Editing Electron mobility (section)

===Relation to electron diffusion===
In a region where n and p vary with distance, a diffusion current is superimposed on that due to conductivity. This diffusion current is governed by [[Fick's law]]:
<math display="block">F=-D_\text{e}\nabla n</math>
where:
*''F'' is flux.
*''D''<sub>e</sub> is the [[diffusion coefficient]] or diffusivity
*<math>\nabla n</math> is the concentration gradient of electrons

The diffusion coefficient for a charge carrier is related to its mobility by the [[Einstein relation (kinetic theory)|Einstein relation]]. For a classical system (e.g. Boltzmann gas), it reads:
<math display="block">D_\text{e} = \frac{\mu_\text{e} k_\mathrm{B} T}{e}</math>
where:
*''k''<sub>B</sub> is the [[Boltzmann constant]]
*''T'' is the [[absolute temperature]]
*''e'' is the electric charge of an electron

For a metal, described by a Fermi gas (Fermi liquid), quantum version of the Einstein relation should be used. Typically, temperature is much smaller than the Fermi energy, in this case one should use the following formula:
<math display="block">D_\text{e} = \frac{\mu_\text{e} E_F}{e}</math>
where:
*''E''<sub>F</sub> is the Fermi energy