We want the concentration of intrinsic carriers as a function of temperature,
in terms of the band gap. We do the calculation for simple parabolic band
edges. We first calculate in terms of the chemical potential the number of
electrons excited to the conduction band at temperature T. In semiconductor
physics is called the Fermi level. At the temperatures of interest we may
suppose for the conduction band of a semiconductor that kBT, so that
the Fermi-Dirac distribution function reduces to