Solid-State Physics for Electronics

Professor Andre Moliton is the head of the group Plastic Optoelectronics at the Xlim Research Institute in the Universite de Limoges, France. This group studies the optoelectronic systems, and micro-electronics and microtechnologies through the use of ion treatment and simulations.

• Foreword xiiiIntroduction xvChapter 1. Introduction: Representations of Electron-Lattice Bonds 11.1. Introduction 11.2. Quantum mechanics: some basics 21.3. Bonds in solids: a free electron as the zero order approximation for a weak bond; and strong bonds 61.4. Complementary material: basic evidence for the appearance of bands in solids 10Chapter 2. The Free Electron and State Density Functions 172.1. Overview of the free electron 172.2. Study of the stationary regime of small scale (enabling the establishment of nodes at extremities) symmetric wells (1D model) 192.3. Study of the stationary regime for asymmetric wells (1D model) with L a favoring the establishment of a stationary regime with nodes at extremities 232.4. Solutions that favor propagation: wide potential wells where L 1 mm, i.e. several orders greater than inter-atomic distances 242.5. State density function represented in energy space for free electrons in a 1D system 272.6. From electrons in a 3D system (potential box) 322.7. Problems 40Chapter 3. The Origin of Band Structures within the Weak Band Approximation 553.1. Bloch function 553.2. Mathieu’s equation 593.3. The band structure 663.4. Alternative presentation of the origin of band systems via the perturbation method 703.5. Complementary material: the main equation 793.6. Problems 81Chapter 4. Properties of Semi-Free Electrons, Insulators, Semiconductors, Metals and Superlattices 874.1. Effective mass (m*) 874.2. The concept of holes 934.3. Expression for energy states close to the band extremum as a function of the effective mass 964.4. Distinguishing insulators, semiconductors, metals and semi-metals 974.5. Semi-free electrons in the particular case of super lattices 1074.6. Problems 116Chapter 5. Crystalline Structure, Reciprocal Lattices and Brillouin Zones 1235.1. Periodic lattices 1235.2. Locating reciprocal planes 1255.3. Conditions for maximum diffusion by a crystal (Laue conditions) 1285.4. Reciprocal lattice 1335.5. Brillouin zones 1355.6. Particular properties 1375.7. Example determinations of Brillouin zones and reduced zones 1415.8. Importance of the reciprocal lattice and electron filling of Brillouin zones by electrons in insulators, semiconductors and metals 1465.9. The Fermi surface: construction of surfaces and properties 1495.10. Conclusion. Filling Fermi surfaces and the distinctions between insulators, semiconductors and metals 1545.11. Problems 156Chapter 6. Electronic Properties of Copper and Silicon 1736.1. Introduction 1736.2. Direct and reciprocal lattices of the fcc structure 1736.3. Brillouin zone for the fcc structure 1786.4. Copper and alloy formation 1816.5. Silicon 1856.6. Problems 190Chapter 7. Strong Bonds in One Dimension 1997.1. Atomic and molecular orbitals 1997.2. Form of the wave function in strong bonds: Floquet’s theorem 2107.3. Energy of a 1D system 2157.4. 1D and distorted AB crystals 2247.5. State density function and applications: the Peierls metal-insulator transition 2287.6. Practical example of a periodic atomic chain: concrete calculations of wave functions, energy levels, state density functions and band filling 2337.7. Conclusion 2397.8. Problems 241Chapter 8. Strong Bonds in Three Dimensions: Band Structure of Diamond and Silicon 2498.1. Extending the permitted band from 1D to 3D for a lattice of atoms associated with single s-orbital nodes (basic cubic system, centered cubic, etc.) 2508.2. Structure of diamond: covalent bonds and their hybridization 2588.3. Molecular model of a 3D covalent crystal (atoms in sp3-hybridization states at lattice nodes) 2688.4. Complementary in-depth study: determination of the silicon band structure using the strong bond method 2758.5. Problems 287Chapter 9. Limits to Classical Band Theory: Amorphous Media 3019.1. Evolution of the band scheme due to structural defects (vacancies, dangling bonds and chain ends) and localized bands 3019.2. Hubbard bands and electronic repulsions. The Mott metal–insulator transition 3039.3. Effect of geometric disorder and the Anderson localization 3119.4. Conclusion 3229.5. Problems 324Chapter 10. The Principal Quasi-Particles in Material Physics 33510.1. Introduction 33510.2. Lattice vibrations: phonons 33610.3. Polarons 35210.4. Excitons 36410.5. Plasmons 36810.6. Problems 373Bibliography 385Index 387