Fermi-Dirac distribution
= Fermi-Dirac distribution
{c}
= Fermi distribution
{c}
{synonym}
The <Fermi-Dirac distribution> follows from <Fermi-Dirac statistics> and is $n(E)=[e^{\beta(E-\mu)}+1]^{-1}$.
The mean occupation of a fermionic one-particle state of energy $E$ is
$$
f(E)=\frac{1}{e^{\beta(E-\mu)}+1},
\qquad \beta=(k_BT)^{-1}.
$$
At zero temperature this becomes the step function $\mathbf 1_{E<E_F}$.