Electron - Phonon scattering, deriving the contribution to

In summary, the conversation discussed electron-phonon scattering and its contribution to electron transport. The equations used involved trigonometry and it was mentioned that the approximation of ΔKF being small and the angle, φ, being small enough for cos(φ) to be approximately 1 were important factors. It was also noted that ΔKF is a difference in magnitudes of vectors rather than the magnitude of the vector difference.
  • #1
rwooduk
762
59
... electron transport.

1. Homework Statement
Electron - Phonon scattering, derive the contribution to electron transport.

Homework Equations


Trig.

The Attempt at a Solution


Am I being REALLY stupid here, I can't see how the equation matches the triangle.

cUQmj9G.jpg


If you resolve KF' doesn't KF' cos theta= KF

The only thing I can think is that it's an approximation and delta KF is very small?
Thanks for any help
 
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  • #2
rwooduk said:
... electron transport.

1. Homework Statement
Electron - Phonon scattering, derive the contribution to electron transport.

Homework Equations


Trig.

The Attempt at a Solution


Am I being REALLY stupid here, I can't see how the equation matches the triangle.

cUQmj9G.jpg


If you resolve KF' doesn't KF' cos theta= KF

The only thing I can think is that it's an approximation and delta KF is very small?
Thanks for any help
Yes, I think you're right about ΔKF needing to be small. Also, I think φ needs to be small enough so that cos(φ) ≈ 1 , while (1 - cos(φ) ) can't be ignored.

It looks to me like ΔKF is just a difference in magnitudes of the vectors and not the magnitude of the vector difference.
 
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  • #3
SammyS said:
Yes, I think you're right about ΔKF needing to be small. Also, I think φ needs to be small enough so that cos(φ) ≈ 1 , while (1 - cos(φ) ) can't be ignored.

It looks to me like ΔKF is just a difference in magnitudes of the vectors and not the magnitude of the vector difference.

Thanks very muvh for the reply.
 

1. What is Electron-Phonon Scattering?

Electron-Phonon Scattering is a phenomenon in which electrons interact with phonons (vibrational energy packets) in a solid material, resulting in the transfer of energy and momentum between the two particles.

2. Why is Electron-Phonon Scattering important?

Electron-Phonon Scattering is an important process in understanding the behavior of electrons in solid materials. It plays a crucial role in the transport of heat and electricity, as well as in the optical and thermal properties of materials.

3. How is the contribution to Electron-Phonon Scattering derived?

The contribution to Electron-Phonon Scattering can be derived using mathematical equations and theoretical models, taking into account factors such as the density of states, electron-phonon coupling strength, and the energy and momentum conservation rules.

4. What factors affect the contribution to Electron-Phonon Scattering?

The contribution to Electron-Phonon Scattering is affected by various factors, including the temperature, the type of material, the strength of electron-phonon coupling, and the energy and momentum of the interacting particles.

5. How does Electron-Phonon Scattering impact the properties of materials?

Electron-Phonon Scattering can significantly impact the properties of materials by influencing their electrical conductivity, thermal conductivity, and optical and thermal properties. It also plays a crucial role in the performance of electronic devices and can affect the overall efficiency and reliability of energy conversion processes in materials.

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