solid-state physics Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state phy ...

and

solid-state chemistry Solid-state chemistry, also sometimes referred as materials chemistry, is the study of the Chemical synthesis, synthesis, structure, and properties of solid phase materials. It therefore has a strong overlap with solid-state physics, mineralogy, cr ...

, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no

electronic state A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The t ...

s exist. In graphs of the

electronic band structure 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 '' ...

of solids, the band gap refers to the energy difference (often expressed in

electronvolt In physics, an electronvolt (symbol eV), also written electron-volt and electron volt, is the measure of an amount of kinetic energy gained by a single electron accelerating through an Voltage, electric potential difference of one volt in vacuum ...

s) between the top of the

valence band In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in ...

and the bottom of the

conduction band In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in ...

insulators Insulator may refer to: * Insulator (electricity), a substance that resists electricity ** Pin insulator, a device that isolates a wire from a physical support such as a pin on a utility pole ** Strain insulator, a device that is designed to work ...

and

semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...

s. 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 physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle denoting the lack of an electron at a position where one could exist in an atom or crystal structure, atomic lattice. Since in ...

in the valence band) are free to move within the crystal lattice and serve as charge carriers to conduct

electric current An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...

. 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 In solid-state physics of semiconductors, carrier generation and carrier recombination are processes by which mobile charge carriers (electrons and electron holes) are created and eliminated. Carrier generation and recombination processes are fund ...

). Therefore, the band gap is a major factor determining the

electrical conductivity Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity in ...

of a solid. Substances having large band gaps (also called "wide" band gaps) are generally

, those with small band gaps (also called "narrow" band gaps) are

semiconductors A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping levels ...

, 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 A proper frame, or comoving frame, is a frame of reference that is attached to an object. The object in this frame is stationary within the frame, which is useful for many types of calculations. For example, a freely falling elevator is a proper f ...

. The solutions can be given with the help of the Mathieu functions.

In semiconductor physics

Every solid has its own characteristic energy-band structure. This variation in band structure is responsible for the wide range of electrical characteristics observed in various materials. Depending on the dimension, the band structure and spectroscopy can vary. The different types of dimensions are as listed: one dimension, two dimensions, and three dimensions. In semiconductors and insulators,

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

s are confined to a number of

bands Bands may refer to: * Bands (song), song by American rapper Comethazine * Bands (neckwear), form of formal neckwear * Bands (Italian Army irregulars) Bands () was an Italian military term for Irregular military, irregular forces, composed of nati ...

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 In science and engineering, an intrinsic property is a property of a specified subject that exists itself or within the subject. An extrinsic property is not essential or inherent to the subject that is being characterized. For example, mass i ...

characteristic of the solid material. Electrons can gain enough energy to jump to the conduction band by absorbing either a

phonon A phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. In the context of optically trapped objects, the quantized vibration mode can be defined a ...

(heat) or a

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...

(light). A

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 semiconductor An intrinsic semiconductor, also called a pure semiconductor, undoped semiconductor or i-type semiconductor, is a semiconductor without any significant dopant species present. The number of charge carriers is therefore determined by the properties ...

s 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

s 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

alloy An alloy is a mixture of chemical elements of which in most cases at least one is a metal, metallic element, although it is also sometimes used for mixtures of elements; herein only metallic alloys are described. Metallic alloys often have prop ...

s, such as GaAlAs,

InGaAs Indium gallium arsenide (InGaAs) (alternatively gallium indium arsenide, GaInAs) is a ternary alloy (chemical compound) of indium arsenide (InAs) and gallium arsenide (GaAs). Indium and gallium are group III elements of the periodic table while ...

, and InAlAs. It is also possible to construct layered materials with alternating compositions by techniques like

molecular-beam epitaxy Molecular-beam epitaxy (MBE) is an epitaxy method for thin-film deposition of single crystals. MBE is widely used in the manufacture of semiconductor devices, including transistors. MBE is used to make diodes and MOSFETs (MOS field-effect transis ...

. These methods are exploited in the design of

heterojunction bipolar transistor A heterojunction bipolar transistor (HBT) is a type of bipolar junction transistor (BJT) that uses different semiconductor materials for the emitter and base regions, creating a heterojunction. The HBT improves on the BJT in that it can handle si ...

s (HBTs),

laser diode file:Laser diode chip.jpg, The laser diode chip removed and placed on the eye of a needle for scale A laser diode (LD, also injection laser diode or ILD or semiconductor laser or diode laser) is a semiconductor device similar to a light-emittin ...

s and

solar cell A solar cell, also known as a photovoltaic cell (PV cell), is an electronic device that converts the energy of light directly into electricity by means of the photovoltaic effect.

s. 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 In solid-state physics, the electron mobility characterizes how quickly an electron can move through a metal or semiconductor when pushed or pulled by an electric field. There is an analogous quantity for Electron hole, holes, called hole mobilit ...

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

s 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), :

E_g(T)=E_g(0)-\frac

, where ''E_g''(0), α and β are material constants. 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 Quantum dots (QDs) or semiconductor nanocrystals are semiconductor particles a few nanometres in size with optical and electronic properties that differ from those of larger particles via quantum mechanical effects. They are a central topic i ...

crystal, the band gap is size dependent and can be altered to produce a range of energies between the valence band and conduction band. It is also known as quantum confinement effect. Band gaps can be either direct or indirect, depending on the

of the material. 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. φ_i is the initial orbital, φ_f is the final orbital, ʃ φ_f^*ûεφ_i 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.

Direct and indirect band gap

Based on their band structure, materials are characterised with a direct band gap or indirect band gap. In the free-electron model, k is the momentum of a free electron and assumes unique values within the Brillouin zone that outlines the periodicity of the crystal lattice. If the momentum of the lowest energy state in the conduction band and the highest energy state of the valence band of a material have the same value, then the material has a direct bandgap. If they are not the same, then the material has an indirect band gap and the electronic transition must undergo momentum transfer to satisfy conservation. Such indirect "forbidden" transitions still occur, however at very low probabilities and weaker energy. For materials with a direct band gap, valence electrons can be directly excited into the conduction band by a photon whose energy is larger than the bandgap. In contrast, for materials with an indirect band gap, a photon and

must both be involved in a transition from the valence band top to the conduction band bottom, involving a momentum change. Therefore, direct bandgap materials tend to have stronger light emission and absorption properties and tend to be better suited for

photovoltaics Photovoltaics (PV) is the conversion of light into electricity using semiconducting materials that exhibit the photovoltaic effect, a phenomenon studied in physics, photochemistry, and electrochemistry. The photovoltaic effect is commerciall ...

(PVs),

light-emitting diode A light-emitting diode (LED) is a semiconductor device that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (corre ...

s (LEDs), and

s; however, indirect bandgap materials are frequently used in PVs and LEDs when the materials have other favorable properties.

Light-emitting diodes and laser diodes

LEDs and

s usually emit photons with energy close to and slightly larger than the band gap of the semiconductor material from which they are made. Therefore, as the band gap energy increases, the LED or laser color changes from infrared to red, through the rainbow to violet, then to UV.

Photovoltaic cells

The optical band gap (see below) determines what portion of the solar spectrum a

photovoltaic cell A solar cell, also known as a photovoltaic cell (PV cell), is an electronic device that converts the energy of light directly into electricity by means of the photovoltaic effect.

absorbs. Strictly, a semiconductor will not absorb photons of energy less than the band gap; whereas most of the photons with energies exceeding the band gap will generate heat. Neither of them contribute to the efficiency of a solar cell. One way to circumvent this problem is based on the so-called photon management concept, in which case the solar spectrum is modified to match the absorption profile of the solar cell.

List of band gaps

Below are band gap values for some selected materials. For a comprehensive list of band gaps in semiconductors, see

List of semiconductor materials Semiconductor materials are nominally small band gap Insulator (electricity), insulators. The defining property of a semiconductor material is that it can be compromised by Doping (semiconductor), doping it with impurities that alter its electronic ...

Optical versus electronic bandgap

In materials with a large

exciton An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb's law, Coulomb force resulting from their opposite charges. It is an electrically neutral quasiparticle regarded as ...

binding energy, it is possible for a photon to have just barely enough energy to create an exciton (bound electron–hole pair), but not enough energy to separate the electron and hole (which are electrically attracted to each other). In this situation, there is a distinction between "optical band gap" and "electronic band gap" (or "transport gap"). The optical bandgap is the threshold for photons to be absorbed, while the transport gap is the threshold for creating an electron–hole pair that is ''not'' bound together. The optical bandgap is at lower energy than the transport gap. 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 single-walled carbon nanotubes, the distinction may be significant.

Band gaps for other quasi-particles

photonics Photonics is a branch of optics that involves the application of generation, detection, and manipulation of light in the form of photons through emission, transmission, modulation, signal processing, switching, amplification, and sensing. E ...

, band gaps or stop bands are ranges of photon frequencies where, if tunneling effects are neglected, no photons can be transmitted through a material. A material exhibiting this behaviour is known as a

photonic crystal A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of Crystal structure, natural crystals gives rise to X-ray crystallograp ...

. The concept of

hyperuniformity Hyperuniform materials are characterized by an anomalous suppression of density fluctuations at large scales. More precisely, the vanishing of density fluctuations in the long-wave length limit (like for crystals) distinguishes ''hyperuniform'' s ...

has broadened the range of photonic band gap materials, beyond photonic crystals. By applying the technique in supersymmetric quantum mechanics, a new class of optical disordered materials has been suggested, which support band gaps perfectly equivalent to those of

crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...

s or

quasicrystal A quasiperiodicity, quasiperiodic crystal, or quasicrystal, is a structure that is Order and disorder (physics), ordered but not Bravais lattice, periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks trans ...

s. Similar physics applies to

s in a phononic crystal.

Materials

Aluminium gallium arsenide Aluminium gallium arsenide (also gallium aluminium arsenide) ( Alx Ga1−x As) is a semiconductor material with very nearly the same lattice constant as GaAs, but a larger bandgap. The ''x'' in the formula above is a number between 0 and 1 - thi ...

Boron nitride Boron nitride is a thermally and chemically resistant refractory compound of boron and nitrogen with the chemical formula B N. It exists in various crystalline forms that are isoelectronic to a similarly structured carbon lattice. The hexago ...

Indium gallium arsenide Indium gallium arsenide (InGaAs) (alternatively gallium indium arsenide, GaInAs) is a ternary alloy (chemical compound) of indium arsenide (InAs) and gallium arsenide (GaAs). Indium and gallium are Group 13 element, group III elements of the peri ...

Indium arsenide Indium arsenide, InAs, or indium monoarsenide, is a narrow-bandgap semiconductor composed of indium and arsenic. It has the appearance of grey cubic crystals with a melting point of 942 °C. Indium arsenide is similar in properties to gallium ars ...

Gallium arsenide Gallium arsenide (GaAs) is a III-V direct band gap semiconductor with a Zincblende (crystal structure), zinc blende crystal structure. Gallium arsenide is used in the manufacture of devices such as microwave frequency integrated circuits, monoli ...

Gallium nitride Gallium nitride () is a binary III/ V direct bandgap semiconductor commonly used in blue light-emitting diodes since the 1990s. The compound is a very hard material that has a Wurtzite crystal structure. Its wide band gap of 3.4 eV af ...

Germanium Germanium is a chemical element; it has Symbol (chemistry), symbol Ge and atomic number 32. It is lustrous, hard-brittle, grayish-white and similar in appearance to silicon. It is a metalloid or a nonmetal in the carbon group that is chemically ...

Metallic hydrogen Metallic hydrogen is a phase of hydrogen in which it behaves like an electrical conductor. This phase was predicted in 1935 on theoretical grounds by Eugene Wigner and Hillard Bell Huntington. At high pressure and temperatures, metallic hydr ...

List of electronics topics

Electronics Electronics is a scientific and engineering discipline that studies and applies the principles of physics to design, create, and operate devices that manipulate electrons and other Electric charge, electrically charged particles. It is a subfield ...

Bandgap voltage reference A bandgap voltage reference is a voltage reference circuit widely used in integrated circuits. It produces an almost constant voltage corresponding to the particular semiconductor's theoretical band gap, with very little fluctuations from variatio ...

Condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and elec ...

* Direct and indirect bandgaps *

Electrical conduction Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity i ...

Electron hole In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle denoting the lack of an electron at a position where one could exist in an atom or crystal structure, atomic lattice. Since in ...

Field-effect transistor The field-effect transistor (FET) is a type of transistor that uses an electric field to control the current through a semiconductor. It comes in two types: junction FET (JFET) and metal-oxide-semiconductor FET (MOSFET). FETs have three termi ...

Light-emitting diode A light-emitting diode (LED) is a semiconductor device that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (corre ...

Photodiode A photodiode is a semiconductor diode sensitive to photon radiation, such as visible light, infrared or ultraviolet radiation, X-rays and gamma rays. It produces an electrical current when it absorbs photons. This can be used for detection and me ...

Photoresistor A photoresistor (also known as a light-dependent resistor, LDR, or photo-conductive cell) is a passive component that decreases in resistance as a result of increasing luminosity (light) on its sensitive surface, in other words, it exhibits pho ...

Photovoltaics Photovoltaics (PV) is the conversion of light into electricity using semiconducting materials that exhibit the photovoltaic effect, a phenomenon studied in physics, photochemistry, and electrochemistry. The photovoltaic effect is commerciall ...

Solar cell A solar cell, also known as a photovoltaic cell (PV cell), is an electronic device that converts the energy of light directly into electricity by means of the photovoltaic effect.

Solid state physics Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state p ...

Semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...

Semiconductor device A semiconductor device is an electronic component that relies on the electronic properties of a semiconductor material (primarily silicon, germanium, and gallium arsenide, as well as organic semiconductors) for its function. Its conductivit ...

s *

Strongly correlated material Strongly correlated materials are a wide class of compounds that include insulators and electronic materials, and show unusual (often technologically useful) electronic and magnetic properties, such as metal-insulator transitions, heavy fermi ...

Valence band In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in ...

References

External links

Direct Band Gap Energy Calculator
* {{DEFAULTSORT:Band Gap Electron states Electronic band structures Quantum mechanics Spectroscopy Nuclear magnetic resonance