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The Fermi energy is an energy difference (usually corresponding to a kinetic energy), whereas the Fermi level is a total energy level including kinetic energy and potential energy. The Fermi energy can only be defined for non-interacting fermions (where the potential energy or band edge is a static, well defined quantity), whereas the Fermi ...
In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied electron states from unoccupied electron states at zero temperature. [1] The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic energy bands .
The surface energy of a liquid may be measured by stretching a liquid membrane (which increases the surface area and hence the surface energy). In that case, in order to increase the surface area of a mass of liquid by an amount, δA, a quantity of work, γ δA, is needed (where γ is the surface energy density of the liquid).
The Fermi level does not necessarily correspond to an actual energy level (in an insulator the Fermi level lies in the band gap), nor does it require the existence of a band structure. Nonetheless, the Fermi level is a precisely defined thermodynamic quantity, and differences in Fermi level can be measured simply with a voltmeter .
where E V is the maximum energy of the valence band. Practically, this effective mass tends to vary greatly between absolute zero and room temperature in many materials (e.g., a factor of two in silicon), as there are multiple valence bands with distinct and significantly non-parabolic character, all peaking near the same energy. [8]
The Pomeranchuk instability is an instability in the shape of the Fermi surface of a material with interacting fermions, causing Landau’s Fermi liquid theory to break down. It occurs when a Landau parameter in Fermi liquid theory has a sufficiently negative value, causing deformations of the Fermi surface to be energetically favourable.
The Fermi energy surface in reciprocal space is known as the Fermi surface. The nearly free electron model adapts the Fermi gas model to consider the crystal structure of metals and semiconductors , where electrons in a crystal lattice are substituted by Bloch electrons with a corresponding crystal momentum .
This energy may be decomposed into a kinetic energy T part and the potential energy −eφ part. Since the chemical potential is kept constant, = = If the temperature is extremely low, the behavior of the electrons comes close to the quantum mechanical model of a Fermi gas.