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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 over the whole material.
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 ...
Copper has one free electron per atom, so n is equal to 8.5 × 10 28 electrons per cubic metre. Assume a current I = 1 ampere, and a wire of 2 mm diameter (radius = 0.001 m). This wire has a cross sectional area A of π × (0.001 m) 2 = 3.14 × 10 −6 m 2 = 3.14 mm 2. The elementary charge of an electron is e = −1.6 × 10 −19 C.
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.
The maximum possible current density of copper in open air is approximately 3.1 × 10 6 A/m 2, above which it begins to heat excessively. [17] Copper is one of a few metallic elements with a natural color other than gray or silver. [18] Pure copper is orange-red and acquires a reddish tarnish when exposed to air.
Then the electron mobility μ is defined as =. Electron mobility is almost always specified in units of cm 2 /(V⋅s). This is different from the SI unit of mobility, m 2 /(V⋅s). They are related by 1 m 2 /(V⋅s) = 10 4 cm 2 /(V⋅s). Conductivity is proportional to the product of mobility and carrier concentration. For example, the same ...
Spin density is electron density applied to free radicals. It is defined as the total electron density of electrons of one spin minus the total electron density of the electrons of the other spin. One of the ways to measure it experimentally is by electron spin resonance, [14] neutron diffraction allows direct mapping of the spin density in 3D ...
The arrows indicate the direction of the electric field E and the electric current density j. Qualitatively, this relationship is based upon the fact that the heat and electrical transport both involve the free electrons in the metal. The mathematical expression of the law can be derived as following.