# 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

*E*_{F}. 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

*E*_{F}/

*k*. The characteristic temperature is on the order of 10

^{5}K 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