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In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no exist. In graphs of the electronic band structure of solids, the band gap refers to the energy difference (often expressed in ) between the top of the valence band and the bottom of the conduction band in insulators and . It is the energy required to promote an electron from the valence band to the conduction band. The resulting conduction-band electron (and the electron hole in the valence band) are free to move within the crystal lattice and serve as charge carriers to conduct electric current. It is closely related to the HOMO/LUMO gap in chemistry. If the valence band is completely full and the conduction band is completely empty, then electrons cannot move within the solid because there are no available states. If the electrons are not free to move within the crystal lattice, then there is no generated current due to no net charge carrier mobility. However, if some electrons transfer from the valence band (mostly full) to the conduction band (mostly empty), then current can flow (see carrier generation and recombination). Therefore, the band gap is a major factor determining the electrical conductivity of a solid. Substances having large band gaps (also called "wide" band gaps) are generally insulators, those with small band gaps (also called "narrow" band gaps) are semiconductors, and conductors either have very small band gaps or none, because the valence and conduction bands overlap to form a continuous band.
It is possible to produce laser induced insulator-metal transitions which have already been experimentally observed in some condensed matter systems, like thin films of , doped manganites, or in vanadium sesquioxide . These are special cases of the more general metal-to-nonmetal transitions phenomena which were intensively studied in the last decades. A one-dimensional analytic model of laser induced distortion of band structure was presented for a spatially periodic (cosine) potential. This problem is periodic both in space and time and can be solved analytically using the Kramers-Henneberger co-moving frame. The solutions can be given with the help of the Mathieu function
In semiconductors and insulators, are confined to a number of bands of energy, and forbidden from other regions because there are no allowable electronic states for them to occupy. The term "band gap" refers to the energy difference between the top of the valence band and the bottom of the conduction band. Electrons are able to jump from one band to another. However, in order for a valence band electron to be promoted to the conduction band, it requires a specific minimum amount of energy for the transition. This required energy is an intrinsic characteristic of the solid material. Electrons can gain enough energy to jump to the conduction band by absorbing either a phonon (heat) or a photon (light).
A semiconductor is a material with an intermediate-sized, non-zero band gap that behaves as an insulator at T=0K, but allows thermal excitation of electrons into its conduction band at temperatures that are below its melting point. In contrast, a material with a large band gap is an insulator. In conductors, the valence and conduction bands may overlap, so there is no longer a bandgap with forbidden regions of electronic states.
The conductivity of intrinsic semiconductors is strongly dependent on the band gap. The only available charge carriers for conduction are the electrons that have enough thermal energy to be excited across the band gap and the that are left off when such an excitation occurs.
Band-gap engineering is the process of controlling or altering the band gap of a material by controlling the composition of certain semiconductor , such as GaAlAs, InGaAs, and InAlAs. It is also possible to construct layered materials with alternating compositions by techniques like molecular-beam epitaxy. These methods are exploited in the design of heterojunction bipolar transistors (HBTs), and .
The distinction between semiconductors and insulators is a matter of convention. One approach is to think of semiconductors as a type of insulator with a narrow band gap. Insulators with a larger band gap, usually greater than 4 eV, are not considered semiconductors and generally do not exhibit semiconductive behaviour under practical conditions. Electron mobility also plays a role in determining a material's informal classification.
The band-gap energy of semiconductors tends to decrease with increasing temperature. When temperature increases, the amplitude of atomic vibrations increase, leading to larger interatomic spacing. The interaction between the lattice and the free electrons and holes will also affect the band gap to a smaller extent. The relationship between band gap energy and temperature can be described by Varshni's empirical expression (named after Y. P. Varshni),
Furthermore, lattice vibrations increase with temperature, which increases the effect of electron scattering. Additionally, the number of charge carriers within a semiconductor will increase, as more carriers have the energy required to cross the band-gap threshold and so conductivity of semiconductors also increases with increasing temperature. The external pressure also influences the electronic structure of semiconductors and, therefore, their optical band gaps.
In a regular semiconductor crystal, the band gap is fixed owing to continuous energy states. In a quantum dot crystal, the band gap is size dependent and can be altered to produce a range of energies between the valence band and conduction band. "Evident Technologies" . Evidenttech.com. Retrieved on 2013-04-03. It is also known as quantum confinement effect.
Band gaps can be either direct or indirect, depending on the electronic band structure of the material. (1996). 9783540614616, Springer. ISBN 9783540614616 (2025). 9780198506133, Oxford Univ. Press. ISBN 9780198506133
It was mentioned earlier that the dimensions have different band structure and spectroscopy. For non-metallic solids, which are one dimensional, have optical properties that are dependent on the electronic transitions between valence and conduction bands. In addition, the spectroscopic transition probability is between the initial and final orbital and it depends on the integral. φi is the initial orbital, φf is the final orbital, ʃ φf*ûεφi is the integral, ε is the electric vector, and u is the dipole moment.
Two-dimensional structures of solids behave because of the overlap of atomic orbitals. The simplest two-dimensional crystal contains identical atoms arranged on a square lattice. Energy splitting occurs at the Brillouin zone edge for one-dimensional situations because of a weak periodic potential, which produces a gap between bands. The behavior of the one-dimensional situations does not occur for two-dimensional cases because there are extra freedoms of motion. Furthermore, a bandgap can be produced with strong periodic potential for two-dimensional and three-dimensional cases.
| III–V | Aluminium nitride | AlN | 6.0 | |
| IV | Diamond | Carbon | 5.5 | |
| IV | Silicon | Si | 1.14 | |
| IV | Germanium | Ge | 0.67 | |
| III–V | Gallium nitride | GaN | 3.4 | |
| III–V | Gallium phosphide | GaP | 2.26 | |
| III–V | Gallium arsenide | GaAs | 1.43 | |
| IV–V | Silicon nitride | Si3N4 | 5 | |
| IV–VI | Lead(II) sulfide | PbS | 0.37 | |
| IV–VI | Silicon dioxide | SiO2 | 9 | |
| Copper(I) oxide | Cu2O | 2.1 |
In almost all inorganic semiconductors, such as silicon, gallium arsenide, etc., there is very little interaction between electrons and holes (very small exciton binding energy), and therefore the optical and electronic bandgap are essentially identical, and the distinction between them is ignored. However, in some systems, including organic semiconductors and Carbon nanotube, the distinction may be significant.
Similar physics applies to in a phononic crystal.
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