# Electrons close to Fermi-Conductivity

As a student of electrical and computer engineering solid state physics is not my thing so I might have fundamental blanks here and there. I really like this course and I try to gain as much as possible from it.

We've started doing a bit on the Fermi level and band theory. Our teacher stated that for a temperature above 0 Kelvin the Fermi-Dirac distribution is no longer a step function(giving 1 for energies lower than Fermi level and 0 for energies above). Now for a given Temperature T1 we have two energy levels E1 ( below Fermi) and E2 (above Fermi) for which f(E1)=0.1 and f(E2)=0.9.

"Only the electrons occupying energy states between E1 and E2 participate in conductivity" I can't find this anywhere online and I can't understand why the higher value electrons (>E2) can't participate since they have greater energy. I could be using the wrong words on Google of course but I haven't had any luck after quite some time. Does this ring any bells?

• Generally, yes, only electrons close to the Fermi energy participate in conduction. But, that is a very complex question involving the band structure, density of states, etc. – Jon Custer Nov 21 '17 at 19:09
• It makes sense but why can't electrons of higher energy than E2 participate? – John Katsantas Nov 21 '17 at 19:13
• Well, they do. The comment seems to be poorly worded at best. In general, one should focus on electrons within ~kT of the Fermi surface, but that is because that is about how wide the Fermi function is. – Jon Custer Nov 21 '17 at 19:18