Semiconductor Band Gap: Fermi Momentum & Dispersion Relation

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SUMMARY

The discussion centers on the relationship between the band gap in semiconductors and Fermi momentum, specifically addressing the implications of Fermi energy (E_F) in the dispersion relation. It is established that if E_F is within the band gap, there is no solution for the corresponding Fermi momentum (k_F). The conversation highlights that summing all k values in a full band results in zero net momentum, indicating that full bands do not contribute to electrical conduction. At absolute zero (T=0), the absence of electrons in the conduction band further confirms the lack of net momentum.

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andrewm
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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?
 
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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
 

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