Forbidden Electron Energies in Band Theory of Solids

[hokhani]

In band theory of solids, when an electron's wave vector lies at the first brillouin zone border, it satisfies the bragg condition and there is some forbidden region for that wave vector. I like to know what happens for such these electrons that they can not have some energies in the forbidden region? are they scattered out of crystal? or are they lose their energy?

 

[DrDu]

At the Brillouin zone, a wave with wavevector k can interfere with the scattered wave with wavevector -k. Instead of solutions exp (ikx) and exp (-ikx) one has to consider cos(kx) and sin(kx). This interference either lowers or rises the energy depending on whether the resulting density maxima of the sin and cos, respectively, coincide with the minima or maxima of the crystal potential.

 

[hokhani]

By this you mean that an electron with wave vector at brillouin zone edge has standing wave function and hence has no role in conduction?

 

[DrDu]

By this you mean that an electron with wave vector at brillouin zone edge has standing wave function and hence has no role in conduction?

Yes, entirely correct. Another argument is the following: As dE/dk is the group velocity, and the energy has either a minimum or maximum at the Brillouin zone, the group velocity vanishes there.

 

[hokhani]

Band gap and diffraction

Is there any relations between band gap and Bragg's reflection?