# Fermi-Dirac Distribution The Fermi-Dirac distribution is a type of quantum statistics (statistical mechanics) describing identical particles that obey the [[Pauli Exclusion Principle]]. The distribution $f(\epsilon)$ gives the probability at thermodynamic equilibrium that a state having energy $\epsilon$ is occupied by an electron. The closer $f$ is to 1, the more likely the state is occupied, and the closer $f$ is to 0, the more likely the space is to be empty. $ f(\epsilon) = \frac{1}{e^{(\epsilon - \mu)/k_BT}+1} $ where: - $T$ is the absolute temperature - $k_B$ is the Boltzmann Constant The location of $\mu$ (the [[Fermi Levels]]) is important in determining the material's electrical behavior. In this formula, the main changed independent variables are usually $\epsilon$ or $kT$.