How about the energy of crystal in a direct transition?

Click For Summary

Discussion Overview

The discussion revolves around the energy and momentum changes in a crystal during a direct transition when a photon is absorbed by an electron. Participants explore the implications of momentum conservation and energy transfer between the electron and the crystal, considering theoretical models and assumptions related to the behavior of conduction and valence bands in solids.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions why the energy of the crystal is not considered when a photon is absorbed, suggesting that the crystal gains momentum alongside the electron.
  • Another participant asks about the energy change of a crystal with infinite mass when its momentum changes by a finite amount.
  • A different viewpoint proposes that if conduction and valence bands are parabolic, the conservation of kinetic energy implies that the photon energy should equal the sum of the changes in kinetic energy of both the electron and the crystal.
  • In response, a participant clarifies that while the crystal's momentum changes, its energy approaches zero in the limit of infinite mass, indicating that the crystal's role is significant for momentum conservation but not for energy conservation.

Areas of Agreement / Disagreement

Participants express differing views on the role of the crystal's energy in the absorption process, with some arguing for its significance and others asserting that it is negligible due to the mass considerations. The discussion remains unresolved regarding the implications of these perspectives.

Contextual Notes

Participants rely on assumptions about the parabolic nature of conduction and valence bands and the implications of infinite mass on energy conservation, which may not be universally accepted or applicable in all contexts.

hokhani
Messages
601
Reaction score
22
When a photon is absorbed by an electron through a direct transition in a crystal, the crystal momentum of electron would not approximately change. Therefore momentum change of electron would neutralize momentum change of crystal. In other words, the crystal would gain momentum as well as electron. But why we don't consider the energy of crystal in this process (we consider all the absorbed energy only as energy of electron transition)?
 
Physics news on Phys.org
How big is the energy change of a crystal of mass ##M \to \infty## if its momentum changes by ##\Delta P##?
 
Suppose conduction and valence bands are parabolic with the same curvature. If we were to consider the conservation of kinetic energy before and after absorption, the photon energy must be equal to " change of electron's kinetic energy + change of crystal's kinetic energy). According to our supposition electron velocity and hence it's kinetic energy doesn't change so the change of crystal's kinetic energy is equal to the photon energy. Therefore all the photon energy is transferred into kinetic energy of crystal! Could you please help me?
 
No, what I mean is that the crystal's momentum changes from 0 to P and its energy from 0 to ##E=P^2/2M##. If P is finite, E becomes 0 in the limit of infinite mass of the crystal.
So the crystal takes care of the conservation of true momentum, but is irrelevant for energy conservation.
 
  • Like
Likes   Reactions: 1 person

Similar threads

  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 19 ·
Replies
19
Views
4K
  • · Replies 3 ·
Replies
3
Views
5K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
37
Views
7K