Electronic Processes in

Organic Crystals and Polymers

Second Edition

MARTIN POPE Professor Emeritus,

New York University

CHARLES E. SWENBERG Physics Department,

George Mason University

New York Oxford Oxford University Press

1999

Contents

Parti

I. OPTICAL PROPERTIES OF ORGANIC MOLECULES AND CRYSTALS

A. Introduction 1

B. Molecular excited states 5 1. Born-Oppenheimer approximations 5 2. Perimeter free electron orbital theory 7 3. Molecular orbital theory 12

C. Spectral properties 15 1. Introduction 15 2. Einstein coefficients for absorption and emission 18 3. Selection rules for optical transitions 23 4. Intensity distribution of absorption bands 26 5. Fate of the excited molecular State 29

a. Quantum yields 31 6. Radiationless processes 32 7. Assignment of the spectral line 38

D. Excited states of aggregates of molecules 39 1. Introduction 39 2. Physical dimers 40 3. Excimers 48 4. Linear molecular crystals 52 5. Crystal states: Excitons 59 6. Hot band-to-band transitions 66 7. Wannier excitons 70 8. Charge-transfer states 73 9. Trapped Frenkel excitons 78

10. Trapped Wannier excitons 81 11. Surface excitons 83 12. Self-trapped excitons 85

E. Generation of excitons 89 1. General remarks 89 2. Direct optical excitation 90

a. Multiphoton absorption 91 3. Generation by high-energy radiation (et, ß, y, X-radiation) 92 4. Generation by carrier recombination 93 5. Generation by electrochemiluminescence 94

k

xx Contents

6. Generation by internally accelerated charges 94 7. Generation by thermal or chemical action 94 8. Generation by indirect excitation 94 9. Generation by other excitons 95

F. Mot ion of excitons in molecular Systems 96 1. Energy transfer: Förster transfer 96 2. Master equations governing exciton migration 102 3. Exciton migration 115 4. Upper excited State transfer 122 5. Energy transfer in isotopic mixed crystals 125

a. The Anderson model 127 b. Percolation model 130

G. Exciton processes 134 1. Effects of quenching processes on natural lifetime 134 2. Delayed fluorescence from organic solids 135 3. Magnetic field modulation of biexcitonic processes 139 4. Effect of a magnetic field on the triplet exciton lifetime 154 5. Singlet-singlet exciton fusion 157 6. Singlet-triplet exciton reactions 161 7. Reaction of excitons with free and trapped charges 164 8. Reactions of excitons with surfaces 166 9. Direct measurement of exciton diffusion coefficient 172

10. Photon-exciton processes 177 11. High density exciton phenomena 180

II. S I N G L E POSITIVE OR N E G A T I V E C A R R I E R S IN O R G A N I C C R Y S T A L S

A. Introduction 192

B. Isolated molecules with excess charges 192

C. Crystals with excess positive or negative charges 202

1. Introduction 202 2. Valence band and the ionization potential of the

crystal 205 3. Band gap and electron affinity of crystals 205 4. Energy levels of bound ionic states 210 5. Energy bands for excess charges 212 6. Fermi energy and contact potential 217

D. Defects and trapped Charge 220 1. Crystal defects 220 2. Chemically induced trapping levels 231

a. Traps situated on the chemical impurity 231

Contents xxi

b. Traps situated on host molecules adjacent to the chemical impurity 233

3. Traps produced at crystal defect sites 234 a. Use of space Charge limited currents to calculate trap

Parameters 236 4. Traps at the surface 248 5. Spatial distribution of trapping sites 256 6. Self-trapping of charges 257

a. Self-trapping by optical modes 261 b. Self-trapping by acoustic modes 263

7. Detrapping mechanisms 267 8. Recombination luminescence 272

E. Charge injection mechanisms at surfaces 273 1. Thermal injection 273

a. Injection from metals 273 b. Injection from electrolytes and Lewis acids and bases 280 c. Recombination current 293 d. Image force effects 301

2. Injection by optically excited electrodes—photosensitization 303 a. Injection into upper conducting levels and hot carriers 316

3. Injection by optical excitation of the crystal 320 a. Interaction of excitons with electrodes 320 b. Interaction of excitons with surface States 332 c. Interaction of excitons with surface molecules 335

F. Carrier transport 337 1. Introduction 337 2. Types of carrier transport: Model Hamiltonian 340

a. Transport in the band model: Case I 343 b. Hopping model of carrier transport: Case II 353 c. Temperature-independent mobility: Case IV 360

3. Positron drift mobilities 369 4. Hall mobility 374

G. Steady current flow 379 1. In the bulk 379

a. Basic one-carrier equations 379 b. General Solution for SCLC: one carrier case 382 c. Exciton probe of total injected Charge 397 d. Photodetrapping in the SCLC regime 404 e. Spatial distribution of trapped Charge as deduced by

exciton-carrier quenching 408 f. Two-carrier current-voltage characteristics 413

2. Surface currents 421

H. Thermally stimulated current flow 425

xxü Contents

I. Chemical effects accompanying the discharge of electrons and holes at electrolytic surfaces 433

J. Photovoltaic effect 436

III. PRODUCTION OF CARRIER PAIRS IN THE BULK

A. Carrier generation mechanisms 456 1. Carrier production by high-energy radiation 456 2. Carrier generation by light absorption 466

a. Single-photon processes 466 b. Multiphoton processes 475

3. Carrier generation by exciton reactions 478 a. Exciton-exciton reactions 478 b. Exciton-photon reactions 480

4. Carrier generation by thermal production 481

B. Carrier recombination 481 1. Unimolecular recombination 481

a. Evaluation of the thermalization distance 489 b. Quantum mechanical description of auto-ionization 497

2. Bimolecular recombination 501 a. Classification of types of recombination 501 b. Temperature dependence of direct hole-electron

recombination 505 c. Radiative carrier recombination 508

IV. PHOTOEMISSION FROM ORGANIC MOLECULAR CRYSTALS

A. Introduction 519

B. Detection of photoemission 521 1. Vacuum method 522 2. Millikan-Pope-Arnold method 528

C. Theory of photoemission from solids 533 1. Introduction 533

a. Optical transition probability 534 b. Transmission probability escape depth L(E) 536 c. Surface escape function 539 d. Contribution of once-scattered electrons 540

2. Threshold behavior of the total photoemission quantum yield 543

D. Photoemission from organic molecular crystals 547 1. Introduction 547

a. Analysis of moving peaks in photoemission spectra 548 2. Density-of-states analysis of photoemission spectra 552

a. Photoemission as a tool in mechanistic studies 557

Contents xxiii

3. Line widths of photoemission spectra 561 4. Effects of auto-ionization in photoemission spectra 564

E. Mult iquantum processes as studied by photoemission spectroscopy 568

1. Singlet-singlet exciton processes 568 2. Exciton-carrier reactions 572

F. Photophoretic spectroscopy 576

V. M A T E R I A L S W I T H H I G H D A R K C O N D U C T I V I T Y

A. Introduction 581

B. Radical-ion salt crystals 588

1. Classification scheme 588 2. Measurement of partial-valence p 595 3. Electrical conductivity 597

C. Charge transfer complexes 607 1. Optical properties 607 2. Photoconductivity 611

D. General properties of one-dimensional crystals 615 1. Definition of one-dimensional Systems 615 2. Types of instabilities 617

a. Peierls transition 617 b. Mott transition 623

E. Polymerie sulfur nitride (SN).,. 624 1. Introduction 624 2. Band strueture of (SN)V 626 3. Optical properties of (SN)V 630 4. Superconductivity in (SN)V 633

F . Superconducting organic radical-ion salts 637 1. Introduction 637 2. Normal State of (TMTSF)2PF6 637 3. Superconducting State of (TMTSF)2PF6 639

VI. M I S C E L L A N E O U S SYSTEMS

A. Introduction 646

B. Dyes 646 1. Optical properties of Single crystal CTIP 646 2. Photoconduction in CTIP 652

C. Phthalocyanines 659 1. Theory of the temperature dependence of dark

conductivity 662

xxiv Contents

a. Extrinsic and non-extrinsic dark conductivity 667 2. Dark conductivity of phthalocyanines: experimental 668

a. Location of dominant energy levels 669 b. Calculation of the densities of the dominant levels 670

3. Photoconductivity of phthalocyanines: activation energy 671

D. Polydiacetylenes 673 1. Optical properties of PTS 677 2. Electroreflectance studies in PTS 679 3. Electrical properties of PTS crystals 681 4. Intrinsic ionization in PTS: band-to-band transitions 686 5. Geminate recombination in PTS 689 6. Bimolecular carrier recombination in PTS 696

E. Polymers 699 1. Optical properties of PVK 704 2. Electrical properties of PVK 706

a. Methods of measuring drift mobility 709 b. Disordered solids 713 c. Transport mechanisms 721

3. Carrier generation efficiency in PVK 737 4. Properties of PVK-TNF 748 5. Carrier recombinations in PVK-TNF 752

F. Liquids 753

Part II

VII. E L E C T R O N I C PROCESSES IN P O L Y A C E T Y L E N E (PA)

A. Theory 777

B. Electronic structure 785

C. Confinement effects 790

D . Transport 793

E. Photoexcitation 796

F . Identity of the Charge carriers 802

G. Summary 806

VIII. E L E C T R O N I C PROCESSES IN P O L Y D I A C E T Y L E N E (PDA)

A. Excitons 809 1. Singlet 809 2. Triplet 811

Contents xxv

3. Wannier excitons 813 4. Polarons and bipolarons 815 5. Nonlinear optical (NLO) effects 817

B. Carriers 817 1. Mobility 817 2. Transport 819 \ 3. Recombination 821

C. Summary of energy levels in PDA-TS 823

IX. E L E C T R O N I C PROCESSES IN POLY(p-PHENYLENE-V I N Y L E N E ) (PPV)

A. Structure and morphology 825

B. Excited states 828 1. Exciton vs. band picture in PPV 828 2. Variety of excited states 830 3. Site-selective fluorescence spectroscopy 832 4. Time-resolved gain (stimulated emission) and absorption 835 5. Luminescence quenching by an electric field 839 6. Exciton binding energy 841 7. Measurement of photoluminescence quantum efficiency 843 8. Bipolarons 844 9. Photoconductivity from lower excited states 846

10. Carrier generation from Upper excited states 848

C. Ladder polymers 850

D. Summary 851 1. Energy levels 852

X. E L E C T R O N I C PROCESSES IN P O L Y A N I L I N E (PAni)

A. Solitons 856

B. Excitons 860

C. Polarons 862

D. Bipolarons 867

E. Pernigraniline base (PNB) 868

F . Leucoemeraldine base (LB) 868

G. Model for photoexcitations 868

H. Summary of photoexcitations 871

I. Polyaniline salts 871

*

xxvi Contents

XI. E L E C T R O N I C P R O C E S S E S IN P O L Y S I L A N E (PS)

A. Poly(methylphenylsilane) (PMPS) 883

1. Triplet excitons 889

B. Exciton-exciton annihilation 891

C. Poly(di-n-hexylsilane) (PDHS) 894

D . Exciton dynamics in PDHS 895

E. Electroabsorption spectra 897

F. Summary 899

XII . E L E C T R O N I C PROCESSES IN F U L L E R E N E S (C60)

A. Geometry 902

B. Preparation 902

C. Chemical bonding 904

D. Electronic structure 906

E. Band gap 913

F. Charge-transfer states 918

G. Carrier mobility 921

H. Photogeneration and recombination 923

XI I I . C A R R I E R G E N E R A T I O N A N D R E C O M B I N A T I O N

A. Carrier generation 927 1. Molecular crystals 927 2. Polymers 928

a. Autoionization 928 b. Field-dependent thermal injection 936

B. Carrier recombination 939 1. Time-dependent geminate recombination 939 2. Geminate recombination in anisotropic media 944 3. Geminate recombination and thermalization distances 945 4. Onsager theory of 1934 946 5. Field-induced drift during thermalization 950 6. Geminate recombination in disordered Systems 953 7. Langevin bimolecular recombination in disordered Systems 958

XIV. C A R R I E R T R A N S P O R T

A. Molecular crystals 963 1. Silinsh-Capek formalism 963

Contents xxvii

2. Kenkre formalism 968 3. High-field and low-temperature effects 971

B. Molecular doped polymers (MDPs) 973 1. Gaussian disorder formalism for MPD transport 974 2. Spatial correlation of energetic disorder 978 3. Exact 1D Solution to MDPs 982 4. Transport in 3D disordered Systems with permanent dipoles 984 5. Transport in 3D disordered Systems with small

dipole moments 986

C. Problems associated with existing MDP theories 987

D. Validity of Einstein's relationship in polymeric Systems 988

E. Quasimetallic transport 991 1. Doped polymers 991 2. Granulär metals 995 3. Emeraldine polymer 996 4. Doped fullerenes 998

XV. SPACE-CHARGE AND EMISSION-LIMITED CURRENTS

A. Contacts 1005 1. Ohmic contacts 1005 2. Emission-limited contacts (ELC) 1010

B. Mobility 1013

C. Trapping 1016

XVI. ORGANIC MAGNETS (OM)

A. Molecular basics 1029

B. Mechanisms involved in stabilizing ferromagnetism 1030

C. Basic magnetic parameters, phenomena, and theory 1037 1. Magnetic susceptibility 1037 2. Spin exchange energy 1040 3. Mean-field approximation 1040 4. Ferromagnetism, ferrimagnetism, and antiferro(ferri)-

magnetism 1041 a. Ferromagnetic solids 1043 b. Ferrimagnetic solids 1050

D. Model spin Systems 1052 1. Pressure dependence 1054 2. Dilution technique 1056 3. Fullerene magnets 1056

t

xxviii Contents

E. Magnetic properties of organic conductors 1059 1. Electron-electron interactions 1061 2. Temperature dependence 1064 3. Spin-density waves 1064

Appendix 1: Special Topics 1066 1. Knight shift and relaxation times 1066 2. Spin-lattice relaxation 1067 3. Magnetic polarons 1072 4. Superexchange interactions 1072

Appendix 2: Glossary 1076

XVII . S U P E R C O N D U C T I V I T Y A N D O T H E R C O L L E C T I V E STATES

A. Nested Fermi surfaces (FS) 1082

1. 1D and quasi-1D materials 1084

B. Charge density waves (CDWs) 1086

C. Spin density waves (SDWs) 1095

1. Field-induced spin density waves (FISDWs) 1099

D. Spin-Peierls transition (S-P) 1103

E. Superconductivity 1106

1. Fullerenes C60 1111

F . Magnetic-field effects 1122

G. Can ferromagnetism and superconductivity coexist? 1130

H. Luttinger liquids 1132

XVIII . N O N L I N E A R O P T I C A L A N D P H O T O R E F R A C T I V E P R O P E R T I E S (NLO)

A. Nonlinear optical susceptibility 1138 1. Condensed media 1138 2. Nonlinear effects in molecules 1141 3. Correlation between bulk and molecular NLO coefficients 1142 4. Third-order polarizability 1148 5. NLO and exciton states 1150

B. Photorefractive effect (PRE) 1152 1. Multilayer structures 1156 2. PRE in organic Compounds 1157

a. Differences between organic and inorganic PRE 1157 b. Basic theory of organic PRE 1159

3. Functionality of Polymerie materials 1161 4. Two-beam coupling 1163

Contents xxix

C. Dendrimers 1166

XIX. M O L E C U L A R E L E C T R O N I C S

A. Langmuir-Blodgett (L-B) films 1172

B. L-B films as rectifiers 1176

C. N L O L-B films 1179

XX. A P P L I C A T I O N S

A. Electrophotography (XER) 1182

B. Photorefraction, hole burning, and nonlinear optics (HOL) 1184

1. Photorefraction 1185 2. Persistent hole burning (PHB) 1188 3. Nonlinear optics (NLO) 1191

C. Electroluminescence (EL) 1193 1. Cell configurations 1193 2. Recombination and emission zones 1196 3. Polymer LED 1199 4. Stability 1204 5. Performance 1204 6. Special techniques 1205

a. Electroabsorption (EA) 1205 b. Ultra violet photoemission spectroscopy (UPS) 1213

D. Transistors 1215

E. Sensors 1219 1. Conductivity sensor 1219 2. Fluorescence sensor 1222

F. Liquid crystals 1222

G. Batteries 1226

Credits 1231

Author Index 1270

Subject Index 1293

t