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The Fermi level does not necessarily correspond to an actual energy level (in an insulator the Fermi level lies in the band gap), nor does it require the existence of a band structure. Nonetheless, the Fermi level is a precisely defined thermodynamic quantity, and differences in Fermi level can be measured simply with a voltmeter.
When a material's Fermi level falls in a bandgap, there is no Fermi surface. Fig. 2: A view of the graphite Fermi surface at the corner H points of the Brillouin zone showing the trigonal symmetry of the electron and hole pockets. Materials with complex crystal structures can have quite intricate Fermi surfaces.
The most important bands and band gaps—those relevant for electronics and optoelectronics—are those with energies near the Fermi level. The bands and band gaps near the Fermi level are given special names, depending on the material: In a semiconductor or band insulator, the Fermi level is surrounded by a band gap, referred to as the band ...
The shade follows the Fermi–Dirac distribution (black: all states filled, white: no state filled). In metals and semimetals the Fermi level E F 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 ...
The electronic structure of a half-metal. is the Fermi level, () is the A half-metal is any substance that acts as a conductor to electrons of one spin orientation, but as an insulator or semiconductor to those of the opposite orientation.
The work function W for a given surface is defined by the difference [1] =, where −e is the charge of an electron, ϕ is the electrostatic potential in the vacuum nearby the surface, and E F is the Fermi level (electrochemical potential of electrons) inside the material.
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 which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states.
A topological insulator is a material that behaves as an insulator in its interior (bulk) but whose surface contains conducting states. This property represents a non-trivial, symmetry protected topological order. As a consequence, electrons in topological insulators can only move along the surface of the material.