Band Gap

In physics especially in the case of solid-state, a bandgap is also called an energy gap. It is the range of energy present in a solid where no other electronic states can exist. In the graphs of the electronic band structure of the solids, the band gap generally denoted to the energy difference. It is done in terms of electron volts in between the upper side of the valence band and the lower side of the conduction band in both insulators and semiconductors. 

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It is the energy that is required to promote a valence electron that is bound to an atom to become a conduction electron. This conduction electron is free to move within the crystal lattice and serves as a charge carrier to conduct the electric current. If the valence band is completely full and the conduction band is completely empty, then the flow of current cannot happen as the electrons cannot move in the solid. If some of these electrons are transferred from the valence band to the conduction band, then the current starts flowing. Therefore, the bandgap is a major factor that helps in determining the electrical conductivity of a solid. Substances that are having large band gaps are generally called insulators, those with smaller band gaps are called semiconductors. In the case of conductors either they have very small band gaps or no band gap is found because the valence and conduction bands overlap.

Let us learn about what is energy bandgap? Its types, its range, etc.

What is Energy Gap?

In solid-state physics, an energy gap is an energy range in a solid where no electron state can exist, that is it is an energy range where the density of states vanishes. Especially in condensed-matter physics, an energy gap is sometimes known more abstractly as a spectral gap, it is a term that is needed not to be specific to electrons or to the solids.

If an energy gap exists in the case of the band structure of a material, then it is called a band gap. The physical properties of semiconductors up to to a large extent can be determined by their band gaps. But for the insulators and metals the band structure, any possible band gaps can govern their electronic properties.

For superconductors, the energy gap is a region of the suppressed density of states found around the Fermi energy level. This has the size of the energy gap that is much smaller than the energy scale of the band structure. The superconducting energy gap is a key aspect in the theoretical description of superconductivity. Here, the size of the energy gap indicates the energy gain for two electrons upon the formation of a Cooper pair.  If a conventional superconducting material is cooled from its metallic state into the superconducting state. Then the superconducting energy gap is absent above the range of critical temperature. If it starts to open upon entering the superconducting state of the superconducting energy gap for the superconductors at zero temperature scale with their critical temperature.

Energy Band Gap in Semiconductors

Every solid has its own characteristic energy-band structure. This variation in band structure is mainly responsible for the wide range of electrical characteristics that are observed in various materials. In the case of semiconductors and insulators, the electrons are confined to a number of bands of energy and forbidden from other regions. The term band gap definition is, it is the energy difference that is present between the top of the valence band and the bottom of the conduction band. Electrons that are able to jump from one band to another band. However, in order for an electron to jump from the state of the valence band to a conduction band, then it requires a specific minimum amount of energy for the transition. The required energy differs from the different materials. Electrons can gain enough energy to jump into the conduction band by absorbing either a “phonon or heat” or a “photon of light”.

A semiconductor is a material that consists of an intermediate-sized but non-zero band gap that behaves as an insulator at the condition of absolute zero. But it allows the thermal excitation of the electrons into its conduction band at temperatures that are mentioned below its melting point. In contrast, a material with a large band gap is considered an insulator. In the case of conductors, the valence and conduction bands may overlap, so they may not have a band gap. The conductivity of intrinsic semiconductors can be strongly dependent on the band gap. The only available charge carriers for the conduction are the electrons that have enough thermal energy to be excited across the band gap and the electron holes are found when excitation occurs.

Band-gap engineering is the process of altering or controlling the band gap of a material. It is done by controlling the composition of certain semiconductor alloys that include InGaAs, GaAlAs, and InAlAs. It is also possible to construct the layered materials by alternating the compositions of the materials by using the techniques like molecular-beam epitaxy. 

The matter of the convention is the distinction between semiconductors and insulators. One of the approaches is to think of semiconductors as a type of insulator with a narrow band gap. Insulators that have a larger band gap, which is usually greater than that of four eV, are not considered semiconductors. Generally, they do not exhibit semiconductive behavior under some practical conditions. Electron mobility can also play a role in determining an informal classification of the material.

The band-gap energy of semiconductors tends to decrease with increasing temperature. When temperature increases, the amplitude of atomic vibrations increases, leading to larger interatomic spacing. The interaction between the lattice phonons 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,

E\[_{g}\](T) = E\[_{g}\](0) - \[\frac{\alpha T^{2}}{T + \beta}\]

Here \[\alpha\] and \[\beta\] represent the material constant.

Energy Gap Sizes

A band gap is a distance that is present between the valence band and the conduction band of electrons. Essentially, the band gap represents the minimum energy that is required to excite an electron up to a state in the conduction band where it can participate in conduction. The lower energy level is found in the valence band, and thus if a gap exists between this level and the higher energy conduction band, energy must be input for electrons to become free. The size and existence of this band gap allow one to visualize the difference present between the conductors, semiconductors, and insulators.

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The figure provided illustrates the difference in the size of the band gap for the conductors, insulators, and semiconductors. The size of this band gap provides the materials with some of their distinct properties. In the case of insulators, the electrons present in the valence band are separated by a large band gap from the state of the conduction band. This means that there is a large "forbidden" gap present in energies that are preventing the electrons from the valence band from jumping up into the conduction band and participating in the conduction. This provides an explanation for the question that why insulators do not conduct electricity well as conductors and semiconductors.

In the case of conductors, the conductor band gap occurs when the valence band overlaps with the level of the conduction band. This overlap can cause the valence electrons to be essentially free to move or excite into the conduction band and to participate in the process of conduction. Since it is not a full overlap, only a fraction of the valence electrons are capable to move through the materials, but this is still enough to make conductors conductive.

In semiconductors, the gap is small enough that it can be connected by some sort of excitation perhaps from the Sun in the case of photovoltaic cells. The energy band gap size for semiconductors is in the range of two to three eV. In this model, a finite number of electrons are capable to reach the conduction band and can conduct small amounts of electricity. The excitation of this electron also allows the additional conduction processes to occur, as a result of the electron-hole is left behind. An electron from an atom that is close by can occupy this space, creating a chain reaction of holes and allows the electron movement that creates current. A small amount of doping material can drastically increase the conductivity of the respective material.