Electrons close to Fermi-Conductivity

Question

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?

user137289 · Answer

The statement is true in some sense, but it is not very useful. It might lead people to expect that conductivity would decrease at lower temperature, which is wrong.

I believe that it is much better to say that all valence electrons participate in conduction. This gives the right drift velocity of electrons (as can be measured by the Hall effect). It also leads to the number of conduction electrons being independent of temperature. The model to explain this picture is that the whole Fermi sphere is displaced by an applied electric field.

The figure shows how the electron velocities are randomly distributed in all directions creating a sphere in velocity space up to the Fermi velocity. When an electric field is applied, the only states that change in occupancy are near the surface of the sphere, but the effect is that the whole sphere gets displaced by the average velocity $v_{rm drift}$.

For more detail see for example here: http://what-when-how.com/electronic-properties-of-materials/electrical-conduction-in-metals-and-alloys-electrical-properties-of-materials-part-1/

Electrons close to Fermi-Conductivity

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