The fermi dirac distribution function given in http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disfd.html is different from what I learnt. What I learnt had the chemical potential $\mu$ in place of $E_F$ . Isn't $\mu$ only equal to $E_F$ when $T = 0$ ? Or am I mixing stuff up?
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In solid state physics, especially in the subfield of electronic devices, it is not uncommon to use Fermi energy as a synonym of chemical potential. Some texts explicitly disclose this possible source of confusion and misusage of the term Fermi energy, others do not.