Editing Hall effect (section)

===Hall effect in semiconductors===
When a current-carrying [[semiconductor]] is kept in a magnetic field, the charge carriers of the semiconductor experience a force in a direction perpendicular to both the magnetic field and the current. At equilibrium, a voltage appears at the semiconductor edges.

The simple formula for the Hall coefficient given above is usually a good explanation when conduction is dominated by a single [[charge carrier]]. However, in semiconductors and many metals the theory is more complex, because in these materials conduction can involve significant, simultaneous contributions from both [[electrons]] and [[Electron hole|holes]], which may be present in different concentrations and have different [[Electron mobility|mobilities]]. For moderate magnetic fields the Hall coefficient is<ref name='Kasap2001'>{{cite web|url=http://mems.caltech.edu/courses/EE40%20Web%20Files/Supplements/02_Hall_Effect_Derivation.pdf |title=Hall Effect in Semiconductors |last=Kasap |first=Safa |archive-url=https://web.archive.org/web/20080821202757/http://mems.caltech.edu/courses/EE40%20Web%20Files/Supplements/02_Hall_Effect_Derivation.pdf |url-status=dead |archive-date=2008-08-21 }}</ref><ref>{{Cite web|url=http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/Hall.html|title=Hall Effect|website=hyperphysics.phy-astr.gsu.edu|access-date=2020-02-13}}</ref><!-- O.V. Emelyanenko, T.S. Lagunova, D.N. Nasledov and G.N. Talakin, Sov. Phys. Sol. Stat. '''7''' 1063 (1965).-->

<math display="block">R_\mathrm{H}=\frac{p\mu_\mathrm{h}^2 - n\mu_\mathrm{e}^2}{e(p\mu_\mathrm{h} + n\mu_\mathrm{e})^2}</math>
or equivalently
<math display="block">R_\mathrm{H}=\frac{p-nb^2}{e(p+nb)^2}</math>
with
<math display="block">b=\frac{\mu_\mathrm{e}}{\mu_\mathrm{h}}.</math>
Here {{math|''n''}} is the electron concentration, {{math|''p''}} the hole concentration, {{math|''μ''<sub>e</sub>}} the electron mobility, {{math|''μ''<sub>h</sub>}} the hole mobility and {{math|''e''}} the elementary charge.

For large applied fields the simpler expression analogous to that for a single carrier type holds.