# Fermi–Dirac distribution

## Description

Fermi–Dirac statistics describes a distribution of particles over energy states in systems consisting of many identical particles that obey the Pauli exclusion principle. Fermi–Dirac (F–D) statistics applies to identical particles with half-integer spin in a system in thermodynamic equilibrium. Additionally, the particles in this system are assumed to have negligible mutual interaction. This allows the many-particle system to be described in terms of single-particle energy states. For a system of identical fermions, the average number of fermions in a single-particle state i, is given by the Fermi–Dirac (F–D) distribution.

The F–D distribution is only valid if the number of fermions in the system is large enough so that adding one more fermion to the system has negligible effect on μ. At zero temperature, μ is equal to the Fermi energy plus the potential energy per electron. For the case of electrons in a semiconductor, μ , which is the point of symmetry, is typically called the Fermi level or electrochemical potential.

## Variables

n_{j} | the average number of fermions in a single-particle state j (dimensionless) |

e | e |

ϵ_{j} | The energy of the single-particle state j (J) |

μ | The total chemical potential (J) |

k | Boltzmann constant |

T | The absolute temperature (K) |