What is the relationship between Fermi energy and temperature?

[AriAstronomer]

Hey everyone,
So unfortunately I haven't taken Stat Mech yet (and my GRE is in a week), but through casual reading and forums I've gathered what the concept of fermi temperature and energy is...or thought I did. From what I understand, below the fermi energy (the fermi energy within an atom corresponding to some highest orbital) all orbitals below it are completely filled, and all orbitals above it are completely empty. I assumed however, that this happens at the fermi temperature, which I thought was going to be close to T=0K, but apparently for most elements is like 10,000K? What gives? Also, what's this about below the fermi temperature things get degenerate (as in, more than one electron configuration corresponding to the same energy), but above there is no degeneracy? I was under the impression that at fermi temperature (which I thought was close to 0Kelvin), all electrons fill the lowest possible orbitals without violating the Pauli Exclusion Principle, and then as you raise temperature as things get more energy they gain more freedom and thus degeneracy starts...

The GRE is in a week, any chance someone can resolve this for me?! I'd really appreciate it!

Ari

 

[xiyangxixia]

If Ec-Ef>>0, they are under degerancy. If 0<Ec-Ef<2KT, they are under weak degenerancy. If Ec-Ef>2KT, they are under nondegenerancy. The energy of electron became larger with temperature increase. Many electrons escaped from feimi energy level.

 

[genneth]

Fermi energy is only defined at 0K. At finite temperatures the relevant quantity is the chemical potential; as T -> 0, this converges to the Fermi energy. The Fermi temperature is the scale one gets from converting the Fermi energy (via k_B) to a temperature. The relevance is that the Fermi distribution has a "width" which is of the order of the Fermi energy, and at high temperatures it converges to a classical Boltzmann distribution; so the Fermi temperature sets the scale between quantum effects dominating (things like degeneracy) and being able to treat the fermions as a classical gas.