Question

Can the electrons be above the Fermi level(in a band gap)?

Answer 1

From the little I understood the Fermi function gives the probability to find an electron at a specific energy level. At temperature above 0 Kelvin f(E) is as shown above, meaning that there is a chance of finding an electron at an energy level in the gap. But then the website states that electrons can't occupy any state in the gap. If that is true the probability would be zero.