`
`NationalLibraryofAustralia
`SetSguingeatin ety
`Green, MatinA
`
`]
`
`|. University of New South Wales i. Title
`
`Includes index.
`ISBN 0 7334 0994 6
`1. Solar cells. 2. Photovoltaic power generation.
`
`Nopart of this book may be reproducedin any form or
`Ali rights reserved.
`by any means without permission from the author.
`
`Publisher. Centre for Photovoltaic Devices and Systems
`of New South Wales
`N.S.W. 2052
`
`March, 1995
`
`PrintedbyO° PrinteryPty.Ltd.,29-35DunningAvenue,Rosebery,
`
`SlLICON SOLAR CELLS
`AdvancedPrinciples
`& Practice
`
`:
`
`:
`
`:
`
`Martin A. Green
`
`
`
`HANWHA 1045
`
`

`

`To Judy, Brie and Morgan
`
`TABLE OF CONTENTS
`
`Chapter 1:
`
`INTRODUCTION
`
`
`
`1
`
`Chapter 2:
`
`CRYSTAL STRUCTURE AND ENERGY BANDS cormerereneresrereee
`
`2.1
`2.2
`2.3
`2.4
`2.5
`2.6
`
`2.7
`
`INTRODUCTION, 00. eee cceeeeenececessteneneteeeeeaeeeseneees 4
`CRYSTAL STRUCTURE......... cc cessssseceeceessesenseeenenens 4
`SCHRODINGER WAVE EQUATION..........cccsceseceees 6
`RECIPROCAL LATTICE...........cccccssscstererereceseneetenenees 7
`ENERGY BANDS...........:::cccseversreereeeesa eeerecesentonnseeens 10
`DENSITY OF STATES & OCCUPATION
`PROBABILITY 0... ccecsc cece ceneeeeesesseseeteeerceeueeerenee ness 13
`MOMENTUM AND EFFECTIVE MASS...........:cc:::eescees 16
`
`Chapter 3
`
`PHONONS, PHOTONS& EXCITONS....ccsccrescesencnsascscssneccccnsnslI
`
`3.1
`3.2
`3.3
`3.4
`3.5
`
`INTRODUCTION. ........0..ccececeeesteececcesaceeeersscercenenenee ees 21
`PHONONS00... seeeccseseees erence ceseceseaeneesessepecsenenseerereneees 22
`PHOTONS.0......cc cscs cceeeeenec eee eecesnensnecesseneaseseasaaeereae res 24
`RAMAN SCATTERING............cones eaneseneeeacoeenmeseceeneces 25
`EXCITONS 000... ceccccceeeccseeceeccereeneeterieeresesereneesrnenasees 28
`
`Chapter 4
`
`OPTICAL PROPERTIES......c.sccssccssssosscoaseseaceestusesnnparnnneenenmecsnasnenenenrDe
`
`4.1
`4.2
`
`4.3
`4.4
`
`4.6
`
`INTRODUCTION. .............0ccscceeeeeeseaceeenssesseeetepenneeeneces 32
`LIGHT ABSORPTION IN PURE SILICON.............:eeeeeee 32
`4.2.1 General... ...ee cece cccntee ene eeteneeesasscseneaaeesneens 32
`4.2.2
`Phonon-Assisted Absorption...................068 34
`4.2.3
`Absorption Edge..........ence nuseeeaaeeestasanecesesesse 37
`4.2.4 Wavelength Modulation Spectroscopy.............. 39
`4.2.5 Multiple Phonon Processes........ se teeeeeeereasene ens 40
`4.2.6
`Direct ADSOIPHION.............ccscccseenesccsseserererecees 43
`4.2.7
`Free Carrier and Lattice Absorption .................- 46
`REFRACTIVE INDEX..............jsanenesseeenedacesconersesceeness 48
`TEMPERATURE DEPENDENCIES... seceeceeee 49
`HEAVILY DOPED SILICON... ccsnessseesseceesececeereees 54
`OTHER ABSORPTION PROCESSES...........-ccsceeeeee eee D4
`
`LETShee
`
`

`

`GENERATION, RECOMBINATION, CARRIER
`TRANSPORT..0..sccccosssnccesarsssaressenensssasaecvnnnnsctneesnoessromansosoranasennannonsoood57
`
`Concentrating Cells... cece eseeneeerees 132
`7.5.2
`MATERIAL REQUIREMENTS............ 2-2. ccceseesneeeeree eee 135
`POTENTIAL FOR EXCEEDINGLIMITS.........0...:.scceeeeee 140
`
`7.6
`7.7
`
`Chapter 8
`
`SUB-THRESHOLD CARRIER GENERATION......-ccns-serencenseonens145
`
`8.4
`8.2
`8.3
`
`8.4
`
`8.5
`
`GENERAL EQUATIONS...........0..ceeeeeseneeteeeeeeeeea rena eeee 57
`GENERATION.... 0... cece ccceccece cece ene cennesneesuneena nese enenes 59
`RECOMBINATION ......cecceeeeeeereeeeeeSeeaeeetcansetes vee,.61
`INTRODUCTION... ccccceseneer ere eeeeusereeeanceeeneseeneauanes 145
`5.3.1
`Gemeral..... cece cee eee cere eee ree een nee eeeeneeeeerene 61
`GERMANIUM ALLOYS........ ee eee eeece scene een eenen ee eeen es 147
`5.3.2
`Radiative Recombination............---- eres 61
`IMPURITY PHOTOVOLTAIC EFFECT............0ecesceseee ee 148
`5.3.3
`Band-to-Band Auger Recombination.............--. 63
`B.3.1
`EMOMUCTION..... 2 eee cece e scence ceeseneene suena ens 148
`5.3.4
`Recombination Through Defect Levels.............. 66
`8.3.2
`Optical Capture Cross Sections..................... 149
`CARRIER TRANSPORT.........ccecccecsceeenenteeseeeeereeuiees 72
`8.3.3
`Design Philosophies...........00...0.::ccscsseeseee ees 160
`5.4.1
`Drift and Diffusion... seeseseeseetsereeneres 72
`8.3.4=Indium Case Study... ects ee ee eee eee es 153
`5.4.2
`Boltzmann Transport Equation..............:..ccseee 73
`8.3.5
`Other Impurities 00... ee ec eeeeeesteneeren ees 157
`5.4.3 Majority and Minority Carrier... cee 75
`8.3.6
`Detailed Balance..........cccsteeestescsseaeesrereees 158
`5.4.4
`High Injection Mobilities................ cscs 80
`OTHER SUGGESTED SCHEMES.......... ccc ceceeeeeseeeeee eens 160
`5.4.5
` Excitomic TranSport........-ceescrseereeteeeernrers 81
`8.4.1.
`Implanted Defect Layer.............. cece aes 160
`5.4.6
`Heavy Doping.............cccceereseeeceneeneeeeerree ers1.83
`8.4.2
`Delta Doping............-. cece eee sees eeeeceeererenenee tees 161
`TANDEM CELLS ..........cecccssececenteserenerceeteeeneeeeepereneeees 162
`
`5.1
`5.2
`5.3
`
`5.4
`
`Chapter 6
`
`LIGHT TRAPPING. w.cscssecsesccsscssnmensserercocosnsvenseessenscessmmemmnaeerssientenenernerOD
`
`6.1
`6.2
`6.3
`
`6.4
`6.5
`6.6
`
`INTRODUCTION.......ccccccccceceeseerreeeseeeseessegesenseenaeeeeees 92
`RANDOMIZING SCHEMES.............06eeeereneceeateeesooeeon® 93
`GEOMETRICAL LIGHT TRAPPING. .........-..:eeeseeeeeeeeeee 97
`6.3.1
`IMRFOCUCTION......... eee eeeeeeceneee erent eenereresensenaees 97
`6.3.2
`Two Dimensional Geometries.................:::+:-98
`6.3.3
`Three Dimensional Geometries..............::.:ceeee 100
`Experimental ResultS.......- ce ececeessereeterseaeesSeeeeeenees 106
`CONCENTRATEDLIGHT............::eeee eeevawtceseepeeseeaeeraes 109
`Light Trapping..........c:ceeeeeceeeserreeesennsstenseeeetnienerenenes 111
`
`
`SIE
`
`Chapter 7
`
`FUNDAMENTALEFFICIENCY LIMITS..........osssscssssmessesssensssrsnes117
`
`7.1
`7.2
`7.3
`
`7.4
`7.8
`
`INTRODUCTION... ...ccceccceeeeeeesteeesseneaeseenseuenpeesegeesanes 117
`PHOTON-GENERATED CURRENTLIMITS...........-.2:000+ 118
`OPEN-CIRCUIT VOLTAGE LIMITS...........-::ccseetere renee 122
`FB.
`Germerab.. ec cece eeencrseeeceaneeenereeeenaeeemeneee 122
`7.3.2
`Low Injection ConditionS.............:..cceeeerees 122
`7.3.3
`Narrow Base, High injection Limits................... 127
`FILL FACTOR..0..cccccccecenecceceseerecnereaasaasrmeseeaeanoeseeeeee 130
`EFFICIENCY LIMITS ......-:-ceccsssssccccesseescaeeseeeeseeesanenee 134
`
`Chapter 9
`
`SURFACE, CONTACT AND BULK PROPERTIES -............166
`
`9.1
`9.2
`
`9.3
`
`INT RODUCTION..........::cceescnteeenesscneneeeeeetsertesearensae nes 166
`SURFACE RECOMBINATION............:-c:setsenseeeecreeeees 166
`9.2.1
`Interface States and Oxide Traps ............ 166
`RECOMBINATION AT INTERFACE STATES................173
`9.3.1
`Independent, Discrete Interface States ............. 173
`9.3.2
`Independent, Continuous States... 173
`9.3.3
`Equal Capture Cross-Sections ............c0c eee 174
`9.3.4
`Constant Capture Cross-Sections................... 174
`9.3.5
`Experimental Interface Densities and
`Capture Cross-Sections 0.0.0... ccccscecseceeenscensenes 175
`CONTACT RECOMBINATION. .......... cc: cccccceeserreee eens 181
`BULK RECOMBINATION. ..00. occ ce ceeccce eee tteeeeeereeee eas 186
`GETTERING ..0.......ccccecceecsentecescneneeseeesaeuaeeesccenseneees 192
`DEFECT PASSIVATION...0...... cece eeecceeeeeeeeeeeeeeenereee 195
`
`‘Chapter 10
`
`EVOLUTION OF SILICON SOLAR CELLS —-nemcscsreoseerseorvere2O11
`
`- 10.1
`10.2
`
`INTRODUCTION...00......cesceecessceasceeeseeeeererssesesannennenens 201
`EARLY SILICON CELLS .........ceeeceetseeeneteesseeeeeeeese sees 202
`
`

`

`
`
`Interdigitated Back-Contact Celll......00.........:400 255
`12.3.1
`Front-Surface Field and Tandem Cells............... 257
`12.3.2
`12.3.3 Double-Sided and Polka-Dot Cells.........sateeeeneas 258
`VERTICAL JUNCTION CELLS 0... cceecessereeeceees 259
`POINT CONTACT SOLAR CELL....oic lc eesseeeeeeees 260
`12.5.1 Structure... cceseseeececsssrsescaecesecereceusees 260
`12.5.2 Recombination Components...........00......c00 262
`12.5.3 Photocurrent Collection .....0......ccccccssseseeeeeceeees 263
`12.5.4 Experimental Resullts........ccccccceccccceeseeee 264
`12.5.5
`Point Contact Cell Stability ........0.00000000 0. 268
`12.5.6 Recent Developments................ccccseccsecsceees 268
`SUMMARY ....... ccc cccccssceueesccceeessssebensorecensesseneses 269
`
`12.4
`12.5
`
`12.6
`
`Chapter 13
`
`MULTICRYSTALLINE AND RIBBONSILICON....._____...273
`
`13.1
`13.2
`13.3
`13.4
`13.5
`13.6
`
`INTRODUCTION. eee cccecesssssscceeeusssssscseeepvastecssseees 273
`HYDROGEN PASSIVATION. ............cccccesssesesssuseececeues 275
`PHOSPHORUS TREATMENT ...........:cccccecceesesesvescereens 276
`OTHER PASSIVATION APPROACHES...........000...0000.- 281
`TEXTURING uo. ee eeeeceeeceeestaataeeeeensecessnssseceeseeess 281
`ADVANCED CELL STRUCTURES..........00.ccssceeccseeeeees 282
`
`Chapter 14
`
`THIN FILM POLYCRYSTALLINE AND
`MULTILAYER CELLS...ssscssssscnressesrsvecerecestersesesansesssruseremaseees288
`
`14.1
`14.2
`
`14.3
`14.4
`14.5
`14.6
`
`INTRODUCTION. 00 ccc ccceesessssesssssneerecnessensesananes 288
`GRAIN BOUNDARIES............cccccccscscesccccssersreeteeeees 289
`14.2.1
`Physical Structure...ci ccsscsssssssesssessssceees 289
`14.2.2 Electronic Properties ...............cccccccsssecenseceeeees 291
`14.2.3 Resistive Effects... sscsccccccsssssecceecees 294
`14.2.4 Recombination Properties.............cccc0 eee 296
`14.2.4.4
`Bulk Regions.............cccceeecereeeees 296
`14.2.4.2
`Horizontal Grain Boundary in
`Depletion Region.............ccceee 303
`Vertical Grain Boundaries ............. 308
`14.2.4.3
`INTRAGRAIN PROPERTIES............00 veseereceeeeessnenees 311
`SINGLE JUNCTION CELLS ...00.......cccscesceccesseseececeseeees 314
`MULTILAYER CELLS...00........cccccsesssearscecerssssteeeceeseacs 318
`SUMMARY... cescecececeeescereesssnecesseneseascusesanacs 322
`
`CONCLUSION..ssscscsescancrsncersrssovesnseseaveescessueterscnsneessotenearnremessnsesnanserenesZO
`
`10.3
`10.4
`10.5
`10.6
`10.7
`10.8
`10.9
`10.10
`10.14
`
`10.12
`
`CONVENTIONAL SPACE CELLS...... cc ccsersert treet: 205
`BACK SURFACE FIELD................. Leceeseasegeeetecarseceuceee 207
`VIOLET CELLS .........cccccceeeeceeeneeeeeneeeepenesta vensseaenenssee 207
`BLACK CELLS 00... cece cec cece cece eeee ee nee seen ere eecennanrareees 209
`OXIDE SURFACE PASSIVATION............--enceseaeeeenens 212
`CONTACT PASSIVATION ........cceseceeeeceereenererereeeneeuee 213
`TOP SURFACE PASSIVATED CELLS....... 05. -cccgeeeee eens 215
`TOP AND REAR PASSIVATED CELLS.........-ceeceeee eres 218
`PERL CELL DESIGN ........cccccccceeceeeeeeeeederueeeeeeneneeceee 221
`10.11.1 Optical features.......ce cganveteccnaatusoseseaeronaneess 221
`10.11.2 Electronic Features ..........c ccc ceececeseeeeecerenere 223
`10.11.2.1 Bulk Recombination................... 223
`10.11.2.2 Surface Recombination................ 224
`10.11.2.3 Contact Area Recombination........ 226
`10.11.2.4 Present Recombination
`Relativities ............ccccccceeeee eee eeees 227
`SUMMARY ....cc:ccccccscceeeeecceeecedcaseeenseeeeeeeeectepeeeaenes 227
`
`
`eT:
`
`
`occastebrares
`paintsatt
`
`2 i
`
`Chapter 11
`
`SCREEN-PRINTED AND BURIED CONTACT CELLS.........234
`
`11.1
`11.2
`
`INTRODUCTION. 00... ccccc cere ceeececeseeeeeeenendarceseeeeesepeens 204
`SCREEN-PRINTED CELLS... eee eescceteeeteeee es 235
`11.2.1
` StMUCture....c cece eeeeereeenseen eedaeeeneeenseensees 235
`11.2.2 Typical Performance ...........ccccceeceeeeneteereeeees 237
`11.2.3
`Improved Technology...... thes eeeeeneeeteceneeereoeeates 238
`BURIED CONTACT. SOLAR CELLS... ieee 239
`11.3.1
`SHUICTUIO.. ee eee e eee re ee eenn eee reeeneaeeeenene 239
`11.3.2 Performance AnalySis............0.. ccecseseeeesseeeeee 241
`11.3.3
`Production Experience................eed egeeeeeeeeeetere 242
`11.3.4 Future Improvement..............cc reer 243
`
`Chapter 12
`
`HIGH PERFORMANCE CONCENTRATOR
`SOLAR CELLS wincecenecsssssernsssensunseessnanersemssecsavossunsesetsnasaineeserensswestte249
`
`12.1
`12.2
`
`INTRODUCTION.......cccrecceeeeeceeteaseescseaeeeeaeeees beceueneeees 249
`CONVENTIONAL CELLS ........... ccc eeeeecesceneeeseenenereees 250
`12.2.1
`Low Cost Approaches... seeseeeeeetseeeees 250
`12.2.2 High Efficiency Space Technology Cells...........252
`42.2.3
`PESC and PERL Cells...eee 253
`12.2.4 V-Groove Silicon Cell.eee 254
`BACK SURFACE CONTACT CELLS20... ee ceeeeeeee ees 255
`
`

`

`Appendix A GREEK ALPHABET
`
`
`
`sororeseonermntssssseresssensseesBLD
`
`Appendix B
`
`PHYSICAL CONSTANTS
`
`
`
`330
`
`Appendix C SPECTRAL DATA...sssaseemssneesersnvectusssssstsnssesessseunsonieeesdoI
`
`Appendix D OPTICAL PROPERTIES OF SILICON wnesnnnsscnasccerecrsammeneereeeesSOO
`
`
`Appendix £ QUASI-FERMI! LEVELS...
`
`ssosssssanensesnneressavvensncnas337
`
`E.1
`E.2
`E.3
`£.4
`E.5
`E.6
`
`INTRODUCTIONL.......cccccssssereeesserereerrrsseereererseneeeeenes 337
`THERMAL EQUILIBRIUM.........::cceececeeeeeeeenneeseceees 337
`NON-EQUILIBRIUM.,.........ccsscsesseereeeeerereneeenneneeeeeneres 338
`INTERFACES 20.0... .cecceecceee setae ereneensseneeene pees eneasennernaes 339
`NON-EQUILIBRIUM P-N JUNCTION peneetecenacerscueeseneses340
`USE OF QUASI-FERMI LEVELS..........::.::::eeeseeeerenerens 341
`
`Appendix F
`
`REFLECTION CONTROL..-—-csssnnsnvseeereemeerenensnreeennrertennar345
`
`F.1.
`F.2
`
`ANTEREFLECTION COATINGS. .............cccceeeeeeereesaane res 345
`SURFACE TEXTURING ......ccccccstteeseeece erate epee nereetens 345
`F.2.1
`Historical and Technological Perspective ........... 345
`F..2.2
`Theory of Reflection Control by Texturing ......... 347
`F.2.2.A Feature Size... ccccsecssteesreecessenneerneereerenna cans 347
`F.2.2.B Macroscopic Features ........cccccceesererseeeeeernrees 348
`F.2.2.C Microscopic Features......---ccccccccesssssereerseeees 353
`
`Appendix G INFRARED SPECTRAL RESPONSE......-.....-cscsccsovssnsesnestenneseveses357
`
`INDEX nnneesssoseeesscccntvereqacenesaevaverecsesaqnssennecenemsiensvs
`
`ansssnsansasenssenaremesesroscnseersdOF
`
`PREFACE
`
`"In the history of technological development, there are past examples
`where an apparently mature technology blossoms into its full state of
`development only when facing the challenge from a newer
`technology. This appears to be happening in the case of butk silicon
`solar cells. Since the early 1980's when thin film solar cell products
`first became available commercially,
`there have been quite
`remarkable improvements in bulk silicon cell performance.
`The
`exciting fact is that, despite the magnitude of recent improvements, it
`has become increasingly clear that there is plenty of potential for
`further increase”.
`
`So began the preface for the author's earlier research monograph
`“High Efficiency Silicon Solar Cells" which was stimulated by the
`first demonstration of 20% cell efficiency and the recognition of the
`potential for even further improvement. A decade further on, about
`half this potential has been realized in practice and some of the
`ideas , then at a laboratory stage, are now appearing in production
`and in field installations.
`
`With the demonstration of viable production technology for obtaining
`20% bulk cell efficiency, and the imminent explosion of interest in
`thin film and polycrystalline silicon cells, it seems appropriate to
`once again take stock of what we have learned and where we are
`heading. The present text includes some of the basic material
`incorporated into the earlier monograph previously mentioned, but
`reworked in a style which may make it also suitable as a graduate
`level textbook.
`It assumes a basic grounding in solar cell device
`9peration, at the level of the author's text, "Solar Cells: Operating
`_ Principals, Technology and Systems Application” (also available
`from the author) as well as some familiarity with semiconductor
`physics at a slightly more advanced level.
`
`_
`
`
`eAnotnitenast
`
`
`
`

`

`It is a pleasure to acknowledge the contributions to many of the
`developments described within the book of past and present
`members of the Centrefor Photovoltaic Devices and Systems.
`I
`would also like to thank those taking the graduate course ELEC9508
`at the University of New South Wales during 1994, who provided
`feedback on an earlier draft of the book, and also Richard Corkish,
`Steve Robinson, Frans Saris and David Thorp for their detailed
`suggestions.
`I also thank Jenny Hansen for her untiring assistance
`in producing this book andits figures. Finally, | would also like to
`thank the authors and copyright holders who gave permission to
`reprint many of the figures liberally scattered through the text,
`including the Royal Radar Establishment for permission to reprint
`Figure 4.4 (Crown copyright material
`reproduced with the
`permission of the Controller of HMSO).
`
`Martin A. Green
`Centre for Photovoltaic Devices and Systems
`University of New South Wales
`Sydney, NSW, 2052
`March, 1995
`
`Chapter
`
`1
`
`INTRODUCTION
`
`Over the last decade, there has been rapid improvementin silicon
`laboratory solar cell efficiency as shown in Fig. 1.1. Maximum
`demonstrated efficiencies have increased from about 17% in 1983 to
`above 24% in 1995.
`
`
`
`Effici
`
`30
`
`9
`
`iciency(%)
`
`10
`
`
` 0 Oo
`1840
`1950
`1960
`1970
`1980
`1990
`2000
` i, - - Figure 1.1: Evolution ofSilicon Laboratory Cell Efficiency.
`
`‘Importantly, some of these improvements are filtering through to
`*commerctal
`practice.
`For
`th
`‘comm
`P
`‘or
`the 1993 World Solar Challenge, the solar
`race across Australia from Darwin to Adelaide, several suppliers
`wertableto provide silicon cells in kilowatt quantities of above 19%
`
`
`
`

`

`the same time, one company had produced close to a megawatt of
`large area cells of efficiency comparable to the best laboratory cells of
`only a decade earlier [1.2].
`:
`
`Without any major technical breakthroughs, the cost of silicon cells
`has also reduced quite markedly. Crystalline silicon technology has
`already reached all that was expected of it in the ambitious program
`of the US Government in the 1970's [1.3], only it has taken twice as
`long as originally planned [1.4]. The important point is that these
`cost reductions have not been driven by new technology, but by the
`economies of scale and the learning experience associated with an
`expanding industry [1.5]. Most of the laboratory improvements over
`the last decade have not yet made commercial impact.
`
`thinking about photovoltaic
`An important aspect of the original
`development [1.3] was that, once benefits from improving crystalline
`silicon technology had been exhausted,
`there would be a second
`period of rapid cost reduction arising from a change from crystalline
`silicon to a thin film technology.
`
`At the present time, it seems as if there are several ways in which this
`second phase of accelerated cost reduction could be realized. One
`might be just by the incorporation of the lessons learned in the
`laboratory in silicon cell design over the last decade into commercial
`practice, combined with increased investment
`in production
`technology.
`In this scenario, a 20% efficient photovoltaic panel based
`on a low-cost, high-efficiency sequence, such as the buried contact
`sequence described in Chapter 11, might be the final product,
`particularly if combined with stationary refractive concentrators to
`reduce the required cell area. Another possibility would be that this
`decrease in cost might come about by successful commercialization of
`a thin film technology. At the present point in time, thin film
`polycrystalline silicon appears one of the stronger candidates for the
`long term. Of other candidates, hydrogenated amorphoussilicon ceil
`development has not progressed at the rate anticipated in the mid-
`1980's. Casting a wider net, the photovoltaic community could be
`doing itself a disservice by promoting, as its ultimate solution, a
`technology such as cadmium telluride which generates legitimate
`environmental concerns. Similarly, the community could be accused
`of a certain lack of ambition in promoting copper indiumgallium
`selenide as this final solution. given the limited contribution to global
`
`upon limited resources of indium andgallium [1.6].
`
`technologies already identified, bulk silicon and thin film
`Of
`polycrystalline silicon cells remain key contenders for providing this
`long-term solution. By consolidating recent developments and
`outlining possible areas for future activity, the present book seeks to
`contribute to the development of these cells. The book is split
`roughly into two sections. The first treats the material parameters
`and basic mechanisms important in silicon Photovoltaic energy
`conversion.
`It
`includes a thorough discussion of absorption
`processes in silicon, particularly sub-bandgap processes, and a
`detailed treatment of light trapping effects which will make sub-
`bandgap absorption more important in future generations of cells.
`Efficiency limits upon cell performance are discussed, as are the
`material properties required to reach these limits. The second half of
`the book deals with device structures.
`It includes an historical
`review of the evolution of cell design, as well as a detailed treatment
`of the device structures appropriate to the different areas of present
`and future interest:
`crystalline cells, concentrating cells, cells
`fabricated on ribbon and multicrystalline Substrates, and thin film
`silicon cells, including the very promising multilayer devices [1.7].
`
`REFERENCES
`
`1.1
`.
`
`1.2
`1:3
`
`1.4
`
`
`
`M.A. Green, “World Solar Challenge 1993: The Trans-
`Australian Solar Car Race", Progress in Photovoltaics, Vol. 2,
`pp. 73-79, 1994,
`PV Insiders Report, June, 1994.
`Final Report, Flat Plate Solar Array Project, Jet Propulsion
`Laboratory, E. Christensen (ed.,), October, 1985.
`G. Landis,
`“Coal and Solar Futures", Progress
`Photovoltaics, Vol. 1, pp. 319-320, 1993.
`K.W. Mitchell, "The Reformation of CZ Si Photovoltaics”, Conf.
`Record, First World Conference on Photovoltaic Energy
`‘Conversion, Hawaii, December, 1994.
`M.A. Green, "Silicon Solar Cells: The Ultimate PV Solution?”,
`Progress in Photovoltaics, Vol. 2, pp. 87-94, 1994.
`“-$.R. Wenham, M.A. Green, S, Edmiston, P. Campbell, L.
`Koschier, C.B. Honsberg, A.B. Sproul, D. Thorpe, Z. Shi and
`G. Heiser, "Limits to the Efficiency of Silicon Multilayer Thin
`3 Film Solar Cells", Conf. Record, First World Conference on
`. Photovoltaic Energy Conversion, Hawaii, December, 1994.
`
`in
`
`

`

`
`
`CRYSTAL STRUCTURE
`AND ENERGY BANDS
`
`
`
`Figure 2.1: Lattice Structure of Silicon.
`
`
`
`
`
`
`
`
`
`
`' 4
`
`{ |
`
`lattine are vecenandbasis vectors, a,, of the face-centred cubic
`The primiti
`|
`p
`ve cell contribute a t
`e corners of the
`vimiti
`g. 2.2. The atoms on th
`located wi
`ive cell ofthe silicon lattice, but has an.
`s cell
`|
`remains a primiti
`otal of one atom to the cell.
`Thi
`”
`lattice [2 De Hence. the silicon lattice is technically a complenx
`cubie lattice vithaon many of the symmetries of the face-centred
`extra at
`’
`ome symmetries of the latter d
`om in the primitive cell.
`estroyed by the
`
`
`
`
`
`
`
`
`
`
`
`
`
`INTRODUCTION
`The optical and electronic properties of silicon important in solar cell
`operation are well explained by the electronic band theory of solids.
`This theory models a solid as an ideal periodic crystal with immobile
`atomic nuclei. The effects of vibrations of these nuclei about their
`equilibrium positions are decoupled by treatment as perturbations.
`ted by an actual solid is reduced
`The "“many-electron" problem presen
`to the much simpler “one-electron” problem by describing the effect
`f all other electrons by an average periodic
`field. This chapter reviews this band theory by discussing the
`upon a single electron 0
`energy band structure resulting from silicon's crystalline nature.
`CRYSTAL STRUCTURE
`ach silicon atom is covalently bonded
`In the silicon lattice (Fig. 2.1), &
`to its four nearest neighbours. The angle between the bonds is 109°
`28'. The lattice is equivalent to two interleaved face-centred cubic
`lattices. One is defined by the cube corresponding to the extremities
`of the unit cell (Fig. 2.1), while the second is displaced by one-
`quarter of the distance along the cube diagonal.
`:
`
`
`
`2:
`cic. . Figure 2.2: The Primi
`
`Centred Cubic Space Lattice
`
`tive Cell and the
`
`Nas Westone of the Pace
`
`

`

`
`
`working with the primitive cell
`In the case of silicon. rather than
`work with the large cubic unit
`shown in Fig. 2.2, it is more usual to
`2,1 and 2.2. This contains a total of 8
`cell apparent in both Figs.
`cell allows an orthogonal set of basis
`silicon atoms. Use of this unit
`f the cube.
`vectors to be chosen in the directions along the edges o
`shown in
`Thelattice constant, a, is the length of the side of the cube
`
`(2.1)
`
`C.T. Sah [2.4], however,
`
`|
`SCHRODINGER WAVE EQUATION
`of atoms are described by wave
`Electron properties in 4 lattice tions to the time-independent
`yw, which are solu
`Schrédinger wave equation {2.2}:
`2
`_ Feyaysvinw=Ey
`2M,
`s the reduced Planck constant, Mp is the free electron mass,
`Vir) is the periodic crystal potential
`r is position within the lattice,
`th lattice atoms and the other
`including the contributions from bo
`electrons in the crystal, and Eis the electron energy.
`"Where did we get that from? Nowhere.
`It is not possible to
`derive itfrom anything you know.
`It came out of the mind of
`Schrédinger " - Richard Feynman {2.3].
`does a good job of explaining how the
`Schrédinger equation is a logical synthesis of two classical laws - the
`conservation of energy and Newton's force jaw, plus two quantum
`postulates, the Planck and de Broglie hypotheses.
`(Sah also gives an
`elementary treatment of band theory ata good level relative to that of
`now well developed. Due to the
`Techniques for solving Eq. (2.1) are be expressed in terms of Bloch
`periodicity of Vir), the solutions can
`(2.2)
`y, (kr) = u,{k, r) exp{i kr)
`is introduced as a quantum mechanical
`ariable of use in ordering the solutions
`
`where the wave vector k
`
`of Eq.
`
`i
`
`vrodtatedby apne (2.2) represents a plane wave, exp(ik.r)
`aosat latticn,
`For ction, u,fk,r}, which has the periodicity of the
`Tee ee ° a crystal incorporating a large numberoflattice
`site a yval
`i osen for k will give allowed solutions of this form
`functions ofthe form ofa @.oywhe seach weve.fas wae
`cormespone® to an allowed energy level, Evtk)Theenergylevels
`comes” ne ‘o different values of k and the same value of n
`conse periodiett enerey band. Since E,{k) varies periodically in k
`with2 Pe
`ty etermined by the lattice structure, all distin t
`nik) can be obtained by restricting & to values in the ange:
`—a<ka,<1
`(2.3)
`
`.
`
`2),
`
`ere
`
`i
`
`where the a; are the basis vectors of the primitive lattice
`
`2.4
`
`RECIPROCAL LATTICE
`
`.
`
`equivalent valuesof k.
`of a reciprocal lattice to describe
`Equation (2.3) suggests the use of
`
`
`,vectors: any lattice site can be defined by the set of
`
`In a general crystal lattice, ar
`
`
`
`i
`
`;
`
`(2.4)
`R=n,@, + Ng@2 + Nz,
`
`where the n; are integers , and th
`
`e a,are the basis vectors of the
`primitive unitcell.
`
`A set of reciprocal lattice vectors, G, can be defined such thatat:
`
`
`(2 5)
`G.R = 2m
`
`
`where mis an integer and where:
`
`G=g,b
`
`;
`
`
`
`
`The
`ar
`are integers and b, are the basis vectors of the reciprocal lattice
`gj
`1
`.. Given by:
`
`
`
`b, = 2n (a,x a)/Q,
`
`(2.7)
`
`
`
`

`

`
`
`where i#j#k and Qp is the volume in real space of the primitive unit
`cell of the crystal lattice, given by:
`(2.8)
`Q,= a; (a, xa)
`The "volume" of the unit cell in reciprocal space formed by the basis
`vectors b;is given by the same formula as Eq.(2.8) with a, replaced
`by b,,, This “yolume” has the units of (length)? and equals (27)°/Qp5.
`Applying Eq. (2.7) shows that the reciprocal lattice of a face-centred
`cubic lattice with lattice constant, a, is 4 body-centred cubic lattice
`with lattice constant, 41/a [2.6].
`Distinct values of E,{k) can be obtained by restricting k to thefirst
`Brillouin zone of the reciprocal lattice. This zone is defined as that
`space surrounding a lattice site in the reciprocal lattice which
`contains all points lying closer to this lattice site than to any other
`such lattice site.
`It can be simply constructed from planes which
`perpendicularly pisect the lines joining the selected lattice site to all
`other lattice sites. This construction is shown in Fig. 2.3 for the case
`of a body centred cubic reciprocal lattice. The smallest volume
`formed by these intersecting planes is the first Brillouin zone,
`commonly referred to simply as the Brillouin zone.
`
`io
`
`the truncated octahedron
`Construction of
`Figure 2.3:
`corresponding to the first Brillouin zone of the body centred cubic
`reciprocal lattice, showing its relationship to the cubic unit cell of
`
`which corres
`|
`2.5(b)).
`
`pond to th
`
`ese symmetry points and lines (see Fig.
`
`v
`_ the difficul
`'
`ty in graphically representing the variation of E,{k) as
`n
`
`a
`
`»
`
`0
`
`The Brillouin zone for the silicon lattice is identi
`
`sointsofsym lattice. Shown in Fig. 2.4oreimportantline© face
`rsofmamewinene,"gee ns ao
`symme
`thin
`es
`[2.7]Teneeandpointeofthemeee in the carly1athcentoy
`theo
`etry
`can be mad
`standard 8tonechideachyare labelled accordingto a
`one at 10.0.0) ven [2.8,2.9]. Some examples aretheconeofri
`articular
`es
`the
`type of s
`pone edge ntA ; e <111> axes (A), and their intersections with
`:
`and their zon " anian/a)and equivalentpoints, the <100>
`me
`e edge
`intersections [X = (0,2x/a,0)] and eqcea 4)
`points, and the <110> axes
`(3x/2a,3x/2a,0)] and equivalent oonons their intersections [K =
`
`,
`
`valen
`
`Figure 2.4: The Fir st Brillouin Zone of the Reciprocal Lattice for
`
`lt
`
`

`

`Various techniques exist for calculating the E,({k) relationships for
`real crystals such as silicon [2.10]. Due to the difficulties in
`quantitatively describing the periodic potentials affecting electrons in
`the crystal, these calculations generally involve parameters whose
`values can be adjusted to give a good fit between theory and
`experiment at selected points. By combining theory and experiment
`in this way, a good qualitative picture of the energy band structure of
`silicon has emerged, although quantitative uncertainties remain.
`
`ENERGY BANDS
`
`The band structure of silicon, as calculated using the empirical
`pseudopotential method {2.11}, is presented in the normal marmer in
`Fig. 2.5fb). Bands of allowed energy levels, E,,(k}, for values of k
`lying along lines of symmetry of Fig. 2.4 are shown. The zero of
`energy is arbitrarily chosen to correspond to the highest valence
`band energy. Hence, negative energies correspond to valence band
`states: positive energies to conduction band states. Both the
`conduction and the valence band are made up of several bands
`(branches of the E,{k) relationship} which are coincident for some
`symmetry lines and which cross (overlap) along others. The labelling
`of these bands and energy levels at the points of high symmetry
`corresponds to that of Fig. 2.4.
`
`The point Fr at the centre of the Brillouin zone (k = 0) is the point of
`highest symmetry, and the band structure displays several
`interesting features at this point. The valence band has its lowest
`energy level labelled ©. The next highest energy for this value of k is
`the "triply degenerate” state (neglecting spin orbit splitting, Section
`2.6) labelled I'g5. This state corresponds to the maximum valence
`band energy. Moving away from towards points of lower symmetry,
`this degeneracy disappears, as demonstrated for k values along the 5
`symmetry line. The four separate bands which make up the valence
`band are apparent in this direction. However,
`in the A and A
`directions, the uppermost band in each case (A3 and As, respectively)
`remains doubly degenerate.
`
`Returning to the IF point, the next highest energy state is I'y5, also
`triply degenerate. The energy difference, I)5 - Ios, gives the direct
`bandgap of silicon, with an experimentally determined value of 3.4
`eV. Moving away from I in both the <100> (A) and <111> (A)
`
`
`
`Ek) aE)
`
`4
`
`x OK
`
`ZS
`
`(b)
`
`Figure 2.5: The energy
`b,
`as Calculated
`By Band structure for s
`ilicon is shown in (b}
`using an empiri
`-
`With the ass
`pirical non loca) p.
`seudopotential scheme
`ociated density of electro;ns
`tates g(E) shown in (a)
`(after Chelikowsky and Cohen [2.11] and
`Boer [2.12)) ,
`Returning again to the
`centre of the Brillouin z
`lowest energy in the cond
`non-degenerate, ry State.
`
`

`

`
`
`Figure 2.7: Constant energy surfaces within the Brillouin
`for an
`energyjust above the conduction band minima {eli
`psoids) and just
`below the valance band maximum {sphere}.
`
`the constant
`For energies just below the uppermost valence band,
`energy intersections near Iwill initially be circular but will become
`distorted to more closely resemble s
`quares for
`larger energy
`departures. Constant energy surfaces in
`Fig. 2.6(a) correspondingly
`change from a generally spherical shape n
`ear the zone centre as also
`shown in Fig. 2.7, to a generally cubic s
`hape as the energy below the
`valence band edge increases.
`
`The calculations of Fig. 2.5 and Fi
`g. 2:6 involve semi-empirically
`fitting predictions to experimental da
`ta at points where there is a high
`level ‘of confidence in the latter. At
`points remotefrom thosefitted,
`the calculated results for the ene
`rgy levels aré accurate to within
`about 0.5 eV [2.13].
`
` | a
`
`
`
`f the samecalculation is
`cr neethe, k (energy-momentum)
`ee-dimensional sket
`:
`aoeshown in Fig. 2.6(b). This shows the
`of high symmetry, rather than al