Question

How can the Fermi level be in between the band-gaps?

Answer 1

I agree with the above. The band gap of a semiconductor is the energy difference between the valence band and the conduction band edges of inorganic materials (or between the HOMO and LUMO of an organic semiconductor). You can estimate the (optical) bandgap of a semiconductor by using optical absorption measurements (from the absorption edge or, more accurately, from the tauc plot). The Fermi level is an energetic level usually located within the band gap of the material which represents the maximum energy occupied with electrons at absolute zero temperature. The position of the Fermi level is a criterion for the type of the semiconductor e.g., when it is near the conduction band edge you have a n-type semiconductor. You can estimate the position of the  Fermi level by measuring the work function which is the energy difference between the fermi and the vacuum level. To measure the work function you need to perform ultra violet photoemission spectroscopy measurements.

Answer 2

Explanation:

In a nutshell, in any system the density of free holes in the valence band and electron is conduction band defines the fermi level. The fermi level for semiconductors is always between the two bands, its exact position determined by doping concent