Forbidden Electron Energies in Band Theory of Solids

In summary, the conversation discusses the band theory of solids and how electrons with wave vectors at the first Brillouin zone border satisfy the Bragg condition and have a forbidden region for their energy. It is mentioned that at the Brillouin zone, interference between waves with opposite wave vectors can either lower or raise the energy. It is also noted that an electron with a wave vector at the Brillouin zone edge has a standing wave function and therefore does not contribute to conduction. Finally, the connection between band gap and Bragg's reflection is briefly mentioned.
  • #1
hokhani
483
8
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?
 
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  • #2
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.
 
  • #3
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?
 
  • #4
hokhani said:
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.
 
  • #5
Band gap and diffraction

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

Related to Forbidden Electron Energies in Band Theory of Solids

1. What are forbidden electron energies in band theory?

Forbidden electron energies, also known as band gaps, are energy levels within a solid material that are not occupied by electrons. These energy levels act as barriers, preventing the electrons from moving freely through the solid.

2. How are forbidden electron energies determined in band theory?

Forbidden electron energies are determined by the arrangement of atoms in a solid material. The energy levels are created by the interactions between the atoms and their surrounding electrons, resulting in energy bands that are either occupied or unoccupied by electrons.

3. What are the implications of forbidden electron energies in band theory?

The presence of forbidden electron energies in a material can affect its electrical and optical properties. Materials with larger band gaps are typically insulators, while those with smaller or no band gaps are typically conductors.

4. Can forbidden electron energies be manipulated or controlled?

Yes, forbidden electron energies can be manipulated through various methods such as doping, applying external electric fields, or altering the material's composition. These techniques can change the band gap and thus, the electrical conductivity of the material.

5. How does band theory of solids explain the behavior of forbidden electron energies?

According to band theory, electrons in a solid material exist in energy bands that are separated by forbidden energy levels. This theory explains how the arrangement of atoms and their interactions with electrons determine the material's electrical and optical properties, including the presence of forbidden electron energies.

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