Hopping conduction in solids:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Akademie-Verlag
1985
|
| Series: | Physical research
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 398 S. 107 graph. Darst. 25 cm |
Staff View
MARC
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| 245 | 1 | 0 | |a Hopping conduction in solids |c by Harald Böttger ; Valerij V. Bryksin |
| 264 | 1 | |a Berlin |b Akademie-Verlag |c 1985 | |
| 300 | |a 398 S. |b 107 graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Physical research |v Vol. 1 | |
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Record in the Search Index
| _version_ | 1808498241273069568 |
|---|---|
| adam_text |
CONTENTS
CHAPTER I. BASIC ELEMENTS OF THE THEORY OF HOPPING TRANSPORT
1. INTRODUCTION AND OVERVIEW . 11
2. GENERAL FORMALISM
2.1. THE HAMILTONIAN FOR A HOPPING SYSTEM.18
2.1.1. THE ELECTRON HAMILTONIAN.18
2.1.2. ELECTRON-PHONON INTERACTION.20
2.1.3. INTERACTION WITH ELECTRICAL AND MAGNETIC FIELDS.22
2.2. THE POLARON CANONICAL TRANSFORMATION.24
2.3. THE EXPRESSION FOR THE CURRENT AND ITS RELATION TO THE KUBO
FORMULA.28
2.4. THE EQUATION OF MOTION FOR THE DENSITY MATRIX IN THE HOPPING
REGIME.30
2.4.1. PERTURBATION THEORY. 30
2.4.2. ONE-ELECTRON APPROXIMATION.33
2.4.3. HARTREE-FOCK DECOUPLING.38
2.5. THE RATE EQUATION FOR WEAK ELECTRICAL FIELDS.40
2.5.1. THE RATE EQUATION FOR ARBITRARY FREQUENCIES.40
2.5.2. THE LOW-FREQUENCY LIMIT AND THE RANDOM-RESISTOR NETWORK WITH
CAPACITORS . 42
2.0. THE STOCHASTIC INTERPRETATION OF HOPPING PROCESSES .45
2.6.1. THE CONDITIONAL-PROBABILITY FUNCTION AND ITS RELATION TO THE
DIFFUSION COEFFICIENT 45
2.6.2. RELATION BETWEEN CHARGE TRANSPORT AND DIFFUSION.48
CHAPTER II. SMALL POLARONS
3. THE SMALL-POLARON MODEL; CRYSTALLINE MATERIALS WITH A NARROW
CONDUCTION
' BAND AND STRONG ELECTRON-PHONON INTERACTION
3.1. THE LOW-MOBILITY PROBLEM AND THE SMALL POLARON.51
3.2. DC CONDUCTIVITY.53
3.2.1. HOPPING CONDUCTION OF NON-ADIABATIC POLARONS.53
3.2.2. THE TWO-SITE MODEL AND THE ADIABATIC POLARON .57
3.2.3. NON-HOPPING TRANSPORT OF SMALL POLARONS IN THE LOW-TEMPERATURE
REGIME . 61
3.3. OPTICAL PROPERTIES IN THE SMALL-POLARON MODEL .66
3.4. THE SMALL POLARON IN A STRONG ELECTRICAL FIELD.70
3.4.1. CURRENT-VOLTAGE CHARACTERISTIC IN THE HOPPING REGIME.70
3.4.2. THE SMALL POLARON IN STRONG FIELDS AT LOW TEMPERATURES AND THE
STARK LADDER 74
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/870103660
8 CONTENTS
3.5. THE HALL EFFECT.75
3.5.1. HAL] MOBILITY VERSUS DRIFT MOBILITY IN THE CASE OF HOPPING
TRANSPORT . 75
3.5.2. THE GENERAL EXPRESSION FOR THE HALL CURRENT IN THE HOPPING
REGIME.76
3.5.3. THE HALL MOBILITY FOR HOPPING TRANSPORT.78
3.5.4. THE HALL MOBILITY IN A LARGE TEMPERATURE RANGE INCLUDING ALSO
NON-HOPPING TRANS
PORT .81
3.6. THERMOELECTRIC POWER.84
3.7. EXPERIMENTAL FINDINGS.85
CHAPTER HI. HOPPING CONDUCTION IN DISORDERED SYSTEMS
4. ELECTRON STATES AND CHARGE TRANSPORT IN DISORDERED SYSTEMS
4.1. EFFECT OF DISORDER ON ELECTRON STATES AND CHARGE TRANSPORT .8S
4.2. LOCALIZATION IN THE ANDERSON MODEL.94
4.3. SCALING THEORY OF LOCALIZATION.98
5. DC HOPPING CONDUCTIVITY
5.1. BASIE FORMULAE AND THE PROBLEM OF AVERAGING THE RANDOM-RESISTOR
NETWORK . . . 104
5.1.1. ' FORMULATION OF THE PROBLEM.104
5.1.2. EXPRESSIONS FOR THE DC HOPPING PROBABILITY.106
5.1.3. THE NETWORK OF MILLER AND ABRAHAMS.107
5.1.4. MOTT'S LAW FOR THE VARIABLE-RANGE HOPPING REGIME.110
5.1.5. POLARON EFFECTS IN DISORDERED SYSTEMS.112
5.2. PERCOLATION THEORY .113
5.2.1. BASIC IDEAS OF THE PERCOLATION THEORY.114
5.2.2. THE PERCOLATION PROBLEM IN THE CONTEXT OF CRITICAL PHENOMENA.126
5.2.3. THE REAL-SPACE RENORMALIZATION-GROUP METHOD.134
5.2.4. RELATIONSHIP BETWEEN PERCOLATION AND EFFECTIVE-MEDIUM TREATMENTS
OF RANDOM-
RESISTOR NETWORKS.141
5.3. THE PERCOLATION APPROACH TO HOPPING CONDUCTION.143
5.3.1. RESISTOR NETWORK ON A SIMPLE CUBIC LATTICE.144
5.3.2. CONCENTRATION DEPENDENCE OF THE HOPPING CONDUCTIVITY
(IF-PERC-OLATION).147
5.3.3. VARIABLE-RANGE HOPPING (I?--PERCOLATION).150
5.3.4. THE PRE-EXPONENTIAL FACTOR OF THE HOPPING CONDUCTIVITY.156
5.3.5. RESULTS OF OTHER METHODS.157
5.4. EFFECTS OF ELECTRON-ELECTRON INTERACTION.159
5.4.1. ON THE INTERPLAY OF RANDOMNESS AND ELECTRON-ELECTRON
INTERACTION.159
5.4.2. THE COULOMB GAP.162
5.4.3. CORRELATION EFFECTS IN HOPPING TRANSPORT.166
6. AC HOPPING CONDUCTIVITY
6.1. INTRODUCTORY REMARKS.169
6.2. THE TWO-SITE MODEL.170
6.2.1. BASIC FORMULAE FOR THE TWO-SITE MODEL.170
6.2.2. THE PHONON CONTRIBUTION TO THE CONDUCTIVITY.175
6.2.3. THE PHONONLESS CONTRIBUTION TO THE CONDUCTIVITY.177
CONTENTS 9
6.3. CLUSTER APPROXIMATION.179
6.3.1. THE BASIC IDEA UNDERLYING THE CLUSTER APPROXIMATION., . . . 179
6.3.2. ONE-DIMENSIONAL SYSTEMS.180
6.3.3. THREE-DIMENSIONAL SYSTEMS.183
6.4. EFFECTIVE-MEDIUM APPROXIMATION.188
6.4.1. EQUATION FOR SELF-CONSISTENT EVALUATION OF THE EFFECTIVE HOPPING
PROBABILITY . . 188
6.4.2. RESULTS FOR THE AC CONDUCTIVITY IN THREE-DIMENSIONAL SYSTEMS.193
6.5. DIAGRAM TECHNIQUE AND SOME PROBLEMS OF DIFFUSION IN DISORDERED
SYSTEMS . . . 198
6.6. USE OF THE TOPOLOGY OF THE BETHE LATTICE (CAYLEY TREE) IN THE
THEORY OF THE AC CONDUC
TIVITY .206
6.6.1. GENERAL EXPRESSION FOR THE AC CONDUCTIVITY OF A BETHE LATTICE.206
6.6.2. RESULTS FOR R-PERCOLATION.209
6.6.3. RESULTS FOR R-A-PERCOLATION.210
6.7. DISCUSSION OF THEORETICAL RESULTS FOR THE AC CONDUCTIVITY AND
COMPARISON WITH EX
PERIMENTAL FINDINGS.213
6.7.1. FOUR CHARACTERISTIC FREQUENCY REGIMES.213
6.7.2. EXPERIMENTAL FINDINGS ON DOPED SEMICONDUCTORS AND AMORPHOUS
MATERIALS . . . 216
6.8. DISPERSIVE TRANSPORT .218
6.8.1. ANOMALOUS CARRIER-PULSE PROPAGATION IN AMORPHOUS
SEMICONDUCTORS.218
6.8.2. RELATIONSHIP BETWEEN AC HOPPING CONDUCTIVITY AND DISPERSIVE
TRANSPORT . 224
6.8.3. CONTINOUS-TIME RANDOM-WALK THEORY.227
7. NON-OHMIC HOPPING CONDUCTION
7.1. BASIC FORMULAE AND RESULTS FOR HOPPING IN STRONG ELECTRICAL FIELDS
.236
7.1.1. THE EXPRESSION FOR THE DC HOPPING CURRENT.236
7.1.2. SOME PROBLEMS AND RESULTS OF THE DC CONDUCTION.238
7.1.3. THE AC CONDUCTIVITY PROBLEM. 243
7.2. PERCOLATION APPROACH TO NON-OHMIC HOPPING CONDUCTION AND DIRECTED
PERCOLATION . 244
7.2.1. EXPRESSION FOR THE CURRENT IN ARBITRARY ELECTRICAL FIELDS FOR
HOPPING ALONG A PER
COLATION PATH.244
7.2.2. SELECTION OF THE OPTIMAL PERCOLATION PATH AND THE EXPRESSION FOR
THE CURRENT . . 246
7.3. EFFECTIVE-MEDIUM THEORY FOR THE CASE OF STRONG FIELDS.253
7.3.1. STATIONARY CURRENTS.253
7.3.2. RELAXATION CURRENTS.256
7.4. NON-OHMIC HOPPING CONDUCTION IN A ONE-DIMENSIONAL MODEL.258
8. THE HALL EFFECT
8.1. THE RANDOM-RESISTOR NETWORK AND THE HALL EFFECT.260
8.2. THE DC HALL EFFECT .264
9. SOME OTHER HOPPING PHENOMENA
9.1. THERMOELECTRIC POWER.276
9.2. MAGNETORESISTANCE .280
9.3. OPTICAL PHENOMENA.287
9.3.1. ABSORPTION OF LIGHT IN DISORDERED MATERIALS WITH STRONG
ELECTRON-PHONON COUPLING 287
9.3.2. RESONANT-RAMAN SCATTERING IN MATERIALS WITH LOCALIZED CHARGE
CARRIERS.291
10
CONTENTS
CHAPTER IV. CLASSICAL HOPPING TRANSPORT
10. DIFFUSIVE ATOMIC MOTION
10.1. SOME BASIC FEATURES OF DIFFUSIVE ATOMIC MOTION.297
10.1.1. MATERIALS EXHIBITING DIFFUSIVE ATOMIC MOTION.297
10.1.2. CLASSICAL DIFFUSION VERSUS QUANTUM DIFFUSION.299
10.1.3. HOPPING RATE FOR OVER-BARRIER HOPPING.302
10.2. SINGLE-PARTICLE HOPPING.305
10.2.1. A ONE-DIMENSIONAL HOPPING MODEL.303
10.2.2. CLASSICAL HOPPING IN DISORDERED SYSTEMS.307
10.2.3. SINGLE-PARTICLE DIFFUSION VERSUS BULK DIFFUSION.309
10.3. CONTINUOUS SINGLE-PARTICLE DIFFUSION.314
10.4. MANY-PARTIELE DIFFUSION.315
CHAPTER V. RECENT DEVELOPMENTS
11. SURVEY OF SOME RECENT DEVELOPMENTS IN THE FIELD OF SMALL POLARONS,
DISORDERED
SYSTEMS AND HOPPING CONDUCTION.318
11.1. POLARON EFFECTS.318
11.2. ELECTRON STATES AND CHARGE TRANSPORT IN DISORDERED SYSTEMS.321
11.2.1. ANDERSON LOCALIZATION AND RELATED PROBLEMS .321
11.2.2. DYNAMICAL ELECTRON-PHONON EFFECTS ON TRANSPORT NEAR A MOBILITY
EDGE.324
11.3. PROBLEMS OF PERCOLATION THEORY.326
11.3.1. PERCOLATION MODELS.326
11.3.2. FRACTALS AND THE STRUCTURE OF PERCOLATION CLUSTERS AND THEIR
BACKBONES.328
11.4. HOPPING TRANSPORT IN DISORDERED SYSTEMS.331
11.4.1. AC CONDUCTIVITY, RELAXATION CURRENTS, AND PARTICLE DIFFUSION.331
11.4.2. MISCELLANEOUS HOPPING PROBLEMS .336
11.5. ATOMIC HOPPING TRANSPORT.338
APPENDIX 1. DIAGRAM TECHNIQUE FOR STRONG ELECTRON-PHONON COUPLING.340
APPENDIX 2. RATE EQUATION IN THE PRESENCE OF A MAGNETIC FIELD.358
APPENDIX 3. PERCOLATION PROBLEMS AND THE POTTS MODEL.363
REFERENCES. 365
REFERENCES ADDED IN PROOF.380
INDEX
.389 |
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| author | Böttger, Harald 1940- Bryksin, Valerij V. |
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| author_facet | Böttger, Harald 1940- Bryksin, Valerij V. |
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| indexdate | 2024-08-27T00:25:23Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017199219 |
| oclc_num | 844864573 |
| open_access_boolean | |
| owner | DE-634 DE-11 |
| owner_facet | DE-634 DE-11 |
| physical | 398 S. 107 graph. Darst. 25 cm |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Akademie-Verlag |
| record_format | marc |
| series | Physical research |
| series2 | Physical research |
| spelling | Böttger, Harald 1940- Verfasser (DE-588)120306828X aut Hopping conduction in solids by Harald Böttger ; Valerij V. Bryksin Berlin Akademie-Verlag 1985 398 S. 107 graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Physical research Vol. 1 Festkörper (DE-588)4016918-2 gnd rswk-swf Hopping-Leitfähigkeit (DE-588)4160650-4 gnd rswk-swf Festkörper (DE-588)4016918-2 s Hopping-Leitfähigkeit (DE-588)4160650-4 s 1\p DE-604 Bryksin, Valerij V. Verfasser aut Physical research 1 (DE-604)BV000651253 1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017199219&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Böttger, Harald 1940- Bryksin, Valerij V. Hopping conduction in solids Physical research Festkörper (DE-588)4016918-2 gnd Hopping-Leitfähigkeit (DE-588)4160650-4 gnd |
| subject_GND | (DE-588)4016918-2 (DE-588)4160650-4 |
| title | Hopping conduction in solids |
| title_auth | Hopping conduction in solids |
| title_exact_search | Hopping conduction in solids |
| title_full | Hopping conduction in solids by Harald Böttger ; Valerij V. Bryksin |
| title_fullStr | Hopping conduction in solids by Harald Böttger ; Valerij V. Bryksin |
| title_full_unstemmed | Hopping conduction in solids by Harald Böttger ; Valerij V. Bryksin |
| title_short | Hopping conduction in solids |
| title_sort | hopping conduction in solids |
| topic | Festkörper (DE-588)4016918-2 gnd Hopping-Leitfähigkeit (DE-588)4160650-4 gnd |
| topic_facet | Festkörper Hopping-Leitfähigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017199219&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000651253 |
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