# Fermi Levels [^1] [^1]: black states indicate full, white indicates empty The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is usually denoted by $\mu$ or $E_F$ . The Fermi Level does NOT correspond to an actual energy, nor does it require the existence of band structures, but IS a precisely defined thermodynamic quantity. The Fermi Levels can be measured by the difference in voltages between two points, ($A$ and $B$) $ V_A - V_B = \frac{\mu_A - \mu_B}{-e} $ where $e$ is the electron charge, ($1.602 \times 10^{-19} \, C$) It is clear that the electrons will move from a body of high $\mu$ (low voltage) to a low $\mu$ (high voltage) if a simple path is provided. This can also apply to [[p-type semiconductors]] and [[n-type semiconductors]] with the [[Fermi-Dirac Distribution]] which gives the probability that (at thermodynamic equilibrium) a state having a specific energy is occupied by an electron. In insulators and semiconductors, the Fermi Level lies within a [[Band Gap]], though in semiconductors the level is very close to the Fermi Level to be populated with electrons or holes.