 Because electrons are fermions, the density of conduction electrons at any particular energy,formula_13 is the product of the density of states,formula_14 or how many conducting states are possible, with the Fermi-Dirac distribution,formula_15 which tells us the portion of those states which will actually have electrons in ″them″

In order to simplify the calculation, instead of treating the electrons as Fermions, according to the Fermi-dirac distribution, we instead treat them as a classical non-interacting gas, which is given by the Maxwell–Boltzmann distribution.This approximation has negligible effects when the magnitude formula_17, which is true for semiconductors near room temperature.This approximation is invalid at very low temperatures or an extremely small band-gap.