Semiconductor Band Gap: Fermi Momentum & Dispersion Relation

[andrewm]

In the first diagram on http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html" , the band gap in a semiconductor is shown.

What is the corresponding Fermi momentum? If you plug E_F into the dispersion relation, you get no solution for k_F, right?

I ask because an equation is given with a sum of all k such that k < k_F, and there is a band gap. Does one sum over all k?

 

[snapback]

late response ;-)

I do not know which equation you mean, but generally if you sum all k in a full band you end up with zero net momentum. This is the same as saying: a full band is not contributing to electrical conduction. In the bandgap, there are no electrons thus there is no contribution to the total momentum. At T=0, there are no elevtrons in the conduction band, so also no net momentum there

as far as I can see it, you can only use the concept of the Fermi momentum if the Fermi energy is at least few kT inside a band. This is the situation, you mya encounterin metals or degenerated (=very heavily doped) semiconductors

cheers