P THE
`HYSICS OF
`SoLARCELLS
`
`Jenny Nelson
`
`Imperial College Press
`
`HANWHA 1018
`
`

`

`THE
`
`PHYSICS OF
`SoLARCELLS
`
`

`

`

`

`Published by
`
`Imperial College Press
`57 Shelton Street
`Covent Garden
`London WC2H 9HE
`
`Distributed by
`
`World Scientific Publishing Co. Pte. Ltd.
`5 Toh Tuck Link, Singapore 596224
`USA office: Suite 202, 1060 Main Street, River Edge, NJ 07661
`UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
`
`British Library Cataloguing-in-Publication Data
`A catalogue record for this book is available from the British Library.
`
`THE PHYSICS OF SOLAR CELLS
`Copyright © 2003 by Imperial College Press
`
`All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
`electronic or mechanical, including photocopying, recording or any information storage and retrieval
`system now known or to be invented, without written permission from the Publisher.
`
`For photocopying of material in this volume, please pay a copying fee through the Copyright
`Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
`photocopy is not required from the publisher.
`
`ISBN 1-86094-340-3
`ISBN 1-86094-349-7 (pbk)
`
`Printed in Singapore by Mainland Press
`
`

`

`

`

`vi
`
`Preface
`
`using crystalline silicon and gallium arsenide cells as examples. Chapter 8
`deals with thin film photovoltaic materials, discussing physical processes
`and design issues relevant to thin films and focusing on the ways in which
`the standard model must be adapted for thin film devices . Chapter 9 deals
`with various techniques for managing light in order to maximise perfor(cid:173)
`mance, and Chapter 10 covers a range of approaches, mainly theoretical,
`to increasing the efficiency of solar cells above the limit for a single band
`gap photoconverter.
`I am grateful to all of the people who have helped me prepare this book.
`In particular, to Keith Barnham for passing the original proposal from Im(cid:173)
`perial College Press in my direction; to Leon Freris and David Infield for
`giving me the opportunity to teach the physics of solar cells to MSc stu(cid:173)
`dents at Loughborough, and so establish the basic course from which this
`book developed; to all the research students in photovoltaics at Imperial
`College for raising so many interesting questions, especially Jenny Barnes,
`James Connolly and Benjamin Kluftinger; to Ralph Gottshalg, Tom Mark(cid:173)
`vart and Peter Wuerfel for help with questions related to material in this
`book; to Ned Ekins-Daukes and Jane Nelson for their helpful comments
`on the text; to Clare Nelson for the cover illustration and to all other col(cid:173)
`leagues who h~ve helped in my endeavours to understand how these things
`work, in particular to Richard Corkish, James Durrant, Michael Gratzel,
`Martin Green, Christiana Honsberg, Stefan Kettemann and Ellen Moons.
`I am grateful to the Greenpeace Environmental Trust for funding me to
`study solar cells before they were popular, and to the UK Engineering and
`Physical Sciences Research Council and for an Advanced Research Fellow(cid:173)
`ship which allowed me to spend my Saturday afternoons writing chapters
`instead of lectures. Finally I am grateful to John Navas for his encourage(cid:173)
`ment to start on this project and to Laurent Chaminade and his staff at IC
`Press and to Lakshmi Narayan and colleagues at World Scientific, for their
`help in seeing it through.
`This book is dedicated to the memory of Stephen Robinson and M.V.
`Mccaughan.
`
`Jenny Nelson
`London, April 2002
`
`

`

`Contents
`
`Preface
`
`1.4.
`
`Introduction
`Chapter 1
`1. 1. Photons In, Electrons Out : The Photovoltaic Effect
`1.2 . Brief History of the Solar Cell . . . . . . . . . . . .
`1.3.
`Photovoltaic Cells and Power Generation . . . . . .
`1.3.1.
`Photovoltaic cells, modules and systems
`1.3.2.
`Some important definitions . . . : . . . .
`Characteristics of the Photovoltaic Qell: A Summary
`1.4.1.
`Photocurrent and quantum efficiency
`1.4.2 .
`Dark current and open circuit voltage .
`1.4.3 .
`Efficiency . . . .. . . . . . . .
`1.4.4.
`Parasitic resistances . . . . .
`1.4.5 .
`Non-ideal diode behaviour
`Summary . .
`1.5.
`References .
`
`2 .1.
`2 .2 .
`2 .3 .
`2.4 .
`
`Chapter 2 Photons In, Electrons Out: Basic
`Principles of PV
`Introduction . . . . . . . . . .. . .
`The Solar Resource . . . . . . . . . .
`Types of Solar Energy Converter
`Detailed Balance
`. . . . . . .
`2.4.1.
`In equilibrium . . . . . .
`2.4.2 . Under illumination
`Work Available from a Photovoltaic Device
`2 .5 .1.
`Photocurrent . . . .
`
`2 .5 .
`
`vii
`
`V
`
`1
`1
`2
`4
`4
`6
`7
`7
`9
`11
`13
`15
`15
`16
`
`17
`17
`17
`22
`24
`24
`26
`28
`28
`
`

`

`viii
`
`Contents
`
`Dark current . . .
`2.5 .2.
`Limiting efficiency
`2 .5 .3 .
`Effect of band gap
`2 .5.4.
`Effect of spectrum on efficiency
`2.5.5.
`Requirements for the Ideal Photoconverter
`2 .6.
`Summary . .
`2 .7 .
`References .
`
`3 .3.
`
`30
`31
`33
`34
`35
`38
`39
`
`41
`41
`42
`42
`44
`46
`46
`48
`49
`50
`51
`54
`55
`56
`56
`57
`58
`60
`61
`61
`62
`63
`65
`65
`66
`66
`68
`69
`72
`72
`75
`
`Chapter 3 Electrons and Holes in Semiconductors
`3 .1.
`Introduction . . . . . . . . . . . .
`3 .2 . Basic Concepts
`. . . . .. . . . . ..
`3.2.1. Bonds and bands in crystals
`Electrons, holes and conductivity
`3 .2 .2.
`Electron States in Semiconductors
`Band structure . . .
`3 .3 .1.
`Conduction band
`3 .3.2.
`3 .3.3.
`Valence band . . .
`Direct and indirect band gaps
`3 .3 .4 .
`3.3.5 .
`Density of states . .. . . . . . .
`Electron distribution function
`3 .3.6.
`3.3.7 .
`-Electron and hole currents
`Semiconductor in Equilibrium . . . . .
`3.4.1.
`Fermi Dirac statistics . . . . .
`3.4.2 .
`Electron and hole densities in equilibrium.
`3 .4.3 . Boltzmann approximation
`. . . . . .. . .
`3.4.4.
`Electron and hole currents in equilibrium . . . . .
`Impurities and Doping
`.
`. . . . .
`3.5.1.
`Intrinsic semiconductors
`3.5 .2 .
`n type doping
`.. . . . . .
`3.5.3.
`p type doping
`. . . . . . . . . . . .
`3 .5.4.
`Effects of heavy doping . . . . . . . . . . . . .
`Imperfect and amorphous crystals
`3.5.5 .
`. . . . . .
`Semiconductor under Bias
`. . . . . . . .. . .
`3 .6 .1. Quasi thermal equilibrium
`. . . .
`. .. .. .
`3 .6.2.
`Electron and hole densities under bias . .
`3.6.3. Current densities under bias
`. . . . . . .
`Drift and Diffusion
`. . . . . . . . . . . . . . . .
`3. 7 .1. Current equations in terms of drift and diffusion
`3 . 7 .2 . Validity of the drift-diffusion equations . . . . . .
`
`3.4.
`
`3.5 .
`
`3.6 .
`
`3 .7 .
`
`

`

`Contents
`
`3 .7.3 . Current equations for non-crystalline solids
`S UOlinary ..
`~
`~
`..
`.
`.
`.,
`..
`.
`..
`..
`.
`.
`..
`.
`.
`.
`.
`.
`.
`
`3 .8 .
`
`4.4 .
`
`Chapter 4 Generation and Recombination
`4 .1 .
`Introduction: Semiconductor Transport Equations
`4 .2 .
`Generation and Recombination . . . . . . . . . . .
`4 .3 .
`Quantum Mechanical Description of Transition Rates
`4.3 .1.
`Fermi's Golden Rule . . . . . .. . . . . .
`4 .3 .2 . Optical processes in a two level system
`Photogeneration . . . . . . . .
`. . . . .
`4.4.1 .
`Photogeneration rate . . . .. . . . . . .
`4.4.2 .
`Thermalisation . . . . . . . . . . . . . .
`4.4.3 .
`Microscopic description of absorption
`4 .4 .4 .
`Direct gap semiconductors .
`4 .4 .5 .
`Indirect gap semiconductors
`4.4.6 .
`Other types of behaviour
`Examples and data . .
`4.4.7.
`4 .5 . Recombination
`. . . . . . . . . .
`Types of recombination
`4 .5 .1.
`4 .5 .2 . Radiative recombination
`Simplified expressions for rap.iative recombination
`4 .5 .3.
`4 .5.4.
`Auger recombination
`. . . . . . . . . . . .
`4.5 .5 .
`Shockley Read Hall recombination . . . . .
`4 .5 .6.
`Surface and grain boundary recombination
`4.5.7 .
`Traps versus recombination centres
`Formulation of the Transport Problem
`. . . . . .
`4.6.1. Comments on the transport problem
`Transport equations in a crystal . .
`4 .6 .2 .
`4 .7 . Summary . .
`References .
`
`4 .6 .
`
`Junctions
`Chapter 5
`5 .1.
`Introduction . . . . . . . . . . . . . . . . .
`5 .2 . Origin of Photovoltaic Action . . . . . . .
`5 .3 . Work Function and Types of Ju:q.ction
`5 .4 . Metal-Semiconductor Junction
`5.4.1.
`Establishing a field
`5 .4 .2 . Behaviour in the light .
`5.4.3 . Behaviour in the dark .
`
`ix
`
`76
`77
`
`79
`79
`81
`83
`83
`85
`87
`88
`89
`90
`93
`94
`96
`98
`99
`99
`99
`102
`105
`106
`110
`111
`112
`113
`114
`115
`117
`
`119
`119
`120
`124
`125
`125
`126
`127
`
`

`

`X
`
`Contents
`
`5.4 .4.
`. . . . . . . . . . . . . . . .
`Ohmic contacts
`Limitations of the Schottky barrier junction
`5.4.5 .
`5 . 5 . Semiconductor- Semiconductor Junctions
`5 .5 . l. p-n junction . . . .
`. . . .
`5 .5 .2 . p-i-n junction . . .
`. . . . .
`p-n heterojunction
`5 .5.3 .
`. . . .
`5 .6 . Electrochemical Junction . . . . . . . .
`5 .7 .
`Junctions in Organic Materials
`. . . .
`5 .8 .
`Surface and Interface States . . .
`Surface states on free surfaces
`5 .8 .1.
`5 .8 .2 .
`Effect of interface states on junctions
`5 .9 .
`Summary .
`References .
`
`129
`130
`131
`131
`132
`133
`133
`137
`139
`139
`141
`143
`144
`
`145
`145
`146
`146
`147
`149
`150
`152
`
`152
`
`154
`156
`156
`160
`160
`160
`165
`165
`167
`169
`172
`172
`172
`173
`
`6 .4 .
`
`6.4.2 .
`
`Chapter 6 Analysis of the p-n Junction
`6 .1.
`Introduction . .. . . . . . . . . . . .
`6 .2 . The p-n Junction . . . . . . . . . .
`6 .2 .1.
`Formation of p-n junction
`6 .2 .2 . Outline of approach . . . .
`6 .3 . Depletion Approximation .
`. . . . . .
`6 .3 .1.
`Calculation of depletion width
`Calculation of Carrier and Current Densities .
`6.4.1. Currents and carrier densities in the neutral
`regions
`. . . . . . . . . . . . . . . . . .
`. . .
`Currents and carrier densities in the space
`charge region . . . . . .
`. . . .
`Total current density
`. . . .
`6.4.3 .
`General Solution for J(V)
`p-n Junction in the Dark . . . .
`6 .6 .1. At equilibrium . . . . .
`6 .6 .2 . Under applied bias
`p-n Junction under Illumination .
`6.7.1.
`Short circuit . . . . . . .
`6 . 7 .2 .
`Photocurrent and QE in special cases
`6. 7.3 .
`p-n junction as a photovoltaic cell . . . .
`Effects on p-n Junction Characteristics
`. . . . .
`Effects of parasitic resistances
`6 .8 .1.
`6 .8 .2 .
`Effect of irradiation .
`6 .8 .3 .
`Effect of temperature . . . . .
`
`6 .5 .
`6 .6 .
`
`6 .7 .
`
`6 .8 .
`
`

`

`Contents
`
`6 .8 .4 . Other device structures . . . .
`6 .8 .5 . Validity of the approximations .
`. . . . . . . . .
`6 .9 . Summary . .
`References . .. . . .
`
`. . . .
`
`7 .3 .
`
`7.4.
`
`Chapter 7 Monocrystalline Solar Cells
`. . . .
`7 .1.
`Introduction: Principles of Cell Design
`. . . .
`7 .2 . Material and Design Issues . . . . . . . . . .
`.
`7 .2 .1. Material dependent factors .
`. . . . . . . . .
`7 . 2 . 2 . Design factors
`7 .2 .3. General design features of p-n junction cells
`Silicon Material Properties . . . . . . . . . . . . .
`7 .3 .1 . Band structure and optical absorption
`7 .3 .2. Doping . . . . . .
`7 .3.3. Recombination . .
`7 .3 .4 . Carrier transport
`Silicon Solar Cell Design .
`7.4.1. Basic silicon solar cell
`7.4.2 .
`Cell fabrication
`7.4.3. Optimisation of siJicon solar cell design . + • •
`7.4.4.
`Strategies to enhance absorption . . . . .
`7 .4 .5 .
`Strategies to reduce surface 'recombination
`7.4.6.
`Strategies to reduce series resistance . . .
`7.4.7 .
`Evolution of silicon solar cell design .
`7.4.8.
`Future directions in silicon <;ell design
`7.4.9 . Alternatives to silicon . . . . . . . . ..
`III-V Semiconductor Material Properties . . ..
`7 .5 .1.
`III-V semiconductor band structure and optical
`absorption . . . . .
`7.5.2 . Gallium arsenide
`7.5.3. Doping . . .
`.
`. .
`7.5.4. Recombination . . .
`7 .5 .5 . Carrier transport
`7.5.6 .
`Reflectivity . . . .
`GaAs Solar Cell Design .
`.
`7 .6.1. Basic GaAs solar cell
`7 .6 .2.
`Optimisation of GaAs solar cell design
`Strategies to reduce front surface recombination
`7 .6.3.
`7.6.4.
`Strategies to reduce series resistance . . . . . . .
`
`7 .5.
`
`7 .6.
`
`xi
`
`174
`174
`175
`176
`
`177
`177
`178
`178
`179
`180
`180
`180
`181
`182
`185
`186
`186
`186
`188
`190
`191
`194
`194
`197
`198
`198
`
`198
`200
`201
`202
`203
`203
`204
`204
`204
`205
`207
`
`

`

`xii
`
`Contents
`
`Strategies to reduce substrate cost .
`7 .6 .5 .
`7 .7 . Summary .
`. . . . . . . . . .
`References .
`. . . . . . . .
`. . . .
`
`208
`208
`210
`
`211
`211
`213
`213
`213
`213
`215
`217
`217
`219
`220
`221
`221
`221
`222
`227
`227
`229
`230
`233
`
`234
`236
`239
`240
`
`242
`243
`243
`244
`245
`246
`246
`247
`248
`
`Chapter 8 Thin Film Solar Cells
`8 .1.
`Introduction . . . . . .. . . . . .. . . . . . . . .
`8 .2 . Thin Film Photovoltaic Materials
`8 .2 .1. Requirements for suitable materials
`8 .3 . Amorphous Silicon
`. . . . . . . . . . .
`8 .3 .1. Materials properties .. . . . . .
`8 .3 .2 . Defects in amorphous material
`8 .3 .3 . Absorption . . .
`. . . .
`8 .3.4. Doping . .
`. . . .
`8 .3.5.
`Transport
`8.3 .6 .
`Stability
`. . . .
`8 .3. 7 . Related alloys
`8 .4 . Amorphous Silicon Solar Cell Design
`8.4 .1. Amorphous silicon p-i-n structures . . . .
`8 .4 . 2 .
`. . .
`p-i-n solar cell device physics
`8.4.3.
`Fabrication of a-Si solar cells . . . . . . . .
`8.4.4 .
`Strategies to improve a-Si cell performance .
`8 .5 . Defects in Polycrystalline Thin Film Materials . .
`8.5.1. Grain boundaries
`. . . . . . . . . . . . .. . . . . .
`8 .5.2 .
`Effects of grain boundaries on transport
`. . . .
`8 .5 .3 . Depletion approximation model for grain
`boundary . . . . . . . . . .
`8 .5.4. Majority carrier transport
`8 .5 .5 .
`. Effect of illumination
`. . .
`8 .5 .6 . Minority carrier transport
`. . . . . .
`8 .5 .7 .
`Effects of grain boundary recombination on solar
`cell performance . . .
`.
`. . . .
`CulnSe2 Thin Film Solar Cells . .
`. . . . . . . . .. . . . . . . .
`8 .6 .1. Materials properties . . . . . . . . . . . .. .
`. . . . .
`8.6 .2 . Heterojunctions in thin film solar cell design . . . .
`8 .6.3 .
`CulnGaSe2 solar cell design
`CdTe Thin Film Solar Cells
`.
`8 .7 .1. Materials properties .
`8.7.2.
`CdTe solar cell design
`Thin Film Silicon Solar Cells . . .
`
`8 .7 .
`
`8 .8 .
`
`8 .6 .
`
`

`

`Contents
`
`8.8.1 .
`. .
`. .. . .
`Materials properties . . . . .
`8.8 .2.
`Microcrystalline silicon solar cell design
`8.9 . Summary . .
`References .
`
`9 .3 .
`
`9.4.
`
`9 .5.
`
`Chapter 9 Managing Light
`9 .1.
`Introduction . . . . . . . . . . . . . . . . . . . .
`9 .2 . Photon Flux: A Review and Overview of Light
`Management . . . .. . . . . . . . . . ..
`. . . . .
`9.2 .1. Routes to higher photon flux . . . . . .
`. . . .
`Minimising Reflection . . . .
`. . . . . . . . .
`9 .3 .1. Optical properties of semiconductors
`9 .3 .2 . Antireflection coatings
`Concentration . . . . . . . . . .
`Limits to concentration .
`9 .4 .1.
`9.4.2 .
`Practical concentrators . . . .
`Effects of Concentration on Device Physics .
`9.5 .1.
`Low injection
`. . . . . . . . . . .
`9.5 .2. High injection . . . . . . . . .
`. .
`9 .5 .3 .
`Limits to efficiency under concentration .
`9.5.4 .
`Temperature . . . . . . .
`9 .5.5 .
`Series resistance . . . . . . .
`9 .5 .6 .
`Concentrator cell design
`9 .5.7. Concentrator cell materials
`Light Confinement
`. . . . . . . . . .
`9 .6.1.
`Light paths and ray tracing
`9.6 .2. Mirrors . . . . .
`9 .6 .3 . Randomising surfaces
`9.6.4.
`Textured surfaces
`. .
`9.6 .5 .
`Practical schemes
`. .
`9.6.6 .
`Light confining structures : restricted acceptance
`areas and external cavities
`. . . . . . . . .
`Effects of light trapping on device physics
`9.6 .7 .
`Photon Recycling . .
`. . . . . . . . .
`Theory of photon recycling
`9 . 7 .1 .
`9 .7 .2 .
`Practical schemes
`Summary . .
`9.8 .
`References . . .
`. .
`
`9.6.
`
`9 .7.
`
`. . . . . . . .
`
`xiii
`
`248
`248
`249
`251
`
`253
`253
`
`255
`257
`258
`258
`260
`263
`263
`264
`266
`266
`267
`269
`270
`270
`270
`271
`272
`272
`274
`275
`276
`278
`
`280
`281
`282
`282
`285
`286
`288
`
`

`

`xiv
`
`Contents
`
`10.6.
`
`Chapter 10 Over the Limit: Strategies for High Efficiency
`10.1. Introduction .
`.
`.
`.
`. . . . . . . . . . . . . . . . . . . . . . . .
`10.2 . How Much is Out There? Thermodynamic Limits to
`Efficiency
`. . . . . . . . . . . . . . . . . . . . .
`10.3 . Detailed Balance Limit to Efficiency, Reviewed
`10.4 . Multiple Band Gaps
`. . . . . . . .
`10.5 . Tandem Cells
`. . . . . . . . . .. . .
`10.5 .1. Principles of tandem cells . . .
`10.5 .2 . Analysis
`. . . . . . . . . . .
`10.5 .3 . Practical tandem systems .
`. . . .
`Intermediate Band and Multiple Band Cells
`10.6 .1. Principles of intermediate and multiple band cells
`10.6 .2 . Conditions . . . . . . . . .. . . . . . . . . . .
`10.6 .3. Practical strategies
`. . . . . . . . . . . .. . .
`Increasing the Work Per Photon using 'Hot' Carriers
`10.7.1. Principles of cooling and 'hot' carriers .
`10. 7 . 2 . Analysis of the hot carrier solar cell .
`10.7 .3. Practical strategies . . . . . . . . .. . . . .
`10.8 . Impact Ionisation Solar. Cells . . . . . . . . . . . . .
`10.8 .1. . Analysis of impact ionisation solar cell
`10.9 . Summary
`References .
`
`10.7 .
`
`Exercises
`
`Solutions to the Exercises
`
`Index
`
`289
`289
`
`291
`292
`297
`298
`298
`300
`301
`302
`302
`303
`306
`309
`309
`311
`316
`318
`320
`323
`324
`
`327
`
`337
`
`355
`
`

`

`Contents
`
`xv
`
`Fundamental constants
`
`£0
`
`h
`n
`
`Planck's constant
`Planck's constant/21r
`dielectric permittivity of free space
`Stefan's constant
`O"B
`speed of light in vacuum
`c
`kB Boltzmann's constant
`rno
`free electron mass
`charge on the electron
`q
`
`Symbols used in the text
`
`a
`f3
`X
`~µ
`£
`
`Es
`e
`¢
`q>
`c/Jo
`T/
`K,s
`.,\
`µ
`µn; µp
`V
`Be
`Bsun
`p
`(T
`
`T
`'n;'p
`w
`n
`'ljJ
`V, Vr
`Vk
`
`absorption coefficient
`spectral photon flux density per unit solid angle
`electron affinity
`quasi Fermi level separation or chemical potential of light
`emissivity i.e. probability of photon emission
`dielectric permittivity of semiconductor
`polarisation vector of light
`electrostatic potential
`work function
`neutrality level
`power conversion efficiency
`imaginary part of refractive index of semiconductor
`wavelength of light
`chemical potential
`electron mobility; hole mobility
`frequency of light
`critical angle at optical interface
`angular width of the sun
`charge density or resistivity
`conductivity
`lifetime
`electron lifetime; hole lifetime
`angular frequency of light
`solid angle
`wavefunction
`grad operator with respect to position
`grad operator with respect to wavevector
`
`

`

`xvi
`
`Contents
`
`probability of photon absorption
`cell area
`spectral photon flux density normal to surface
`coefficient for bimolecular capture by trap of electrons;
`holes
`coefficient of bimolecular radiative recombination
`diffusion coefficient
`diffusion coefficient of electron; diffusion coefficient of hole
`energy
`electromagnetic field strength
`Fermi energy or Fermi level
`electron quasi-Fermi energy level; hole quasi-Fermi level
`band gap
`energy of trap state
`energy of valence band edge
`energy of conduction band edge
`intrinsic energy level
`vacuum energy level
`electrostatic field
`force
`probability occupation function for electronic state at k, r
`Fermi Dirac probability occupation function
`geometrical factor relating normal to angular photon flux
`density for emission from: ambient; cell; sun; concentrated
`light source
`fill factor
`spectral photogeneration rate per unit volume
`generation rate per unit volume
`electron generation rate per unit volume
`hole generation rate per unit volume
`density of electronic states per unit energy per unit crystal
`volume
`Hamiltonian operator
`current
`incident light intensity
`current density
`short circuit current density
`dark current density
`electron current density; hole current density
`
`Brad
`D
`Dn; Dp
`E
`Ea
`EF
`EFn; EFp
`Eg
`Et
`Ev
`Ee
`Ei
`Evac
`F
`F
`f(k, r)
`Jo
`Fa; Fe; Fs; Fx
`
`FF
`g
`G
`Gn
`Gp
`g(E)
`
`H
`I
`Io
`J
`Jsc
`
`Jdark
`Jn; Jp
`
`

`

`Contents
`
`xvii
`
`Jn; Jp
`k
`L
`Ln; Lp
`1Tl,
`m* C
`m* V
`M
`n
`no
`ni
`ns
`Na
`Nd
`Ne
`Nv
`Ni
`Nt
`Ns
`p
`p
`p
`Po
`Q
`QE
`r
`r
`R
`Rs
`Rsh
`s
`Sn
`Sp
`t
`T
`Ts
`UE
`u
`Un
`
`spectral electron current density; spectral hole current density
`crystal wavevector
`diffusion length or length of crystal sample
`diffusion length of electron; diffusion length of hole
`diode ideality factor
`conduction band effective mass
`valence band effective mass
`dipole matrix element
`density of electrons per unit volume
`equilibrium electron density
`intrinsic carrier density
`refractive index of semiconductor
`density of acceptor impurity atoms
`density of donor impurity atoms
`effective conduction band density of states
`effective valence band density of states
`charged background doping in intrinsic layer
`density of trap states
`density of interface states per unit area
`density of holes per unit volume
`momemtum
`power density
`equilibrium hole density
`charge
`quantum efficiency
`position
`transition rate
`reflectivity
`series resistance
`shunt or parallel resistance
`vector defining a point on surface
`electron surface recombination velocity
`hole surface recombination velocity
`time
`temperature
`temperature of sun
`energy density of radiation per unit volume
`recombination rate per unit volume
`electron recombination rate per unit volume
`
`

`

`Contents
`
`xviii
`
`V
`
`hole recombination rate per unit volume
`Auger recombination rate
`radiative recombination rate
`Shockley Read Hall recombination rate
`volume
`velocity
`voltage or bias
`built in bias
`open circuit voltage
`donor ionisation energy
`acceptor ionisation energy
`thickness of depletion region in n layer; in p layer
`concentration factor
`
`Acronyms
`
`e .m .f.
`ac
`de
`AM
`AMl.5
`STC
`CB
`VB
`FGR
`PV
`a-Si
`c-Si
`µ-Si
`a-Si:H
`a-SiC
`a-SiGe
`DOS
`JDOS
`i region
`SCR
`QE
`SRH
`GaAs
`CdTe
`
`standard for solar cell calibration
`
`electromotive force
`alternating current
`direct current
`air mass
`air mass 1 .5 spectrum -
`standard test conditions
`conduction band
`valence band
`Fermi's golden rule
`photovoltaics
`amorphous silicon
`crystalline silicon
`microcrystalline silicon
`hydrogenated amorphous silicon
`amorphous silicon-car hon alloy
`amorphous silicon-germanium alloy
`density of states
`joint density of states
`intrinsic or undoped region of a p-i-n junction
`space charge region
`quantum efficiency
`Shockley-Read-Hall
`gallium arsenide
`cadmium telluride
`
`

`

`xix
`
`Contents
`
`CIGS
`AR
`PERL
`PESC
`TCO
`PR
`QD
`QW
`LO
`
`copper indium gallium diselenide
`antireflection
`passivated emitter, rear locally diffused solar cell
`passivated emitter solar cell
`transparent conducting oxide
`photon recycling
`quantum dot
`quantum well
`longitudinal optical ( of phonons)
`
`

`

`

`

`2
`
`The Physics of Solar Cells
`
`however, there is some built-in asymmetry which pulls the excited electrons
`away before they can relax, and feeds them to an external circuit. The extra
`energy of the excited electrons generates a potential difference, or electro(cid:173)
`motive force (e.m .f.) . This force drives the electrons through a load in the
`external circuit to do electrical work.
`The effectiveness of a photovoltaic device depends upon the choice of
`light absorbing materials and the way in which they are connected to the
`external circuit. The following chapters will deal with the underlying phys(cid:173)
`ical ideas, the device physics of solar cells, the properties of photovoltaic
`materials and solar cell design. In this chapter we will summarise the main
`characteristics of a photovoltaic cell without discussing its physical function
`in detail.
`
`1. 2. Brief History of the Solar Cell
`
`The photovoltaic effect was first reported by Edmund Bequerel in 1839
`when he observed that the action of light on a silver coated platinum elec(cid:173)
`trode immersed in electrolyte produced an electric current. Forty years
`later the first solid state photovoltaic devices were constructed by work(cid:173)
`ers investigating the recently discovered photoconductivity of selenium. In
`1876 William Adams and Richard Day found that a photocurrent could
`be produced in a sample of selenium when contacted by two heated plat(cid:173)
`inum contacts. The photovoltaic action of the selenium differed from its
`photoconductive action in that a current was produced spontaneously by
`the action of light. No external power supply was needed. In this early pho(cid:173)
`tovoltaic device, a rectifying junction had been formed between the semi(cid:173)
`conductor and the metal contact. In 1894, Charles Fritts prepared what
`was probably the first large area solar cell by pressing a layer of selenium
`between gold and another metal. In the following years photovoltaic effects
`were observed in copper-copper oxide thin film structures, in lead sulphide
`and thallium sulphide. These early cells were thin film Schottky barrier
`devices, where a semitransparent layer of metal deposited on top of the
`semiconductor provided both the asymmetric electronic junction, which is
`necessary for photovoltaic action, and access to the junction for the inci(cid:173)
`dent light. The photovoltaic effect of structures like this was related to the
`existence of a barrier to current flow at one of the semiconductor- metal
`interfaces (i. e ., rectifying action) by Goldman and Brodsky in 1914. Later ,
`during the 1930s, the theory of metal-semiconductor barrier layers was
`developed by Walter Schottky, Neville Mott and others.
`
`

`

`Introduction
`
`3
`
`However, it was not the photovoltaic properties of materials like sele(cid:173)
`nium which excited researchers, but the photoconductivity. The fact that
`the current produced was proportional to the intensity of the incident light,
`and related to the wavelength in a definite way meant that photoconductive
`materials were ideal for photographic light meters . The photovoltaic effect
`in barrier structures was an added benefit, meaning that the light meter
`could operate without a power supply. It was not until the 1950s, with the
`development of good quality silicon wafers for applications in the new solid
`state electronics, that potentially useful quantities of power were produced
`by photovoltaic devices in crystalline silicon.
`In the 1950s, the development of silicon electronics followed the discov(cid:173)
`ery of a way to manufacture p-n junctions in silicon. Naturally n type silicon
`wafers developed a p type skin when exposed to the gas boron trichloride .
`Part of the skin could be etched away to give access to the n type layer
`beneath. These p-n junction structures produced much better rectifying
`action than Schottky barriers, and better photovoltaic behaviour. The first
`silicon solar cell was reported by Chapin, Fuller and Pearson in 1954 and
`converted sunlight with an efficiency of 6%, six times higher than the best
`previous attempt. That figure was to rise significantly over the following
`years and decades but, at an estimated production cost of _some $200 per
`Watt, these cells were not seriously consider~d for power generation for sev(cid:173)
`eral decades. Nevertheless, the early silicon solar cell did introduce the pos(cid:173)
`sibility of power generation in remote locations where fuel could not easily
`be delivered. The obvious application was to satellites where the require(cid:173)
`ment of reliability and low weight made the cost of the cells unimportant
`and during the 1950s and 6ds, silicon solar cells were widely developed for
`applications in space.
`Also in 1954, a cadmium sulphide p-n junction was produced with an
`efficiency of 6%, and in the following years studies of p-n junction pho(cid:173)
`tovoltaic devices in gallium arsenide, indium phosphide and cadmium tel(cid:173)
`luride were stimulated by theoretical work indicating that these materials
`would offer a higher efficiency. However, silicon remained and remains the
`foremost photovoltaic material, benefiting from the advances of silicon tech(cid:173)
`nology for the microelectronics industry. Short histories of the solar cell are
`given elsewhere (Shive, 1959; Wolf, 1972; Green, 1990].
`In the 1970s the crisis in energy supply experienced by the oil-dependent
`western world led to a sudden growth of interest in alternative sources of
`energy, and funding for research and development in those areas. Photo(cid:173)
`voltaics was a subject of intense interest during this period, and a range of
`
`

`

`4
`
`The Physics of Solar Cells
`
`strategies for producing photovoltaic devices and materials more cheaply
`and for improving device efficiency were explored. Routes to lower cost in(cid:173)
`cluded photoelectrochemical junctions, and alternative materials such as
`polycrystalline silicon, amorphous silicon, other 'thin film' materials and
`organic conductors. Strategies for higher efficiency included tandem and
`other multiple band gap designs . Although none of these led to widespread
`commercial development, our understanding of the science of photovoltaics
`is mainly rooted in this period.
`During the 1990s, interest in photovoltaics expanded, along with grow(cid:173)
`ing awareness of the need to secure sources of electricity alternative to
`fossil fuels . The trend coincides with the widespread deregulation of the
`electricity markets and growing recognition of the viability of decentralised
`power. During this period, the economics of photovoltaics improved pri(cid:173)
`marily through economies of scale. In the late 1990s the photovoltaic pro(cid:173)
`duction expanded at a rate of 15-25% per annum, driving a reduction in
`cost. Photovoltaics first became competitive in contexts where conventional
`electricity supply is most expensive, for instance, for remote low power ap(cid:173)
`plications such as navigation, telecommunications, and rural electrification
`and for enhancement of supply in grid-connected loads at peak use [An(cid:173)
`derson, 2001] . -As prices_ fall, new markets are opened up . An important
`example is building integrated photovoltaic applications, where the cost of
`the photovoltaic system is offset by the savings in building materials.
`
`1. 3. Photovoltaic Cells and Power Generation
`
`1.3.1. Photovoltaic cells, modules and systems
`
`The solar cell is the basic building block of solar photovoltaics. The cell can
`be considered as a two terminal device which conducts like a diode in the
`dark and generates a photovoltage when charged by the sun. Usually it is a
`thin slice of semiconductor material of around 100 cm 2 in area. The surface
`is treated to reflect as little visible light as possible and appears dark blue
`or black. A pattern of metal contacts is imprinted on the surface to make
`electrical contact (Fig. 1.2(a)) .
`When charged by the sun, this basic unit generates a de photovoltage of
`0 .5 to 1 volt and, in short circuit, a photocurrent of some tens of milliamps
`per cm2 . Although the current is reasonable, the voltage is too small for
`most applications. To produce useful de voltages, the cells are connected to(cid:173)
`gether in series and encapsulated into modules. A module typically contains
`
`

`

`

`

`

`

`Introduction
`
`7
`
`that illumination. Thus both I and V are determined by the illumination
`as well as the load. Since the current is roughly proportional to the illumi(cid:173)
`nated area, the short circuit current density Jsc is the useful quantity for
`comparison. These quantities are defined for a simple, ideal diode model of
`a solar cell in Sec. 1 .4 below.
`
`Box 1 . 1. Solar cell compared with conventional battery
`
`The photovoltaic cell differs from a simple de battery in these respects:
`the e .m .f. of the battery is due to the permanent electrochemical potential
`difference between two phases in the cell, while the solar cell derives its
`e.m.f. from a temporary change in electrochemical potential caused by light.
`The power delivered by the battery to a constant load resistance is relatively
`constant, while the power delivered by the solar cell depends on the incident
`light intensity, and not primarily on the load (Fig. 1.4) . The battery is
`completely discharged when it reaches the end of its life, while the solar cell,
`although its output varies with intensity, is in principle never exhausted,
`since it can be continually recharged with light.
`The battery is modelled electrically as a voltage generator and is char(cid:173)
`acterised by its e.m.f. ( which, in practice, depends- upon the_ degree of dis(cid:173)
`charge), its charge capacity, and by a polarisation curve which describes
`how the e.m.f. varies w ith current (Vincent~ 1997] . The solar cell, in con(cid:173)
`trast, is better modelled as a current generator, since for all but the largest
`loads the current drawn is independent of load. But its characteristics de(cid:173)
`pend entirely on the nature of the illu