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E-raamat: Physics Of Electrons In Solids

(Ecole Polytechnique, France)
  • Formaat: 388 pages
  • Sari: Advanced Textbooks in Physics
  • Ilmumisaeg: 02-Jun-2021
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786349743
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Physics Of Electrons In SolidsSuurem pilt
  • Formaat: 388 pages
  • Sari: Advanced Textbooks in Physics
  • Ilmumisaeg: 02-Jun-2021
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786349743
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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.
Preface xv
About the Author xvii
1 Solids as Quantum Systems
1(22)
1.1 Introduction
1(3)
1.2 Basic Principles of the Physics of Electrons in Solids
4(11)
1.2.1 Conduction electrons
5(3)
1.2.2 Quantum character of the electronic properties
8(5)
1.2.3 Relevance of the spatial configuration and of the chemical nature of the atoms
13(2)
1.3 Microscopic Origin of the Properties of Solids
15(4)
1.3.1 Thermal conduction
15(1)
1.3.2 Mechanical properties
16(1)
1.3.3 Optical properties
17(1)
1.3.4 Optical infrared properties of insulators
18(1)
1.3.5 Dielectric permittivity of insulators
18(1)
1.4 Organization of the Book
19(4)
Bibliography
20(3)
2 The Crystalline Order
23(40)
2.1 Crystal Structure and Periodicity
23(7)
2.1.1 Introduction
23(2)
2.1.2 Observations at the atomic scale
25(2)
2.1.3 Generalization: Crystal structure space-symmetry
27(3)
2.2 Bravais Lattices
30(6)
2.2.1 Definition
30(1)
2.2.2 Properties
31(5)
2.3 Unit Cells
36(6)
2.3.1 Primitive unit cells
36(1)
2.3.2 Conventional unit cells
37(2)
2.3.3 Classification of the Bravais lattices: Cubic lattices
39(2)
2.3.4 Wigner-Seitz unit cell
41(1)
2.4 Examples of Crystal Structures
42(10)
2.4.1 Simple monoatomic structures: Packings
43(6)
2.4.2 Structures derived from simple packings
49(2)
2.4.3 Simple covalent structures: Diamond and semiconductors
51(1)
2.5 Classification of Crystal Symmetries
52(5)
2.5.1 Symmetry transformations: Space-group
52(1)
2.5.2 Point-group and Bravais lattice
53(1)
2.5.3 Enumeration of point-groups
54(1)
2.5.4 Symmetry of the Bravais lattice
54(1)
2.5.5 Classification of Bravais lattices
55(1)
2.5.6 Constraints on other translations
56(1)
2.5.7 Classification of space-symmetries
56(1)
2.6 Complex Translational Orders
57(6)
Bibliography
61(2)
3 The Reciprocal Space as a Space of Quantum Numbers
63(28)
3.1 Introduction
63(1)
3.2 Bloch's Theorem
64(6)
3.2.1 Quantum operator associated to a translation
64(1)
3.2.2 Eigenvalues and eigenfunctions of translation operators
65(2)
3.2.3 Hamiltonian and lattice translations
67(1)
3.2.4 Formulation of Bloch's theorem: Band index
68(2)
3.3 Reciprocal Lattice
70(8)
3.3.1 Equivalence between quantum numbers
71(1)
3.3.2 Range of the quantum numbers
71(1)
3.3.3 Properties of the reciprocal lattice
72(1)
3.3.4 First Brillouin zone
73(1)
3.3.5 Surface of the first Brillouin zone
74(1)
3.3.6 Discretization of the quantum numbers
75(3)
3.4 Energy Bands
78(4)
3.4.1 iVth Brillouin zone: Reduced and extended zone schemes
80(2)
3.5 Appendix: Reminder of Quantum Mechanics
82(9)
3.5.1 A few ideas
82(3)
3.5.2 Formalism and determination of the stationary states
85(5)
Bibliography
90(1)
4 The Reciprocal Space as a Space of Diffraction Patterns
91(28)
4.1 Introduction
91(1)
4.2 Atomic Scattering Process
92(3)
4.3 Diffraction by a Crystal
95(9)
4.3.1 Diffraction by a crystal with a monoatomic-basis
96(2)
4.3.2 Polyatomic crystal: Structure factor
98(3)
4.3.3 Effect of the thermal vibrations of atoms
101(1)
4.3.4 Bragg equation
102(1)
4.3.5 The Ewald construction
103(1)
4.4 Diffraction and Lattice Planes
104(3)
4.4.1 Lattice planes and reciprocal vectors: Miller indices
105(1)
4.4.2 Bragg equation for lattice planes
106(1)
4.5 The Determination of Crystal Structures
107(12)
4.5.1 Specification of the Bravais lattice
107(4)
4.5.2 Determination of the atomic configuration
111(1)
4.5.3 Comparison of the use of X-rays, neutrons and electrons
112(3)
4.5.4 Diffraction by partly or fully disordered solids
115(2)
Bibliography
117(2)
5 Quantum States of an Electron in a Crystal
119(42)
5.1 Introduction
119(2)
5.2 Almost-Free Electron Approximation
121(20)
5.2.1 Uniform potential: Free electron
122(3)
5.2.2 Periodic potential: Qualitative results
125(4)
5.2.3 Periodic potential: First-order perturbation study
129(6)
5.2.4 Vicinity of the gaps: Quasi-degenerate states
135(1)
5.2.5 Representations of the energy-spectrum
136(5)
5.3 Tight Binding Approximation
141(11)
5.3.1 Qualitative origin of the energy-bands
141(4)
5.3.2 Principle of the band calculation
145(7)
5.4 Band Structure of Real Crystals
152(9)
5.4.1 Bandwidth and electron-localization
152(4)
5.4.2 Examples of the band structure of real crystals
156(2)
5.4.3 Experimental studies of the band structure of a solid
158(1)
Bibliography
159(2)
6 Equilibrium Electronic Properties of Solids
161(30)
6.1 Introduction
161(1)
6.2 Thermodynamic Equilibrium: Fermi Energy
162(6)
6.2.1 Electron states and Pauli principle
162(2)
6.2.2 Fermi factor: Fermi level
164(3)
6.2.3 Calculation of the equilibrium properties
167(1)
6.3 Sommerfeld Model for Metals
168(7)
6.3.1 Degenerate free-electrons quantum gas
168(3)
6.3.2 Properties of the degenerate free-electron gas
171(4)
6.4 Energy Bands: Conductors and Insulators
175(11)
6.4.1 Distinction between conductors and insulators
175(2)
6.4.2 Factors determining the band occupation
177(2)
6.4.3 Formation of composite bands: Degeneracy and overlap
179(3)
6.4.4 Simple examples of band occupation
182(4)
6.5 Diversity of the Equilibrium Properties in Solids
186(5)
6.5.1 Effective valences in metals
187(2)
6.5.2 Electronic specific heat: Static effective mass
189(1)
Bibliography
190(1)
7 The Dynamics of Electrons in a Crystal
191(36)
7.1 Introduction
191(1)
7.2 Collective Dynamics of a Free-Electrons Gas
192(18)
7.2.1 Classical approximation: Wavepacket and group velocity
193(1)
7.2.2 Classical approximation: Dynamical equation
194(3)
7.2.3 Dynamics induced by an electric field
197(2)
7.2.4 Irrelevance of occupied and empty states
199(2)
7.2.5 Individual dynamics induced by a magnetic field
201(2)
7.2.6 Collective dynamics of the electron gas
203(2)
7.2.7 Quantum levels of the electron gas in a magnetic field
205(5)
7.3 Collective Dynamics of Bloch-Electrons
210(17)
7.3.1 Origin of the apparent change of mass of the electron
211(1)
7.3.2 Semi-classical dynamical equation
212(3)
7.3.3 Dynamical effective mass
215(3)
7.3.4 Trajectories of Bloch electrons in a field
218(5)
7.3.5 Holes
223(4)
8 Electronic Transport Properties of Solids
227(20)
8.1 Introduction
227(1)
8.2 Physical Origin of the Finite Conductivity
228(8)
8.2.1 Drude model of collision with the fixed ions
228(2)
8.2.2 Shortcomings of Drude's model
230(1)
8.2.3 Irrelevance of collisions between electrons
231(1)
8.2.4 Interaction with collective oscillations
232(3)
8.2.5 Interaction between electrons and structural defects
235(1)
8.3 Electron Dynamics in the Presence of Collisions
236(3)
8.3.1 Boltzmann equation
237(1)
8.3.2 Relaxation time and local equilibrium
237(2)
8.4 Electronic Transport Properties
239(8)
8.4.1 Evolution in local equilibrium
240(1)
8.4.2 Electrical conductivity
241(2)
8.4.3 Electronic heat conduction
243(3)
Bibliography
246(1)
9 Intrinsic and Doped Semiconductors
247(30)
9.1 Introduction
247(1)
9.2 Properties of Intrinsic Semiconductors
248(11)
9.2.1 Location of the Fermi level
248(4)
9.2.2 Number of carriers, conductivity, and mobility
252(2)
9.2.3 Real band structures of intrinsic semiconductors
254(5)
9.3 Doped Semiconductors
259(7)
9.3.1 Donor impurity in silicon (n-doping)
259(2)
9.3.2 Acceptor impurity in silicon (p-doping)
261(1)
9.3.3 Number of carriers at equilibrium
262(4)
9.4 Principles of Two Semiconductor Devices
266(11)
9.4.1 P-n junction and semiconducting rectifier
266(6)
9.4.2 P-n-p transistor
272(2)
Bibliography
274(3)
10 Solids as Systems of Particles in Interaction
277(20)
10.1 Introduction
277(1)
10.2 Justification of the Independent Electrons Approximation
277(10)
10.2.1 Born-Oppenheimer approximation
279(2)
10.2.2 Hartree solution of the electronic equation
281(3)
10.2.3 Shortcoming of the Hartree method
284(3)
10.3 Structural Properties of Solids
287(10)
10.3.1 Ground state of the atomic configuration
287(4)
10.3.2 Collective oscillations of the atoms: Phonons
291(5)
Bibliography
296(1)
11 Ferromagnetism and Superconductivity
297(18)
11.1 Introduction
297(1)
11.2 Magnetic Properties of Solids
298(1)
11.2.1 Bohr-Van Leuwen theorem
298(1)
11.3 Ferromagnetism
299(6)
11.3.1 Relation between the signatures of the magnetic transition
300(3)
11.3.2 Microscopic origin of ferromagnetism
303(2)
11.4 Superconductivity
305(10)
11.4.1 Introduction
305(3)
11.4.2 Microscopic mechanism, qualitative description
308(1)
11.4.3 Microscopic mechanism, quantitative description
309(4)
Bibliography
313(2)
Appendix A Exercises
315(20)
A.1 Examination Text No. 1 Hexagonal Boron Nitride
315(6)
A.1.1 Direct and reciprocal lattices
315(1)
A.1.2 Electronic states in the tight binding approximation
316(3)
A.1.3 Occupation of the bands of boron nitride
319(1)
A.1.4 Comparison with graphite
320(1)
A.2 Examination Text No. 2 Metallic Binary Alloys
321(4)
A.2.1 Diffraction
321(2)
A.2.2 Electronic energy and stability of the alloys
323(2)
A.3 Examination Text No. 3 Properties of Bismuth
325(10)
A.3.1 Part I: Crystal structure, Bravais and reciprocal lattices
326(1)
A.3.2 Part II: Band structure in the free-electrons approximation
327(3)
A.3.3 Part 3: Fourier coefficients of the crystal potential
330(1)
A.3.4 Part 4: Effect of the potential on the properties of bismuth
331(4)
Appendix B Solutions of Exercises
335(26)
B.1 Examination Text No. 1 Hexagonal Boron Nitride
335(8)
B.2 Examination Text No. 2 Metallic Binary Alloys
343(7)
B.2.1 Part 1
343(2)
B.2.2 Part 2
345(5)
B.3 Examination Text No. 3 Properties of Bismuth
350(11)
Appendix C Constants Values
361(2)
C.1 Notations
361(2)
Index 363
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