[Encyclios]

Electron distribution in a band according to fermi-dirac statistics

When the Fermi level corresponds to a permitted band, this band is only partially occupied and therefore, by applying a potential difference, an electric current is produced and the solid is a conductor. In insulators, instead, the Fermi level is a forbidden band.

At 0 K the allowed bands below this level are completely occupied and the upper ones are completely empty; therefore, in no case, electric current is produced. At temperatures other than 0 K, due to thermal agitation, some electrons may jump into a permitted band, but the energy required is high and the probability of such a jump occurring is low; therefore, in each case, the corresponding electric current is very weak.

When the forbidden band containing the Fermi level is very narrow this probability is greater and the corresponding current can appreciate. The types of solids that fall into this pattern are called intrinsic semiconductors.