Abstract
Based on an analytical approximation (recently proposed by Joyce and Dixon) for the Fermi energy of an ideal Fermi gas, an expression for the Fermi energy of zincblende-symmetry narrow-gap semiconductors with spherical energy bands is derived. A formula for the Fermi-Dirac integral for such semiconductors is given and certain properties of the integral are discussed. As an additional study, the role of this Fermi-Dirac integral towards the convergence of the expansion of the screening charge density for impurity ions in semiconductors is described.