Valence band

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For other uses, see Valence (disambiguation).

In solids, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature.

Semiconductor band structure

The valence electrons are bound to individual atoms, as opposed to conduction electrons (found in conductors and semiconductors), which can move freely within the atomic lattice of the material. On a graph of the electronic band structure of a material, the valence band is located below the conduction band, separated from it in insulators and semiconductors by a band gap. In metals, the conduction band has no energy gap separating it from the valence band.

Filling of the electronic Density of states in various types of materials at equilibrium. Here the vertical axis is energy while the horizontal axis is the Density of states for a particular band in the material listed. In metals and semimetals the Fermi level EF lies inside at least one band. In insulators and semiconductors the Fermi level is inside a band gap; however, in semiconductors the bands are near enough to the Fermi level to be thermally populated with electrons or holes.

To understand the concept of a valence band, it is important to consider the atomic structure of a metal first. For example lithium (Li) atoms with electronic configuration 1s22s1 can form only one covalent bond. However, when forming a bulk metal, Li atoms come to a resonance structure by taking 1 electron from its neighbouring Li atom and the resultant electronic configuration becomes 1s22s12p1 (e-). As a result of this electron sharing, its neighbouring Li atom loses an electron and comes to an electronic configuration of 1s2 (e+). The Li (e-) atoms now gain the capability to form two covalent bonds thus can form a bulk metal. Inside the metal Li (e+) remain alone (not bonded) but nullify the negative charges of the neighbouring Li atoms thus forming a lithium metal matrix.

In a three-dimensional (3D) metal structure of Li, the molecular orbital formation starts from the lower energy level orbitals, i.e. first 1s, then 2s, then 2p. The molecular bond formation is a rapid process and as a result it is seen that 2s orbitals come to totally filled condition whereas the 2p orbitals only partially filled during that time span, and the remaining part of the 2p orbitals remain empty (no electron). In between there is an overlapped zone of totally filled 2s and totally filled 2p orbitals, called overlapped zone.

For any metal this is the rule of forming a metal from its atoms. The totally filled orbitals with highest range of electron energies form valence band (the filled 2s orbitals in the example of Li), the empty orbital with no electrons is called the conduction band (the empty region of 2p orbitals in the example of Li).

The overlapping depends on the interatomic distance (rd) and also on the energy level of the orbitals. If (rd) is large or the orbitals are of large energy level then there may be small overlapping or no overlapping leaving a band gap (Eg). The electrical conductivity of a metal depends on its capability to flow electrons from valence band to conduction band. Hence in case of a metal with large overlapped region the electrical conductivity is high along with good metallic property. If there is a small forbidden zone then the flow of electron from valence to conduction band is only possible if an external energy (thermal etc.) is supplied and these groups with small Eg are called semiconductors. If the Eg is sufficiently high then flow of electron from valence to conduction band become negligible under normal conditions, these groups are called insulators.

Semiconductors and insulators owe their low conductivity to the properties of the valence band in those materials. The number of electrons in the solid is precisely equal to the number of states available up to the top of the valence band (assuming the valence band is full). There are no available states in the band gap. This means that when an electric field is applied, the electrons cannot increase their energy (i.e., accelerate) because there are no states available to the electrons where they would be moving faster than they are already going.

There is some conductivity in semiconductors, however. This is due to thermal excitation—some of the electrons get enough energy to jump the band gap in one go. Once they are in the conduction band, they can conduct electricity, as can the hole they left behind in the valence band. The hole is an empty state that allows electrons in the valence band some degree of freedom.

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