Empirical approximations for the Fermi energy in a semiconductor with parabolic bands

Approximate expressions are presented which are useful for computing the position of the Fermi level in a semiconductor when the carrier concentration is known. A simple approximation formula is applicable for η=EF/kT⩽5.7, while an extended approximation can be used up to η⩽20, the error in EF being less than 10−2kT in both cases.