Fermi energy
In
physics, some particles (for example
electrons) follow the
Pauli exclusion principle – i.e. that no two particles may occupy the same state at the same time. When a number of electrons are put into a system, electrons will occupy higher
energy levels when the lower ones are filled up. Loosely speaking, the
Fermi energy is the energy of the highest occupied state at zero
temperature. It is given the symbol
EF. Fermi energy is a concept which finds application in
semiconductor theory and device design.
Fermi energy was named after Enrico Fermi, who with Paul Dirac, derived the Fermi-Dirac statistics. These statistics allow one to predict the behaviour of large numbers of electrons under certain circumstances, especially in solids. The equations of quantum mechanics would otherwise be too hard to solve in such situations.
The Fermi energy of a three-dimensional, non-interacting, non-relativistic Fermi gas (or free electron gas) is related to the chemical potential by the equation
where ε
F is the Fermi energy,
k is the
Boltzmann constant and
T is
temperature. Hence, the chemical potential is approximately equal to the Fermi energy at temperatures of much less than the characteristic temperature of the Fermi energy
EF/
k. The characteristic temperature is on the order of 10
5K for a metal, hence at room temperature (300K), the Fermi energy and chemical potential are essentially equivalent. This is significant since it is the chemical potential, not the Fermi energy, which appears in Fermi-Dirac statistics.
Related fields: solid state physics, semiconductors, electrical engineering, electronics, statistical mechanics, thermodynamics\n