Optoelectronics of molecules and polymers/ Andre Moliton

Contents
Preface by Richard H.Friend
List ofabbreviations
Introduction
Part One: Concepts:Electronic and optical processes in organic solids
Chapter I: Band and electronic structures in regular 1-dimensional
media ^
I An introduction to approximations of weak and strong
bonds 3
1 Materials with weak bonds 3
2 Materials with strong bonds 4
II Band Structure in weak bonds 6
1 Prior result for zero order approximation 6
2 Physical origin offorbidden bands 6
3 Simple estimation ofthe size of the forbidden
band 8
III Floquet's theorem: wavefunctions for strong bonds 9
1 Form of the resulting potential 9
2 The form ofthe wavefunction 10
3 Floquet's theorem:effect of potential periodicity
on wavefunction form 11
IV A study on energy 12
1 Defining equations(with x = r: 1 — D) 12
2 Calculation ofenergy for a chain ofN atoms 13
3 Additional comments: physical significance of
terms(Eq -a)and p; simple calculation of E;
and the appearance of allowed and forbidden
bands in strong bonds 16xviii Contents
V 1-D crystal and the distorted chain 19
1 AB type crystal 19
2 The distorted chain 20
VI Density function and its application, the metal insulator
transition and calculation of Erdax 22
1 State density functions 22
2 Filling up zones and Peierls insulator-metal
transition 24
3 Principle ofthe calculation of Erd;,x E)r a distorted
chain 25
VII Practical example: calculation of wavefunction energy
levels, orbital density function and band filling for a
regular chain ofatoms 26
1 Limits of variation in k 26
2 Representation ofenergy and the orbital density
function using N = 8 26
3 Wavefunction forms for bonding and antibonding
states 27
4 Generalisation regarding atomic chain states 30
VIII Conclusion 30
Chapter II: Electron and band structure 33
I Introduction 33
II Going from l-D to 3-D 34
1 3-D General expression of permitted energy 34
2 Expressions for effective mass, band size and
mobility 35
III 3-D covalent crystal from a molecular model: sp^
hybrid states at nodal atoms 36
1 General notes 36
2 Independent bonds: formation of molecular
orbitals 38
3 Coupling of molecular orbitals and band
formation 40
IV Band theory limts and the origin of levels and bands
from localised states 41
1 Influence of defaults on evolution of band
structure and the introduction of'localised levels'. 41
2 The effects of electronic repulsions, Hubbard's
bands and the insulator-metal transition 43
3 Effect of geometrical disorder and Anderson
localisation 47
V Conclusion ■; 57Contents xix
Chapter III: Electron and band structures of'perfect'organic solids ... 59
I Introduction: organic solids 59
1 Context 59
2 Generalities 59
3 Definition of conjugated materials; an
aide-memoire for physicians and electricians 62
II Electronic structure of organic intrinsic solids:
TT-conjugated polymers 63
1 Degenerate n-conjugated polymers 63
2 Band scheme for a non-degenerate tt-conjugated
polymer: poly(/wra-phenylene) 65
III Electronic structure of organic intrinsic solids: small
molecules 68
1 Evolution of energy levels in going from an
isolated chain to a system ofsolid state condensed
molecules 68
2 Energy level distribution in Alq3 69
3 Fullerene electronic levels and states 70
IV Conclusion: energy levels and electron transport 74
Chapter IV: Electron and band structures of'real'organic solids 77
I Introduction: 'reaE organic solids 77
II Lattice-charge coupling—polarons 77
1 Introduction 77
2 Polarons 78
3 Model of molecular crystals 79
4 Energy spectrum ofsmall polaron 83
5 Polarons in ji-conjugated polymers 85
6 How do we cross from polaron-exciton to
polaron? 87
7 Degenerate Ti-conjugated polymers and solitons .. 88
III Towards a complete band scheme 90
1 Which effects can intervene? 90
2 Complete band scheme accumulating different
possible effects 91
3 Alq3 and molecular crystals 93
IV Conclusion 95
Chapter V: Conduction in delocalised,localised and polaronic states .. 99
I Introduction 99
II General theories ofconduction in delocalised states .... 100
I General results of conductivity in a real crystal:
limits of classical theories 100XX Contents
2 Electrical conduction in tcrnis of inobilities and
the Kubo-Grecnwood relationship: reasoning in
reciprocal space and energy space lor delocalised
states 101
III Conduction in delocalised band states: degenerate and
non-degenerate organic solids 103
1 Degenerate systems 103
2 Non-degenerate systems: limits of applicability
of the conduction theory in bands of delocalised
states for systems with large or narrow bands
(mobility condition) 105
IV Conduction in localised state bands 109
1 System 1: Non-degenerated regime; conductivity
in the tail band 1 10
2 System 2: degenerate regime; conductivity in
deep localised states I l l
V Transport mechanisms with polarons 1 16
1 Displacements in small polaron bands and
displacements by hopping 116
2 Characteristics of hopping by small polarons 117
3 Precisions for the 'semi-classical' theory:
transition probabilities 120
4 Relationships for continuous conductivity
through polaron transport 122
5 Conduction in 3D in TT-conjugated polymers 124
VI Other envisaged transport mechanisms 128
1 Sheng's granular metal model 128
2 Efros—Shklovskii's model from Coulombic
effects 128
3 Conduction by hopping from site to site in a
percolation pathway 128
4 Kaiser's model for conduction in a heterogeneous
structure 129
VII Conclusion: real behaviour 129
1 A practical guide to conducting polymers 129
2 Temperature dependence analysed using the
parameter w =—[(9In p)/9 In T] 131
Chapter VI: Electron transport properties 133
I Introduction 133
II Basic mechanisms 133
1 Injection levels 133
2 Three basic mechanisms 134
III Process A: various(emission)currents produced by
electrodes 135Contents xxi
1 Rectifying contact(blocking metal —> insulator).. 135
2 Thermoelectronic emission(T 5:^: 0; E;,=0) 136
3 Field effect emission (Shottky): Ey is'medium
intense' 136
4 Tunnelling effect emissions and
Fowler-Nordheim's equation 137
IV Process B(simple injection): ohmic contact and current
limited by space charge 138
1 Ohmic contact(electron injection) 138
2 The space charge limited current law and
saturation current(/v)for simple injection in
insulator without traps 139
3 Transitions between regimes 143
4 Insulators with traps and characteristics oftrap
levels 144
5 Expression for current density due to one carrier
type (Jsp) with traps at one discreet level (E,);
effective mobility 147
6 Deep level traps distributed according to Gaussian
or exponential laws 151
V Double injection and volume controlled current:
mechanism C in Figure VI-2 154
1 Introduction: differences in properties of organic
and inorganic solids 154
2 Fundamental equations for planar double
injection (two carrier types) when both currents
are limited by space charge: form of resulting
current Jvcc(no trap nor recombination centres) . 155
3 Applications 157
VI The particular case ofconduction by the Poole-Frenkel
effect 159
1 Coulombic traps 160
2^ Conduction due to Poole-Frenkel effect(as
opposed to Schottky effect) 160
Chapter VII: Optical processes in molecular and macromolecular solids 163
I Introduction 163
II Matrix effects due to insertion ofatoms with incomplete
internal electronic levels 164
1 Electronic configuration of transition elements
and rare earths 164
2 Incorporation oftransition metals and rare earths
into dielectric or a semiconductor matrix: effects
on energy levels 165xxii Contenis
III
^ Trtinsitions studied tor atoms w ith incomplete
layers inserted in a matrix 1(^,7
Classic i)ptical applications using transition and rare
earth elements
1 El^'ctroluminescence in passive matrices 17}
2 Insertion into semiconductor matrix 172
3 Light amplification: erbium lasers 173
IV Molecular edifices and their general properties 174
1 Aide memoire: basic properties 174
2 Selection rule with respect to orbital parities for
systems with centre of"symmetry |7f)
3 More complicated molecules: classical examples
of existing chromophores 177
V Detailed description of the absorption and emission
processes in molecular solids 179
1 Electron-lattice coupling effects during electron
transitions 179
2 Selection rules and allowed transitions |8()
3 Modified Jablonsky diagram and modification
of selection rules: fluorescence and
phosphorescence I 1
4 Experimental results: discussion 183
Excitons
1 Introduction
2 Wannier and charge transfer excitons 186
3 Frenkel excitons I^g
4 States,energy levels and transitions in physical
dimers
5 System containing an infinite number of
interacting molecules and exciton band: Davidov
displacement and breakdown j92
6 Aggregates I94
7 Forster and Dexter mechanisms for transfer of
electron excitation energy 195
VI
Part Two: Components: OLEDs, photovoltaic cells and electro-optical
modulators
Chapter VIII: Fabrication and characterisation of molecular and
macromolecular optoelectronic components 201
I Deposition methods 201
1 Spin coating 201
2 Vapour phase deposition 202Contents xxiii
3 Polymerisation in the vapour phase
(VDP method) 203
4 Film growth during vapour deposition: benefits
due to deposition assisted by ion beams 204
5 Comment:substrate temperature effects 209
II Fabrication methods: OLEDs and optical guides for
modulator arms 210
1 OLED fabrication 210
2 Fabrication of modulator guides/arms from
polymers 212
III Photometric characterisation of organic LEDs
(OLEDs or PLEDs) 217
1 General definitions 217
2 Internal and external fluxes and quantum yields:
emissions inside and outside ofcomponents 221
3 Measuring luminance and yields with a
photodiode 226
IV Characterisation of polymer based linear wave guides .. 232
1 Measuring transversally diffused light 232
2 Loss analyses using 'Cut- Back'and 'Endface
Coupling' methods 233
Chapter IX: Organic structures and materials in optoelectronic
emitters 235
I Introduction 235
II How CRTs work 235
III Electroluminescent inorganic diodes 236
1 How they work 236
2 Display applications 237
3 Characteristic parameters 237
4 In practical terms 238
IV Screens based on liquid crystals 239
1 General points 239
2^ How liquid crystal displays work 240
3 LCD screen structure and the role of polymers ... 242
4 Addressing in LCD displays 243
5 Conclusion 244
V Plasma screens 244
VI Micro-point screens(field emission displays(FED)) ... 245
VII Electroluminescent screens 246
1 General mechanism 246
2 Available transitions in an inorganic phosphor .... 247
3 Characteristics of inorganic phosphors from
groups II-VI 249xxiv Contents
4 Eleclmluniine cent think tilni displays; iiovv they
work with alternating currents 250
5 Electroluminescent devices opcratitig under direct
current conditions ->^1
VIII Organic (OLED) and polymer (PLED)
electroluminescent diodes -><^3
1 Brief history and resume ->53
2 The two main developmental routes 253
3 How OLEDs function and their interest 254
Chapter X: Electroluminescent organic diodes ->57
I Introduction
II Comparing electronic injection and transport models
with experimental results
1 General points: properties and methods applied to
their study ->58
2 Small molecules(Alq3) 259
3 Polymers
III ^f'^^fcgies for improving organic LEDs and yields Ill
1 Scheme of above detailed processes 272
2 Different types of yields 273
3 Various possible strategies to improve organic
LED performances 274
IV Adjusting electronic properties of organic solids for
electroluminescent applications 276
1 A briefjustification of n- and p-type organic
conductivity 276
2 The problem ofequilibrating electron and hole
injection currents 977
3 Choosing materials for electrodes and problems
encountered with interfaces 277
4 Confinement layers and their interest 279
• V Examples oforganic multi-layer structures 279
1 Mono-layer structures and the origin of their poor
performance 279
2 The nature ofsupplementary layers 280
3 Classic examples ofthe effects ofspecific organic
280
4 Treatment ofthe emitting zone in contact with the
. 284
VI Modification of optical properties of organic solids for
applications 285
1 Adjusting the emitted wavelength 285
2 Excitation energy transfer mechanisms in films
doped with fluorescent or phosphorescent dyes ... 286Contents xxv
3 Circumnavigating selection rules: recuperation of
non-radiative triplet excitons 288
4 Energy transfer with rare earths and infrared
LEDs 290
5 Microcavities 292
6 Electron pumping and the laser effect 292
VII Applications in the field of displays: flexible screens ... 294
1 The advantages 294
2 The problem ofageing 294
3 The specific case of white diodes 296
4 The structure oforganic screens 296
5 A description of the fabrication processes used
for organic RGB pixels 298
6 Emerging organic-based technologies: flexible
electronic 'pages' 304
VIII The prospective and actual production at 2002 306
IX Conclusion 309
X Actual state-of-the-art and prospectives 310
Chapter XI: Organic photovoltaic devices 313
I Principles and history of organic based photovoltaics... 313
1 General points: the photovoltaic effect 313
2 Initial attempts using organic materials: the
phthalocyanines 316
3 Solar cells based on pentacene doped with iodine . 318
4 The general principle of Graetzel and current
organic solar cells 320
II Ti-Conjugated materials under development for the
conversion of.solar energy 321
1 Metal-Insulator-Metal structures 321
2 How bilayer hetero-structures work and their
limits 322
3 Volume heterojunctions 325
III Additional informations about photovoltaic cells and
organic components 328
1 Discussion about mechanisms leading to the
generation ofcharge carriers in organics 328
2 Electric circuit based on an irradiated pn-junction;
photovoltaic parameters 330
3 Circuit equivalent to a solar cell 334
4 Possible limits 336
5 Examples;routes under study and the role of
various parameters 337
6 Conclusion 339xxvi Contents
Chapter XII: The origin of nonlinear optical properties 341
I Introduction: basic equations for electron-optical
effects 341
1 Context 341
2 Basic equations used in non-linear optics 341
II The principle of phase modulators and organic
materials 343
1 Phase modulator 343
2 The advantages of organic materials 345
3 Examples of organic donor-acceptor non-linear
optical systems 346
4 General structure of molecules used in non-linear
optics 348
III The molecular optical diode 349
1 The centrosymmetric molecule 349
2 Non-centrosymmetric molecules 350
3 Conclusion 351
IV Phenomenological study of the Pockels effect in
donor-spacer-acceptor systems 353
1 Basic configuration 353
2 Fundamental equation for a dynamic system 355
3 Expressions for polarisability and susceptibility .. 355
4 Expression for the indice—and the insertion of
the electro-optical coefficient r 356
V Organic electro-optical modulators and their basic
design 358
1 The principal types of electro-optical modulators . 358
2 Figures of merit 359
3 The various organic systems available for use in
electro-optical modulators 361
VI Techniques such as etching and polyimide polymer
structural characteristics 363
1 Paired materials: polyimide/DRl 363
2 Device dimensions—resorting to lithography 364
3 Etching 365
4 Examples of polymer-based structures 367
VII Conclusion 368
Appendices
Appendix A-1: Atomic and molecular orbitals 373
I Atomic and molecular orbitals 373
1 Atomic s- and p-orbitals 373
2 Molecular orbitals 376Contents xxvii
3 o- and Tt-bonds 380
II The covalent bond and its h>bridisation 381
1 Hybridisation of atomic orbitals 381
2 sp-^ Hybridisation 383
Appendix A-2: Representation of states in a chain of atoms 389
I A chain of atoms exhibiting a-orbital overlapping 389
1 a-orbitals and a compliment to the example of8
atoms in a chain 389
2 General representation of states in a chain of
overlapping a s-orbitals 391
3 General representation of states in a chain of
overlapping a p-orbitals 393
II 7t Type overlapping of p-orbitals in a chain of atoms:
Tt-p- and 7T*-p-orbitals 393
III a-s- and a-p-bonds in chains of atoms 394
IV Comments 395
1 The Bloch function 395
2 Expression for the effective mass(m*) 396
Appendix A-3: Electronic and optical properties of fullerene-C60 in the
solid (film)state 397
I Electronic properties of fullerene-C60 397
II Optical properties and observed transitions 401
Appendix A-4: General theory of conductivity for a regular lattice 403
I Electron transport effected by an external force and its
study 403
1 Effect of force on electron movement and
reasoning within reciprocal space 403
2 Boltzmann's transport equation 404
II State density function, carrier flux and current density
in the reciprocal space 406
U General expressions for fluxes of particles 406
2 Expressions for the state density function 406
3 Expression for flux 408
4 Expression for current density in reciprocal
space 408
III Different expressions for the current density 409
1 Usual expression for current density in energy
space 409
2 Studies using various examples 410
3 Expressions for mobility 412
4 The Kubo- Greenwood expression for
conductivity 413xxviii Contents
IV Complementary comments 414
1 Concerning the approximation of the effective
mass and isotropic diffusions 414
2 Concerti laws for changes in mobility with
temperature 415
Appendix A-5: General theory of conductivity in localized states 417
I Expression for current intensity associated with
hopping transport 417
1 Transcribing transport phenomena into
equations 417
2 Calculating the current intensity due to hopping
mechanisms 419
II Expression for current density and thermally activated
mobility 419
1 Expression for current density relative to transport
at a particular energy level 419
2 Generalisation of the form of Kubo-Greenwood
conductivity 49Q
3 Thermally activated mobility 420
III Approximations for localised and degenerate states .... 421
Appendix A-6: Expressionsforthermoelectric power in solids:conducting
polymers 423
I Definition and reasons for u.se 423
1 Definition 423
2 Reasons for use 423
II TEP of metals (E
III TEP of semiconductors(SC)(Ep in the gap) 424
1 Preliminary remark 425
2 An ideal n-type semiconductor 425
3 An ideal n-type semiconductor 426
4 Comment on amorphous semiconductors 426
5 A non-ideal amorphous semiconductor with Ep
below its states in the band tails 426
IV TEP under a polaronic regime 427
1 High temperature regime 427
2 Intermediate temperature regime 427
3 Other regimes 427
V The TEP for a high density of localised states
around Ep 427
1 Initial hypothesis 427
2 The result in VRH 428Contents xxix
VI General representation 429
VII Real behaviour 429
1 General laws 429
2 Behaviour as a function of doping levels 430
3 Representational graph 431
4 An example result 431
Appendix A-7: Stages leading to emission and injection laws at
interfaces 433
I Thermoelectric emission and the DushmanRichardson law 433
II Schottky injection (field effect emissions) 434
1 The potential barrier at the atomic scale 435
2 Emission conditions: Schottky emission law and
the decrease in the potential barrier by field effect. 435
III Injection through tunnelling effect and the
Fowler-Nordheim equation 437
1 The problem 437
2 Form of the transparency(T)of a triangular
barrier 438
3 The Fowler-Nordheim equation 440
Appendix A-8: Energy levels and permitted transitions(and selection
rules)in isolated atoms 443
I Spherical atoms with an external electron 443
1 Energy levels and electron configuration 443
2 Selection rules 444
II An atom with more than one peripheral electron 445
1 First effect produced from the perturbation Hge
due to exact electronic interactions 445
2 Perturbation involving the coupling energy
between different magnetic moments exactly tied
to kinetic moments 446
3 Selection rules 447
Appendix A-9: Etching polymers with ion beams: characteristics and
results 449
I Level of pulverisation(Y) 449
1 Definition 449
2 The result Yphysicai=f(E):3zones 450
3 Level of chemical pulverisation 451
II The relationship between etching speed and degree of
pulverisation 451
1 At normal incidence 451
2 At oblique incidence 452XXX Contents
III Speed of reactive etching(IBAE Ar^/O: or /O2)... 452
IV Preliminary modelling of Physical tor PI 2566 454
1 Levels of carbon pulverisation using ions 454
2 Comparing simulations of Ypi„s.cai(6)= f(6)and
the Thompson and Sigmund models 454
V Results Irom etching of polyimides 455
1 Self-supporting polyimide; UPILEX 455
2 A study of the etching ofPI 2566 456
AppendixA-10: A.n aide-memoire on dwXQcirics 459
I Definitions of various dielectric permittivities 459
1 Absolute permittivity 459
2 Relative permittivity 459
3 Complex relative permittivity 460
4 Limited permittivities 460
5 Dielectric conductivity 461
6 Classification of diverse dielectric phenomena 461
II Relaxation of a charge occupying two position
separated by a potential barrier 463
1 Aide-memoire 463
2 Transportation in a dielectric with trapping levels,
and the effect of an electric field on transitions
between trap levels 464
3 Expression for the polarisation at an instant t
following the displacement of electrons 466
4 Practical determination of potential well depths... 467
Appendix A-11: The principal small molecules and polymers used in
organic optoelectronics 471
I Chemical groups and electron transport 47j
II Examples of polymers used for their
electroluminescence 471
1 The principal emitting polymers 471
2 The'polymer for hole injection layers(HIL) 472
3 Example of a polymer used in hole transport
layers(HTL) 473
4 Example of a polymer used in electron transport
layer(ETL) 473
III Small molecules 473
1 The principal green light emitting ligands 473
2 Principal electron transporting small molecules
emitting green light 474
3 Example electron transporting small molecules
emitting blue light 474
4 Example small molecules which emit red light ... 474Contents xxxi
5 Examples of small molecules which serve
principally as hole injection layers(HIL) 475
6 Examples of small molecules serving principally
in hole transport layers(HTL) 475
7 Example of a small molecule serving principally
to confine holes in 'hole blocking layers'(HBL).. 476
Appendix A-12: Mechanical generation of the second harmonic and the
Pockels effect
I Mechanical generation to the second harmonic (in
one-dimension) 477
1 Preliminary remark: the effect of an intense
optical field (E'") 477
2 Placing the problem into equations 477
3 Solving the problem 480
II Excitation using two pulses and the Pockels effect.... 481
1 Excitation from two pulses 481
2 The Pockels Effect 482