Fermi Level and Electrostatic Screening Factor in Degenerate Semiconductors and Metal Alloys

An analytical solution has been found for the calculation of the Fermi level and the electrostatic screening factor for semiconductors and metal alloys in the degenerate limit using non-parabolic energy bands and Fermi statistics. The solution yields a more accurate determination of Fermi levels than methods that assume parabolic energy bands and a more accurate determination of screening factors than the Thomas–Fermi formula, which also assumes parabolic bands and thus predicts screening that is too weak relative to self-consistent field screening in highly degenerate systems, including metal alloys. Mobility and resistivity calculations using this analytical solution yield results that are closer to experimental data than traditional formulas derived assuming parabolic bands.