A simple accurate expression of the reduced Fermi energy for any reduced carrier density

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Abstract

Based on the two correct asymptotic forms of the reduced Fermi energy η, its simple accurate approximate expression for any reduced carrier density is proposed. It is suggested that (i) its maximal relative error in absolute value is found to be equal to 2.11×10−4 at fairly large η (=3.6), (ii) and, in particular, in the neighborhood of η=0, its relative errors in absolute values are small and regular, while whose obtained from the formulas by Nilsson [Phys. Status Solidi A 19, K75 (1973)], and Chang and Izabelle [J. Appl. Phys. 65, 2162 (1989)] are found to be large and unstable to different degrees.

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