Fermi-Dirac statistics

Fermi-Dirac statistics is a branch of quantum statistics. It is named after Enrico Fermi and Paul Dirac. It is used to describe the macroscopic state of a system which is made of many simliar particles (Fermions). One example is to describe the state of electrons in metals and semimetals, to describe electrical conductivity.

Fermi-Dirac statistics makes the following assumptions:

• None of the states of the particles can hold more than one particle (known as Pauli exclusion principle)
• Exchanging a particle for another similar particle will not lead to a new state, but will give the same state (known as Identical particles)

The Fermi distribution tells with what probability, a Fermi gas, at a given temperature and energy level, will have a particle in the given state.

Fermi-Dirac Statistics Media

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  Comparison of average occupancy of the ground state for three statistics

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  Fermi function F(\varepsilon) with μ = 0.55 eV for various temperatures in the range 50 K ≤ T ≤ 375 K

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  Energy dependence. More gradual at higher T. \bar{n} = 0.5 when \varepsilon = \mu. Not shown is that \mu decreases for higher T.

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  Temperature dependence for \varepsilon > \mu.