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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.
Fermi-Dirac distribution () vs. energy , with μ = 0.55 eV and for various temperatures in the range 50 K ≤ T ≤ 375 K. In the band theory of solids, electrons occupy a series of bands composed of single-particle energy eigenstates each labelled by ϵ. Although this single particle picture is an approximation, it greatly simplifies the ...
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 ]
A Fermi gas is an idealized model, an ensemble of many non-interacting fermions.Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin.
[3]: 34 However the pertinent probability distribution in Fermi–Dirac statistics is actually a simple Bernoulli distribution, with the probability factor given by the Fermi function. The logistic distribution arises as limit distribution of a finite-velocity damped random motion described by a telegraph process in which the random times ...
When a semiconductor is in thermal equilibrium, the distribution function of the electrons at the energy level of E is presented by a Fermi–Dirac distribution function. In this case the Fermi level is defined as the level in which the probability of occupation of electron at that energy is 1 ⁄ 2. In thermal equilibrium, there is no need to ...
The Fermi–Dirac distribution implies that each eigenstate of a system, i, is occupied with a certain probability, p i. As the entropy is given by a sum over the probabilities of occupation of those states, there is an entropy associated with the occupation of the various electronic states.
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.