Free electron model

As Sommerfeld theory (after Arnold Sommerfeld) is referred to in solid state physics that theory, which describes the conduction electrons in a metal as a Fermi gas. Sommerfeld she worked from 1933 and thus improved the Drude theory, which had considered the conduction electrons as a classical ideal gas.

In a Fermi gas can because of the Pauli principle does not accept the same impulse, the individual particles. At temperatures very close to zero Kelvin the electrons therefore fill a sphere in momentum space. The radius of this sphere is the Fermi energy of the corresponding pulse. The influence of the grid of the ions is taken into account that one expects instead of the true electron mass with the so-called effective mass.

The Sommerfeld theory explains in particular that the electron contribution to the specific heat of a metal compared to the contribution of the ions can be neglected, so that the experimentally found Dulong - Petit law of the specific heat monatomic solid is considered. The Drude theory, however, is inconsistent with this Act.

The Sommerfeld theory also explains that the electronic contribution to the specific heat increases proportionally to the temperature. It also gives the correct value of the proportionality constant in the Wiedemann - Franz law and the magnitude of the thermoelectric power of the Seebeck effect.