"In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands)."
Theory explaining the properties of solids in terms of energy bands of electrons.
Basics of Quantum Mechanics: An understanding of quantum mechanics is essential to understanding band theory. It involves the principles of wave-particle duality, Schrödinger's equation, wave functions, and the quantization of energy levels.
Atomic Orbitals: Atomic orbitals are the areas of probability where an electron is most likely to be found around an atom. These orbitals help us in understanding the energy levels of the electrons' arrangement.
Crystal Structure: Solid-state physics involves understanding the structure of crystals. This includes concepts like lattice symmetry, primitive cells, and Miller indices.
Bravais Lattice: Bravais lattices are the 14 unique types of 3D lattice structures. Each lattice type has its own arrangement of points, which are repeated infinitely to give the solid structure desirable properties for specific purposes.
Bloch Theorem: Bloch theorem relates a wave's behavior in a crystal lattice structure to its behavior in free space. This theorem permits band theory's assumption wherein the wave packet that makes up the electron is periodic.
Energy Bands: Energy bands are continuous ranges of energies in a solid. In solids, electrons are not confined to fixed energy levels like atoms and molecules, and Energy Bands assist us in describing this.
Valence and Conduction Bands: The valence band is the highest energy band that is entirely filled with electrons; it establishes the properties of insulators and semiconductors. The empty band above it is known as the conduction band.
Band Gap: The band gap is the energy range between the valence and conduction bands. In semiconductors and insulators, there is a band gap that the electron must overcome to jump from the valence band to the conduction band.
Conductivity Types: Solids can be classified as conductors, semiconductors, or insulators based on their band structure, and the dopants added to them. Metals are conductors since they have partially filled bands, whereas dopants increase the reach of the bands in semiconductors.
Density of States: It is a measure of the number of available states at each energy level along with the energy bands.
Fermi Energy: Fermi Energy is the energy level in a solid-state material where there is a 50% probability of finding an electron at a given time.
Fermi Dirac Distribution: It is an equation that gives the probability of an electron occupying a given energy level at a specific temperature.
Carrier Concentration: In a solid, carriers refer to electrons or electron vacancies. Carrier concentration is the number of these carriers per unit volume.
Hall Effect: The phenomenon in which a magnetic field applied perpendicular to an electric current induces a voltage perpendicular to both the magnetic field and current.
Filling of Sigma and Pi Bonds: Band theory reports that the electrons in molecules are distributed amongst σ and π bonds, replacing traditional Lewis structures.
Tight-Binding Approximation: It is used when calculating the energy of a system that is a composite structure of two different systems.
Band-to-Band Transitions: It depicts the transition of the valence band to the conduction band by an electron or a hole.
Semiconductors: The impact of doping and the resulting rise of the electron levels, as well as p-n junctions, are all essential concepts in the study of semiconductors.
Theoretical Band Theory: This type of band theory is based on mathematical models and theoretical calculations to describe the electronic structure of solids.
Empirical Band Theory: This type of band theory is based on experimental data and observations, and is used to analyze the electronic structure of solids.
Tight-Binding Band Theory: This type of band theory is based on a semi-empirical method that considers interactions between neighboring atoms in a solid to describe its electronic structure.
Density Functional Theory: This type of band theory is based on a mathematical formalism that uses the density of electrons in a solid as the key variable to describe its electronic structure.
Molecular Orbital Theory: This type of band theory is based on a quantum mechanical model that describes the electron density in individual atoms and molecules, and is used to understand the electronic structure of solids.
Band Structure Theory: This type of band theory describes the electronic structure of solids in terms of energy bands, which are areas of allowed energies for electrons to occupy.
Kronig-Penney Model: This type of band theory is a simplified model of a crystalline solid that assumes the potential energy varies periodically throughout the material, leading to the formation of allowed energy bands.
Wannier Function Theory: This type of band theory is based on the concept of Wannier functions, which are localized functions that represent the electronic wave functions in solid-state materials.
Electronic Transport Theory: This type of band theory describes the behavior of electrons in solids when subjected to external electric or magnetic fields, and is used to understand the properties of electronic devices like transistors and diodes.
Green’s Function Theory: This type of band theory is based on mathematical functions known as Green’s functions, which describe the behavior of electrons in a solid when subjected to an external perturbation or excitation.
"Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules."
"Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption."
"Band theory forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.)."
"...as well as the ranges of energy that they may not have (called band gaps or forbidden bands)."
"The electronic band structure... describes the range of energy levels that electrons may have within it..."
"Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules."
"Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption."
"Band theory forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.)."
"Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity..."
"Band theory has been successfully used to explain many physical properties of solids, such as... optical absorption..."
"Band theory forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.)."
"...ranges of energy that they may not have (called band gaps or forbidden bands)."
"...ranges of energy that they may not have (called band gaps or forbidden bands)."
"Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron..."
"Band theory has been successfully used to explain many physical properties of solids..."
"Band theory forms the foundation of the understanding of all solid-state devices..."
"...ranges of energy that they may not have (called band gaps or forbidden bands)."
"Band theory forms the foundation of the understanding of all solid-state devices..."
"The electronic band structure... describes the range of energy levels that electrons may have within it..."