Quantum wells, wires and dots: theoretical and computational physics of semiconductor nanostructures
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| Format: | Electronic eBook |
|---|---|
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley-Interscience
2005
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | FRO01 UBR01 UBT01 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 0470010827 9780470010822 |
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| 245 | 1 | 0 | |a Quantum wells, wires and dots |b theoretical and computational physics of semiconductor nanostructures |c Paul Harrison |
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| adam_text | CONTENTS
Preface xv
Acknowledgements xix
About the author xxi
About the book xxiii
Introduction xxv
1 Semiconductors and heterostructures 1
1.1 The mechanics of waves 1
1.2 Crystal structure 4
1.3 The effective mass approximation 6
1.4 Band theory 7
1.5 Heterojunctions 8
1.6 Heterostructures 9
1.7 The envelope function approximation 11
1.8 The reciprocal lattice 12
vii
Vlii CONTENTS
2 Solutions to Schrodinger s equation 17
2.1 The infinite well 17
2.2 In plane dispersion 21
2.3 Density of states 23
2.4 Subband populations 26
2.5 Finite well with constant mass 31
2.6 Effective mass mismatch at heterojunctions 36
2.7 The infinite barrier height and mass limits 38
2.8 Hermiticity and the kinetic energy operator 40
2.9 Alternative kinetic energy operators 42
2.10 Extension to multiple well systems 44
2.11 The asymmetric single quantum well 47
2.12 Addition of an electric field 48
2.13 The infinite superlattice 51
2.14 The single barrier 58
2.15 The double barrier 60
2.16 Extension to include electric field 68
2.17 Magnetic fields and Landau quantisation 68
2.18 In summary 71
3 Numerical solutions 73
3.1 Shooting method 73
3.2 Generalised initial conditions 76
3.3 Practical implementation of the shooting method 79
3.4 Heterojunction boundary conditions 82
3.5 The parabolic potential well 83
3.6 The Poschl Teller potential hole 87
3.7 Convergence tests 88
3.8 Extension to variable effective mass 89
3.9 The double quantum well 93
3.10 Multiple quantum wells and finite superlattices 95
3.11 Addition of electric field 97
3.12 Quantum confined Stark effect 97
3.13 Field induced anti crossings 98
3.14 Symmetry and selection rules 99
3.15 The Heisenberg uncertainty principle 101
3.16 Extension to include band non parabolicity 103
CONTENTS iX
3.17 Poisson s equation 107
3.18 Self consistent Schrodinger Poisson solution 112
3.19 Computational implementation 114
3.20 Modulation doping 115
3.21 The high electron mobility transistor 116
3.22 Band filling 117
4 Diffusion 119
4.1 Introduction 119
4.2 Theory 121
4.3 Boundary conditions 124
4.4 Convergence tests 124
4.5 Constant diffusion coefficients 126
4.6 Concentration dependent diffusion coefficient 128
4.7 Depth dependent diffusion coefficient 129
4.8 Time dependent diffusion coefficient 132
4.9 £ doped quantum wells 133
4.10 Extension to higher dimensions 136
5 Impurities 137
5.1 Donors and acceptors in bulk material 137
5.2 Binding energy in a heterostructure 140
5.3 Two dimensional trial wave function 146
5.4 Three dimensional trial wave function 153
5.5 Variable symmetry trial wave function 160
5.6 Inclusion of a central cell correction 167
5.7 Special considerations for acceptors 168
5.8 Effective mass and dielectric mismatch 169
5.9 Band non parabolicity 170
5.10 Excited states 170
5.11 Application to spin flip Raman spectroscopy 171
5.11.1 Diluted magnetic semiconductors 171
5.11.2 Spin flip Raman spectroscopy 173
5.12 Alternative approach to excited impurity states 176
5.13 The ground state 177
5.14 Position dependence 179
5.15 Excited States 180
X CONTENTS
5.16 Impurity occupancy statistics 184
6 Excitons 189
6.1 Excitons in bulk 189
6.2 Excitons in heterostructures 191
6.3 Exciton binding energies 192
6.4 Is exciton 197
6.5 The two dimensional and three dimensional limits 202
6.6 Excitons in single quantum wells 207
6.7 Excitons in multiple quantum wells 210
6.8 Stark Ladders 212
6.9 Self consistent effects 214
6.10 Spontaneous symmetry breaking 215
6.11 2s exciton 217
7 Strained quantum wells, V. D. Jovanovic 219
7.1 Stress and strain in bulk crystals 219
7.2 Strain in quantum wells 224
7.3 Strain balancing 227
7.4 Effect on the band profile of quantum wells 230
7.5 The piezoelectric effect 233
7.6 Induced piezoelectric fields in quantum wells 236
7.7 Effect of piezoelectric fields on quantum wells 239
8 Quantum wires and dots 243
8.1 Further confinement 243
8.2 Schrodinger s equation in quantum wires 246
8.3 Infinitely deep rectangular wires 248
8.4 Simple approximation to a finite rectangular wire 251
8.5 Circular cross section wire 255
8.6 Quantum boxes 259
8.7 Spherical quantum dots 260
8.8 Non zero angular momentum states 263
8.9 Approaches to pyramidal dots 264
8.10 Matrix approaches 265
8.11 Finite difference expansions 266
8.12 Density of states 267
CONTENTS Xi
9 Carrier scattering 271
9.1 Fermi s Golden Rule 271
9.2 Phonons 272
9.3 Longitudinal optic phonon scattering of bulk carriers 275
9.4 LO phonon scattering of two dimensional carriers 283
9.5 Application to conduction subbands 296
9.6 Averaging over carrier distributions 298
9.7 Ratio of emission to absorption 301
9.8 Screening of the LO phonon interaction 302
9.9 Acoustic deformation potential scattering 303
9.10 Application to conduction subbands 309
9.11 Optical deformation potential scattering 310
9.12 Confined and interface phonon modes 313
9.13 Carrier carrier scattering 314
9.14 Addition of screening 322
9.15 Averaging over an initial state population 324
9.16 Intrasubband versus intersubband 326
9.17 Thermalised distributions 328
9.18 Auger type intersubband processes 329
9.19 Asymmetric intrasubband processes 330
9.20 Empirical relationships 331
9.21 Carrier photon scattering 332
9.22 Quantum cascade lasers 338
9.23 Carrier scattering in quantum wires and dots 342
10 Multiband envelope function (k.p) method, Z. Ikonic 345
10.1 Symmetry, basis states and band structure 345
10.2 Valence band structure and the 6 x 6 Hamiltonian 347
10.3 4x4 valence band Hamiltonian 350
10.4 Complex band structure 352
10.5 Block diagonalisation of the Hamiltonian 353
10.6 The valence band in strained cubic semiconductors 355
10.7 Hole subbands in heterostructures 357
10.8 Valence band offset 359
10.9 The layer (transfer matrix) method 361
10.10 Quantum well subbands 365
10.11 The influence of strain 367
XM CONTENTS
10.12 Strained quantum well subbands 368
10.13 Direct numerical methods 368
11 Empirical pseudopotential theory 371
11.1 Principles and Approximations 371
11.2 Elemental Band Structure Calculation 373
11.3 Spin orbit coupling 381
11.4 Compound Semiconductors 383
11.5 Charge densities 386
11.6 Calculating the effective mass 390
11.7 Alloys 390
11.8 Atomic form factors 392
11.9 Generalisation to a large basis 393
11.10 Spin orbit coupling within the large basis approach 396
11.11 Computational implementation 398
11.12 Deducing the parameters and application 399
11.13 Isoelectronic impurities in bulk 402
11.14 The electronic structure around point defects 406
12 Microscopic electronic properties of heterostructures 411
12.1 Trie superlattice unit cell 411
12.2 Application of large basis method to superlattices 415
12.3 Comparison with envelope function approximation 4I9
12.4 In plane dispersion 421
12.5 Interface coordination 422
12.6 Strain layered superlattices 422
12.7 The superlattice as a perturbation 425
12.8 Application to GaAs/AlAs superlattices 430
12.9 Inclusion of remote bands 432
12.10 The valence band 433
12.11 Computational effort 433
12.12 Superlattice dispersion and the interminiband laser 435
12.13 Addition of electric field 436
13 Application to quantum wires and dots 443
13.1 Recent progress 443
13.2 The quantum wire unit cell 444
CONTENTS XiM
13.3 Confined states 447
13.4 V grooved quantum wires 447
13.5 Along axis dispersion 448
13.6 Tiny quantum dots 449
13.7 Pyramidal quantum dots 451
13.8 Transport through dot arrays 454
13.9 Anti wires and anti dots 456
Concluding Remarks 457
Appendix A: Materials parameters 459
References 461
Topic Index 477
|
| adam_txt |
CONTENTS
Preface xv
Acknowledgements xix
About the author xxi
About the book xxiii
Introduction xxv
1 Semiconductors and heterostructures 1
1.1 The mechanics of waves 1
1.2 Crystal structure 4
1.3 The effective mass approximation 6
1.4 Band theory 7
1.5 Heterojunctions 8
1.6 Heterostructures 9
1.7 The envelope function approximation 11
1.8 The reciprocal lattice 12
vii
Vlii CONTENTS
2 Solutions to Schrodinger's equation 17
2.1 The infinite well 17
2.2 In plane dispersion 21
2.3 Density of states 23
2.4 Subband populations 26
2.5 Finite well with constant mass 31
2.6 Effective mass mismatch at heterojunctions 36
2.7 The infinite barrier height and mass limits 38
2.8 Hermiticity and the kinetic energy operator 40
2.9 Alternative kinetic energy operators 42
2.10 Extension to multiple well systems 44
2.11 The asymmetric single quantum well 47
2.12 Addition of an electric field 48
2.13 The infinite superlattice 51
2.14 The single barrier 58
2.15 The double barrier 60
2.16 Extension to include electric field 68
2.17 Magnetic fields and Landau quantisation 68
2.18 In summary 71
3 Numerical solutions 73
3.1 Shooting method 73
3.2 Generalised initial conditions 76
3.3 Practical implementation of the shooting method 79
3.4 Heterojunction boundary conditions 82
3.5 The parabolic potential well 83
3.6 The Poschl Teller potential hole 87
3.7 Convergence tests 88
3.8 Extension to variable effective mass 89
3.9 The double quantum well 93
3.10 Multiple quantum wells and finite superlattices 95
3.11 Addition of electric field 97
3.12 Quantum confined Stark effect 97
3.13 Field induced anti crossings 98
3.14 Symmetry and selection rules 99
3.15 The Heisenberg uncertainty principle 101
3.16 Extension to include band non parabolicity 103
CONTENTS iX
3.17 Poisson's equation 107
3.18 Self consistent Schrodinger Poisson solution 112
3.19 Computational implementation 114
3.20 Modulation doping 115
3.21 The high electron mobility transistor 116
3.22 Band filling 117
4 Diffusion 119
4.1 Introduction 119
4.2 Theory 121
4.3 Boundary conditions 124
4.4 Convergence tests 124
4.5 Constant diffusion coefficients 126
4.6 Concentration dependent diffusion coefficient 128
4.7 Depth dependent diffusion coefficient 129
4.8 Time dependent diffusion coefficient 132
4.9 £ doped quantum wells 133
4.10 Extension to higher dimensions 136
5 Impurities 137
5.1 Donors and acceptors in bulk material 137
5.2 Binding energy in a heterostructure 140
5.3 Two dimensional trial wave function 146
5.4 Three dimensional trial wave function 153
5.5 Variable symmetry trial wave function 160
5.6 Inclusion of a central cell correction 167
5.7 Special considerations for acceptors 168
5.8 Effective mass and dielectric mismatch 169
5.9 Band non parabolicity 170
5.10 Excited states 170
5.11 Application to spin flip Raman spectroscopy 171
5.11.1 Diluted magnetic semiconductors 171
5.11.2 Spin flip Raman spectroscopy 173
5.12 Alternative approach to excited impurity states 176
5.13 The ground state 177
5.14 Position dependence 179
5.15 Excited States 180
X CONTENTS
5.16 Impurity occupancy statistics 184
6 Excitons 189
6.1 Excitons in bulk 189
6.2 Excitons in heterostructures 191
6.3 Exciton binding energies 192
6.4 Is exciton 197
6.5 The two dimensional and three dimensional limits 202
6.6 Excitons in single quantum wells 207
6.7 Excitons in multiple quantum wells 210
6.8 Stark Ladders 212
6.9 Self consistent effects 214
6.10 Spontaneous symmetry breaking 215
6.11 2s exciton 217
7 Strained quantum wells, V. D. Jovanovic 219
7.1 Stress and strain in bulk crystals 219
7.2 Strain in quantum wells 224
7.3 Strain balancing 227
7.4 Effect on the band profile of quantum wells 230
7.5 The piezoelectric effect 233
7.6 Induced piezoelectric fields in quantum wells 236
7.7 Effect of piezoelectric fields on quantum wells 239
8 Quantum wires and dots 243
8.1 Further confinement 243
8.2 Schrodinger's equation in quantum wires 246
8.3 Infinitely deep rectangular wires 248
8.4 Simple approximation to a finite rectangular wire 251
8.5 Circular cross section wire 255
8.6 Quantum boxes 259
8.7 Spherical quantum dots 260
8.8 Non zero angular momentum states 263
8.9 Approaches to pyramidal dots 264
8.10 Matrix approaches 265
8.11 Finite difference expansions 266
8.12 Density of states 267
CONTENTS Xi
9 Carrier scattering 271
9.1 Fermi's Golden Rule 271
9.2 Phonons 272
9.3 Longitudinal optic phonon scattering of bulk carriers 275
9.4 LO phonon scattering of two dimensional carriers 283
9.5 Application to conduction subbands 296
9.6 Averaging over carrier distributions 298
9.7 Ratio of emission to absorption 301
9.8 Screening of the LO phonon interaction 302
9.9 Acoustic deformation potential scattering 303
9.10 Application to conduction subbands 309
9.11 Optical deformation potential scattering 310
9.12 Confined and interface phonon modes 313
9.13 Carrier carrier scattering 314
9.14 Addition of screening 322
9.15 Averaging over an initial state population 324
9.16 Intrasubband versus intersubband 326
9.17 Thermalised distributions 328
9.18 Auger type intersubband processes 329
9.19 Asymmetric intrasubband processes 330
9.20 Empirical relationships 331
9.21 Carrier photon scattering 332
9.22 Quantum cascade lasers 338
9.23 Carrier scattering in quantum wires and dots 342
10 Multiband envelope function (k.p) method, Z. Ikonic 345
10.1 Symmetry, basis states and band structure 345
10.2 Valence band structure and the 6 x 6 Hamiltonian 347
10.3 4x4 valence band Hamiltonian 350
10.4 Complex band structure 352
10.5 Block diagonalisation of the Hamiltonian 353
10.6 The valence band in strained cubic semiconductors 355
10.7 Hole subbands in heterostructures 357
10.8 Valence band offset 359
10.9 The layer (transfer matrix) method 361
10.10 Quantum well subbands 365
10.11 The influence of strain 367
XM CONTENTS
10.12 Strained quantum well subbands 368
10.13 Direct numerical methods 368
11 Empirical pseudopotential theory 371
11.1 Principles and Approximations 371
11.2 Elemental Band Structure Calculation 373
11.3 Spin orbit coupling 381
11.4 Compound Semiconductors 383
11.5 Charge densities 386
11.6 Calculating the effective mass 390
11.7 Alloys 390
11.8 Atomic form factors 392
11.9 Generalisation to a large basis 393
11.10 Spin orbit coupling within the large basis approach 396
11.11 Computational implementation 398
11.12 Deducing the parameters and application 399
11.13 Isoelectronic impurities in bulk 402
11.14 The electronic structure around point defects 406
12 Microscopic electronic properties of heterostructures 411
12.1 Trie superlattice unit cell 411
12.2 Application of large basis method to superlattices 415
12.3 Comparison with envelope function approximation 4I9
12.4 In plane dispersion 421
12.5 Interface coordination 422
12.6 Strain layered superlattices 422
12.7 The superlattice as a perturbation 425
12.8 Application to GaAs/AlAs superlattices 430
12.9 Inclusion of remote bands 432
12.10 The valence band 433
12.11 Computational effort 433
12.12 Superlattice dispersion and the interminiband laser 435
12.13 Addition of electric field 436
13 Application to quantum wires and dots 443
13.1 Recent progress 443
13.2 The quantum wire unit cell 444
CONTENTS XiM
13.3 Confined states 447
13.4 V grooved quantum wires 447
13.5 Along axis dispersion 448
13.6 Tiny quantum dots 449
13.7 Pyramidal quantum dots 451
13.8 Transport through dot arrays 454
13.9 Anti wires and anti dots 456
Concluding Remarks 457
Appendix A: Materials parameters 459
References 461
Topic Index 477 |
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| any_adam_object_boolean | 1 |
| building | Verbundindex |
| bvnumber | BV021649218 |
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| collection | ZDB-35-WIC ebook |
| ctrlnum | (OCoLC)255177428 (DE-599)BVBBV021649218 |
| dewey-full | 537.6226 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 537 - Electricity and electronics |
| dewey-raw | 537.6226 |
| dewey-search | 537.6226 |
| dewey-sort | 3537.6226 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 2. ed. |
| format | Electronic eBook |
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| id | DE-604.BV021649218 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:02:31Z |
| indexdate | 2024-07-09T20:40:46Z |
| institution | BVB |
| isbn | 0470010827 9780470010822 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014863890 |
| oclc_num | 255177428 |
| open_access_boolean | |
| owner | DE-83 DE-355 DE-BY-UBR DE-703 DE-861 |
| owner_facet | DE-83 DE-355 DE-BY-UBR DE-703 DE-861 |
| physical | 1 Online-Ressource |
| psigel | ZDB-35-WIC ebook FHR_PDA_WIC UBG_PDA_WIC UBT_Wiley_EK_2006 ZDB-35-WIC FRO_PDA_WIC ZDB-35-WIC UBT_Wiley_EK_2006 |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Wiley-Interscience |
| record_format | marc |
| spelling | Quantum wells, wires and dots theoretical and computational physics of semiconductor nanostructures Paul Harrison 2. ed. Chichester [u.a.] Wiley-Interscience 2005 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Quantendraht (DE-588)4263397-7 gnd rswk-swf Quantenpunkt (DE-588)4263396-5 gnd rswk-swf Quantenwell (DE-588)4124010-8 gnd rswk-swf Quantenwell (DE-588)4124010-8 s DE-604 Quantenpunkt (DE-588)4263396-5 s Quantendraht (DE-588)4263397-7 s Harrison, Paul Sonstige oth Erscheint auch als Druckausgabe 0-470-01079-7 Erscheint auch als Druckausgabe 0-470-01080-0 Erscheint auch als Druckausgabe 978-0-470-01079-2 Erscheint auch als Druckausgabe 978-0-470-01080-8 https://onlinelibrary.wiley.com/doi/book/10.1002/0470010827 Verlag Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014863890&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Quantum wells, wires and dots theoretical and computational physics of semiconductor nanostructures Quantendraht (DE-588)4263397-7 gnd Quantenpunkt (DE-588)4263396-5 gnd Quantenwell (DE-588)4124010-8 gnd |
| subject_GND | (DE-588)4263397-7 (DE-588)4263396-5 (DE-588)4124010-8 |
| title | Quantum wells, wires and dots theoretical and computational physics of semiconductor nanostructures |
| title_auth | Quantum wells, wires and dots theoretical and computational physics of semiconductor nanostructures |
| title_exact_search | Quantum wells, wires and dots theoretical and computational physics of semiconductor nanostructures |
| title_exact_search_txtP | Quantum wells, wires and dots theoretical and computational physics of semiconductor nanostructures |
| title_full | Quantum wells, wires and dots theoretical and computational physics of semiconductor nanostructures Paul Harrison |
| title_fullStr | Quantum wells, wires and dots theoretical and computational physics of semiconductor nanostructures Paul Harrison |
| title_full_unstemmed | Quantum wells, wires and dots theoretical and computational physics of semiconductor nanostructures Paul Harrison |
| title_short | Quantum wells, wires and dots |
| title_sort | quantum wells wires and dots theoretical and computational physics of semiconductor nanostructures |
| title_sub | theoretical and computational physics of semiconductor nanostructures |
| topic | Quantendraht (DE-588)4263397-7 gnd Quantenpunkt (DE-588)4263396-5 gnd Quantenwell (DE-588)4124010-8 gnd |
| topic_facet | Quantendraht Quantenpunkt Quantenwell |
| url | https://onlinelibrary.wiley.com/doi/book/10.1002/0470010827 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014863890&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT harrisonpaul quantumwellswiresanddotstheoreticalandcomputationalphysicsofsemiconductornanostructures |