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In solid state physics the term electron gas refers to a conceptual model for the free electrons in the conduction band of metals or semiconductors. Under this model, the free electrons to be understood as a base for the conductivity of metals, and the electrical resistance is characterized by the scattering of electrons, and phonons of crystal defects. The electron gas is a gas in the chemical sense.

Delocalized electrons

Electrons in the conduction band are delocalized, which means that they can be assigned to any particular lattice atom, as is the case in chemical compounds. In other words, an electron to each lattice atom has such a non-zero probability, and is therefore distributed over the whole crystal. A free, non- interacting electron has a (kinetic ) energy E and a ( quantum mechanical ) wave vector. Both depend on the so-called dispersion relation

Together. Relations of this type determine the band structure in the wave vector space. The described so-called free electron gas (with a parabolic band ) is only a simple model for the description of the electron in the conduction band. In more complex models (for example, approximation of a quasi- free electron or tight-binding model) describing the reality better the periodic potential of the crystal is taken into consideration, which leads to complex band structures. However, this can be described in a first approximation by the above parabolic dispersion, if for m is the effective mass of each band is set.

Since electrons are fermions, no two electrons can agree on all quantum numbers. Thus, the energy levels at temperature T = 0 K of (zero point energy) ago are filled to the so-called Fermi energy. The distribution of energy is described by the Fermi -Dirac statistics, which is at T> 0 K at the " Fermi surface " in a region of width ~ 2 kT softened.

Degenerate electron gas

Is referred to as a degenerate electron gas when the ( largely independent of temperature ), the Fermi energy EF of the electrons in a potential well is much larger than the absolute temperature T, multiplied by the Boltzmann constant KB:

In particular, each electron gas is degenerate at T → 0 K. The term has degenerated to understand so that almost all states have the same probability of being occupied. The distribution function is a (compared to the Fermi level ) large area constant.

Numerical examples:

For the conduction electrons in copper ( at room temperature).

For the electrons in the center of white dwarfs ( despite high temperature).

For the electrons in the center of the sun, the ratio is against: (ie non- degenerate ).

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