter settings.

6.5.3 Testing on Different Multicrystalline Silicon Materials The EPD setup and the software routine have been tested and optimized by measuring different multicrystalline Si materials. These materials include Si thin films fabricated by ZMR and epitaxy, cast mc-Si wafers, Edge-defined Film-fed growth (EFG) foils and Ribbon Growth on Substrate (RGS) sheets.

Silicon Thin Films by ZMR and Epitaxy Typical features of epitaxial thickened ZMR Si seed films are stripes with increased dislocation density (see Fig. 7.3). These are induced by subgrain boundaries in the seed film (see Fig. 7.2). Therefore, the EPD map in Figure 6.12 exhibits a regular structure with alter- nating stripes of high and low dislocation density. Within the sample EPD varies between 1 × 105 cm−2 and 1 × 107 cm−2. A comparison between the different

Figure 6.12 EPD map measured on an epitaxially thickened ZMR Si seed film.

6.5 Etch Pit Density Mapping 113 grains shows that average EPD depends on the structure of subgrain boundaries.

In grains with parallel running subgrain boundaries, marked A1 to A3 in Figure 6.12, the average EPD is within the range of 1 × 106 cm−2 to 1.5 × 106 cm−2. Contrary to this, in grains with irregular running subgrain boundaries EPD is much higher. For example, in the grain marked B an EPD value of 6.3 × 106 cm−2 is measured. Main issues for EPD measurements are the generally high dislocation density level and the clustering of etch pits. Inevitably, the measurement error increases with the percentage of clustered etch pits. Firstly, etch pits may overlap and secondly, the estimated number of single etch pits composing a cluster object directly depends on the calculated average area of the single etch pit.

Multicrystalline Wafers by Directional Solidification Today, ingot growth by directional solidification is the standard method to produce multicrystalline silicon (mc-Si) wafers. The EPD map shown in Figure

Figure 6.13 (a) EPD map and (b) grain boundary map measured on a small grained area of a standard mc-Si wafer.

114 CHARACTERIZATION METHODS

6.13a is taken on a small grained area of such a wafer. The measurement reveals enhanced dislocation density with EPD values ≥ 107 cm−2. Within the grains typical EPD is in the range of 1 × 105 cm−2 to 1 × 106 cm−2. In Figure 6.13b a map of objects belonging to the class »grain boundary« is plotted. These objects are discarded in the EPD map. The resulting grain boundary map corresponds very well to grain orientation maps from the same sample obtained by electron backscatter diffraction (EBSD) pattern [206].

EFG Ribbons From the large number of ribbon growth technologies invented in the 1970s and 1980s the Edge-defined Film-fed Growth (EFG) method is the only one with a significant production level [35] (see also Sec. 2.2). The EPD map in Figure 6.14a shows areas with very different EPD levels, marked A and B. This finding is also well visible in the EPD histogram, which displays a first peak at 1.5 × 105 cm−2 and a second one at 3 × 106 cm−2, a difference of more than one order of magnitude. The corresponding grain boundary map (Fig. 6.14b) displays numerous parallel boundaries in area A, which for the most part cannot be resolved separately. In contrast, in area B only few and irregular running grain boundaries are found. Figure 6.15 illustrates the connection between twinning and dislocation density. In the highly twinned area (image A) only very few dislocations are found, while in the area without twins (image B) dislocation density is quite high. This behavior is well known for the EFG material [44]. For EPD measurements of EFG material, reliable filtering of grain boundaries is of utmost importance. Misinterpretation of a single grain boundary as a dislocation cluster results in a major error. Note that the area of one twin boundary in Figure 6.15 (left image) is larger than the sum of all single etch pits. Twin boundaries are known to be electrically largely ineffective. Therefore, exact filtering is also important for correlation with electrical measurements. The measurement results in Figure 6.14 also illustrate the necessity to weight between resolution and statistics. For the highly dislocated areas, 50 × 50 µm2 AOIs are favored from the viewpoint of resolution. In the twinned areas, EPD values based on 50 × 50 µm2 AOIs are not very meaningful. For example, a single dislocation in a 50 × 50 µm2 area corresponds to the EPD value 4 × 104 cm−2,

6.5 Etch Pit Density Mapping 115

Figure 6.14 (a) EPD map and (b) grain boundary map measured on a typical EFG wafer.

Figure 6.15 Representative optical micrographs from the areas marked A (EPD ≈ 5 × 105 cm−2) and B (EPD ≈ 1 × 107 cm−2) in Fig. 6.14a. two dislocations in the same area correspond to the value 8 × 104 cm−2. There- fore, the histogram would show discrete peaks. Consequently, the histogram shown in Figure 6.14 has been calculated on a 200 × 200 µm2 AOI basis.

116 CHARACTERIZATION METHODS

RGS Sheets The Ribbon Growth on Substrate (RGS) process represents a horizontal growth technology, i.e., the growth direction is perpendicular to the pulling direction (see Sec. 2.2). Compared to the materials examined in the preceding sections, the EPD map shown in Figure 6.16 is quite homogeneous, with a high average EPD level of 5 × 106 cm−2. Both the EPD map and the grain boundary map exhibit a similar structure. The optical micrograph in Figure 6.17 shows that single RGS grains can be rather small. For the sheet analyzed in Figure 6.16 numerous grains were found to be smaller than the 50 × 50 µm2 AOI. In this case, the employed algorithms cannot distinguish between dislocation clusters and grain boundaries. Strictly speaking, the method would not be applicable. Therefore, the EPD measurement results are associated with a considerable error.

Figure 6.16 (a) EPD map and (b) grain boundary map measured on a typical RGS wafer.

6.5 Etch Pit Density Mapping 117

Figure 6.17 Representative optical micrograph from the RGS wafer analyzed in Fig. 6.16.

Summary of Test Measurements and Optimization Strategies For optimum accuracy, the developed EPD image analysis routine requires material specific classification schemes. This is one major conclusion from the discussion in the preceding sections. This finding is best illustrated by the very different materials EFG ribbon and epitaxially thickened ZMR thin-film. For EFG material, focus has to be put on reliable removal of twin grain boundaries. In areas with low dislocation density, the misinterpretation of a single grain boundary as a dislocation cluster results in a large error. In comparison, the risk of missing a dislocation cluster in high dislocation regions results in a smaller error. The situation is different for epitaxially thickened ZMR thin films. Average dislocation density is higher than in EFG material and clustered dislocations make up a large fraction. Clusters that are not considered by the EPD routine can yield a significant measurement error. »Real« grain boundaries do not occur very often and the misinterpretation as a dislocation cluster results in a small error only. Generally, the measurement error increases with the percentage of clustered etch pits. For pure single etch pits the measurement error is estimated to be around 10%. One possible error source is the dislocation angle, which affects depth and diameter of the etch pits and therefore image contrast. For clustered etch pits one major error source is overlapping etch pits. In this case, the number of dislocations is underestimated. For dislocation densities ≥ 107 cm−2 etch pits unavoidably partly overlap even for short etching time.

118 CHARACTERIZATION METHODS

Furthermore, the estimated number of single etch pits composing a cluster object directly depends on the calculated average area of the single etch pit. Among other things, this value is affected by the threshold setting. Therefore, for clustered etch pits a counting error of at least 50% has to be assumed. For successful identification of grain boundaries, the implemented routines require the AOI to be smaller than typical grain size. The algorithms are therefore not very applicable to material with very small grains such as RGS sheets.

6.5.4 Correlation of Effective Diffusion Length and Etch Pit Density The ideal specimen to study the dependence of effective diffusion length on dislocation density would satisfy the following requirement: around the point of carrier generation, dislocation distribution and recombination activity would be homogeneous. The minimal volume with homogeneous material properties would be a spherical cap with radius several (> 3) times the effective diffusion length. The junction plane would have ideal collection properties and besides dislocations, no recombination active features would be present. Normally, real multicrystalline Si material significantly differs from this situation. Dislocations distribution is inhomogeneous, recombination activity varies, and recombination additionally occurs at impurities, grain boundaries etc. Furthermore, different effects may be connected, such as segregation of impurities at dislocations. A quantitative correlation of effective diffusion length with dislocation density in inhomogeneous materials requires (i) matching of both coordinate systems and (ii) taking into account the diffusion of charge carriers from the point of generation into surrounding areas. The first task can either be accomplished by very precise sample adjustments in both measurement systems or by coordinate transformation of the mapped data. To give an impression of the requirements for the first option, consider the following example: if sample size is 10 mm × 10 mm and misalignment by rotation within a single scanned line should be below 20 µm, then the accuracy regarding rotation has to be better than 0.1°. Therefore, in this work the option of data transformation by translation and rotation was chosen, although it introduces some alteration of data by interpolation.

6.5 Etch Pit Density Mapping 119

The principle proceeding is described, e.g., in Ref. [205]. Striking features are identified in both, the LBIC and the EPD map, and subsequently used as »registration points«. Knowing the coordinates of the registration points in both systems the transformation is calculated, which maps LBIC onto EPD data. For translational and rotational transformation two registration points would be sufficient, but the precision is increased if more than two points are taken into account. In this case, the transformation is determined by minimizing the squared errors for the complete set of coordinate pairs. For this kind of coordinate transformation, the employed image analysis software provided an integrated routine. It also included data interpolation to the new coordinates. A solution to the second task – consideration of carrier diffusion from the point of generation into neighboring areas – is more complicated. The question on how far carriers diffuse from the point of generation requires a priori knowledge of (effective) diffusion length. Rinio et al. have developed a method that already considers measured effective diffusion length at the stage of dislocation density computation [204, 226]. Around the point of carrier generation, a grid of concentric circles is defined. In each annulus, i.e., the area between two concentric circles, a dislocation density is calculated. Afterwards, each value is multiplied by a weighting factor. This factor describes the probability that a charge carrier reaches the respective annulus by diffusion. To take advantage of this concept the injection beam must have a small diameter, i.e., the diameter is small compared to typical effective diffusion length. Indeed Rinio et al. have implemented a spot diameter37 of 12.5 µm [204]. However, the radial weighting function has a significant effect on the calculated »dislocation density« value. The approach used in this work is different. Firstly, a virtual grid is superim- posed on the sample’s surface and an EPD value is calculated for each quadratic cell (see 6.5.2). Beam profile and carrier diffusion are then considered in a second step. This is done by computing the convolution of the EPD map with a discrete filter kernel matrix. The resulting data were named effective dislocation density (EDD). Figure 6.18 visualizes the effect of the convolution process. In

37 Measured with the 1/e2 criterion (see Footnote 33 in this chapter). Assuming a Gauss normal distribution the FWHM is 7.4 µm.

120 CHARACTERIZATION METHODS

Etch pit density Effective dislocation density

Leff [µm] 100 100 Fit by Donolato model 90 50 50 [µm]

eff eff

AOI L

10 10 10

106 107 108 106 107 108 Grid line (a) (b) EPD [cm-2] EDD [cm-2]

8 8 10 Convolution 10

106 106

Figure 6.18 Post-processing of etch pit density data. To account for the LBIC beam profile and carrier diffusion from the point of injection, the etch pit density (EPD) map is convolved with the kernel function visualized in Fig. 6.19 yielding an effective dislocation density (EDD) map. (a) Effective diffusion length versus EPD, (b) effective diffusion length versus EDD. The data plotted in the graphs is taken from the marked AOIs only.

Figure 6.18a for each map coordinate (represented by one pixel), one data point is plotted in the Leff vs. EPD graph, with the EPD value as the abscissa and the

Leff value as the ordinate. The same is done in Figure 6.18b for Leff and EDD values. Visible at first sight, the EDD map looks like a blurred version of the EPD map, fitting much better to the Leff map. As an evident result the Leff vs. EDD graph shows less scatter than the Leff vs. EPD one. Figure 6.19 shows the radial kernel function as well as a three-dimensional graphical representation of the resulting discrete 9 × 9 kernel matrix used in the convolution. The LBIC beam intensity profile is considered by the Gaussian function g(r), where r is the radial coordinate with origin at the intensity maximum. Diffusion of charge carriers from the location of generation is taken into account by the function f(r). The radial decay of excess charge carrier density for a point source is given by [227]

6.5 Etch Pit Density Mapping 121

1.0

0.8

2σ = 50 µm 0.6

0.4 (f*g)(r)

Normalized Value Normalized L = 50 µm 0.2 g(r) eff f(r) 0.0 -100 -50 0 50 100 Distance r [µm] (a) (b)

Figure 6.19 Filter kernel used for post-processing of EPD data. (a) Radial kernel function and (b) three-dimensional graphical representation of the resulting discrete 9 × 9 kernel matrix. The LBIC beam intensity profile is considered by the Gaussian function g(r) (plotted as dashed line). Diffusion of charge carriers from the point of generation is taken into account by the function f(r) (dotted line). Both effects are combined in the convolved function (f*g)(r) (solid line).

f (r) = cK0 (r / Leff,l ) , (6.7) where c is a normalization constant, K0 is the modified Bessel function of the second kind of order zero and Leff,l is the local effective diffusion length. To combine both effects the convolution of g(r) and f(r) is computed, yielding the final radial kernel function (f*g)(r) (Fig. 6.19a). From this radial function a discrete kernel matrix is calculated (Fig. 6.19b) and convolved with the EPD map. Figure 6.19 shows that for the assumed data the net function (f*g)(r) is largely determined by the LBIC beam profile function g(r). Since for the investigated thin films, effective diffusion length is in the same range as beam width, the above-mentioned analysis method by Rinio et al. would not yield any benefit. A general remark has to be made concerning the effective diffusion length value to be inserted into Eq. (6.7). A priori, this value is not known. Theoreti- cally, the problem could be solved iteratively only, since the dependence of Leff on EPD has to be used as input. As an approximate approach, the average diffu-

122 CHARACTERIZATION METHODS sion length within the analyzed AOI was used, as also done by Rinio et al. [204].

6.6 SUMMARY Analysis of IQE data is one of the preferred methods to extract recombination parameters of finished solar cells. Commonly, base effective diffusion length is determined by a linear fit to the IQE−1 vs. α−1 curve. However, the implied approximations are not valid if bulk diffusion length exceeds base thickness. For the investigated solar cell structure, the possible error was analyzed and quantified by numerical calculations. For analysis of SR-LBIC data, the error by linear fitting can be even more important than for large area IQE data. For example, this is the case in inhomogeneous material with average effective diffusion length smaller than base thickness, but locally high diffusion lengths. For typical SR-LBIC data effective diffusion length was, on one hand, determined by linear fitting, and on the other hand, by fitting the data with the »exact« function. Histograms revealed significantly different diffusion length distributions. For carrier lifetime measurements of unprocessed Si thin films, the technique of modulated free carrier absorption (MFCA) was investigated. Data quality was found to be strongly dependent on surface topography. On films with comparatively flat surfaces, the method yielded reliable results, while it turned out not to be usable for highly defective films with a relief like surface structure. For spatially resolved measurements of dislocation density, a system for automated etch pit density (EPD) mapping has been developed. It is built up on an automated microscope and digital image analysis. Within manageable time, the setup is able to acquire EPD maps resulting from the analysis of several ten- thousand images. A flexible object classification scheme has been implemented in order to deal with clustered etch pits and to filter out grain boundaries and preparation artifacts. The system has been extensively tested and optimized for different multicrystalline materials. Parameter optimization has been found to be material specific. For quantitative correlation of effective diffusion length with dislocation density, matching coordinate systems are a prerequisite. Translational and rotational transformations are used to ensure this requirement. Quality of the data is sig-

6.6 Summary 123 nificantly improved by accounting for the LBIC beam profile and by considering diffusion of charge carriers from the point of generation into surrounding areas. This has been accomplished through a convolution of the EPD map with a kernel matrix that takes into account both effects. The resulting data were named effective dislocation density (EDD). The developed tools provide a solid basis for application of the Donolato model to experimental data, and for the determination of dislocation recombination strength.

7 Optimization of Silicon Film Quality

This chapter summarizes main results on the characterization and optimization of Si thin films formed by zone-melting recrystallization (ZMR) and chemical vapor deposition (CVD). The first section qualitatively examines how defects in the seed film are generated during the ZMR process, and how these defects influence the subsequently deposited epitaxial layer. In the following sections, the effect of process parameters and material properties on crystal quality and solar cell performance is studied. These investigations consider capping type, Si film thickness, scan speed, and substrate material. Finally, the correlation between dislocation density and effective diffusion length is examined on a quantitative level. This analysis makes use of the theoretical model developed in Chapter 4 and the new measurement techniques presented in Chapter 6. As an important result, open circuit voltage is found to be limited by space charge region defects.

7.1 MICROSTRUCTURE AND ORIGIN OF DEFECTS

7.1.1 ZMR Growth Morphologies Figure 7.1 shows in situ images of typical growth morphologies observed during ZMR processing. Generally, such extremely differing growth morphologies cannot be produced solely by adjusting process parameters like scan speed and heater settings. Therefore, the images were taken of different sample types: The samples shown in Figures 7.1a–c were all prepared on oxidized Cz-Si substrates, employing a 150 nm thick thermal oxide capping. Si seed film thickness was 2 µm for the samples in Figures 7.1a and 7.1b, and 15 µm for the one in Figure 7.1c. The sample in Figure 7.1d was prepared on a SiSiC substrate with ONO intermediate layer, a 10 µm thick Si seed film and 2 µm thick PECVD oxide capping. 125 126 OPTIMIZATION OF SILICON FILM QUALITY

(a) (b)

(c) (d) Figure 7.1 Crystallization front morphologies observed in situ during ZMR processing. (a) Stable, faceted cellular growth interface, (b) unstable, faceted growth interface, (c) planar growth interface, (d) dendritic growth interface.

The most stable growth modes are those with faceted cellular interface (Fig. 7.1a) and planar interface (Fig. 7.1c). However, the planar interface results in much more defective films than the faceted cellular one. Reasons might be: (i) the observed »planar« interface is not really free from a supercooled region but grows unstable on microscopic scale, or (ii) the planar interface is not compatible with grain orientation supported by interfacial free energies at the Si–SiO2 interface and orientation dependent growth speed. As a general finding, an increase in upper heater power results in an increase of molten zone width and a decrease in cell size. For high power settings a wide molten zone and a planar interface is found. These observations are consistent with supercooling theories (see Sec. 3.5.2), and experimental and theoretical results presented in literature [124, 132]. Dendritic growth has not been observed on standard Si substrates. It must be either attributed to a very low temperature gradient (e.g., supported by a substrate of very high thermal conductivity) or impurity segregation.

7.1 Microstructure and Origin of Defects 127

Figure 7.1a clearly verifies the growth model illustrated in Figure 3.6. Furthermore, high angle grain boundaries can be identified at locations where facet angles and direction of elsewhere parallel subgrain boundaries change. For ZMR growth with thin capping layers, the surface additionally exhibits a relief- like surface structure.

7.1.2 Correlation between Defects in ZMR Film and Epitaxial Layer In the solar cell structure investigated in this work, the ZMR thin-film acts as a seed for subsequent epitaxial thickening by high temperature CVD. The p-n junction is formed in the epitaxial layer, and most photons are absorbed there. Therefore, defects in the epitaxial layer are most crucial and their correlation with defects in the ZMR seed film is a central issue. Figure 7.2 shows a typical cross section of a ZMR Si seed film after epitaxial thickening by Si CVD. To reveal defects, the sample was polished and subsequently etched with a Secco solution (see p. 26). Etching also shows significant changes in doping concentration, since the etch rate increases with doping density. This way, the highly doped seed film can be distinguished from the normally doped epitaxial layer. The most prominent features of the two-layer system are the V-shaped bunches of dislocations that originate from subgrain boundaries in the ZMR seed film – looking like bushes with trunks in the seed film and treetops in the epitaxial layer. Figure 7.3 shows a corresponding surface image, prepared from a sample with compatible structure. Stripes of high dislocation density in the epitaxial layer reproduce the run of subgrain boundaries in the seed film. These stripes are the tops of dislocation bunches visible in cross sections (Fig. 7.2). In MFCA (Fig. 7.14) and LBIC (Fig. 6.4) maps, the highly dislocated stripes are noticeable as regions with low lifetime or diffusion length. Moreover, Figure 7.3 illustrates a connection between dislocation density and subgrain boundary run. Grain A is characterized by parallel subgrain boundaries all running in the scan direction, and exhibits a maximum dislocation density of approximately 7 × 106 cm−2. In contrast, subgrain boundaries in grain B are not parallel and do not run parallel to the scan direction. Here dislocation density exceeds 5 × 107 cm−2, which is nearly one order of magnitude higher than the value in grain A.

128 OPTIMIZATION OF SILICON FILM QUALITY

Figure 7.2 Cross-sectional optical micrograph of an epitaxially thickened ZMR seed film on a SiO2 coated Si substrate. Subgrain boundaries (SGB) induce dislocations in the epitaxial layer. Defects are revealed by a Secco etch.

Figure 7.3 Optical micrograph of a polished and Secco-etched surface of an epitaxially thickened ZMR seed film. The stripes with high dislocation density arise from subgrain boundaries in the seed film (Fig. 7.2).

Electron backscatter diffraction (EBSD) pattern38 was used to investigate the connection between subgrain orientation and defect density in more detail. This technique uses a scanning electron microscope (SEM) operated in backscatter mode to produce so-called pseudo-Kikuchi patterns. These patterns are examined by digital image analysis yielding the crystal orientation for each measurement point. EBSD measurements were done at the University of Erlangen- Nürnberg with a JEOL JSM 6400 SEM and an Oxford Instruments EBSD setup.

38 The method is also referred to as orientation imaging microscopy (OIM).

7.1 Microstructure and Origin of Defects 129

Figure 7.4 Correlation between grain structure and texture. First row: SEM image, second row: EBSD orientation image of surface normal, third row: EBSD standard triangle representation. The high quality Si film (left column) is characterized by subgrain boundaries running parallel to the scan direction and a 〈001〉 texture. In the low quality film (right column) different orientations coexist.

130 OPTIMIZATION OF SILICON FILM QUALITY

Figure 7.4 compares typical EBSD results measured on a high quality and a low quality epitaxially thickened ZMR film. In the high quality film (left column) the surface normal coincides nearly perfectly with a 〈100〉 direction (Figs. 7.4a-2 and a-3). Furthermore, orientation in the scan direction was also found to be close to a 〈100〉 direction (data not shown in the figures). Again, these findings are well consistent with the growth model sketched in Figure 3.6. If the film’s surface normal and its scan direction are both 〈100〉 oriented, a straightforward relationship follows between thickness of the epitaxial layer W1 and width of the dislocated stripe Wd (see Fig. 7.2). For a point defect located at the interface between seed film and epitaxial layer, the maximum volume in the epitaxial layer that can be affected during epitaxial growth is given by a top- down pyramid. The sides of this pyramid are {111} planes, constituting the glide planes for dislocations in a face centered cubic crystal. Defect geometry is therefore analogous to that of epitaxial stacking faults [228], and Wd = 2W1. In contrast to the high quality film, the low quality one exhibits different grain orientations (Fig. 7.4, right column). Numerous small grains (brown color) with orientation significantly different from the dominating orientation (blue color) are noticeable. This behavior was found to be typical for the examined films. Cross sections often showed crystallites with different orientation directly above subgrain boundaries (see also Fig. 6.7). A straightforward strategy to decrease the harm of subgrain boundaries has been to grow ZMR film with subgrain boundary spacing as large as possible [145]. However, the results in this section indicate that for defect density in the epitaxially thickened films, macroscopic subgrain boundary structure (direction, parallelism) is at least as important as their spacing.

7.1.3 Microscopic Analysis The discussion in Section 7.1.1 showed that enhanced dislocation density in the epitaxial layer at subgrain boundaries seems to be inevitable. However, dislocation density within the stripes was found to vary (see Fig. 7.3). For more detailed investigations, beveled sections were prepared and examined with optical microscopy. In addition, surface and cross-sectional samples were analyzed by transmission electron microscopy (TEM).

7.1 Microstructure and Origin of Defects 131

Figure 7.5 Beveled section of an epitaxially thickened ZMR seed film. The optical micrographs in the upper and lower part were taken after different preparation steps (see text). The vertical scale is a projection of the z scale on the beveled surface which is declined 2°52’ relative to the sample’s surface.

The sample shown in Figure 7.5 was prepared as follows: Firstly, it was beveled on a frosted glass plate at an angle of 2°52’ relative to the sample’s surface. The small bevel angle »stretches« the section in the z direction by a factor of 20. Next, defects were revealed with a Secco etch. The upper part image in Figure 7.5 is from this stage. Subsequently, the beveled surface was polished and again treated with the Secco etch. After polishing, the surface quality had improved, but the sharp edge between surface and beveled part was lost, due to the soft polishing pad. Therefore, only the lower part image in Figure 7.5 shows the sample after the polishing process. The ZMR seed film shown in Figure 7.5 is characterized by a faceted surface. Such a structure was found to be typical for ZMR films grown with a thin thermal capping oxide (see Sec. 7.2.1). This finding fits with in situ observations during the ZMR growth process (see Fig. 7.1a). Dislocations in the epitaxial layer clearly originate at subgrain boundaries, located at the inner corner of two

132 OPTIMIZATION OF SILICON FILM QUALITY

(a) (b) (c) Figure 7.6 Details of the beveled section shown in Fig. 7.5. To enhance the contrast the dark background in the seed film region was removed by image processing. adjacent facets. Different from the seed film, the epitaxial layer exhibits a wavelike surface. Figures 7.6a–c show details of the beveled section of Figure 7.5. The images show a clear correlation between dislocation density in the seed film and the epitaxial film. Three different types of structures can be distinguished. In Figure 7.6a dislocation density in the region between the two subgrains is enhanced, but no explicit boundary is visible. Compared to Figure 7.6a, dislocation density in Figure 7.6b is much higher. Etch pits overlap and form clusters. The dislocation density in the epitaxial film is also much higher than in the former case. Figure 7.6c differs from the two other images by a straight subgrain boundary line. Around this line dislocation density in the seed film is enhanced, and the dislocation density in the epitaxial film is at its highest. The experimental observations discussed above can be well explained by a model of subgrain boundary formation developed by Baumgart and Phillipp [229]. Using high-voltage electron microscopy, they were able to investigate relatively large volumes without the preparational effort required for conventional TEM. Figure 7.7a sketches their central observation: the nucleation of slip dislocations and their transition into a low angle grain boundary. Baumgart and Phillipp explained their finding by polygonization, i.e., the rearrangement of thermally activated dislocations into a configuration with lower energy (Figs. 7.7b and 7.7c). The images from the seed film part in Figure 7.6 can be imag-

7.1 Microstructure and Origin of Defects 133

n o ti c e ir d n a c S

(b)

(a)

(c) Figure 7.7 Model for low angle grain boundary development by Baumgart and Phillipps [229]. (a) Rearrangement of dislocations along the scan direction. (b) Initial dislocation distribution. (b) Low angle grain boundary configuration after polygonization. ined to be sequential cross-sectional views of the specimen in Figure 7.7 perpendicular to the scan direction. The findings by optical microscopy were confirmed by TEM investigations. Contrary to optical microscopy, TEM allows one to »view« dislocations directly without special preparation. Furthermore, the high resolution enables one to resolve single dislocations even in the case of very high density. However, only a small area can be examined at a time and a high preparational effort is necessary for sample thinning. Unfortunately, the investigations did not succeed in viewing subgrain boundaries and dislocations at the transition of seed and epitaxial film at the same time. TEM samples were prepared and analyzed at the University of Erlangen-Nürnberg. Figure 7.8 shows a typical TEM surface-sectional view of a subgrain boundary in a ZMR seed film. The subgrain boundary can be identified as an array of dislocations. Close to the subgrain boundary two single dislocations are visible, a finding that matches with enhanced dislocation density near subgrain boundaries observed by optical microscopy (see Fig. 7.6).

134 OPTIMIZATION OF SILICON FILM QUALITY

Figure 7.8 TEM surface-sectional image of a subgrain boundary (SGB) and two singular dislocations (D) in a 2 µm thick ZMR seed film.

Figure 7.9 TEM cross-sectional image of a 2 µm thick ZMR seed film thickened by epitaxy.

The TEM cross-sectional image in Figure 7.9 shows two regions with evi- dently different dislocation densities. Based on known film thicknesses the two regions must be attributed as seed and epitaxial layer. In the upper region, dislocation density is very high with a value of approximately 109 cm−2. Since no contrast is visible between the seed and the epitaxial layer, it is unlikely that dislocation nucleate at the interface between the two layers. Possibly, the sectional view is positioned as shown in the inset in Figure 7.9.

7.2 EFFECT OF THE CAPPING LAYER

ZMR processing of Si films on SiO2 intermediate layers requires a capping layer to prevent balling-up of the molten Si (see Sec. 3.5.4). As an alternative to standard 1–2 µm thick LPCVD or PECVD SiO2 layers, in this work a thermally grown oxide was tested. This RTO capping oxide was directly grown in the

7.2 Effect of the Capping Layer 135

ZMR furnace before recrystallization. Such a process could save manufacturing costs, since model calculations indicate that capping deposition by PECVD would contribute significantly to total manufacturing costs [55]. Restricting the growth to a manageable process time, means that a thermal oxide must be much thinner than a PECVD one. Basic parametric studies on the dependence of oxide thickness on oxidation time are presented in Section 3.5.4. In this section, results on crystal quality and on solar cell parameters are presented, comparing a 0.15 µm thick RTO capping with a 2 µm thick PECVD

SiO2 one. Mainly 650–700 µm thick Cz-Si wafers were used as substrates, covered with a 1 µm thick thermally grown intermediate layer oxide. For the seed film, either 2 µm or 8 µm of Si was deposited, employing the processes S-IIa and S-IIb specified in Table 3.3. On the 2 µm thick Si films only the RTO capping worked properly, while balling-up occurred with the PECVD one. Therefore, the 2 µm thick Si films are excluded from comparisons. Solar cell results are additionally presented for 700–800 µm thick mc-Si wafer substrates covered with a 2 µm thick PECVD SiO2 intermediate layer. On the SiO2 coated mc-Si substrates 5– 10 µm of Si was deposited by process S-I (Table 3.3). Recrystallization scan speed was 10 mm min−1 for all samples.

7.2.1 Film Properties ZMR Si seed films grown with the 0.15 µm thick RTO capping differ from those grown with the 2 µm thick PECVD capping regarding (i) surface flatness and (ii) subgrain boundary spacing. (i) Figure 7.10 shows the surface of a 2 µm and a 8 µm thick seed film, both recrystallized with the thin RTO capping. Different from films grown with thick PECVD capping, these films show a faceted surface revealing individual subgrains. This observation is in accordance with results by Geis et al. who found that surface smoothness depends on capping layer thickness [109].39 (ii) Average subgrain boundary spacing in films grown with the thin RTO capping oxide was found to be higher than in films grown with the thick PECVD capping. Additionally, for the thin RTO oxide it was noticed that the

39 Differences between the 2 µm and the 8 µm thick Si film are discussed in Sec. 7.3.1.

136 OPTIMIZATION OF SILICON FILM QUALITY

Figure 7.10 Optical surface micrographs of ZMR Si seed films grown with a 150 nm thick RTO capping oxide. CVD Si film thickness was (a) 2 µm and (b) 8 µm, respectively. same width of the molten zone was reached with less electrical power for the focused lamp. The last two observations were confirmed theoretically applying a simplified model for radiation transfer during ZMR processing. In this model the Si film was assumed to be optically thick, i.e., thickness is much larger than wavelength and within the film light is completely absorbed. Si optical properties were taken from Ref. [219] neglecting the differing properties of liquid Si in the molten zone. SiO2 was considered to have a real refraction index of 1.46 [168] and no absorption. Temperature dependent material properties of Si and SiO2 were not taken into account. The lamp heater was modeled as a black body emitter with Planck’s energy distribution.

Energy absorption of the SiO2 coated Si was evaluated for 3300 K temperature, which was assumed as the temperature of the lamp emitter. The 150 nm thick SiO2 layer has a reflection minimum at 876 nm. According to Wien’s law, this value is close to the peak intensity wavelength of the 3300 K emitter.

Therefore, for the 3300 K emitter, the 150 nm thick SiO2 coated Si is an ideal absorber. Absorbed energy was computed to be approximately 9% higher for the

150 nm SiO2 coated Si than for the 2000 nm SiO2 coated Si. The still solid Si close to the molten zone was assumed to have a temperature of 1650 K. For this temperature energy emission of the SiO2 coated Si was

7.2 Effect of the Capping Layer 137 evaluated. Emitted energy was computed to be approximately 4% lower for the

150 nm SiO2 coated Si than for the 2000 nm SiO2 coated Si.

In summary, the 150 nm SiO2 coated Si film is the better selective absorber, explaining why less power is needed for ZMR processing. The effect on subgrain boundary spacing may be constructed as follows: The »gray« solid Si generally is a better absorber than the metallic liquid Si. Therefore, from improved optical properties, the solid Si profits more than the liquid one does. Assuming the model of radiative supercooling (Sec. 3.5.2) the effects of superheating and supercooling are strengthened, yielding increased width of the supercooled zone, and therefore increased subgrain boundary spacing. The above considerations relied on very rough approximations, and the only variable parameter taken into account was SiO2 thickness. Still, they show that capping film optical properties cannot be neglected, a finding also emphasized by other authors (e.g., see Refs. [230, 231]).

7.2.2 Solar Cell Results Figure 7.11 provides solar cell results of devices from films grown with both capping types. Solar cells fabricated from the 0.15 µm RTO capping films generally show better performance than those from 2 µm PECVD SiO2 capping films. This is due to significantly higher values of open circuit voltage Voc and short circuit current density Jsc. The better performance of solar cells from the 0.15 µm RTO capping films is valid on both substrate types, Cz-Si substrate and mc-Si substrate, respectively. The solar cell results fit well to crystallographic film quality. The films grown with thin RTO capping were found to be superior regarding parallelism of subgrain boundaries and subgrain boundary spacing. Both are criteria for films with low defect density (see Sec. 7.1.2) and therefore high effective diffusion length.

Voc and Jsc reflect the differences in effective diffusion length.

138 OPTIMIZATION OF SILICON FILM QUALITY

600 76.3 80 574 75 552 64.9 65.7 70 550 531 64.5 523 [mV] 65 oc FF [%]

V 60 500 55 17 16.5 7.0 7 ]

2 16.0 6.0 16 15.5 6 5.2 5.2 14.9 [%] [mA/cm 15 5 η

sc J 14 4

O D VD T V C R RTO RTO RTO EC PE PECVD PECVD P mc-Si Cz-Si mc-Si Cz-Si Substrate Substrate Substrate Substrate Figure 7.11 Solar cell parameters of devices from ZMR seed films grown with different capping types. Either a 0.15 µm thick RTO capping or a 2 µm thick PECVD SiO2 capping was employed for the ZMR process. Data with error bars are the average from two identically processed solar cells. The cells do not have surface texture, hydrogen passivation, or ARC.

7.3 EFFECT OF SCAN SPEED AND SEED FILM THICKNESS For costs of the ZMR process, scan speed is the most crucial parameter. Takami et al. [232] and Naomoto et al. [141] from the group at Mitsubishi Electric Corp. studied the effect of ZMR scan speed on film quality and solar cell results. They found that for »thick« films (≥ 1 µm) defect density significantly increased with increasing scan speed, while for »thin« films (< 1 µm) a high film quality could be fabricated even with high scan speed. Naomoto and co-workers proposed that defect density, as a first approximation, depends on the product of seed film thickness and scan speed. Development at Mitsubishi focused on reusable substrates while the concept in this work focuses on low cost substrates. Cost effectiveness of the low cost substrate concept requires compromises regarding surface roughness and flat-

7.3 Effect of Scan Speed and Seed Film Thickness 139

Table 7.1 Overview on investigated combinations of seed film thickness, capping type, and scan speed. Characterization was after epitaxial thickening by 30 µm CVD Si.

Substrate Seed film Capping Scan speed [mm min−1] thickness oxide 10 20 50 100

Cz-Si 2 µm RTO z1) z1) z1) z1) PECVD |3) |3) |3) |3) 8 µm RTO z1) 2) z1) 2) z1) 2) z1) PECVD z1) | z1) |

z - combination tested, | - combination not tested 1) solar cell results, 2) MFCA lifetime measurements, 3) balling-up ness, and the use of very thin films in the sub-micron range cancels out. There- fore, results presented in this section are for film thicknesses in the range of 2 µm to 10 µm. Investigations on scan speed were performed on standard Si wafer »model« substrates to ensure reproducible conditions, and to avoid simultaneous depend- encies on different parameters. For this purpose 650–700 µm thick Cz-Si wafers were used, coated with a 1 µm thick thermally grown oxide as an intermediate layer. For the seed film, either 2 µm or 8 µm of Si was deposited, employing the processes S-IIa and S-IIb specified in Table 3.3. During ZMR, Si films were covered by a 0.15 µm thick RTO capping. A few additional samples were also recrystallized with a 2 µm thick PECVD SiO2 capping. After removal of the capping, the seed film was epitaxially thickened with 30 µm Si, using process E- II specified in Table 3.3. Table 7.1 summarizes the investigated combinations of film thickness, capping type, and scan speed.

7.3.1 Crystallization Front Morphology and Film Properties Figure 7.12 shows typical in situ images of the molten zone during ZMR processing with 10 mm min−1 and 100 mm min−1 scan speed. Comparing the image at high scan speed to that at low scan speed, three main differences are

140 OPTIMIZATION OF SILICON FILM QUALITY

(a) (b) Figure 7.12 In situ images of molten zone and crystallization front morphology during ZMR. (a) For 10 mm min−1 scan speed, and (b) for 100 mm min−1 scan speed. Si film thickness was 8 µm and a 0.15 µm thick RTO capping was used. noticeable: (i) a wider molten zone, (ii) a less regularly structured crystallization front, and (iii) larger maximum size of faceted cells. (i) With an increase in scan speed, an increase in molten zone width was generally necessary to ensure complete melting of the Si film. At the melting front (upper interface in Figures 7.12a and 7.12b) a »slush« region can be identified where small islands of still not molten Si exists (visible as dark dots). The width of this region increases with increasing speed. To compensate for it, an increase in lamp power is necessary, yielding an increase in molten zone width. This behavior is consistent with theoretical and experimental results described in literature (e.g., see Refs. [102, 233]). (ii) With an increase in scan speed, the crystallization front morphology becomes temporally less stable. Faceted growth cells move laterally, cells vanish, or new cells evolve. As a result, subgrain boundaries do not run parallel anymore, but combine and split up frequently. This behavior fits with the finding that with increasing scan speed the percentage of grains with 〈100〉 texture decreases [109]. (iii) The maximum size of the growth cells increases with scan speed. According to the models discussed in Section 3.5.2 this behavior is caused by an increase in depth of the supercooled region. Connected with the increase in cell size is an increase in subgrain boundary spacing, which has been experimentally verified by different groups (e.g., see Refs. [109, 134]). Although maximum subgrain boundary spacing is desirable from the viewpoint of subgrain boundary

7.3 Effect of Scan Speed and Seed Film Thickness 141

(a) 2 µm, 10 mm/min (b) 2 µm, 100 mm/min

Figure 7.13 Typical grain structure of ZMR Si films using different combinations of film thickness (first value) and scan speed (second value). All samples were recrystallized with a 0.15 µm thick RTO capping, which was subsequently removed. The 8 µm thick films were additionally etched with a CP133 solution. related defects, the decreased stability of the crystallization front discussed above annihilates this positive effect. Figure 7.13 shows the grain structure of 2 µm and 8 µm thick Si films recrystallized with 10 mm min−1 and 100 mm min−1 scan speed, respectively. The 8 µm thick samples (lower row, Figs. 7.13c and 7.13d) were treated with a CP133 etch after capping removal. Therefore, different grain orientations manifest in different gray values. Comparing the 100 mm min−1 sample (Fig. 7.13d) with the 10 mm min−1 one (Fig. 7.13c), average grain size is significantly

142 OPTIMIZATION OF SILICON FILM QUALITY smaller. While for slow processing, grain length can be as long as the complete sample, grain length in the high-speed sample is in the centimeter range. The shorter grains and the different grain orientations mainly reflect the worse temporal crystallization interface stability, discussed as effect (ii) above. Further, the high-speed sample exhibits a less smooth surface than the low speed one. On the 2 µm thick samples, grain structure enhancement by etching was not possible, due to the danger involved in removing the complete film. Therefore, the dominating structures visible in the photograph are the relief like structures at subgrain boundaries. Comparing both samples recrystallized at 10 mm min−1 (left column, Figs. 7.13a and 7.13c), the thinner one is characterized by subgrain boundaries that are largely parallel to each other within a single grain, but which do not run parallel to the scan direction. The same effect is visible in Figure 7.10. This effect may be an indication that the thin thermal oxide capping is not able to stabilize the thin Si film sufficiently.

Electronic Properties After epitaxial thickening, carrier lifetime was measured by MFCA for selected samples. Due to interference with surface structure (see Sec. 6.4), the method could only be applied to samples from 8 µm thick seed films recrystallized at 10 mm min−1, 20 mm min−1, and 50 mm min−1 scan speed (Table 7.1).

Before MFCA measurements, surfaces were passivated by a hydrogen rich SiNx

Figure 7.14 Comparison of etch pit density (EPD) with minority carrier lifetime measured by MFCA. Data are for an epitaxially thickened 8 µm ZMR Si seed film recrystallized at 10 mm min−1.

7.3 Effect of Scan Speed and Seed Film Thickness 143

Lifetime τ [µs] 1.0 0.8 0.6 0.4 0.2 6 Scan speed: 50 mm/min 3 4 2

] 2 2 1 ] 3

[10 τ 20 mm/min 3 6 2 4

2 1

Counts Lifetime Etch Pit Density Counts Etch Pit Density [10 Density Pit Etch Counts 6 10 mm/min 3

4 2

2 Lifetime 1

106 10 7 108 -2 Etch Pit Density [cm ] (a) (b)

Figure 7.15 Dependence of EPD and minority carrier lifetime on ZMR scan speed. (a) EPD maps of epitaxially thickened 8 µm ZMR Si seed films. (b) EPD and MFCA lifetime histograms from the rectangular areas marked in (a). layer, which has proven to yield a very low effective surface recombination velocity [223]. After lifetime measurements, the samples were polished and defects were revealed by Secco etching, before EPD maps were acquired. Figure 7.14 shows an EPD and a MFCA map from the same region. Compar- ing the data, a good spatial correlation between carrier lifetime and EPD is found. Stripes with high dislocation density in the region of subgrain boundaries are well reproduced in the MFCA map as stripes with low lifetime. EPD maps for varying ZMR scan speeds are shown in Figure 7.15a. On the same samples, MFCA lifetime maps were measured. However, due to long acquisition time, MFCA measurements were restricted to the marked 4 × 5 mm areas. Still one measurement took around 17 h. The corresponding histograms in Figure 7.15b show a clear correlation between EPD and lifetime distribution. With an increase of scan speed from 10 mm min−1 to 50 mm min−1, average EPD increased from 4 × 106 cm-2 to

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2 × 107 cm-2, while simultaneously average lifetime decreased from approximately 0.72 µs to 0.56 µs. Maximum dislocation density is in accordance with the above-mentioned ZMR results by Naomoto et al. [141]. The result also fits with values published for EFG material [34]. For an increase of scan speed from a typical value of 10–20 mm min−1 to 100 mm min−1, an increase in dislocation density from 107 cm−2 to 108 cm−2 was reported. However, two remarks should be made concerning measurement accuracy. Firstly, it has to be noted that absolute lifetime measurement values by MFCA seem to be too high (see Sec. 6.4 for a discussion on possible causes). Further- more, the second peak in the EPD histogram (~2 × 107 cm-2) largely represents clustered etch pits. Therefore, total dislocation density may be underestimated.

7.3.2 Solar Cell Results Figure 7.16 shows measured illuminated solar cell parameters (bars) in dependence of ZMR scan speed, for devices from 2 µm and from 8 µm thick seed films. For all parameters a significant decrease with increasing scan speed is found, which is in accordance with the measurement results of minority carrier lifetime (Fig. 7.15). For the solar cells from 8 µm thick seed films, the tenfold increase of scan speed from 10 mm min−1 to 100 mm min−1 results in a decrease in solar cell conversion efficiency of 2.6% absolute, or approximately 35% relative. For the solar cells from 2 µm thick seed films, the absolute decrease is similar, on a generally lower level. In addition dark I-V curves were measured and fitted with the two-diode model by Eq. (4.28), yielding the dark saturation current densities J01 and J02

(Fig. 7.17). Using n1 = 1 and n2 = 2, the model could be well fitted to data from 8 µm seed film devices. On devices from the more defective 2 µm thick seed films, the curves deviated significantly from the ideal behavior and only the parameter J02 could be obtained reliably. The parameters J01 and J02 show a systematic increase with increasing ZMR scan speed. Particularly high are the J02 40 values. To study the effect of J02 on open circuit voltage more quantitatively,

40 Principally, open circuit voltage Voc can also be limited by parallel resistance Rp. However, 3 6 Rp values extracted from the fits are in the range 3.4 × 10 Ω to 5 × 10 Ω, and in this case Rp does not affect Voc.

7.3 Effect of Scan Speed and Seed Film Thickness 145

600 80 575 Limit by J Limit by J 02 02 75 550 70 525 65 500 60 [mV] oc 475 55 [%] FF V 450 50 425 45 17 7 16 ] 2 6 15 14 5

4 [%] [mA/cm 13 η

sc J 12 3 11 2 10 20 50 100 10 20 50 100 Scan speed [mm/min] Scan speed [mm/min]

Seed film thickness: , : 2 µm; , : 8 µm

Figure 7.16 Dependence of solar cell parameters on ZMR scan speed for devices fabricated from epitaxially thickened 2 µm and 8 µm thick seed films. Bars represent measured data, symbols calculated values (see text). Data are for solar cells without surface texturing, hydrogen passivation, and ARC.

Voc and FF were computed by the two-diode model, taking the experimentally determined J02 values as input parameters. All other parameters were kept fixed −2 using typical experimental values of a good solar cell: JL = 15 mA cm , −12 −2 J01 = 3 × 10 A cm , Rp = 10000 Ω, and Rs = 1.1 Ω (for 8 µm thick seed films) or Rs = 2.1 Ω (for 2 µm thick seed films). The calculated values are plotted additionally in Figure 7.16 (symbols) resem- bling the trend of the experimental values. It can be concluded that the observed decrease in Voc and FF is largely due to a high recombination current density J02 in the space charge region. This result fits the findings of other groups, who stressed the importance of space charge region recombination in thin-film solar cells [234, 235].

146 OPTIMIZATION OF SILICON FILM QUALITY

10 8 ] ]

data not fitable -2 -2 8 with two diode model 6

6 A cm A cm 4 -7 -12 4 [10 [10

2 02

01 2 J J 0 0 10 20 50 100 10 20 50 100 Scan speed [mm/min] Scan speed [mm/min]

Figure 7.17 Dependence of saturation current densities J01 and J02 on ZMR scan speed for devices from 8 µm thick seed films. Data were measured on the same solar cells for which the illuminated parameters are shown in Fig. 7.16.

The generally worse performance of solar cells from the 2 µm thick seed films is in accordance with film properties discussed in the sections above. At first sight, this result contradicts to that of Takami et al. [232] and Naomoto et al. [141] who found an increase of solar cell performance with decreasing film thickness. However, one major difference between the samples used in this work and that employed by the Mitsubishi group is the capping type. All samples investigated in this section were recrystallized with 0.15 µm thick RTO capping while the Mitsubishi results are for a »standard« capping stack of 1 µm SiO2 and

30 nm Si3N4. As shown in Figure 7.10, the thin RTO capping does not hinder the film from developing a strongly faceted surface. Therefore, it might be possible that results would be different for a thicker and more stable capping. Since balling up occurred at ZMR of 2 µm thick Si films with the standard PECVD

SiO2 at Fraunhofer ISE (Table 7.1) this hypothesis could not be proved.

7.4 EFFECT OF SUBSTRATE Cz-Si and mc-Si wafers used for the investigations discussed in the previous sections represented »model« substrates. In parallel, substrate materials with low-cost potential have been tested. However, these materials, or the special product fabricated from these materials, are largely not yet established. Being at this stage of development meant that reliable processing of Si thin films turned

7.4 Effect of Substrate 147

Figure 7.18 Cracked Si film on a RBSN ceramic substrate (Composition 4-1). out to be difficult. The following sections discuss key issues regarding material requirements and compatibility with CVD Si deposition and ZMR processing.

7.4.1 Thermal Expansion One essential requirement on the substrate material is the match of its thermal expansion to that of Si. Although this criterion was considered in the selection of investigated materials, cracks have been a typical cause for failure of the substrate/Si film stack. The cooling down phase after CVD epitaxial thickening turned out to be the most critical process for crack formation. A typical sample at this stage is shown in Figure 7.18, in the case of a SiN ceramic substrate. A short CP133 etch enhanced the cracks and additionally revealed dislocations. The stripes of high dislocation density represent the run of the subgrain boundaries in the ZMR seed film. Therefore, the image allows an instructive geometric correlation between the run of cracks and subgrain boundaries. The cracks form a network of perpendicular lines. A slight tilting can be detected between the left and the right part of the image, indicating a high angle grain boundary (dashed line). Parallel subgrain boundaries intersect the cracks with an angle of approximately 45° (indicated by short dashed lines with

148 OPTIMIZATION OF SILICON FILM QUALITY

0.8 SiN 2-5 0.7 ZrSiO 4 [%]

0 0.6 Si l / SiN 4-5 ∆ 0.5

0.4 SiN 4-1 0.3

0.2

0.1 Change in length Change in length 0.0 200 400 600 800 1000 1200 1400 1600 1800 Temperature [K]

Figure 7.19 Linear thermal expansion of different ceramic compositions compared to the expansion of Si. Data for Si and ZrSiO4 were taken from Refs. [62] and [236] respectively. arrows). This finding fits well with the growth geometry shown in Figure 3.6. Assuming a cellular growth interface, the subgrain boundaries are in a 〈100〉 direction and the surface coincides with a {100} plane (see the crystal axis sketched in Fig. 7.18). With this geometry cracks then must be in {111} planes, which are well known to be the easiest breakage or cleavage planes of Si crys- tals [168]. During solar cell processing, cracks can result in shunting or may lead to isolated cell areas. For the SiN ceramic substrates, different compositions have been investigated. Thermal expansion was studied by dilatometric measurements performed at Ceramic for Industries (CFI)41, Rödental. Figure 7.19 compares typical curves of the relative change in length of Si to three different SiN compositions. Com- position 4-1 resulted in the cracked Si film shown in Figure 7.18, while no cracks were found for compositions 2-5 and 4-5, both prepared with additives. Composition 4-5 provides the best match to Si but shows a rapid contraction

41 Now fused with Technical Ceramics (TeCe), Selb to HC Starck Ceramics.

7.4 Effect of Substrate 149 below 1600 K. This behavior might be explained by the melting and escape of additives or of excess free Si.

Additionally plotted in Figure 7.19, is the expansion of ZrSiO4, taken from literature data. Similar to SiN ceramic composition 2-5, Si films on ZrSiO4 ceramics could be processed without cracks. In summary, ceramics with thermal expansion slightly higher than that of Si could be processed successfully, while those with thermal expansion slightly lower than that of Si failed. This observation is reasonable: in the first case, the Si film is subject to compressive stress during the cooling down phase, while in the second case tensile stress is present. Although the compressive stress did not result in any cracks, other harmful effects on crystal quality cannot be ruled out. From the measurement results discussed above, it must be concluded that for typical Si film thickness the maximum tolerable difference in change of length is well below 1‰. Two general conclusions can be drawn for the high temperature concept. Firstly, it is useful to work with the temperature dependent thermal expansion coefficient α(T) instead of the mean coefficient α (Sec. 3.2.1). Secondly, the T0 ,T most relevant issue for practical applications is the relative change in length between the Si and the substrate material.

7.4.2 Surface Roughness and Intermediate Layer Stability Effects of surface roughness on Si thin-film formation have been observed regarding three aspects: (i) During deposition of CVD Si for the seed film, a surface roughness that is too high may prevent the formation of a closed film. (ii) A Si film with very inhomogeneous thickness may not be stable during ZMR processing and may result in holes. Furthermore, a nonuniform temperature distribution may arise and result in poor crystal quality. (iii) Interaction between the substrate and the intermediate layer may damage the intermediate layer, supporting diffusion of impurities and risking the stability of the complete stack. Effect (i) and (ii) can only be prevented if the layer thickness exceeds the total surface roughness Rt. The experimental results are in accordance with a rule of thumb, which states that the maximum roughness should be less than one third of the seed film thickness (Ref. [59], p. 96). Issue (iii), stability of the intermediate layer, turned out to be a more complex issue. It is especially difficult to

150 OPTIMIZATION OF SILICON FILM QUALITY

(a) (b)

Figure 7.20 (a) Grinded surface of a ZrSiO4 substrate. (b) Cross section revealing a damaged ONO stack intermediate layer after Si deposition. judge whether a failure of the intermediate layer is primarily due to mechanical overload or chemical instability.

Figure 7.20 illustrates the latter effect for a ZrSiO4 substrate. Although the substrate was grinded, the surface is quite rough with an average roughness

Ra = 0.4µm and a total roughness Rt = 7.3 µm, due to open pores (Fig. 7.20a). A cross section prepared after Si CVD shows that the intermediate layer is no longer intact at this stage (Fig. 7.20b). The ONO layer adapts well to the surface topology with homogeneous thickness, but exhibits several vertical cracks. One reason might be that ZrSiO4 is actually a SiO2-ZrO2 System ([60], p. 136). It may tend to incorporate further SiO2 and therefore decompose the intermediate layer [237]. Damaged intermediate layers like in Figure 7.20b were found to be responsible for the agglomeration of liquid Si during ZMR processing. This balling-up

Figure 7.21 Agglomeration of liquid Si (dark spots) during ZMR processing due to a damaged intermediate layer. Marked with dashed lines are the locations of cracks that are pene- trating the intermediate layer and the ZrSiO4 substrate.

7.4 Effect of Substrate 151

Figure 7.22 Correlation between ZMR growth morphology (in situ observation, left and right) and grain structure (middle) for a Si film on a SSP substrate. effect is visible in situ by dark spots (Fig. 7.21), which arise from crystallized islands within the molten zone. On Si substrates, damaged intermediate layers were found to manifest in a somewhat different way. Holes in the intermediate layer hinder lateral over- growth, since dominant heat transfer is into the substrate and not into the already crystallized Si film. An example of this effect is shown in Figure 7.22 for Si film formation on a SSP substrate. The right part of the finished film (middle image) exhibits large longitudinal grains, as is typical for ZMR films. In situ images captured during ZMR film growth (right image) reveal a faceted, columnar crystallization interface. In contrast, the left part of the finished film (middle image) is composed of very small grains with no preferential orientation. The corresponding in situ image of the crystallization front shows an »island growth mode«. A cross- sectional image (Fig. 7.23) reveals that crystal growth indeed starts at holes in the intermediate layer from the underlying substrate. A clear indication is the

Figure 7.23 Cross section of a ZMR seed film on a SSP substrate with a damaged intermediate barrier layer (arrow).

152 OPTIMIZATION OF SILICON FILM QUALITY grain boundary that extends from the substrate into the recrystallized seed film. It has to be mentioned that on Si substrates this kind of damage was solely found on SSP substrates fabricated with an in situ carbon and oxygen-containing layer.

7.4.3 Thermal Properties Morphology and stability of the ZMR crystallization front are largely determined by the thermal gradient at the solid-liquid interface (see Sec. 3.5). The thermal gradient decides on the degree of supercooling and therefore on the stability or instability of the crystallization front structure. The substrate can affect the thermal gradient directly through its thickness and its thermal conductivity. Consequently, inhomogeneous thickness or inhomogeneous thermal conductivity results in inhomogeneous thermal gradients and therefore prevents homogeneous growth. Furthermore, the substrate can affect ZMR growth indirectly. For example, inhomogeneous substrate thickness may yield inhomogeneous Si film thickness. This will affect thermal conductivity within the Si film. Based on theory, dendritic growth as in Figure 7.1d is expected for a very low thermal gradient. Indeed the thermal conductivity of the employed SiSiC ceramics is approximately five times as high as that of Si3N4 ceramics, on which cellular growth morphologies prevailed. Nevertheless, in the concrete case, dendritic growth may further be stipulated by a high impurity concentration. Another situation is illustrated in Figure 7.24. Inhomogeneous thickness of the employed SSP substrate results in a wavelike molten zone with inhomogeneous width. In this case, ideal growth conditions can only be achieved locally and not at different positions at the same time. A remark shall be given on the option to compensate substrate properties by adequate process control. Principally the temperature gradient can be adjusted in the ZMR furnace by the power ratios of lower heater and focused lamp. How- ever, the desired vertical growth mode (Sec. 2.2.1) requires the heat of fusion transferred into the already grown film and not into the substrate. Therefore, strong heating from beneath the sample is inevitable. For the employed ZMR system the maximum power of the lower heater is 60 kW compared to 2 kW for the focused lamp. Within the full range of power settings for the focused lamp,

7.4 Effect of Substrate 153

Figure 7.24 Molten zone with inhomogeneous width due to nonuniform thermal conductivity of the SSP substrate beneath (ZMR in situ observation). the ratio of upper and lower heater power only changes marginally. As for the SiSiC substrates, it was found that in many cases the thermal properties of the substrate cannot be compensated by process control. Generally, on thick substrates more stable growth and better film quality was achieved than on thin substrates. This was also true for mc-Si wafers, where a thickness in the range of 600 µm to 800 µm turned out to be superior to the standard thickness of around 300 µm.

7.4.4 Summary on Substrate Investigations In the preceding sections, three key issues concerning substrate requirements have been discussed: (i) match of thermal expansion coefficient, (ii) stability of intermediate layer during CVD and ZMR processing, and (iii) homogeneity of thermal properties and their compatibility with ZMR growth. At this point in time, none of the potential low-cost substrates investigated in this work are completely suitable for the applied technology yet. For future successful Si film preparation, the attention has to be directed more into details. This includes fine adjustment of the TEC, a precise control of surface roughness, thickness tolerances, and homogeneity of material properties. The material chosen for the intermediate barrier layer has to be checked for compatibility with both, liquid Si and substrate material. Despite these difficulties, several Si films on ceramics and SSP substrates have successfully been processed to thin-film solar cells. Table 7.2 summarizes the parameters of the best solar cells achieved so far on the investigated substrate types. Performance of the solar cells on ceramic substrates is primarily limited by low fill factors FF and secondarily by low open circuit voltages Voc. Therefore, it is likely that both effects are caused by a highly defective space charge region yielding a high saturation current density J02 (see also the discussion in Sec. 7.6).

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Table 7.2 Parameters of the best thin-film solar cells fabricated on ceramic and SSP ribbon substrates.

Substrate Voc Jsc FF η Remark Reference [mV] [mA cm−2] [%] [%] for details

Si3N4 537 26.1 66.7 9.4 Reaction bonded, [238] ceramics composition 4-5

ZrSiO4 536 26.7 58.1 8.3 Composition [239] ceramics containing free Si SiSiC 554 28.9 66.8 10.7 Reaction bonded [91] ceramics SSP ribbon 578 25.7 76.4 11.3 In situ SiC barrier [240] layer, no surface leveling

7.5 DEPENDENCE OF EFFECTIVE DIFFUSION LENGTH ON DISLOCATION DENSITY In this section, quantitative results on recombination activity of dislocations are presented. Their effect on effective diffusion length was studied by analyzing typical thin-film devices with the characterization methods described in Chapter 6 and by applying the theoretical model developed in Chapter 5. For these experiments 300 µm thick mc-Si wafers were used as substrates, coated with a 2 µm thick PECVD SiO2 intermediate layer. CVD Si for the seed film and for the epitaxial layer was deposited by the processes S-I and E-I as specified in Table 3.3. The seed films were recrystallized with 10 mm min−1 scan speed, using a 2 µm thick PECVD SiO2 capping. The finished solar cells were passivated in a remote hydrogen plasma and a double layer antireflection coating was deposited. For electrical characterization SR-LBIC maps were recorded. Effective diffusion length was calculated by fitting the data points with the function given in Appendix D [Eq. (D.1)]. The effective surface recombination velocity at the p-p+ junction was calculated from thickness and doping data as done in Section 6.3.1. After SR-LBIC measurements, the samples were polished, Secco-etched, and EPD maps were acquired. Then the EPD map was transformed into an EDD map as described in Section 6.5.4, taking into account the LBIC beam profile and carrier diffusion. Finally, the LBIC map

7.5 Dependence of Effective Diffusion Length on Dislocation Density 155

Figure 7.25 EPD map of the sample for which Leff data are shown in Fig. 6.4. In the marked areas of interest (AOI), Leff and EPD data were correlated and fitted with the modified Donolato model (see Fig. 7.26). coordinate system was matched to the EPD/EDD one, and the data were fitted by the modified Donolato model (see Sec. 5.4.2). Figure 7.25 shows a typical EPD map of an epitaxially thickened ZMR seed film together with normalized recombination strength values. The corresponding

AOI-1 AOI-2 AOI-3

[µm] 100 100 100

eff L = 63 µm L = 80 µm L = 52 µm 0 0 80 0 80 80

60 Γ = 0.009 60 60 d Γ = 0.013 Γ = 0.015 d d 40 40 40 20 20 20 0 0 0 106 107 108 106 107 108 106 107 108 Eff. Diffusion Length L Length Diffusion Eff. Effective Dislocation Density EDD [cm-2]

Figure 7.26 Correlation of EPD and Leff data (symbols) from the areas of interest (AOI) marked in Fig. 7.25, and simulation with the modified version of Donolato’s model (line). Data points drawn with open symbols were not considered in the fit.

156 OPTIMIZATION OF SILICON FILM QUALITY

Table 7.3 Sensitivity of the fit parameters L0 and Γd on the effective diffusion length Leff,l. The parameter Leff,l describes carrier diffusion from the point of generation and affects the convolution kernel used to transform the EPD map into an EDD map.

Area of interest Leff,l [µm] L0 [µm] Γd

AOI-1 15 48 0.008 30* 52 0.009 50 57 0.010

AOI-2 20 54 0.012 35* 63 0.013 60 85 0.015

AOI-3 25 66 0.013 40* 80 0.015 60 111 0.016

* Average effective diffusion length within AOI =Leff

Leff map of the same sample is shown in Figure 6.4b. Fit parameters were the normalized recombination strength Γd and the bulk diffusion length in the non- dislocated material L0. Best-fit curves for the three marked areas of interest

(AOI) are plotted in Figure 7.26, yielding recombination strength values Γd from

0.009 to 0.015 and diffusion length values L0 in the range of 52 µm to 80 µm. In the EPD to EDD transformation algorithm, carrier diffusion from the point of generation into neighboring regions is taken into account by convolving the effective diffusion length map with a filter kernel. The local decay constant Leff,l, which is entered into the kernel function given by Eq. (6.7), is not known a priori. As described in Section 6.5.4, Leff,l was approximated by the average diffusion length within the examined AOI Leff. The effect of Leff,l on best-fit parameters was investigated by a sensitivity analysis (Table 7.3). The recombination strength Γd varies only slightly with Leff,l, and compared to other uncertainties, such as measurement errors, the effect is negligible. In particular, a dislocation line has a low dimension, compared to surface and volume recombination entities, and therefore major changes in Γd are necessary to produce a significant change in the overall recombination activity. The effect of Leff,l on L0

7.5 Dependence of Effective Diffusion Length on Dislocation Density 157

Figure 7.27 EPD map from a sample produced with the same technology as the one analyzed in Fig. 7.25. In the marked areas of interest (AOI), the Leff and EPD data were correlated and fitted with the modified Donolato model.

is more pronounced, but due to the lack of data points near ρd = 0 (Fig. 7.26), the accuracy of the fit value for L0 is limited anyway. The EPD map shown in Figure 7.27 was measured on a sample produced with the same technology as the one analyzed in Figure 7.25. Ranging from 0.006 to

0.016, recombination strength values Γd are of similar magnitude as those in the former sample. The corresponding best-fit values for L0 in the areas labeled »AOI-1«, »AOI-2«, and »AOI-3« are 177 µm, 67 µm, and 76 µm, respectively.

7.5.1 Discussion on Recombination Strength Results In both thin-film solar cells presented above, similar recombination strength values were measured. The difference between minimum and maximum value is less than a factor of three. This is not a substantial variation, when taking into account the fact that a dislocation line is a one-dimensional entity and therefore only affects recombination in a small volume fraction. Even for surfaces, recombination velocity must usually vary by about one order of magnitude in order to have a significant affect on solar cell performance. The fairly regular distribution of defects resulting from the ZMR process supports the finding of homogeneous recombination strength. However, we have to be aware that the minimum area yielding a single recombination strength value with sufficient accuracy is approximately 1 mm2 (corresponding to ∼400 data points). The

158 OPTIMIZATION OF SILICON FILM QUALITY

Table 7.4 Recombination strength data found in literature.

Sample type τ meas. Typical Γd Remarks Reference (all based on method (Extreme Γd) mc-Si) Unprocessed SPV 0.01–0.04 [202] wafers Solar cells LBIC 0.001–0.008 [202] Solar cells LBIC 0.001–0.006 Tube furnace and [204] (< 0.0003–0.016) RTP diffusion Solar cells LBIC < 0.001–0.008 Values are reduced to [205] ∼20% after hydr. passivation Solar cells LBIC 0.003–0.006 Values are reduced to [241] ∼20% after hydr. passivation Heterojunction LBIC 0.0001–0.005 Low temp. a-Si [241] solar cells emitter

SiNx passivated CDI / 0.0006–0.003 [206] wafers ILM Not published Not 0.2 Fit to data from [198] published Ref. [201] method is therefore not suitable to study microscopic effects, such as enhanced recombination activity at single dislocation clusters.

Remarkably, in both EPD maps (Figs. 7.25 and 7.27) the lowest Γd values are found in AOIs with the highest »contrast«, i.e., regions including points with very low as well as very high dislocation density. However, it has to be taken into account that with increasing dislocation density the amount of clustered, overlapping etch pits increases and therefore measurement accuracy decreases. The experimental values determined in this work fit well to the data found in literature (Table 7.4). Extensive work has been published by a group at TU Bergakademie Freiberg [202, 204, 205, 241]. Largely, the experimental methods used by Lawerenz et al. and Rinio et al. are similar to those presented here. For diffusion length measurements on unprocessed wafers, they used the surface photo-voltage (SPV) method, while for finished solar cells LBIC was employed. Etch pit counting was also done by optical microscopy and automated image analysis. However, differences exist concerning data processing: (i) dislocations

7.6 Dependence of Open Circuit Voltage on Dislocation Density 159 near the point of carrier injection were considered in a partly different way [204], and (ii) LBIC quantum efficiency data were taken for a single wavelength only. Effective diffusion length was then calculated through a numerical model for the specific solar cell type, while in our calculation only analytical expressions are involved. However, the recombination strength values determined in this work for thin-film solar cells are similar to the ones measured for conventional mc-Si solar cells. This holds, even though for the investigated thin-film Si samples dislocation density was much higher (1 × 106 cm−2 to 5 × 107 cm−2) than for typical mc-Si solar cells (1 × 104 cm–2 to 5 × 106 cm–2). The results found here are also in line with earlier results by Riepe et al., investigating recombination strength using carrier density imaging (CDI) for effective lifetime measurements [206]. The only incompatible data in Table 7.4 are the one from Ref. [198]. The recombination strength given in this work is one to two orders of magnitude higher than the other values. Donolato obtained these results by applying his model to the data published in Ref. [201]. However, in the original publication neither the techniques for dislocation density and carrier lifetime measurement are mentioned nor is a statement made regarding whether the values were measured on raw wafers or on finished solar cells.

7.6 DEPENDENCE OF OPEN CIRCUIT VOLTAGE ON DISLOCATION DENSITY

In Section 7.3.2 a strong decrease in open circuit voltages Voc was observed for an increase in ZMR scan speed, and therefore an increase in dislocation density (see Fig. 7.16). In this section, based on Donolato’s description for the effect of dislocations, a model is presented that describes the experimentally observed dependence of open circuit voltage on dislocation density ρd. Experimental data were determined for the same series of solar cells that was used for the study on scan speed (see Sec. 7.3). The combinations of seed film thickness and scan speed were chosen to represent samples with significantly different dislocation densities. Table 7.5 shows the technological parameters of the analyzed samples together with the resulting values of dislocation density and effective diffusion length. Illuminated I-V curves were measured after metallization and after hydrogen passivation and ARC deposition. On the finished devices with ARC, IQE curves

160 OPTIMIZATION OF SILICON FILM QUALITY

Table 7.5 Technological parameters of analyzed samples together with measured values of dislocation density and effective diffusion length. The thicknesses W1 and W2, respectively, refer to the final thickness in the solar cell, taking into account reduction by etching steps. Further assumptions that enter into the calcula-

tion of the effective surface recombination velocity s1 are: Leff,2 = 6.5 µm and S2 = 105 cm s−1.

ZMR seed p+ layer ZMR scan p layer Dislocation Effective film thickness thickness speed thickness density diffusion length −1 −2 [µm] W2 [µm] v [mm min ] W1 [µm] ρd [cm ] Leff,IQE [µm]

8 6.5 20 27 8.9 × 106 30 8 6.5 50 27 1.6 × 107 23 2 2 20 27 3.3 × 107 12 were also determined.42 As can be taken from Table 7.5, Si film thickness and effective diffusion length are in the same range, and therefore strictly speaking, the function IQE−1(α−1) cannot be described by a linear relationship. Thus, for the solar cell with the highest diffusion length, the exact nonlinear curve [Eq. (D.1)] was fitted to the measured quantum efficiency data. As before, the effective surface recombination velocity at the p-p+ junction was calculated from thickness and doping data. Then, based on the data from the fit by the exact function, the error made when using the approximate linear fit was quantified. Consulting Figure 6.1 the systematic error using the linear fit is below 2% relative, and therefore it is negligible compared to the error stemming from measurement inaccuracies of the IQE data. In conclusion, the more sophisticated fitting routine does not yield improved accuracy in this case. For that reason, all effective diffusion values given in Table 7.5 were determined by linear fitting. Dislocation density was measured on samples either from the same wafer or from a wafer recrystallized with identical parameters. An average dislocation density value was calculated from the 14 000 to 32 000 data points in each EPD map. The method of averaging was chosen from the viewpoint of effective diffusion length. Let us assume that the effective diffusion length extracted from a full area IQE measurement has the value Leff,IQE. The average dislocation den-

42 The significantly lower reflection after ARC deposition yields lower error in the calculated IQE data.

7.6 Dependence of Open Circuit Voltage on Dislocation Density 161

650 [µm] [mV] eff 100 oc J only Exp. data 600 01,B

30 Exp. data 550 before hydr. Modeling after hydr. Γ = 0.008 10 d Γ = 0.017 d J + J Γ = 0.04 500 01,B 02 d Open circuit voltageV 105 106 107 108 105 106 107 108 Effective diffusion length L -2 -2 Dislocation density ρ [cm ] Dislocation density ρ [cm ] d d (a) (b)

Figure 7.28 (a) Dependence of effective diffusion length Leff on dislocation density ρd. The experimental data points Leff,i(ρd,i) (Table 7.5) are fitted with the modified version of Donolato’s model. Modeled curves are shown for

the recombination strength value yielding the best-fit (Γd = 0.017) as well as

for Γd = 0.008 and Γd = 0.04. (b) Dependence of open circuit voltage Voc on dislocation density ρd. The relationship is modeled using the same recombination parameters as in Fig. (a). The curves drawn with thin lines take into account a dislocation dependence on J01,B only, while those drawn with thick lines additionally consider space charge region recombination (J02). Fixed −1 parameters were ε = 0.01 µm, W1 = 27 µm, and s = 0.004 µm .

sityρd is then defined as the value that, in a reference device with homogeneously distributed dislocations, would yield the same effective diffusion length value Leff,IQE. To a first approximation, Leff,IQE is linear in the logarithm of ρd. Therefore, the averaging was performed on the logarithmic EPD values.

In Figure 7.28a the data of Leff,IQE and ρd from Table 7.5 are plotted together with simulated curves using the modified Donolato model [given through Eqs.

(5.40), (4.37), (5.6), and (5.8)]. Taking ε = 0.01 µm, W1 = 27 µm, and s1 = S1/D1 −1 = 0.004 µm as fixed parameters, the best-fit values obtained are L0 = 119 µm and Γd = 0.017. Additional curves are plotted for recombination strength values of approximately one-half and two times the best-fit value (i.e., Γd = 0.008 and

Γd = 0.04). Note that in the logarithmic scale, a variation in Γd yields a parallel displacement of the Leff vs. ρd curve.

162 OPTIMIZATION OF SILICON FILM QUALITY

Based on his model for the effect of dislocations on effective diffusion length,

Donolato has also calculated the effect on open circuit voltage Voc [197]. In this work he considered the dislocation dependence of Voc through the base saturation current J0,B. Insertion of Eq. (5.7) into Eq. (6.3) yields

kBT  J L Leff (ρd )  Voc (ρd ) = ln +1 . (7.1) q  qDnn0 

In Figure 7.28b (thin lines) the function Voc(ρd) is plotted, which results when inserting the function Leff(ρd), shown in Figure 7.28a, into Eq. (7.1). As light −2 generated current JL, the maximum Jsc value (= 17.7 mA cm ) from the three solar cells listed in Table 7.5 was inserted.

However, in the investigated solar cells, Voc is strongly affected by space charge region recombination, as has been discussed in Section 7.3.2 (see Figs. 7.16 and 7.17). In order to account for this effect, the forward bias recombina- + tion current Jrg was considered by Eq. (4.27), where the space charge region 2 lifetime τ0 was replaced by the function Leff(ρd) /Dn. The term for J02 was inserted into Eq. (4.28) (two-diode model), and the equation was solved for Voc with Rs = 0, Rp = ∞, n1 = 1, and n2 = 2. For simplification, equal lifetimes were taken for both carrier types (τp = τn), mobilities for p-type quasineutral and space charge region were assumed to be equal, and band-gap narrowing was neglected. The resulting curves are plotted in Figure 7.28b (thick lines). While a change in the recombination strength Γd produces a parallel shift of the curve, the slope is determined by the nature of the recombination channel. In the quasineutral region, the recombination current is proportional to τ−1/2 [Eq. (5.8), and L=(Dτ)1/2], while in the space charge region it is proportional to τ−1 [Eq. (4.27)].

Therefore, in the later case a much steeper decrease of the Voc vs. ρd curve is found. For fitting the model to the experimental data, the effective width of the space charge region Weff was used as additional variable parameter, yielding an opti- mal result for Weff = 1 µm (thick lines in Fig. 7.28b). This value is much larger than estimations for Weff obtained from a numerical modeling of the investigated solar cell structure with the software PC1D [242]. In this simulation a maximum

7.6 Dependence of Open Circuit Voltage on Dislocation Density 163

−1 field strength Emax of ∼33 kV cm was found. Inserting this value into the 43 approximation by Eq. (4.26) yields Weff = kBT/πqEmax = 0.025 µm.

Instead of an increase of Weff, the enlarged J02 component could equally be attributed to an increase of the intrinsic carrier concentration or a decrease in the lifetime τ0 [see Eq. (4.27)]. It has to be kept in mind that Donolato’s model is based on a solution of the transport equation in quasineutral regions and it does not consider electric fields. The consideration of such electric fields could be important if recombination at dislocations is not adequately described by the Shockley-Read-Hall model but with the model of charge-controlled recombination as proposed by Wilshaw et al. [208, 210, 243]. However, results on fine-grained Si films support the theory of a pure geometric enlargement of the space charge region. For thin-film solar cells from fine-grained Si films, Beaucarne et al. found that the width Weff has to be much wider than the effective width derived from the maximum field strength, in order to explain the measured recombination current. Firstly, they proposed an extension of the space charge region due to depleted grains, caused by a high density of grain boundaries [244]. Later they modified their model and successfully explained their experimental findings by preferential diffusion of phosphorus at grain boundaries [245]. The replacement of the diffused junction by a heterojunction indeed led to a strong decrease of the SCR saturation current and supports the latter interpretation [246]. In analogy, in the Si thin films studied in this work, preferential diffusion of phosphorus at dislocations and/or grain boundaries may extend the junction area. For the devices investigated in Ref [245], in addition an increase of carrier collection efficiency has been observed. In contrast, in our devices effective diffusion length decreases with increasing dislocation density (see Table 7.5). However, this finding can be explained with the ratio of effective space charge region width Weff to effective diffusion length Leff. The dimension of Weff was found to be ∼1 µm, while for Leff values were in the range of 12 µm to 30 µm. Therefore, the effect of enhanced carrier collection would be negligible. An

43 A similar is obtained when alternatively using the linear potential variation Emax = 2(Vbi –

V)/Wscr. The values Vbi − V ≈ Vbi = 0.6 V (small forward bias) and Wscr = 0.17 µm, estimated from PC1D simulations, lead to Weff = 0.023 µm.

164 OPTIMIZATION OF SILICON FILM QUALITY additional effect of the preferential doping might be an effective decrease of the emitter doping concentration. This effect could decreases the electric field and therefore enhance the width Weff as argued in Ref. [246].

7.7 SUMMARY AND OUTLOOK Fabrication of the Si thin films investigated in this work involves two key processes: creation of a seed film by ZMR, and thickening of this film by CVD epitaxy. The completed films are characterized by large grain size, comparable to that of standard cast mc-Si material, but a significant number of intragrain defects. These defects originate at subgrain boundaries, which are an inevitable feature of the ZMR process. While a natural strategy to decrease the harm of subgrain boundaries has been to increase their spacing, it has been demonstrated that their run is of equal importance. Parallel subgrain boundaries, which run in the scan direction, yield the lowest defect density in the epitaxial film. A clear correlation between dislocation density within the subgrain boundaries and the epitaxial film could be proven. The experimental observations fit a model by Baumgart and Phillipp well, which explains subgrain boundary formation by rearrangement of single dislocations into an energetically more favorable state [229]. To prevent agglomeration of liquid Si, the ZMR process requires the use of a capping oxide. As an alternative to standard 1 µm to 2 µm thick PECVD or

LPCVD SiO2, a 0.15 µm thick RTO capping was tested, which was directly grown in the ZMR system. Films grown with this thin RTO capping are characterized by a relief-like faceted surface. For 8 µm thick Si seed films, a gain in solar cell performance was observed when using the thin RTO capping instead of a standard 2 µm thick PECVD SiO2 one. For the costs of the ZMR process, scan speed is the most crucial parameter. The automated process control developed in this work enabled high-speed recrystallization. The effect of scan speed was studied by EPD and minority carrier lifetime measurements, as well as fabrication of test solar cells. All analyzed data show a significant decrease in film quality with increasing scan speed. For the two examined seed film thicknesses, the 8 µm films generally yielded better results than the 2 µm ones. This finding does not fit well with the result of other groups, but may be explained by the different capping type.

7.7 Summary and Outlook 165

In this work, ceramics from Si3N4, ZrSiO4, SiSiC, and ribbons from the SSP process have been tested as potential low cost substrates. While all these materials fulfill principal requirements, reliable processing of Si thin films on these substrates turned out to be difficult. Key issues that were identified are: match of thermal expansion coefficient, integrity of the intermediate layer during CVD and ZMR processing, and homogeneity of thermal properties and their compatibility with ZMR growth. The modified Donolato model developed in Chapter 5 has been applied to the analysis of the Si thin films investigated in this work. From SR-LBIC effective diffusion length and EPD data recombination strength values Γd in the range of 0.006 to 0.016 have been determined. These fit very well to results measured on conventional multicrystalline Si solar cells. In the future, the developed methods may be applied to the evaluation of Si thin-film quality before device processing, but also for process optimization. Based on Donolato’s model for the effect of dislocations on minority carrier effective diffusion length, the dependence of open circuit voltage on dislocation density has been simulated. With the consideration of space charge region recombination, the experimental data could be modeled very well. However, in order to obtain satisfactory fitting results, it had to be assumed that the region of high recombination is much wider than the »effective depletion region width« calculated from the electrical field strength. This finding is in accordance with results reported for solar cells from fine-grained Si thin films. Both, the experiments on ZMR scan speed, and the modeling of the effect of dislocations on open circuit voltage, showed that space charge region recombination severely limits device performance. While low bulk diffusion length may be compensated for by a reduction of film thickness, good surface passivation and the use of efficient light trapping, similar solutions are not available for space charge region recombination. One strategy for the investigated film structure therefore would be to drop the two-layer concept. If no epitaxial layer is used, dislocations are confined to the subgrain boundary. Indeed, Reber et al. could prove that for solar cells without an epitaxial layer, open circuit voltage is much less affected by an increase in ZMR scan speed [247, 248].

8 Solar Cell Device Optimization The preceding chapter dealt with the optimization of Si thin-film quality by understanding the mechanisms of defect generation and their connection to device parameters. In this chapter, a different approach is taken. For a given Si thin-film quality, device design and process modifications are investigated that are suitable to improve solar cell performance. These include: (i) the use of a lowly doped passivated emitter, (ii) light trapping by front surface texturization, (iii) hydrogen bulk defect passivation, and (iv) double layer antireflection coating. Combining all these methods, nearly a doubling of initial conversion efficiency is demonstrated. For the best solar cell fabricated with an optimized process, a conversion efficiency of 13.5 % is measured. The chapter closes with an outlook on process transfer to industrial manufacturing methods.

8.1 EMITTER PASSIVATION Recombination in the emitter region is one of the main loss mechanisms in industrial type solar cells. Emitter recombination becomes even more important in solar cells with good light trapping properties, where long wavelength light can pass the emitter several times. In this work two different emitter types have been employed (see Sec. 3.6): a 80 Ω/sq emitter, and 100 Ω/sq emitter that was coated by a ∼10 nm thick thermally grown oxide. The thin oxide on one hand serves as a surface passivation feature. On the other hand, in the case of textured surfaces, it prevents unwanted deposition of silver during galvanic thickening of the metallization. Such silver precipitation may be caused due to strong electric fields at random pyramid tips. For comparison, thin-film solar cells on mc-Si and SSP substrates were fabricated with both emitter types.

167 168 SOLAR CELL DEVICE OPTIMIZATION

mc-Si SSP Substrate Substrate

600 +14.1 580 +12.3 +11.4 +20.9 560 [mV]

oc 540 V

520 Figure 8.1 Comparison of open circuit voltage Voc and conversion 12 +0.9 efficiency η for solar cells with 11 +0.9 80 Ω/sq and passivated 100 Ω/sq 10 +1.6 emitter. Parameters were measured [%] 9 +1.0 η after photoresist lift-off (open sym- 8 bols) and on finished cells after bulk hydrogen passivation and double

. . layer ARC (filled symbols). q /s /sq Ω . pass. Ω . pass. q q 80 /s 80 /s Ω Ω 00 00 1 1

On finished solar cells with passivated 100 Ω/sq emitter, open circuit voltage was found to be 12 mV to 14 mV higher than on devices with a nonpassivated 80 Ω/sq emitter, as shown in Figure 8.1. For short circuit current density, a difference of approximately 1 mA cm−2 was observed (not shown in Fig. 8.1). The net effect is close to a 1% absolutely higher conversion efficiency for the passivated 100 Ω/sq emitter compared to the 80 Ω/sq one. The same tendency was already found before contact sintering, although measurement values scatter more at this stage. Figure 8.2 shows external quantum efficiency curves measured on solar cells with both emitter types. The improved short circuit current density on solar cells with a passivated 100 Ω/sq emitter can be attributed to an enhanced response in the wavelength region between 350 nm and 500 nm. Increased open circuit voltage is due to a lower saturation current in the emitter and a lower surface recombination velocity at the front side.

8.2 Surface Texturization 169

1.0

100 Ω/sq. pass. emitter 0.8

0.6

80 Ω/sq. emitter 0.4

0.2

External quantum efficiency (EQE) 0.0 400 600 800 1000 1200

Wavelength [nm] Figure 8.2 Comparison of external quantum efficiency for solar cells with an 80 Ω/sq and a passivated 100 Ω/sq emitter. Both solar cells were fabricated from the same recrystallized film.

8.2 SURFACE TEXTURIZATION With the objective of a robust process, the investigations presented in Chap- ter 7 were conducted on planar solar cells. However, light trapping is inevitable for crystalline Si thin-film solar cells in order to reach high short circuit currents (see Sec 3.3.1). In this work, light trapping was achieved by anisotropic etching of the Si film surface. The preferential 〈100〉 orientation of the ZMR Si films yields a random pyramid structure. A back reflector is provided through the

SiO2 or ONO stack intermediate layer. On solar cells with textured surfaces, the short circuit current was typically 4 mA cm−2 to 5 mA cm−2 higher than on comparable planar devices. Regarding solar cell conversion efficiency, the increased short circuit current density mani- fested in an increase of approximately 2% absolute. This finding matches former investigations by the author well [138]. For the same structure as employed in this work, rear and front side internal reflectance were estimated to be larger than 90% based on numerical modeling of measured data.

170 SOLAR CELL DEVICE OPTIMIZATION

1.0 1.0 100 Ω/sq., text. surface 0.9 0.8 0.8 IQE 0.7 refl. + esc. 0.6 0.6 80 Ω/sq., planar surface 0.5 0.4 0.4 0.3 0.2 0.2 0.1 Internal quantum efficiency (IQE) Internal Surface reflectance + escape 0.0 0.0 400 600 800 1000 1200

Wavelength [nm] Figure 8.3 Internal quantum efficiency and total reflectance (surface reflectance + escape) for an 80 Ω/sq emitter thin-film solar cell with a planar surface (dashed lines) and for an equivalent 100 Ω/sq emitter device with a textured surface (solid lines).

Figure 8.3 compares typical internal quantum efficiency and reflectance curves for a surface textured and an equivalent planar cell. The device with a textured surface was fabricated with the oxidized 100 Ω/sq emitter type due to the risk of parasitic silver deposition mentioned above. The effect of improved carrier generation and collection in the long wavelength regime is clearly visible by an enhanced IQE and reduced light escape at the front surface. In addition, the reflectance data clearly show reduced surface reflectance in the short wavelength regime on the surface textured device. Corresponding short circuit current densities for the planar and the surface textured solar cell were 25.5 mA cm−2 and 30.8 mA cm−2, respectively.

8.3 BULK HYDROGEN PASSSIVATION

Bulk passivation by hydrogen containing SiNx layers is a standard process in industrial manufacturing of mc-Si based solar cells. In the investigated Si thin films, dislocation density is about two orders of magnitude higher than in typical

8.3 Bulk Hydrogen Passsivation 171

] 17.7

2 18 15.9 +2.2 16 14.5 14 +2.3 +2.2

[mA/cm 12 sc J

600 586 563 534 +15 550 +33

[mV] 500 +50 oc V

75 74.0 69.7 70 +0.3 +2.0 65 62.1

FF [%] 60 +3.1

8 7.7 7 6.2 +1.2 6 4.8 +1.3 5 Figure 8.4 Improvement of solar [%] 4 +1.3 η cell parameters due to bulk hydro- 3 gen passivation by RPHP on typical 7 7 6 3.3 x 10 1.6 x 10 8.9 x 10 devices. The values are for planar Dislocation density ρ d samples without ARC.

mc-Si wafers. Therefore, efficient bulk passivation is inevitable in order to reach the efficiency goal. The effect of bulk hydrogen passivation was studied through the same set of samples that was used to examine the dependence of open circuit voltage on dislocation density (Section 7.6). The technique employed was remote plasma hydrogen passivation (RPHP). This process was chosen due to its flexibility and the compatibility with the employed double layer ARC. However, comparative studies indicate that similar results should be achieved by hydrogenation from

SiNx layers [161, 164]. The RPHP process was carried out after metallization at 350°C for 30 min. Figure 8.4 shows the improvement of solar cell parameters after the RPHP process for samples with different dislocation densities. For short circuit current density, a constant increase of ∼2.2 mA cm−2 was measured, independent of dislocation density. In contrast, the improvement in open circuit voltage and in

172 SOLAR CELL DEVICE OPTIMIZATION fill factor depends on dislocation density. The higher the dislocation density, the higher the increase in Voc and FF. Therefore, after hydrogen passivation the relative difference in conversion efficiency between the different samples is decreased, but performance still depends significantly on dislocation density.

The finding that the improvement in Voc is parallel with that in FF, and not with that in Jsc, again indicates a dominating effect of space charge region recombination, as discussed in Section 7.6.

8.4 OPTIMIZED SOLAR CELL PROCESS All steps discussed above were combined in an optimized process. It was applied to high quality ZMR Si thin films, recrystallized at 10 mm min−1 scan speed, in order to demonstrate maximum possible conversion efficiency. For a typical solar cell of this batch, the gain in solar cell parameters by each step is visualized in Figure 8.5. Parameters for the planar and textured stages

620 610 610 605 599 +5 600 +6

[mV] 590 +29 oc

V 580 570 570

30.0 30 ] 2 +6 25 22.8 24.0 +1.2 20 +7.1 15.7

[mA/cm Figure 8.5 Improvement of solar

sc 15

J cell parameters through different process steps on a typical device. 13.2 14 Measurement values displayed in 12 10.8 +2.4 the three columns on the right are 9.9 10 +0.9 for the same solar cell, while those [%] +3.0 η 8 6.9 in the left column were measured on 6 a nontextured solar cell fabricated from the same Si film. ter emit . Planar cell AR coated ass p Bulk passivated cell; t. Tex

8.5 Transfer to Industrial Processes 173

Table 8.1 Dimensional and electrical parameters of the best 1 cm2 thin-film solar cell fabricated with ZMR and Si-CVD technology.

Thickness Doping Voc Jsc FF η [µm] [cm−3] [mV] [mA cm−²] [%] [%]

Seed film 5.5 ± 0.5 (2.5 ± 1.0) × 1018 610 30.9 71.7 13.5 Epitaxial film 26.0 ± 1.0 (9.5 ± 1.0) × 1016 were not measured on the same device, but data for all other stages were determined on the identical solar cell. For open circuit voltage, the improvement is firstly due to reduced emitter recombination in combination with surface passivation, and secondly due to bulk passivation. Regarding short circuit current density, the major improvements are on the optical side: light trapping by surface texturing and antireflection coating make up the main contributions. In total, the initial conversion efficiency is nearly doubled. The best cell of this batch achieved a conversion efficiency of 13.5%, verified at the Fraunhofer ISE calibration laboratory. Detailed data of this cell are summarized in Table 8.1, including thickness and doping data. The latter data were measured by spreading resistance profiling and optical microscopy on the same substrate/Si film stack from which the final solar cell was fabricated. Open circuit voltage and short circuit current density are on quite a good level, close to values achieved in industrially manufactured mc-Si solar cells. The solar cell demonstrates that adequate design enables one to reach high short current density with only a fraction of typical bulk Si thickness. From the solar cell parameters given in Table 8.1 the fill factor is clearly below potential. If the fill factor had been affected by material quality, this would have also affected open circuit voltage. Therefore, the relatively low value must be due to deficiencies in the solar cell process. In the same solar batch fill factors up to 76.6% were reached and conversion efficiencies exceeding 14% should be easily achievable by using the applied technology.

8.5 TRANSFER TO INDUSTRIAL PROCESSES The solar cell data in the section above demonstrated the potential of the investigated technology. However, the employed laboratory type process dif-

174 SOLAR CELL DEVICE OPTIMIZATION fered from industrial processing. The main differences were: (i) the use of a lowly doped passivated emitter, (ii) metallization by photolithography, and (iii) deposition of a double layer TiO2/MgF2 antireflection coating. Furthermore, for the 1 cm2 solar cells test structure, the contacting scheme could be kept simple since the lateral conductivity in the base was sufficient and allowed for the base contacts to be outside the active cell area. Parallel to the work for this thesis, the development of industrially feasible contacting schemes was addressed. Within the framework of the European thin- film research project SUBARO, an interdigitated contact structure was developed at Fraunhofer ISE. The so-called BBC (buried base contact) concept relies on structuring by plasma etching and screen printing [249–251]. Within the German national PRISMA project, a process for a mini-module was developed at ZAE Bayern [252]. It provides integrated series interconnection, enabled by the SOI structure. For this process, structuring is also by plasma etching, while base and emitter metallization is by evaporated Al contacts. Both, the BBC and the ZAE process, were applied to ZMR Si seed films fabricated by the author. Table 8.2 summarizes the first solar cell results. On Cz-Si reference cells, both processes have proven to reach 11% to 12% in conversion efficiency. Still, these values are significantly below typical parameters of standard industrial solar cells. The deficit is mainly due to the low short circuit current density, and is essentially caused by large inactive areas. The inactive area used for metallization and isolation trenches makes up 20% in the BBC structure and 18% in the ZAE structure. Application of both concepts to Si thin films fabricated by ZMR and CVD resulted in low conversion efficiencies of 3% for the BBC and 6.3% for the ZAE concept, respectively. The very low fill factor for the BBC cell indicates major technological difficulties. Among others, the uneven surface caused problems in metallization alignment, yielding short circuits. Shunting was also a major problem for the ZAE concept. The above results indicate that successful transfer to an industrial process is very challenging. While for wafer-based technology, individual measurements enable one to sort out defective devices and to optimally match cells in a serial string, this cannot be done for integrated devices. For acceptable production

8.6 Summary and Outlook 175

Table 8.2 First results of thin-film solar cell arrays fabricated from ZMR films on insulating substrates. Both, emitter and base metallization are located on the front side.

* Device Jsc Voc FF η Reference [mA cm−2] [mV] [%] [%]

Three 1.3 × 4 cm2 interdigi- 15.3 509 39.1 3.0 tated grid solar cells on 5 × 5 cm2 substrate [251] Reference (Cz wafer) 26.5 596 73.2 11.5 9 solar cells mini module with 18.7 544 62.0 6.3 2 86 cm aperture area [252] Reference (Cz SOI wafer) 24.7 601 74.0 11.0

* avg. value per cell yields, error rates and scatter in electrical cell parameters would have to be on a level that is significantly below today’s standard in wafer based technology. In conclusion, at Fraunhofer ISE the focus of development has been directed towards the concept of so-called wafer equivalents [157]. The use of conducting substrates and intermediate layers, e.g., made from conducting SiC, enables metallization analogous to standard technology.

8.6 SUMMARY AND OUTLOOK In this chapter, device design and process modifications have been investigated that can improve solar cell performance for a given Si thin-film quality. Emitter recombination constitutes an important loss mechanism, and in thin- film solar cells, it not only affects short wavelength light since long wavelength light may pass the emitter more than once due to light trapping. Use of a 100 Ω/sq passivated emitter resulted in a significant improvement compared to an 80 Ω/sq nonpassivated emitter. Typical improvements are between 12 mV and 14 mV in open circuit voltage, around 1 mA cm−2 in short circuit current density, and approximately 1% absolute in conversion efficiency. Light trapping is important to compensate for the weak absorption of long wavelength light in crystalline Si. Again, this issue is of major importance for thin-film devices. By applying a texturization process, an efficient light trapping structure was achieved in combination with the SiO2 or ONO stack intermediate

176 SOLAR CELL DEVICE OPTIMIZATION layer. Typical improvements in short circuit current density are 4 mA cm−2 to 5 mA cm−2, and approximately 2% absolute in conversion efficiency. The investigated Si films exhibits dislocation densities in the range of 106 cm−2 to 108 cm−2. Hydrogen passivation is a well-known method used to reduce recombination activity of these defects. By a RPHP process, significant improvements in solar cell parameters were demonstrated. For short circuit current density a typical improvement of 2.2 mA cm−2 was found, independent of dislocation density. In contrast, the improvement in open circuit voltage and in fill factor depended on dislocation density. The net improvement in conversion efficiency was about 1.3% absolute. Although a structured surface also provides reduced front surface reflection, a further significant gain in short circuit current density (approximately 5 mA cm−2) could be achieved by a double layer antireflection coating. This yielded another increase of at least 2% absolute in conversion efficiency. Combining all steps in an optimized process, conversion efficiencies up to 13.5% were demonstrated for a thin-film solar cell with a ∼31 µm thick active layer. The relatively low fill factor indicates opportunities for further improvements. While the potential of the investigated technology was successfully demonstrated, the transfer to industrial manufacturing technologies is still a challenging task. On one hand, the employed ZMR scan speed would not allow cost effective production. On the other hand, fabrication of Si thin-film modules with interconnected solar cells requires very low error rates and very small scatter in electrical characteristics.

Appendix A Symbols, Acronyms, and Constants

A.1 LIST OF SYMBOLS Symbol Unit Description

Latin Symbols 44 A cm2 Area c cm−3 Concentration 2 −1 Dn cm s Diffusion coefficient for electrons as minority carriers 2 −1 Dp cm s Diffusion coefficient for holes as minority carriers E kV cm−1 Electric field (strength)

Ea eV Activation energy

Eg eV Band-gap energy E W m−2 Irradiance −2 −1 Eλ W m nm Spectral irradiance −1 −2 Ep s m Photon flux (photon irradiance) −1 −2 −1 Ep,λ s m nm Spectral photon flux (photon irradiance) EQE External quantum efficiency FF Fill factor fabs Fraction of absorbed photons fdop Doping ratio factor fgeom Geometry factor fopt Function describing the optical properties in Leff,c g µm−1 Normalized generation rate G cm−3 s−1 Generation rate −3 −1 −1 Gλ cm nm s Spectral generation rate I A Current

Isc A Short circuit current

Imp A Current at maximum power point

44 In the main the notation follows the recommendations given in Refs. [253, 254]. 177 178 APPENDIX A SYMBOLS, ACRONYMS, AND CONSTANTS

Symbol Unit Description IQE Internal Quantum Efficiency J A cm−2 Current density −2 J0 A cm Saturation current density −2 Jn A cm Electron current density −2 Jp A cm Hole current density −2 JL A cm Light generated current density −2 Jmp A cm Current density at maximum power point −2 Jrg A cm Recombination current −2 Jsc A cm Short circuit current density k µm−1 Wave vector −1 kB J K Boltzmann constant −1 ks cm s Surface reaction rate constant L µm (Bulk) diffusion length

Leff µm Effective diffusion length

Leff,c µm Collection effective diffusion length for spatially homogeneous generation

Leff,D µm Effective diffusion length as defined by Donolato

Leff,IQE µm Quantum efficiency effective diffusion length

Leff,J0 µm Current-voltage effective diffusion length

Leff,l µm Local effective diffusion length −3 NA cm Density of acceptors −3 ND cm Density of donors n cm−3 Density of free electrons −3 n0 cm Density of free electrons at thermal equilibrium −3 ni cm Intrinsic carrier concentration n1, n2 Ideality factors in the two-diode model ∆n cm−3 Excess electron density p cm−3 Density of free holes −3 p0 cm Density of free holes at thermal equilibrium ∆p cm−3 Excess hole density

A.1 List of Symbols 179

Symbol Unit Description q C Elementary charge R Reflectance

Ra µm Average roughness

Rp Ω Parallel resistance

Rs Ω Series resistance

Rt µm Total roughness s cm−1 Reduced surface recombination velocity S/D S cm s−1 Surface recombination velocity

Sjct Junction surface SR A W−1 Spectral response t s Time T K Absolute temperature

Tm °C Melting temperature + −3 −1 U max cm s Maximum forward bias recombination rate −3 −1 Un cm s Electron recombination rate −3 −1 Up cm s Hole recombination rate −2 −1 Us cm s Surface recombination rate v mm min−1 Scan speed (ZMR) −1 vi mm min Growth speed (interface) −1 vp mm min Pull speed V V (Applied) voltage

Vbi V Built-in potential

Vmp V Voltage at maximum power point

Voc V Open circuit voltage

Vt V Thermal voltage W µm Thickness of electrically active cell region

Weff µm Effective thickness of the recombination region

Wsc µm Depth of supercooled region

Wsub µm Substrate thickness

We µm Thickness of emitter region

180 APPENDIX A SYMBOLS, ACRONYMS, AND CONSTANTS

Symbol Unit Description

Wb µm Thickness of base region

Wscr µm Thickness of space charge region

W1 µm Thickness of p-doped base region

W2 µm Thickness of p+-doped base region

zn µm Location of space charge region edge on n-type side

−zp µm Location of space charge region edge on p-type side Greek symbols α µm−1 Absorption coefficient α−1 µm Absorption length α(T) K−1 Thermal expansion coefficient −1 Mean thermal expansion coefficient αT0,T K 2 −1 γd cm s Recombination strength

Γd Normalized recombination strength ε µm Radius of dislocation core −1 −1 ε0 A s V cm Permittivity in vacuum

εs Relative permittivity of semiconductor η Conversion efficiency

ηc (Charge) collection efficiency ρ C cm−3 Space charge density −2 ρd cm Dislocation density Φ W Radiant power (radiant energy flux) −1 Φp s Photon flow −1 −1 Φp,λ s nm Spectral photon flow ϕ Charge collection probability φ V Electrostatic potential λ nm Wavelength

λsgb µm Subgrain boundary spacing 2 −1 −1 µn cm s V Mobility of electrons as minority carriers

A.1 List of Symbols 181

Symbol Unit Description 2 −1 −1 Mobility of electrons as majority carriers µnn cm s V 2 −1 −1 µp cm s V Mobility of holes as minority carriers 2 −1 −1 Mobility of holes as majority carriers µpp cm s V θ ° Angle of refraction/reflection

θc ° Critical angle for total reflection τ µs (Bulk) lifetime

τn µs Lifetime of electrons as minority carriers

τp µs Lifetime of holes as minority carriers

182 APPENDIX A SYMBOLS, ACRONYMS, AND CONSTANTS

A.2 PHYSICAL CONSTANTS Symbol Value Description c 299 792 458 m s−1 Speed of light −23 −1 kB 1.380 650 3 × 10 J K Boltzmann constant 8.617 342 × 10−5 eV K−1 h 6.626 068 76 × 10−34 J s Planck's constant 4.135 667 27 × 10−15 eV s q 1.602 176 462 × 10−19 C Elementary charge

Vt 0.025 852 03 V Thermal voltage kBT/q at 300 K Reference: CODATA-1998 [255].

A.3 LIST OF ACRONYMS AOI Area of interest APCVD Atmospheric pressure chemical vapor deposition ARC Antireflection coating BBC Buried base concept BSF Back surface field CCD Charge coupled device CDI Charge carrier imaging CMOS Complementary metal oxide semiconductor CP133 Chemical polishing solution CVD Chemical vapor deposition Cz-Si Czochralski-grown silicon DAQ Data acquisition DS Directional solidification EBIC Electron beam induced current EBSD Electron backscatter diffraction EFG Edge-defined Film-fed Growth EDD Effective dislocation density

A.3 List of Acronyms 183

EPD Etch pit density EQE External quantum efficiency Fraunhofer ISE Fraunhofer Institute for Solar Energy Systems FWHM Full width at half maximum FZ-Si Float zone silicon HF Hydrofluoric acid ILM Infrared lifetime mapping IMS Institut für Mikroelektronik Stuttgart IQE Internal quantum efficiency LBIC Light beam induced current LPCVD Low pressure chemical vapor deposition mc-Si Multicrystalline silicon MFCA Modulated free carrier absorption MPP Maximum power point ODBC Open database connectivity OIM Orientation imaging microscopy OLE Object linking and embedding ONO Oxide/nitride/oxide (stack) OPC OLE for process control PECVD Plasma enhanced chemical vapor deposition PID Proportional integral differential (controller) PLC Programmable controller PSG Phosphosilicate glass PV Photovoltaics RBSN Reaction bonded silicon nitride RCA Si cleaning sequence developed by RCA Corp. RIE Reactive ion etching RGS Ribbon Growth on Substrate RPHP Remote plasma hydrogen passivation RTCVD Rapid thermal chemical vapor deposition RTO Rapid thermal oxidation / oxide RTP Rapid thermal processing

184 APPENDIX A SYMBOLS, ACRONYMS, AND CONSTANTS

SCR Space charge region SEM Scanning electron microscopy SGB Subgrain boundary SIMOX Separation by implantation of oxygen SOC Spin on coating SOI Silicon on insulator SPC Solid phase crystallization SPV Surface photovoltage SR Spectral response SR-LBIC Spectrally resolved light beam induced current SRP Spreading resistance profiling SRV Surface recombination velocity SSN Sintered silicon nitride SSP Silicon sheets from powder TCS Trichlorosilane TEM Transmission electron microscopy ZMR Zone-melting recrystallization

Appendix B Silicon Material Properties

B.1 SELECTED PROPERTIES Property Symbol Value Reference

10 −3 Intrinsic carrier concentration at ni 1.01 × 10 cm [256] 300 K

Melting point (recommended value) Tm 1414°C [139]

B.2 MOBILITIES For analytical calculations the doping dependence of the mobilities was considered by the empirically model given by Caughey and Thomas [257]

µmax − µmin µ = µmin + . (B.1) α µ  N D + NA  1+    N ref  The coefficients used are summarized in Table B.1 and are those suggested in the simulation software PC1D (v5.8) [242]. These coefficients are for T = 300 K, the temperature dependence is discussed in Ref. [258]. From the mobilities, diffusion coefficients were calculated through the Einstein relation k T D = B µ . (B.2) q

Table B.1 Coefficients at T = 300 K used in the mobility model by Eq. (B.1)

Electrons Holes

2 −1 −1 µmax [cm V s ] 1417 470 Majority Minority Majority Minority

2 −1 −1 µmin [cm V s ] 60 160 37.4 155 −3 16 16 17 17 Nref [cm ] 9.64 × 10 5.6 × 10 2.82 × 10 1.0 × 10

αµ 0.664 0.647 0.642 0.9

185 186 APPENDIX B SILICON MATERIAL PROPERTIES

B.3 BAND-GAP NARROWING In the n-type emitter and p+-type BSF region of the solar cells investigated band-gap narrowing significantly affects carrier densities. To take this effect into account the following empirical expression was used as implemented in PC1D [242]

  N  E ln A  , N > N ∆E = 1, p   A 0, p . (B.3) g,A   N0, p   0 , N A ≤ N0, p The formula for donors in n-type material is equivalent. The coefficients used are summarized in Table B.2.

Table B.2 Coefficients used in the band-gap narrowing model given by Eq. (B.3).

−3 Onset N0 [cm ] Slope E1 [meV] Reference

n-type 1.4 × 1017 14.0 [242] p-type 2.3 × 1017 17.8 [259]

Appendix C Thermal Oxidation To grow a thermal oxide, the oxidizing specimen has to diffuse through the already existing oxide to react with the Si atoms at the Si surface. A straightforward analytical solution to this problem can be derived based on the following assumptions: 1. The concentration of the oxidizing specimen at the surface of the oxide is

equal to its concentration in the ambient c0. This assumption can be made since the mass transfer coefficient in the gas phase is high. 2. In the oxide, there is a linear change in concentration between the concentra-

tion c0 at the oxide surface and the concentration cs at the oxide–Si interface.

3. The reaction rate at the Si surface is proportional to the concentration cs.

With the initial condition x(0) = d0, the oxide thickness x after an oxidation time t is then given by (Ref. [154], p. 346)

D  2c k 2 (t + t )  x(t) =  1+ 0 s 0 −1 , (C.1) k Dc s  1  where

 2 2Dd0  c1 t0 = d0 +  , (C.2)  ks  2Dc0 which represents a time coordinate shift to account for the initial oxide of thickness d0. D is the diffusion coefficient of the oxidizing species, ks is the surface reaction rate constant, and c1 is the number of molecules of the oxidizing specimen in a unit volume of the oxide, with value 2.2 × 1022 cm−3 for dry oxygen. For small values of t, Eq. (C.1) reduces to

ksc0 x(t) ≅ (t + t0 ) , (C.3) c1 and for large values of t, it reduces to

2Dc0 x(t) ≅ (t + t0 ) . (C.4) c1

187 188 APPENDIX C THERMAL OXIDATION

The linear relationship of Eq. (C.3) is valid for the initial stage of the oxide growth when surface reaction is the rate-limiting factor, while the parabolic expression (C.4) holds when the rate is limited by the diffusion through the existing oxide. The ratio ksc0/c1 in Eq. (C.3) is referred to as linear rate constant and 2Dc0/c1 as parabolic rate constant. Experimental results show that the linear rate constant, as well as the parabolic rate constant, can be well described by the exponential law exp(Ea/kBT), where

Ea is the activation energy [155]. Insertion of the ansätze ks = a exp(Ea,l/kBT) and

D = b exp(Ea,p/kBT) into Eq. (C.1) yields

bexp(−E / k T)  2a2c exp(−2E / k T)(t + t )  x(t,T) = a,p B  1+ 0 a,l B 0 −1 . (C.5) aexp(−E / k T) bc exp(−E / k T) a.l B  1 a,p B  For constant oxidation time t this equation reduces to

 (E − E )   (E − 2E )   x(T) = Aexp a,l a,p  1+ Bexp a,p a,l  −1 . (C.6)  k T   k T   B   B  

Appendix D Effective Diffusion Length Evaluation by Nonlinear Fit

For solar cells of finite base thickness Wb and finite surface recombination velocity at the back s, the charge collection probability ϕ is given by Eq. (4.37). Inserting ϕ and the generation function by Eq. (4.7) into Eq. (4.46) yields

−1 −1 IQE (L,s,Wb ,θ,α ) = W      b  −1  −1  Wb  Wb  α −1 cosθ  L − α cosθ  L + α cosθ  cosh  + Lssinh  e          L   L   W       b  −1  −1  Wb   2 −1  Wb  α −1 cosθ  LLsα cosθ − L +  L − Lsα cosθ  cosh  +  L s − α cosθ  sinh  e             L   L       (D.1)

The Leff,IQE values referred to as obtained by »nonlinear fit« were calculated by fitting the IQE−1 vs. α−1 data by this function, and then inserting the best fit

value(s) into Eq. (5.10), yielding Leff,IQE( = Leff,J0) through Eq. (5.9).

189

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Publications

• T. Kieliba, S. Riepe, and W. Warta, Effect of dislocations on open circuit voltage in crystalline silicon solar cells, J. Appl. Phys. 100, 093708 (2006). • T. Kieliba, S. Riepe, and W. Warta, Effect of dislocations on minority carrier diffusion length in practical silicon solar cells, J. Appl. Phys. 100, 063706 (2006). • S. Reber, T. Kieliba, and S. Bau, Crystalline silicon thin-film solar cells on foreign substrates by high-temperature deposition and recrystallization, in Thin Film Solar Cells: Fabrication, Characterization and Applications, edited by J. Poortmans and V. Arkhipov (John Wiley & Sons, Chichester, 2006), pp. 39–95. • G. Andrä, J. Bergmann, A. Bochmann, F. Falk, E. Ose, S. Dauwe, and T. Kieliba, Characterization and simulation of multicrystalline LLC-Si thin film solar cells, in Proceedings of the 20th Photovoltaic Solar Energy Confer- ence, Barcelona, Spain, 2005, pp. 1171–1174. • A. Eyer, F. Haas, and T. Kieliba, A zone melting recrystallisation (ZMR) processor for 400 mm wide samples, in Proceedings of the 19th European Photovoltaic Solar Energy Conference, Paris, France, 2004, pp. 931–934. • S. Riepe, G. Stokkan, T. Kieliba, and W. Warta, Carrier Density Imaging as a tool for characterising the electrical activity of defects in pre-processed multicrystalline silicon, in Proceedings of the 10th International Autumn Meeting on Gettering and Defect Engineering in Semiconductor Technology (GADEST), Zeuthen, Germany, 2003, edited by H. Richter and M. Kittler [Solid State Phenom. 95–96, 229–234 (2004)]. • T. Kieliba, J. Pohl, A. Eyer, and C. Schmiga, Optimization of c-Si films formed by zone-melting recrystallization for thin-film solar cells, in Pro- ceedings of the 3rd World Conference on Photovoltaic Energy Conversion, Osaka, Japan, 2003, pp. 1170–1173.

219 220 PUBLICATIONS

• S. Bau, S. Janz, T. Kieliba, C. Schetter, S. Reber, and F. Lutz, Application of PECVD-SiC as intermediate layer in crystalline silicon thin-film solar cells, in Proceedings of the 3rd World Conference on Photovoltaic Energy Conver- sion, Osaka, Japan, 2003, pp. 1178–1179. • J. Rensch, D.M. Huljic, T. Kieliba, R. Bilyalow, and S. Reber, Screen printed c-Si thin film solar cells on insulating substrates, in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion, Osaka, Japan, 2003, pp. 1486–1489. • A. Slaoui, A. Focsa, S. Bau, S. Reber, T. Kieliba, A. Gutjahr, R. Bilyalov, and J. Poortmans, Silicon films on ceramic substrates (SOCS): growth and solar cells, in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion, Osaka, Japan, 2003, pp. 1186–1189. • T. Kieliba, S. Bau, R. Schober, D. Oßwald, S. Reber, A. Eyer, and G.

Willeke, Crystalline silicon thin-film solar cells on ZrSiO4 ceramic substrates, Sol. Energy Mater. Sol. Cells 74, 261–266 (2002). • T. Kieliba, S. Bau, D. Oßwald, and A. Eyer, Coarse-grained Si films for crystalline Si thin-film solar cells prepared by zone-melting recrystallization, in Proceedings of the 17th European Photovoltaic Solar Energy Conference, Munich, Germany, 2001, pp. 1604–1605. • S. Bau, T. Kieliba, D. Oßwald, and A. Hurrle, Chemical vapour deposition of silicon on ceramic substrates for crystalline silicon thin-film solar cells, in Proceedings of the 17th European Photovoltaic Solar Energy Conference, Munich, Germany, 2001, pp. 1575–1577. • T. Kieliba, S. Bau, D. Oßwald, R. Schober, S. Reber, A. Eyer, and G.

Willeke, Crystalline silicon thin-film solar cells on ZrSiO4 ceramic substrates, in Technical Digest of the 12th International Photovoltaic Science and Engineering Conference, Cheju Island, Korea, 2001, pp. 557. • A. Eyer, F. Haas, T. Kieliba, D. Oßwald, S. Reber, W. Zimmermann, and W. Warta, Crystalline silicon thin-film (CSiTF) solar cells on SSP and on ceramic substrates, J. Cryst. Growth 225, 340–347 (2001).

PUBLICATIONS 221

• S. Reber, W. Zimmermann, and T. Kieliba, Zone melting recrystallization of silicon films for crystalline silicon thin-film solar cells, Sol. Energy Mater. Sol. Cells 65, 409–416 (2001). • T. Kieliba and S. Reber, Enhanced zone melting recrystallization for crystalline silicon thin-film solar cells, in Proceedings of the 16th European Photo- voltaic Solar Energy Conference, Glasgow, UK, 2000, pp. 1455–1458. • S. Reber, G. Stollwerck, D. Oßwald, T. Kieliba, and C. Häßler, Crystalline silicon thin-film solar cells on silicon nitride ceramics, in Proceedings of the 16th European Photovoltaic Solar Energy Conference, Glasgow, UK, 2000, pp. 1136–1139. • S. Reber, W. Zimmermann, and T. Kieliba, Zone melting recrystallization of silicon films for crystalline silicon thin-film solar cells, in Tech. Digest of the 11th International Photovoltaic Science and Engineering Conference (PVSEC-11), Sapporo, Japan, 1999, pp. 729–730.