Computing the resistivity due to electron collision with 1BZ

We also know that the resistivity due to electron "collision" with the 1st Brillouin zone boundary changes as a function of the number of valence electrons in a metal. The fermi wavevector also plays a role in this change, as it will eventually get longer and cause more electrons to interact with the Brillouin zone boundary. In summary, the resistivity in a solid changes as the number of valence electrons increases, due to the longer fermi wavevector and increased interaction with the Brillouin zone boundary. However, calculating the exact change in resistivity is complex and depends on various factors such as temperature and impurity concentration.
  • #1
Jonsson
79
0
Hello there,

Id like to estimate how the resistivity due to electron 'collision' with 1st Brillouin zone changes as a function of number of valence electrons in a metal.

Say you start with Na, then add some other material with 2 valence electrons instead of 1, then the fermi wavevector will eventually get so long that it there will be electrons interacting with the Brillouin zone boundary.

How does the resistivity change as a function of number of valence electrons in such a solid?

Thank you for your time.

Kind regards,
Marius
 
  • #3
The calculation of the resistivity is a highly non-trivial task. Also, resistivity depends very strongly on temperature (especially in very pure samples and at low temperatures) and on the concentration of impurities.
 

1. What is the 1BZ in the context of computing resistivity?

The 1BZ, or first Brillouin zone, is a concept in solid state physics that represents the set of all possible momentum states for an electron in a crystal lattice. In the context of computing resistivity, it is used to calculate the scattering rate of electrons due to collisions within the crystal lattice.

2. How does electron collision affect resistivity?

Electron collision with the crystal lattice results in a scattering of the electrons, which in turn increases the resistance of the material. This is because the collisions disrupt the flow of electrons, making it more difficult for them to pass through the material and increasing the overall resistivity.

3. What factors affect the resistivity due to electron collision in the 1BZ?

The resistivity due to electron collision in the 1BZ is affected by several factors, including the density of the crystal lattice, the strength of the electron-phonon interaction, and the temperature of the material. These factors can all impact the scattering rate of electrons and therefore influence the resistivity.

4. How is the resistivity due to electron collision in the 1BZ calculated?

The resistivity due to electron collision in the 1BZ can be calculated using the Matthiessen's rule, which takes into account the different scattering mechanisms in the material. It involves summing the individual resistivities due to each scattering mechanism, including electron-phonon, impurity, and defect scattering.

5. What applications does understanding the resistivity due to electron collision in the 1BZ have?

Understanding the resistivity due to electron collision in the 1BZ is important in various fields, such as materials science, semiconductor device design, and condensed matter physics. It can also have practical applications in the development of new materials with desired electrical properties, as well as in improving the performance of electronic devices.

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