Approximation for the Fermi–Dirac integral with applications to the modeling of charge transport in heavily doped semiconductors

Analytical formulas for evaluating Fermi–Dirac integral of order (1)/(2) has been proposed. The formulas exhibit a degeneracy factor C which controls essentially the applicability of the integrals both to the nondegenerate as well as highly degenerate semiconductors. The accuracies with which the derivative can be evaluated by differentiation and integration of the proposed formulas are acceptable. The formulas have been successfully used in the calculation of effective carrier concentration and current density.