Fermi Level and Electrostatic Screening Factor in Degenerate Semiconductors and Metal Alloys
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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.
KeywordsDegenerate semiconductors non-parabolic bands Fermi statistics ionized impurity screening ionized impurity scattering metal alloy resistivity
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This work is supported by the Air Force Office of Scientific Research through Project FA9550-17RYCOR490. The authors wish to thank D. C. Look for enlightening and useful discussions. In addition, we wish to thank Tim Cooper for performing the Hall-effect measurements. Finally, we express our gratitude to John D. Wiley for pointing out the existence of this problem 43 years ago; we are sorry it took this long to repair.
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