Simple approximation for Fermi energy in nonparabolic semiconductors

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Abstract
We propose a simple approximation relating the Fermi energy to carrier concentration in both parabolic and nonparabolic semiconductors. The solution is in the form of a polynomial correction to Boltzmann’s approximation of semiconductor statistics. The method is similar to the Joyce–Dixon series approximation, but uses polynomial regression to obtain series coefficients which extends the range of the model’s validity. For nonparabolic semiconductors, polynomial coefficients are calculated using Kane’s k■p model for the density of states. The new approximation demonstrates an acceptable accuracy for band gaps larger than 2 kT and for the Fermi energy up to 10 kT. The expression is simple and should be useful in the modeling of advanced semiconductor devices.