Approximation for the Fermi–Dirac integral with applications to degenerately doped solar cells and other semiconductor devices

An analytical formula for evaluating Fermi–Dirac integral of order 1/2 has been proposed. The formula exhibits essentially the same form as that of Joyce and Dixon, but is accurate enough to be used in the heavily doped regions of semiconductor devices as well as in those cases where the degeneracy occurs at nonequilibrium. It has been shown that the accuracy with which the derivative can be evaluated by differentiation of the proposed series is remarkable and the error never exceeds 0.4%. To justify its applicability the formula has been used to calculate the effective charge carrier concentration of degenerate heavily doped material.