Physics of Electrons in Solids
- Length: 388 pages
- Edition: 1
- Language: English
- Publisher: World Scientific Publishing Europe Ltd
- Publication Date: 2021-06-14
- ISBN-10: 1786349728
- ISBN-13: 9781786349729
- Sales Rank: #0 (See Top 100 Books)
Primarily aiming to give undergraduate students an introduction to solid state physics, Physics of Electrons in Solids explains the properties of solids through the study of non-interacting electrons in solids. While each chapter contains a qualitative introduction to the main ideas behind solid state physics, it also provides detailed calculations of utmost importance to graduate students.The introductory chapters contain crystallographic and quantum prerequisites. The central chapters are devoted to the quantum states of an independent electron in a crystal and to the equilibrium properties of conductors, insulators, and semiconductors. The final chapters contain insights into the assumptions made throughout, briefly describing the origin of ferromagnetism and superconductivity. The book ends with exercises and solutions based on a physics course taught by the author at École Polytechnique.
Contents Preface About the Author 1 Solids as Quantum Systems 1.1 Introduction 1.2 Basic Principles of the Physics of Electrons in Solids 1.2.1 Conduction electrons 1.2.2 Quantum character of the electronic properties 1.2.3 Relevance of the spatial configuration and of the chemical nature of the atoms 1.3 Microscopic Origin of the Properties of Solids 1.3.1 Thermal conduction 1.3.2 Mechanical properties 1.3.3 Optical properties 1.3.4 Optical infrared properties of insulators 1.3.5 Dielectric permittivity of insulators 1.4 Organization of the Book Bibliography 2 The Crystalline Order 2.1 Crystal Structure and Periodicity 2.1.1 Introduction 2.1.2 Observations at the atomic scale 2.1.3 Generalization: Crystal structure space-symmetry 2.2 Bravais Lattices 2.2.1 Definition 2.2.2 Properties 2.3 Unit Cells 2.3.1 Primitive unit cells 2.3.2 Conventional unit cells 2.3.3 Classification of the Bravais lattices: Cubic lattices 2.3.4 Wigner–Seitz unit cell 2.4 Examples of Crystal Structures 2.4.1 Simple monoatomic structures: Packings 2.4.2 Structures derived from simple packings 2.4.3 Simple covalent structures: Diamond and semiconductors 2.5 Classification of Crystal Symmetries 2.5.1 Symmetry transformations: Space-group 2.5.2 Point-group and Bravais lattice 2.5.3 Enumeration of point-groups 2.5.4 Symmetry of the Bravais lattice 2.5.5 Classification of Bravais lattices 2.5.6 Constraints on other translations 2.5.7 Classification of space-symmetries 2.6 Complex Translational Orders Bibliography 3 The Reciprocal Space as a Space of Quantum Numbers 3.1 Introduction 3.2 Bloch’s Theorem 3.2.1 Quantum operator associated to a translation 3.2.2 Eigenvalues and eigenfunctions of translation operators 3.2.3 Hamiltonian and lattice translations 3.2.4 Formulation of Bloch’s theorem: Band index 3.3 Reciprocal Lattice 3.3.1 Equivalence between quantum numbers 3.3.2 Range of the quantum numbers 3.3.3 Properties of the reciprocal lattice 3.3.4 First Brillouin zone 3.3.5 Surface of the first Brillouin zone 3.3.6 Discretization of the quantum numbers 3.4 Energy Bands 3.4.1 Nth Brillouin zone: Reduced and extended zone schemes 3.5 Appendix: Reminder of Quantum Mechanics 3.5.1 A few ideas 3.5.2 Formalism and determination of the stationary states Bibliography 4 The Reciprocal Space as a Space of Diffraction Patterns 4.1 Introduction 4.2 Atomic Scattering Process 4.3 Diffraction by a Crystal 4.3.1 Diffraction by a crystal with a monoatomic-basis 4.3.2 Polyatomic crystal: Structure factor 4.3.3 Effect of the thermal vibrations of atoms 4.3.4 Bragg equation 4.3.5 The Ewald construction 4.4 Diffraction and Lattice Planes 4.4.1 Lattice planes and reciprocal vectors: Miller indices 4.4.2 Bragg equation for lattice planes 4.5 The Determination of Crystal Structures 4.5.1 Specification of the Bravais lattice 4.5.2 Determination of the atomic configuration 4.5.3 Comparison of the use of X-rays, neutrons and electrons 4.5.4 Diffraction by partly or fully disordered solids Bibliography 5 Quantum States of an Electron in a Crystal 5.1 Introduction 5.2 Almost-Free Electron Approximation 5.2.1 Uniform potential: Free electron 5.2.2 Periodic potential: Qualitative results 5.2.3 Periodic potential: First-order perturbation study 5.2.4 Vicinity of the gaps: Quasi-degenerate states 5.2.5 Representations of the energy-spectrum 5.3 Tight Binding Approximation 5.3.1 Qualitative origin of the energy-bands 5.3.2 Principle of the band calculation 5.4 Band Structure of Real Crystals 5.4.1 Bandwidth and electron-localization 5.4.2 Examples of the band structure of real crystals 5.4.3 Experimental studies of the band structure of a solid Bibliography 6 Equilibrium Electronic Properties of Solids 6.1 Introduction 6.2 Thermodynamic Equilibrium: Fermi Energy 6.2.1 Electron states and Pauli principle 6.2.2 Fermi factor: Fermi level 6.2.3 Calculation of the equilibrium properties 6.3 Sommerfeld Model for Metals 6.3.1 Degenerate free-electrons quantum gas 6.3.2 Properties of the degenerate free-electron gas 6.4 Energy Bands: Conductors and Insulators 6.4.1 Distinction between conductors and insulators 6.4.2 Factors determining the band occupation 6.4.3 Formation of composite bands: Degeneracy and overlap 6.4.4 Simple examples of band occupation 6.5 Diversity of the Equilibrium Properties in Solids 6.5.1 Effective valences in metals 6.5.2 Electronic specific heat: Static effective mass Bibliography 7 The Dynamics of Electrons in a Crystal 7.1 Introduction 7.2 Collective Dynamics of a Free-Electrons Gas 7.2.1 Classical approximation: Wavepacket and group velocity 7.2.2 Classical approximation: Dynamical equation 7.2.3 Dynamics induced by an electric field 7.2.4 Irrelevance of occupied and empty states 7.2.5 Individual dynamics induced by a magnetic field 7.2.6 Collective dynamics of the electron gas 7.2.7 Quantum levels of the electron gas in a magnetic field 7.3 Collective Dynamics of Bloch-Electrons 7.3.1 Origin of the apparent change of mass of the electron 7.3.2 Semi-classical dynamical equation 7.3.3 Dynamical effective mass 7.3.4 Trajectories of Bloch electrons in a field 7.3.5 Holes 8 Electronic Transport Properties of Solids 8.1 Introduction 8.2 Physical Origin of the Finite Conductivity 8.2.1 Drude model of collision with the fixed ions 8.2.2 Shortcomings of Drude’s model 8.2.3 Irrelevance of collisions between electrons 8.2.4 Interaction with collective oscillations 8.2.5 Interaction between electrons and structural defects 8.3 Electron Dynamics in the Presence of Collisions 8.3.1 Boltzmann equation 8.3.2 Relaxation time and local equilibrium 8.4 Electronic Transport Properties 8.4.1 Evolution in local equilibrium 8.4.2 Electrical conductivity 8.4.3 Electronic heat conduction Bibliography 9 Intrinsic and Doped Semiconductors 9.1 Introduction 9.2 Properties of Intrinsic Semiconductors 9.2.1 Location of the Fermi level 9.2.2 Number of carriers, conductivity, and mobility 9.2.3 Real band structures of intrinsic semiconductors 9.3 Doped Semiconductors 9.3.1 Donor impurity in silicon (n-doping) 9.3.2 Acceptor impurity in silicon (p-doping) 9.3.3 Number of carriers at equilibrium 9.4 Principles of Two Semiconductor Devices 9.4.1 P–n junction and semiconducting rectifier 9.4.2 P–n–p transistor Bibliography 10 Solids as Systems of Particles in Interaction 10.1 Introduction 10.2 Justification of the Independent Electrons Approximation 10.2.1 Born–Oppenheimer approximation 10.2.2 Hartree solution of the electronic equation 10.2.3 Shortcoming of the Hartree method 10.3 Structural Properties of Solids 10.3.1 Ground state of the atomic configuration 10.3.2 Collective oscillations of the atoms: Phonons Bibliography 11 Ferromagnetism and Superconductivity 11.1 Introduction 11.2 Magnetic Properties of Solids 11.2.1 Bohr–Van Leuwen theorem 11.3 Ferromagnetism 11.3.1 Relation between the signatures of the magnetic transition 11.3.2 Microscopic origin of ferromagnetism 11.4 Superconductivity 11.4.1 Introduction 11.4.2 Microscopic mechanism, qualitative description 11.4.3 Microscopic mechanism, quantitative description Bibliography Appendix A: Exercises A.1 Examination Text No. 1 Hexagonal Boron Nitride A.1.1 Direct and reciprocal lattices A.1.2 Electronic states in the tight binding approximation A.1.3 Occupation of the bands of boron nitride A.1.4 Comparison with graphite A.2 Examination Text No. 2 Metallic Binary Alloys A.2.1 Diffraction A.2.2 Electronic energy and stability of the alloys A.3 Examination Text No. 3 Properties of Bismuth A.3.1 Part I: Crystal structure, Bravais and reciprocal lattices A.3.2 Part II: Band structure in the free-electrons approximation A.3.3 Part 3: Fourier coefficients of the crystal potential A.3.4 Part 4: Effect of the potential on the properties of bismuth Appendix B: Solutions of Exercises B.1 Examination Text No. 1 Hexagonal Boron Nitride B.2 Examination Text No. 2 Metallic Binary Alloys B.2.1 Part 1 B.2.2 Part 2 B.3 Examination Text No. 3 Properties of Bismuth Appendix C: Constants Values C.1 Notations Index
Donate to keep this site alive
1. Disable the AdBlock plugin. Otherwise, you may not get any links.
2. Solve the CAPTCHA.
3. Click download link.
4. Lead to download server to download.