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Energy Transfer Processesin Condensed MatterEdited by
Baldassare Di BartoloBoston CollegeChestnut Hill, Massachusetts
Assistant Editor
Aliki KaripidouBoston CollegeChestnut Hill, Massachusetts
Fachbereich 5
Plenum PressNew York and LondonPublished in cooperation with NATO Scientific Affairs Division
CONTENTS
INTRODUCTION TO ENERGY TRANSFER AND RELEVANTSOLID-STATE CONCEPTS • 1
J. E. Bernard, D, E. Berry and F. Williams
ABSTRACT 2
I. INTRODUCTION 3
II. BASIC CONCEPTS UNDERLYING ENERGY TRANSFER IN SOLIDS 5
II.A. Separation of Electronic and Nuclear Motion 5
II.B. One-Electron Approximation -•• '— • 8
II.C. Electronic Band Structure • • 14
1. Case I: Nearly Free Electrons 202. Case II: Tightly Bound Electrons 26
II.D. Lattice Dynamics and Phonons — 32
1. Case I: The Case of Small q-Values 372. Case II: The Case of q = i 38
II.E. The Electron-Phonon Interaction ~ — 41
1. Deformation Potential Theory 44
2. FrShlich Hamiltonian 47
III. GENERAL METHODS OF ENERGY TRANSFER 49
III.A. Resonant Energy Transfer 49
III.B. Nonresonant Energy Transfer '•— 54
III.C. Electronic Charge Transport and Energy Transfer - 58
III.D. Energy Transfer by Excitons 65
1. Exciton Structure 652. Exciton Transport 69
x CONTENTS
III.E. Auger Processes as Energy Transfer 73
III.F. Inelastic Collisions. Hot Electron
Excitation 77
IV. CLOSING REMARKS 82
APPENDIX: EFFECTIVE MASS APPROXIMATION FOR DOPANTS
WITH COULOMB FIELDS 83
GLOSSARY 86
REFERENCES 95
ENERGY TRANSFER AMONG IONS IN SOLIDS 103
B. Di Bartolo
ABSTRACT 103
I. INTERACTION AMONG ATOMS 103
I.A. Two-Atom System ; 103
I.B. Dynamical Effects of the Interaction 107
1. Coherent Energy Transfer in a Two-Atom System 109
2. Incoherent Energy Transfer in a Two-Atom System H I
3. Coherent Energy Transfer in a LinearChain 114
4. Incoherent Energy Transfer in aLinear Chain 116
I.C. The Relevant Energy Transfer Hamiltonian 117
I.D. Interaction Between Two Atoms in Solids 119
II. DIFFERENT TYPES OF INTERACTIONS . 124
II.A. Multipolar Electric Interactions 124
II.B. Exchange Interactions 128
II.C. Electro-Magnetic Interactions 131
II.D. Phonon-Assisted Energy Transfer 133
CONTENTS
III. STATISTICAL TREATMENT OF ENERGY TRANSFER.
MODES OF EXCITATION 134
III.A. Introduction 134
III.B. Pulsed Excitation 135
III.C. Continuous Excitation 137
IV. STATISTICAL TREATMENT OF ENERGY TRANSFER.
CASE WITH NO MIGRATION AMONG DONORS 139
IV. A. Basic Equation 139
IV.B. Simple Models 141
1. Perrin Model 141
2. Stern-Volmer Model 142
IV.C. Multipolar Interactions 142
IV.D. Exchange Interactions 152
V. STATISTICAL TREATMENT OF ENERGY TRANSFER.
CASE WITH MIGRATION AMONG DONORS 156
V. A. Migration ' 156
V.B. Diffusion 157
V.C. Migration as Diffusion Process 159
1. Diffusion Only 1602. Diffusion and Relaxation 160
3. Diffusion, Relaxation and Transfer 160
V.D. Migration as Random Walk 165
V.E. Comparison of Two Models — 174
"V7F. Calculations of Transfer Rates 175
1. Diffusion Model 1752. Hopping Model : 177
V.G. Regimes of Donor Decay 1801. No Diffusion 1802. Diffusion-Limited Decay • 1803. Fast Diffusion 180
xii CONTENTS
V.H. Migration in the Case of Inhomogeneous
Broadenings of Donors' Levels 181
VI. COLLECTIVE EXCITATIONS 183
VI. A. Introduction 183
VLB. Eigenfunctions 186
VI.C. Dispersion Relations 190
VI.D. Effective Mass 192
VI.E. Generalization to Three Dimensions 195
VI.F. Periodic Boundary Conditions andDensity of States 196
VI.G. Interaction of Photons with Collective
Excitations 200
ACKNOWLEDGEMENTS 202
REFERENCES 203
MATHEMATICAL METHODS FOR THE DESCRIPTION OF ENERGY
TRANSFER 205
V. M. Kenkre
ABSTRACT 205
I. INTRODUCTION 205
I.A. Preliminary Remarks 205
I.B. Processes and Questions of Interest 207
I.C. Some Experiments 208
I.D. Outline of This Article 209
II. THE BASIC TRANSPORT INSTRUMENT: THEEVOLUTION EQUATION 210II.A. Introduction and the Coherence-
Incoherence Problem 210
CONTENTS xiii
-II.B. Motivation for the GME 214
II. C. Derivation and Validity of the GME 216
II.D. Solution of Foerster's Problem — 219
II. E. General Remarks About the GME 220
III. MEMORY FUNCTIONS: EXPLICIT CALCULATIONS 221
III.A. Outline 221
III.B. Exact Results for Pure Crystals — 221
III.C. Exact Results for an SLE 224
III.D. Perturbative Evaluation for Linear
Exciton-Phonon Coupling 226
III.E. Evaluation from Spectra 227
IV. CALCULATION OF OBSERVABLES 229
IV.A. Prelude: Calculation of Propagators 229
IV.B. Application to Grating Experiments ' 232
IV.C. Capture Experiments 237
V. MISCELLANEOUS METHODS AND CONCLUSIONS 242
V.A. Methods for Cooperative Trap
Interactions 242
V.B. Conclusion 246
ACKNOWLEDGEMENTS 247
REFERENCES 247
y ENERGY TRANSFER IN INSULATING MATERIALS 251
G. Blasse
ABSTRACT 251
I . INTRODUCTION 251
xjv CONTENTS
II. SINGLE-STEP ENERGY TRANSFER 252
III. MULTISTEP ENERGY TRANSFER 257
IV. CHARACTERISTICS OF MATERIALS 261
V. STRONG TEMPERATURE DEPENDENCE 262
VI. WEAK TEMPERATURE DEPENDENCE 264
VI.A. Transition Metal Compounds 264
V L B . Hexavalent Uranium Compounds 268
VI.C. Trivalent Rare Earth Compounds 271
VII. FLUORESCENCE LINE NARROWING IN GLASSES 280
ACKNOWLEDGEMENT 281
REFERENCES : 281
ENERGY TRANSFER IN SEMICONDUCTORS 285
C. Klingshirn
ABSTRACT 285
I. INTRODUCTION, OR THE PHYSICAL PROBLEM OFLOOKING THROUGH A WINDOW 285
II. ENERGY TRANSFER FROM AN EXTERNAL PHOTON FIELD
INTO A SEMICONDUCTOR 287
II.A. Photons in Vacuum 287
II.B. A Mechanical Model for a Medium 292
II. C. The Dielectric Function 295
II. D. Polaritons 301
II.E. What Happens at the Surface 303
II.F. Phonon Polaritons 307
II.G. Excitons: Oscillators with SpatialDispersion 311
CONTENTS xv
II.H. Exciton-Polaritons and the Problem ofAdditional Boundary Conditions 315
I L L Experimental Proofs for the Conceptof Exciton-Polaritons 320
III. ENERGY TRANSFER FROM EXCITON-POLARITONS TOTHE PHONON-FIELD 326
III.A. Review of Energy Transfer Processesin Semiconductors 326
III.B. Interaction Mechanisms Between Excitons
and Phonons 330
III.C LO-Phonon Assisted Luminescence 333
III.D. Resonant Brillouin Scatterin 338
III.E. Raman Scattering 342
III.F. Resonant Raman Scattering, HotLuminescence, Thermalisationand Photoluminescence — 346
IV. ENERGY TRANSFER BETWEEN VARIOUS EXCITON- *
POLARITON MODES BY NONLINEAR INTERACTION 348
IV. A. Nonlinear Interaction Between Phonons 348
IV.B. Two-Photon Raman Scattering 349
IV. C. Degenerate Four Wave Mixing 351
IV. D. Laser Induced Gratings • 353
V. CONCLUSION 355
APPENDICES 355
APPENDIX A:" Exciton-Polaritons in Real Semiconductors 355
APPENDIX B: Surface Polaritons 359
APPENDIX C: The Role of Impurities 363
ACKNOWLEDGEMTNTS 366
REFERENCES 367
XVI CONTENTS
TRIPLET EXCITATION TRANSFER STUDIES IN ORGANIC CONDENSED
MATTER VIA COOPERATIVE EFFECTS 371
V. Ern
ABSTRACT 371
I. INTRODUCTION 371
II. INTRODUCTION TO MOLECULAR CRYSTAL BAND STATES 373
III. DIRECT APPROACH FOR STUDY OF TRIPLETTRANSPORT VIA DELAYED FLUORESCENCE 381
IV. THE TRIPLET EXCITON MACROSCOPIC DIFFUSIONEQUATION 387
V. EXPERIMENTAL DETERMINATION OF THE TRIPLETEXCITON DIFFUSION TENSOR 390
V.A. Time-Dependent Buildup and DecayTransient Experiments 391
1. Buildup of Delayed Fluorescence 392
2. Decay of Delayed Fluorescence 39 3
V.B. Phase-Lag Steady-State Experiments 396
VI. POSSIBILITY OF DETECTING COHERENCE EFFECTS
IN TRIPLET TRANSPORT 401
VI.A. Buildup and Decay Transient Experiments 403
VLB. Phase-Lag Steady-State Experiments 409
REFERENCES 413
ENERGY TRANSFER IN SOLID RARE GASES 417
N. Schwentner, E. E. Koch and J. Jortner
ABSTRACT 417
I. INTRODUCTION — 418
II. ELEMENTARY EXCITATIONS OF RARE GAS CRYSTALS 419
II.A. Lattice Vibrations 419
CONTENTS xv"
II.B. Resonant Electronic States 420
II.C. Localized Electronic States 424
II.D. Localization (Self-Trapping) of
Excitons 428
1. Exciton-Phonon Scattering 4282. Self-Trapping 4293. Microscopic Picture 430
III. ELECTRONIC STATES OF GUEST ATOMS AND MOLECULES
IN RARE GAS MATRICES 432
III.A. Transition Energies 432
III.B. Lattice Relaxation and Line Shapes 434
IV. ELECTRONIC AND VIBRATIONAL RELAXATION 434
V. ENERGY TRANSFER 437
V.A. Concepts 437
V.B. Migration of Free Excitons 441
1. Transfer to Guests 441
2. Transfer to Boundaries 449V.C. Energy Transfer Between Localized Centers 454
1. Electronic Energy Transfer of Self-Trapped Excitons to Guest Centers 454
2. Electronic Energy Transfer BetweenGuest Centers 456
,3. Vibrational Energy Transfer BetweenGuest Molecules 456
V.D. Energy and Mass Transport in Liquid Rare
Gases ' 459
VI. HIGH EXCITATION DENSITIES 460
VI.A. Laser Applications 460
V L B . Loss Processes and Electron Plasma 463
REFERENCES 467
xviii CONTENTS
ENERGY TRANSFER AND LOCALIZATION IN RUBY 471
G. F . Imbusch
ABSTRACT 471
I. THE LOCALIZATION OF OPTICAL EXCITATION IN A SOLID 471
II. ENERGY TRANSFER IN RUBY - EARLY EXPERIMENTS 474
III. THE SEARCH FOR MOBILITY EDGES IN THE RUBY Rl LINE 480
IV. FLUORESCENCE LINE NARROWING AND HOLE BURNING
EXPERIMENTS IN RUBY 482
V. DEGENERATE FOUR WAVE MIXING EXPERIMENTS IN RUBY:AN ATTEMPT TO DIRECTLY MEASURE THE ENERGYMIGRATION DISTANCE 486
VI. ELECTRIC FIELD EXPERIMENTS IN RUBY 489
REFERENCES 493
ENERGY TRANSFER AND IONIC SOLID STATE LASERS 497
F. Auzel
ABSTRACT • 497
. 1 . INTRODUCTION 497
II. ENERGY TRANSFER SCHEME FOR PUMPING EFFICIENCY
IMPROVEMENT 498
II.A. Stokes Processes 498
1. Energy Transfer Towards Pumping Levels 4982. Deactivation by Energy Transfer of
Levels in Self-saturating and CascadeLasers 501
I I . B . Ant i -Stokes Processes and Up-Conversion
Pumped Lasers 504
I I I . DRAWBACKS INTRODUCED BY ENERGY TRANSFER 504
I I I . A . Stokes Processes • 505
CONTENTS XIX
1. Self-Quenching by Energy Diffusionand Cross-Relaxation 505
2. Role of Crystal Field Strength 506
III.B. Anti-Stokes Processes Up-converslon
and Reabsorption 508
IV. CONCLUSION 509
REFERENCES 510
A SCALAR FIELD STRENGTH PARAMETER FOR RARE-EARTH IONS:
MEANING AND APPLICATION TO ENERGY TRANSFERS 511
F. Auzel
ABSTRACT 511
I. INTRODUCTION 511
II. THEORETICAL INVESTIGATION OF MAXIMUM STARK SPLITTINGS 513
III. DISCUSSION OF THE APPROXIMATION 516
IV. APPLICATION TO MAXIMUM STARK SPLITTING/CALCULATIONS: COMPARISON WITH EXPERIMENTS 518
IV. A. Given Ion (Nd3"1") and Crystal (LaF3) ,Comparison of, N^ from Maximum Splittingto N* from Bq. 's for Different J-Terms 518
IV.B. Given J-Term (4Ig/2) of Given Ion (Nd3*),Study of Maximum Splitting for DifferentCrystals with Different Site Symmetry 518
IV.C. Given J-Term ( I13/2) and Crystal (LaF3>,
Study for Different Ion 519
V. CONCLUSION 520
REFERENCES 520
ENERGY TRANSFER BETWEEN INORGANIC ION IN GLASSES 521
R. Reisfeld
xx CONTENTS
ABSTRACT 521
I. INTRODUCTION 521
II. URANYL ION AND RARE EARTH IONS 524
III. Bi34", Eu3"1" and Nd 3* 5 24
IV. Cr3* and Nd 3* and Yb 3* IN LANTHANUM PHOSPHATE GLASS — 525
V. ENERGY TRANSFER FROM Mn 2 + to E r ^ IN FLUORIDEGLASSES AND Mn 2 + to Nd3*, Ho34" and Er 3* INOXIDE GLASSES 529
V.A. Manganese 529
V.B. Erbium 532
V.C. Energy Transfer Between Manganese and Erbium 533
VI. CONCLUSIONS 533
ACKNOWLEDGEMENT 534
REFERENCES 534
NON-EQUILIBRIUM CONCEPTS IN SOLAR ENERGY CONVERSION 537
P. T. Landsberg
ABSTRACT 537
I. GENERAL CONCEPTS FOR RADIATION 537
L A . Introduction 537
I.B. Photons in Discrete Quantum States 538
I.C. Continuous Photon Spectrum 540
L D . Photon Fluxes 541
I.E. The Case of Black-Body Radiation 542
L F . Simple Applications of the Energy Flux"~——••——•——————____•___•__.___ _ _ _ _ — _ _ _ _ _ _ _ . ^ _ ^ . » . 3 A 3
I .G. Fluxes Compared with Equil ibr ium Quan t i t i e s 545
CONTENTS xxi
II. DILUTED BLACK-BODY RADIATION 547
II.A. DBR: Definition and Properties 547
II.B. Fluxes of DBR 549
II. C. DBR as Non-Equilibrium Radiation 551
II.D. Application of DBR to Solar Energy
Conversion 552
II. E. Discussion 554
II.F. A More Rigorous Version of Section II.D 556
II.G. An Argument from Availability 558
III. STATISTICAL THERMODYNAMICS OF CASCADE CONVERTERS 559
III.A. Some Thermodynamic Results 559
III.B. Discussion 562
III.C. The Absorption Coefficient; The Photon
Chemical Potential 564III.D. Solar Cell Equation in Terms of Photon
(Number) Fluxes 566
III.E. The Maximum Efficiency of an InfiniteStack of Solar Cells 568
III.F. Additional Comments: IndependentDerivation of S for the Stack 573
III.G. Additional Comment: The Solar CellEquation and Standard Approximations : 576
III.H The Finite Stack 581
IV. PROBLEMS 586
V. MAIN SYMBOL USED AND REFERENCES 587
VI. APPENDIX 589
REFERENCES 590
xxi i ' CONTENTS
LONG SEMINARS
MAGNETO-OPTICAL STUDY OF ENERGY TRANSFER IN RUBY 593
M. Ferrari, L. Gonzo, M. Montagna, 0. Pilla,and G. Viliani
ABSTRACT 593
I. INTRODUCTION 593
II. EXPERIMENTAL 594
III. EXPERIMENTAL RESULTS 594
III.A. Lifetime Measurements 594
III.B. Transferred Intensities vs. Magnetic Field 595
III.C. Excitation Spectra 597
IV. DISCUSSION 598
ACKNOWLEDGEMENT 601
REFERENCES 601
SPECTROSCOPIC STUDIES OF ENERGY TRANSFER IN SOLIDS 603
G. Boulon
ABSTRACT 603
I. INTRODUCTION '• 603
II. MATERIAL AND EXPERIMENTAL EQUIPMENT 604
III. USEFUL DATA ABOUT THEORETICAL APPROACHES TO
THE ENERGY .TRANSFER 604
III.A. Resonant Radiative Energy Transfer 604
III.B. Resonant Nonradiative Energy Transfer 605
1. Without Diffusion Among S Ions 605
2. With Diffusion Among S Ions 607
CONTENTS xxiii
III.C. Up-conversion Processes by Energy Transfer 608
III.D. Influence of the Traps in the Materials 608
IV. ENERGY TRANSFER IN DOPED MATERIALS 611
O_|_ O i
IV.A. Bi - Eu Codoped Germanate Glassor Lu.Si^O- Crystal 611
IV.B. Ky3F10(Eu2+) 6 1 2
IV.C. LaCl3 - Gd34" 6 1 4
V. ENERGY TRANSFER IN STOICHIOMETRIC MATERIALS 615
V.A. ^Manganese Compounds 616
V.B. Rare-earth Compounds 617
VI. SUMMARY 619
ACKNOWLEDGEMENTS 620
REFERENCES 620
DYNAMICAL MODELS OF ENERGY TRANSFER IN CONDENSED MATTER 621
J. Klafter and A. Blumen
ABSTRACT 621
I. INTRODUCTION 621
II. DIRECT TRANSFER 623
III. DIFFUSION IN THE FRAMEWORK OF THE CTRW 628
IV. TRAPPING IN THE CTRW MODEL 633
ACKNOWLEDGEMENTS . 636
REFERENCES 636
xxiv CONTENTS
ENERGY TRANSFER AND ELECTRON TRANSFER IN PHOTOBIOLOGICAL,PHOTOCHEMICAL, AND PHOTOELECTROCHEMICAL PROCESSES(Abstract only) 639
A. Nozik
AN EXAMPLE OF IDENTIFYING THE SPECIFIC MECHANISM OFRESONANT ENERGY TRANSFER: Sb31" -+• M n 2 + IN FLUORO-PHOSPHATE PHOSPHORS (Abstract only) : 641
R. L. Bateman
ENERGY TRANSFER AND ANDERSON LOCALIZATION IN RUBY
ELECTRIC FIELD AND UNIAXIAL STRESS EFFECTS 643
E. Duval and A. Monteil
ABSTRACT 643
I. INTRODUCTION 643
II. E-SUBLATTICES AND a-SUB LATTICES, 644
III. EXPERIMENTAL 645
IV. DISCUSSION 647
IV.A. Rapid or Slow Nonradiative Resonant
Transfer? 647
IV.B. Anderson Transition 650
IV.C. Internal Electric Fields and Energy
Transfer 651
V. CONCLUSION 652
REFERENCES. ; 653
TIME-RESOLVED STUDIES -OF ENERGY TRANSFER 655
R. C. Powell
ABSTRACT • 655
CONTENTS xxv
I . INTRODUCTION 655
I I . ORIGIN OF THE TIME DEPENDENCE * 656
I I I . METHODS OF THEORETICAL ANALYSIS 658
IV. EXPERIMENTAL TECHNIQUES 660
V. EXAMPLES OF TIME-RESOLVED ENERGY TRANSFER STUDIES 662
3+V.A. Energy Transfer Between Eu Ions in
Eux Y1_x p
5 ° 1 4 C rys t a l s 662
V.B. Energy Transfer Among Nd Ions in
Lightly Doped Solids 665
V. C. Exciton Diffusion in Nd La1 P<- 0,, Crystals - 667
VI. CONCLUSIONS , 669
REFERENCES 670
TRENDS IN SCIENTIFIC COMPUTING 673
C. K. Landraitis
ABSTRACT r 673
I. THE PROBLEM-SOLVING CYCLE 673
II. PROVIDING A BETTER ENVIRONMENT FOR
SCIENTIFIC COMPUTING 674
II.A. Computer-Based Local and Long-Distance
Networks 674
II.B. Hardware and Software Tools 674
1. Video Display Technology 674
2. Direct Input 675
3. Software 675
III. ACHIEVING FASTER COMPUTATION 675
III.A. The Need for Faster Computation 675
III.B. Historical Trends 676
xxvi CONTENTS
III.C. Conventional Processor Designs 676
III.D. Concurrent Operation of Computer
Subsystems 677
III.E. Pipelining 677
III.F. The Potential for Exploiting Parallelism 677
III.G. Radical Innovations in Processor Design 678
IV. COMPUTATIONAL MODELLING AND SIMULATION 679
REFERENCES 679
SHORT SEMINARS
PHOTOCONDUCTIVITY OF INDIUM IN SILICON 681
R. Lindner
NONLINEAR ENERGY TRANSFER IN SEMICONDUCTORSYIELDING BISTABILITY 682
K. Bohnert ,
LUMINESCENCE AND ENERGY TRANSFER IN YAlG:Nd,Ce 683
J . Mares
ENERGY TRANSFER EFFECTS IN NaEuTiO^ 684
P. A. M. Berdowski
ENERGY TRANSFER IN ANTIFERROMAGNETIC ALKALI MANGANESEHALIDE CRYSTALS 685
U. Kambli
CONTENTS xxvii
AUGER EFFECT DUE TO SHALLOW DONORS IN CdF2:Mn LUMINESCENCE — 68 6
A. Suchock i
ENERGY TRANSFER PROCESSES IN ZnSe :Ni ,Fe 6 8 7
A. K a r i p i d o u
ON THE ROLE OF NONLOCALIZED EXCITATION MECHANISMS IN THEGENERATION OF RED Er34" EMISSION IN CdF^Er^Yb 688
A. Stapor
THE GENERAL THREE-DIMENSIONAL HAKEN-STROBL MODEL 689
I . Rips
THE LUMINESCENCE SPECTRUM OF UO^oO^ T 690
W. M. A. Smit
CONTRIBUTORS 691
INDEX 693
