Crystalline Silicon Solar Cells

252

Transcript of Crystalline Silicon Solar Cells

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Crystalline Silicon Solar Cells

Adolf Goetzberger Joachim Knobloch Bernhard Vo13 Fraunhofer Institute for Solar Energy Systems, Freiburg, Germany

Translated by Rac he1 Wadding ton Swadlincote, UK

John Wiley & Sons Chichester New York Weinheim - Brisbane . Singapore. Toronto

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@ B.G. Teubner Stuttgart 1994: GoetzbergerNoS/Knobloch. Sonnenenergie: Photovoltaik. Translation arranged with the approval of the publisher B.G. Teubner Stuttgart, from the original German edition into English.

Copyright @ 1998 by John Wiley & Sons Ltd. Baffins Lane, Chichester, West Sussex PO19 IUD, England

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Library of Congress Cataloging-in-Publication Data

Goetzberger, Adolf. [Sonnenenergie. English] Crystalline silicon solar cells / Adolf

Goetzberger, Joachim Knobloch, Bernard VoB ; translated by Rachel Waddington.

p. cm. Includes bibliographical references and index. ISBN 0-471-97144-8 (alk. paper) 1. Solar cells. 2. Silicon crystals. 3. Photovoltaic power

generation. I. Knobloch, Joachim, 1934- . 11. VoB, Bernhard, 1926- . 111. Title. TK2960.G64 1998 62 1.3 1 ‘244-dc2 1 97-42008

CIP

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN 0 47 I 97 144 8

Produced from camera-ready copy supplied by the translator

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About the Authors

Prof. Dr, rer. nat. Adolf Goetzberger Born 1928 in Munich. Studied Physics at the University of Munich, 1955 Doctorate. 1955-5 8 Semiconductor development SIEMENS, Munich. 195 8- 63 colleague of W. Schockley (Nobel Prize Winner and co-inventor of the transistor) in Palo Alto, Ca. USA. 1963 Bell Telephone Labs in Murray Hill, N.J., USA. 1968-81 Director of the Fraunhofer Institute for Applied Solid State Physics in Freiburg. From 1971, honorary Professor at the University of Freiburg. From 1981 to retirement in 1993, Director of the Fraunhofer Institute for Solar Energy Systems (ISE) in Freiburg. 1995 Farringten Daniels Award of the Int. Solar Energy Society, Dr. h.c. Uppsala University, Sweden. 1997 Karl W. Boer Medal and EU Bequerel Prize. Currently Director of TNC Consulting GmbH, Freiburg and President of the German Solar Energy Society.

Dipl. Phys. Bernard Vol3 Born 1926 in Miinster, studied Physics at the University of Munster, Diploma 1956. 1956-61 Semiconductor development, VALVO, Hamburg; 196 1-65 Development Director for Power Semiconductor Devices, Semikron, Niirnberg; 1965-80 BBC, Mannheim, of which 11 years Development Director for Power Semiconductor Components; From 198 1 to retirement in 1991, Director of “Crystalline Si Solar Cells” Department at ISE, Freiberg; Main emphasis high efficiency (clean room technology).

Dr. rer. nat. Joachim Knobloch Born I934 in LiegnitdSchlesien. Studied Physics at Munich Technical University, Diploma 1959, Doctorate 1962. 1963-65 Scientific Assistant “Radiation and Solid State Laboratory” at the University of New York, N.Y., USA. 1966-68 Department of Development E. Leitz, Wetzlar; 1969- 82 Department of Development for Power Semiconductor Devices, BBC, Mannheim. From 1982 Deputy Departmental Manager in the Department

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of "Crystalline Si Solar Cells" at ISE, Freiburg. Responsible for analysis and technology for crystalline silicon solar cells of very high efficiency. The department has achieved several international records and is amongst the world leaders in this specialist field.

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Preface

Increased environmental awareness and the knowledge that all current energy sources are limited, make it appear ever more imperative that solar energy be made usable for the creation of electrical power. The principle of converting sunlight into electrical power is very simple indeed. It is converted directly into electrical power - the most valuable form of energy - using solar cells. The advantages and elegance of this photovoltaic energy transfer are obvious:

there are no inoving parts, unlike conventional energy generation; this automatically reduces the need for maintenance; and no fuel is necessary, this eliininates aln~ost all environinental impact.

Furthennore, the technical and technological procedures for the in anufacture of solar cells and solar plants are basically understood, and long plant. lifetinie can be expected.

Despite these positive arguments, the set-up costs for photovoltaic arrays, which are many times higher than those for conventional power stations, have prevented a widespread breakthrough of this new technology up until now. Photovoltaics have, however, conquered the field of power generation for satellites, as the question of cost does not play such a decisive role for this application. The advantages of long lifetime, maintenance-free operation and the lack of normal fuels as well as weight considerations are of decisive importance in this field.

Crystalline silicon dominates the field of space technology, as well as terrestrial applications, as a starting material for solar cells. The consumer market, on the other hand, e.g. clocks and pocket calculators, is dominated by solar cells niade of amorphous silicon, because in these cells the serial connection necessary for current multiplication can be created simultaneously with the production of the cells.

This book, which is concerned with the photovoltaic conversion of sunlight into energy, therefore concentrates on the physical basics and

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technological realisation options for solar cells made of crystalline silicon. All relevant analysis and measuring techniques are dealt with.

The book is aimed at students of science and technology, as well as engineers and technicians working in the development and production of solar cells. It contains practical and theoretical results and experience gained from many years’ work in research and development in the field of crystalline silicon solar cells in the Fraunhofer Institute for Solar Energy Systems (ISE Freiburg). The substance is presented in such a way that it can easily be built upon at a later date.

The solar cell itself is a semiconductor component, specifically a large area diode. The manufacture of solar cells therefore requires, as we will discover, a large amount of knowledge and experience in the fields of the physics and technology of semiconductor components. We will therefore describe the basics of semiconductor physics in the first chapters, and then concentrate on the physics of solar cells made of crystalline silicon. Apart from a basic knowledge of physics and mathematics there are no specific prerequisites to understanding this book.

Particular attention is paid to the physical and technical prerequisites for attaining high efficiency. The high efficiency of solar cells can contribute significantly to reducing the costs of a solar array.

The content and structure of this book follow the pattern below. After a brief introduction to the history and significance of photovoltaics,

the first chapters are concerned with basic semiconductor physics. The next chapter is concerned with the physics and technology of

crystalline silicon solar cells, and specifically the achievement of the highest efficiencies.

The first section of Chapter 8 deals with different designs of solar cell made of crystalline silicon. The subject of thin film solar cells made of crystalline silicon is dealt with in some detail. This has been at the centre of work in all relevant research institutions for some years. The cost situation is expected to improve in the future. In the second section of Chapter 8, some selected types of solar cells made of other materials are described to complete the picture.

The final chapter deals in detail with all important measuring and analysis procedures for the deterniination of physical semiconductor and solar cell parameters.

We wish to thank everyone who, whether in a professional or personal field, showed patience, understanding and helpfulness during the intensive phase of creation of this book.

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Preface xiii

We would like to thank Dr Glunz for writing some subsections in the

We also thank Prof. Luther for allowing us to use the infrastructure of final chapter.

the ISE.

A. Goetzberger, B. VoB, J . Knobloch

Freiburg, Summer 1997

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Contents

1 1.1 1.2 1.3

2 2.1 2.2

3 3.1

3.2

3.3

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . About the Authors ............................ Photovoltaics ................................ The History of Photovoltaics . . . . . . . . . . . . . . . . . . . . . The Principles of Photovoltaics . . . . . . . . . . . . . . . . . . .

The Importance of Photovoltaics . . . . . . . . . . . . . . . . . .

Solar Power ................................. The Sun as a Source of Radiation . . . . . . . . . . . . . . . . . . Standard Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The Principles of Photovoltaics .................. Crystalline Structure and the Energy Band Diagram for Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 The Energy Band Diagram for Tetrahedronal

Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Electrons and Holes in a Semiconductor . . . . . . . . 3.1.3 Energy Levels: the Fermi Level . . . . . . . . . . . . . . . 3.1.4 Density of States for Electrons and Holes . . . . . . . 3.1.5 Thermal Equilibrium . . . . . . . . . . . . . . . . . . . . . . The Conduction Mechanism in Semiconductors . . . . . . . . 3.2.1 Intrinsic Conduction, Field Current and Mobility . . 3.2.2 Impurity Conduction . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Diffusion Current and Diffusion Constant . . . . . . . The, Generation of Charge Carriers by the Absorption of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Absorption in Semiconductors . . . . . . . . . . . . . . . .

3.3.1.1 Absorption in Direct Semiconductors . . . .

xi

xv

5 5 6

9

9

10 14 14 16 19 20 20 24 27

29 30 30

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3.4

3.5

4 4.1 4.2

4.3

5 5.1

5.2

3.3.1.2 Absorption in Indirect Semiconductors . . . Recombination. Carrier Lifetime . . . . . . . . . . . . . . . . . . . . 3.4.1 Radiative Recombination . . . . . . . . . . . . . . . . . . . 3.4.2 Auger Recombination . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Recombination via Defect Levels . . . . . . . . . . . . . 3.4.4 Recombination by Doping . . . . . . . . . . . . . . . . . .

3.5.1 The Current Density Equations . . . . . . . . . . . . . . . 3.5.2 Poisson's Equation . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 The Continuity Equations . . . . . . . . . . . . . . . . . . .

Basic Equations of Semiconductor Device Physics . . . . . .

Thep-n Junction ............................. Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Space Charge Region . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Potential Difference . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Electric Field and Electric Potential . . . . . . . . . . . . 4.2.3 Space Charge Region Width and Capacitance . . . . . The Biased p-n Junction . . . . . . . . . . . . . . . . . . . . . . . .

Weak Injection . . . . . . . . . . . . . . . . . . . . . . . . . . .

Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.1 The p-n Junction with Low Recombination and

4.3.2 Forward Current Characteristic and Saturation

The Physics of Solar Cells ...................... The Illuminated Infinite p-n Junction . . . . . . . . . . . . . . 5.1.1 The Current-Voltage Characteristic of an Infinite

Solarcell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1.1 Short Circuit Current . . . . . . . . . . . . . . . 5.1.1.2 Open Circuit Voltage . . . . . . . . . . . . . . . 5.1.1.3 Fill Factor . . . . . . . . . . . . . . . . . . . . . . . 5.1.1.4 Efficiency . . . . . . . . . . . . . . . . . . . . . . .

Real Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Photocurrents in a Real Solar Cell . . . . . . . . . . . . .

5.2.1.1 Photocurrent from the Base . . . . . . . . . . 5.2.1.2 Photocurrent from the Emitter . . . . . . . . . 5.2.1.3 Photocurrent from the Space Charge

Region . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Saturation Currents in a Real Solar Cell . . . . . . . . .

Saturation Current from the Base . . . . . . . Saturation Current from the Emitter . . . . .

5.2.3 Ohmic Resistance in Real Solar Cells Shunt Resistance (R, ) . . . . . . . . . . . . . . .

5.2.2.1 5.2.2.2

5.2.3.1 . . . . . . . . . .

32 34 35 36 37 42 44 44 45 45

49 49 50 51 54 57 59

60

61

67 67

69 69 70 71 71 72 73 73 75

76 76 76 78 79 79

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Contents

5.2.3.2 Series Resistance (R, ) . . . . . . . . . . . . . . . 5.2.4 The Two Diode Model . . . . . . . . . . . . . . . . . . . . .

5.2.4.1 Equivalent Circuit of a Real Solar Cell . . 5.2.4.2 The Influence of Ohmic Resistances . . . . .

6 6.1 6.2

6.3

6.4 6.5

7 7.1

High Efficiency Solar Cells ..................... The Significance of High Efficiency . . . . . . . . . . . . . . . . Electrical Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Recombination Losses . . . . . . . . . . . . . . . . . . . . .

Recombination Losses in the Base . . . . . . Photocurrent and Saturation Current from theEmitter . . . . . . . . . . . . . . . . . . . . . . . The Influence of Base Doping . . . . . . . . . Recombination in the Space Charge Region . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.2 Ohmic Resistance Losses . . . . . . . . . . . . . . . . . . . 6.2.2.1 Contact Resistance Metal-Semiconductor . 6.2.2.2 Ohmic Losses in the Semiconductors . . I . 6.2.2.3 Ohmic Losses in the Metal Contacts . . . .

6.3.1 Antireflection Processes . . . . . . . . . . . . . . . . . . . . 6.3.1.1 Antireflection Using a Thin Coating . . . . 6.3.1.2 Textured Surfaces . . . . . . . . . . . . . . . . . .

6.3.2 Losses due to Non-Absorbed Light . . . . . . . . . . . . 6.3.3 Shadowing Losses by Contact Fingers . . . . . . . . . . The Structure of a High Efficiency Solar Cell . . . . . . . . . Manufacturing Process for High Efficiency Silicon Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Process Sequence for the Highest Efficiency . . . . . 6.5.2 The Simplified Manufacturing Process . . . . . . . . . .

6.2.1.1 6.2.1.2

6.2.1.3 6.2.1.4

Optical Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Si Solar Cell Technology ....................... Techology for the Manufacture of Silicon . . . . . . . . . . . . 7.1 . 1 Basic Material . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Refractioning Processes . . . . . . . . . . . . . . . . . . . . 7.1.3 The Manufacture of Polycrystalline Si Material . . . 7.1.4 Crystal Pulling Process . . . . . . . . . . . . . . . . . . . . .

7.1.4.1 The Czochralski (CZ) Process . . . . . . . . . 7.1.4.2 Float Zone Pulling . . . . . . . . . . . . . . . . .

7.1.5 The Manufacture of Silicon Wafers . . . . . . . . . . . . 7.1.6 Polycrystalline Silicon Material . . . . . . . . . . . . . . . 7.1.7 Sheet Materials . . . . . . . . . . . . . . . . . . . . . . . . . .

7.1.7.1 The EFG Process . . . . . . . . . . . . . . . . . .

vii

79 79 81 83

87 87 90 90 90

95 98

101 102 103 110 113 114 114 115 118 120 121 122

123 124 128

133 133 133 135 135 136 136 138 139 139 141 142

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7.2 7.1.7.2 The SSP Process . . . . . . . . . . . . . . . . . . 143

Si Solar Cell Technology . . . . . . . . . . . . . . . . . . . . . . . . 143 7.2.1 Technologies for the p-n Junction . . . . . . . . . . . . . 144

7.2.1.1 Diffusion Technologies and the Theory of Diffusion . . . . . . . . . . . . . . . . . . . . . . . . 144

7.2.1.2 Diffusion Technologies . . . . . . . . . . . . . . 148

7.2.3 Auxiliary Technologies . . . . . . . . . . . . . . . . . . . . . 155 7.2.3.1 Etching and Cleaning Techniques . . . . . . . 155

156

7.2.4.2 High Vacuum Evaporation Technologies . . 157

7.2.2 Oxidation Technologies . . . . . . . . . . . . . . . . . . . . 152

7.2.3.2 Photolithography . . . . . . . . . . . . . . . . . . 156

7.2.4.1 The Structuring of the Finger Grid . . . . . . 156

7.2.4.3 Thick Film Technology . . . . . . . . . . . . . . 158 7.2.5 Antireflection Technologies . . . . . . . . . . . . . . . . . . 159

7.2.5.1 Applying an Antireflection Coating . . . . . 159 7.2.5.2 The Manufacture of Textured Silicon

Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . 160

7.2.4 The Metallising of Solar Cells . . . . . . . . . . . . . . . .

8 Selected Solar Cell Types ....................... 163 8.1 Crystalline Silicon Solar Cells . . . . . . . . . . . . . . . . . . . . 163

8.1.1 Crystalline Silicon Concentrator Cells . . . . . . . . . . 163 8.1.2 Bifacial Solar Cells . . . . . . . . . . . . . . . . . . . . . . . 166 8.1.3 Buried Contact Solar Cells . . . . . . . . . . . . . . . . . . 166 8.1.4 MIS Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . 168 8.1.5 Polycrystalline Silicon Solar Cells . . . . . . . . . . . . . 169 8.1.6 Crystalline Silicon Thin Film Cells . . . . . . . . . . . . 171

8.1.6.1 Advantages and Requirements . . . . . . . . . 171 8.1.6.2 The Relationship between Electrical and

Cell Parameters . . . . . . . . . . . . . . . . . . . 173 8.1.6.3 Manufacturing Technology for Si Thin

Film Solar Cells . . . . . . . . . . . . . . . . . . . 176 8.1.7 Multilayer Silicon Solar Cells . . . . . . . . . . . . . . . . 178

8.2 Thin Film Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . 181 8.2.1 Amorphous Silicon Solar Cells . . . . . . . . . . . . . . . 181 8.2.2 Gallium-Arsenide Solar Cells . . . . . . . . . . . . . . . . 185 8.2.3 Cadmium-Telluride Solar Cells . . . . . . . . . . . . . . . 189 8.2.4 Copper-Indium-Diselenide Solar Cells . . . . . . . . . 190

8.3 Tandem Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 8.4 Dye-Sensitised Solar Cells . . . . . . . . . . . . . . . . . . . . . . . 193

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Contents

9 9.1

9.2

9.3 9.4

9.5 9.6 9.7 9.8

Analysis and Measuring Techniques . . . . . . . . . . . . . . . Measuring the I-V Curve Under Illumination . . . . .

9.1.2 Measuring the Dark Current Characteristic . . . . . . .

Solar Cell Spectral Response . . . . . . . . . . . . . . . . . . . . .

The Current-Voltage Characteristics . . . . . . . . . . . . . . . . 9.1.1

9.1.2.1 Dependence of Efficiency on Radiation . . 9.1.2.2 Dependence of Efficiency on Temperature

9.2.1 Spectral Response of a Front Illuminated Solar Cell 9.2.2 Spectral Response of a Back Surface Illuminated

SolarCell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The PCD Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.1 Determining the Emitter Saturation Current . . . . . . 9.4.2 Determination of the Surface Recombination

Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Microwave Detected Photocurrent Decay . . . . . . . . . . . . Modulated Charge Carrier Absorption . . . . . . . . . . . . . . . Short Circuit Current Topography (LBIC) . . . . . . . . . . . . The DLTS Process . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The PCVD Measurement Techniques . . . . . . . . . . . . . . .

Appendix A: List of Symbols .......................... Appendix B: Physical Constants. Selected Si Parameters

a t 3 0 0 K ............................... Index ............................................

ix

201 201 202 203 205 206 208 208

210 212 214 215

217 217 220 225 227

231

233

235

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Photovoltaics

1.1 THE PRINCIPLES OF PHOTOVOLTAICS

As the name suggests, the absorption of light - photons - in a semiconductor can, under certain conditions, create an electric current. The transformation principle is based upon the fact that in a semiconductor fixed electrons can be converted into freely moving conduction electrons. This simultaneously creates a positively charged ‘hole’ and thus a second charge carrier with an opposing charge.

If a potential difference exists in the semiconductor material, whether due to a p-n junction or an appropriate surface charge, then this charge carrier can be forced to travel in an external circuit, i.e. an electrical current c m be produced. In many cases, in particular in the case of crystalline silicon, the charge carriers that have been created can only reach this potential barrier because of thermal vibrations. No other force drives them in this direction. This means that the charged particles will have to exist until they reach the potential barrier. This lifetime or diffusion length (the average distance travelled) is one of the key factors for the efficiency of photovoltaic energy generation. Of course, a multitude of other physical characteristics, such as cell design, help to determine functionality and efficiency.

1.2 THE HISTORY OF PHOTOVOLTAICS

The physical effect which underlies photovoltaics was first observed by Becquerel [l] in 1839, when he produced a current by exposing silver electrodes to radiation in an electrolyte. The effect was described in more detail by Adams and Day [2] in 1877. They observed that the exposure of selenium electrodes to radiation produced an electric voltage, thus allowing

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2 Crystalline Silicon Solar Cells

them to produce electric current. The effect was then put on hold until the discovery of transistors and

the explanation of the physics of the p-n junction by Shockley [3] and Bardeen and Brattain [4] in 1949, the year that marked the beginning of the semiconductor era. Then, in 1954 Chapin et a1 [5] at the Bell Laboratories in the USA developed the first solar cell based on crystalline silicon, which had an efficiency of 6% - considerable at the time. This efficiency was increased to 10% within a few years. The first viable use for solar cells was in satellite power supplies. Photovoltaics proved their worth convincingly in this application. The initial problem of high degradation of efficiency by cosmic radiation has now for the most part been solved.

The main driving force behind the widespread use of photovoltaics for terrestrial power supplies came in 1973 with the notorious oil shock. From this point onwards numerous research and development institutions were set up around the world, the majority of which were publicly financed. New institutes were founded. All the available options for cost reduction were examined, as it was already recognised that the excessive costs of photovoltaic plants posed the largest obstacle for the widespread use of photovoltaics.

The wide range of work on the reduction of the cost of silicon serves as an example of these efforts. These are:

The development of a polycrystalline silicon material which could be produced significantly cheaper than monocrystalline material by using casting instead of the familiar pulling process. (See Chapter 7, Section 7.1.6 for further details.) The development of methods for the production of sheet material to eliminate the costs associated with the pulling of rods and the sawing of wafers and to eliminate the wastage associated with cutting. The development of low cost technological processes for the manufacture of cells, e.g. silk screening processes instead of high vacuum evaporation processes.

Apart from silicon, which is now used almost exclusively in the generation of photovoltaic power, investigations were undertaken in numerous institutions into other semiconductor materials. These were successful in the development of amorphous silicon (a-Si) - a silicon hydrogen compound [6]. This material has conquered the consumer market (e.g. clocks, pocket calculators). The critical factor is not so much high energy generation as electrical voltage at currents in the milli- and microamp range. a-Si solar cells achieve the required voltage multiplication - a solar cell only produces approximately 0.5 V - very easily by monolithic integration during the manufacture of cells. Of all the other materials made of III-V or II-VI semiconductors or heterocompounds, until

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Photovoltaics 3

now copper-indium-diselenide (CIS) has been at the forefront [7]. One obvious advantage of this material is the adequate long-term stability of solar cell parameters and the achievement of a relatively high level of efficiency. So-called tandem cells represent a further sphere of work, in which solar cells with differing absorption ranges are optically connected in series in order to better utilise the solar spectrum.

At the beginning of the 1980s it was recognised that high efficiency in solar cells was of great importance for the reduction of the costs of the complete system. From this point onwards research and development has mainly concentrated on achieving high levels of efficiency.

1.3 THE IMPORTANCE OF PHOTOVOLTAICS

The volume of solar cells currently produced world wide is approximately 100 Mega ‘peak watts’ (peak watts are the capacity of a solar power plant at maximum sunshine). This order of magnitude is of course completely unimportant with regard to energy generation. However, there are numerous applications for which solar power brings great advantages. Thus, for example, many signal stations are driven by solar power. Another field which will grow significantly in the near future is photovoltaic power supplies for isolated houses, for which connection to the grid is very expensive. In the small appliance sector, e.g. power supplies for independent mobile equipment (meters, electrical tools, etc.), solar cells are becoming more popular.

Usage in the Third World will increase. Electrical lighting and the operation of fridges, etc. alone represent a large improvement in the standard of living in these countries. The operation of water pumps using photovoltaics is another viable application in this area, which is certain to become more and more common.

In the more distant future environmental concerns and the finite supply of fossil fuels make it certain that the sun, as the only inexhaustible energy source, will also be used for large scale power supplies. Just a fraction of the solar energy that falls upon the earth would cover our entire current energy demand. Thus, no restrictions are presented by the original energy supply.

References

111 Becquerel A. E., Compt. Rendus de L’ Acadernie des Sciences 9, 1839, p.561

Adams W. and Day R., Proc. Roy. SOC. A 25, 1877, p. 113 [2]

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4 Crystalline Silicon Solar Cells

[3]

[4]

[5]

Shockley W., Bell Syst. Tech. Journ. 28, 1949, p. 435

Bardeen J. and Brattain W.H., Phys. Rev. 74, 1948, p. 230

Chapin D. M., Fuller C. S. and Pearson G. L., J A p p f . Phys. 25, 1954, p. 676

Carlson D. E. and Wronski C.R., Appl. Phys. Lett. 28, 1976, p. 671

Mitchell K. W., Eberspacher C . et a\., Trans Elec. Dev. 37, 1990, p. 469

[6]

[7]

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2 Solar Power

2.1 THE SUN AS A SOURCE OF RADIATION

The sun as a source of radiation is dealt with in detail in several well known books such as [ 11. We will therefore only concern ourselves with the most important points here.

According to current knowledge, the energy of the sun is created by the nuclear fusion reaction of hydrogen and helium which occurs inside the sun at several million degrees. The mass difference that occurs in this process is converted into energy, As the sun is in radiation equilibrium with the cold universe, it is principally its surface temperature which is determined by this. This is 5900 K. Most fixed stars have surface temperatures of the same magnitude owing to radiation equilibrium. Because all elements are ionised to some degree at this temperature, and their spectral lines are strongly broadened, the radiation consists of a multitude of spectral lines, so that the gaseous surface of the sun radiates like a black body. The solar energy that reaches the surface of the earth is determined by the ratio of the diameters of the sun and earth and their distance apart. If we disregard the deviations arising from the rotation of the earth around the sun, the most recent measurement of the radiation power outside the atomosphere is Do = 1.353 kW/mz. The value Do is known as the solar constant [2].

This radiation is then partially absorbed and scattered by its journey through the atmosphere, thus being weakened. In the infrared region this weakening is caused by the water and carbon dioxide in the air, while the absorption in the visible range is caused mainly by the oxygen, and in the ultraviolet range it is mainly caused by the ozone content. As well as a reduction in radiation there is also a spectral shift. Rayleigh scattering, for example, scatters the short wavelength light much more than the long wavelength light. Figure 2.1 shows the spectral distribution of solar energy.

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6 Crystalline Silicon Solar Cells

2.2 STANDARD RADIATION

The terms AM0 and AM1.5 used in Figure 2.1 are definitions for specific radiation conditions. AM (‘air mass’) gives information about the amount of air mass the radiation passes through in the individual case. The terms are :

the extraterrestrial radiation, e.g. applicable to satellites in space; the vertical incidence of sunlight at the equator at sea level; sunlight radiating through an air mass 1.5 times greater than the vertical case.

AM0

AM1 A M 1 3

x-

Figure 2.1 Spectral distribution of radiation intensity

It can be easily calculated that the radiation condition AM 1.5 is fulfilled if the sun is at an angle of 41.8” above the horizon.

Both weather and location conditions have a great influence on the composition of radiation. Diffuse light contains a large proportion of blue radiation. Certain standards have been agreed for the determination of efficiency. For terrestrial photovoltaics the standard is AM 1.5 global. The term ‘global’ stands for the sum of direct and indirect radiation.

In the laboratory and in the production of solar cells, sun simulators very closely approximate this spectrum using the light from a xenon ultra high pressure lamp through various filters. All the following information about

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Solar Power 7

efficiency and other results of solar cells are based on this standard spdctrum.

References

[ 11 Duffie J. and Beckmann W., Solar Engineering of Thermal Processes,

[2] Thekeara M. P., Solar Energy 18, 1970, p. 309

2nd Edition, J Wiley & Sons

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The Principles of Photovoltaics

3.1 CRYSTALLINE STRUCTURE AND THE ENERGY BAND DIAGRAM FOR SEMICONDUCTORS

The direct transformation of light into electrical energy always requires a semiconducting material. Semiconductors are solids and, like metals, their electrical conductivity is based upon movable electrons. Ionic conductors are not considered here. The primary consideration here is the level of conductivity. Materials are known as

conductors at a conductivity of Q > lo4 (SZcm)-’; semiconductors at a conductivity of lo4 > a > 10” (ncm)’; non-conductors (insulators) at a conductivity of Q < lo-’ (ncm)-’.

This simple categorisation is, however, hardly an adequate criterion for a definition and it is predominantly other characteristics, in particuiar the thermal behaviour of conductivity, that form the basis for classification. This is where metals and semiconductors behave in an opposing manner. Whereas the conductivity of metals decreases with increasing temperature, in semiconductors it increases greatly. Madelung [l] defined semiconductors as follows:

Semiconductors are crystalline solids, which in their pure state insulate at temperatures approaching absolute zero, but at higher temperatures either possess a clearly demonstrable electronic conductivity, become conductive due to the disruption of the ideal lattice structure, or in which the external effect of conductivity can at least be induced.

So what is a crystalline solid? At this point we wish to differentiate between two separate categories. On the one hand there are the so-called amorphous substances. In these, the structure of individual atoms and molecules displays almost no periodicity or regularity. Crystalline solids, on the other hand, are distinguished by a perfect (or near perfect) periodicity

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of atomic structure. These materials naturally make it much easier to understand the physical characteristics of solids. Therefore, the explanation of semiconductor characteristics and the physical principles of photovoltaics should be based upon crystalline semiconductors, and in particular crystalline silicon.

3.1.1 The Energy Band Diagram for Tetrahedronal Semiconductors

The bonding or arrangement of atoms in nature can occur in numerous different ways. The deciding factor is the characteristics of the electrons in the outer shell of the atom, the so-called valence electrons. Depending upon symmetry and energy conditions, the arrangement of atoms can give rise to different crystalline structures.

Figure 3.1 The diamond lattice [2]

In common with all elements of the fourth group of the periodic table, silicon has four valence electrons. These atoms are arranged in relation to each other, such that each atom is an equal distance from four other atoms and that each electron forms a stable bond with two neighbouring atoms. This type of lattice is known as the diamond lattice, because diamond - comprising of tetrahedronal carbon - has this lattice structure. The bond is known as a homopolar (or covalent) bond, and is also present in the hydrogen molecule, for example. These bonds are extremely pronounced.

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The Principles of Photovoltaics I 1

This is demonstrated by other physical characteristics, such as the hardness of these materials.

Figure 3.1 [2] shows the structure of a diamond lattice. We do not wish to go into further details about this structure at this point. Please refer to the specialist literature [3].

For electrical conductivity to occur in this type of crystal, some of these bonds must be broken. Clearly, this can only occur if energy is expended. At a temperature of T = 0 K no bonds are broken, i.e. no free electrons are present. At T = 0 K the semiconductor is an insulator.

So what is the energy level structure in this type of crystal? We know that according to Bohr's theory of the atom, electrons in an isolated atom can only occupy well-defined energy levels. If we bring two atoms close together in an imaginary experiment, then an interactive effect will occur, splitting the energy levels of these two bonded atoms. This splitting principle can be briefly described in terms of a mechanical theory of coupled vibrations (Figure 3.2).

Figure 3.2 The principle of coupling mechanical oscillators

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I2 Crystalline Silicon Solar Cells

A 2.

F 5

Each of the two individual systems shown are tuned to one and the same oscillation frequency. If they are not connected, then both have only one oscillation frequency. However, if these systems are coupled together (by a fictitious mass-free spring), then several oscillatory states with differing frequencies occur due to the interactive effect. The number of frequencies increases with the number of oscillators coupled. The stronger the bond, the farther apart are the oscillation frequencies generated from the original frequency.

\ L

I

I I I 2- d

interatomic distance

Figure 3.3 The splitting of energy levels in a semiconductor

If we transfer this analogy to the interactive effect in a crystal lattice, then the splitting of energy levels can be represented as follows.

The vertical axis of Figure 3.3 represents electron energy, and the horizontal axis represents the distance of atoms from one another. As the distance decreases, the energy levels of the atoms split up more and more. Similar to the mechanical analogy, the energy bands become increasingly broad. At a specified distance between atoms (4, it is clear that there is an energy gap between the two upper bands, the valence band and the conduction band, in which there can be no electrons. The energy gap is called the band gap, Eg, of a semiconductor. It further applies that when T = 0 K, because no bonds are broken, none of the energy levels in the outer

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The Principles of Photovoltaics 13

conduction band will be occupied. In the valence band, however, all available energy levels are occupied. This means that no energy can be absorbed from a connected external electrical field, i.e. electric current cannot flow. The semiconductor is then an insulator. Only at higher temperatures does it show conductivity, because then some electrons occupy the energy levels in the conduction band.

This band structure, with an energy gap between the two outer energy bands, also occurs in insulators. Semiconductors and insulators differ only in the size of the band gap. In a semiconductor, even at ‘normal temperatures’ (e.g. at room temperature) some electrons can jump the band gap thus giving rise to electrical conductivity. In insulators the band distance is so large that at normal temperatures no electrons can jump the gap. Normal values for the energy of this band gap for semiconductors lie within the range of a few tenths of electron-volts to approximately 2 eV, whereas for insulators these energies are significantly higher.

4 I

Interatomic distance Figure 3.4 The splitting of energy levels in an electrical conductor

Metals, on the other hand, behave in a totally different manner. They seldom possess the strict periodicity of the crystal lattice. Electrons are therefore not so closely linked as in a diamond lattice. The energy gap diagram shows the case where the outer conduction band is partly occupied by electrons. Thus, if an electrical potential is connected, then electricity

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I 4 Crystalline Silicon Solar Cells

can flow. In some metals, the other variant occurs and the energy bands overlap. This leads to the same physical behaviour as the first case. Figure 3.4 shows an example of the band structure of a metal.

3.1.2 Electrons and Holes in a Semiconductor

In this section we work out the number of free electrons in a semiconductor in relation to temperature.

First, however, some explanations concerning the phenomenon of conduction itself. As we will demonstrate in more detail later, in the broad temperature range of ‘normal’ temperatures the conduction band is ‘almost empty’ and the valence band ‘almost full’ of electrons. ‘Almost empty’ in the conduction band means that only a few electrons are in the permitted energy states. Although, as the calculations given later will demonstrate, all these states lie near the edge of the band, there still are numerous unoccupied states close to the occupied levels, so these electrons are capable of reaching a higher level by an almost continuous process. This means that when connected to an electric field, energy can be continuously taken up. It is then possible to treat the conduction electrons as the electrons in metals are treated in classical physics. Owing to the level of dilution they influence each other very little, but they are in a state of continuous close interaction with the lattice of the crystal. This interaction is highly complex and can only be considered statistically. However, these interaction forces are extremely significant for the conduction process. To take these into account, instead of the elemental electron mass m, an effective mass mi is introduced.

Analogous to this is the behaviour in the ‘almost full’ valence band. Some energy levels in this band are not occupied by electrons and these energy levels also lie close to the edge of the valence band. As in the conduction band, these empty states are surrounded by numerous occupied states. This means that one such empty state can wander around within the valence band. This empty state is known as a hole or defect electron. It has proved sensible to treat this hole as an individual, i.e. as a charge carrier. It is evident that this charge carrier has a positive charge and, like electrons, is assigned an effective mass mi due to interaction with the lattice. The defect electron or hole, like the electron, is a second type of charge carrier. This is an extremely useful formalism for dealing with the phenomenon of conductivity in semiconductors.

3.1.3 Energy Levels: The Fermi Level

Which of the permitted energy levels in the conduction band are occupied depends upon the probability of one electron achieving a specific energy

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The Principles of Photovoltaics 1.5

level due to the temperature. This probability underlies the Pauli Principle, which states that each available state can be occupied by a maximum of two electrons (with different ‘spin’).

Figure 3.5 Fermi-Dirac distribution function

The result of statistical behaviour based on this selection principle gives the Fermi-Dirac distribution, which we have reproduced here without giving in further details. According to this, the probability f(E) of an energy level being occupied is

(3.1.1)

where

E, is the so-called Fermi energy, which will be described in more detail later, k is the Boltnnann constant, and T is the absolute temperature.

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16 Crystalline Silicon Solar Cells

Figure 3.5 shows the probability for three different temperatures. When T = 0 the probability of occupation for all energy levels where E > E, is 0 and when E < E, it is 1. At a finite temperature, the variables are dependent upon temperature. If at this finite temperature E = E,, then - where eo = 1 in the formula (3.1.1) - the occupation probability is 0.5. The Fermi energy is defined such that the probability of occupation of this energy level is 0.5.

To determine which energy levels are actually occupied, the distribution of permitted energy levels must be determined.

3.1.4 Density of States for Electrons and Holes

We begin with the distribution of electrons in the conduction band. How large is the number N(E) of permitted energy levels for electrons per volume unit in the conduction band in an energy range dE? We will spare the complex calculations at this point. According to the rules of statistics and quantum mechanics this number is found to be

N ( E ) dE = (3.1.2) h 3

where

h is Planck's constant. rn; is the effective mass of the electrons, and E, is the band-edge energy of the conduction band.

The number of permitted states is proportional to the square root of the difference between the energy of the current state and the band-edge energy of the conduction band. We also find from (3.1.2), that the number of permitted states immediately at the conduction band edge is zero. Figure 3.6 shows the relation graphically. The upper curve is for electrons, and the lower curve is for holes.

Now we can use equations (3.1.1) and (3.1.2) to calculate the number n of electrons per volume unit in the conduction band. This is found to be

n = ff(E)N(E)dE (3.1.3) Bc

For the solution in closed form we make two simplifications. Since at normal temperatures E - E, N kT (at 25°C kT z 0.026 eV), we may approximate

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The Principles of Photovoltaics 1 7

Figure 3.6 Number of permitted states in an intrinsic semiconductor

E, - E 1 E - E , (3.1.4)

and because almost no states are occupied above Em,, we can select an infinite integration limit instead of Ern,. Therefore

8 f i - m

n = - m *”’ exp(E,lkT) ( ( E - EC)”’exp(- ElkT)dE (3.1.5) h 3 0

After some manipulation this is found to be

3

2xm,*kT 7 EF - E C (3.1 .6) = ’ [ h 2 ] exp( kT

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18 Crystalline Silicon Solar Cells

The expression before the exp function is called the effective density of states, N,, of electrons in the conduction band. Therefore

n = N , exp( EF - E C ) k T

(3.1.7)

We see that in a semiconductor, in addition to the energy of the Fermi level, the number of free electrons in the conduction band - and therefore its conductivity - depends decisively upon temperature!

The number of holes in the valence band can be calculated in the same way. This is found to be

3

2zmp*kT 1 EV - E F (3.1.8) = ' [ h2 ] exp( k T ) or

EV - E F P "v exp( kT ) (3.1.9)

Nv is thus by definition the effective density of holes in the valence band. Figure 3.7 gives another overview of the energy levels scheme of an

intrinsic semiconductor at a finite temperature. It is apparent from Figure 3 . 7 ~ that the density distribution depends upon the two variables in Figure 3.7a and Figure 3.7b. The shaded areas can in Figure 3.7a be assigned the densities N , and N,, and in Figure 3 . 7 ~ the intrinsic carrier concentration.

For the ideal non-defective semiconductor in thermal equilibrium the number of electrons in the conduction band must be equal to the number of holes in the valence band. Therefore n = p, i.e.

N, exp( EF - E C ) = N , eXp("' -EF) (3.1.10) k T k T

We thus find the energy of the Fermi level to be

E, +Ev k T EF = + - ln(N,IN,) 2 2

(3.1.1 1)

For silicon with an effective mass of rn~=1.09rn0 and rni=1.15rn0 [4] the Fermi level is approximately 0.023 eV above the middle of the forbidden band. If we take the product of n and p, we find

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The Principles of Photovoltaics

E E E 4 t

-1

(a) (b) (a 0 N(E) - 0 f(E1 1 0 [ l - f (E l I .NIE l '

Figure 3.7 Term scheme of an intrinsic semiconductor

I9

E n p = N c N , expiEV - E c ) = N , N , exp(- 2) k T (3.1.12)

k T

If we define np=nf, where ni is designated as the intrinsic carrier densitv. then for Si at 300 K we obtain the following values r41:

I , " L 1

N, = 2.86 x 1019 cm" N , = 3.10 x 10'' cm1.3 ni = 1.08 x 10" cm"

E,, = 1.124 eV

The important point is that this value for ni deviates significantly from the values given in the literature (e.g. ni is approximately equal to 1.4 x 10" ~ m - ~ ) . The new value, published in 1990, is fundamentally in agreement with the values that were published in 1977 [ 5 ] and by our institute in 1985 [6].

3.1.5 Thermal Equilibrium

The thermal equilibrium in the intrinsic case (i.e. an undoped semiconductor crystal) will now be examined in more detail. The concentrations of electrons and holes at a set temperature are the result of dynamic equilibrium between the formation of electron-hole pairs

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20 Crystalline Silicon Solar Cells

(generation) and the destruction of pairs (recombination) when electrons from the conduction band fall back into the valence band. The generation of charge carriers is certainly independent of the number of electron-hole pairs that have already been formed, as the number of currently bound electrons is incomparably higher than the concentration of free electrons.

As soon as charge carriers are formed, however, recombination is set in action. This depends upon the concentration of charge carriers, and is, according to the mass-action law, directly proportional to their number. If we call R the recombination rate per volume unit and time unit, then

R = r p n (3.1.13)

where r is the recombination probability.

recombination rate R. Therefore In thermal equilibrium the generation rate G is equal to the

G = R = r n p or where n p = n , 2 (3.1.14)

It holds that

G l r = n I 2 (3.1.15)

i.e. the intrinsic carrier density is determined by the ratio of the generation rate and recombination probability. As the latter is a constant, ni is only dependent upon G and thus temperature. It is very important to note that this relationship applies not only for intrinsic semiconductors, but also for all extinsic semiconductors in which the number of electrons and holes has been altered by the addition of a dopant (which is normally the case for semiconductor devices).

3.2 THE CONDUCTION MECHANISM IN SEMICONDUCTORS

3.2.1 Intrinsic Conduction, Field Current and Mobility

We wish to demonstrate that, in general, Ohm's law applies in a homogeneous semiconductor.

As already mentioned, in a semiconductor free electrons and holes carry the current. Electrons move in an electric field under the influence of a force

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The Principles of Photovoltaics 21

K = - q E = m b (3.2.1)

where E is the electric field, q is the elementary charge and b is the acceleration.

In a vacuum with a constant electric field, an electron will very quickly reach a high velocity due to constant acceleration. This is dependent only upon the distance ‘starting point to end point’ and the magnitude of the electric field, The situation is very different in a solid, i.e. also in a homogeneous semiconductor. Although the same forces are in effect (where we must replace m, with m: ), after a ‘short’ distance the electrons collide with a lattice atom or an impurity atom, or occasionally with another electron. This scattering process causes the electron to lose the energy taken from the electric field, which is transfered to the lattice_ in the form of heat. Therefore after travelling an average free path length 1 and after an average relaxation time f, a ‘collision’ occurs.

3

Figure 3.8 The path of a free electron in a crystal lattice: (a) without an electric field; (b) with an electric field

Figure 3.8 gives a graphic picture of the situation. Whereas by purely thermal movement the electron on average covers no distance, when an electric field is connected it gains an additional velocity component Vdnn in the opposite direction to the field, where

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22 Crystalline Silicon Solar Cells

The average of all velocities gives half of this value, thus

- Vdrin = -!- Q E t (3.2.3)

2 mn*

This drift is very small compared with the thermal velocity (with the exception of very high fields, where a carrier multiplication also occurs).

The movement of charge carriers in an electric field results in an electric current, which we will call the field current. The current density is found to be

I,, = nq VdriA

and thus

1 g i 2 m,'

In = n q - - - E

If we define

as the electron mobility, then

I, = n 4 P n E

or

In = Q E

where the electrical conductivity Q is

= = n 4 P n

The same applies for the holes and thus for the hole mobility

(3.2.4)

(3.2.5)

(3.2.6)

(3.2.7)

(3.2.8)

(3.2.9)

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The Principles of Photovoltaics 23

p = - - t 1 4 - 2 mpf P (3.2.10)

The total conductivity of a semiconductor is thus

cr = 4 ( w , +PIUP) (3.2.1 1)

i.e. conductivity is dependent upon the number and mobility of both types of charge canier.

Mobility is itself dependent upon temperature, as well as the number of dopant atoms (Section 3.2.2). Figure 3.9 shows this relationship for electrons and holes [7].

104

103 Pn [el

102

lo 0 100 200 300 lo 0 100 200 300 T [ O C I T I"C1

Figure 3.9 Mobility of electrons and holes as a function of temperature and dopant concentration [7]

If we look at the situation for metals, on the other hand, the number of free electrons is very high and independent of temperature. This high number has the result that even with a low level of drift velocity, high currents can be achieved, i.e. only a low field strength occurs during current flow.

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24 Crystalline Silicon Solar Cells

3.2.2 Impurity Conduction

In Section 3.1.4 we calculated the number of available charge carriers in relation to temperature in a ‘pure’ semiconductor. The resistivity p of intrinsic silicon at T = 300 K is found to be approximately 300,000 a m . This varies very significantly with temperature according to the formulae (3.1.7) and (3.1.9).

There is, however, in addition to increasing the temperature another highly effective method of altering the concentration of charge carriers in a semiconductor and thus its conductivity, namely by the purposeful introduction of certain impurity atoms into the crystal.

If we replace a silicon atom in the crystal structure with an element from the fifth group of the periodic table for example (e.g. phosphorus), this atom ‘brings’ five valence electrons with it. Only four of these electrons are required to bond to the crystal structure. It is therefore plausible that the fifth electron is relatively loosely bound and can therefore be ‘ionised’ even at low temperatures. We call these elements from the fifth group of the periodic table ‘donors’, as they can easily ‘donate’ electrons. Their number per volume unit is designated by ND . In addition to phosphorus, the elements arsenic and antimony are also used as donors in semiconductor technology.

How high is the bonding energy of the fifth electron of these substances? Bohr’s atomic theory helps us to determine this. Owing to the

Silicon atom . . . . . . . . . . . . . e m . . . . . . . . . . . . . . . . . . . . Phosphorus atom . . . . .+*G . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . Figure 3.10 Electron orbits of a donor atom in a semiconductor

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The Principles of Photovoltaics 25

relatively weak bond, this electron is located on an equivalent, relatively large Bohr’s atomic radius - it is better to talk of the applicable wave function here - which encompasses many silicon atoms (Figure 3.10).

To determine the bonding energy we can proceed as if calculating the ionisation energy Ei of hydrogen in a vacuum. This works out as

(3.2.12)

where: E, is the permittivity in vacuum; E is the relative permittivity of the material; and h is Planck’s constant.

This ionisation energy works out as E, % 13.6 eV (E = 1 in a vacuum). To estimate the separation energy for the fifth electron of a donor

replace E with the value of relative permittivity for silicon, E,~ = 11.9 and replace m, with m:. We can then estimate by comparison that the bonding energy of the ‘fifth phosphorus electron’ is

m,*/mn E, =EiH - = 0.105 eV

‘Si‘

(3.2.13)

Considering the energy band diagram, this corresponds to an energy level only slightly (approximately 10% of the energy of the band gap) below the edge of the conduction band. It is therefore plausible that even at very low temperatures (< 70 K) all these electrons will be ionised and located within the conduction band. We can therefore expect an additional 10l6 cm” conduction electrons for a doping of, for example, ND = 10l6 ~ m - ~ . This figure exceeds the number of electrons attributable to intrinsic conductivity at room temperature of approximately 10” cm-3 by six orders of magnitude. Conductivity increases to the same degree. This further means that in a wide temperature range conductivity is no longer dependent upon temperature (or, to be precise, only slightly due to the dependency of mobility on temperature), but rather on the number of dopant atoms. Because conductivity is mainly determined by the negative conduction electrons, a semiconductor that is doped in this manner is known as an n- type conductor and the electrons are known as majority charge carriers, whereas the holes - which are present in much lower numbers - are known as minority charge carriers.

So how high is the number of holes in this example? We still have neutrality of charge. The laws of the recombination and generation

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26 Crystalline Silicon Solar Cells

processes also impurity level found to be

still apply, i.e. the product np must equal nf. Because at an of 10l6 ~ r n - ~ n is almost equal to the number of donors, p is

p =ni’lN; = lo4 cm - 3 (3.2.14)

i.e. the number of holes is dramatically lower than the number of electrons. We now consider the position of the Fermi level. It is plausible that in

this case the Fermi level must be much closer to the edge of the conduction band.

Where n = ND

4 -Ec ND = N C exp( k T ) (3.2.15)

or

E, -Ec = k T l n (NJN,) (3.2.1 6)

We then find for E, - E, in silicon at room temperature where ND = 10l6 cm” and Nc = 10’’ cm-3 a value of approximately 0.18 eV, i.e. the Fermi level lies approximately 0.18 eV below the edge of the conduction band. This situation is shown in Figure 3.11 [8]. It also demonstrates visually that the number of holes is significantly lower than the number of electrons. This difference of several orders of magnitude cannot be shown graphically.

We can also use elements from the third group of the periodic table as dopants. The elements boron, aluminium, gallium and indium are used in semiconductor technology. The missing bonding electron of a trivalent dopant atom leads to the creation of a hole and thus an increase in the positive conductivity of the semiconductor. This is therefore called a p-type conductor and these types of dopant are known as acceptors; their quantity per unit volume is designated NA. The holes are now dominant, i.e. the majority charge carriers, and the electrons are the minority charge carriers. The same regularity applies as in the case of doping with pentavalent atoms, i.e. even at low temperatures all holes are active. It is therefore clear that the Fermi level must be located close to the edge of the valence band.

Similarly to (3.2.16) the gap is

E, - E , =kTln(N,lN,) (3.2.1 7)

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E E E

ND

4

27

0 a ) b) C)

Figure 3.11 N-type semiconductor: (a) Energy level of the donors; (b) Fermi-Dirac distribution; (c) electron density in the bands [8]

5.2.3 uirrusion Lurrent ana uirrusion Lonstant

As well as the field current considered in Section 3.2.1, there is a second tvDe of current transDort. namelv the movement of carriers due to UlLlGlGl lGGb I l l GUIIGGILLI illlU11.

Since, as we have seen, electrons and holes move within semiconductors according to statistical rules, we can apply the rules of diffusion to them.

If, for example, a concentration difference of electrons exists, then these will be ‘driven’ from the higher to the lower concentration, i.e. they move in the direction of the negative gradient and the flow dnldt in the direction x (we only wish to consider the one-dimensional aspect here as this is often adequate for semiconductor devices) is proportional to this concentration gradient. Thus

(3.2.18)

where D, is defined as the diffusion coefficient of the electron.

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28 Crystalline Silicon Solar Cells

t

X

Figure 3.12 Diffusion current dnldt as a function of the concentration gradient

The corresponding electric current density is

(3.2.19)

The diffusion current density of holes for a given concentration gradient is found in the same way. Taking the sign into account, with Dp being the diffusion coeficient of holes, this is found to be

(3.2.20)

We can sum up the four possible components of current density in a semiconductor. For electrons

" d x (3.2.21)

and similarly for holes

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The Principles of Photovoltaics 29

p d x

(3.2.22)

We now consider that the diffusion and field currents are not independent of each other. Both come about due to statistical movements and collisions. This connection between the diffusion coefficient and mobility gives the so-called Einstein formula. This reads

k T 4

D =-p (3.2.23)

and is often used in semiconductor physics. Unlike in a metallic conductor, where there is almost no diffusion

current due to the lack of concentration differences, in a semiconductor an electric current is not automatically associated with an electric field, because the diffusion current and the field current can oppose each other and cancel each other out. As we will see later, it is precisely this fact that is so important for the physical behaviour of a p-n junction.

3.3 THE GENERATION OF CHARGE CARRIERS BY THE ABSORPTION OF LIGHT

Unlike opaque metals, semiconductors display what is for them characteristic absorption behaviour. The most important characteristic is the existence of the so-called absorption edge. For wavelengths, at which the photon energy (E=hc/h) (c=speed of light in a vacuum) is greater than the energy of the forbidden band, light is, depending upon the thickness of the material, almost completely absorbed. In the case of long wavelength light almost no absorption takes place due to its low energy. In this spectral region the semiconductor is transparent. In the case of silicon the band edge lies within infrared at 1-1.11 pm. Therefore silicon is excellently suited as a base material for infrared optics.

The intensity of the light entering the crystal is weakened during its passage through the crystal by absorption. The absorption rate is thus - as in many other cases of physical behaviour - proportional to the intensity that is still present. This leads familiarly to an exponential reduction in intensity and can be described mathematically as follows:

(3.3.1)

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30 Crystalline Silicon Solar Cells

where

F, F,,o a, is the absorption coefficient.

The latter is itself dependent upon the wavelength, and determines the penetration depth of the light and therefore the thickness of crystal necessary to absorb most of the penetrating light. The absorption length xL is also often introduced, corresponding to the value xL = l/u. At this absorption length the intensity F, is reduced to l / e x F,,o (approximately 37%).

is the number of photons at point x ; is the number of photons on the surface x = 0; and

3.3.1 Absorption in Semiconductors

Absorption in semiconductors is a so-called basic lattice absorption, in which one electron is excited out of the valence band into the conduction band, leaving a hole in the valence band. Certain peculiarities of this process should be taken into account. A photon possesses a comparatively large amount of energy, but according to the De Broglie relationship p = hu/c = h A has a negligibly small momentum. The conservation principles of energy and momentum demand that during the absorption process the crystal energy rises, but the crystal momentum remains almost unchanged. This leads to certain selection rules.

In addition, we consider the relationship between energy and momentum. For an electron in free space the following relationship applies:

E = - P 2 (3.3.2) 2m

Results from quantum mechanics [9] show that with some modifications the physical conditions of electrons in free space can be transferred to electrons in a semiconductor. We want to exploit this with regard to absorption.

3.3. I . I Absorption in Direct Semiconductors

The absorption process is best demonstrated in direct semiconductors. As we see from Figure 3.13 the minimum energy of the conduction band in relation to the crystal momentum p lies directly above the maximum of the valence band. When a photon is absorbed the energy E=hv is the energy difference between the initial and final condition of the energy of the crystal

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The Principles of PhotovoItaics 31

E, -E, = h v (3.3.3)

If we now write the energy for the charge carrier according to equation (3.3.2), we find the energy of the electron in the conduction band is

and the energy of the hole in the valence band is

(3.3.4)

(3.3.5)

If we add the equations (3.3.4) and (3.3.5) taking (3.3.2) and (3.3.3) into account, we find

(3.3.6)

We see from this that the crystal momentum increases with the rising energy of the photon.

The probability of this absorption process naturally depends upon the density of electrons and holes. As this nears zero at the edge of the band and increases significantly farther away, it is clear that at higher photon energies the absorption probability increases significantly, because the photon energy is then sufficient for absorption to take place even when the crystal moment lies outside the min/max situation. From theoretical deliberations, which we do not wish to reconstruct here, we find the following expression for the absorption coefficient:

a, = C h - -Eg = C ( h v -Eg)," ( ; 1'" (3.3.7)

The value for the constant C is approximately 2 x lo4 for a direct semiconductor, if the absorption coefficient a is given in cm-' [lo].

In the case of direct GaAs semiconductor where Eg=1.42 eV and for light with a photon energy of 1.52 eV (correspond to 3L=0.8 pm) the

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32

t

Crystalline Silicon Solar Cells

I hv

Crystal momentum, p

Figure 3.13 Energy of the conduction band as a function of crystal momentum (direct semiconductor)

absorption coefficient is found to be the value Q = 6.3 x 10’ cm-’ giving an absorption length of x,, = 1.6 pm.

Light with a shorter wavelength is absorbed even better. It is characteristic of a direct semiconductor that even in very thin layers of a few pm the photovoltaically useful sunlight is almost completely absorbed.

3.3. I .2 Absorption in Indirect Semiconductors

The situation is different in an indirect semiconductor. In this case the minimum of the conduction band and the maximum of the valence band lie at different crystal momentums. The absorption behaviour is demonstrated using Figure 3.14. The direct transition from the valence band to the conduction band requires a higher energy level than hv = E,.

It is, however, possible to excite to the conduction band minimum if the necessary change in momentum can be induced by thermal vibrations in the lattice, i.e. a phonon. A phonon itself, although it only has a low energy level in comparison to a photon, has a very high momentum. The important point here is the fact that the probability of absorption is much

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The Principles of Photovoltaics 33

---___

Phonon absorption ! +

b Crystal momentum, p

Figure 3.14 Conduction band energy in relation to crystal momentum (indirect semiconductor)

lower than for a direct semiconductor due to the involvement of two different particles.

Different experimental measurements exist for crystalline silicon [11],[12]. New results have been published in 1995 [13]. Figure 3.15 shows this relationship between absorption coefficient, absorption length and wavelength. In silicon, the absorption length for light with a wavelength of 1 pm is 140 pm where a = 72 cm-I. Therefore, for a high level of absorption in silicon a crystal thickness of approximately 200 pm is required, unless the light is locked into the crystal using reflection method (optical confinement).

It should be mentioned that, as well as this type of absorption, which is connected with the generation of charge carriers, there are also other absorption mechanisms. For example, a photon can also give up its energy by raising up an electron in the conduction band to a higher energy level. From there the electron gives up its energy to the lattice in stages, thus

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34 Crystalline Silicon Solar Cells

1 0 4 I,-. . - 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Wavelength (pm)

Figure 3.15 Absorption coefficient ct and absorption length of silicon in relation to wavelength X , [ 131

increasing the energy of the lattice vibrations, i.e. the temperature in the semiconductor. This absorption occurs at high electron concentrations.

3.4 RECOMBINATION, CARRIER LIFETIME

If ‘excess’ charge carriers are created in a semiconductor, either by the absorption of light or by other means, i.e. the thermal equilibrium is disturbed, then these excess charge carriers must be annihilated after the source has been ‘switched o f f , As already mentioned, this process is called recombination.

Three different mechanisms for recombination will be considered here.

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The Principles of Photovoltaics 35

3.4.1 Radiative Recombination

Radiative recombination is when electrons ‘fall back’ from the conduction band into the valence band, thus annihilating the same number of holes. The process is the exact inverse to absorption, and it is clear that this recombination energy must correspond to the energy E, of the band gap. Therefore for this energy

E = E g = h v = h c l h (3.4.1)

or

h = h c l E g (3.4.2)

In silicon this recombination is just as unlikely as absorption, which means that indirect semiconductors should have long charge carrier lifetimes. Figure 3.16 demonstrates this recombination process in direct and indirect semiconductors.

Crystal momentum, p (a)

I h V- E pi j hv+ E p ! I

Crystal momentum, p (b)

Figure 3.16 Radiative recombination: (a) in direct semiconductors; (b) in indirect semiconductors

The lifetime of charge carriers with this recombination process was first calculated by van Roosbroek and Shockley [14]. They obtained values of approximately 0.75 s for silicon, independent of the concentration of donors and acceptors. This result sharply contradicted all observations. Firstly, a very small carrier lifetime had been measured and secondly a relationship with dopant concentration had definitely been measured. It was therefore obvious that this radiative recombination must play a very secondary role

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36 Crystalline Silicon Solar Cells

and that it is other mechanisms that primarily influence the lifetime of charge carriers.

Before we examine the most important recombination process based on impurities and defects in the material, we first consider the so-called Auger recombination.

3.4.2 Auger Recombination

In the Auger effect one electron gives up its extra energy to a second electron in the conduction or valance band during recombination thus moving it to a higher energy level. The excited electron then gives up this additional energy in a series of collisions with the lattice, thus returning to its original energy state. Figure 3.17 illustrates these two processes.

Figure 3.17 Auger recombination: (a) in the conduction band; (b) in the valence band

The Auger process is assigned a lifetime. It is clear that this recombination is more probable, the higher the concentration of charge carriers. Landsberg and others conducted theoretical deliberations on this subject [15],[16]. For a simple reaction mechanism we can expect that for

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The Principles of Photovoltaics 37

this three-particle process, e.g. for the electron-hole-hole process the reaction mechanism will be proportional to p2n and for an electron- electron-hole process, it will be proportional to n’p. This means that the recombination rate R, for electrons, for example, is

R, = B n 2 p

or thus the Auger lifetime rAug

, P - 1 TAug - - - -

R, B n 2

(3.4.3)

(3.4.4)

The value of the Auger coefficient B for silicon works out as 4 x 1 OS3’ cm6 s-’ [ 17],[ 181. We can estimate that the Auger recombination first becomes noticeable at dopant concentrations higher than 10” cm-’. In most semiconductor devices it is therefore of lesser significance.

More recent measurements [19], however, in the dopant range 10’6-10’8 cmS3 yield a twenty times higher value for the constant B.

3.4.3 Recombination via Defect Levels

It is a known fact that the lifetime in semiconductors is determined fundamentally by the presence of impurities and crystal defects. It is plausible that the inclusion of atoms that do not have the electron structure of a pentavalent or trivalent dopant will give rise to defect levels, with energy levels that need not lie near the edge of the band. They may lie deeper in the forbidden band, and are thus called deep defects.

Figure 3.18 shows a large number of these energy levels for different substances in silicon.

These impurity levels, also called ‘trap levels’ because they are traps for charge carriers, determine the recombination of charge carriers to a high degree.

The theory of this mechanism was developed by Shockley and Read [20], and Hall [21]. It was further developed and completed at a later date [22],[23]. This theory can be explained with reference to Figure 3.19.

For an energy level in the forbidden band four fundamental processes are possible:

an electron is captured by an unoccupied energy level (1); an electron is emitted from an occupied level into the conduction band (2); a hole is captured by an occupied energy level (3); a hole is emitted into an unoccupied state in the valence band (4).

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38 Crystalline Silicon Solar Cells

Li Sb P As Bi Ni S Mn. A9 Pi H9 r

B At Ca In T t Co Zn Cu Au Fe 0

Figure 3.18 Defect levels of some elements in silicon

Figure 3.19 Recombination by defect levels

If we calculate the corresponding probabilities for these processes and make the, in many cases permissible, assumptions that

there is no transition between levels; the state of the energy level is not dependent upon its state of charge; the duration of emission and capture is low compared with the average time elapsed between capture and emission; and the number of energy levels N, is small compared to doping,

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The Principles of Photovoltaics 39

then we find the following relationship for the recombination rate R (s-’ cm”) of excess charge carriers:

where

Vth is thermal velocity, n p N, Q,

op

is electron concentration in equilibrium, is hole concentration in equilibrium, is the number of the trap levels, is the capture cross section for the electrons, and is the capture cross section for the holes.

The variables n, and p l mean

Et - E, n, =ni exp( k T )

and

Ei - E, PI =n;exp( kT )

(3.4.6)

(3.4.7)

where E, is the energy of the defect level. Typical values for Q, and oP are lo-’’ cm’. Vth is approximately lo7 cm/s at 300 K.

The driving force behind the recombination process is the term (np - n:) if the charge carrier concentration deviates from the thermal equilibrium condition.

By introducing the definition for charge carrier lifetime

(3.4.8) 1 and - = N Q V 1 ‘ P t h

- = NtOnVth

‘no tPO

and

An R

T = - (3.4.9)

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40 Crystalline Silicon

we find from the equation (3.4.5)

Po + P , + A n no i n , i An no + p o + An 7 = tn0 =Po

no +Po +An

Solar Cells

(3.4.10)

if we equate An = np - nf . We consider two cases:

1. For high level injection An >> no, n , , po , p , . We then find from equation (3.4.10) the camer lifetime t is

7 = t,, + tp0 (3.4.1 1)

The result can also be explained in that, in the case of high injection in both energy bands, enough carriers are present, and lifetime is only dependent upon the capture probability of electrons and holes and not on their concentration [24].’

2. For low level injection no >> p o An n, , p , (i.e. for n doping) then for the holes as minority charge carriers

PO tp = T (3.4.1 2)

and for p doping where p >> no An n, , p , . For the electrons as minority charge carriers

(3.4.13)

i.e. the minority carrier lifetimes are, refemng to (3.4.8), inversely proportional to the number of impurities.

To show the dependency of carrier lifetime on the energy state of the impurity level and the dopant concentration under the conditions of low injection, we make the simplifying assumption that in equation (3.4.5) oP = Q,. We furthermore assume a constant value for N, and set the value for carrier lifetime, which is created by an impurity level in the mid-band, equal to 1. After some manipulation, we find that for a p-material with doping NA (cm-’) the following relationship applies for the relative lifetime of electrons:

’ Shockley and Read [ 141 demonstrated that where Nt is small compared with doping, An of electrons can be equated to Ap of holes.

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The Principles of Photovoltaics 41

(3.4.1 4)

Figure 3.20 shows this relationship. It is clear from the representation that the energy level is most effective in the mid-gap area and that lifetime is independent of doping in this region.

1 I 1 " " 1 " " 1 " " ~ " " ~ ~ '

0 0.2 0.4 0.6 0.8 1 .o EC Energy (eV) EV

Figure 3.20 Dependency of relative carrier lifetime on basic doping and impurity energy level

For an energy level where E, = 0.2 eV, however, there is a strong dependency. We will explain this using the examples of gold (Ep0.54 eV) and titanium (EpO.2 eV). The capture cross-section is of equal magnitude in both these cases, being

on x opx 1 . 0 ~ 1 0 + ~ cm (3.4.15)

and N, is 1.0 x lOI3 ~ r n . ~ . We use the expression for diffusion length L. This describes the average distance which a charge carrier covers in its lifetime. This works out as L=(Dx.r)O.'. D is the diffusion coefficient. Then

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42 Crystalline Silicon Solar Cells

Specific resistance (Qcm) 100 50 20 10 5 3 15 1 O X 0.2

h

s g 300 - C 0 u) .- 3 200

100

Figure 3.21 Relationship between diffusion length and background doping at fixed concentrations of gold and titanium

the diffusion length as a function of doping yields the values shown in Figure 3.21.

It is clear that with gold as the impurity level the diffusion length is almost independent of doping. However, with titanium as the impurity level with an energy state below the band-edge, there is a marked dependency on the basic doping of the material.

We can deduce the following: because many impurity levels and defects in crystal lie between + 0.2 and 0.2 eV, then for a basic doping greater than 10l6 ~ m - ~ , the normal level for solar cells, these have just as decisive an effect as gold.

3.4.4 Recombination by Doping

The lifetime, calculated according to the above three recombination processes, is thus

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The Principles of Photovoltaics 43

(3.4.16) 1 - 1 1 1

'total 'radiation '~ugsr 'trap

- - - + - + -

All three depend to some degree upon dopant concentration. Figure 3.22 shows a summary of these dependencies.

Doping N, [cm-'1 Figure 3.22 Dependency of the different charge carrier lifetime processes on

doping

We again see that for doping less than 10" cm" (normal for almost all Si devices) radiative recombination plays virtually no role, and carrier lifetime is determined by the impurity level; and only at doping levels greater than lo'* ~ m ' ~ does Auger recombination become dominant.

In the range 10l6 to 10l8 cm" there is a marked discrepancy between theoretical considerations and experimental results. This has already been investigated by numerous authors [25]-[3 13. The relationship obtained

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44 Crystalline Silicon Solar Cells

empirically by Kendall [quoted in [lS]], is frequently used at the moment, according to which the lifetime in this range is calculated as

'50

1 +- 7 x 10l5

T = N D

(3.4.17)

In this equation the carrier lifetime T~ in pure, undoped silicon was previously assumed to be 400 ps.

3.5 BASIC EQUATIONS OF SEMICONDUCTOR DEVICE PHYSICS

To calculate current and voltage relationships in semiconductor devices we need, in addition to the current density equations developed in the above section, the relationship between the electric charge in the crystal and the field strength, as well as an equation governing continuity in the semiconductor. Once again we limit ourselves here to the one-dimensional point of view (positional coordinate x).

3.5.1 The Current Density Equations

According to the equations which we developed in the previous section, both field and diffusion currents can occur in a semiconductor device. We repeat these formulae here to provide a better overview.

For the electrons

dx

and likewise for the holes

(3.5.1)

(3.5.2)

The signs correspond to the conventional current direction.

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The Principles of Photovoltaics 45

3.5.2 Poisson's Equation

If we assume that excess electric charges exist within a semiconductor, i.e. that not all charges are completely neutralised, then there is obviously an electric field. The relationship between the electric charge present and the electric field arising from it is governed by Poisson's equation, which follows from the general Maxwell equation. For the coordinates in the x direction this can be written in the form:

- - d2<p = - - - dE - Q (3.5.3) dxz dx EEO

where Q is the total electric charge in the crystal, E and E~ are the relative permittivities in the material and in a vacuum, and cp is the potential.

To determine the total charge, we must remember, that the donors ND are positively charged after they have given up an electron, whereas the acceptors NA have a negative charge after creating a hole. Poisson's equation for this case reads

(3.5.4)

Or, in words: the gradient of the field strength is equal to the total charge divided by the relative permittivity of the material.

3.5.3 The Continuity Equations

So what is the relationship between absorption, recombination and electric current? If we consider an infinitesimally small volume dV (Figure 3.23) where

dV =dx dy dz (3 S . 5 )

a particle flow F,(x) may flow across the area dyxdz = A into this volume. And at the same time a particle flow F,(x) emerges from this volume, after the distance dx at the point x + dx. It is clear that F2(x) and F,(x) are the same size if additional carriers are neither created nor destroyed in the volume.

Now, however, we want to consider the situation in which changes occur within this volume. We can then determine the particle flow F2(x) in terms of F,(x) if we develop F2(x) to F,(x) in a Taylor series. With a small

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46 Crystalline Silicon Solar Cells

enough value of 6 x we can restrict ourselves to the first term of this series. We can write

F*(x) = F , ( x ) + - W X ) 6 x dx

(3.5.6)

Now if F,(x) is greater than F,(x), i.e. if the additive term on the right- hand side of the formula is positive, then more particles will flow out of the volume than into it. This means that in the volume more charge carriers must be created per unit of time than simultaneously recombine.

A

X x+dx Figure 3.23 Particle flow in a small volume

Therefore the difference in particle flows in this unit volume is equal to the difference between the generation and recombination of these particles. This means

AF =- dF(x) 6x dy dz = (G - R ) 6 x dy dz (3.5.7) dx

We convert these particle flows to electrons and holes and find the following equation for the current density, taking the sign into account:

(3.5.8)

and similarly for holes

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The Principles of Photovoltaics 47

-- 1 q , ( x ) = G - R (3.5.9)

These equations are called the continuity equations. They govern the relationship between current density and the size of generation and recombination. We have now covered the most important equations for the calculation of semiconductor devices.

4 d x

References:

Madelung O., Handbuch der Physik, Bd. XX Halbleiter, Springer -Verlag, 1957

Salow et al., Der Transistor, Springer-Verlag, 1963

McKelvey S. P., Solid State and Semiconductor Physics, Harper and ROW, New York, 1966

Green M. A,, J . Appl. Phys. 67 , 1990, p. 2944

Wasserrab T., Zeitschrgt fur Naturforschung 32a, 1977, p. 746

Ruckteschler R., Dissertation, Univ. Freiburg, 1987

Wolf H. F., Silicon Semiconductor Data, Pergarnon Press, 1969

Frank F. and Snejdar V., Physik and Technik der Halbleiterwerkstofle, Band 1, Akademie Verlag, Berlin, 1964

McKelvey J. P., Solid State and Semiconductor Physics, Harper and Row, New York, 1966, p. 79

Pankove J. I., Optical Processes in Semiconductors, Prentice-Hall, Englewood Cliffs, New Jersey, 197 1

Runyan W. R., NASA Report S.M.U-83-13, University of Dallas, 1967

Jellisson G. E. Jr. and Modine S.A., Report ORNL ITM-8002, 1982

Green M. A. and Keevers M. J., Progress in Photovoltaics 3 , 1995, p. 189

van Roosbroek W. and Shockley W., Phys. Rev. 94, 1954, p. 1558

Landsberg P. T., Solid State Electron. 30, 1987, p. 1107

Landsberg P. T., Appl. Phys. Lett. 50, 1987, p. 745

Beck S. D. and Conradt, Solid State Comun. 13, 1973, p. 93

Rohatgi A., IEEE - TED 31, 1984, p. 597

Hangleiter A. and Hacker R., Phys. Rev. Lett. 65 , 1990, p. 215

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48 Crystalline Silicon Solar Cells

Shockley W. and Read W. T., Phys. Rev. 87, 1952, p. 835

Hall R. N., Phys. Rev. 83, 1951, p. 228

Sah C. T. and Shockley W., Phys. Rev. 109, 1957, p. 109

Sah C. T., et al, Solid State Electron. 13, 1970, p. 759

Shockley W. and Read W. T., Phys. Rev. 94, 1954, p. 1558

Landsberg P. T. and Kousik G. S., J . Appl. Phys. 56, 1983, p. 1696

Hu C. and Oldham W. G., Appl. Phys. Lett. 35, 1979, p. 636

Bennett H. S., Solid State Electron. 27., 1984, p. 893

Tyagi M. S., J . Appl. Phys. 54, 1983, p. 2857

Fossum J. G., Mertens R. P., Lee D. S. and Nijs J. F., Solid State Electron. 26, 1983, p. 569

Tyagi M. S. and v. Overstraeten R., Solid State Electron. 26, 1983, p. 577

Mertens R. P., v. Meerbergen J. L., Nijs J. F. and v. Overstraeten R., ZEEE - TED. 27, 1980, p. 949

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The p-n Junction

4.1 BASIC EQUATIONS

At the beginning of this chapter, the basic equations are summed up once again as follows:

1. Current equations

I,, = q ( p n n E +Dn- dx "1

2. Poisson's equation

3. Continuity equations

(4.1.1)

(4.1.2)

(4.1.3)

(4.1.4)

(4.1.5)

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50 Crystalline Silicon Solar Cells

4.2 SPACE CHARGE REGION

To understand the function of semiconductor devices and thus of solar cells, a precise understanding of the processes within a p-n junction is crucial. The base unit of many semiconductor devices is a semiconductor body, in which two different dopants directly adjoin one another. This is called a p-n junction if a p-doped area merges into an n-doped area within the same lattice.

In a simple example we assume that - in silicon - both dopants are of the same magnitude and merge together abruptly. Figure 4.1 may clarify this behaviour.

Figure 4.1 Doping and concentration distribution of a symmetrical p-n junction in thermal equilibrium

The left-hand side x<O would, for example, be doped with boron atoms with a concentration of N A = 10l6 atoms per ~ m - ~ , making it p-conductive. The right-hand side x>O, on the other hand, could be doped with phosphorus atoms, at N, = 10l6 ~ m - ~ , making it n-conductive.

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The p-n Junction 51

If we consider the behaviour of a p-n junction at room temperature, we know almost all of the donors and acceptors are ionised. We can approximate N; w N A = p p and A$ = ND = n, where

p , is the hole concentration in the p-neutral area, and n, is the electron concentration in the n-neutral area.

Thermally generated charge carriers can be ignored in this context. Owing to the thermal equilibrium between pair creation and

recombination, np = nf. Therefore, the concentration of electrons in the p- neutral region is np = lo4 and in the n-neutral region the number of holes is p , =lo4 ~ m - ~ .

The freely moving charge carriers will not follow the abrupt change in concentration from N A to ND. Rather, the carriers will diffuse due to the difference in concentration, i.e. the holes from the p region will move into the n region, and the electrons from the n area will move into the p region. Diffusion currents will arise. The ionised acceptors and donors, which are no longer electrically compensated, remain behind as fixed space charges (Figure 4.1 above). Negative space charges will arise on the left-hand side in the p region and positive space charges arise on the right-hand side in the n region. Correspondingly - as occurs in a plate capacitor - an electric field is created at the p-n junction, which is directed so that it drives the diffusing charge carriers in the opposite direction to the diffusion. This process continues until an equilibrium is created, or in other words until the diffusion flow is compensated by a field current of equal magnitude. An (extremely large) internal electric field exists - even if both sides of the semiconductor are grounded.

1. How large is this electric field? 2. What is the distribution of the electric voltage and of the electric field? 3. What is the capacity of this p-n junction?

Three questions remain to be answered:

4.2.1 Potential Difference

This calculation utililises the fact mentioned above that in equilibrium the field current must equal the diffusion flow in the opposite direction. We first consider the case for electrons. In this case

dn q n p n E = - ( I D , - dx

and where

(4.2.1)

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52

dcQ E = - - dx

Crystalline Silicon Solar Cells

(4.2.2)

we find

d q - D n dn 1 - - - - - dx p, n dx

(4.2.3)

Simplifying, using Einstein's formula (3.2.23), we find that

k T d n 1 * =--- dx q n d x

(4.2.4)

This equation can be integrated straight away. The potential difference is found to be

(4.2.5)

where UD is the diffusion voltage. U, is defined as U, = kT/q (thermal voltage), approximately 25.9 mV at 300 K.

If we also introduce np = nf/NA and n, N,, we find that

U, = U, ln(NDNA/ni2) (4.2.6)

In our case where ND and NA = 10l6 cm-3 diffusion potential is approximately 0.72 V for silicon at 300 K .

We have used classical methods for this calculation. We now demonstrate the much more elegant method for determining the influences of potential using Figure 4.2. In a p-n junction in thermal equilibrium the Fermi level must be of the same magnitude in both regions. If this were not the case, then we would have a perpetual motion engine.

It is thus clear that q x U, is equal to the energy of the band gap minus the two respective distances of the Fermi level from the corresponding band edges, i.e.

qUD = E g - E , - E 2

and where

(4.2.7)

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The p n Junction 53

Figure 4.2 The position of the Fermi level in a p-n junction

E, = kTln(Nv/NA)

E, = kTln(N,/N,)

we quickly obtain

q U , = Eg - kTln(N,N,/N,N,)

and since niz = NaVexp(-E,/kT), it follows that

(4.2.8)

(4.2.9)

(4.2.1 0)

We previously showed the classical method, as we believe that this introduction can be very helpful for a deeper understanding of the physics of a p-n junction.

U , = -ln(N,N,/n:) kT 4

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54 Crystalline Silicon Solar Cells

4.2.2

We now know the functional relationship between the concentration of charge caniers and voltage levels. The local distribution of voltage and field can be determined using Poisson’s equation.

To obtain the density of space charge, we again put in space charges

Electric Field and Electr,ic Potential

- dE =-* - Q (4.2.1 1) dx du* EE,

and thus

(4.2.12)

The analytical solution of this equation is not possible in general form. We therefore use an approximation, which was suggested by Schottky as early as 1942 [l]. According to this, in the case of the abrupt p-n junction observed here, and under the given concentrations, we can disregard at room temperature the concentrations of n and p compared to the fixed charges. We further introduce sharp limits to the ‘fluid’ limits of the space charge region and divide the zone into the familiar two sections (Figure 4.1). In the region x, x < 0, the p region, the density of volume charge is solely determined by the acceptors NA- and similarly in the n region, 0 < x < x, the density of volume charge is determined by the concentration of donors ND+. In the other regions x < x, and x > x, the concentrations of the respective charge carriers are constant. We find that for the space charge region on the p side

= - - N i (4.2.13) dE - dx EO

and for the n side

d E - L N ; - dx EE,

(4.2.14)

Outside these zones dEldx = 0.

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The p n Junction 55

By integration - and taking into account the boundary conditions Ex=, = 0 and Ex, = 0 - we obtain the following paths for the electricfield In the p region of the space charge region

9 N*- E ( x ) = - - ( x - X I ) € 0

and in the n region of the space charge region

(4.2.15)

(4.2.16)

The field path is thus linear with the positional coordinates and always negative.’ Where x = 0 the field strength is at its maximum and both values must be of equal magnitude. It then holds that

NA-x, = Nix, (4.2.17)

This means that the distances x, and x, - the distances in the space charge region - are inversely proportional to the corresponding dopant concentration and that the number of positive and negative space charges are of equal magnitude on both sides.

We now determine the potential distribution in the space charge region by integrating equations (4.2.15) and (4.2.16) with the following boundary condition:

- d v = 0 for x = x , and x = x I dx

We find that

(4.2.18)

~

I We note that x, is negative.

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56 Crystalline Silicon Solar Cells

9% 1 & E o 2

cp(x)= - -(x, - x)’ + D n region of the depletion layer

(4.2.19) 4% 1 EEo 2

cp(x)= -- -(xr - x)’ + C p region of the depletion layer

The point of origin for voltage is selected, so that cpx.o = 0. This allows us to determine the constants C and D. We find that potential in the space charge region is

- 9 ND+ cpx+ - + - [x: - (x, + x)’] n region

E = o

The distribution of the field strength and voltage are represented in Figure 4.3.

t

Figure 4.3 Field and potential distribution in a p-n junction

Outside the space charge region the potential is as follows:

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The p-n Junction 57

qNA- 2 vx- = - - xI p region CEO

(4.2.21)

- qND+ 2 vx+ - + - x, n region Eo

4.2.3 Space Charge Region Width and Capacitance

To determine the width of the space charge region we introduce a potential difference between x, and x, and find that

U,, = - 4 (N,,x: -NAx,') 2EEo

we first substitute x, in accordance with formula (4.2.17) with

and considering the sign we find that

(4.2.2 2)

(4.2.23)

(4.2.24)

For later consideration of the dependency of the p-n junction on an externally applied voltage UA we replace U, with U, minus UA and thus find that for x,

we also calculate

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58 Crystalline Silicon Solar Cells

and it holds for the space charge region width W = xr + x, that

The peak electric field is found to be

(4 .2 .26 )

(4 .2 .2 7 )

- 1 UD- UA (4 .2 .28)

Empx W

The peak field strength is proportional to the voltage which is applied and inversely proportional to the width of the space charge region.

The p-n junction can, as described above, be viewed as a plate capacitor. Two different fixed space charges exist, which must be of equal magnitude on both sides. Thus the charge is

If we put in these values for x, and x, as in equations (4 .2 .25) and (4 .2 .26 ) we find that

Q

and thus for the capacitance C = dQ/dU

(4.2.3 0 )

(4.2.3 1)

Solving equation for UD- UA we find that

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The p n Junction 59

(4.2.3 2)

Because in practice the doping of a p-n junction is markedly unsymmetrical in both semiconductor devices and solar cells, it is clear that by measuring the space charge capacitance in relation to U, - the external voltage - the dopant concentration (i.e. the specific resistance) of the weakly doped side can be determined.

Figure 4.4 Dopant profile and concentration distribution in a symmetrical p-n junction in the conducting state

4.3 THE BIASED p-n JUNCTION

If we now connect an electric voltage UA with the positive terminal to the p-doped side and the negative terminal to the n-doped side, we thus reduce

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60 Crystalline Silicon Solar Cells

the diffusion current from that in the uncharged state. This is connected with an increase in the concentration of free charge carriers. The product np is now greater than nf. This means that the recombination rate R = r p increases accordingly in the space charge region. A new stationary state thus occurs in which excess recombinations are immediately compensated by flows into the junction region. This means that compensating amounts of carriers are driven into the space charge region from the high carrier densities in the n and p regions. The zone becomes narrower and its resistance is reduced. The current that now flows is known as the forward bias current.

It is plausible that with a reversal of polarity the free carriers will be drawn away from the space charge region. If the voltage is increased, then the region will become wider and thus have a higher resistance. This polarity is known as the reverse bias direction. The diode blocks the current. In theory this reverse leakage current takes on a constant value even at low reverse voltages. This is known as the saturation current of the diode. The reverse direction is not relevant to solar cells, therefore we do not explain this further. The saturation current, on the other hand, plays a very important role in the physics of solar cells, and we now examine this.

4.3.1 The p-n Junction with Low Recombination and Weak Injection

Shockley [2] showed that given low recombination rates, the p-n junction has specific characteristics. Low recombination rates mean a high carrier lifetime, which is connected with a diffusion length that is large compared with the width of the space charge region.

Because the respective minority charge carriers in the space charge zone hardly ever recombine, they are driven far into the opposite region. They are injected into this region and only recombine here. For the following discussion, we also assume that this injected charge carrier concentration is small compared with the concentration of majority charge carriers.

If we disregard the (very low) level of recombination in the space charge region completely, then at point x, for example, the injected flow of electrons must be compensated by the high number of available holes. We can imagine that the high number of holes are driven there by a very weak electric field, whereas the electrons conduct the current by diffusion due to the concentration gradient. The field current of the electrons, on the other hand, is negligible due to the very weak field, i.e. forward current has only diffusion characteristics.

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The p-n Junction 61

4.3.2 Forward Current Characteristic and Saturation Cu rren t

To determine the current we first find the increase in concentration of charge carriers at the space charge limits x, and x,. Under the above assumptions of low recombination and low injection, the concentration gradient within the space charge region hardly changes. However, the concentration of charge carriers within the space charge region in our case (Figure 4.1) must fall by 12 orders of magnitude so that the weak additional concentration hardly alters the total gradient. This means that the potential distribution behaves in the same way as in an ‘unbiased p-n junction’. The concentration distribution and potential are connected by an exponential function here. Therefore this is still true in the case of a biased p-n junction, but now the potential difference is reduced by UA. This means that the concentrations of minority carriers at the points x, and x, increase by the factor exp(U,lU,). Therefore

(4.3.1)

(4.3.2)

where npo and pno are the respective concentrations in the unbiased case

For the sake of clarity, we wish to establish the relationship by another means. We have assumed that the very high opposing field and diffusion currents within the space charge region remain almost unchanged by the application of voltage. If we equate these currents to holes we find that

[U, = 01.

or

k T Dp = Pp 7

(4.40)

(4.41)

and the designation - dcp I dx = E

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62 Crystalline Silicon Solar Cells

(4.3.5)

If we now integrate from x, to x, and consider that the voltage at the boundaries is 0 and (U,, minus UA), we find where UT = kT/q

Pn, =Pp exp - <qJq (4.3.7)

we find the concentration of holes in the biased state at point x, is again

P~(~ , , ) = P, , ~ X P ( UA 1 UT 1 (4.3.8)

So whst is the diffusion current density of the injected charge carriers? For holes it is true that

f = - q D - dP pdx

and

9 dx. as there is no generation here. For R

A P

‘‘P

R = -

(4.3.9)

(4.3.10)

(4.3.11)

where AF = (Pn(x,r) - P n o 1. If we combine this with the previous three formulae, we find that

D p d y Z - - d2pn - AP (4.3.12) TP

As it is also true that

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The p-n Junction 63

- d 'PnO = o (4.3.13) dx2

(there is by definition no longer a gradient for pno at point xr), taking into account

LP = rl*PTP

we can write the differential equation as

(4.3.14)

(4.52)

The general solution for this differential equation is

A p = A exp(xlLp) + B exp( - x l L p ) 4.53)

Since we take as a basis an infinitely elongated area n and p, it holds that Ap(.o) = 0. This yields A = 0.

The constant B can be determined by the boundary conditions

Pn(x,,) = PnO exp ('A' 'T)

After some manipulation we find that

(4.3.17)

P,@> =pn0 +pno (exp(U,/U,) - 1 ) exp(-X/Lp) (4.3.18)

For the diffusion flow density of holes

Ip =-qo - dP p d x

we need the first differentiation. If we substitute this, we find that

(4.3.19)

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64 Crystalline Silicon Solar Cells

Similarly, for the electron current density we find that

(4.3.21) qDn ' n o

Ln In = - (exp(UA/UT) - 1 ) exp(-x/Ln)

We have determined this current density at the limits of the space charge region. To find the total current density we must determine the current at the point x = 0. We assume for this purpose that within the space charge region the injected currents are constant at the first approximation, and there is no change in the current. We can then equate the current densities at the edges of the space charge region to the current density at the point x = 0 and thus find the total current density as the sum of the two.

'total = 'p + I n (4.3.22)

and thus

This equation is known as the diode equation, and the first expression in parentheses is the saturation current density I,. If we now introduce for P n o and npo

p,, =ni' lND resp. npo = n i 2 INA (4.3.24)

we find that for I,

(4.3.25)

The current density at a p-n junction - in a diode - is thus found to be

I = I , (expUA/UT - 1 ) (4.3.26)

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The p-n Junction

References

[ l ]

[2]

Schottky W., Zeitschriyt fur Physik 118, 1942, p. 23

Shockley W., Bell Syst. Techn. 28, 1949, p. 435

65

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5 The Physics of Solar Cells

5.1 THE ILLUMINATED INFINITE p-n JUNCTION

For a simple theoretical treatment, we once again consider a crystal with a p-n junction, in which the two doped regions are infinitely extended. (In practice a crystal thickness which is very large compared to the diffusion length of the charge carrier is sufficient).

We once again start from Figure 4.1. We now illuminate the entire crystal equally, in such a way that there is a homogeneous generation of charge carrier pairs in the crystal. This can be achieved in practice if the silicon crystal is exposed to infrared light near to the band edge. Then the absorption coefficient of the light is very small, or in other words the absorption is weak and thus almost equal throughout the crystal.

Using the continuity equation under these assumptions, we find a similar differential equation to (4.3.12). However, in this case we must also take generation into account.

For holes as the minority carriers on the n-side, it holds that

and also

(5.1.1)

(5.1.2)

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68 Crystalline Silicon Solar Cells

Since generation is assumed to be constant and L, is also a constant, a similar solution applies here as for (4.3.12), i.e.

A p = G T ~ + A exp(x/Lp) + B exp(-xILp) (5.1.3)

With the boundary conditions of an infinite p-n junction we find that for the hole current density

Zp = -(exp(U/U,)- Dp P n o 1) exp( - x/Lp) -qGLpexp( -xILp) (5.1.4) LP

and similarly for the electron current density in the p region

I , = -(exp(U/U,) q’n npo - l)exp( - x/L,) -qGLnexp( -xILn) (5.1.5) L n

If we again disregard recombination in the space charge region and add the two above current densities (at the point where x = 0) to the current density from the space charge region, where

IR = q G W (5.1.6)

then the current density in the solar cell is

I =Z,(exp[U/U,] - 1 ) -qG(Ln +Lp + W) (5.1.7)

If we designate q x G x (Ln+Lp+W) with ZL (the current density generated by the light), we find that

I =Zo(exp[U/U,] -I) -IL (5.1.8)

We note that only those charge carriers generated either in the space charge region or at a distance of one diffusion length from the p-n junction contribute to current. Only this region of a solar cell is ‘active’.

The corresponding charge carrier distribution is shown in Figure 5.1 and the current-voltage characteristic is shown in Figure 5.2.

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The Physics ofsolar Cells 69

A

* I xr X

Figure 5.1 Charge carrier distribution in an illuminated infinite solar cell

5.1.1 The Current-Voltage Characteristic of an Infinite Solar Cell

We see that the I-V characteristic of an illuminated solar cell lies in the fourth quadrant (electro-technical standardisation).

For the purpose of comparison with this I-V characteristic, the current-voltage characteristic of an unilluminated solar cell is also drawn in Figure 5.2. The voltages are the same in both cases, whereas the current in the illuminated solar cell is negative, i.e. the solar current flows against the conventional direction of a forward biased diode.

We now describe the most important parameters of a solar cell.

5. I. 1. I Short Circuit Current

As its name suggests, this current is obtained if the solar cell is short circuited, i.e. there is no voltage at the cell. This current is designated Z,, (from short circuit current).

From equation (5.1.8) we find that ZBc=-ZL, i.e. the short circuit current is equal to the absolute light-current amount. We note here that the

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70 Crystalline Silicon Solar Cells

Figure 5.2 Voltage-current characteristic of an infinite solar cell

magnitude of the current, disregarding all losses in the cell, with AM1.5 radiation, can reach a peak of 44 mA/cmZ.

5. I . I .2 Open Circuit Voltage

The open circuit voltage V, is obtained when no current is drawn from the solar cell. From (5.1.8) this is found to be

V,, = U, In (1, /Io + 1 ) (5.1.9)

Since even at very low current densities we can disregard the value 1 compared with ZL/Io and IL= I,, , we find that for V,,

Voc = UT In (L 110) (5.1.10)

i.e. the open circuit voltage is proportional to the logarithm of the ratio of short circuit current to dark current. Since in good solar cells the short circuit current very quickly nears a saturation value, the increase in the

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The Physics of Solar Cells 71

open circuit voltage and thus efficiency is basically a question of reducing the saturation current. From equation (4.3.25), following (5.2.13) we find that for small dark current values the following three conditions must be fulfilled:

diffusion length of minority charge carriers as high as possible, doping concentration NA, No high, and crystal volume as low as possible (thin wafer).

The first two parameters are linked to each other to some degree. Considerations about optimal parameter combinations are dealt with in Chapter 6.

5.1.1.3 Fill Factor

As always in electrical engineering, optimal power output requires a suitable load resistor I?,, which corresponds to the ratio V,/I, (Figure 5 .2 ) . V, and I, are, by definition, the voltage and current at the optimal operating point and P, is the maximum achievable power output. We now form the ratio of peak output (V, I,) to the variable (Voc Isc) and call this ratio the fill factor FF of a solar cell:

FF = V , I , I VocIsc (5.1.1 1)

The fill factor is so named because when graphically represented it indicates how much area underneath the I-V characteristic is filled by the rectangle V , I, in relation to the rectangle Voc Isc. The fill factor normally lies in the range 0.75 to 0.85.

5.1.1.4 Efficiency

The efficiency of a solar cell is defined as the ratio of the photovoltaically generated electric output of the cell to the luminous power falling on it:

(5.1.12)

The current record for efficiency is held by a solar cell made of monocrystalline silicon using very complex technology at approximately 23-24% (area 2x2 cm', radiation AM1 3. Commercially produced cells currently have an efficiency of between 14% and 16%. In individual special cases large area cells (and modules) have been produced with 17%

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72 Crystalline Silicon Solar Cells

-19%. The significance of high efficiency for reducing the cost of a complete solar array will be described in Chapter 6.

In general, the efficiency of photovoltaic energy conversion is very limited for physical reasons. Around 24% of solar radiation has such a long wavelength that it is not absorbed. A further 33% is lost as heat, as the excess photon energy (in the short wavelength region) is converted into heat. Further losses of approximately 15-20% occur because the cell voltage only reaches around 70% of the value which corresponds to the energy gap.

5.2 REAL SOLAR CELLS

The following investigations are based upon the structure of a modem solar cell. The cross-section of such a cell is shown in Figure 5.3.

The base, the starting material for a solar cell, is almost always p-doped.

Emitter SC region Base -,a L.1 r 7 - 7

x=o x : x;+w

I4 H' J J b

* N

Figure 5.3 Cross-section of a real silicon solar cell

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The Physics of Solar Cells 73

The n-doped region is called the emitter, a designation which has been adopted from transistor physics. It is more highly doped than the base by some orders of magnitude. The p-n junction is therefore unsymmetrically doped. The space charge region, with width W therefore extends mainly into the p region. The point xj marks the penetration depth of the p-n junction. In practice it amounts to only a few tenth pm, so that for a crystal thickness H of approximately 200 pm, the thickness of the base H’ is roughly equal to H.

5.2.1 Photocurrents in a Real Solar Cell

To calculate photocurrents we assume that the light enters on the emitter side. The calculation is first made for monochromatic light. In the case of the illumination by a spectrum we must integrate over all wavelength regions of this spectrum. The integration limits for this are kin, the smallest occurring wavelength, and A,,, the wavelength corresponding to the energy of the semiconductor band gap, as longer wavelengths are not absorbed. For sunlight h,, is around 0.3 pm, as at shorter wavelengths there is almost no radiation, and in the case of silicon h,, z 1.11 pm.

We now need to calculate the current densities in the three regions, emitter [El, space charge region [SCR], and base [B], so that

and the total current density is

(5.2.1)

(5.2.2)

5.2. I . I Photocurrent from the Base

Because in general the base is homogeneously doped, and a low level of injection is present with normal solar radiation, a precise solution can be found for the photocurrent in the base (in the short circuit case). The applicable differential equation for the electrons is thus

+ R d 2(An) Dn-T- = - G

(5.2.3)

After some manipulation this yields

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74 Crystalline Silicon Solar Cells

dZ(An) An - G - = - - d x z ~ , 2 Dn

(5.2.4)

In the case of monochromatic radiation this generation of charge carrier pairs at distance x is

G(x) = a F ( l - R r ) e x p ( - a x ) ( 5 . 2 . 5 )

where a is known to be the absorption coefficient of light in the semiconductor, R, is the reflection coefficient and F is the photon flux (the radiation power) supplied to the surface of the solar cell. These three variables are all dependent upon wavelength. We thus find for equation (5.2.3)

An Dn 7 d ’(An) + a F ( l - R , ) e x p ( - a x ) - - = O (5.2.6) ‘n

The general solution for this is

An(x) =Acosh(x/L,) + Bsinh(x/L,)

where

a F ( l -R,)rn (5.2.7)

a’L,2 - 1

(5.2.8)

following two boundary To determine the constants we apply the conditions, i.e. we take into account that recombination takes place at the surface. The surface recombination velocity, measured in cm/s, is designated S,.

SnAn = -Dn- d(An) at x=H dx (5.2.9)

An = O at x qj +W

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The Physics of Solar Cells

After some manipulation we find that

+ aLn exp(- a H ‘ )

/ \ / \ a L n -

75

X

X

- + a L p - e x p ( - a x j ) sPLP

D P

L s i n h - +cosh - Dn Ln [ y , ] (5.2.10)

The bracketed expression is called the geometry factor (see also [l]).

5.2.1.2 Photocurrent from the Emitter

If the emitter is homogeneously doped, then the solution for the photoelectric current from the emitter is found to be the same as for the base:

However, homogeneous doping hardly ever occurs in practice. For a diffused emitter, high dopant effects such as band gap narrowing and the

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76 Crystalline Silicon Solar Cells

dead layer’ must be taken into account. The dopant profile also has the consequence that lifetime and the

diffusion constant depend upon doping. This is described in further detail in Chapter 6.

5.2.1.3 Photocurrent from the Space Charge Region

This photocurrent is very easily determined, since the charge carriers generated in this region are drawn out of this area very quickly due to the electric field. They virtually cannot recombine and therefore contribute entirely to the current. This is found to be

I,,,(k) = q F ( l - R f ) exp( -ax , ) (1 - exp( -aW)) (5.2.12)

5.2.2 Saturation Currents in a Real Solar Cell

To calculate the saturation current density of a real cell we must once again take into account the recombination effect at the surface.

5.2.2.1 Saturation Current from the Base

From a similar calculation to that for the photocurrent we find the following relationship:

(5.2.13)

where G, is a geometry factor which reads

cosh(H’lL,) + (SJS,) sinh(H’lL,) (5.2.14)

(S , /S , ) cosh(H’lL,) + sinh(H’/L,) G, =

where S, = D,/Ln, the recombination velocity in the crystal.

’ A dead layer is a highly doped region near the surface with such a short lifetime that photons absorbed in it cannot contribute to the photoelectric current.

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The Physics of Solar Cells 77

The geometry factor is determined by the two variables S,/S,, and H’IL, i.e. by the ratio of inner to outer recombination and the ratio of base thickness H’ to diffusion length L .

Figure 5.4 [ 2 ] shows this relationship. If the diffusion length is around half the cell thickness, then the surface recombination no longer has any effect on the dark current. The geometry factor is 1.

10’2 10-1 100 H l L n

Geometry factor as a function of the base thicknessldiffusion length relationship

Figure 5.4

If, however, the diffusion length is greater than cell thickness, then we can differentiate between three cases:

where S,, > S, then G, > 1. In this case the dark current increases, thus decreasing the efficiency of the solar cell. where S,, = S, then G, = 1. The cell behaves like an ‘infinite’ cell. where S, < S, then G, < 1. The dark current decreases with the decreasing value of S,,. The dark current decreases, circuit voltage increases and the efficiency of the solar cell is improved. This behaviour opens the potential for increasing open circuit voltage and

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78 Crystalline Silicon Solar Cells

thus efficiency in thin solar cells made of silicon [3],[4].

5.2.2.2

The saturation current from the emitter is much more complex to determine than that from the base. Since in reality the emitter always has a doping profile, it follows that:

internal fields are present, the diffusion length and the mobility of charge carriers are not constants due to their dependence upon dopant concentration, band gap narrowing takes place due to the high level of doping.

Saturation Current from the Emitter

10.5

9 .o

7.5

6 .O

4 . 5

3.0

1.5

1.0 L 1018 1019 1020

NS Icm -31 Figure 5.5 Saturation current of an emitter as a function of surface

concentration, with S, being parameter

A solution to this problem is given in the literature [ 5 ] using multiple

We can demonstrate the influence of surface concentration and the integration.

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The Physics of Solar Cells 79

surface recombination rate on the saturation current of the emitter by looking at Figure 5 . 5 . The n’-doped emitter has a Gaussian type dopant profile, its penetration depth is 1 pm.

We find from this, that for low saturation current - and thus high open circuit voltages - two requirements must be fulfilled:

a surface recombination velocity less than lo3 cm/s, and a surface concentration less than 2 ~ 1 0 ’ ~ cm”.

At high recombination rates (1 0’-l O6 cm/s) the surface concentration should be approximately lozo ~ m - ~ . Detailed investigations are made in Chapter 6.

5.2.3 Ohmic Resistance in Real Solar Cells

Ohmic resistances also influence the efficiency of solar cells. We divide these resistances into shunt resistance and series resistance.

5.2.3.1 Shunt Resistance (RJ

The magnitude of this resistance is determined by leaking currents along the edges of the solar cell. Point defects in the p-n junction can also lead to low parallel resistance. Such defects can be interruptions of the p-n junction, which originate during the diffusion of the n emitter, impurity particles have hindered diffusion at certain points. The base material can also be in electrical contact with the finger system at some points, thus creating a short circuit (if only a small one).

5.2.3.2 Series Resistance (R&

This resistance has the following components:

a contact resistance metal-semiconductor, ohmic resistance in the metal contacts, ohmic resistance in the semiconductor material.

Further considerations follow in Chapter 6.

5.2.4 The Two Diode Model

The simple exponential relationship between voltage and current density as given by (4.3.26) is almost never observed at low voltages in the forward direction [0.1-0.5 V] in real solar cell p-n junctions. For conventional

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80 Crystalline Silicon Solar Cells

diodes this is of very little significance, but for solar cells the functional dependency in this voltage range is very important. As we will discover later, the fill factor and thus efficiency are considerably influenced by this. Therefore, we want to investigate this in detail. For this purpose, we need to investigate recombination in the space charge region more closely.

The SRH recombination formula (3.4.5) after some manipulation, reads

(5.2.15)

We make the simplifying assumption that the following apply: The impurity level lies exactly at the intrinsic Fermi level, i.e. roughly in the mid-band region and it is distributed completely uniformly in the space charge region. At both sides of the p-n junction dopant level, lifetime and mobility are of equal magnitude.

Then n , and p , are equal to n, [equations (3.4.6) and (3.4.7)]. If we first consider the case where we apply a reverse voltage, then it becomes clear that both types of charge carrier are very quickly ‘washed out’ due to the high electric field in the space charge region, so that their densities become small compared with n,. The equation (5.2.15) is then reduced to a generation rate of

- R = n i / 2 r , (5.2.16)

where we also define T~, = T~,= T,. However, if a voltage is applied in the forward direction, then the

recombination is slightly different. In the middle of the space charge region the concentration of n and p must be equal. Since

np = niz exp(U,/U,) (5.2.17)

we find that

n = p = n , exp(UA/2UT) (5.2.18)

The recombination rate at the limits of the space charge region is therefore

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The Physics of Solar Cells 81

(5.2.19) n.

R = I expUA/2U, 2=0

and the recombination rate decreases - without giving further explanation - (more detail in [ 6 ] ) exponentially on either side of the space charge barrier, with a characteristic length of

k T

9Ema.x (5.2.20)

where Em, is the electric field at the p-n junction. We then find that for the recombination current

2kTqni I* = exp [.. / y] 4 =,Emax

(5.2.21)

Precise calculations show that a multiplication by xl2 is required, giving

(5.2.22)

The factor before the exp function is designated IOz and now the diode equation can be expanded to

I = I,, exp U,lU, + Io2 exp UA/2 U, (5.2.23)

5.2.4.1 Equivalent Circuit of a R e d Solar Cell

If we also take into account the resistances in the following equation for the current-voltage characteristic line, then we find that

' - I R ~ (5.2.24) V -IRS V -IRs I( V ) i , , exp - -1 +Io2 exp - -1 +- [ n l v T 1 [ n2VT ] R p

The corresponding equivalent circuit diagram is shown in Figure 5.6 .

considerable deviations have been determined. Theoretically, we should find that n ,= l and n2=2. In practice, however,

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82 Crystalline Silicon Solar Cells

Figure 5.6 Equivalent circuit diagram for the two diode model of a real solar cell

After some manipulation [6],[7], we can expand formula (5.2.22) to the very complex equation

where y.', is the built-in voltage, 0, and mP is the potential of the quasi Fermi level, W is the space charge region width.

As well as precise knowledge of the dependency of the space charge region W on the applied voltage and the applicable corrected built-in voltage [7], it is mainly the factor f(b) that is decisive for the current distribution in this starting region. The most decisive factors inf(b) are the

and T,,,, but above all their ratio to one another. Choo [S] expande 2 on the theory of Sah et a1 [9]. He found that the dependency of the valueffi) at room temperature is dependent upon the applied voltage as shown in Figure 5.7, where E,-E,, is a measure for the energetic distance of the recombination centre from the intrinsic energy level Ei and the ratio TpO/rnO is a parameter.

The bend of the curve is larger, the greater is the difference between T,, and T,,. Consequently, the increase in initial current is no longer

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The Physics of Solar Cells 83

I I I 1 I 0.0 0.1 O L 03 OW4 0 5 0'6

Figure 5.7 f(b) as a function of voltage, parameter T,,,, / T , ~ [7]

proportional to exp(V/2VT), but increases less sharply, which itself has the consequence that the diode characteristic has a negative curvature in the starting region. The typical shape of a characteristic is shown in Figure 5 . 8 .

This can have consequences for efficiency, mainly if the charge carrier generation rate is low [sun < AM1.51, [10],[11]. Particularly solar cells with a p-n junction lying very close to the surface may have severe space charge defects, i.e. significantly differing values for T~~ and T~~ may occur. Such cells are therefore bound to have a curved characteristic. Other new investigations show that different conditions of surface recombination lead to similar characteristics [ 12 1.

5.2.4.2 The Influence of Ohmic Resistances

The influence of ohmic resistances on solar cell parameters are shown in Figure 5.9 and Figure 5.10.

Figure 5.9 shows the influence of shunt or parallel resistance. With decreasing resistance the fill factor FF decreases in the first approximation and only at very small values (below 100 ncm2 ) does the open circuit voltage also decrease. Short circuit current is not influenced by parallel

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84 Crystalline Silicon Solar Cells

Figure

-

5.8

o o o o m o

o o o o 0

0 0

8

0 0

10-9 1 O I I I I I I I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

lJ PI The dark current characteristic of a Si solar cell

.a

resistance. As the shunt resistance in monocrystalline cells is greater than 1000 SZcm', we barely need to consider its influence. In polycrystalline cells, on the other hand, due to internal shunt resistance at the grain boundaries we should expect the parallel resistance to have an effect.

Figure 5.10 shows the influence of series resistance. Here too it is primarily the fill factor that is influenced by increasing resistance. Only at high (normally not possible) values does the short circuit current fall off. To obtain the highest efficiency possible it is imperative that series resistance is kept as low as possible (I 0.5 Clcm*).

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The Physics of Solar Cells 85

- u [Volt] 0.1 0.2 0.4 0.5 0.6 0.7

- -20 -

Figure 5.9 The influence of shunt resistance on solar cell parameters

- u [Volt] 0.0 0,3 0,s 0,6 0,7

-5 - n -10 - N E U -15 - h E -20 - -

-35 - -40 L

Figure 5.10 The influence of series resistance on solar cell parameters

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86

References

Crystalline Silicon Solar Cells

Sze S. M. Physics of Semiconductor Devices, 2nd Edn, 1981, p. 802

Aberle A,, Thesis, Univ. Freiburg, 1991

Knobloch J., Von B. and Goetzberger A., Proc. of th 6th PVSEC, London, 1985, p. 285

Goetzberger A,, Knobloch J. and Von B., Proc. of the 1st PVSEC, Kobe, Japan, 1984, p. 517

Park S. S, Neugroschel A. and Lindholm F. A,, IEEE-TED 33, 1986, p 240

Sah Ch. T., Noyce R. N. and Shockley W., Proc. of the IRE 45, 1957, 1228

Chawla B. R. and Gummel H. K., ZEEE - TED 18, 1971, p. 178

Choo S. C., Solid State Electron. 11, 1968, p. 1069

Sah Ch.T., Noyce R. N. and Shockley W., Proc. of the IRE 45, 1957, p. 1228

Baier J., Thesis, Univ. Freiburg, 1992

Beier J. and Von B., Proc. of the 23th IEEE-PVSC, Louisville, Kentucky, 1993, p. 321

Robinson S. J., Wenham S. R. et al., J. Appl. Phys. 78, 1995, p. 4746

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High Efficiency Solar Cells

6.1 THE SIGNIFICANCE OF HIGH EFFICIENCY

At this point we wish to briefly explain the degree to which the total costs of a photovoltaic array can be reduced by high efficiency solar cells.

Figure 6.1 The cost breakdown of a solar array

The manufacturing costs of a solar array - power related costs such as inverters and accumulators are not considered here - made up of crystalline solar cells can be divided into four main categories. These are costs for

silicon wafers, process technology, module manufacturing, and

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88 Crystalline Silicon Solar Cells

I

Module efficiency 1

-

-

1

land, land preparation, electrical connections, etc.

The percentage cost breakdown shown in Figure 6.1 applies approximately for large solar arrays.

All costs in the first approximation are proportional to area, and thus for a solar array roughly inversely proportional to efficiency. Many writers have dealt with this subject in detail [1]-[5]. High efficiency solar cells require high grade silicon and costly technology. Cost estimates show, however, that despite the increased cell cost, an increase in efficiency of approximately 40% (relative) will reduce the cost of a large area solar array by approximately 20% [6]-[8].

Looking at the matter from another point of view, we can calculate the permissible module costs at different efficiencies for the desired cost of electricity (planning target). This relationship is shown in Figure 6.2 [9].

150

- N

E 100 -tit L

8 8 Q)

3 50 I

0

Figure 6.2 Permissible module costs as a function of given electricity costs, calculated for different efficiencies [ 91

According to this, given a desired cost of 6 centskWh, an increase of efficiency from 10% to 15% makes a module three times as expensive permissible.

Since the 1980s, therefore, the majority of all research and development work in the photovoltaic sector has concentrated on driving the efficiency level as high as possible.

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High Eflciency Solar Cells 89

The basis for achieving high efficiency is the reduction of the total amount of loss. We investigate this area intensively in this chapter. The following considerations and calculations are based exclusively on solar cells made of crystalline silicon. Many results will however - at least partially - be applicable to other solar cell configurations. Figure 6.3 gives an overview and classification of the different mechanisms for loss. These can be divided principally into two areas.

I electrical

ohmic recombination 1

Emitter - Contact material

Finger Collection bus Junction

Figure 6.3 Loss mechanisms in a solar cell

I

- Emitter region SC material Surface

- Base region SC material Surface - Space charge region

Optical losses reduce the level of solar radiation by reflection and shadowing of the light as well as inadequate absorption of long wavelength radiation, whereas electrical losses have a detrimental effect on both the current and, above all, the voltage of a solar cell.

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90 Crystalline Silicon Solar Cells

The final type of loss is based on semiconductor physics and technology. Minimising this is therefore at the centre of work into achieving high efficiency solar cells.

We begin by investigating electrical losses, and specifically the influences related to semiconductor physics, i.e. losses by recombination, and we investigate ohmic losses in the second section. We conclude by considering optical losses and procedures for their reduction.

6.2 ELECTRICAL LOSSES

6.2.1 Recombination Losses

For this analysis we use the formulae for photocurrents and saturation currents in real solar cells, and investigate the influences of

diffusion length of the charge carrier, dopant concentration and dopant profile, and surface recombination velocity.

These sensitivity analyses are based on the most common solar cell structure - emitter n+- and p-doped [10’6cm”] base. The penetration depth of the emitter varies within the range 0.2-1 pm. The emitter surface concentration varies within the range 5x10” to 1x1OZo ~ m ’ ~ . We have selected a crystal thickness of 200 pm, if not otherwise specified.

6.2.1.1 Recombination Losses in the Base

The photocurrent and saturation current from the base area are described by the formulae (5.2.10) and (5.2.13).

In order to better demonstrate the function of the base area we assume that

the emitter has no influence (ideal emitter), and there are no shadowing and reflection or unabsorbed radiation.

Figure 6.4 shows short circuit current I C as a function of diffusion length L , in the base with Surface Recombination Velocity [SRV] S, on the back surface of the solar cell being a parameter.

This representation yields the following results: If the diffusion length L , of the charge carrier is more than twice the crystal thickness, then the short circuit current will reach a saturation value.

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High Efficiency Solar Cells

LL

42

LO - “E 38

-8 34

u \

4 I E 36

32

91

1 I I I I I I

1,lO

- 100 - 1000 - - 104

105,106 -

- - S n = c m l s

- - - -

For very high photocurrents the surface recombination rate S, must be less than 100 cm/s. If the diffusion length L , falls below the value of the crystal thickness, then the photocurrent will drop sharply. If, however, the diffusion length L , is less than half the crystal thickness, then the short circuit current I,,, although reduced, will be almost independent of the surface recombination velocity S, . Figure 6.5 shows the dependency of open circuit voltage V,, on

diffusion length L,, again with S, being a parameter. This representation yields the following information:

For high values of S,, (10’-106 cm/s) diffusion lengths higher than the crystal thickness are of no advantage, V,, achieves a saturation value. For high open circuit voltages, S, must be <lo2 cm/s.’ Unlike a short circuit current, open circuit voltage does not approach saturation as S, becomes smaller, but rises continuously.

’ We note that even at small values S, is still strongly dependent upon carrier concentration, i.e. on the level of sunlight [lo].

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92 Crystalline Silicon Solar Cells

c

> E u

>O

74 0

720

700

680

660

640

620

600

580 0 200 Loo 600 800 loo0 1200 1400 1600

Ln [ p m l Figure 6.5 V, of a base dominated n'p solar cell as a function of diffusion

length in the base with recombination velocity at the reverse side being the parameter

The result of this calculation is that for very high efficiencies the diffusion length in the base represents a cardinal parameter. At diffusion lengths greater than the crystal thickness, the reduction of surface recombination on the back surface is decisive for the achievement of high levels of efficiency.

6.2.1.1.1 The Back Surface Field The reduction of reverse side recombination is, however, hindered by various constraints.

Since the back of a normal solar cell is completely metal coated, it goes without saying that there is a high surface recombination velocity (Ohmic metal-semiconductor contacts require high recombination velocities).

One familiar technical measure to improve this situation is the creation of a highly doped p'-zone on the back surface of the solar cell base. This p+-p junction (high-low-junction) is also known as a 'back surface field' (BSF). Owing to the electric field which is created, less of the minority

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High Efficiency Solar Cells 93

660

charge camers created in the base can recombine on the back surface. The BSF functions like an electrical mirror, 'throwing back' the charge carriers into the inside of the cell. Its behaviour depends upon several parameters:

the surface concentration of p+ doping as well as its concentration profile and penetration depth, recombination in the p'-layer itself, and charge carrier density at the junction, i.e. the relationship between diffusion length and crystal thickness.

There is a whole range of methods for calculating this behaviour precisely. We now give the results from [lo], which were calculated with the help of the PC-ID programme Ell].

- Gauss profile S, = 1 xlO6 cmls

d

I I I I I I 1 I I

720 I I I I I I I I I I I

c > E - 8 >

71 0

700

690

680

6 70

Figure 6.6 shows the influence of the BSF layer penetration depth and surface concentration on V,, where S,, is lo6 cm/s (full metal coating). A more technologically practicable value for penetration depth of approximately 1 pm still does not yield a sufficient reduction in the effective recombination rate to achieve very high efficiency.

An improvement on this structure was suggested by van Overstraaten and Nijs in 1969 [12]. Like a graded base transistor, this was based on a graduated p-doping throughout the entire base, increasing from the p-n

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94 Crystalline Silicon Solar Cells

junction to the back surface. Their calculations showed that in comparison with a homogeneously doped base, it was possible to reduce the saturation current by a factor of 20. Technological realisation is however extremely costly, and to our knowledge has never occurred.

Recently, other ways have been found to reduce S,. The solution is to coat a significant section of the back surface with a thermally generated SiO, film, thus electrically passivating it. For the bonding of the cell, this layer contains a number of holes of fixed distance and diameter, whose total area is only approximately 1%-4% of the total area.

Metal Si02 2 1 1 ' n+ emitter

Base

Si 02

Metal

Figure 6.7 Schematic structure of a high efficiency solar cell with a local B SF

Figure 6.7 shows schematically the cross-section of this type of cell. For a good ohmic contact we also require high doping p+ under the contact point, which also functions as a local BSF. We now have an effective surface recombination rate which is composed of the recombination of charge carriers at the Si-SiO, barrier and the - small percentage - contribution of the metal area.

SiO, layers are of course also used for the passivation of the emitter. Therefore, we now therefore examine some of their main characteristics.

6.2.1.1.2 SiO, Layer The SiO, layer has played a decisive role in almost all silicon semiconductor devices right from the start. Its relatively simple manufacturing process by high temperature treatment under oxygen, but predominantly the masking behaviour of the SiO, toward dopants and its passivating effect, contributed decisively to making silicon the basic material for most semiconductor devices. There are countless investigations, mostly for use in IC or MOS structures. A comprehensive overview is

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High Efficiency Solar Cells 95

provided by Nicollian and Brews [13]. Fundamental work on this theme has also been carried out by Goetzberger [14],[15].

The effect of the SiO, layer can be described as follows. The abrupt ending of the crystal at the surface leads to a density of defects of approximately 10’’ cm-’, which are traps in the forbidden band, thus giving rise to a high recombination rate. These traps are largely saturated by the SiO, layer and thus become ineffective. By additional annealing, e.g. in forming gas, the trap density can be reduced to values between 10’’ and 10” ern-', thus achieving surface recombination rates of 10-100 cm/s.

There are currently, for solar cell production, no better alternatives to this passivating method. For further information, see Sze [16].

6.2.1.2 Photocurrent and Saturation Current from the Emitter

We can make the following statements about the photocurrent in the emitter of a high efficiency solar cell, As the emitter is very thin, with a penetration depth of a few tenths pm, and as the surface concentration of the dopant concentration in high effrciency cells is only some 10’’ cm”, the diffusion length of the minority carriers (holes) created here is several times greater than the thickness of the emitter. They do not recombine in the emitter, either recombining at the surface or travelling to the p-n junction as photocurrent. This combined effect is enhanced at the p-n junction by the electric field, which is caused by the doping concentration gradient. This type of emitter is called transparenf. When considering the photocurrent we can therefore restrict ourselves to the influence of the surface recombination rate Sp at the emitter surface.’

For an emitter with a surface concentration of 1 x 10’’ cm-3 - required for low saturation current, as shown in Figure 5 . 5 - and a penetration depth of x=OS pm, Figure 6.8 shows the influence of Sp on photocurrent. To ihustrate this effect we have selected the term ‘Spectral Response’ (see Chapter 9). The photocurrent is determined for radiation with light of different wavelengths. Since the short wavelength light is predominantly absorbed in the emitter, the current that is created in this region can show very clearly the influence of Sp. This shows that a value Sp of around lo3 cm/s is sufficiently low for an optimal photocurrent.

The saturation current density of an emitter depends on many p arm eters :

An emitter with the above penetration depth absorbs approximately 10% of AM1.5 radiation.

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96

110 100 90 80

h

$?

8 v

- 50

+i 30 - 20

10

C

Crystalline Silicon Solar Cells

1 1 ’ 1 I I I I 1 100,1000 1

NS = 1 x1019 ~ r n - ~ , x = 0,Spm

0 300 400 500 600 700 800 900 1000 1100 1200

Wavelength (nm)

Figure 6.8 Internal spectral response of a solar cell (emitter with a Gaussian profile, N,=10’9 cmS3, xj=0.5 pm)

the dopant profile, the surface doping concentration, the penetration depth of the emitter, and the surface recombination velocity.

The calculations for this were carried out by Aberle [lo] and Ruckteschler [ 171, based upon the model of serial development of multiple integrals suggested by Park [18]. The calculation has been carried out for a Gaussian doping profile, since current diffusion technology gives high efficiency solar cells this profile (see Chapter 7). This calculation takes into account the band gap narrowing (reduction of the band gap at high doping) and the dopant dependent mobility of charge carriers. For a real solar cell we must also take into account the recombination under the metal coated finger.

Figure 6.9 shows this relation~hip.~ From this representation we see that: For all values where Sp>103 cm/s the dark current density is at a minimum.

Figure 6.9 is identical to Figure 5.5 as we wish to explain this in more detail here.

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High Eflciency Solar Cells 97

12.0 I I I I I I l r l r

NS

x j = l p m I I I I I 1 1 1 1

Figure 6.9 Saturation current of an emitter as a function of surface concentration N , where Sp is a parameter

For all values where Sp>103 cm/s the dark current density is at a minimum. S, values <lo3 cm/s are sufficient (as for the photocurrent) to achieve an optimally low dark current density. The lowest values for the dark current density are achieved only by the combination N, 12x 10’’ ~ r n - ~ and Sp <lo3 cm/s.

If we now consider the role of emitter thickness, Figure 6.10 shows that in the case of a surface passivated with SiO, the emitter depth must be as small as possible. On the other hand, at the desired surface concentration of < 2x10” cm” the emitter transverse resistance between the contact fingers is very high, thus giving rise to considerable ohmic resistance losses. A workable compromise is a penetration depth of 0.3 pm. As shown in Figure 6.11, a penetration depth of 2 pm is required under the metal coated surface of the contact fingers, whereby the surface concentration should be approximately 1x1OZo ~ m - ~ .

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98 Crystalline Silicon Solar Cells

n N

E s :: 0 rl=J rn _. v) 0 n aj 0

so

25

20

5

lo

5

n " 0 2 4 6 8 x)

Emitter penetration depth x j [ pm]

Figure 6.10 Saturation current density in a passivated emitter as a function of emitter depth xj, where the surface concentration is the parameter

We see from this that to achieve high efficiency a so-called 'two step emitter', as shown in Figure 6.12, must be used.4

6.2.1.3

According to formula (5.2.13), saturation current density in the base is inversely proportional to the doping concentration. This should therefore be as high as possible. However, the lifetime of minority charge carriers decreases with higher doping (formula (3.4.17)). In this formula T~ is assumed to be 400 ps. Recent results show that this value can also be much higher. However, as this is usually not achieved due to material quality and subsequent technological processes, we have based the following discussion on a value of 200 ps.

The Influence of Base Doping

' The manufacture of a two step emitter using the double diffusion process is described in Chapter 7 .

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99 High Eflciency Solar Cells

I I I I 1 0 2 4 6 B 10

Emitter penetration depth x j [pm]

Figure 6.11 Saturation current density of an emitter with a high SRV as a function of emitter depth xj where N , is the parameter.

Finger LDD emitter SiO,

++ I P . P+ SiO

BS F Al contact Figure 6.12 Schematic structure of a solar cell with a 'two step emitter and

BSF'

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100 Crystalline Silicon Solar Cells

Cell thickness = 100,200,400 pm 2350 - Sn = I O O O cm/s -

Furthermore, for the purposes of clarity we have assumed no ohmic resistance losses.

Other selected parameters for this calculation are: emitter penetration depth 550.2 pm, back surface S,, = 1000 cmh, and 2% shadowing by the finger grid.

Figure 6.13 shows the relationship between cell thickness, dopant concentration and efficiency.

From this we find that for a 200 pm thick solar cell the optimal base doping is approximately 4x 10l6 cm” resistivity 0.4 ncm. However, if we consider that at higher basic doping the carrier lifetime is also reduced by impurity levels that lie outside the middle of the forbidden band (equation (3.4.14) and Figure 3.20), it is advisable to select a lower basic doping level. This also goes a long way towards compensating for the influence of material manufacturing tolerances for resistivities of *15 ‘30.

The results of Section 6.2.1 for recombination losses are as follows:

2425

2275

I 1 1 1 1 1 1 1 ( I I 1 1 1 1 1 1 ~ I I I 1 1 1 1 1 ~ I I l l l l l l

-

Dopant concentration (cm-3)

Figure 6.13 Efficiency of a n’p-Si solar cell as a function of doping N , of the base, with cell thickness as a parameter

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High Efficiency Solar Cells I O I

The dopant level in the base N A lies between 1.5 and 4 x 10l6 cm-’ (in general the lower value is more favourable in practise). The surface concentration N , of emitter doping is approximately 2 x loi9 cm-’. For high efficiency a two stage emitter is required. Both surfaces of the solar cell should be SO,-passivated, so that surface recombination velocities of S,<lOO cm/s and S,< 1000 cm/s can be achieved. The diffusion length must be extremely high to achieve high eficiency, but should be at least two to three times greater than the cell thickness.

6.2. I . 4 Recombination in the Space Charge Region

In Chapter 5 we showed the dependence of the recombination current in the space charge region under simplifying assumptions. According to this

I IL=40mA/cm* j

10-10 10-9 10-8 10-7 10-6 1 0 5 104 [A/C+l

Figure 6.14 Dependency of the fill factor on the saturation currents I,, and I,,

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102 Crystalline Silicon Solar Cells

(6.2.1)

We see that the fill factor in particular is dependent upon the magnitude of the current Zo2. If at voltage V, this reaches noticeable values in comparison with Zol, the saturation current from the base and emitter, then the fill factor will fall. Figure 6.14 shows the dependency of the fill factor on the two saturation currents in the two diode model. (For the sake of clarity we have assumed ohmic resistance losses to be zero.) We can see from this that for high fill factors (FF > 0.80), Zol values of lo‘* A/cm2 must not be exceeded and Zo2 values have to be less than lo-” A/cm2.

6.2.2 Ohmic Resistance Losses

Figure 6.15 shows the ohmic series resistances of a solar cell.

Figure 6.15 Series resistance in a solar cell

The individual resistances are:

R , R2 the semiconductor material (base), R3

R4

the metal-semiconductor-contact on total back surface,

the emitter between two grid fingers, the metal-semiconductor-contact on the grid finger,

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High Efficiency Solar Cells

R5 the grid finger, and R6 the collection bus.

6.2.2.1 Contact Resistance Metal-Semiconductor

To determine the contact resistances R , and R, we shall examine the metal-semiconductor contact in more detail. The theory explaining its physical behaviour was worked out by Schottky [19] as early as 1939 (the quick switching metal-semiconductor contact diode was named the ‘Schottky diode’ in his honour). With the discovery of the transistor [20] contact technology become a very important branch of semiconductor technology. In many cases, particularly for high performance components, these contacts must also fulfil additional conditions. Owing to the very high current load they must have an extremely low contact resistance, and also tolerate extreme thermal shock stress.

In this section, we deal with the behaviour of an ‘ohmic’ contact, i.e. the functional relationship between the current and voltage drop in a metal-semiconductor contact should be linear, or at least quasi-linear and the contact resistance should be low enough that the lost energy is small in comparison with other losses in a semiconductor device. Thermal fatigue plays only a minor role here.

6.2.2.1.1 Schottky Contact If a metal is brought into contact with a pure semiconductor surface, a potential banier similar to that in a p-n junction in a semiconductor is created, fulfilling the requirement for thermal equilibrium between different electron concentrations. Figure 6.16 clarifies this state.

It is true (further explanation in [21]) for a metal-n-semiconductor contact

Figure 6.16 Potential barrier between metal and semiconductor

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104 Crystalline Silicon Solar Cells

= q P m 4 . 1 (6.2.2)

and for a metal-p-semiconductor contact

(6.2.3)

is the barrier height of the metal-semiconductor contact, is the work function of the metal, i.e. the energy difference between Fermi level and vacuum level, and

qxs is the work function of the semiconductor; energy difference between the edge of the conduction band and the vacuum.

According to formulae (6.2.2) and (6.2.3) the barrier height should be directly proportional to the work function of the metal. In reality we find a very much lower dependency. In Figure 6.17 the experimentally determined barrier heights applied to n-silicon are plotted as a function of the work function of the metal [21].

EC

- 2 0.6 c 0.L - rn - * 0.2 -

I I I I 0 EV 3.5 4 4.5 5 5.5

@,,, ( e V ) Figure 6.17 Barrier height in relation to the work function of the metal [21]

For the barrier height metal-n-silicon we find the approximation line

a,, z 0 . 2 q - 0.1 (6.2.4)

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High Efjiciency Solar Cells 105

6.2.2.1.2 Ohmic Metal-Semiconductor Contact How can we make a naturally rectifying contact show ohmic behaviour? The basic principle rests upon a tunnelling process [21]. If a metal is deposited directly onto a highly doped semiconductor, then a narrow space charge region is created which electrons can ‘tunnel through’. Figure 6.18 demonstrates this effect.

F

Low barrier height

High doping

Figure 6.18 Charge transfer with ohmic contact: (a) tunnel effect, (b) themionic effect

A further possibility for the transfer of electrons at low doping is provided by the fact that charge transport takes place by the so-called ‘thermionic’ effect. A low barrier height and thus a metal with a low work function [Om] is a prerequisite for this.

The specific contact resistance [Clcm2] for an n-semiconductor is found to be as follows according to the theory [22],[23].

~ ~.

For the tunnel effect:

4 x & 7

h k

P, =- q T A *

where A* is an effective Richardson’s contact in For the thermionic effect:

which A * = A (m*/m,).

P, =- k exp [ >] q T A *

(6.2.6)

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106 Crystalline Silicon Solar Cells

107

105

103

- 101

u 1 N

E

- 10'1

10-3

10-5

u a

300 K - Theory x P t S i - S i

o A l - Si

I 11 I

5 10 " 30 ( 10-1oC,3/* I

Figure 6.19 Theoretical relationship between the contact resistance and doping level, as well as barrier height [24]

We find from the formulae that in the first case the contact resistance decreases with increasing doping, whereas in the second case it is dependent only on the barrier height. This dependency is shown in Figure 6.19 (including some experimental results) [24],[25].

The left-hand side shows tunnel behaviour according to formula (6 .2.5) and the right-hand side shows thermionic behaviour according to formula (6.2.6). As we will see later, for a necessary contact resistance of Rcm', for example, a surface doping concentration of approximately 1OZo cmS3 is required in order to permit the use of many metals as contact

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High Efficiency Solar Cells 107

materials. However, for a surface concentration of approximately 1 OI9 cm” the barrier height must be < 0.5 eV. The selection of a suitable metal is very restricted in this case however, as we saw from Figure 6.17.

6.2.2.1.3 Contact Resistance [R J of a Grid Finger

If we consider the current path under the grid finger as shown in Figure 6.20, it immediately appears plausible that the width of the current path - the distribution of current density - is directly dependent upon the level of specific contact resistance pc [see Section 6.2.2.1.21. For very small values of pc the current travels mainly along the edge of the grid finger. Conversely, high transition resistance leads to an expansion of the current path.

Figure 6.20 Current path under the grid finger: 1 = length of grid finger, L = width of grid finger, I = electric current

This behaviour can, as seen in Figure 6.21, be explained using a resistance network. Voltage [Ul at the metallic grid finger is kept at zero, grounded. As the metal film is some pm thick in practice, the voltage

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I08 Crystalline Silicon Solar Cells

Figure 6.21 Distributed resistance network for the contact resistance me tal-semiconduc tor

along the entire grid finger is also virtually zero. We are also justified in making the assumption that the current path in the emitter is homogeneous, i.e. that at right angles to the grid finger in the longitudinal direction the same current density applies everywhere. Then in the layer dx the two longitudinal and contact resistances dR, and dR, are determined as follows:

(6.2.7)

where R , = FIX, is designated as the sheet resistance [measured in U O , ohmslsquare) (dimension Ohms). The contact resistance is then found to be

dR, = - pc (6.2.8) ldx

where pc in [Ckm2] is the specific contact resistance. Further mathematical analysis requires the solution of differential

equations, which we wish to avoid here. Please refer to the literature

The voltage distribution under the grid finger (at right angles to it) thus [26]-[28].

works out as:

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High Eficiency Solar Cells

Figure 6.22 represents this voltage distribution.

Figure

Contact - X

U(X) = u0 e LT

\& \ \ \ - LT - - X

0 6.22 Voltage distribution under the grid finger

Contact - X

- X

0 6.22 Voltage distribution under the grid finger

109

(6.2.9)

If we designate (p, / Rd0.’ as the transport length L,, the voltage drops to l / e after the distance L,, and the current under the grid finger reduces accordingly. The transport length is therefore a characteristic variable for the current path.

The above mathematical analysis yields the following value for contact resistance:

R, = I coth [L * IF] or where L , = (p, I Rd0.’ we find that

pc R, = - coth l * L ,

(6.2.10)

(6.2.1 1)

Two approximate solutions are of particular interest:

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110 Crystalline Silicon Solar Cells

1 . If L, 2 2L, then the value of coth nears 1 and the resistance R, is

(6 .2 .12)

2 . If L , I 2L, then coth nears the value of the factor in front of L . We thus find the contact resistance to be

P C R, =- I * L

Result: If L , I O S L , then the resistance is the contact finger. If L , 2 2L, then the width of the contact resistance.

( 6 . 2 . 1 3 )

independent of the width of

finger alone determines the

As an example of a high efficiency solar cell we wish to clarify the high influence of the specific contact resistance pc and thus the transport length

5 pm, i.e. where L , = (pc/R,Jo.’ with a normal R, of approximately 100 CUD we find the required pc of 2 . 5 ~ lo-’ a m 2 . As demonstrated in Figure 6 .17 and Figure 6 .19 , for a surface dopant concentration ND of approximately l O I 9 cm” this can only be achieved using titanium as the contact material.

LT. For a desired grid finger width of 10 pm, L,

6.2.2.2 Ohmic Losses in the Semiconductors

6.2.2.2. I Base Resistance R, is the resistance of the solar cell base material, which in simple form is found to be

R, = ps, D.A (6 .2 .14 )

where A is the cell area for an Si wafer with a resistivity of p=l Rcm and a thickness D of 200 pm yields R, = 0 .020 SZ, and is negligible in most cases.

6.2.2.2.2 Resistance in the Emitter Figure 6.23 shows the current distribution in the emitter and the grid fingers. The current flowing vertically from the base is diverted horizontally within the emitter into the grid fingers.

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High Eflciency Solar Cells 111

Figure 6.23 Current path in the emitter: left: side view; right: aspect

To calculate the resistance R , we proceed by calculating power loss P, in the emitter between two fingers and dividing this power by P (since P, = ZE2 R3) , where Z, is the lateral current in the emitter. We further assume that the current in the base of the solar cell flows homogeneously. It is then clear that precisely half way between the fingers ( x = 0) no lateral current will flow. We can therefore limit ourselves to Calculating one-half of the intermediate area between two fingers. The current (Z,,,=), which reaches the contact finger from the side, is now equal to the photocurrent density j , multiplied by the area, from which the current is collected, i.e.

d 2

Imax - - j l - (6.2.15)

The current after distance x is then I(x) = jlx due to its homogeneity. We now need to find the resistance dR in the infinitesimally thin layer dx. This works out, as we can easily verify, to

-

P dR =-dx x, 1

(6.2.16)

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112 Crystalline Silicon Solar Cells

where p is the average resistivity of the emitter and xj its penetration depth. Since

P - = R , X .

J

is equal to the sheet resistivity in W O , dR is found to be

R , dR =-dx 1

The power loss dP in the sheet dx is then calculated to be

dP = I ' M

R , dP = ( j l x ) ' - dx 1

and by integration we find the total loss, i.e.

d l Z

P = j 2 1 R , f x z d x 0

It follows from this that

d' P = j Z l R , - - 24

(6.2.17)

(6.2.18)

(6.2.19)

(6.2.20)

(6.2.21)

(6.2.22)

This means that the power loss in the emitter increases by the cube of the distance between the contact fingers. To find the value of R, we manipulate the equation (6.2.23) to obtain P = I,,,, Re, = I,, R,. We then find that

(6.2.23)

R , is thus found to be

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High EfJciency Solar Cells 113

R~ d 1 6 R , = - (6.24)

R, is therefore equal to one-third of the electrical resistance of the emitter layer between x = 0 and d/2.

6.2.2.3 Ohmic Losses in the Metal Contacts

6.2.2.3.1 Contact Finger Resistance We proceed in a similar manner as for the calculation of R,. Again, 1 is the length, L the width and u the thickness of the finger. pmct is the resistivity of the metal. The result for R, is as before, equal to one-third of the series resistance for the entire contact finger, i.e.

(6.25)

6.2.2.3.2 Busbar Resistance

The calculation of the resistance R, is also identical to the procedure in the two previous sections. We must ensure that the current connection is in the middle of the busbar (Figure 6.24). In this case, where a is thickness, L , the width and I, the total length of the busbar, the resistance of half the busbar is

(6.2.26)

As we can easily calculate, if we collect the current at the end of the busbar, the resistance R, will be four times greater than for a contact in the middle.

The total serial resistance is found by linking the individual resistance values R, to R, together in a suitable resistance network. If we once again calculate all six resistances with regard to their contribution to serial resistance R,:

Resistance R, (the resistance of the metal-semiconductor-contact on the entire back surface) and R, (resistance of the semiconductor material (base)) can be disregarded in all practical cases. If the contact material and the finger width are correctly selected, then R, (the resistance of the metal-semiconductor contact under a grid finger) also makes no significant

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114 Crystalline Silicon Solar Cells

Figure 6.24 Structure of the contact grid

contribution. The resistances R, (resistance in the emitter between two grid fingers), R, (resistance of a grid finger) and primarily R, (resistance of the bus bar) primarily determine R,. For R, and R, a very careful compromise must be sought between ohmic losses and shadowing losses (see Figure 6.3 1).

6.3 OPTICAL LOSSES

Three factors are responsible for optical losses in solar cells:

The Si surface reflects 35%-50% of the light, depending upon wavelength. The grid structure shadows 3%-12% of the light, depending upon design. Absorption in silicon-indirect semiconductor-is very low in the long wavelength sunlight range, i.e. near to the band edge. This light is absorbed in the back surface contact without any photovoltaic effect.

Various technological measures are implemented to prevent or reduce these losses.

6.3.1 Antireflection Processes

An antireflection effect can be achieved in two different ways. On the one hand by a thin film of ‘antireflection coating’, and on the other hand by the

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High Efficiency Solar Cells 115

texturising of the cell surface. In the latter, the surface is structured so that multiple reflections allow most of the light to be absorbed in the cell.

6.3. I . 1 Antireflection Using a Thin Coating

A reduction in reflection can be achieved by the 'optical quarter wave length' principle. As shown in Figure 6.25, the penetrating light beam is reflected at the barrier layer between the antireflection medium and the silicon.

"0 Air or glass

"1 d 1 Antireflection layer

Silicon "2

Figure 6.25 Antireflection behaviour of a thin film.

Owing to continuity conditions and conservation of energy, an electromagnetic wave undergoes a phase shift of x/2 upon entry into an optically denser medium. If the thickness of the antireflection layer is chosen so that the optical path, i.e. the product of refractive index and layer thickness is equal to a quarter of the wavelength, then light of this wavelength falling vertically is completely extinguished (destructive interference). Written as a formula this condition reads:

h n . d = - 4

(6.3.1)

According to Fresnel's formula the reflection factor is

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116 Crystalline Silicon Solar Cells

(6.3.2) rf + r i + 2 r , r 2 c o s 2 8

1 + r l rz + 2 r , r 2 c o s 2 9 2 2 R =

with

no - n , r , = - no + n ,

where

no n , n,

is the refractive index of the uppermost layer (air or glass), is the refractive index of the antireflection layer, and is the refractive index of the silicon.

Reflection is at its minimum where nldl = W4.

R,, is equal to zero when

2 n , =nOnz

(6.3.3)

(6.3.4)

(6.3.5)

(6.3.6)

(6.3.7)

i.e. when

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High ESficiency Solar Cells 117

7

-

- Silicon

-

-

I . 1 . 1 . I . I I I " ' I ' '

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Wavelength (pm)

Figure 6.26 Refractive index of silicon in relation to wavelength and photon energy

(6.3.8)

To calculate total reflection at thickness d, in relation to the wavelength, we must consider that the refractive index of silicon changes according to wavelength. Figure 6.26 shows this relationship.

Based on this relationship and with a reflection layer thickness such that minimum reflection occurs where h = 0.6 pm: Figure 6.27 shows the distribution of reflection in relation to the wavelength.

' The lowest total reflection under AM1.5 is when the minimum is at 1=0.6pm.

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118 Crystalline Silicon Solar Cells

-..-..-..-. Bare silicon TiOz 70 nm

---I-- TiOz 70 nm + MgF2 110 nm

--..-..-..-..-..- ....._.._.._....,_. ~ _... ... ........_ ..I.._..-.. _, , -.._ ..-. .-....._., .-..- '.

8

20 - *.

10 - s 8 ,

8

I 0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Wavelength (pm)

Figure 6.27 Reflection on pure silicon with one and two antireflection films, in relation to wavelength

Total reflection, e.g. at AM13 sunlight, is easily obtained by superimposing the radiation intensity and the reflection curves.

A further improvement can be achieved by using two antireflection layers - naturally of different refraction indices and of different thicknesses. The upper antireflection layer must have a lower refractive index than the antireflection layer on the silicon. Figure 6.27 shows that the double antireflection layer gives two reflection minima. Correct selection of parameters can reduce total reflection to 3%4%.

6.3.1.2 Textured Surfaces

In Figure 6.28 the silicon has a pyramidic surface. These structures can be produced by anisotropic etching, with the angle at the peak being 70.5' (on ~ 1 0 0 ) surfaces). A vertical beam meets the silicon surface at an angle of 35.25".

Reflection is at the same angle. The reflected part meets the opposite surface, so that again part of this light penetrates the crystal. The calculation for total reflection shows, that for (AMl.5) sunlight instead of approximately 35%, only 10% of the light is reflected.

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High Eficiency Solar Cells 119

Figure 6.28 Radiation paths for a textured silicon surface

Figure 6.29 Inverted pyramid structure after anisotropic etching. Dimension of the pyramid is 20 x 20 pmZ

An additional antireflection coating allows a further reduction to approximately 3%. In practice the best success has been achieved with so- called inverted pyramids. Figure 6.29 shows an electron microscopic picture of such a structure.

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I20 Crystalline Silicon Solar Cells

6.3.2 Losses due to Non-Absorbed Light

The percentage of non-absorbed sunlight (AM 1.5) in a 200 pm thick solar cell made of silicon is approximately 10%. To increase absorption, the light is reflected by a reflecting metal on the back, thus doubling the absorption path. Better techniques provide multiple reflection. The light is locked in the crystal (light confinement).

An effective method is to fit the back surface of the solar cell with a so- called random surface structure (Lambert's reflection), as shown in Figure 6.30.

Figure 6.30 Reflection behaviour with random Lambert's surface structure

As can be seen from this illustration, the radiation can only exit via a

The angle a, of this leakage cone is calculated as narrow leakage cone due to the high refraction index of Si.

(6.3.9) 1 sin2@, = - n z

For a value n,, = 3.5 we find that OC = 17". If we calculate the radiation loss for light reflected into this cone, it

amounts to approximately 8.5% of the total light 1291. Further improvements can be made by additional structuring to the front surface of the cell. For further information we refer you to the literature [30]-[32].

We note here that the principle of confinement is more important the thinner the silicon wafer. The thinner the wafer, the more often the light must travel backwards and forwards within the crystal. For an efficient

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High Efjciency Solar Cells 121

- 40- 8 Y

30: 0

([I

- - - 20-

10 -

0 .

crystalline Si thin film cell (sheet thickness 30-50 pm) good confinement is the most important prerequisite. To sum up: Shadowing, reflection and lack of absorption reduce photoelectric current. If this loss can be reduced in the best case to 6%, the photoelectric current - which can be achieved with AM 1.5 solar radiation - is approximately 41 mA/cmZ. (The theoretical maximum is 44 mA/cm2.) Electrical losses, however lead to a further reduction in the above current.

-.---- 50 vm

100 pm ......-.,-..

.

6.3.3 Shadowing Losses by Contact Fingers

Shadowing losses are in proportion to the number of fingers. The losses in the emitter, on the other hand, are proportional to the cube of the distance between the fingers, equation (6.2.23). Figure 6.3 1 shows this relationship.

The width of the contact finger at a given sheet resistance of 100 W O varies between 30-100 pm. Minimum loss exists with 10-15 fingers. After this minimum the loss climbs relatively slowly, but as it nears a low number of fingers it rises sharply. Calculations show that the dependency in the emitter sheet resistance is relatively low.

From this discussion we find that the number of fingers should be slightly higher than the calculated minimum, in order to compensate for certain tolerances in manufacture.

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122 Crystalline Silicon Solar Cells

We find the minimum for these losses when the shadow loss is around the same size as the ohmic loss in the emitter. Shadowing can be reduced by another one-third by tapering the fingers and bus. Tapering of the fingers occurs from the busbar.

6.4 THE STRUCTURE OF A HIGH EFFICIENCY SOLAR CELL

If we put all the knowledge and experience from this section into practice, we get a solar cell structure as shown in Figure 6.32. To sum up the parameters for a high efficiency solar cell:

Figure 6.32 The structure of a high efficiency solar cell made of monocrystalline silicon

The base material is monocrystalline, float zone pulled and p-doped (approximately 1 . 5 ~ 10l6 ~ m - ~ ) , with a resistivity of approximately 1 a m .

The base thickness is approximately 200 pm, primarily due to technological manufacturing and handling processes.

The front surface facing the light is textured, preferably with inverted pyramids.

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High Eflciency Solar Cells 123

The front surface, apart from the grid structure, is coated with a thermally grown layer of silicon dioxide for passivation.

The emitter is two stage and has a surface doping concentration of approximately 1 x lOI9 cmS3 and a penetration depth of 0.5-1 pm under the SiO, layer, the surface concentration is approximately 1 x 10'' cm" and the penetration depth approximately 2-3 pm under the metal of the grid structure.

The back surface of the cell is coated with a thermally grown SiO, layer for passivation except for the point contacts (approximately 1%-2% of the total area).

The local p'-doped BSF has a surface concentration of >lozo cm-' and a penetration depth of 2-3 pm.

The SiO, passivation has a thickness of approximately 100 nm to achieve a high antireflection effect on the emitter side (light entry).

The back surface contact has reflective characteristics and consists, for example, of vapour-deposited aluminium.

For a cell of dimensions 2x2 cmz the gridJingers have a width of approximately 15 pm and a thickness of around 8 pm (tapering away from the busbar).

The busbar has a width of approximately 150 pm, and the contact connection is located in the middle of the busbar.

As well as these constructive measures it must be ensured technologically that the diffusion length in the base remains high throughout all the process stages (see Chapter 7).

By implementing these measures it is possible to increase the efficiency of monocrystalline solar cells in the laboratory under AM 1.5 to 23%-24%, very close to the theoretical efficiency [33]-[35].

A further increase in efficiency can be achieved in crystalline silicon by using thinner cells of approximately 10-30 pm. However, this requires excellent passivation of the crystal surface and very good 'optical confinement'.

6.5. MANUFACTURING PROCESS FOR HIGH EFFICIENCY SILICON SOLAR CELLS

In order to fulfil the requirements for these types of solar cells described in the previous section, highly complex technologies are necessary which call for a large number of technological steps. However, in the sequence of these many steps of high temperature, photolithography and chemical processes, the crucial point is the compatibility of the process steps that follow one another. These must be selected and coordinated, so that they

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124 Crystalline Silicon Solar Cells

do not interfere with each other. The design of such process chains is one of the most important developmental tasks for all semiconductor devices.

We now describe two process sequences for high efficiency Si solar cells, which have been developed in our institute. They naturally rely on many known technologies. The first manufacturing process achieves an efficiency of 23%. This is naturally also the more complex procedure. However, since its high cost overcompensates for the cost reducing potential brought by high efficiency, a simpler, more economical process has been developed, whereby attention is focused on keeping the sacrifice of efficiency as low as possible.

All the process stages described in the following section are described and explained in more detail in Chapter 7. References are made at certain points.

6.5.1

In Figure 6.33 the entire process sequence is divided into eight process blocks, with each individual block containing several individual steps. The process is explained based on this illustration. The starting point is - as already mentioned - Fz-Si (float zone pulled Si material, see Chapter 7, Section 7.15) with a resistivity between 0.5 and 1.5 R, a wafer thickness of approximately 250 pm and a crystal orientation of (100) at right angles to the surface of the Si wafer. The surfaces are etched or polished on both sides. The wafer diameter is 3 in. or 4 in.

Texturizing: The silicon wafer is given an approximately 80 nm thick film of SiO, by means of a high temperature process (see Chapter 7, Section 7.2.2.). A window structure is then created on one side of the Si wafer (to be the front side, the side turned towards the light) using photolithography and an etching process in buffered hydrofluoric acid, creating a multitude of oxide-free square windows with dimensions 20 x 20 pm'. Deep etching then takes place in these windows in a hot alkaline solution. Inverted pyramids are created by this anisotropic etching with (1 11) orientation (see Chapter 7, Section 7.2.5.2). The remaining SiO, ridgetops, not affected by the alkaline solution, are then removed in an HF solution.

Boron-BSF Dvfision: By a further oxidation process, an SiO, film is created with a thickness of 200 nm. On the other side - to be the back of the cell - some windows are opened using a photoresist processes. Boron is diffused into these windows in a high temperature process to create a local pt back surface field. The remainding oxide is later removed by etching.

Process Sequence for the Highest Efficiency

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High EfJiciency Solar Cells

Figure 6.33 Process sequence for the manufacture of a LBSF (Local Back Surface Field procedure) solar cell with very high efficiency

I25

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I26 Crystalline Silicon Solar Cells

n++ Diffusion: Another oxidation process follows with an oxide thickness of 200 nm. Windows are opened along long ridges on the front (again using photoresist and etching processes). An n++ diffusion takes place in a high temperature process using phosphorus (see Chapter 7, Section 7.2.1.2). The remaining oxide is again removed and is followed by n+ diffusion.

n+ Drfusion: This stage begins with a further protective oxidation with an oxide thickness of 200 nm. In this high temperature process the phosphorus, which was previously only diffused into the surface, is diffused to a depth of approximately 1-2 pm. When the oxide film on the front is opened, an n+ diffusion takes place.6

Oxide Passivation: In a further high temperature process a 105 nm thick SiO, film is created which, as mentioned, firstly serves as a single layer antireflection coating on the front surface, and secondly, it also provides the required surface passivation on both sides, keeping the surface recombination velocity of charge carriers as low as possible. This completes the semiconductor specific processes.

Metalising (back): of the cell. Again using photoresist, holes are opened in the SiO, on the back of the cell for contact points, exactly at the points where boron has been diffused. On top of this a continuous aluminium layer with a thickness of 2 pm is vacuum evaporated. This aluminium also serves as a mirror for the photons that have not yet been absorbed.

Metalising front): of the solar cell. Oxide windows are also opened on the ridges and on the busbar, and using the ‘Lift Off Technique’ (see Chapter 7, Section 7.2.4.1) a sequence of layers of Ti-Pd-Ag is vacuum evaporated with a total thickness of approximately 0.1 pm.

Contact Reinforcement, Annealing: Because the galvanic resistance in the grid contact is a critical variable for total serial resistance, the metal of the fingers and the busbar is reinforced by electroplating to approximately 10 pm. Since the fingers should if possible not be wider than they are high, great efforts are required to achieve narrow, but high fingers. This galvanic film, to improve contact with the evaporated silver, then undergoes tempering at approximately 400°C in forming gas (6% hydrogen), This also has the advantage of significantly improving the quality of the oxide. The multitude of processes can be seen in Table 1. The highest level of efficiency achieved using this method is over 23% (cell area 4 cm2) [3 61,[371.

n+ means high surface concentration.

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High Efficiency Solar Cells 127

Figure 6.34 Reduced process sequence for the LBSF (Local Back Surface Field) procedure for the manufacture of a high efficiency Si solar cell

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128 Crystalline Silicon Solar Cells

LBSF Process

5 High temperature oxidations

3 Dopant diffusions

6 Photolithography processes

6.5.2 The Simplified Manufacturing Process

The aim was to reduce the processing cost compared with the process described above. The process described below uses significantly fewer process stages (see Figure 6.34 and Table 1 right). The resulting solar cell structure is called a RP-PERC structure.’

RP-PERC Process

2 High temperature oxidations

1 Dopant diffusion

3 Photolithography processes

Texturizing: The surface of the Si-wafer (the same starting material as described in Section 6.5.1), is etched in a hot alkali-alcohol mixture after an oxidation process and the uncovering of what will become the front side. This creates statistically distributed vertical pyramids (‘random texture’). Then, without any intermediate step (only rinsing and cleaning), n+ diffusion takes place.

n+ Diffusion: Diffusion of phosphorus onto the texturised side, creating a phosphorus glass layer on both sides (see Section 7.2.1.2.1).

Oxide Passivation: After the etching of this phosphorus glass film, the 105 nm thick passivating and antireflection SiO, film is created in a second high temperature process. Metallising (Jront contact): Using photoresist processes and the ‘Lift-off technique, contact points on the front and back are opened and the Ti-Pd-Ag contact system is vacuum evaporated onto the front.

Metallising (back surface): Contact windows are opened on the back surface and aluminium is vacuum evaporated over the entire area. Finally, the galvanic reinforcement of the contact grid takes place and it is annealed under the forming gas.

’ Random Pyramids - Passivated Emitter Rear Cell

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High Eflciency Solar Cells 129

Material

Cell area [cm’]

n (in YO)

Fz-Si Fz-Si Cz-Si

4 21 4

21.6 20.9 19.7

The efficiency levels achieved are shown in Table 2. With Fz-Si and an area of 4 cmz an efficiency of 21.6% can be achieved instead of > 23% with the more complicated procedure. It is worth noting that even with Cz- Si (Czochralski material, crucible pulled) a very economic Si material, with efficiencies of almost 20 %, can be achieved.

Altering the process, as an experiment, an additional p+ back surface field is added by the diffusion of boron. Efficiency increases, due to the lower level of recombination on the back surface, so that for example, with Fz-Si and an area of 4 cm’, 22.6% efficiency is achieved. It is thus documented that even with greatly simplified processes, very high efficiencies can be achieved.

Table 1 shows the number of process stages for the LBSF process and for the RP-PERC process. Table 2 shows the efficiencies achieved by the RP-PERC process.

References

Wolf M., Proc. 3rd EC PV Solar Energy ConJ, Cannes, France, 1980, p. 204

Goldmann H., Proc. 14th IEEE PVSpec . Conf San Diego, California, 1980, p. 923

Redfield S., Proc. 13th IEEE P V S p e c . ConJ, Washington, DC, USA, 1978,

Ross jr. R. G., Proc 13th IEEE PV Spec. C o n f , Washington, DC, USA, 1 9 7 8 , ~ . 1067

Grenon L. A. and Coleman M. G., Proc. 13th IEEE PV Spec. Conf., Washington, DC, USA, 1978, p. 246

Vofl B., Statusreport Photovoltaik, 1987, p. 73

Knobloch J., Aberle A. and Vofl B., Proc. 9th EC PV Solar Energy ConJ, Freiburg, Germany, 1989, p. 777

Von B. and Knobloch J., Internationales Sonnenforum, 1988, p. 468

p. 911

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130 Crystalline Silicon Solar Cells

[91 DOE-Studie zitiert von Fan J.C.C. in Proc. 5th PVSEC, Kyoto, Japan, 1990, p. 607

Aberle A., Thesis Univ. Freiburg, 1992

Basore P. A. Proc. 22nd IEEE PV Spec. Con$, Las Vegas, Nevada, USA, 1991, p. 299

van Overstraaten R. and Nijs J. JEEE TED 16, 1969, p. 632

Nicollian E. H. and Brews J. R., MOS Physics and Technology, Wiley & Sons, New York, 1982

Goetzberger A., Bell Syst. Techn. 45, 1966, p. 1097

Goetzberger A. et al., Appl. Phys. Lett. 12, 1968, p. 95

Sze S. M., Physics Of Semiconductor Devices, 2nd Edn, Wiley & Sons, New York, 1981

Ruckteschler R., Thesis, Univ. Freiburg, Germany, 1986

Park J. S., Neugroschel A. and Lindholm F. A., IEEE TED 33, 1986, p. 240

Schottky W., ZeitschriftJ Physik 113, 1939, p. 367

Shockley W., Bell System Techn. 28, 1949, p. 435

Schroder D.K. and Meier D.L., IEEE TED 31, 1984, p. 637

Chang C. Y. and Sze S. M., Solid State Electron. 13, 1970, p. 727

Padovani F. A. and Stratton R., Solid State Electron. 9, 1966, p. 695

Yu A. Y. C., Solid State Electron. 13, 1970, p. 239

Chang C. Y. et al., Solid State Electron. 14, 1971, p. 541

Meier D. L. and Schroder D. K., IEEE TED 31, 1984, p. 647

Hower P. L., Hooper W. W., et al. in Semiconductors and Semimetals, Willsrdson R. K. and Beer A. C., eds. Academic Press, New York, 1971, pp. 178-183

Murman H. and Widmann D., IEEE TED, ED 16, 1969, p. 1022

Goetzberger A,, Proc. JSth IEEE PVSpec. Con$, Kissimmee, Florida, USA, 1981, p. 867

Campbell P., Wenham S. R. and Green M. A., IEEE TED. 37,1990, p. 331

Campbell P., Wenham S. R. and Green M. A., IEEE TED 35, 1988, p. 713

Uematsu T., Ida M., Hane K., Kokunai S. and Saitoh T., IEEE TED 37, 1990, p. 344

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High Eflciency Solar Cells 131

[33] Green M. A,, Proc. 10th EC PV Solar Energy Con$, Lissabon, Portugal, 1991, p. 250

Sterck S., Knobloch J. and Wettling W., Progress in Photovoltaics, 2, 1994, [34] p. 19

[35] Knobloch, J., GlUnz S. W., Biro D., Warta W., Schaffer E. and Wettling W., Proc. 25th IEEE P V S p e c . ConJ, Washington, DC, USA, 1996, p. 405

[36] Zhao J., Wang A., Altermatt P. P., Wenham S. R. and Green M. A,, First World Conference on Photovoltaic Energy Conversion, Hawaii, USA, 1994, p. 1477

[37] Glum S. W., Knobloch J., Biro D. and Wettling W., Proc. 24rh EC PV Solar Energy Con/, Barcelona, Spain, 1997, in press

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7 Si Solar Cell Technology

7.1 TECHNOLOGY FOR THE MANUFACTURE OF SILICON

In this chapter we first of all wish to describe in detail the process for the production of highly pure crystalline silicon. We then want to explain the technological processes which are applied to the manufacture of solar cells from this material.

7.1.1 Basic Material

Apart from oxygen, silicon is the most commonly occurring element on the earth. It mainly occurs as silicon dioxide (SiO,) in quartz and sand. Its synthesis has been familiar for many decades. It is extracted from (mainly) quartzite reduction with carbon in an arc furnace process. Figure 7.1 gives an overview of the manufacturing process [l].'

The pulverised quartz and carbon are put in a graphite crucible. An arc causes them to melt at approximately 1800°C. Then the reduction process takes place according to the formula

SiO, + 2C -+ Si + 2CO (7.1.1)

The liquid silicon collected at the bottom of the crucible (melting point 1415°C) can then be drawn off. Its purity is approximately 98%. This is called metallurgic-grade silicon (MG-Si) and a large quantity is used in the iron and aluminium industries. More than 500,000 tonnes are manufactured per year worldwide .

' The first six illustrations are direct copies of the originals, as listed in [ 11 and [2]

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Figure 7.1 A smelting furnace for the production of metallurgic silicon [ 11

As the energy consumed by this process is very high at 14 kWhkg, production takes place in areas of the world where excess hydroelectric power is available (e.g. Noway, Canada).

However, for silicon to be used in the semiconductor industry, the impurities must be removed almost completely by further processes. The remaining impurities in electronic grade silicon may only be some lo-''%. For such a high purity grade, multistage processes must be implemented.

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7.1.2 Refractioning Processes

The processes described here and in the following Section 7.1.3 are based on developments by Siemens in the 1950s. They are now the standard processes for the production of electronic grade silicon.

In the first stage pulverised metallurgic silicon is exposed to hydrochloric gas in a fluidized-bed reactor. Trichlorosilane and hydrogen are produced by the chemical reaction Si + 3 HCl + SiHCI, + H, (exothermic reaction). Since trichlorosilane is a liquid at temperatures below 30°C it can easily be separated from hydrogen.

The chlorides of the impurities from the process must now be separated from the trichlorosilane. In a second stage the trichlorosilane is freed from these impurities in fractional distillation columns. The other silicon chlorides are also removed. Trichlorosilane distilled in this way fulfils the requirements for electronic grade silicon. The impurity level is less than 1 O-'O%.

7.1.3 The Manufacture of Polycrystalline Si Material

The manufacture of high purity silicon takes place according to the principle demonstrated in Figure 7.2 [2].

Polycrystalline silicon is deposited in a reactor vessel following the CVD principle (Chemical Vapor Deposition). The process is as follows: a thin silicon rod (in this case u-shaped) is electrically heated to a temperature of approximately 1350°C. A mixture of hydrogen (which must also be high-purity) and trichlorosilane is introduced into the reactor vessel. Trichlorosilane is reduced to silicon on the hot surface of the silicon, which deposits itself on the rod surface. The process takes place according to the following formula:

4 SiHC1, + 2 H, + 3 Si + SiC1, + 8 HCI (7.1.2)

Thus, high-purity polycrystalline silicon is produced in a continuous process to rod diameters up to 30 cm and rod lengths up to approximately 2 m.

More recently another process has been developed, based upon similar chemical principles. In a type of fluidized-bed reactor, silicon is deposited on the surface of fine silicon balls using silane created in situ. The silicon powder manufactured in this manner with a particle size of some tenths of a millimetre can be used either in the CZ pulling process described below (Section 7.1.4.1) or for the direct manufacture of silicon foil (Sections 7.1.7.1 and 7.1.7.2).

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Figure 7.2 Equipment for the industrial precipitation of polysilicon [2]

7.1.4 Crystal Pulling Process

For the manufacture of semiconductor devices, as well as having high purity levels, the silicon should be in single crystal form and free of defects. Two processes have become established, the crucible pulling process, also known as the Czochralski Process [3], and the float zone pulling process.

7. I. 4. I The Czochralsh (CZ) Process

Figure 7.3 [4] shows the principle of the CZ process. Polycrystalline material in the form of fragments obtained from polysilicon as described in Section 7.1.3, is placed in a quartz crucible, which is itself located in a graphite crucible, and melted by induction heating under inert gases. The pulling process begins with the immersion of the single crystal silicon seed. The vertical pulling movement and the rotary movement silicon to grow in monocrystalline form on the seed crystal. Extremely precise balancing and

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control of both movements, and precise control of the temperature of the silicon melt allows the diameter of the crystal to be precisely adjusted. Adding highly doped silicon fragments permits the simultaneous adjustment of the desired doping, dependent upon level and type of conductivity.

Figure 7.3 Single crystal pulling by the Czochralski process [3]

It is unavoidable that a certain amount of oxygen, originating from the quartz crucible, is incorporated in the crystal during this process. For most semiconductor applications this is of minor importance, and in some cases is even used to good effect to achieve gettering. For high efficiency solar cells, however, it is a disadvantage as oxygen forms precipitates, which act as recombination centres to reduce the lifetime of charge carriers. Our institute, however, has managed to achieve an efficiency of 22% using this material and suitable technologies.

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7 .1 .4 .2 Float Zone Pulling

In float the CV desired 7.4 [ 5 ] .

zone pulling the starting point is a polycrystalline rod, produced by ‘D process described in Section 7.1.3 (but a straight rod of the diameter). The principle is explained in more detail based on Figure

Figure 7.4 Single crystal pulling by the float zone pulling method [ 5 ]

The puller is located within an enclosure flushed with inert gas. At the lower end a single crystal seed is again melted onto the polycrystalline rod by induction heating. After melting, a region of liquid silicon is propelled

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upwards by the vertical movement of the induction coil whilst being rotated.

When the silicon cools, it solidifies in single crystal form. The desired doping is achieved by the addition of a suitable dopant in gaseous form (e.g. phosphine PH, or diborane B,H,) to the inert gas. One advantage of this process is the additional cleaning of the crystal. Impurities (in particular metallic impurities) possess a very low segregation coefficient

), i.e. their solubility in liquid silicon is some orders of magnitude higher than in solids. Thus these substances are largely carried with the fluid zone and transported to the upper end of the crystal. This process makes it possible - particularly with repeated pulling - to achieve very perfect crystals of high purity and thus - if desired - high resistivity.

to

7.1.5 The Manufacture of Silicon Wafers

Most semiconductor devices, including solar cells, require thin wafers with a thickness of approximately 0.2 to 0.5 mm. The standard process for wafers used the so-called inner diameter saw (ID), where diamond particles are imbedded around a hole in the saw blade. The process is very cost intensive and has the disadvantage that up to 50% of the material is wasted. A new process has been established in the form of the so-called multiwire saw, in which a wire of several kilometres in length is moved across the crystal rod in several coils within an abrasive suspension, whilst being wound from one coil to another (Figure 7.5) [6 ] .

The advantage of this is that thinner wafers can be produced and the sawing losses are reduced by approximately 30% in comparison with the ID saw process. Also crystal defects on the surface of the silicon slice are significantly lower, reducing the manufacturing cost and increasing the efficiency of the solar cells.

7.1.6 Polycrystalline Silicon Material

As the cost of silicon is a significant proportion of the cost of a photovoltaic array [Chapter 61, great efforts have been made to reduce these costs since the beginning of worldwide photovoltaic activities in 1973. One principle which has emerged from these efforts is so-called block casting, which does not involve the costly crystal pulling process. This is shown in Figure 7.6 [7]. Silicon melted in a quartz crucible 1 is poured into a square graphite crucible 8. Controlled cooling produces a polycrystalline silicon block with a large grain structure. Precise control of the cooling mechanism ensures that the grain boundaries are columnar, i.e. aligned vertically to the surface. The grain size is some mm to cm. The

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U Figure 7.5 Sawing Si slices by the "wire cutting technique" [6]

silicon blocks, with dimensions of up to 30 x 30 cm2 are initially sawn into blocks with surfaces of 20 x 20 cm' or 10 x 10 cm'. Then, the above sawing processes are used to produce square Si wafers of 10 x 10 cm2 and 0.3-0.4 mm thickness (very recently dimensions of 15 x 15 cm2 have also been produced). Thus this starting material for solar cells is called polycrystalline silicon.

This material is widely used and currently covers about 30% of all silicon requirements for terrestrial energy photovoltaics. New research and development work has made great progress both in relation to homogeneous crystal growth and, more importantly, in reducing the number of crystal defects in the individual grains [8]. We will go into more details about solar cells made of this material in Chapter 8. One important point is that unlike CZ material, this material contains non-critical quantities of oxygen as it is crystallised in a graphite crucible, but on the other hand does contain residual impurities from the crucible walls. Improvements have been achieved here too by appropriate surface coating of the crucible.

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Figure 7.6

%Y Cross-section of a block casting equipment [7]

7.1.7 Sheet Materials

To avoid sawing processes in the manufacture of silicon wafers, activities have for years been concentrated on the production of so-called sheet material. In past decades a multitude of processes have been developed and tested worldwide. With a few exceptions almost none of these got past the laboratory testing stage. There are two reasons for this. For one thing in many cases the required level of purity could not be achieved, as too many impurities were introduced by the apparatus used at the high process temperatures. Secondly, many defects and faults are created in the crystal during the recrystallisation process, due to the high cooling speed which is sometimes required. We will restrict ourselves to the reproduction of two selected processes here.

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7. I. 7. I The EFG Process

The EFG process (Edge defined Film Growth), based on the principle shown in Figure 7.7 [9], consists of an octagonal tube being drawn from a silicon melt using suitable graphite templates. The edge length of the octagonal segments is a little above 100 mm, giving a total tube diameter of approximately 30 cm. The thickness of the tube wall and thus the thickness of the slices produced of a few tenths mm is set by the shape of the graphite capillary as well as the prevailing temperature and pulling speed (some cm/min). Tubes with a length of 4-5 m can be pulled using this technique.

Crystal Growth of Silicon Ribbons

LI

level in crucible

Figure 7.7 The principle of an EFG plant [9]

The separation of individual wafers - dimensions lOOx 100 mm2 - is by laser cutting. The material itself is polycrystalline, as in block cast silicon. Solar cells in pilot production have achieved efficiencies of 13% to 15%. This corresponds to the efficiency of solar cells made of polycrystalline block cast Si material as well as monocrystalline CZ material in industrial production.

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7. I . 7.2 The SSP Process

The SSP process (silicon sheet from powder) as shown in Figure 7.8 [lo] consists of silicon powder being placed in a quartz form (e.g. the above mentioned spherical silicon powder can be used). In the first stage the powder is sintered together. In the second stage the now self-supporting foil undergoes a zone melting process. A polycrystalline material with very large grains (millimetres to centimetres) is created. The melting process is brought about by focused, incoherent light. Silicon sheets with a thickness of approximately 400 pm can be produced in this manner. Solar cells have been produced on a laboratory scale with an efficiency of approximately 13%.

Figure 7.8 Silicon foil production by the SSP process [ 101

To conclude Section 7.1 we should mention the work which was aimed at replacing expensive gas phase refractioning processes for the manufacture of high-purity starting silicon by metallurgic preparation methods (leaching, gas blowing, etc.). Despite great efforts, the necessary purity has never been achieved using these methods. The efficiencies of solar cells made of this material are too low. This work was stopped a few years ago.

7.2 Si SOLAR CELL TECHNOLOGY

In this section we want to demonstrate the technologies for producing solar cells from crystalline silicon. We can divide this field into four areas, i.e.

Technologies for the production of p-n junctions. Technologies for the growing of SiO, layers. Technologies for the production of electrical contacts. Technologies for the reduction of reflection on the silicon surface,

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We also briefly describe the necessary auxiliary technologies such as etching and cleaning techniques and photolithography.

7.2.1 Technologies for the p-n Junction

In semiconductor technology two basic procedures are known for the production of p n junctions. These are diffusion and ion implantation techniques. The latter however only plays a minor role in the production of solar cells due to the high costs associated with it. It is only used in the manufacture of specialised solar cells for satellite technology. The third process, the alloying technique, was the dominant technology in early semiconductors at the beginning of the 1950s. However, it is rarely used today due to the wide dispersion of electrical parameters and high costs. We will therefore only describe diffusion technologies.

7.2. I . I Difflusion Technologies and the Theory of D ffusion

The diffusion of solid substances in the Si solid obeys Fick's second law, which in one-dimensional form reads:

(7.2.1)

where

N(x, t)

D

We will consider two solutions to this partial differential equation here.

is the concentration of diffusing substances at point x and time t ; is the diffusion coefficient specific to each material, which depends very strongly on temperature.

7.2. I. 1.1 The dopant source is inexhaustible. The concentration on the surface (N,) is thus constant throughout the entire diffusion process. The concentration within the silicon is only dependent upon diffusion time and diffusion temperature (Figure 7.9).

N , = constant where 0 < t < 00 and N(x) = 0 where t = 0 and 0 < x < 00

where N, is the surface concentration.

The Complementary Error Function Distribution

The boundary conditions for the mathematical solution are:

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Figure 7.9 Concentration distribution of dopant for an inexhaustible dopant source

The solution for the differential equation (7.2.1) is thus

X

(7.2.2)

The expression in parentheses is called the complementary error function distribution, and is represented by the letters erfc, thus

X N ( x , t ) = N, erfc - 2 fi7

(7.2.3)

Figure 7.10 shows the relationship between the ratio of concentrations (NJN,) and the argument x i (Dt)"'.

To calculate the penetration depth xj of a p-n junction, we first find the ratio of background concentration in the base silicon to surface

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Figure 7.10 Concentration distribution according to the complementary error function distribution

concentration. If this value is that

for example, we find from Figure 7.10,

X - = 5.4 $7

and thus

x. = 5.4 $7 I

(7.2.4)

(7.2.5)

choosing diffusion constant, temperature and time leads to the penetration depth.

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7.2. I. I. 2 In this diffusion process there is an exhaustible dopant source on the surface with a concentration Q (cm-*). The solution of the partial differential equation (7.2.1) for this reads:

Gaussian Distribution

N ( x , t ) = - Q exp - ( x / ~ J D ; ) Z (7.2.6) & D t

where the surface concentration Ns is found to be

Q S , E i

Ns =- (7.2.7)

and is thus dependent upon the diffusion parameters. Figure 7.11 shows this relationship. As is clear, the desired surface concentration (high or low) can be adjusted - as discussed in Chapter 6.

1 f T

x-------+ Figure 7.1 1 Concentration profiles of dopants with an inexhaustible diffusion

source

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7.2.1.1.3 Diffusion CoeSficient The diffusion process takes place in semiconductors according to two main principles. The diffusing substances can move across interstitials or diffuse via vacancies. The speed of migration is very variable, but in both cases is strongly dependent upon temperature. The quantative relationship is given by the formula (7.2.8):

D = D o exp(-AlkT) (7.2.8)

where for a given substance Do and A are constant over wide temperature and concentration ranges. The variable A is also called the activation energy.

The functional dependency of coefficients on temperature can be represented in the form of a so-called Arrhenius curve (log D + l/T). Figure 7.12 shows the diffusion coefficients for many elements in relation to temperature [l l] . Most of these values were determined in the early 1950s [12].

We see from Figure 7.12 that metals (e.g. Ti, Ag, Au) have higher diffusion coefficients than dopants (e.g. Ph, B, As) by several orders of magnitude, and therefore diffuse significantly quicker in silicon (substances such as Cu and Fe not shown in this representation diffuse even quicker). Therefore semiconductor technology requires extreme cleaness of laboratory and process equipment. We also see that due to the exponential temperature dependency of diffusion coefficients, the process temperature must be very strictly adhered to.

Diffusion time, on the other hand, is much less critical, because the penetration depth according to the formula (7.2.5) is proportional to dt.

7.2.1.2 Diffusion Technologies

In the diffusion process and the subsequent oxidation process, an electrically heated tube furnace with a quartz tube is usually used. In solar cell technology diffusion temperatures vary between 800°C and 1200°C. The silicon slices to be treated are put into the constant temperature zone of the furnace in quartz trays. Temperature consistency across the zone length and over the diffusion times is better than 1"C, achieved using modem diffusion equipment. Figure 7.13 shows the principle of the standard diffusion process.

Both gaseous and liquid diffusion sources are used. Nitrogen, argon and oxygen are used as carrier gases in the so-called open tube process. The quantity and mix ratios must be adjusted according to the application, but require very precise control.

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l / T - Figure 7.12 Temperature dependency of the diffusion coefficients of different

elements in silicon (according to Landolt-Barnstein)

The diffusion process requires, in addition to precise control of time and temperature, certain heating and cooling phases. Slow cooling can be used to produce a getter effect [13]-[14]. In this case impurities, mainly metals, wander to the surface due to the drastic reduction of their solubility in silicon with the sinking temperature, and their still high diffusion rate at low tempzratures. They are absorbed there and are therefore harmless as recombination centres.

The diffusion processes used in solar cell manufacture are described in detail below.

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Wafers on carrier

# bh - Valvesand flow meter

Wafers on carrier

I!@, I f lrkDopant liquid

Figure 7.13 Principle of the diffusion process (open tube process)

7.2.1.2. 1 Emitter Diffusion Processes Since the starting wafers for solar cells are almost always doped with boron and are thus p-conductive (concentrations from 10” to l O ” ~ m - ~ ) , an n- doped emitter is created using phosphorus.

Gas diffusion processes are used almost exclusively, whereby phosphorus is introduced into the diffusion furnace either in the form of phosphine (PH) or gaseous phosphorus oxychloride (POCI,). The latter is introduced using nitrogen as a carrier gas. At the high temperatures of approximately 800°C the dopant gases react with the surface of the silicon when oxygen is added. In accordance with Si + 0, => SiO, silicon dioxide is produced on the surface and secondly, phosphine is converted according to

2PH + 3 0 , -+P,O, +H,O (7.2.9)

to phosphorus pentoxide. The P,O, created combines with the silicon dioxide growing on the

silicon surface to form liquid phosphorus silicate glass. This glass then becomes the diffusion source.

The process using POC1, is similar. P,O, is also created in this process. In addition, chlorine is released. Its significance for the cleaning of silicon surfaces is well known in semiconductor technology as chlorine creates volatile metal compounds [15].

In practice, however, phosphorus diffusion shows deviating behaviour from the simple theory for the case of low penetration depth. In the case of an inexhaustible source, the diffusion profiles obtained do not match the above diffusion theory. Concentration profiles are obtained which are more like those shown in Figure 7.14.

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Figure 7.14 Phosphorus profiles at diffusion temperatures of 950°C in relation to diffusion time [ 161

This anomalous behaviour has been explained by various authors [ 161-[ 191, by the fact that the diffusion coefficient rises sharply with high concentrations and only at a certain low concentration does it behave according to the familiar diffusion coefficients. This effect has the disadvantage for solar cells that a dead layer is created, as already mentioned. A dead layer of, for example, 0.3 pm depth will reduce efficiency to approximately 10% (relatively).

A dead layer can be impeded using the following diffusion process for reducing the surface concentration of the emitter. In a double diffusion process [20],[21] the first diffusion step is a predisposition coat - a low level diffusion of phosphorus at a temperature of approximately 800°C. Then the phosphorus-silicate glass layer is removed by chemical means. In a second diffusion step - this time at a temperature of 1000-1 100 "C - the desired penetration depth of the phosphorus is achieved. A diffusion profile

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is obtained which follows the Gauss distribution. Both diffusion steps are coordinated with each other in temperature and time, such that instead of the saturation concentration of approximately 10” cm”, surface concentrations of approximately 10’’ cm-, can be produced.

7.2.1.2.2 As we have already mentioned, a so-called back surface field (BSF) is necessary for high efficiency solar cells.

The required pi doping is achieved by the diffusion of boron. BBr, can serve as the boron source for this purpose, which can be handled in a very similar manner to POCI,.

In industrial practice, aluminium is used for the creation of a BSF. The technological doping process is that aluminium is introduced onto the surface using vacuum evaporation or in the form of an ink by screen printing, and alloyed at approximately 800°C (eutectic point 577°C). At this temperature the aluminium partially diffuses and creates a p+ doping. The recrystallised layers also act as good getter sinks.

The Diffusion Process for the Back Surface Field

1.2.2 Oxidation Technologies

The thermal oxidation process (dry, i.e. without the addition of water vapour) is, as mentioned above, according to the following formula:

Si + 0, +SiO, (7.2.10)

Oxygen diffuses through the SiO, layer which is forming. With this process there is therefore no saturation thickness although the rate of growth slows with the increasing thickness. At the outset the layer thickness grows in proportion to time, at greater layer thicknesses (>1 pin) approximately in proportion to the square root of time. An SiO, layer requires a silicon layer of approximately 45% of its own thickness.

Wet oxidation (with water vapour) takes place according to the formula

2Si +O, +2H,O +2SiO, +2H, (7.2.1 1)

The rate of growth in this case is significantly higher than for dry oxidation, since the reaction process is clearly stimulated by the hydrogen. Figure 7.15 shows the influence on the SiO, layer thickness of dry or wet oxidation as a function of the reaction time and the oxidation temperature P21.

Other influences can also alter the growth rate of SiO,. The oxidation of highly doped silicon (>lozo cm-’) is around 20% faster. Likewise the oxide grows approximately 30% faster on the (111) orientated surfaces than on

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t i h l 1 10

10

1

xO [PI

10-1

10-2 10 102 103

t I min 1 Figure 7.15 The oside layer thickness with dry and wet oxidation

the (100) surfaces. The addition of chlorine ions during the oxidation process is also

beneficial [23],[24]. As well as the removal of traces of metal by volatile metal chloride, alkali atoms such as sodium are also removed and the passivating characteristics of the SiO, layer thus improved. Chlorine can be added to the process, e.g. by the addition of trichloroethane (TCA); (formula C,H,CI,). The reaction for this oxidation process is

C,H,Cl, + 2 0 , +3HC1 +2CO, (7.2.12)

and

4HC1 + O , +2H,O +2C1, (7.2.13)

When TCA is added the supply of oxygen must be ensured, as otherwise the highly poisonous phosgene may be formed because TCA is

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now replaced by trans-LCD (also contains chlorine) for environmental protection. The results are very similar.

New research - including that in our institute - into the use of SiO, as a passivation layer in solar cells has yielded the following sumniarised results:

Dry oxidation under high oxidation temperatures yields the lowest values for the interface trap density and thus very low surface recombination rates. The density can be reduced even further by an annealing process at approximately 45OOC (preferably in forming gas). The lowest densities are achieved with (100) surfaces.

The masking effect of an SiO, layer in the diffusion process relies upon the fact that the rate of diffusion of many diffusants in silicon dioxide is lower by orders of magnitude than in silicon itself. The required SiO, layer thickness for different diffusion temperatures and times is shown in Figure 7.16 for the two diffusants boron and phosphorus [25]-[26]. It is evident that boron is masked by significantly thinner SiO, layers than is phosphorus.

Fkherniore, SiO? is used for masking in alkaline etching processes as well as for surface texturing. We will return to this subject in Section 7.2.5.2.

1

x O [ p m l

10-1

10 -2

Figure 7.16 Necessary oxide layer thickness for complete masking against boron and phosphorus [ 251 ,[ 261

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7.2.3 Auxiliary Technologies

Before examining in inore detail the technologies of solar cell surface treatments, such as metal coating, antireflection coating and texturing, we wish to comment upon the auxiliary teclinologies such as etching, cleaning and photolithography.

7.2.3. I Etching and Cleaning Techniques

Various different etching and cleaning techniques are necessary for the manufacture of semiconductor devices.

The surfaces of the silicon wafers must be free of contaminants as far as is possible. These contaminants may be of molecular, ionic, or atomic nature. Residues of the lapping, polishing and photoresist processes are, for example, of molecular nature. Contamination by ions usually occurs by the absorption of ions from the etching solution, whilst heavy metals such as silver, copper and gold have an atomic character.

The most widely used procedure for surface cleaning is currently the so- called RCA cleaning 1271.' This process is based upon the use of hydrogen peroxide (H202) firstly as an addition to a weak solution of ammonium hydroxide (NH,OH), and secondly hydrochloric acid (HCI). The cleaning process is as follows: After preliminary cleaning in hot dilute nitric acid (HNO,) and etching in buffered hydrofluoric acid (HF) the silicon wafers are exposed to the peroxide solution at 80°C. Due to the severe oxidising effect the organic residues are oxidised and simultaneously a large part of the metallic traces complexed. In the subsequent cleaning stages - in the hydrochloric acid again at 80°C - the remaining traces of metals are converted into volatile metal chlorides and thus removed.

Etching the silicon dioxide layers occurs mainly in a weak solution of hydrofluoric acid. Depending upon the desired etching rate the HF-solution can be buffered with ammonium fluoride (NH,F).

Isotropic ,etching of silicon occurs in a solution of nitric acid and hydrofluoric acid. The nitric acid oxidises the silicon to SiO,, which is then dissolved by the hydrofluoric acid. The mix ratio determines the etching rate and the surface structure created. To obtain, for example, a very smooth, almost mirror finished surface, or a very low dissolve rate, the etching mixture can be buffered with acetic acid (CH,COOH) and phosphoric acid (H,PO,). Comprehensive information can be found in [28].

This cleaning process is named after the company RCA.

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Following all cleaning processes rinsing with deionised water must take place as the final stage. The current state of the art is a specific resistance of 17-1 8 MRcm (near the theoretical value due to natural dissociation).

A separate branch of the chemical industry developed decades ago concerned with the preparation of the necessary chemicals in extremely pure form. As well as pure chemicals a multitude of compounds with different mix ratios are available. All processes are performed in ‘clean room s * .

7.2.3.2 Photolithography

Photolithography is used to structure the silicon dioxide used in the various masking processes as described above. A thin film of photoresist is spun in a yellow area - due to the light sensitivity of the photosensitive resist - on the silicon wafer. Depending upon viscosity and revolution speed (some thousands of revolutions per minute) a homogeneous film is created with a thickness of 0.5-2 pm. After the film has been dried, it is passed through suitable masks and illuminated with short wavelength light (approximately 0.4 pm). This process occurs in mask aligners, which permit structural precision of about 1 pm.

In the case of a positive resist, the long molecule chains are cracked at the illuminated points and thus prepared for dissolving in alkaline solutions. After successful etching of the SiO, layer the remaining resist is removed using acetone.

In the case of a negative resist the illuminated points remain. It is used if silicon is to be etched locally (positive resist is not resistant to this). The resist is dissolved in hot chemicals.

1.2.4 The Metallising of Solar Cells

Of the many contact technologies which are used for semiconductors, we only wish to describe those which are used in solar cell technology. We first examine the structuring of the finger grid.

7.2.4.1 The Structuring of the Finger Grid

Three methods are used for the structuring of the contact finger. In the first a vacuum evaporation template with a perforated strip pattern is used, which has the disadvantage that the smallest finger width is approximately 100 pm - or at best 50 pm. If narrower contact fingers are required to reduce shadowing, the photoresist technique must be used.

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Photoresist Solvent Metal

I P P+ I !----- /- - -.

Mask illumination Photoresist development

Evaporation of after dissolution c.g. of photoresist

Ti, Pd, Ag

Figure 7.17 The principle of the ‘lift-off process

As shown in Figure 7.17, the required sequence of layers is vacuum evaporated as a complete layer upon a structured photoresist. The crucial point is that the photoresist layer has to be thicker than the vacuum evaporated metal layer, so that the edges can be accessed during the dissolution of the photoresist. The simultaneous use of ultrasound is helpful during dissolving. In this way it is possible to produce structures which are only some pm wide.

The third method, screen printing, in which metal paste is used, dominates in a wide range of production techniques as it is particularly cost effective, but the maximum finger width is about 100 pm.

7.2,4.2 High Vacuum Evaporation Technologies

The most up to date method for contacting is the vacuum evaporation of metal layers, in many cases in several layers [2S]. The contact material to the semiconductor is selected from the point of view of the required banier height. Since, as described in Chapter 6 , the surface concentration of dopant must be low ( -10”9 crns3) in a high efficiency solar cell to reduce the surface recombination velocity, almost only titanium, with a barrier height of approximately 0.5 eV can be considered. Owing to its low vapour pressure and the necessary high temperature almost exclusively electron beam evaporation is used.

Experiments involving theniial evaporation from a tungsten boat have been carried out to determine how high the negative influence of the electron beam evaporation is on the SiO, passivating layer. The sharp

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increase in the surface recombination velocity which occurs can, however, be completely eliminated by subsequent annealing under forming gas [29].

As well as its low barrier height, titanium also has the advantage that it belongs to the easily oxidizable metals and thus can reduce thin SiO, layers whilst retaining good adhesion to the silicon. The normal layer thickness is 30 to 50 nm.

Titanium must, however, be protected from external oxidation by another metal. Metals can be considered which themselves barely corrode and which are compatible with the contact material, i.e. do not diffuse too highly with the bonding agent and the subsequent covering material. Nickel and palladium are suitable partners, these are deposited in approximately the same thickness as titanium (m50 nm).

For the external contacting a third metal layer with good conductivity and very low corrosion must be evaporated. Silver is preferred in many cases. The silver layer is evaporated with a thickness of approximately 0.1 pm. The subsequent sintering at a temperature of approximately 400°C under forming gas ensures a good adhesion between the contact layers. For the necessary reduction of the electrical resistance of the contact finger it is reinforced by the electroplating of Ag. Approximately 8 pm Ag is grown onto the approximately 15 pm wide fingers of high efficiency solar cells.

In the case of a high emitter surface concentration (approximately lozo ~ m ' ~ ) Cr-Ni contacts also give very good results. The back surface contact on high efficiency cells consists of vacuum evaporated aluminium, which produces a very good ohmic contact to the p-base material due to its p-doping effect. In the case of solar cells with a local BSF, the silicon dioxide on 98% of the surface is coated with aluminium. This functions as a very effective optical reflector.

7.2.4.3 Thick Film Technology

The advantage of thick film metal coating using the screen printing process, which is, as mentioned, widespread in industrial solar cell manufacturing [30]-[32], lies on the one hand in the low investment cost and on the other hand in the scope for automating the process. The metallic pastes used have, in addition to an organic binder which determines viscosity, a flux, also known as sintered glass. Typically, such pastes contain, in addition to 70% Ag in the form of platelets a few pm thick and approximately 5 to 15 pm wide for the front contact, approximately 2% sintered glass. The sintered glass is composed of lead oxide, lead-boron-silicate or zinc-boron-silicate, the rest is binder. After depositing, the layer is sintered at temperatures of approximately 600°C. The sintered glass components melt and dissolve a small layer of silicon. At the same time, this melt is enriched by silver. Upon cooling a

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Si Solar Cell Technology 1.59

recrystallised Si layer is created as with normal alloying, which contains a high proportion of Ag and thus creates a good ohmic contact. This process only gives sufficiently low contact resistances at surface concentrations on the n+ emitter of approximately 10'' cm-3 .

Only aluminium (in the form of a paste) is used for the manufacture of back surface contacts. Aluminium has two advantages. It forms alloys at 577°C (eutectic point) and has a relatively good solubility with concentrations of approximately 10'' cm" in silicon. Thus in the recrystallised layer formed upon cooling a p+ doping is achieved and thus a BSF created. Normally sintering takes place at temperatures around 800°C since the best results are achieved thus. The significant increase in open circuit voltage observed in practice at high sintering temperatures can be explained by the above mentioned gettering effect. Since A1 is not directly solderable, a silver-palladium paste is also sintered onto this layer [331.

1.2.5 Antireflection Technologies

7.2.5. 1 Applying an Antireflection Coating

High vacuum evaporation technologies and thick film techniques are also used for the manufacture of antireflection coatings. For a single layer antireflection coating, titanium dioxide (TiO,) is used almost exclusively. Its refraction index can be adjusted within a specific range during the evaporation process by the selection of evaporation rate and the addition of small quantities of oxygen. We thus obtain values of n=1.9 to n=2.3 with very good transparency. The latter is a very important prerequisite for high efficiency.

Thick film technologies are also used in mass production for costs reasons. A paste containing titanium dioxide compounds is deposited onto the surface of the silicon, either by spinning on or by the screen printing technique. Finally, sintering takes place at temperatures of 600-800°C.

These antireflection processes can be linked to the above metal coating by screen printing. The TiO, paste previously dried at temperatures around 200°C has silver paste added to it for the grid structure. Both are then simultaneously sintered. As the thickness variance of the antireflection layer only influences total reflection behaviour slightly (AM 13) , then this gives good antireflection characteristics.

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160 Crystalline Silicon Solar Cells

7.2.5.2 The Manufacture of Textured Silicon Surfaces

To produce such structures the chemical-physical effect is used, that the etching rate of silicon in an alkaline solution is dependent upon the crystal direction [34],[35]. For example, the dissolution rate of silicon in the (111) crystal orientation is one or two orders of magnitude smaller than in the (100) direction. The reason for this is that in the (111) plane for the cubic face centred diamond lattice of silicon there is only one free valence to the surface per atom, whereas for the (100) direction two valences are available. It is therefore plausible that a considerably higher energy expenditure is required to dissolve an atom from the (1 11 ) direction as for the (100) direction. Therefore in high efficiency solar cells the (100) crystal orientation, vertically to the surface, is selected.

The etching process takes place in an alkaline solution at approximately 70°C. Weak solutions of KOH or NAOH with a concentration of 10%-30%

Figure 7.18 Electron microscopic picture of silicon wafers with random pyramids

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Si Solar Cell Technology 161

are normal. To achieve the desired pyramid structures, the silicon surface must be first fitted with a corresponding SiO, stripe structure, which, as mentioned, will not be attacked by the alkaline solution. As the etch depth and of course also the undercut is dependent upon the distance between the individual SiO, strips and their width, these parameters must be carefully matched to each other. Etching continues until the two neighbouring sides underneath make contact. Inverted pyramid structures have become dominant.

As mentioned, a reduction in reflection is achieved if the deposited SiO, passivating layer has a thickness of 100 nm, so that with a refraction index n=l.46 the h/4 condition is fulfilled.

References

[ 11 Diet1 J., Helmreich D. and Sirtal E., Crystals: Growth, Properties and Appli- cations, Vol. 5 , Springer-Verlag, 1981, p.57

Zulehner W. and Huber D., Crystals: Growth, Properties and Applications, Vol. 8, Springer-Verlag, 1982, p. 92

Czochralski J., Z. Phys. Chernie 92, 1977, p. 219

[2]

[3]

[41 see P I , p.4

PI see P I , P. 6

[6] see [l] , p. 73

[7] see [ l ] , p. 67

[8] Schtitzel P., Zollner Th., Schindler R. and Eyer A., Proc 23rd IEEE PV Spec. Con$, Louisville, Kentucky, 1993, p. 78

[9] Wald F. V., Crystals: Growth, Properties and Applications, Vol. 5 , Springer-Verlag, 198 1, p. 157

[ 10) Eyer A., Schillinger N., Reis I. and Rtiuber A., Cryst. Growth, 104, 1990, p. 119

[ 111 Landolt-Bornstein Vol. 17 Part C Springer-Verlag, 1984, p. 494

[ 121 Fuller C. S. and Ditzenberger J. A., J. Appl. Phys., 27, 1956, p. 544

[13] Goetzberger A. and Schockley W.,J. Appl. Phys., 31, 1960, p. 1821

[ 141 Clays C. L., Proc. 2nd Brazillian Workshop on Microelectronics, Sao Paulo, 1980

[ 151 Rouen R. S. and Robinson P. H., J . Electrochem. Soc., 119, 1972, p. 747

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162 Crystalline Silicon Solar Cells

1301

Tsai S. C., Proc. IEEE, 57, 1969, p. 1499

Fair R. B. and Tsai S. C., J . Electrochem. Soc., 127, 1977, p. 1107

Jeppson K. 0. and Anderson D. J., J . Electrochem. SOC., 136, 1986, p. 397

Hu S. M. et al., J. Appl. Phys., 54, 1983, p. 6912

Knobloch J., Aberle A. and Vofl B., Proc. 9th EC PV Solar Energy Conj , Freiburg, Germany, 1989, p. 777

Blakers A. W., et al., Proc. 9th EC PV Solar Energy Conj , Freiburg, Germany, 1989, p. 328

Wolf H. F., Silicon Semiconductor Data, Pergamon Press, 1976

Convell E. M., Proc. IRE, 46, 1958, p . 1281

Cosway R. G. and Wu C. F., J . Electrochem. Soc., 132, 1985, p. 15 1

Sah C. T. et al., J. Phys. Chem. Solids, 11, 1959, p. 288

Morinche S. and Yamaguchi S., Jpn. Appl. Phys., 1, 1962, p. 3 14

Kern W. and Puotinen D. A,, RCA-Review, 1970, p. 187

Bogenschutz A. L., Atzpraxis f i r Halbleiter, Hanser Verlag, 1967

Kopp J., Knobloch J. and Wettling W., Proc. 11th EC PV Solar Energy ConJ:, Montreux, 1992, p. 49

Cheek C., et al., IEEE TED, 31, 1984, p. 602

[3 11 Mertens R., et. al., Pmc. 14th EC PVSolar Energy Conj , San Diego, 1980, p. 1347

[32] Dubey G. C., Solar Cells, 15, 1985, p. 1

[33] Ralph E. L., Proc. 11th IEEE PVSpec. Conj , 1975, p. 315

[34] Heuberger A., Mikromechanik, Springer-Verlag, 1989

[35] Price J. B., Semiconductor Silicon, Princeton, NJ, 1983, p. 339

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Selected Solar Cell Types

In the first part of this Chapter we will describe four specific solar cell configurations made of crystalline silicon. These are:

Cells for concentrator applications. Cells manufactured according to MIS technology [Metal Insulator Semiconductor]. Cells made of polycrystalline silicon. Cells with thin base layers [20-50 pm].

In the second part of this Chapter we will concentrate on some thin film solar cells made of other semiconductor materials, i.e.

Cells made of amorphous silicon (a-Si). Cells made of semiconducting compounds e.g. gallium-arsenide (GaAs). and cadmium-telluride (Cd-Te). Cells made of copper-indium-diselenide, known by the abbreviation CIS. We will conclude with some consideration of tandem cells and dye

sensitized solar cells.

8.1 CRYSTALLINE SILICON SOLAR CELLS

8.1.1 Crystalline Silicon Concentrator Cells

The concentration of sunlight brings two advantages for solar cells. Firstly, the required area can be reduced according to concentration, so the cell can be based on good monocrystalline silicon and use costly technologies. As concentration rises, cell cost becomes less of a factor for the solar array. Furthermore, open circuit voltage increases with the higher short circuit current of the cell, which in the first approximation is proportional to

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164 Crystalline Silicon Solar Cells

radiation power. This effect is intensified because due to the high injection of charge carriers, their diffusion lengths are greater than in the case of low injection (one sun). Thus the saturation current is reduced and therefore open circuit voltage increased. At 100-fold concentration an increase in efficiency of 20% (relatively) is achieved. For even higher radiation, however, the influence of Auger recombination becomes so noticeable due to the high carrier density that the increase in efficiency flattens out considerably. Sinton et al. [ l ] redefined the Auger coefficient from the dependence of open circuit voltage as a function of radiation, obtaining a value approximately four times larger than was previously realised.

First generation concentrator cells were a development of conventional solar cells with a finger structure on the surface facing the light. The main problem was the minimising of serial resistance, which is primarily determined by the layer resistance of the emitter and the resistance of the contact finger. The distance between fingers therefore had to be very low and to minimise shadowing, the fingers had to be very narrow.

Figure 8.1 The structure of an IBIC cell for concentrated light [ 5 ]

A word on the history of the solar cell. In 1977 Burgess et al. [2] introduced a cell with what was at the time a high efficiency of 15% at 50- fold solar radiation. In 1980 Khemthong et al. [3] increased this value to over 20% (at 40 suns). A decisive improvement was achieved by Sinton et al. [4] and Swanson et al. [5 ] when they implemented and improved the

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Selected Solar Cell Types I65

structure suggested by Lammert et al. [6] in 1974, the IBC [Interdigitated Back Contact]. As the name suggests, both n+ and p+ diffusion structures (Figure 8.1) and therefore also both connection contacts lie on the back of the cell. This structure has the following advantages:

There is no shadowing of light by the finger structure. The metal contacts can be broad and take up almost the entire back surface. They are therefore of very low impedance, thus achieving a very low series resistance. The penetration depth of n+- and p+- layers are non-critical. There are no losses due to a dead layer. A disadvantage is that the diffusion length in the base of the cell must

be very high (if possible five times greater than the cell thickness), and the surface recombination on the side facing the light must be extremely low. Short wavelength light also increased the surface recombination velocity on the front surface and caused degradation in the first cells. The problem was solved, however, [7] by applying a very thin (a few tenths pm thick) p+ zone with a surface concentration in the region of approximately 10" cm-3 to the side facing the light. A disadvantage of this cell is that the nt- and p'-connections must be insulated from each other at the points of contact in a module.

Efficiencies of approximately 27% are achieved with this type of solar cell at 100 suns. For lower concentrations around 50 suns, a cell has recently been developed in which the p+ layer is again applied to the side facing the light. Efficiencies of 26% have been achieved with these cells PI.

The application of concentrator cells is limited to use in sun rich areas. The problems of cost effective light concentration and sun tracking must be solved.

This cell, in a slightly modified form, has proved that it can be used under normal sunlight conditions. In the World Solar Challenge, the race for solar powered automobiles over 3000 km in Australia from Darwin to Adelaide in 1993, the company Sun Power Corporation, California, in cooperation with Honda, Japan, manufactured 7000 solar cells of this type [9]. The cells had dimensions of 7.3 x 2.4 cmz. They were manufactured from Fz-Si with a resistivity of approximately 50 Rcm to achieve a very high carrier lifetime of up to 2 ms. The cell thickness was 160 pm, reduced using etching techniques. The contact layout was altered from the original design. It consisted of many interlinked contact fingers with two longitudinal collecting contacts. For the electrical insulation of the contacts, as in many power semiconductors, the plastic polyimide is used.

In the manufacture of the 7000 cells a yield of ~ 9 0 % was achieved referred to a cell efficiency of >20%. The average cell efficiency was

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166 Crystalline Silicon Solar Cells

21.1%. This is an exceptionally good result. The solar powered car fitted with with these cells won the race.

8.1.2 Biracial Solar Cells

If, instead of the very wide interdigitated fingers, an interdigitated finger grid is deposited with a similar layout, but narrow like the high efficiency solar cells, as shown in Figure 8.1, then this cell can be illuminated from both sides. Various laboratories have worked on this type of cell [lo]-[13]. Such a cell, for example, is capable of collecting diffused light from the back surface, thus increasing total efficiency. One variant of this cell consists of a cell with an n+ layer on its back surface. This gives a structure similar to a transistor. Cells built in our Institute according to this principle have achieved efficiencies of 21.4% when illuminated on the non- metallised side (under AM13 global) and 20.2% when illuminated on the grid side (somewhat lower due to shadowing). This is the first bifacial solar cell with efficiency on both sides >20%. These high, and very consistent, values show both that the two sided surface passivation is very effective, and that the carrier lifetime in the base material must be very high. Both indicate a high standard of technology.

8.1.3 Buried Contact Solar Cells

Another type of high efficiency solar cell is the Buried Contact Si solar cell shown in Figure 8.2.

This structure was first suggested in 1985 [14], and is patented in many countries. The significant difference in this cell is the buried contact. Using laser technology, grooves of approximately 20 pm wide and up to 100 pm deep are cut in Si wafers texturised according to the principle of random pyramids to hold the grid fingers. The etching process which follows removes the silicon destroyed by this process. These grooves provide two advantages. Firstly, shadowing is reduced significantly when compared with the normal grid structure of commercial solar cells. Values of only 3% surface shadowing are obtained. Secondly, the grooves can be filled with contact material. Thus, approximately the height of the grooves and thus the metallisation can be five times its width [15]. In conventional cells, even vacuum evaporated contacts and contacts reinforced by electrodepositing, the ratio is 1:1, i.e. the metal contact height is equal to its width. The five-fold height means a reduction in the resistance of the contact finger by a factor of 5 , resulting in a significantly better fill factor. The technology of metallising consists of an electroless deposited nickel contact, which is reinforced after sintering with copper. Since this

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Selected Solar Cell Types 167

Figure 8.2 Cross-section through a buried contact solar cell

technique does not require photomask processes or high vacuum evaporation technologies, and is thus significantly more economic, it is predestined for use in serial production. The double stage emitter is used for the emitter structure, whereby the highly doped n++ film is restricted to the groovss. The p+ back surface field permits higher efficiencies.

Owing to the low process costs, several solar cell manufacturers have bought a licence. It was shown that the manufacturing process was somewhat more economic that the widely used screen printing technique [161,[171.

A further advantage of this cell is the textured back surface, which increases the confinement of light and thus the total efficiency. With this type of cell (large area), average efficiencies of 18% have been achieved in production [ 161. With specific techniques, such as an improved antireflection coating and a local back surface field, efficiencies of up to 2 1% have been achieved in the laboratory [ 181. This beneficial structure is still undergoing further development. In this case, too, attempts are being made to reduce the number of process stages, in particular the high temperature processes, thus achieving more economical solar cells [ 181.

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I68 Crystalline Silicon Solar Cells

8.1.4 MIS Solar Cells

The fundamental difference between the MIS solar cell developed by Hezel and his colleagues and the conventional Si solar cell is the fact that it does not contain a p-n junction (Figure 8.3). The side of the cell facing the light is coated by a very thin (approximately 2-4 nm) thermally grown silicon dioxide film [19]. The finger grid is vacuum evaporated onto this and finally, the entire surface is coated with a silicon nitride film, which may be relatively thick due to its good transparency (some pm). This coating - a dielectric - has four tasks:

Protects against environmental influences. Functions as an antireflection layer. Reduces surface recombination velocity. Creates an n conducting inversion layer in the p semiconductor.

A decisive step towards increasing efficiency was achieved by the use of caesium in this dielectric [20]. Caesium's property of creating stable charges was reported by Sixt and Goetzberger in the early 1970s [21].

Figure 8.3 Cross-section through an MIS solar cell [ 191

One advantage of this solar cell lies in its manufacturing, which does not require any high temperature procedures. The thin SiO, layer is produced at a temperature of approximately 500°C. The number of process stages is low. A disadvantage is that the n-inversion layer has a sheet resistance which is between five and ten times higher than in conventional silicon solar cells. This necessitates a finger structure with very small distance between fingers, which means that the fingers must be very thin due to shadowing. Electrical contacting can therefore only take place using

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Selected Solar Cell Types I69

a high vacuum evaporation procedure. Furthermore, to prevent degradation the cells must be bedded under glass which has been coated to allow the absorption of ultraviolet light. After further improvements [22] 10 x 10 cm2 solar cells have been produced which achieve 15% efficiency.

8.1.5 Polycrystalline Silicon Solar Cells

Figure 8.4 shows a cross-section through a solar cell made of polycrystalline silicon, We described the manufacture of the starting material in the preceding section. The grain boundaries should be as columnar as possible, i.e. they should run vertically to the surface of the silicon wafer. It is clear that parallel grain boundaries severely detract from the formation of a good p-n junction (leakage current, high saturation current).

Figure 8.4 Cross-section through a polycrystalline silicon solar cell

Many publications have appeared on the theory of polycrystalline Si solar cells since 1977 [23]-[27]. Ref. [28] contains a model of the crystal boundaries in polycrystalline solar cells. More recent research has been more concerned with the defects in individual grains, as it has been established that these reduce efficiency [29] much more than do the grain boundaries themselves, if their average distance apart is greater than the average diffusion length by a factor of between five and ten, Such defects can be, for example, the precipitation of impurities and crystal defects such as vacancies and dislocations. One theory of the influence of the variables

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I70 Crystalline Silicon Solar Cells

is that of de Pauw [30]. Three processes have been established to minimise the recombination and efficiency reduction caused by defects and grain boundaries. These are:

Passivation using hydrogen ions Gettering using phosphorus Gettering using aluminium. In the first process, hydrogen ions created in an ion source and

accelerated to 1000 eV are implanted into the - finished - solar cell. The precise mechanism of passivation has not yet been completely explained. However, it has been proved [31],[32], that the free valences, the so-called dangling bonds, are saturated by the stable silicon-hydrogen compounds SiH, SiOH created [33],[34]. This type of hydrogen passivation primarly increases the photocurrent [35],[36].

The second method, the gettering of impurities by phosphorus has already been described in Chapter 6 . According to this, the phosphorus-silicate-glass film traps many impurities during diffusion. When the silicon wafer is cooled from its diffusion temperature (approximately 1100°C) these migrate to the surface due to their dramatic reduction in solubility with decreasing temperatures, thus becoming harmless with regard to recombination. The diffusion rate for these impurities, even in the average temperature range (400-800°C) is known to be considerable (see also Chapter 6). In [37] successful phosphorus gettering in polycrystalline material is described in detail.

Various writers have described in detail the gettering of impurities by aluminium [38]-[40]. According to these, two effects are responsible for gettering. Firstly, the traps at the grain boundaries are saturated and secondly, a p-p+-BSF structure can form on the boundary, because the diffusion rate of aluminium along the grain boundaries is higher by orders of magnitude than in the crystalline material [41]. Recently, some authors have shown [42],[43], that a simultaneous gettering of phosphorus and aluminium provide the best results. A comprehensive overview of defects and their gettering is given by Schindler [44].

The efficiency of polycrystalline silicon solar cells has been continually improved in recent years. With the option of high efficiency technologies, efficiencies of approximately 16% are now being achieved [45]. On a laboratory scale, over 18% efficiency has been achieved [46], although on an area of 1 cm’. Efficiency on this type of small area cannot simply be transferred to larger cells, as in this case the distribution of crystal boundaries and defects plays a significant role.

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Selected Solar Cell Types I71

8.1.6 Crystalline Silicon Thin Film Cells

8.1.6. I Advantages and Requirements

The cost of the solar cell still contributes more than 50% to the cost of the commercial solar module (see Figure 6.1). Of the 50% approximately two- thirds can be attributed to the silicon material itself. Therefore an important target of research and development is to reduce these material costs. In numerous industrial and public institute laboratories, work on thin film solar cells made of crystalline silicon is at the centre of research and development. The thickness of this type of thin film solar cell should total around 10-50 vm. This is much larger than solar cells made of semiconducting compounds, which are described in a later section. In these, thicknesses are in the region of a few pm. Since silicon, unlike the semiconducting compounds described below, is an indirect semiconductor, its suitability for this type of thin film solar cell is limited, due to the low absorption of photovoltaically useful sunlight. There are, however, strong arguments in favour of silicon.

Silicon will never present any resource problems [see Chapter 7, Section 7.1.11. The material is non-toxic both in the operation of solar cells and for disposal purposes. Solar cells made of crystalline silicon do not show any degradation of efficiency. The manufacturing technologies are closely related and linked with the technologies for the manufacture of semiconductor devices, both integrslted circuits and large area high performance semiconductor devices. Therefore the technologies for the production of solar cells from crystalline silicon can participate in the large pool of experience relating to the manufacture of extremely pure starting material and process technologies. In addition to the advantage of low material usage, calculations show that the efficiency of such a thin film solar cell can be increased.

A thin film solar cell made of crystalline silicon, however, places additional demands on manufacturing technologies:

Owing to low absorption in the crystal, the light penetrating into the solar cell must be reflected several times at the inner boundaries and pass backwards and forwards in the Si crystal material, so that sufficient absorption takes place. The light must be locked in (optical confinement).

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I72 Crystalline Silicon Solar Cells

The boundaries (front and back surface) of the solar cell must be very well passivated, to keep the recombination of charge carriers - in particular at the back surface (the side turned away from the light) - as low as possible [electrical confinement]. Unlike in a thick solar cell, significantly more charge carriers are created near to the back surface, where there is a much greater danger of undesired recombination on the surface. Since such a solar cell is not self supporting, the selection of a suitable substrate is one of the most important tasks, after depositing technologies.

Many years ago Loferski [47] and Wolf [48] pointed out the theoretical high efficiency of thin film solar cells made of crystalline silicon. The authors of this book reported the most important requirements of this type of cell in 1984 [49]. The reader is referred to Figure 5.4 in this book, which demonstrates very clearly the potential of a thin film solar cell. A recent review is given in [50].

21

20 n

8 >r '9 W

Y L

.a, 18 0 E W 17

16

15

14

Diffusion length I-,,, (pm) in the base

1 1 1 I 1 I 0 50 100 150 200 250 300

Solar cell thickness (pm)

Figure 8.5 Efficiency in relation to cell thickness, with diffusion length in the base being a parameter

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Selected Solar Cell Types I73

8.1.6.2 The Relationship between Electrical and Cell Parameters

In the following illustration, we show the efficiency in relation to the various cell parameters. These are:

Solar cell thickness. Diffusion length of minority charge carriers in the base. Recombination velocity on the back and front surface. Optical confinement, i.e. the reflection characteristics of the inner surfaces.

8. I . 6.2. I Solar Cell Thickness

Figure 8.5 shows the path of efficiency in relation to cell thickness. The parameters used in the calculation are:

Resistivity of the base 1 Rcm. Surface concentration of the emitter 10” cm-3. Emitter penetration depth 1 pm. Shadowing and reflection losses on the emitter surface 8%. Reflection on the inner emitter surface 90%. Reflection on the inner back surface 95%. Surface recombination velocity at the emitter 1000 cm/s. Surface recombination velocity at the back surface 100 cm/s. All assumed parameters have been realised in high efficiency solar cells. In the investigations which follow, the above values are used, if not

We see from Figure 8.5, that very high efficiency values (for different

In the calculations which follow, we have concentrated on one cell

stated otherwise.

diffusion lengths) can be achieved with cell thicknesses of 20-50 pm.

thickness of 30 pm, which can also be realised.

8.1.6.2.2 Back Surface Recombination Figure 8.6 shows the influence of back surface recombination on efficiency for different base diffusion lengths. High efficiency levels are only achievable if the diffusion length in the base is at least 3-10 times the cell thickness, and the back surface recombination velocity is less than 100 cm/s. Such values can only be realised using high efficiency technologies.

8.1.6.2.3 Recombination at the Emitter Figure 8.7 shows that the emitter recombination must only amount to around 103-104 cm/s for high efficiency. Owing to the low penetration

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174 Crystalline Silicon Solar Cells

21

20

19

18

17

16

15

14

13

. * I @ I I , , ( , , ( I ,

' ( 4

' ',' *, ,300 - -

==..... , . . . . . . . . 106' b. '*, * '

- '. * . *'. . Diffusion length 45

* ' *., in the base urn) .. -

\'* 8' i.

- r'. 30 8.. :

- -

10' 102 103 104 105 106 Back surface recombination Sb& (cm/s)

Figure 8.6 The influence of back surface recombination for cell thickness 30 pm with diffusion length in the base being a parameter

depth, only a small part of the total photocurrent is generated in the emitter. Lower recombination values could not be realised in any case, due to the high doping in the emitter. The illustration demonstrates very clearly the importance of good electrical confinement. Recombination at both surfaces must be suppressed as far as possible.

8.1.6.2.4 Optical Confjnement In Chapter 6 , Section 6.3.2 we considered this problem in detail. We once again refer you to references [28]-[30] in Chapter 6. Further details are also provided in reference [49] for this section. Figure 8.8 shows the high influence of inner surface reflection characteristics on efficiency. Efficiency increases from around 17% without inner reflection to almost 20% with very good reflection characteristics. The question of how high back surface reflection can be achieved in thin film solar cells has still not been answered.

The above analyses have also been carried out for thin film solar cells with a thickness of 5 pm. The relationships which were found were naturally similar. A diffusion length of 50 pm is adequate for good

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Selected Solar Cell Types 175

c 20

25 t

*!2 16 0 E W

14

12

10

c I

10' 102 103 104 I 05 106 Emitter recombination Sfront (cm/s)

Figure 8.7 The influence of recombination on front and back surface (electrical confinement) on efficiency

efficiency, instead of the 300 pm required for 30 pm cell thickness.

influences; Shack - recombination, and Rback - back surface reflection . The results of the analyses are summed up here for the two dominant

Cell thickness 30 pm 5 Irm

Shack 2 lo6 cm/s (no BSF) q = 13% 10% A.

Shack = lo4 cm/s average passivation q = 16% 14% Shack = 10' LBSF structure q = 20% 16%

B. Rback IOW - 0.4 q = 17% 12% Rback very good - 0.9 T l = 20% 16% These considerations of the efficiencies of thin film silicon solar cells

have been confirmed experimentally. With a 50 pm thick layer of monocrystalline silicon, grown epitaxially onto a insulating substrate, solar cells have been created in our institute with an efficiency of 19.2% [51].

As shown in Figure 8.9 an insulating SiO, layer is implanted onto a silicon substrate. On top of this a layer of approximately 45 pm thick monocrystalline silicon is epitaxially grown. Due to the insulating

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176 Crystalline Silicon Solar Cells

20.0

19.5

- 19.0 $

18.5 v

a, 0 .-

E 17.5

17.0

0.9.. 0'

#'

Reflection coefficient on the /'

inside of the front surface /

16.5 I I 1 I I

0.0 0.2 0.4 0.6 0.8 1 .o Reflection coefficient on the inside of the back surface

Figure 8.8 Influence of optical confinement (inner surface reflection) on efficiency

intermediate layer the contacts for n++ and p+ are both on the front. High efficiency technology was put to use in cell manufacture.

8.1.6.3 Manufacturing Technology for Si Thin Film Solar Cells

All concepts have in common that on a suitable substrate a thin silicon film must be deposited, which is almost always subject to an additional recrystallisation step. In addition, suitable technologies should be developed, facilitating a high optical confinement and low surface recombination velocities.

8.1.6.3.1 Substrate Many alternatives are currently under investigation. These are: MG silicon (see Chapter 7, Section 7.1,1), or MG silicon with significantly reduced impurities by various gettering or float zone pulling processes. This material is called UMG silicon (upgraded metallurgical silicon). It can

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Selected Solar Cell Types 177

Figure 8.9 Cross-section through a thin film solar cell on an insulating substrate. All contact grids are on the front surface

economically be used directly as a sheet material in addition to conventional techniques (rods, blocks, sawing).

A further interesting substrate material is ceramic, as it can be manufactured to a high quality and can tolerate the high temperature processes, which are necessary for recry stallising and cell processes. Even the first silicon thin film cells by Barnett [52], in the late 1970s used a ceramic substrate material. To name further materials under investigation: graphite, steel, aluminium, glass and quartz. All these materials - except for silicon - are afflicted by the problem of thermal-mechanical mismatching. Before the active Si film can be deposited, the substrate must be provided with an intermediate layer, a buffer. This intermediate layer should first and foremost prevent the diffusion of impurities from the substrate into the active Si layer, while also acting as an optical reflector and serving as passivation for the back surface. Silicon dioxide, silicon nitrite and silicon carbide come under consideration as materials. Aluminium can be used as an optical reflector.

8.1.6.3.2 Two possible concepts are followed: depositing from the liquid and from the vapour phase. Depositing from the liquid phase takes place using the so-called LPE technology (liquid phase epitaxy). For depositing from the vapour phase, PECVD technology (plasma enhanced chemical vapour deposition) has proved to be the best option.

Techniques for Depositing the Active Si Layer

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In the vast majority of cases the particle size of the crystallites immediately after depositing does not correspond with the requirements for high efficiency. The layer must be recrystallised, remelted. The float zone pulling process is suitable. The necessary melting heat can be created by laser or lamp techniques.

8.1.6.3.3 Cell Technology The manufacturing process for the p-n junction and for contacting differ only slightly from the technologies described in Chapter 7, Section 7.2. However, for a non-electrically conducting substrate, a front side contact of the base material must be made, doubling the shadowing losses. Figure 8.10 shows the two concepts.

Figure 8.10 Concepts for thin film silicon solar cells [53]

The intention behind Section 8.1.6 was to make a significant step forward in the economics of photovoltaics. Significant practical difficulties still stand in the way of realising an economical silicon cell [53]. For more detailed information on this field, the following entries in the reference list give a comprehensive overview [54]-[56].

8.1.7 Multilayer Silicon Solar Cells

A few years ago an interesting new concept was suggested for crystalline silicon thin film solar cells [56]. The principle and the manufacturing technologies are explained based on Figure 8.11. The schematic cross- section shows a multilayer structure of alternate n-and p-doped layers. The boundaries are highly doped (n") on the substrate side, whereas on the front surface, the side turned towards the light, the n-layer contains a

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moderate surface concentration (n'). Both layers are extremely thin, at 0.1 vm. The total thickness of this cell has been selected as 10-20 pm.

Figure 8.1 1 Multilayer crystalline silicon cell [ 581 schematic and manufacturing diagram

During the manufacturing process,' the starting point is a substrate made, for example, of glass with a non-conducting coating. Then alternate layers of p and n are deposited with a concentration of approximately 10"

' 1. Glass substrate, 2. Layer separation, 3. Groove for first polarity, 4. Groove for second polarity, 5. Metallising.

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atoms/cm3 (e.g. using CVD), approximately 2 orders of magnitude higher than for conventional solar cells. The upper layer is covered by an insulator, e.g. of SIN or SiO,.

Normal recrystallisation is only necessary to obtain grains on average > 3 pm. Then grooves are cut using a laser, as in the buried contact solar cell. It has recently been possible to cut these grooves with a minimum of slack [58]. Afterwards, diffusion of a dopant is used to give the grooves polarity. A second laser process is used to remove the doping which has just been applied on one side of the groove. Now the opposite polarity is diffused in. Finally, as in the case of the buried contact, electroless metallising takes place in the grooves.

This multilayer cell gives the following advantages.

As the individual layers are only a few pm thick, high efficiency can be achieved with low diffusion length or low charge carrier lifetime. At a permitted carrier lifetime of up to 0.1 pm, the doping of this layer may be up to 10l8 atoms/cm3 and the grain boundaries can have dimensions less than 3 pm. Both permit depositing under less severe cleanliness requirements. The high doping leads to a low dark current, thus giving a higher open circuit voltage. A further advantage of this cell lies in its relative insensitivity to surface recombination. Most of the light is absorbed in layers away from the surface and the charge carriers created thus do not often come into contact with the surface. One very interesting aspect of the multilayer structure is the capacity to minimise lateral resistance losses by injection of the charge carriers between the layers due to lateral differences in voltage [59]. A two- dimensional simulation of this effect shows that in cases where the diffusion lengths are greater than the thickness of the layer, the charge carriers are injected into the other layers, thus injection takes place [60]. Therefore a distance from the contact finger of up to 1 cm is permitted, with the result that shadowing is kept very low and the contribution to dark current by the metal-silicon interface is very low too.

The optimal number of layers and thus the total thickness depends primarily o n the two factors optical confinement and surface recombination. We can see from [61] that with very good confinement of the light (Lambert's Reflection), two layers give the highest efficiency. If, however, specular reflection is only present on the back surface, then the optimal number of layers is approximately 7-8, only slightly dependent on the charge carrier lifetime.

An the efficiency value of 17.6% has been reported [62]. This 32 pm thick cell consisted of five layers of high-grade silicon. The substrate was made of highly doped silicon, the surface of which was coated with an

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insulating layer. It is hoped that with a 50 pm thick cell, efficiencies up to 20% will be achieved.

Many technological hurdles must still be overcome to turn the theoretical possibilities into practical concepts [61].

8.2 THIN FILM SOLAR CELLS

Great efforts have been made in research and development in the field of thin film solar cells made of other materials, with cell thicknesses of a few pm. Thin film solar cells can be expected to provide cost reduction and energy savings in cell manufacture. All known semiconductor compounds [III-V or II-IV materials] are direct semiconductors, so the absorption of sunlight occurs within a crystal thickness of a few pm. For applications in terrestrial solar technology, however, these cells must have an efficiency of the same magnitude as those of crystalline silicon as well as high stability. Of the large variety of solar cell types investigated, we have selected the few which are at the forefront of current work due to the above criteria. We thus consider four types of cell in this section, these are cells made of

amorphous silicon [a-Si], gallium arsenide [GaAs], cadmium telluride [CdTe], and copper-indium-diselenide [CuInSe,].

8.2.1 Amorphous Silicon Solar Cells

Amorphous materials - glass is a typical example - differ from crystalline structures primarily because the strict periodicity of the lattice is not present. As a consequence, the normal selection rules for crystal do not apply. In particular, the absorption of light occurs directly. Amorphous silicon [a-Si] - a compound of silicon and hydrogen - has this characteristic. The atomic structure is as shown in Figure 8.12.

The band gap of this semiconductor is approximately 1.7 eV, but varies between certain limits due to the hydrogen content.

We will consider these solar cells in more detail due to their broad application in the consumer market. In 1969 the physical characteristics of amorphous silicon were described for the first time [63]. In 1977 the first solar cells were produced in the RCA laboratory by Carlson [64],[65]. They still had a very low efficiency of 2%. The rapid development which followed has led to efficiencies of approximately 13% today.

The field of these solar cells is summarised in the references [66]-[68]. Hamakawa and Stafford provide very good detailed overviews [69],[70].

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Figure 8.12 The atomic structure of amorphous silicon

VP

Figure 8.13 Production process of a-Si solar cells using glow discharge [65] . S: substrate; C, A: electrodes; VP: vacuum pump; RF: transmitter

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The current production method for a-Si solar cells involves depositing the individual layers in a high frequency glow discharge reactor as shown schematically in Figure 8.13. Silane (SiH,) in a mixture with hydrogen is split into hydrogen and silicon. The a-Si can then be deposited onto glass or metal. The required p and n doping for the manufacture of solar cells is achieved by the addition of diborane (B,H,) or phosphine (PH,). In the case of evaporation onto glass the electrical contact is made using a conductive oxide film (TCO). Indium-Tin-Oxide (ITO) is often used for this purpose.

Light

20 nma(pc)-Si (Ge) : H : Metal, TLO c *

------- --f n

Figure 8.14 The structure of an a-Si p-i-n solar cell [65]

An important discovery on the road to higher efficiency was that the diffusion length of the charge carriers was very strongly influenced by doping and was so extremely small that only a small part of charge carriers could be collected. The solution to this problem was an intrinsic layer (Figure 8.14), with a very thin (approximately 50 nm) p+- and n*- coating on either side. This requires the highest degree of cleanliness for process equipment and procedures. A wide space charge region is created in which such high fields exist that almost all of the charge carriers created here can reach the p-n junction. As the absorption in this cell structure takes place almost exclusively in the intrinsic film, the efficiency could be raised to more than 5% [71] for the first time.

A further improvement was achieved by depositing a silicon-carbon compound (silicon carbide) onto the p+ side facing the light (by the addition of methane CH, during the production process). This compound (also a semiconductor with a band gap of over 2 eV) is transparent to light,

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and functions as a so-called window layer.2 This overcame for the first time the 8% hurdle [72]. Then Hamakava [73] went one step further by creating two solar cells directly above one another by deposition (Figure 8.15). Owing to the intrinsic film, which was now only half as thick, together with better deposition techniques (low defect density) and with the use of antireflection films, efficiencies of 13% are currently achieved.

n- I Aluminium I/

Figure 8.15 The structure of a a-Si solar cell with two intrinsic layers [40]

The critical problem of a-Si solar cells is their stability. The efficiency drops, is degraded. The degradation acts primarily on the fill factor and the short circuit current, whereas open circuit voltage remains almost constant. Degradation can be reversed, but only by exposing the cells to a temperature of approximately 160°C. This degradation was first researched by Staebler and Wronski [74]. This effect was named the Staebler-Wronski effect after them. Even today it has not been fully explained. The most probable explanation is that the recombination of light generated charge carriers causes weak silicon-hydrogen bonds to be broken in the amorphous material, thus creating additional defects, which lower the collective efficiency and increase serial resistance. Much research work is underway to explain the cause of this effect, so that it can at least be reduced by the use of technical measures [75].

One decisive advantage of the a-Si cell is that the necessary serial connection of cells can take place simultaneously during manufacture. As

This semiconductor with a high band gap is transparent to sunlight and functions like surface passivation

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shown in Figure 8.16 an entire layer of TC03 is first deposited onto a glass substrate, and then a stripe pattern created, for example by a laser beam. Then the a-Si solar cell structure is deposited in a reactor. Then the cells are structured, again using a laser, so that the subsequent evaporated metal has contact to the TCO on the back of the glass substrate. Finally, the evaporated metal coating must be separated at a suitable offset. It is thus clear that in this case five cells are connected in series. This effect is decisive in making a-Si solar cells dominate almost exclusively the small output market (clocks, pocket calculators, etc.).

Glass substrate TLO a-Si:H Metal (Pin)

Figure 8.16 Integrated serial connection of a-Si solar cells

Currently, solar cells made of amorphous silicon make up some 20% of current annual production (measured in peak watts). Their use in high performance applications is still strictly limited due to the importance of efficiency (see Chapter 6), unless they are used more for architectonic reasons, e.g. in faGades.

8.2.2 Gallium-Arsenide Solar Cells

The semiconductor material GaAs has won widespread approval in electronics. As early as the beginning of the 1950s GaAs was used in some research laboratories as a substrate for future semiconductor devices. Current applications are mainly in the field of optoelectronics, such as diodes and laser. In the foreseeable future increased miniaturisation and faster data processing are predicted. The physical and technological aspects of this material have have been thoroughly investigated during more than 40 years.

’ Transparent Conductive Oxide

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AM 1.5 Si 300 K

iAs Cd Ta

USb

A 2

P

S

L 3

Eg (aV)

Figure 8.17 Maximum solar cell efficiency for radiation of 1 sud1000 suns (300 K) versus energy gap

GaAs is also a very interesting material for photovoltaics. The energy gap of this semiconductor is 1.42 eV and, as we can see from Figure 8.17, it promises an almost optimal adaptation to solar radiation. Further advantages are: GaAs is also a direct semiconductor and therefore up to 90% of the sunlight is absorbed in a film thickness of 2 pm. The temperature dependency of efficiency in a GaAs solar cell is only one-third of that of silicon due to the higher energy gap.

Furthermore, this binary semiconductor can be easily transformed into a ternary semiconductor by the addition of elements from the third or fifth group of the periodic table. This means that semiconductors with larger

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band gaps can be produced, which can then act as a window layer, or with smaller band gaps for tandem solar cells.

In addition GaAs solar cells have a much lower sensitivity to cosmic radiation than do Si solar cells.

The GaAs solar cell is a cell with a p-n junction. There are currently three manufacturing processes in use. These are:

Liquid phase epitaxy (LPE). Metal organic vapour phase epitaxy (MOVPE). Molecular beam epitaxy (MBE), carried out in an ultra high vacuum, therefore used almost exclusively in research and development laboratories.

Sliding rod Graphite crucible Thermojunction

Furnace

Temperature

HZ

Figure 8.18 Principal arrangement for liquid phase epitaxy of GaAs solar cells

In the first process (Figure 8.18) a molten mass of Ga is almost completely saturated with As in a graphite crucible at a temperature of approximately 850°C and dopants such as zinc and aluminium are added. For processing, this is placed with the crucible open at the bottom over an n-doped GaAs substrate. Firstly, a very small quantity of the n-GaAs is dissolved from the surface and secondly, during contact with the molten mass, zinc diffuses into the GaAs substrate thus doping a small part of the substrate surface to a p-material (creation of a p-n junction) and thirdly, within the dissolved layer near the surface some 85% of Ga is exchanged for A1 (Alo,85Gao,~5As), thus creating a semiconductor with a band gap of approximately 1.9 eV. Using this elegant method - in which all necessary layers are created in a single step - an efficiency of >22% can now be achieved (AM1.5) [76]. The process itself was described by Woodall and Hovel as early as 1977 [77].

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Figure 8.19 The structure of a high efficiency GaAs solar cell [78]

To improve efficiency still further n'-GaAs is required on the back surface. Both epitaxy processes mentioned permit the creation of any chosen layer sequence and dopant level. The structure of one such cell by the MOVPE process is shown in Figure 8.19. This technique has been used to produce the highest efficiency yet of 25% under AM1.5 conditions, or with the same cell, 29% at 100 suns [78].

The use of a GaAs substrate is a large cost disadvantage. Great efforts have therefore been made to deposit GaAs on another substrate. One option is germanium, which has a thermal expansion mismatch of only 0.27% and therefore permits a relatively fault free precipitation of GaAs [79]. Cells produced in this manner are already used in satellite technology and possess an average efficiency of approximately 18% (AMO) and could have a big future in this field.

Silicon would be very desirable as a substrate material for reasons of cost and better heat conductivity, but has an expansion mismatch of approximately 4%. High stress would occur in the epitaxy layer and thus high dislocation densities. A range of technologies is currently being tested to circumvent this problem using a buffer layer. The individual layers are heated several times and thus made stress free. A state is reached where the

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efficiency at 100 suns is approximately 24% [80]. Figure 8.20 shows the layer structure of a GaAs/Si solar cell produced using MBE or LPE [81].

Figure 8.20 The structure of a GaAs solar cell on a silicon substrate [53]

Two problems stand in the way of increased use. One is the very high price of the GaAs cell, if it has to be built on a GaAs substrate. The use of another material for the substrate offers the best potential for development here. The second is a problem with acceptability since Ga and As are toxic substances.

However, perhaps the GaAs cell is one which could be used in the concentrator application, where the cell price, even for a moderate concentration of > 30 fold, as previously mentioned, is of less importance. A further possibility for the use of GaAs may be in tandem solar cells (see Section 8.3 below).

8.2.3 Cadmium-Telluride Solar Cells

Of the binary semiconductors it only remains to describe solar cells made of CdTe. This material, with a band gap of 1.45 eV, is, like GaAs described above, an almost optimal semiconductor for the conversion of sunlight.

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The first work dates back to the 1960s and early 1970s, when an efficiency of 6% was achieved [82],[83]. Then work was put on hold until the 1980s, when it was taken up again by numerous laboratories around the world with different technologies. As well as the classical CVD technique, and high vacuum evaporation technique, other techniques were successfully developed such as electrolytic deposition and chemical spraying as well as screen printing. A good overview is provided by Bonnet [84].

Like GAS, CdTe is a direct semiconductor and therefore sunlight is totally absorbed in a layer of a few pm thickness. This also means, however, that recombination on the surface must be prevented. In CdTe solar cells n-CdS has proved successful as a window film. This heterojunction (two semiconductor materials with different band gaps) has the problem, however, that sunlight with a wavelength of -c 520 pm is absorbed in the window film. Therefore, other substances are currently being investigated. According to all tests to date, solar cells made of this material possess high stability. The best laboratory cells have achieved efficiencies of 10-14% [85],[86]. The advantage of this technology is that with different, relatively cost effective technologies, efficiencies of 10% can be achieved. However, the question of acceptability is just as critical as for GaAs, since cadmium is poisonous and its hazardous nature both in production and in accidents must be carefully considered.

8.2.4 Copper-Indium-Diselenide Solar Cells

Of the different semiconductor compounds which are suitable for solar cells, e.g. the so-called chalcopyrite semiconductor, the copper-indium- diselenide cell has been the most highly acclaimed. This was described as early as 1978 [87]. A good overview of this is provided by Schock [88] and Mitchell [89]. The fact that high efficiencies were being achieved for these thin film cells with no degradation being observed was partially responsible for the increase in research activity in this field. Figure 8.21 shows the structure of a cell of this type. A layer of approximately 1 pm thick molybdenum is deposited onto a glass substrate. Then the active layer of Cu-In-Se, is deposited with a thickness of 1-3 pm in a high vacuum using a multi layer evaporation process. As with all thin film cells a window film of ZnO (band gap approximately 3.2 eV) is then deposited onto a thin buffer layer of CdS with a thickness of 0.3 pm.

The CuInSe, layer itself is polycrystalline, so the influences of grain boundaries and electronic states which exist in them strongly influence the characteristics of photocurrent and open circuit voltage. In addition, low defect densities are decisive for the very high efficiency of > 15% and these can only be achieved using high vacuum evaporation techniques. The

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- Al grid

n+ window film

n- buffer p-absorber

p+-a bso r be r

Back contact

Figure 8.21 Schematic layout of a CIS solar cell

cheaper screen printing technique has also been tested for the purposes of cost reduction.

With a band gap of approximately 1 eV, CuInSe, is somewhat unfavourable. The optimal utilisation of solar radiation, however, is achieved by the addition of Ga into the In layer. This creates a quaternary semiconductor, the band gap of which increases continuously with increasing Ga concentrations. If the In is completely replaced, i.e. the structure is CuGaSe, the band gap achieved is approximately 1.7 eV. It is thus possible to achieve the optimal band gap of 1.4 eV.

In addition the surface layers have recently been improved, both in the quality of the CdS buffer layer and the window film. Using this process several laboratories have been able to achieve an efficiency of up to 17% [901,[911.

Of the numerous research works in the field of CIS cells, we want to mention those which attempt to replace selenium by sulphur [92]. Many encouraging results have already been achieved in this field. CIS is one of the main directions of attack for research in the field of thin film solar cells.

8.3 TANDEM SOLAR CELLS

For reasons of high utilisation of solar radiation it is desirable to connect several solar cells with different band gaps together in series. For this

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purpose the band gap of the solar cell material must reduce from the side turned to the sunlight to the back surface. For two cells, the optimum absorption of sunlight is achieved if the uppermost cell is made of a semiconductor with a band gap of 1.9 eV and the semiconductor material of the lower cell has a band gap of 1.2 eV. The upper cell then absorbs short wavelength light while the long wavelength light is allowed to pass through and create charge carriers in the lower cell. The total efficiency is approximated by taking the sum of the efficiencies of the individual cells.

Transparent el. contact llI

Glass

-- !‘I -a-Si-solar cell / -Optical coupler

,CIS solar cell +-

Metal Glass

Figure 8.22 Schematic structure of a four terminal tandem cell

However, the disadvantage of a serial connection of solar cells once again appears. The weakest current from both cells determines the total current and thus efficiency. By a suitable choice of band gaps it is possible to roughly equalize the individual currents for radiation at AM1.5, but if the intensity and spectrum of solar radiation changes a considerable reduction in efficiency must be expected. Therefore, instead of a two terminal contact each cell can be contacted individually. This involves an additional cost. A conductive, transparent intermediate layer must also be added. Furthermore, the electrical energy must now be managed by two electrical charge regulators instead of one. We see that tandem cells are connected with high costs and particularly complex technologies. Figure 8.22 shows the structure of a four terminal solar cell.

Two of this type of tandem cells currently at the research and development stage are described here:

A GaAs tandem cell connected in series with a GaSb cell. A concentration of 200 suns produces an efficiency of approximately

A combination comprising a cell made of a-Si on a CIS cell, whereby the efficiency at one sun is 10%.

35%[93].

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A multitude of different combinations is conceivable because it is possible to alter the band gap of many thin film cells. Kriihler gives a comprehensive overview of the entire field [94].

8.4 DYE-SENSITISED SOLAR CELLS

A semiconductor-electrolyte-contact cell can also be used to convert light energy into electrical energy. The photovoltaic effect of this type of layout was first observed by Becquerel in 1839.

Figure 8.23 The structure of a dye sensitised solar cell

A concept was developed by Gratzel in the late 1980s, which we will explain using the schematic drawing in Figure 8.23 [95]. Nanoporous TiO, is sintered at 500°C onto a glass plate, which is coated with a transparent conductive oxide (TCO). A tin oxide doped with fluorine, which has a sheet resistance of approximately 10 W O is used here as the conductive film. The significantly more conductive IT04 cannot, unfortunately, be used as it would not survive the sintering process. The semiconductor TiO, is not an option for photovoltaics due to its band gap of approximately 3 eV. It is transparent to sunlight; almost no absorption is possible. Therefore the porous TiO, structure is coated with a dye based on ruthenium, such that a monomolecular layer is created. The dye bonds chemically with the TiO, surface. Visible light can be absorbed in this dye.

Indium Tin Oxide.

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194 Crystalline Silicon Solar Cells

Sunlight is almost completely absorbed by the surface of the TiO, colloids, which is now increased 1000-fold compared with a plain surface, despite the extremely low absorption in the dye layer.

semiconductof aye ekcuolyte metal counrer.elecrro5e

Figure 8.24 Schematic representation of a regenerative dye sensitised cell to demonstrate cell voltage

The Ti0,-dye combination is placed in an electrolyte containing iodide and triiodide. This cell is sealed by a further layer of TCO coated glass, which is also platinum coated (using its catalytic effect). This is a very flat cell, which is not clear from Figure 8.23. The dye coated TiO, layer is only a few pm thick.

The functionality of this cell is based on the fact that light is absorbed in the dye and thereb electrons are elevated to a higher energy level (Figure 8.24, process (6). This level is above the conduction band edge of titanium dioxide. Electrons are injected into the conduction band of the TiO, (a) from this state. This charge injection, however, is in competition with deactivation processes such as radiating and non-radiating recombination. To get a good yield from the injection, the junction from dye to TiO, must be such that the rate constant of charge injection is at least 100 times greater than the rate of deactivation in the dye. With newly developed dyes, charge injection of 90% is currently being achieved [96]. Unlike other solar cells, the electrons in TiO, are majority charge carriers, which are thus not dependent on diffusion length.

The flow of electrons comes about because the electron loss from the dye is quickly replaced by the iodide in the electrolyte, because it becomes charged by giving up electrons, thus becoming triiodide ions (a). These

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electrons are neutralised at the backplate electrodes (0). The missing electrons come through the outer circuit of TiO, (a). The flow of current is thus ensured. These individually very complex processes can be found in publications [97]-[ 1001.

Efficiencies of over 10% are currently being achieved. Despite the simple structure of the cell - it requires no high temperature processes, no expensive vacuum evaporation processes and no clean room technologies - there are still a number of questions which require answers. One significant problem is still long-term stability. A further question is the acceptability of liquid solar cells. Attempts have been underway for years to replace liquid electrolytes by a solid electrolyte. Conductive polymers are a starting point in the search for a solid electrolyte. However, up until now, no usable results have been achieved. Module manufacture is naturally an important question - parallel and serial connection - with the familiar problem of achieving as narrow a distribution of cell parameters as possible. This cell concept is still at the research stage.

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Schindler R. et al., Statusreport Photovoltaik, BEO, Julich, 1996, Section 15

Narasirnha S. , Kamra S., Rohatgi A., Khattak C. P. and Ruby D., Proc. 25th IEEE PV Spec. Con$, Washington, DC, USA, 1995, p. 449

Spitzer M., Shewchun J., Vera E. S. and Loferski J. J., Proc. 14th IEEE PV Spec. Con$, San Diego, California, USA, 1980, p. 375

Wolf M., Proc. 14th IEEE PV Spec. Conf., San Diego, California, USA, 1980, p. 647

Goetzberger A,, Knobloch J. and VoR B., Technical Digest PVSEC-I, Kobe, Japan, 1984, p. 517

Goetzberger A., Proc. of the 26th IEEE PV Spec. Conf.

Hebling C., Glunz S. W., Schetter C. and Knobloch J., Proc. 14th EC PV Solar Energy Con$, Barcelona, Spain, 1997, in print

Barnett, A. M. and Rothwarf, A,, IEEE-TED, 27 (4), 1980, p. 615.

Stocks, M. J., Cuevas, A. and Blakers, A. W., Progress in Photovoltaics, 4, 1996, p. 35

Statusreport Photovoltaik, BMBF, Projektrager BEO, Jiilich, 1996, Chapters 17 to 24

Wagner, B. F., Dissertation, Darmstadt, 1995.

Werner H. J., Bergmann R. and Brendel R., Festkorperprobleme, Vol. 34, R. Helbig, p. 11 5

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I98 Crystalline Silicon Solar Cells

Honsberg C. B. and Yun F. et al., Proc. 12th EC PV Solar Energy Con/:, Amsterdam, Netherlands, 1994, p. 63

Sproul A. B., Shi, 2. et al., First World Conference on Photovoltaic Energy Conversion, Hawaii, USA, 1994, p. 1410

Wenham S. R., Green M. A. et al., First World Conference on Photovoltaic Energy Conversion, Hawaii, USA, 1994, p. 1234

Honsberg C. B., Edmiston S. et al., First World Conference on Photovoltaic Energy Conversion, Hawaii, USA, 1994, p. 14 13

Stocks M. J., Cuevas A. and Blakers A. W., Progress in Photovoltaic, Research and Applications 4, 1996, p. 35

Green M. A. and Zhao J., 14th EC Proc. Solar Energy Con/: Barcelona, Spain, 1997, in print

Chittik R. C. et al., J . Electrochem. Soc. 116, 1969, p. 77

Carlson D. E. and Wronski C. R., Appl. Phys. Lett. 28, 1976, p. 671

Carlson D. E., US Patent No. 4,064,521, 1977

Kfihler W., in Solarzellen, Meissner D., ed. Vieweg, 1993, p. 109

Fuhs W., Proc. 14th IEEE PV Spec. Conf., San Diego, California, USA, 1980, p. 59

Pankove J. I., Semiconductor and Semimetals, Vol. 21-A, Academic Press, 1985

Hamakawa Y., Proc. of Material Research SOC., Vol. 49, 1985, p. 23

Stafford B. L. et al., Proc 21st IEEE PV Spec. Con/:, Kissimmee, Florida, USA, 1990, p. 1409

Hamakawa Y. et al., Appl. Phys. Lett. 35, 1979, p. 187

Okuda K., Abstracts of the 15th Conference on Solid State Devices and Materials, 1983, p. 189

Hamakawa Y., Proc. of the 14th IEEE-PV Spec. Con$, San Diego, California, USA, 1980, p. 1074

Staebler D. L. and Wronski C. R., Appl. Phys. Lett. 31, 1977, p. 292

Beyer W. and Wagner H., Forschungsverbund Sonnenenergie, Vols. 9 1-92, P. 9 Bett A. et al., Proc. of 22nd IEEE PV Spec. C o n j , Las Vegas, Nevada, USA, 1991, p. 137

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Selected Solar Cell Types I99

Woodall J. M. and Hovel H. S., Appl. Phys. Lett. 30, 1977, p. 492

Tobin S. P. et al., Proc. of 21st IEEE PV Spec. Con$, Kissimmee, Florida, USA, 1990, p. 158

Chu C. and Iles P. A,, Proc. of the 22nd IEEE PV Spec. Con$, Las Vegas, Nevada, USA, 199 1, p. 15 12

Vernon S. M. et al., Proc. of the 22nd IEEE PV Spec. Con$, Las Vegas, Nevada, USA, 1991, p. 3 5 3

Wettling W., in Solurzellen, Meissner, D., ed. Vieweg, 1993, p. 176

Cusano D. A,, Solid State Electronics 6, 1963, p. 217

Bonnet D. and Rabenhorst H., Proc. of the 9th IEEE PV Spec. Con$, Silver Spring, Maryland, USA, 1972, p. 129

Bonnet D., in Solurzellen, Hrsg. Meissner D., ed. Vieweg, 1993, p. 119

Mitchel K. W. et a\., Solar Cells 23, 1988, p. 49

Skorp J. et al., IEEE-TED 37, 1990, p. 434

Loferski J. et al., Proc. 13th IEEE PV Spec. Con$, Washington, DC, USA, 1978, p. 190

Schock H. W., in Solurzellen, Meissner D., ed. Vieweg, 1993, p. 44

Mitchell K. et al., Proc. 20th IEEE PV Spec. Con$, Las Vegas, Nevada, 1988, p. 889

Hedstrdm J. et al., Proc. 23rd IEEE PV Spec. Con$, Louisville, Kentucky, USA, 1993, p. 364

Zweibel K. et al., in Photovoltaic Insider's Report, Vol. XII, September, 1993

Tarrant R. and Ermer J., Proc. 23rd IEEE PV Spec. Con$, Louisville, Kentucky, USA, 1993, p. 372

Fraas L. M. et al., Proc. 21sf IEEE PV Spec. Con$, Kissimmee, Florida, USA, 1990, p. 190

Krtlhler W., in Solurzellen, Meissner D., ed. Vieweg, 1993, p. 109

Desilvestro J., Grtitzel M., et al., J. Am. Chem. SOC. 107, 1985, p. 2988

0 Regan B., Moser J., Anderson M. and Grlitzel M., J . Phys. Chem. SOC. 94, 1990, p. 8720

Grtitzel M., Proc. Indian Acad. Sci., Vol. 107, No 6, 1995, p. 607

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200 Crystalline Silicon Solar Cells

[98] Ferber J., Stangl R. and Luther J., Solar Energy, Materials and Solar Cells, in print

Hagfeldt A. and Gratzel M., Chem. Rev. 95, 1995, p. 49 [99] [loo] Sadergreen S., Hagfeld, A,, et al., J . Phys. Chem. 98, 1994, p. 5552

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Analytic and Measuring Techniques

Measuring individual parameters and determining their complex relationships is a fundamental prerequisite for the development and advancement of solar cells. The more precisely these relationships and dependencies can be determined, the more precisely can concepts for the improvement of parameters be implemented. Because of the familiar cost situation, two guiding principles must be followed. On the one hand, it is necessary to make the solar cell efficiency as high as possible; on the other hand, more cost effective technologies must be developed. An optimal compromise between cost reduction and efficiency must be achieved. It is for this reason that analysis is of such great importance.

9.1 CURRENT-VOLTAGE CHARACTERISTICS

As already mentioned, there is an international agreement that the efficiency of solar cells should be measured under the AM13 spectrum. In the laboratory, this radiation is approximated by a sun simulator. Figure 9.1 shows the block diagram for one such measuring set-up.

The light source is a xenon ultra high pressure lamp, which gives an almost white spectrum, as the individual xenon spectral lines undergo a high level of pressure broadening. The high intensities which still occur in some spectral ranges are reduced by special filters to the extent that a good approximation of the AM1.5 spectrum is achieved. The intensity is calibrated using a specially calibrated solar cell, which must conform to certain requirements. Its short circuit current must be in strict proportion to radiation output. This means, for example, that diffusion length and surface recombination of the calibration cell in its field of application must be independent of the radiation.

To increase measuring precision, the intensity variations of the light source are reduced by feedback of the measured intensity to the power

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202 Crystalline Silicon Solar Cells

Sun simulator AM1.S

Figure 9.1 Block diagram of a sun simulator

supply. Even higher precision is achieved if the data from the test cell and the calibration cell, and thus the radiation intensity, are measured simultaneously.

9.1.1 Measuring the I-V Curve under Illumination

The current-voltage characteristic is measured by monitoring the current from the solar cell point by point from zero to the short circuit current using an electrical load regulator. From the current and voltage data measured the computer calculates:

the open circuit voltage V,,, the short circuit current I,,, the current I, and voltage V, at the maximum power point, the fill factor FF, and the efficiency q.

All cell parameters are thus available, which are required for an assessment of the quality of the cell and which the user needs, e.g. for the construction of modules.

The actual analysis begins with the determination of the physical variables that are responsible for the solar cell parameters.

Based on the discussion in the previous chapters, these are dependent upon

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Analysis and Measuring Techniques 203

the dark currents or saturation currents in the emitter and base, the diffusion lengths of the charge carriers, the surface recombination velocities on the front and back surface, and the serial and parallel resistances.

In addition, shadowing by contacts, surface reflection and long wavelength radiation, which is not absorbed, must also be determined.

9.1.2 Measuring the Dark Current Characteristic

The dark current characteristic, which determines the current-voltage characteristic line for the solar cell as a normal diode, can be found using the measuring system described above. The typical form of such a characteristic is shown in Figure 9.2. The individual ranges of the characteristic can be assigned different variables in the two diode model. The diode equation ( 5 . 2 . 2 4 ) is repeated here.

V -IR, V -IRs

In the starting region from 0 to approximately 0.15 V the two first terms in equation (9.1.1) are negligible and the dark current is thus mainly determined by the shunt resistance R p (in the logarithmically linear representation the linear proportionality is represented as a curved line). In the adjoining area (from 0.2 to 0.4 V) the dark current can be assigned to the second term of the two diode model. As already mentioned, in practice there is rarely a relationship with n,=2. In the range 0.4 to 0.6 V the dependency on the first term of the expression is dominant. If the dependency is according to n=1, then the saturation current lo,, which is responsible for open circuit voltage, can be determined from it. In the region around 0.6 V serial resistance has a considerable influence on the characteristic.

Based on this assignment of the different parameters to the various regions of the dark current characteristic, the individual solar cell parameters can be determined using a fit programme for the measured dark current characteristic.

Series resistance R, can be determined more precisely by using measurements under illumination as well as those in the dark. For the dark current measurement a higher voltage (V,) is required than the open circuit voltage (V ,J to obtain a current which has the same value as the short circuit current, because the additional voltage drop at the series resistance

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204 Crystalline Silicon Solar Cells

Voltage (V)

Figure 9.2 The typical shape of a dark current characteristic line

must be overcome. The series resistance can be determined from the difference between the two voltages:

and thus ’ (9.1.2)

’ In most cases - but in particular in the case of high efficiency solar cells with a back surface point contact (LBSF) - this resistance is not identical with R, in illuminated conditions, because the flow of current differs substantially in the ‘light’ and ‘dark’ cases.

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Analysis and Measuring Techniques 205

(9.1.3)

Determining the dark current characteristic offers another advantage. It can also serve to calculate the behaviour of solar cells - and therefore solar modules - in advance for different climatic conditions, such as radiation and temperature [ 1],[2]. Normally these dependencies can only be determined by measurements of the I-V curve under illumination. However by transferring the ratings from the dark current measurement to the measurement under light (superimposition principle), these relationships can be determined based on the much simpler temperature and intensity relationships of the dark current characteristic. Good predictions can thus be obtained about the energy yield of the solar plant.

Since it is of great importance to know how the efficiency of solar cells depends upon temperature and radiation, we will include the calculation for temperature and intensity dependencies at this point .

9. I . 2.1 Dependence of Efficiency on Radiation

We assume that the short circuit voltage I,, (in the first approximation) is proportional to the level of radiation. We also replace Yo, in the formula for efficiency by

(9.1.4)

Thus the formula for efficiency reads

(9.1.5)

where Plight is the light input. The temperature dependency of the fill factor can be disregarded here. After some manipulation we find that for the relative change in efficiency

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206 Crystalline Silicon Solar Cells

(9.1.6)

where n is the air mass factor of light radiation [n = 1: one sun; n = 0.5: half a sun].

Introducing Voc we find for the relative efficiency change

With the value for silicon of

we find as a rule of thumb

The efficiency approximately 3%

k T

4 - x 0.04 -

v o c

A - r [YO] x 4 x l n n rl

(9.1.7)

(9.1.8)

(9.1.9)

of a silicon solar cell thus decreases, for example to (relative) at half the radiation intensity.

9.1.2.2 Dependence of Efficiency on Temperature

We here assume radiation and therefore short circuit voltage to be constant. The fill factor can also be assumed to be constant here. The relative change in efficiency is then equal to the relative change in open circuit voltage. So

(9.1.10)

where

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Analysis and Measuring Techniques

L p NrJ

20 7

(9.1.11)

We further assume that in the first approximation the temperature dependency of the diffusion length and the diffusion coefficients can be disregarded. I, then changes with the temperature only due to changes in n,. Then where

ni 2 = const. exp ( Eg I kT) (9.1.12)

we can write for the dark current density

Z, = B exp (-E, I k7') (9.1.13)

where B contains several constant factors. Then where V,,%(kTlq)x ln(ZJ1,)

Voc = - k T [ ln- g] + - Eg

4 4

(9.1.14)

If we differentiate this equation for temperature - disregarding the small change in band gap with temperature - we find that by replacing B with an expression for V,,

As a rule of thumb we find that for silicon

d(V,,) 1 - - - - (Voc - 1.1) d T T

(9.1.15)

(9.1.16)

and, with V,, being, for example, approximately 0.6 V, we find that at room temperature

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208 Crystalline Silicon Solar Cells

(9.17)

The relative change in the open circuit voltage and thus efficiency is approximately 0.3% per degree.

9.2 SOLAR CELL SPECTRAL RESPONSE

9.2.1 Spectral Response of a Front Illuminated Solar Cell

Spectral response is defined as the dependence of the collected charge carriers (solar current) on the radiated photons of different wavelength ranges. In the case of so-called external spectral response the total number of radiated photons is counted, whereas in the internal case only those entering the crystal are counted.

To determine this value the solar cell is illuminated with light from different spectral regions. The layout of this measuring instrument is shown in the block diagram Figure 9.3. The xenon high pressure lamp is again used as the light source. Its light is guided through different colour filters by a UV transparent fibre optic. The filter wheel is typically fitted with 19 filters, covering a wavelength range of 350-1019 nm (350 nm is the limit for short wavelength light, where sunlight is still present; 1019 nm is the approximate band edge of silicon; Ga-As cells can naturally also be measured because their band edge lies below the value for silicon). The band width of the individual filters is 8-10 nm.’

The light is first ‘chopped’, e.g. using a frequency a little above 100 Hz (integral multiples of the mains frequency must be avoided due to coupling mechanisms). After travelling through the filter the light is guided by a beam splitter onto the test cell (half of the light) and the reference cell (second half of the light).

Here, too, specific requirements are made of the reference cell. In the intensity range from roughly 1/100 to 1/1000 sun the short circuit current must be proportional to the intensity of the radiated light. It may not be a

In more recent measuring systems the colour filter is replaced by a double monochromator. This permits a continuous ‘scanning’ of the total frequency range.

2

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Analysis and Measuring Techniques 209

UV fibre

Reference cell

Oscilloscope

compensation *lLz I=

Figure 9.3 Block diagram of a measuring system for determining the spectral response of a solar cell

cell with a local back surface field, as the recombination velocity in these is dependent upon the number of charge camers generated, and strict linearity of the short circuit current is therefore no longer preserved.

The short circuit current in both cells is measured by the ‘lock-in’ technique. The advantage of the ‘lock-in’ technique is that firstly a very small current (< lo-’ A) can be determined. Secondly, it is possible to irradiate the test cell with constant light - of very high intensity compared with spectral light - without influencing the measurement results. The dependencies of the solar cell parameters, e.g. surface recombination velocity and charge carrier lifetime, on radiation intensity can now be investigated. The measured values from the test and reference cells are fed into a PC and processed.

To determine the internal spectral response it is also necessary to know the precise reflection conditions on the surface in relation to the wavelength. They must either be measured, or the measurement takes place with a polished surface, because then the theoretical reflection values can be included in the analysis [3],[4]. Figure 9.4 shows the internal spectral response of a high efficiency cell with a transparent emitter. The

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210 Crystalline Silicon Solar Cells

100

90

3 80

93 70 v

8 60

2 50

- 1 . 1

0.9 1.0 1.1 1.2 Wavelength (nm)

Figure 9.4 Internal spectral response of a high efficiency cell with a transparent emitter

illustration further shows the response of the emitter, the space charge region and the base in relation to the wavelength of the radiated light.

Two predictions can be made from this 'fit'. The diffusion length in the base and the effective surface recombination on the back surface are responsible for the spectral response in the long wavelength region. In high efficiency cells the effect of these two variables cannot, however, be separated. Only if the diffusion length is less than the thickness of the cell can the spectral response in the long wavelength region give the effective recombination velocity.

Secondly, the response in the short wavelength region permits predictions to be made about the surface recombination velocity of the emitter. As shown in Chapter 5 , this can only be determined for values greater than lo3 cm/s.

9.2.2 Spectral Response of a Back Surface Illuminated Solar Cell

In order to determine smaller surface recombination velocities as well, Lillington and Garlick [ 5 ] suggested a method which is described in what follows.

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Analysis and Measuring Techniques

Metal

21 I

SiO, n+

p-base

Local BSF

SiO,

Figure 9.5 Structure of a solar cell for illumination from the rear side

In this case the test cell is not, as normal, illuminated on the emitter side, but on the opposite side. Figure 9.5 shows the cross-section of a cell produced especially for this purpose. This cell, which can be illuminated from both sides, is called a bifacial cell (see Chapter 8, Section 8.1.2).

The back surface of this cell also has a finger grid in which the distance between fingers must be ten times greater than the diffusion length of the charge carriers in the base. This prevents the influence of high recombination under the contact fingers. In addition, it is also advantageous to apply a BSF under the metal coating to reduce recombination still further. The calculated internal spectral response of such a cell is shown in Figure 9.6.

As the short wavelength light is absorbed near the surface and thus charge carriers are created some distance from the p-n junction, the surface recombination velocity S,, has a strong influence on spectral behaviour. We see from the illustration that values of S,, less than 10’ cm/s can still be detennined. The prerequisite for this, however, is that the diffusion length of minority charge carriers in the base is almost double the crystal thickness.

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21 2 Crystalline Silicon Solar Cells

I I 1

1

- S,, = 100 cm/s

- 1000

-

- 10'

I I

- E

5: v

100

80

60

40

20

0 300 500 700 900 1100

Wavelength (nm)

Figure 9.6 Calculated internal spectral behaviour of a back surface illuminated solar cell

9.3 THE PCVD MEASUREMENT TECHNIQUE

We know from the above discussion that the diffusion lengths in high efficiency solar cells with values greater than the thickness are very difficult to determine. The process described in what follows offers an improvement. The measuring layout is shown in Figure 9.7.

The process follows the principle of measuring the decay of short circuit current and open circuit voltage after prior illumination (Photo-Current- Vo 1 t age- Decay) [ 61, [ 71.

This dynamic measuring principle has the advantage over the above static process in that

no absolute measurement of the light intensity is necessary and thus no knowledge of surface reflection must be available and the precise absorption coefficient need not to be known.

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Analysis and Measuring Techniques 213

generator

Pre-amplifier

Figure 9.7 Block diagram for a PCVD apparatus

The cell under investigation is excited, preferably by laser pulses. To be precise this measuring apparatus is operated by an Nd-YAg laser which emits light with a wavelength of 1064 nm. We thus obtain a consistently high level of charge carrier creation in the entire base (due to the very low absorption coefficient for this wavelength). A diode laser can also be implemented, which emits light at a wavelength of 904 nm.

The decay of V,, and I,, is measured. From the different states and distributions of the charge carriers produced, the following variables can be determined:

the effective surface recombination velocity of the emitter, the emitter saturation current (with good passivation), the diffusion length in the base, and the effective surface recombination velocity on the back surface.

However, it is also true that only those recombination parameters that are dominant in the test cell can be relatively precisely determined.

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214 Crystalline Silicon Solar Cells

HF generator

However, it is still possible to determine the individual influencing variables in a high efficiency solar cell with good surface passivation.

The test cell is first measured with the passivating surface. Then the silicon dioxide on the back surface is removed. A In-Ga friction contact is then deposited on the back surface, thus obtaining a surface recombination speed greater than lo6 cm/s. The cell is measured once again and the individual influencing variables can now be separated [8],[9].

HF bridge Low pass filter

9.4 TKE PCD METHOD

The measuring techniques described up to now all have in common that ohmic contacts must be attached to take measurements. Therefore a complete separation of recombination values, based upon the volume or originating from the surface, cannot be achieved. With the PCD method (Photo-Current-Decay) this is possible, since it does not require ohmic contacts [ 1 01.

As shown in Figure 9.8 the silicon wafer under investigation is placed in a high frequency resonant circuit, operated at a frequency of 13.56 MHz

Nd YAg laser: 1064 nm, pulse I

Figure 9.8 Block diagram of a PCD measuring apparatus

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Analysis and Measuring Techniques 215

(the frequency permitted for research and industry) at about 1 mm distance. Its electrical conductivity results in the damping of the resonant circuit. The high frequency bridge is adjusted before measuring, such that the differential current in the bridge is close to zero.

For the measurement, charge carrier pairs are created in the silicon wafer using a flash bulb or a laser. The conductivity of the silicon wafer is thus greatly increased, and the resulting detuning of the resonant circuit causes a bridge current. After the light source is switched off the conductivity of the silicon wafer returns to its original state, and the bridge current decays. The decay of this current is measured (the filter serves to suppress the upper harmonics). The data are picked up by a storage oscillograph and processed by a PC. This measuring process allows us to determine two parameters: (a) the emitter saturation current, and (b) the surface recombination velocity.

9.4.1 Determining the Emitter Saturation Current

This saturation current is becoming ever more important because the dominance of saturation current from the base decreases with the increasing diffusion length of the charge carriers and lowered surface recombination on the back surface. For very high efficiency the saturation current from the emitter region must therefore be reduced.

To determine the emitter saturation current an n+ emitter is diffused from both sides into high resistivity p-Si (> 100 S2cm). The important point is that the cell is illuminated with such a high level intensity that high level injection occurs in the base, whereas the emitter remains in low injection due to its high dopant concentration. It follows from this that after the light source has been switched off, the recombination of charge carriers in the base is directly proportional to the carrier density, whereas the recombination rate in the emitter is proportional to the square of the carrier density. It is therefore possible to separate these two recombination effects.

The carrier density at different times during the decay is found from the conductivity at the time, which is closely linked to the carrier density by mobility. Based on this data, the computer reports the decay transient for the carrier density. The result is given here, without going into the theory [ 1 01.

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216

SO0

loo0

A

5 v

& n

G= b 500

0

Crystalline Silicon Solar Cells

I I

JK23.181 I oc = 3.3~lO-~ A/crn2 -rHi = 3.6~6~’ s

I I

1 6 11 Average carrier density (cm-3)

16

*lo“

Figure 9.9 Decay transient for a test cell with face and back emitter [ 111

If we plot the reciprocal momentary decay time T,,,,~ against the corresponding average carrier density n, we find the following relationship:’

where

T,,,,~

thli s w q is the unit charge.

is the momentary decay time, is the high injection carrier lifetime, is the surface recombination velocity, is the thickness of the base, and

(9.4.1)

’ We have intentionally used the same designations as used in the above mentioned literature of Kane and Swanson [ 101.

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Analysis and Measuring Techniques 21 7

From the gradient of the straight line we can find the saturation current in the emitter. This gradient is

(9.4.2)

The value thli can be determined from the intercept of the axis.

9.4.2 Determination of the Surface Recombination Velocity

A test wafer is coated on both sides with the SiO, under investigation. Because there is no emitter, we determine 1hhli + s/w direct.

The SiO, film is then removed and the Si wafer submerged in a special container (teflon case with a transparent plastic sheet window) filled with hydrofluoric acid. The fact that the surface recombination velocity nears zero when a silicon surface is covered with pure hydrofluoric acid is used here.4 The measurement is now taken once again. The charge camer lifetime is determined directly and therefore so is the surface recombination speed.

In this manner it is possible to determine firstly extremely low surface recombination speeds and secondly diffusion lengths that are significantly higher than crystal thickness [ 113.

9.5 MICROWAVE DETECTED PHOTOCURRENT DECAY

An improved method for determining the recombination parameters of a silicon sample is microwave detected photocurrent decay (MW-PCD) [12]-[15]. This differs from the inductive coupled PCD described in the preceding section in the detection method of changes in conductivity.

The sample is located on a microwave antenna (see Figure 9.10) and is illuminated by pulses from a Nd-YAg laser (wavelength = 1064). The charge camers created in this manner An alter the conductivity Q of the sample by Ao:

In Section 9.5 the modem, safe technique is described. In this method the hydrofluoric acid is replaced by an iodinelethanol solution.

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218 Crystalline Silicon Solar Cells

=401 ,+Pp)An (9.5.1)

where /, and pp are the mobility of electrons and holes. The 2.8 GHz signal created by a microwave oscillator is guided via a circulator to the sample of thickness W and reflected from there. For a fairly small change in charge carrier concentration, the change in reflectivity is proportional to the change in charge carrier concentration. The reflected microwave signal is then guided via the circulator to a microwave detector, so that it is possible to observe the exponential charge carrier decay using the connected oscilloscope. If we now plot the measured transient in semi- logarithmic scale, the decay constant can be determined by a fit from the mono-exponential part.

Microwave Circulator Detector source

Figure 9.10 Principle layout of MW-PCD (from [ 151)

This effective decay constant depends upon the volume lifetime ‘b and the recombination speeds on both surfaces S, and S, from [16],[17):

(9.5.2) Y(S, +q with tan(y W ) = 1 1 - =-+Dy’

‘cff ‘b (Dy - s,s,

The variable y must therefore be defined with an eigen value equation, which is dependent only upon the surface. For the case where S, = S, an approximation can be found which can be directly solved [18],[19]:

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Analysis and Measuring Techniques 219

(9.5.3) 1 [?.s A[$ - a _ + - + - -

'eff 'b

The term W/2S describes the surface influence at small values of S, and the term 1/D (W/n)* describes the surface influence at very large values of S.

Time us) Figure 9.11 Typical MW-PCD decay transient (from [ 151)

MW-PCD can be applied for very varied reasons. One important application, for example, is the determination of the bulk lifetime for different materials, since this variable, as shown in the previous chapters, is decisive for solar cell efficiency. For this, the influence of the surface recombination speeds must be reduced as far as is possible, so that the measured variable corresponds with T~ as well as possible. One method for minimizing S is the deposition of the wafer in an iodine/ethanol solution during the measurement [ 2 0 ] . After a dip in hydrofluoric acid the wafer is briefly rinsed and placed in a 1% iodine/ethanol solution and measured. Using this method recombination velocities of 1 cm/s can be achieved, i.e. the surface influence can be disregarded during the measurement and T~ is measured direct. In this manner it is not only possible to measure unprocessed starting material, but also the change in

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220 Crystalline Silicon Solar Cells

bulk lifetime in silicon after various processing stages, since MW-PCD works without contact and is non-destructive.

MW-PCD can also be used to determine surface recombination velocities. To determine the value of S for an SiO, film, for example, the effective lifetime of a SiO, wafer, passivated on both sides, is measured. The highest level of precision for the value of S is achieved for silicon with a high lifetime, since then T~~ is determined primarily by recombination on the surface. The passivating film is then removed from both sides and the wafer is measured in the iodine/ethanol solution (see above), so that tb can be measured. This value of T~ allows us, with the help of the equation (9.5.2), to determine the surface recombination velocity of the SiO, layer or other passivating mediums with a high degree of precision.

9.6 MODULATED CHARGE CARRIER ABSORPTION

The modulated free charge carrier absorption, MFCA [21], represents analternative method of determining minority charge carrier lifetime. An IR laser beam transmitted by the sample (hv > E,) is used to determine the charge carrier density [22],[23]. Owing to the free charge carrier absorption, the absorption of the IR laser beam at a not too high charge carrier density is directly proportional to the integral charge carrier density N

(9.6.1)

where AZ is the change in laser intensity, I is the original laser intensity and K is the absorption constant for the free charge carrier absorption. This absorption constant increases quadratically with the laser wavelength used

The free charge carriers are not generated by pulses as is the case for most other methods of measuring lifetime, but sinusoidally. Since a phase displacement occurs between generation light and charge carrier dynamics, due to the lifetime of the charge carriers, the recombination parameters can be determined from this. The time dependent continuity equation serves as a basic equation for the derivation of the relationship between phase displacement Y and the recombination parameters:

~ 4 1 .

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Analysis and Measuring Techniques

- 8An An - - D- - - at a x 2 ‘b

+ G(x,t)

221

(9.6.2)

where An is the time and position dependent excess charge carrier concentration, D is the diffusion constant, x is the depth coordinate, Tb is the bulk lifetime and G(x,r) is the generation function. The boundary conditions of this differential equation are given by the surface recombination velocities S , and S,, and the surface recombination rates U s , and Us2:

(9.6.3)

where W is the sample thickness. After a long calculation using a Fourier transformation we find the following complex function for the integral charge carrier density, in relation to the modulation frequency a:

where

L ( 0 ) = (9.6.5)

The phase shift Y(o) is calculated from the quotients of the imaginary and real parts of the above expression, and the frequency dependent amplitude A(o) of charge carrier modulation from the amount:

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222 Crystalline Silicon Solar Cells

A(w) = IAN1 ImAN(w) v(w) = -tan-' R e m ( o )

(9.6.6)

In the case of a negligible surface recombination velocity this expression can be greatly simplified to:

(9.6.7) 'b "(0) = - arctan(or,) A h )

Figure 9.12 shows the calculated phase and amplitude distribution for different recombination parameters.

1 1)

8 O8

5 P O.4

k

3 .c 0 08 -

02 m 5

OD

1

, . I . . . . . . I . . . ....., . . , . . . . . I . . . . .... 2

-.-.-. .I 1ops.s -0- -7- loo )If. s - 0 cmk

n

I . . . , .... I , . , .,...I . . , . . . . . I . , . . 1M) lo00 loo00 1OOOOO 1OOOOOO

Frequency (Hz)

Figure 9.12 Amplitude and phase curves for different recombination parameters (from [ 151)

Thus the higher the volume lifetime or the lower the surface recombination velocity, the earlier the increase in phase or the reduction in amplitude begins.

Figure 9.13 shows the experimental realisation of the methods described above at ISE.

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Analysis and Measuring Techniques 223

HeNe laser 3390 nm

! ’

Laser diode

0

Signal Reference signal

- - Figure 9.13 Layout of MFCA (from [ 151)

The IR beam ( h = 3.4 pm) emitted from a HeNe laser penetrates the sample and is detected by an InSb IR detector (A). At the same point of the sample, free charge carriers are generated by a GaAlAs laser diode ( h = 780 nm), the intensity of which is sinusoidally modulated. As the free charge carriers follow this modulation with a certain phase shift, the intensity of the transmitted IR laser beam also changes sinusoidally due to the absorption of IR light by the free charge carriers. The signal of the IR detector (A) is passed on by a current-voltage converter to the signal input of a ‘lock-in’ amplifier. The sinusoidal signal from the function generator, which also serves as a modulation source for the driver of the laser diode, is used as a reference for the ‘lock-in’ amplifier. To improve the signal to noise ratio, half of the IR beam is guided to a second similarly constructed IR detector (B) by a beam splitter and its signal is subtracted from the signal of the signal detector (A) so that in the ideal case the noise background of the HeNe laser is negligible. The phase shift between signal

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224 Crystalline Silicon Solar Cells

Figure 9.14 Lifetime topography of a multicrystalline Si probe

and reference input of the ‘lock-in’ amplifier or the signal amplitude can now be measured for different frequencies using a computer and evaluated.

As the sample is installed in an X-Y table and the IR detection beam focused at approximately 100 pm, it is possible to plot lifetime topography. Figure 9.14 shows the lifetime topography of an unprocessed multicrystalline silicon sample. The crystal structure is clearly recognisable in the measured lifetime. Although the lifetime is significantly reduced at the grain boundaries and in micro-crystalline regions, within the grains much better values are obtained.

The degree to which this local lifetime fluctuation is reflected in the solar cell characteristics is of course of great interest. For this reason a solar cell is processed from the sample shown in Figure 9.14 and the short circuit current measured locally, Figure 9.15. The LBIC (Light Beam Induced Current) method used will be described in detail in the next section. A very good correspondence between the short circuit current and lifetime topography can be clearly recognised. This shows once again the increasing significance of lifetime for solar cell efficiency, but also the opportunity to use the MFCA method to determine the material quality in an unprocessed starting material.

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Analysis and Measuring Techniques 225

Figure 9.15 Short circuit current topography of the same multicrystalline Si probe as in Figure 9.14

9.7 SHORT CIRCUIT CURRENT TOPOGRAPHY (LBIC)

The LBIC method (Light Beam Induced Current) allows us to show the local distribution of the short circuit current in a solar cell. It is particularly important to know this distribution in the case of polycrystalline solar cells. Figure 9.16 shows the block diagram for the measuring apparatus developed and constructed in our institute [25]. A tungsten halogen lamp is used as a light source, the light from which is chopped with a frequency of 2 kHz and transferred to the test cell via a fibre optic cable. The illuminated surface of the solar cell has a diameter of approximately 0.1 mm. The X-Y table has a minimum step size of 10 pm and permits tracing at 100 points per second also using a computer programme developed in our institute [26]. For a test cell with dimensions of 2 x 2 cm with a density of 200 x 200 points the measurement procedure is completed in approximately 7 min. The apparatus also allows the additional illumination of the test cell with constant light. A coloured filter wheel further permits the selection of the wavelength of the measuring light.

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226 Crystalline Silicon Solar Cells

Filter

Reference

Fibre optic light guide Reflection

Y I Lock-in

Computer

AID , converter *

*+ IEEE488 *-

Figure 9.16 Block diagram of an LBIC mapping measuring instrument

The short circuit current of the test cell is measured for each point illuminated. The level of current is then stored and converted for display on a screen or output to a colour printer in different colours. From the assignment of colours to currents we very clearly see the effective and less efficient regions of the solar cell.

Figure 9.17 shows in black and white contrast the local distribution of the short circuit current in a solar cell made of polycrystalline Si material.

In monocrystalline high efficiency solar cells with a local BSF structure, this apparatus can be used to clarify the influence range of the back surface point contacts. A wavelength is used which lies close to the band edge for silicon, in order to create as many charge carriers as possible on the back surface BSF structure. It can be demonstrated in this manner that the region of influence is greater than the diameter of a point contact. It extends by

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Analysis and Measuring Techniques 22 7

Figure 9.17 LBIC picture of a multicrystalline Si solar cell

roughly the amount of the cell thickness [27].

9.8 THE DLTS PROCESS

We should briefly mention the DLTS process, developed by Lang [28]. We cannot and do not want to go into this any further and refer to the specialist literature [29],[30]. Using this method it is possible to determine an extremely low impurity concentration in a semiconductor according to type and quantity. It permits the determination of concentrations that lie up to five orders of magnitude below the dopant concentration.

Furthermore, the process permits the determination of the energetic level and density of the states in a surface passivated with SO, [31],[32]. These investigations show that the surface recombination velocity depends upon the carrier density and thus the strength of the solar radiation.

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228

References

Crystalline Silicon Solar Cells

Baier J., Thesis, Univ. Freiburg, 1992

Raicu A,, Thesis, Univ. Freiburg, 1991

Hulthen R., Physica Scr: 12, 1975, p. 342

Phillip M. R. and Taft E. A,, Phys. Rev. 120, 1960, p. 37

Lillington P. R. and Garlick G. F. J., Proc. 18th IEEE PV Spec. C o n f , Las Vegas, 1985, p. 1677

Rose B. M. and Weaver H. T., Proc. 27th IEEE PVSpec. C o n f , Kissimmee, 1984, p. 626

Rose B. M. and Weaver H. T., J . Appl. Phys. 54, 1983, p. 238

Bergmann R., Dissertation, Univ. Freiburg, 1988

Warta W., Bergmann R. and Vol3 B., Proc. 8th EC PV Solar Energy C o n f , Florenz, 1988, p. 1416

Kane D. E. and Swanson R. M., Proc. 18th IEEE PV Spec. C o n f , Las Vegas, Nevada, USA, 1985, p. 578

Kopp J., Knobloch J. and Wettling W., Proc. Zlth EC PV Solar Energy ConJ, Montreux, Switzerland, 1992, p. 49

Oteredian T., Thesis, Univ. Delft, 1992

Creutzburg U., Thesis, Univ. Bremen, 1991

Schafthaler M., Brendel R., J . Appl. Phys. 77 (7), p. 3162

Glunz S., Thesis, Univ. Freiburg, 1995

Ehrhardt A., Wettling W. and Bett A., Appl. Phys. AS3, 1991, p. 123

Luke K. L. and Cheng L., J . Appl. Phys, 61, 1987, p. 2282

Grivickas V., Noreika D. and Tellefsen J. A., Sov. Phys. Collect. 29, 1989, p. 591

Sproul A. B., J . Appl. Phys. 76, 1994, p. 2851

Horanyi T. S., Pavelka T. and TUttd P., Appl. Surf Sci. 63, 1995, p. 1147

Glum S. W. and Warta W., J . Appl. Phys. 77, 1995, p. 3243

Sanii F., Schwartz R. J., Pierret R. F. and Au W. M., Proc. 20th IEEE PV Spec. C o n f , Las Vegas, Nevada, USA, 1988, p. 575

Waldmeyer J., J . Appl. Phys. 63, 1988, p. 1977

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Analysis and Measuring Techniques 229

Schroder D. K., Semiconductor A4aterial and Device Characterization, John Wiley&Sons, New York

Praschek S., Thesis, FH Mihchen, 1988

Wagner B., Thesis, TH Darmstadt, 1989

Aberle A., Thesis, Univ. Freiburg, 1991

Lang D. V., J. Appl . Phys. 45, 1974, p. 3023

Miller G. L., Lang D. V. and Kimmerling L. C., Ann. Rev. Mater. Sci., 1977, p. 377

Lefevre H. and Schulz M., J. Appl. Phys. 12, 1977, p. 45

Aberle A,, Glunz S. and Warta W., J. Appl. Phys. 71, 1992, p. 4422

Glunz S. W., Sproul A. B., Warta W. and Wettling W., J. Appl. Phys. 75 (3) 1994. p. 1611

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Appendix A

LIST OF SYMBOLS

Absorption coefficient Relative permittivity Efficiency Wavelength Electron mobility Hole mobility Electrical conductivity Lifetime Barrier height Resistivity Electric potential Activation energy Effective Richardson constant Air mass Speed of light in vacuum Capacity Diffusion constant Electron diffusion coefficient Solar constant Hole diffusion coefficient Energy Electric field strength

Energy at the bottom of the conduction band Fermi energy Energy at the top of the valence band Photon quantity Fill factor Generation rate Geometry factor Planck's constant Solar cell thickness Width of base Saturation current Saturation current in the 2 diode model Current from base Current from emitter Current generated by light Current at maximum power point Electron current Hole current Current from the space charge region Short circuit current

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232 Crystalline Silicon Solar Cells

i

k L n

ND "i

"n

"0

"P

Electric current density Boltzmann constant Electron diffusion length Hole diffusion length Transport length Effective mass of electron Effective mass of hole Doping concentration Refraction index of the antireflection layers Acceptor concentration Effective density in the conduction band Donor concentration Intrinsic carrier dcnsity Number of electrons in the n-region Refraction index in air Number of electrons in the p-region Surface concentration Effective density of states in the valence band

P prn Pn

PP

R, s n

VLX "th W

Electrical power Maximum power Number of holes in the n region Number of holes in the p region Elementary charge Total electric charge Recombination rate Various serial resistances Reflection coefficient Parallel resistance Serial resistance Surface recombination velocity of electrons Surface recombination velocity of holes Temperature Applied voltage Diffusion voltage Temperature voltage Voltage at maximum power point Open circuit voltage Thermal velocity Width of space charge region Penetration depth

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Appendix B

PHYSICAL CONSTANTS

4 h Planck’s constant = 6 . 6 2 5 ~ JS m, k

kT/q €0

Elementary charge = 1.602 x 10 - I 9 C

Electron rest mass = 1.1096~ 10”’ kg Boltzmann’s constant = 1.38 1 x IO”’ J/K

Thermal voltage = 0.02586 V (500 K) Permittivity in vacuum = 8 . 8 5 4 ~ 10‘” F/m

c Speed of light in vacuum = 2 . 9 9 8 ~ lo8 m / s

SELECTED SI PARAMETERS AT 300 K

E, Energy gap = 1.124 eV N , Effective density of states in the conduction band = 2 . 8 6 ~ loL9 cm” N , Effective density of states in the valence band = 3 . 1 0 ~ 1 0 ’ ~ cm” “i Intrinsic carrier concentration = 1 . 0 8 ~ 10” cm.’ P” Mobility of electrons (lO%rn” 300K) = 1110 crn2/Vs ,up Mobility of holes (1016cm” 300K) = 410 cmZNs Y Density = 2.33 g / 6311.’ eSi / e, Dielectric constant 11.9

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INDEX

Index Terms Links

A

Absorption 29

coefficient 30

Acceptance problems 189

Acceptor 26

Activation energy 148

Antireflection coating 115 159

Antireflection process 114 159

Arrhenius curve 148

Auger coefficient 37

B

Back surface field 92

Band gap 12

Band gap narrowing 96

Band structure 13

Barrier height 104

Bond, homopolar 10

Buffer layer 177

Busbar 113

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C

Capture cross-section 39

Charge carrier

concentration 60

intrinsic density 19

lifetime 34

majority 25

minority 25

Cleaning techniques 155

Concentrator cell 163

Conduction band 12

Confinement, optical 33

Contact finger 97

Contact resistance 107

Contaminants 155

Continuity equation 45

Crystal momentum 30

Crystal pulling 136

Crystal structure 30

Current

forward bias 60

reverse bias 60

saturation 76 95

short circuit 69 90

Current-voltage characteristic 69 201

CVD principle 135

Czochralski process 136

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D

Dark current characteristic 84 203

Dead layer 151

Defect level 27

Degradation 165

Diamond lattice 10

Diffusion

coefficients 148

constant 27

current 27

length 41

technology 148

Diode equation 64

DLTS process 226

Donor 24

Doping 24 25

base 98

influence of 42

Double diffusion process 151

Drift 22

E

Efficiency 71 87

EFG process 142

Einstein formula 29

Electrical conductivity 11

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Electron 14

Emission 37

Emitter 73

penetration depth 90

two step 98

Energy gap 12

Energy level 12

Equivalent circuit 81

Error function distribution 144

Etching 155

anisotropic 118

isotropic 155

F

Fermi-Dirac distribution 27

Fermi level 26 53

Field current 20 22

Field strength 58

peak 58

Field, electric 54

Fill factor 71

Float zone pulling 136

Foil material 143

Fresnel's formula 115

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G

Gaussian distribution 141

Generation 20

Gettering 137 170

Glow discharge reactor 181

Grain boundary 139

H

Hole 14

Impurity conduction 24

Injection

high 40

low 40

weak 60

I

Intrinsic conduction 20

K

Kendall equation 44

L

Lambert's reflection 120

Lattice absorption 30

Lift off technique 157

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Light, monochromatic 73

Liquid phase epitaxy 187

Loss 90

due to non-absorbed light 120

optical 114

recombination 90

shadowing 121

M

Manufacturing costs 87

Masking 154

Mobility 20

Molecular beam epitaxy 187

MOVPE 187

O

Occupation, probability 14

Oxidation process 152

P

p–n junction 50

infinite 67

p and n neutral region 51

Passivation 94

PCVD method 211

Phonon 32

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Phosphor profile 150

Photocurrent 90

Photolithography 156

Photon energy 30

Poisson's equation 45

Potential difference 51

Potential, electric 51

Pulling speed 142

Pyramids, inverted 119

R

Rayleigh scattering 5

Recombination 20

Auger 36

by doping 42

radiative 35

SRH 80

via defect levels 37

Reflection factor 115

Refractioning procedure 135

Refractive index 116

Relative permittivity 25

Resistance

base 102

parallel 83

series 79 85 113

sheet 108

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Resistance (Cont.)

shunt 79 85

S

Segregation coefficient 139

Semiconductor 9

direct 30

indirect 32

Separation process 142

Shottky contact 103

Silicon

columnar 139 169

metallurgic 133

polycrystalline 135

powder 143

Solar array 87

Solar cell physics 67

Solar cell

amorphous 181

bifacial 166 210

buried contact 166

cadmium telluride 189

CIS 190

dye sensitised 193

gallium arsenide 185

IBIC 164

MIS 168

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Solar cell (Cont.)

real 72

tandem 191

thin film 170

Solar constant 5

Solid 9

Space charge 51

Space charge region 50

capacitance 57

width 57

Spectral response 210

SSP process 143

Sun simulator 201

Surface concentration 90

Surface recombination velocity 74

T

Texturising 118

Thermionic effect 109

Thick film technology 158

Total charge 45

Transport length 109

Trap level 37

Tunnel effect 105

Two diode model 79

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V

Vacuum evaporation technology 157

Valence band 12

Voltage

built-in 82

diffusion 52

open circuit 70 91

thermal 52

W

Window layer 184