where formula_29 is the energy-dependent conductivity, and formula_30 is the Fermi–Dirac distribution function. These equations are known as the Mott relations, of Sir Nevill Francis Mott. The derivativeformula_31 is a function peaked around the chemical potential (Fermi level) formula_32 with a width of approximately formula_33. The energy-dependent conductivity (a quantity that cannot actually be directly measured — one only measures formula_34) is calculated as formula_35 where formula_36 is the electron diffusion constant and formula_37 is the electronic density of states (in general, both are functions of energy).