Editing Free electron model (section)

=== Fermi level ===
The [[chemical potential]] <math>\mu</math> of electrons in a solid is also known as the [[Fermi level]] and, like the related [[Fermi energy]], often denoted <math>E_{\rm F}</math>. The [[Sommerfeld expansion]] can be used to calculate the Fermi level (<math>T>0</math>) at higher temperatures as:<ref group="Ashcroft & Mermin">{{Harvnb|Ashcroft|Mermin|1976|pp=45-48}}</ref>
:<math>E_{\rm F}(T) = E_{\rm F}(T=0) \left[1 - \frac{\pi ^2}{12} \left(\frac{T}{T_{\rm F}}\right) ^2 - \frac{\pi^4}{80} \left(\frac{T}{T_{\rm F}}\right)^4 + \cdots \right], </math>

where <math>T</math> is the temperature and we define <math display="inline">T_{\rm F} = E_{\rm F}/k_{\rm B}</math> as the [[Fermi temperature]] (<math>k_{\rm B}</math> is [[Boltzmann constant]]). The perturbative approach is justified as the Fermi temperature is usually of about 10<sup>5</sup> K for a metal, hence at room temperature or lower the Fermi energy <math>E_{\rm F}(T=0)</math> and the chemical potential <math>E_{\rm F}(T>0)</math> are practically equivalent.