Regions in the electronic band structure

In summary, the conversation discusses the movement of electrons in different energy valleys in semiconductors. These valleys are energetically degenerate, meaning that while electrons in one valley move in the same direction, overall there is no net current. This is due to the Fermi-Dirac statistics, where most electrons have a high momentum and only on average is their momentum zero. This results in a cancellation of currents, but the net result is 0 A.
  • #1
erst
21
0
I'm thinking mainly within the context of the useful semiconductors here (Si, GaAs, etc.)...

What does it mean for an electron to be in the L or X valley instead of the Gamma valley? If Gamma is the k = 0 point, then momentum p = 0. Does that mean being in L or X means all the electrons there are moving in some particular direction in real space (since k ≠ 0, so p ≠ 0, giving them some non-zero velocity vector). Does that mean that in the indirect bandgap materials like Si, electrons are moving together in some direction even with no applied E-field?
 
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  • #2
There are several L (and X) valleys which are energetically degenerate. Hence while all electrons in one valey move in the same direction, on the average over all valleys, there is no net current.
 
  • #3
Ok, I see. But with just thermal energy, we have large numbers of electrons moving in a direction rather than randomly scattering about. Sure, they're canceled by another set of electrons doing the very same thing in exactly the opposite direction. But this just seems very "unnatural".

Physically in real space (just making up numbers in 1-D), do we have case of 1 A of current being canceled by -1 A, or is the net result of 0 A the only meaningful interpretation?
 
  • #4
Hm, finally this is a consequence of the Fermi-Dirac statistics. At finite density most electrons move at a high momentum whose absolute value is known as the Fermi-momentum. Only on the average the momentum of the electrons is zero.
 

1. What is the electronic band structure?

The electronic band structure refers to the distribution of energy levels or bands that electrons can occupy in a solid material. It is a representation of the allowed energy states of electrons in a material, and it helps to explain the properties and behavior of materials, such as their electrical conductivity and optical properties.

2. What are the different regions in the electronic band structure?

The electronic band structure is typically divided into three regions: the valence band, the conduction band, and the band gap. The valence band is the region of lower energy levels that are occupied by electrons in their ground state. The conduction band is the region of higher energy levels that are not occupied by electrons in their ground state. The band gap is the region between the valence and conduction bands where no electron energy states exist.

3. How do the regions in the electronic band structure affect the properties of a material?

The regions in the electronic band structure have a significant impact on the properties of a material. The valence band determines the material's chemical and physical properties, such as its thermal and electrical conductivity. The conduction band dictates the material's ability to conduct electricity and heat. The size of the band gap affects the material's optical and electronic properties, such as its color and ability to absorb or emit light.

4. Can the electronic band structure be manipulated?

Yes, the electronic band structure can be manipulated through various methods, such as doping, applying external electric or magnetic fields, and changing the composition or structure of the material. These manipulations can alter the band gap, energy levels, and the number of available energy states, resulting in changes in the material's properties.

5. How does the electronic band structure differ between conductors, insulators, and semiconductors?

The electronic band structure differs between conductors, insulators, and semiconductors. In conductors, the valence and conduction bands overlap, allowing electrons to move freely and conduct electricity. Insulators have a large band gap, which makes it difficult for electrons to move, leading to poor conductivity. Semiconductors have a small band gap, allowing some electrons to move, making them intermediate in their ability to conduct electricity.

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