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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.
The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted by μ or E F [1] for brevity. The Fermi level does not include the work required to remove the electron from wherever it came from.
[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 ...
For comparison, the average number of fermions with energy given by Fermi–Dirac particle-energy distribution has a similar form: ¯ = / +. As mentioned above, both the Bose–Einstein distribution and the Fermi–Dirac distribution approaches the Maxwell–Boltzmann distribution in the limit of high temperature and low particle density ...
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 kinetic energy expression of Thomas–Fermi theory is also used as a component in more sophisticated density approximation to the kinetic energy within modern orbital-free density functional theory. Working independently, Thomas and Fermi used this statistical model in 1927 to approximate the distribution of electrons in an atom.
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.
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.