Electron transport in nanostructures and mesoscopic devices: an introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
ISTE [u.a.]
2008
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | X, 387 S. Ill., graph. Darst. |
| ISBN: | 9781848210509 |
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MARC
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| 020 | |a 9781848210509 |9 978-1-84821-050-9 | ||
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| 035 | |a (DE-599)GBV562581235 | ||
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| 100 | 1 | |a Ouisse, Thierry |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Electron transport in nanostructures and mesoscopic devices |b an introduction |c Thierry Ouisse |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a London |b ISTE [u.a.] |c 2008 | |
| 300 | |a X, 387 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Electron transport | |
| 650 | 4 | |a Nanostructured materials |x Electric properties | |
| 650 | 4 | |a Nanostructures |x Electric properties | |
| 650 | 4 | |a Mesoscopic phenomena (Physics) | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0811/2008008768-d.html |3 Publisher description | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016780985&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016780985 | ||
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| _version_ | 1804138086864519168 |
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| adam_text | Titel: Electron transport in nanostructures and mesoscopic devices
Autor: Ouisse, Thierry
Jahr: 2008
Table of Contents
Chapter 1. Introduction 1
1.1. Introduction and preliminary warning 1
1.2. Bibliography 7
Chapter 2. Some Useful Concepts and Reminders 9
2.1. Quantum mechanics and the Schrodinger equation 9
2.1.1. A more than brief introduction 9
2.1.2. The postulates of quantum mechanics 12
2.1.3. Essential properties of observables 14
2.1.4. Momentum operator 16
2.1.5. Stationary states 17
2.1.6. Probability current 18
2.1.7. Electrons in vacuum and group velocity 20
2.2. Energy band structure in a periodic lattice 22
2.3. Semi-classical approximation 25
2.4. Electrons and holes 27
2.5. Semiconductor heterostructure 30
2.6. Quantum well 31
2.6.1. ID case 31
2.6.2. Coupled quantum wells 37
2.6.3. Quantum-confined Stark effect 40
2.7. Tight-binding approximation 43
2.8. Effective mass approximation 49
2.8.1. Wannier functions 49
2.8.2. Effective mass Schrodinger equation 51
2.9. How good is the effective mass approximation in a confined structure? . 55
2.10. Density of states 57
2.10.1. 3D case 57
vi Electron Transport in Nanostructures and Mesoscopic Devices
2.10.2. 2D case 58
2.10.3. ID case 59
2.10.4. Summary 60
2.11. Fermi-Dirac statistics 60
2.12. Examples of 2D systems 62
2.13. Characteristic lengths and mesoscopic nature of electron transport ... 65
2.14. Mobility: Drude model 67
2.15. Conduction in degenerate materials 69
2.16. Einstein relationship 71
2.17. Low magnetic field transport 73
2.18. High magnetic field transport 75
2.18.1. Introduction 75
2.18.2. Some reminders about the particle Hamiltonian in the presence of
an electromagnetic field 76
2.18.3. Action of a magnetic field (classical) 77
2.18.4. High magnetic field transport 78
2.19. Exercises 94
2.19.1. Exercise 94
2.19.2. Exercise 95
2.19.3. Exercise 97
2.19.4. Exercise 99
2.20. Bibliography 100
Chapter 3. Ballistic Transport and Transmission Conductance 103
3.1. Conductance of a ballistic conductor 103
3.2. Connection between 2D and ID systems 109
3.3. A classical analogy 110
3.4. Transmission conductance: Landauer s formula Ill
3.5. What if the device length really does go down to zero? 114
3.6. A smart experiment which shows you everything 117
3.7. Relationship between the Landauer formula and Ohm s law 120
3.8. Dissipation with a scatterer 123
3.9. Voltage probe measurements 127
3.10. Comment about the assumption that T is constant 129
3.11. Generalization of Landauer s formula: Buttiker s formula 130
3.11.1. Buttiker s formula 130
3.11.2. Three-terminal device 133
3.11.3. Four-terminal device 134
3.12. Non-zero temperature 135
3.12.1. Large applied bias nru2»0 135
3.12.2. Incoherent states 136
Table of Contents vii
3.12.3. Coherent states 138
3.12.4. Physical parameters included in the transmission probability. . . . 141
3.12.5. Linear response (ui-u2 kBT or T(E)=Cst) 142
3.13. The integer quantum Hall effect 143
3.13.1. The experiment 143
3.13.2. The explanation 145
3.14. Exercises 150
3.14.1. Exercise 150
3.14.2. Exercise 151
3.14.3. Exercise 152
3.14.4. Exercise 153
3.14.5. Exercise 155
3.15. Bibliography 157
Chapter 4. S-matrix Formalism 159
4.1. Scattering matrix or S-matrix 159
4.2. S-matrix combination rules 163
4.3. A simple example: the S-matrix of a Y-junction 164
4.4. A more involved example: a quantum ring 166
4.5. A final more complex example: solving the 2D Schrodinger equation . . 169
4.5.1. Calculation principle 169
4.5.2. Some numerical examples 178
4.6. Exercises 181
4.7. Bibliography 182
Chapter 5. Tunneling and Detrapping 183
5.1. Introduction 183
5.2. Single barrier tunneling 185
5.3. Two coherent devices in series: resonant tunneling 189
5.4. Physical meaning of the terms appearing in the resonant transmission
probability 194
5.5. Tunneling current 197
5.6. Resonant tunneling in the real world 199
5.7. Discrete state coupled to a continuum 201
5.8. Fano resonance 210
5.9. Fano resonance in a quantum-coherent device 212
5.10. Fano resonance in the real world 217
5.11. Exercises 219
5.11.1. Exercise 219
5.11.2. Exercise 220
5.11.3. Exercise 221
5.11.4. Exercise 222
viii Electron Transport in Nanostructures and Mesoscopic Devices
5.11.5. Exercise 222
5.11.6. Exercise 223
5.12. Bibliography 224
Chapter 6. An Introduction to Current Noise in Mesoscopic Devices 225
6.1. Introduction 225
6.2. Ergodicity and stationarity 226
6.3. Spectral noise density and Wiener-Khintchine theorem 228
6.4. Measured power spectral density 230
6.5. Shot noise in the classical case 231
6.6. Why the shot noise formula is not valid in a macroscopic conductor . . . 235
6.6.1. Current pulse shape 235
6.6.2. Non-ballistic conductor 237
6.7. Classical example 1: a game with cannon balls 238
6.8. Classical example 2: cars and anti-cars 238
6.9. Quantum shot noise 240
6.9.1. Fluctuations and Pauli exclusion principle 240
6.9.2. Shot noise power spectrum at T=0 241
6.10. Bibliography 247
Chapter 7. Coulomb Blockade Effect 249
7.1. Introduction 249
7.2. Energy balance when charging capacitors 251
7.3. Coulomb blockade in a two-terminal device 253
7.4. Coulomb blockade in a single-electron transistor 258
7.5. Single-electron turnstile 265
7.6. Coulomb blockade in the real world 265
7.7. Exercises 268
7.7.1. Exercise 268
7.7.2. Exercise 269
7.7.3. Exercise 270
7.8. Bibliography 271
Chapter 8. Specific Interference Effects 273
8.1. Classical Lagrangian with a magnetic field 273
8.2. Classical Lagrangian without a magnetic field 275
8.3. Phase shift due to a magnetic field 275
8.4. Aharonov-Bohm effect in mesoscopic rings 276
8.4.1. Theory 276
8.4.2. Aharonov-Bohm effect in the real world 279
Table of Contents ix
8.5. ID localization 280
8.5.1. Interference effects when I® exceeds the distance between
impurities 280
8.5.2. ID localization 281
8.6. Weak localization 283
8.7. Universal conductance fluctuations 286
8.8. Bibliography 289
Chapter 9. Graphene and Carbon Nanotubes 291
9.1. Introduction 291
9.2. Graphene band structure 293
9.3. Integer quantum hall effect in graphene 301
9.4. Carbon nanotube band structure 304
9.5. Carbon nanotube bandgap 309
9.6. Carbon nanotube density of states and effective mass 313
9.7. Electron transport in and quantum dots from carbon nanotubes 315
9.8. Exercises 321
9.8.1. Exercise 321
9.8.2. Exercise 322
9.8.3. Exercise 323
9.9. Bibliography 323
Chapter 10. Appendices 325
10.1. The uncertainty principle 325
10.2. Crystalline lattice; some definitions and theorems 326
10.3. The harmonic oscillator 330
10.4. Stationary perturbation theory 336
10.4.1. Non-degenerate perturbation theory 336
10.4.2. Degenerate perturbation theory 338
10.5. Method of Lagrange multipliers 342
10.6. Variational principle 344
10.7. Wiener-Khintchine theorem 348
10.8. Binomial probability law 349
10.9. Random Poisson process 350
10.10. Transformation of the Cartesian wavevector coordinates into
transverse and parallel components 351
10.11. Useful physical constants 353
Solutions to Exercises 355
Exercise 2.19.1 355
Exercise 2.19.2 356
Exercise 2.19.3 357
x Electron Transport in Nanostructures and Mesoscopic Devices
Exercise 2.19.4 360
Exercise 3.14.1 361
Exercise 3.14.2 363
Exercise 3.14.3 363
Exercise 3.14.4 365
Exercise 3.14.5 367
Exercise 5.11.1 368
Exercise 5.11.2 369
Exercise 5.11.3 370
Exercise 5.11.4 371
Exercise 5.11.5 372
Exercise 5.11.6 373
Exercise 7.7.1 374
Exercise 7.7.2 375
Exercise 7.7.3 376
Exercise 9.8.1 378
Exercise 9.8.2 379
Exercise 9.8.3 380
Index 383
|
| adam_txt |
Titel: Electron transport in nanostructures and mesoscopic devices
Autor: Ouisse, Thierry
Jahr: 2008
Table of Contents
Chapter 1. Introduction 1
1.1. Introduction and preliminary warning 1
1.2. Bibliography 7
Chapter 2. Some Useful Concepts and Reminders 9
2.1. Quantum mechanics and the Schrodinger equation 9
2.1.1. A more than brief introduction 9
2.1.2. The postulates of quantum mechanics 12
2.1.3. Essential properties of observables 14
2.1.4. Momentum operator 16
2.1.5. Stationary states 17
2.1.6. Probability current 18
2.1.7. Electrons in vacuum and group velocity 20
2.2. Energy band structure in a periodic lattice 22
2.3. Semi-classical approximation 25
2.4. Electrons and holes 27
2.5. Semiconductor heterostructure 30
2.6. Quantum well 31
2.6.1. ID case 31
2.6.2. Coupled quantum wells 37
2.6.3. Quantum-confined Stark effect 40
2.7. Tight-binding approximation 43
2.8. Effective mass approximation 49
2.8.1. Wannier functions 49
2.8.2. Effective mass Schrodinger equation 51
2.9. How good is the effective mass approximation in a confined structure? . 55
2.10. Density of states 57
2.10.1. 3D case 57
vi Electron Transport in Nanostructures and Mesoscopic Devices
2.10.2. 2D case 58
2.10.3. ID case 59
2.10.4. Summary 60
2.11. Fermi-Dirac statistics 60
2.12. Examples of 2D systems 62
2.13. Characteristic lengths and mesoscopic nature of electron transport . 65
2.14. Mobility: Drude model 67
2.15. Conduction in degenerate materials 69
2.16. Einstein relationship 71
2.17. Low magnetic field transport 73
2.18. High magnetic field transport 75
2.18.1. Introduction 75
2.18.2. Some reminders about the particle Hamiltonian in the presence of
an electromagnetic field 76
2.18.3. Action of a magnetic field (classical) 77
2.18.4. High magnetic field transport 78
2.19. Exercises 94
2.19.1. Exercise 94
2.19.2. Exercise 95
2.19.3. Exercise 97
2.19.4. Exercise 99
2.20. Bibliography 100
Chapter 3. Ballistic Transport and Transmission Conductance 103
3.1. Conductance of a ballistic conductor 103
3.2. Connection between 2D and ID systems 109
3.3. A classical analogy 110
3.4. Transmission conductance: Landauer's formula Ill
3.5. What if the device length really does go down to zero? 114
3.6. A smart experiment which shows you everything 117
3.7. Relationship between the Landauer formula and Ohm's law 120
3.8. Dissipation with a scatterer 123
3.9. Voltage probe measurements 127
3.10. Comment about the assumption that T is constant 129
3.11. Generalization of Landauer's formula: Buttiker's formula 130
3.11.1. Buttiker's formula 130
3.11.2. Three-terminal device 133
3.11.3. Four-terminal device 134
3.12. Non-zero temperature 135
3.12.1. Large applied bias nru2»0 135
3.12.2. Incoherent states 136
Table of Contents vii
3.12.3. Coherent states 138
3.12.4. Physical parameters included in the transmission probability. . . . 141
3.12.5. Linear response (ui-u2 kBT or T(E)=Cst) 142
3.13. The integer quantum Hall effect 143
3.13.1. The experiment 143
3.13.2. The explanation 145
3.14. Exercises 150
3.14.1. Exercise 150
3.14.2. Exercise 151
3.14.3. Exercise 152
3.14.4. Exercise 153
3.14.5. Exercise 155
3.15. Bibliography 157
Chapter 4. S-matrix Formalism 159
4.1. Scattering matrix or S-matrix 159
4.2. S-matrix combination rules 163
4.3. A simple example: the S-matrix of a Y-junction 164
4.4. A more involved example: a quantum ring 166
4.5. A final more complex example: solving the 2D Schrodinger equation . . 169
4.5.1. Calculation principle 169
4.5.2. Some numerical examples 178
4.6. Exercises 181
4.7. Bibliography 182
Chapter 5. Tunneling and Detrapping 183
5.1. Introduction 183
5.2. Single barrier tunneling 185
5.3. Two coherent devices in series: resonant tunneling 189
5.4. Physical meaning of the terms appearing in the resonant transmission
probability 194
5.5. Tunneling current 197
5.6. Resonant tunneling in the real world 199
5.7. Discrete state coupled to a continuum 201
5.8. Fano resonance 210
5.9. Fano resonance in a quantum-coherent device 212
5.10. Fano resonance in the real world 217
5.11. Exercises 219
5.11.1. Exercise 219
5.11.2. Exercise 220
5.11.3. Exercise 221
5.11.4. Exercise 222
viii Electron Transport in Nanostructures and Mesoscopic Devices
5.11.5. Exercise 222
5.11.6. Exercise 223
5.12. Bibliography 224
Chapter 6. An Introduction to Current Noise in Mesoscopic Devices 225
6.1. Introduction 225
6.2. Ergodicity and stationarity 226
6.3. Spectral noise density and Wiener-Khintchine theorem 228
6.4. Measured power spectral density 230
6.5. Shot noise in the classical case 231
6.6. Why the shot noise formula is not valid in a macroscopic conductor . . . 235
6.6.1. Current pulse shape 235
6.6.2. Non-ballistic conductor 237
6.7. Classical example 1: a game with cannon balls 238
6.8. Classical example 2: cars and anti-cars 238
6.9. Quantum shot noise 240
6.9.1. Fluctuations and Pauli exclusion principle 240
6.9.2. Shot noise power spectrum at T=0 241
6.10. Bibliography 247
Chapter 7. Coulomb Blockade Effect 249
7.1. Introduction 249
7.2. Energy balance when charging capacitors 251
7.3. Coulomb blockade in a two-terminal device 253
7.4. Coulomb blockade in a single-electron transistor 258
7.5. Single-electron turnstile 265
7.6. Coulomb blockade in the real world 265
7.7. Exercises 268
7.7.1. Exercise 268
7.7.2. Exercise 269
7.7.3. Exercise 270
7.8. Bibliography 271
Chapter 8. Specific Interference Effects 273
8.1. Classical Lagrangian with a magnetic field 273
8.2. Classical Lagrangian without a magnetic field 275
8.3. Phase shift due to a magnetic field 275
8.4. Aharonov-Bohm effect in mesoscopic rings 276
8.4.1. Theory 276
8.4.2. Aharonov-Bohm effect in the real world 279
Table of Contents ix
8.5. ID localization 280
8.5.1. Interference effects when I® exceeds the distance between
impurities 280
8.5.2. ID localization 281
8.6. Weak localization 283
8.7. Universal conductance fluctuations 286
8.8. Bibliography 289
Chapter 9. Graphene and Carbon Nanotubes 291
9.1. Introduction 291
9.2. Graphene band structure 293
9.3. Integer quantum hall effect in graphene 301
9.4. Carbon nanotube band structure 304
9.5. Carbon nanotube bandgap 309
9.6. Carbon nanotube density of states and effective mass 313
9.7. Electron transport in and quantum dots from carbon nanotubes 315
9.8. Exercises 321
9.8.1. Exercise 321
9.8.2. Exercise 322
9.8.3. Exercise 323
9.9. Bibliography 323
Chapter 10. Appendices 325
10.1. The uncertainty principle 325
10.2. Crystalline lattice; some definitions and theorems 326
10.3. The harmonic oscillator 330
10.4. Stationary perturbation theory 336
10.4.1. Non-degenerate perturbation theory 336
10.4.2. Degenerate perturbation theory 338
10.5. Method of Lagrange multipliers 342
10.6. Variational principle 344
10.7. Wiener-Khintchine theorem 348
10.8. Binomial probability law 349
10.9. Random Poisson process 350
10.10. Transformation of the Cartesian wavevector coordinates into
transverse and parallel components 351
10.11. Useful physical constants 353
Solutions to Exercises 355
Exercise 2.19.1 355
Exercise 2.19.2 356
Exercise 2.19.3 357
x Electron Transport in Nanostructures and Mesoscopic Devices
Exercise 2.19.4 360
Exercise 3.14.1 361
Exercise 3.14.2 363
Exercise 3.14.3 363
Exercise 3.14.4 365
Exercise 3.14.5 367
Exercise 5.11.1 368
Exercise 5.11.2 369
Exercise 5.11.3 370
Exercise 5.11.4 371
Exercise 5.11.5 372
Exercise 5.11.6 373
Exercise 7.7.1 374
Exercise 7.7.2 375
Exercise 7.7.3 376
Exercise 9.8.1 378
Exercise 9.8.2 379
Exercise 9.8.3 380
Index 383 |
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| index_date | 2024-07-02T22:18:27Z |
| indexdate | 2024-07-09T21:22:36Z |
| institution | BVB |
| isbn | 9781848210509 |
| language | English |
| lccn | 2008008768 |
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| publisher | ISTE [u.a.] |
| record_format | marc |
| spelling | Ouisse, Thierry Verfasser aut Electron transport in nanostructures and mesoscopic devices an introduction Thierry Ouisse 1. publ. London ISTE [u.a.] 2008 X, 387 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Electron transport Nanostructured materials Electric properties Nanostructures Electric properties Mesoscopic phenomena (Physics) http://www.loc.gov/catdir/enhancements/fy0811/2008008768-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016780985&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ouisse, Thierry Electron transport in nanostructures and mesoscopic devices an introduction Electron transport Nanostructured materials Electric properties Nanostructures Electric properties Mesoscopic phenomena (Physics) |
| title | Electron transport in nanostructures and mesoscopic devices an introduction |
| title_auth | Electron transport in nanostructures and mesoscopic devices an introduction |
| title_exact_search | Electron transport in nanostructures and mesoscopic devices an introduction |
| title_exact_search_txtP | Electron transport in nanostructures and mesoscopic devices an introduction |
| title_full | Electron transport in nanostructures and mesoscopic devices an introduction Thierry Ouisse |
| title_fullStr | Electron transport in nanostructures and mesoscopic devices an introduction Thierry Ouisse |
| title_full_unstemmed | Electron transport in nanostructures and mesoscopic devices an introduction Thierry Ouisse |
| title_short | Electron transport in nanostructures and mesoscopic devices |
| title_sort | electron transport in nanostructures and mesoscopic devices an introduction |
| title_sub | an introduction |
| topic | Electron transport Nanostructured materials Electric properties Nanostructures Electric properties Mesoscopic phenomena (Physics) |
| topic_facet | Electron transport Nanostructured materials Electric properties Nanostructures Electric properties Mesoscopic phenomena (Physics) |
| url | http://www.loc.gov/catdir/enhancements/fy0811/2008008768-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016780985&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ouissethierry electrontransportinnanostructuresandmesoscopicdevicesanintroduction |