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).
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, and forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.).
The electrons of a single, isolated atom occupy atomic orbitals each of which has a discrete energy level. When two identical atoms join to form a molecule, their atomic orbitals overlap. Since electrons are fermions, the Pauli exclusion principle prohibits them from having the same energy. As the atoms get closer together the orbitals split (hybridize) into molecular orbitals with different energies.
Similarly, if a large number N of identical atoms come together to form a solid, such as a crystal lattice, the atoms' atomic orbitals overlap with the nearby orbitals. Each discrete energy level splits into N levels, each with a different energy. Since the number of atoms in a macroscopic piece of solid is a very large number (N~1022) the number of orbitals is very large and thus they are very closely spaced in energy (of the order of e-22eV). The energy of the adjacent levels is so close together that they can be considered as a continuum, an energy band.
This formation of bands is mostly a feature of the outermost electrons (valence electrons) in the atom, which are the ones involved in chemical bonding and electrical conductivity. The inner electron orbitals do not overlap to a significant degree, so their bands are very narrow.
Band gaps are essentially leftover ranges of energy not covered by any band, a result of the finite widths of the energy bands.
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
In solid state physics, a particle's effective mass (often denoted ) is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles in a periodic potential, over long distances larger than the lattice spacing, can be very different from their motion in a vacuum.
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions. The theorem is named after the physicist Felix Bloch, who discovered the theorem in 1929. Mathematically, they are written where is position, is the wave function, is a periodic function with the same periodicity as the crystal, the wave vector is the crystal momentum vector, is Euler's number, and is the imaginary unit.
In quantum mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the periodic structure of the crystal creating an electromagnetic field so electrons are subject to a regular potential inside the lattice. It is a generalization of the free electron model, which assumes zero potential inside the lattice. When talking about solid materials, the discussion is mainly around crystals – periodic lattices.
This course aims to give a solid introduction to semiconductors, from Silicon to compound semiconductors, making the connection between the physics and their application in real life. We will explore
The course treats the main surface analysis methods for the characterization of surfaces, interfaces and thin films. It discusses how these methods can be applied to gain specific knowledge about stru
Interactive course addressing bulk and thin-film magnetic materials that provide application-specific functionalities in different modern technologies such as e.g. wind energy harvesting, electric art
Explores electronic band structure, material properties, and density of states in periodic potentials, including energy levels and wavefunctions.
Explores photonic band structure, band gaps, and optomechanical coupling in photonic crystal cavities.
Explores the optical properties of TMDCs, band gap tuning, and emerging photoluminescence in Monolayer MoS₂, as well as the integration of photodetectors in IT systems.
We present first-principles calculations of the dynamic susceptibility in strained and doped ferromagnetic MnBi using time-dependent density functional theory. In spite of being a metal, MnBi exhibits
Electronic-structure simulations have been impacting the study of materials properties thanks to the simplicity of density-functional theory, a method that gives access to the ground state of the syst
EPFL2022
, ,
Non-covalent bonding patterns are commonly harvested as a design principle in the field of catalysis, supramolecular chemistry, and functional materials to name a few. Yet, their computational descrip