Fermi energy

The energy of the highest occupied quantum state in a system of fermions at absolute zero. It sets the boundary between occupied and unoccupied states in the ground state.

Fermion: A particle with half-integer spin that obeys Fermi–Dirac statistics and the Pauli exclusion principle. Only one fermion can occupy each available single-particle state, determining how states fill up to this energy.
Fermi gas: A model of fermions treated as noninteracting particles subject to quantum statistics. Filling its energy levels gives a direct calculation of the Fermi energy.
Metal: A material whose electronic states support electrical conduction, typically with partially filled bands or overlapping bands. In a simple metal, the Fermi energy helps characterize conduction electrons and their response.
Chemical potential: The change in a system’s thermodynamic energy when one particle is added, at fixed entropy and volume. At zero temperature it coincides with the Fermi energy under common conventions, but not generally at finite temperature.
Pauli exclusion principle: The quantum rule forbidding identical fermions from occupying the same quantum state. It forces fermions into progressively higher-energy states as particles are added.
Free electron model: A model that treats conduction electrons in a solid as freely moving particles in a uniform potential. Its parabolic energy bands yield the familiar relation between electron density and Fermi energy.
Semiconductor: A material whose electrical conductivity lies between that of conductors and insulators and can be controlled by doping or fields. Doping shifts the Fermi level relative to the band edges, changing carrier populations.
Work function: The minimum energy required to remove an electron from a solid to the vacuum level. It measures an electron’s escape energy, not the highest occupied state’s energy.
Fermi–Dirac statistics: The statistical distribution governing the occupation of quantum states by fermions in thermal equilibrium. At zero temperature, its occupation becomes a sharp step at the Fermi energy.
Fermi wave vector: The wave-number magnitude at the boundary of occupied states in momentum space at zero temperature. For free particles, this boundary determines the Fermi energy through the dispersion relation.

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