In all of the textbooks, the Fermi Energy was interpreted as the energy level below which all possible energy states are filled. However with a Fermi-Dirac type of distribution, which has asymptotes at both edges why would there even be any such energy level which restricts energy levels higher than itself?, does then the idea of Fermi energy make sense only at zero temperature?
Also, there is a confusion between the idea of chemical potential and the Fermi energy at temperature other than zero.
