In understanding the behavior of semiconductors, I'm coming across a description of the Fermi Energy here and at Wikipedia's page (Fermi Energy, Fermi Level). If I understand correctly, the Fermi Level refers to the energy state at which there's a 50% chance of finding an electron. This varies with temperature. The Fermi Energy is the highest occupied energy state of fermions at absolute zero.
I'm a little confused as to the relation of the two terms. Additionally, in a semiconductor, the Fermi Energy falls between the valence band and the conduction band. However, my understanding is that electrons cannot exist between the two bands -- so why isn't the Fermi Energy the top of the valence band?