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Electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typically denoted as either ρ ( r ) {\displaystyle \rho ({\textbf {r}})} or n ( r ) {\displaystyle n ...
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.
All quantities are in Gaussian units except energy and temperature which are in electronvolts.For the sake of simplicity, a single ionic species is assumed. The ion mass is expressed in units of the proton mass, = / and the ion charge in units of the elementary charge, = / (in the case of a fully ionized atom, equals to the respective atomic number).
where c is the speed of light and ε 0 the vacuum permittivity, =, e and m e the electron charge and rest mass respectively. Stopping Power of Aluminum for Protons versus proton energy, and the Bethe formula without (red) and with corrections (blue) Here, the electron density of the material can be calculated by
where is the number density of electrons, is the electric charge, is the effective mass of the electron, and is the permittivity of free space. Note that the above formula is derived under the approximation that the ion mass is infinite. This is generally a good approximation, as the electrons are so much lighter than ions.
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m −3), at any point in a volume.
where D is the diffusion coefficient for the electron in the considered medium, n is the number of electrons per unit volume (i.e. number density), q is the magnitude of charge of an electron, μ is electron mobility in the medium, and E = −dΦ/dx (Φ potential difference) is the electric field as the potential gradient of the electric potential.
The number density of the electron gas was assumed to be =, where Z is the effective number of de-localized electrons per ion, for which Drude used the valence number, A is the atomic mass per mole, [Ashcroft & Mermin 10] is the mass density (mass per unit volume) [Ashcroft & Mermin 10] of the "ions", and N A is the Avogadro constant.