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A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac , each of whom derived the distribution independently in 1926. [ 1 ] [ 2 ] Fermi–Dirac statistics is a part of the field of statistical mechanics and uses the principles of quantum mechanics .
For example, in a piece of aluminum there are two conduction bands crossing the Fermi level (even more bands in other materials); [10] each band has a different edge energy, ϵ C, and a different ζ. The value of ζ at zero temperature is widely known as the Fermi energy , sometimes written ζ 0 .
A Kurie plot (also known as a Fermi–Kurie plot) is a graph used in studying beta decay developed by Franz N. D. Kurie, in which the square root of the number of beta particles whose momenta (or energy) lie within a certain narrow range, divided by the Fermi function, is plotted against beta-particle energy.
µ is the total chemical potential of electrons, or Fermi level (in semiconductor physics, this quantity is more often denoted E F). The Fermi level of a solid is directly related to the voltage on that solid, as measured with a voltmeter. Conventionally, in band structure plots the Fermi level is taken to be the zero of energy (an arbitrary ...
While the Pauli principle and Fermi-Dirac distribution applies to all matter, the interesting cases for degenerate matter involve systems of many fermions. These cases can be understood with the help of the Fermi gas model. Examples include electrons in metals and in white dwarf stars and neutrons in neutron stars.
Physically, the integrals represent statistical averages using the Fermi–Dirac distribution. When the inverse temperature β {\displaystyle \beta } is a large quantity, the integral can be expanded [ 1 ] [ 2 ] in terms of β {\displaystyle \beta } as
The Fermi temperature is defined as =, where is the Boltzmann constant, and the Fermi energy. The Fermi temperature can be thought of as the temperature at which thermal effects are comparable to quantum effects associated with Fermi statistics . [ 3 ]
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states.