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The name "Fermi energy" was named after Enrico Fermi, who derived with Paul Dirac, the FermiDirac statistics. These statistics allow one to predict the behaviour of large numbers of electrons under certain circumstances, especially in solids. The equations of quantum mechanics would otherwise be too hard to solve in such situations.
The Fermi energy of a threedimensional, noninteracting, nonrelativistic Fermi gas (or free electron gas[?]) is related to the chemical potential by the equation
where ε_{F} is the Fermi energy, k is the Boltzmann constant and T is temperature. Hence, the chemical potential is approximately equal to the Fermi energy at temperatures of much less than the characteristic temperature of the Fermi energy E_{F}/k. The characteristic temperature is on the order of 10^{5}K for a metal, hence at room temperature (300K), the Fermi energy and chemical potential are essentially equivalent. This is significant since it is the chemical potential, not the Fermi energy, which appears in FermiDirac statistics.
Related fields: solid state physics, semiconductors, electrical engineering, electronics, statistical mechanics, thermodynamics
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