I have gotten myself confused about the band structure explanation of semi-conductors vs insulators. The Wikipedia picture
and the explanation surrounding it seem to suggest that Fermi Level is a property of the material. I understand how Fermi-Energy is a property of the material: it is the highest energy occupied by an electron at zero temperature. But Fermi level as shown in the picture doesn't make sense to me as there is nothing special about that level intrinsically for semi-conductors and insulators. Furthermore, there is no state there to occupy.
If I think of Fermi-Level as the external voltage (or chemical potential in the grand canonical ensemble) the pictures make sense but then its not an intrinsic property of the material (which is not the way its usually stated) and in that case I also do not see the difference between a semi-conductor and an insulator.