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BK

Berlin : Springer, [2018]

xviii, 517 stran : ilustrace (některé barevné) ; 25 cm

ISBN 978-3-662-55920-8 (vázáno)

Graduate texts in physics, ISSN 1868-4513

Obsahuje bibliografie a rejstřík

001479075

Contents // Part I Electronic Structure // 1 Crystal Lattices in Real and Reciprocal Space... 3 // 1.1 Introduction... 3 // 1.2 Crystalline Lattices: Real Space... 4 // 1.2.1 Bravais Lattices... 4 // 1.2.2 Unit Cells... 5 // 1.3 Lattices in Reciprocal Space... 6 // 1.3.1 Crystal Planes and Miller Indices... 6 // 1.3.2 Reciprocal Lattice Vectors... 7 // 1.4 The Brillouin Zone... 8 // 1.4.1 Graphene and Boron Nitride... 8 // 1.4.2 Diamond and Zinc Blende Lattices... 9 // Problems... 11 // 2 Electronic Properties of Solids... 13 // 2.1 Introduction... 13 // 2.2 Hamiltonian of the System... 13 // 2.3 The Electronic Problem... 14 // 2.3.1 The Hartree Method... 14 // 2.3.2 Hartree-Fock (HF) Method... 15 // 2.3.3 Density Functional Theory... 16 // 2.4 Plane Wave and Localized Basis Sets... 19 // 2.5 Hamiltonian Matrix Elements... 21 // 2.6 Bloch Functions... 23 // 2.7 The Slater-Koster Approach... 25 // References... 26 // 3 Weak and Tight Binding Approximations for Simple // Solid State Models ... 29 // 3.1 Introduction... 29 // 3.2 One Electron Ł(K) in Solids... 29 // xi // xii Contents // 3.2.1 Weak Binding or the Nearly Free Electron // Approximation... 29 // 3.2.2 Tight Binding Approximation... 37 // 3.2.3 Comparison of Weak and Tight Binding // Approximations... 46 // 3.2.4 Tight Binding Approximation with 2 // Atoms/Unit Cell... 47 // Problems... 52 // Suggested Reading... 54 // 4 Examples of Energy Bands in Solids... 55 // 4.1 Introduction... 55 // 4.2 Metals... 57 // 4.2.1

Alkali Metals-e.g., Sodium... 57 // 4.2.2 Noble Metals... 58 // 4.2.3 Polyvalent Metals... 62 // 4.3 Semiconductors // 4.3.1 PbTe . // 4.3.2 Germanium... 66 // 4.3.3 Silicon... 69 // 4.3.4 III-V Compound Semiconductors... 70 // 4.3.5 Zero Gap Semiconductors - Gray Tin... 72 // 4.3.6 Transition Metal Dichalcogenides, Such as M0S2 // and WS2... 73 // 4.3.7 Molecular Semiconductors - Fullerenes... 73 // 4.4 Semimetals... 75 // 4.4.1 Graphene... 75 // 4.4.2 Bismuth... 76 // 4.5 Insulators... 77 // 4.5.1 Rare Gas and Ionic Crystal... 77 // 4.5.2 Boron Nitride... 79 // 4.5.3 Wide Bandgap Semiconductors... 79 // Problems... 81 // Suggested Readings... 87 // Reference... 87 // 5 Effective Mass Theory... 89 // 5.1 Introduction... 89 // 5.2 Wavepackets in Crystals and the Group Velocity // of Electrons in Solids... 89 // 5.3 The Effective Mass Theorem... 92 // 5.4 Application of the Effective Mass Theorem to Donor // Impurity Levels in a Semiconductor...;... 95 // 5.5 Quasi-classical Electron Dynamics... 98 // 3 3 // Contents // Xlll // 5.6 Quasi-classical Theory of Electrical // Conductivity - Ohm’s Law... 99 // Problems... 102 // Suggested Readings... 104 // 6 Lattice Vibrations... 105 // 6.1 Introduction... 105 // 6.2 Quantum Harmonic Oscillators... 105 // 6.3 Phonons in ID Solids... 108 // 6.3.1 A Monoatomic Chain... 108 // 6.3.2 Diatomic Linear Chain... Ill // 6.4 Phonons in 3D Crystals... 113 // 6.5 Electron-Phonon Interaction... 115 // Problems... 118 // Reference... 121 // Part

II Transport Properties // 7 Basic Transport Phenomena... 125 // 7.1 Introduction... 125 // 7.2 The Boltzmann Equation... 126 // 7.3 Electrical Conductivity... 128 // 7.4 Electrical Conductivity of Metals... 130 // 7.5 Electrical Conductivity of Semiconductors... 131 // 7.5.1 Ellipsoidal Carrier Pockets... 134 // 7.6 Electrons and Holes in Intrinsic Semiconductors... 136 // 7.7 Donor and Acceptor Doping of Semiconductors... 140 // 7.8 Characterization of Semiconductors... 144 // Problems... 148 // Suggested Readings... 153 // 8 Thermal Transport... 155 // 8.1 Introduction... 155 // 8.2 Thermal Conductivity... 155 // 8.2.1 General Considerations... 155 // 8.2.2 Thermal Conductivity for Metals... 159 // 8.2.3 Thermal Conductivity for Semiconductors... 161 // 8.2.4 Thermal Conductivity for Insulators... 163 // 8.3 Thermoelectric Phenomena... 164 // 8.3.1 Thermoelectric Phenomena in Metals ... 168 // 8.3.2 Thermopower for Intrinsic Semiconductors... 170 // 8.3.3 Effect of Thermoelectricity on the Thermal // Conductivity... 173 // 1 // xiv Contents // 8.4 Thermoelectric Measurements... 174 // 8.4.1 Seebeck Effect (Thermopower)... 174 // 8.4.2 Peltier Effect... 175 // 8.4.3 Thomson Effect... 176 // 8.4.4 The Kelvin Relations... 177 // 8.4.5 The Thermoelectric Figure of Merit... 178 // 8.5 The Phonon Drag Effect... 179 // Problems... 180 // Suggested Readings... 183 // References... 183 // 9 Electron and Phonon Scattering... 185 // 9.1 Electron Scattering... 185 // 9.2 Scattering Processes

in Semiconductors... 188 // 9.2.1 Electron-Phonon Scattering in Semiconductors... 188 // 9.2.2 Ionized Impurity Scattering... 192 // 9.2.3 Other Scattering Mechanisms... 193 // 9.2.4 Screening Effects in Semiconductors... 194 // 9.3 Electron Scattering in Metals... 197 // 9.3.1 Electron-Phonon Scattering in Metals... 197 // 9.3.2 Other Scattering Mechanisms in Metals... 201 // 9.4 Phonon Scattering... 202 // 9.4.1 Phonon-Phonon Scattering... 202 // 9.4.2 Phonon-Boundary Scattering... 204 // 9.4.3 Defect-Phonon Scattering... 205 // 9.4.4 Electron-Phonon Scattering... 205 // 9.5 Temperature Dependence of the Electrical and Thermal // Conductivity... 205 // Problems... 207 // Suggested Readings... 209 // 10 Magneto-Transport Phenomena... 211 // 10.1 Introduction... 211 // 10.2 Magneto-Transport in the Classical Regime (coct <1)... 211 // 10.2.1 Classical Magneto-Transport Equations... 212 // 10.2.2 Magnetoresistance... 213 // 10.3 The Hall Effect... 214 // 10.4 Derivation of the Magneto-Transport Equations from the // Boltzmann Equation... 216 // 10.5 Two Carrier Model... 218 // 10.6 Cyclotron Effective Mass ... 220 // 10.7 Effective Masses for Ellipsoidal Fermi Surfaces... 222 // 10.8 Dynamics of Electrons in a Magnetic Field... 222 // Problems... 226 // Suggested Readings... 230 // Contents // XV // 11 Transport in Low Dimensional Systems... 231 // 11.1 Introduction... 231 // 11.2 Observation of Quantum Effects in Reduced Dimensions... 231 // 11.3 Density of States in Low Dimensional

Systems... 233 // 11.3.1 Quantum Dots... 234 // 11.4 Ballistic Transport and the Landauer Formula... 235 // 11.4.1 Relationship Between the Mean Free Path and the // Transmission Coefficient... 237 // 11.4.2 Relationship to the Boltzmann Transport... 239 // 11.4.3 Relationship to Mobility Calculations... 239 // 11.4.4 Dependence of the Fermi Energy on Gate Voltage ... 241 // 11.4.5 Ballistic Phonon Transport... 241 // 11.5 Quantum Point Contacts (QPC) Effects... 242 // 11.6 Coulomb Blockade and Single Electron Transistors (SETs)... 243 // Problems... 244 // References... 246 // 12 Two Dimensional Electron Gas, Quantum Wells and // Semiconductor Superlattices... 247 // 12.1 Two-Dimensional Electronic Systems... 247 // 12.2 MOSFETS... 247 // 12.3 Two-Dimensional Behavior... 251 // 12.3.1 Quantum Wells and Superlattices... 253 // 12.4 Bound Electronic States... 256 // 12.5 Review of Tunneling Through a Potential Barrier... 257 // 12.6 Quantum Wells of Different Shape and the WKB // Approximation... 258 // 12.7 The Kronig-Penney Model... 261 // 12.8 3D Motion Within a 1-D Rectangular Well... 263 // 12.9 Resonant Tunneling in Quantum Wells... 265 // Problems... 271 // Suggested Readings... 274 // 13 Magneto-Oscillatory and Other Effects Associated with Landau // Levels... 275 // 13.1 Introduction to Landau Levels... 275 // 13.2 Quantized Magnetic Energy Levels in 3D... 275 // 13.2.1 Degeneracy of the Magnetic Energy Levels in kx... 277 // 13.2.2 Dispersion of the Magnetic Energy Levels

Along // the Magnetic Field... 278 // 13.2.3 Band Parameters Describing the Magnetic Energy // Levels... 281 // 13.3 Overview of Landau Level Effects... 282 // 13.4 Quantum Oscillatory Magnetic Phenomena... 285 // XVI // Contents // 13.5 Selection Rules for Landau Level Transitions... 289 // 13.6 Landau Level Quantization for Large Quantum Numbers... 290 // Problems... 291 // Suggested Readings... 294 // 14 The Quantum Hall Effect (QHE)... 295 // 14.1 Introduction to the Quantum Hall Effect... 295 // 14.2 Basic Relations for 2D Hall Resistance... 297 // 14.3 The 2D Electron Gas and the Quantum Hall Effect... 299 // 14.4 Effect of Edge Channels and the Quantum Field Effect... 304 // 14.5 Precision of the Quantized Hall Effect and Applications... 307 // 14.6 Fractional Quantum Hall Effect (FQHE)... 308 // Problems... 312 // Suggested Reading... 313 // Part III Optical Properties // 15 Review of Fundamental Relations for Optical Phenomena... 317 // 15.1 Introductory Remarks on Optical Probes... 317 // 15.2 The Complex Dielectric Function and the Complex Optical // Conductivity... 317 // 15.2.1 Propagating Waves... 319 // 15.3 Relation of the Complex Dielectric Function to Observables ... 321 // 15.4 Units for Frequency Measurements... 325 // Problems... 325 // Suggested Reading... 327 // 16 Drude Theory-Free Carrier Contributfon to the Optical // Properties... 329 // 16.1 The Free Carrier Contribution... 329 // 16.2 Low Frequency Response: ??? «C 1... 332 // 16.3 High Frequency

Response: ??? 1... 333 // 16.4 The Plasma Frequency... 333 // 16.5 Plasmon Resonant Nanoparticles... 337 // 16.6 Surface Plasmon Polaritons in Graphene... 338 // Problems... 341 // Suggested Readings... 344 // 17 Interband Transitions... 345 // 17.1 The Interband Transition Process... 345 // 17.2 Hamiltonian for a Charge in an Electromagnetic Field... 348 // 17.3 Relation Between Momentum Matrix Elements and the // Effective Mass... 350 // 17.4 The Joint Density of States... 352 // Contents // xvii // 17.5 Connecting Optical Properties and the Joint Density // of States... 353 // 17.6 Critical Points... 356 // 17.7 Critical Points in Low Dimensional Materials... 360 // Problems... 361 // Suggested Readings... 364 // References... 364 // 18 Absorption of Light in Solids... 365 // 18.1 The Absorption Coefficient... 365 // 18.2 Free Carrier Absorption in Semiconductors... 366 // 18.3 Free Carrier Absorption in Metals... 369 // 18.4 Direct Interband Transitions... 370 // 18.4.1 Temperature Dependence of Eg... 374 // 18.4.2 Dependence of the Absorption Edge on Fermi // Energy... 374 // 18.4.3 Dependence of the Absorption Edge on Applied // Electric Field... 376 // 18.4.4 Dependence of the Absorption Edge on Applied // Magnetic Field... 377 // 18.5 Conservation of Crystal Momentum in Direct Optical // Transitions... 379 // 18.6 Indirect Interband Transitions... 380 // Problems... 386 // Suggested Readings... 388 // 19 Optical Properties of Solids over a Wide Frequency Range... 391

19.1 Kramers-Kronig Relations... 391 // 19.2 Optical Properties and Band Structure... 397 // 19.3 Modulated Reflectivity Experiments... 398 // 19.4 Effipsometry and Measurement of the Optical Constants... 403 // 19.5 Kramers-Kronig Relations in 2D Materials... 406 // 19.6 Summary... 407 // Problems... 407 // Suggested Readings...•... 409 // References... 410 // 20 Impurities and Excitons... 411 // 20.1 Impurity Level Spectroscopy... 411 // 20.2 Shallow Impurity Levels... 412 // 20.3 Departures from the Hydrogenic Model... 416 // 20.4 Vacancies, Color Centers and Interstitials... 416 // 20.4.1 Schottky Defects... 418 // XVlll // Contents // 20.5 The Concept and Spectroscopy of Excitons... 420 // 20.5.1 Exciton Effects in Bulk Materials... 424 // 20.5.2 Classification of Excitons... 426 // 20.5.3 Optical Transitions in 2D Systems: Quantum Well // Structures...*... 430 // 20.5.4 Excitons in 0D and ID Systems: Fullerene ??? // and Carbon Nanotubes... 435 // 20.5.5 Excitons and Trions in Transition Metal // Dichalcogenides... 437 // 20.5.6 Excitons in Transition Metal Dichalcogenide // Heterojuctions... 438 // Problems... 439 // Suggested Readings... 441 // References... 441 // 21 Luminescence and Photoconductivity... 443 // 21.1 Classification of Luminescence Processes... 443 // 21.2 Emission and Absorption ... 445 // 21.3 Photoconductivity... 451 // 21.4 Photoluminescence in 2D Materials... 454 // Suggested Reading... 455 // References... 455 // 22 Optical Study of Lattice Vibrations

... 457 // 22.1 Lattice Vibrations in Semiconductors... 457 // 22.1.1 General Considerations... 457 // 22.2 Dielectric Constant and Polarizability... 460 // 22.3 Polariton Dispersion Relations... 461 // 22.4 Light Scattering...f... 471 // 22.5 Feynman Diagrams for Light Scattering... 475 // 22.6 Raman Spectra in Quantum Wells and Superlattices... 478 // 22.7 Raman Spectroscopy of Nanoscale Materials... 480 // Problems... 483 // Suggested Readings... 488 // References... 488 // Appendix A: Time-Independent Perturbation Theory... 489 // Appendix B: Time-Dependent Perturbation Theory... 499 // Index... 507