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The density of states related to volume V and N countable energy levels is defined as: = = (()). Because the smallest allowed change of momentum for a particle in a box of dimension and length is () = (/), the volume-related density of states for continuous energy levels is obtained in the limit as ():= (()), Here, is the spatial dimension of the considered system and the wave vector.
Density of states (DOS) of a Fermi gas in 3-dimensions. For the 3D uniform Fermi gas, with fermions of spin- 1 / 2 , the number of particles as a function of the energy () is obtained by substituting the Fermi energy by a variable energy ():
Van Hove singularity. A Van Hove singularity is a singularity (non-smooth point) in the density of states (DOS) of a crystalline solid. The wavevectors at which Van Hove singularities occur are often referred to as critical points of the Brillouin zone. For three-dimensional crystals, they take the form of kinks (where the density of states is ...
The density of states function g(E) is defined as the number of electronic states per unit volume, per unit energy, for electron energies near E. The density of states function is important for calculations of effects based on band theory.
Free electron model. In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, [1] principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the ...
Effective mass (solid-state physics) In solid state physics, a particle's effective mass (often denoted ) is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement ...
Statistical mechanics. Fermi–Dirac statistics is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac, each ...
Charge carrier density. Charge carrier density, also known as carrier concentration, denotes the number of charge carriers per volume. In SI units, it is measured in m −3. As with any density, in principle it can depend on position. However, usually carrier concentration is given as a single number, and represents the average carrier density ...