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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.
The Fermi energy can only be defined for non-interacting fermions (where the potential energy or band edge is a static, well defined quantity), whereas the Fermi level remains well defined even in complex interacting systems, at thermodynamic equilibrium.
The linear response of a metal to an electric, magnetic, or thermal gradient is determined by the shape of the Fermi surface, because currents are due to changes in the occupancy of states near the Fermi energy. In reciprocal space, the Fermi surface of an ideal Fermi gas is a sphere of radius
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.
Shown is the graphical definition of the Schottky barrier height, Φ B, for an n-type semiconductor as the difference between the interfacial conduction band edge E C and Fermi level E F. Whether a given metal-semiconductor junction is an ohmic contact or a Schottky barrier depends on the Schottky barrier height, Φ B, of the junction.
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.
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.
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 with electrons or holes .