What Determines the Fermi Level of Semiconductors?

[LayMuon]

Hi Guys, I read that the Fermi level of semiconductor, like germanium, is in-between the completely occupied upper band and conduction band, i.e. right in the gap. Why is that? shouldn't it have beed exactly the highest occupied level ?

 

[Simon Bridge]

Only for low temperatures, and only if there are no impurities.
The band theory of solids is a bunch of rules so you don't have to deal with the fine details of the potential and the impact of the impurities.

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html