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The number density (symbol: n or ρ N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number density, two-dimensional areal number density, or one-dimensional linear number density.
In quantum chemical calculations, the electron density, ρ(r), is a function of the coordinates r, defined so ρ(r)dr is the number of electrons in a small volume dr. For closed-shell molecules, ρ ( r ) {\displaystyle \rho (\mathbf {r} )} can be written in terms of a sum of products of basis functions, φ:
The carrier density is important for semiconductors, where it is an important quantity for the process of chemical doping. Using band theory, the electron density, is number of electrons per unit volume in the conduction band. For holes, is the
where is the current density, is the external electric field, is the electronic density (number of electrons/volume), is the mean free time and is the electron electric charge. Other quantities that remain the same under the free electron model as under Drude's are the AC susceptibility, the plasma frequency , the magnetoresistance , and the ...
Under the free electron model, the electrons in a metal can be considered to form a uniform Fermi gas. The number density / of conduction electrons in metals ranges between approximately 10 28 and 10 29 electrons per m 3, which is also the typical density of atoms in
The formula for evaluating the drift velocity of charge carriers in a material of constant cross-sectional area is given by: [1] =, where u is the drift velocity of electrons, j is the current density flowing through the material, n is the charge-carrier number density, and q is the charge on the charge-carrier.
The density of electrons in the material is simply the integral of the Fermi–Dirac distribution times the density of states: / = () Although there are an infinite number of bands and thus an infinite number of states, there are only a finite number of electrons to place in these bands.
TEC is the total number of electrons integrated between two points, along a tube of one meter squared cross section, i.e., the electron columnar number density. It is often reported in multiples of the so-called TEC unit, defined as TECU=10 16 el/m 2 ≈ 1.66 × 10 −8 mol⋅m −2. [1]