Fermi Level


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Fermi level

[′fer·mē ‚lev·əl]
(statistical mechanics)
The energy level at which the Fermi-Dirac distribution function of an assembly of fermions is equal to one-half. Also known as Fermi energy.

Fermi Level

 

the energy level below which all energy states of the particles of a degenerate gas that obey Fermi-Dirac statistics are occupied at a temperature of absolute zero (seeSTATISTICAL MECHANICS). Particles of a degenerate gas that obey Fermi-Dirac statistics are called fermions. The existence of the Fermi level is a consequence of the Pauli exclusion principle, according to which not more than (2s + 1) particles, where s is the spin of a particle, may occupy a state with a specified momentum p. The Fermi level coincides with the values of the chemical potential of a fermion gas at T = 0°K.

The Fermi level ℰF can be expressed in terms of the number n of gas particles per unit volume: ℰF = [(2πℏ)2/2m] [3n/4π(2s + 1)], where m is the particle mass. The quantity Fermi Level is called the Fermi momentum. At T = 0°K, the particles occupy all states with momenta p < pF; all states with p > pF are empty. In other words, at T = 0°K, fermions occupy states in momentum space that lie within a sphere p2 = 2mF of radius pF; this sphere is called the Fermi sphere. Upon heating, some particles move from a state with p < pF to a state with p > pF. Vacant sites, called holes, occur within the Fermi sphere. The quantity Fermi Level is called the Fermi velocity and specifies the upper limit to the velocities of fermions at T = 0°K.

A degenerate gas consisting of conduction electrons in a solid at T = 0°K occupies surfaces of more complex shape in momentum space (see).

REFERENCE

Landau, L. D., and E. M. Lifshits. Statisticheskaia fizika, 2nd ed. Moscow, 1964. (Teoreticheskaia fizika, vol. 5.)

M. I. KAGANOV

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