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I am currently studying Introductory Semiconductor Device Physics by Parker. Chapter 2.5 The concept of effective mass says the following:

Figure 2.8 shows two hypothetical energy-momentum diagrams for an indirect and a direct band-gap semiconductor. We can gain a lot of information about the hypothetical semiconductor materials these diagrams depict from what we have just covered. Look at Figure 2.8(a) first, the indirect band-gap material. The first thing we note is that there is a maximum in the valence band curve at $k = 0$, and a minimum in the conduction band curve at a different $k$ value. If an electron sitting near the conduction band minimum (where its energy is the lowest) is to recombine with a hole sitting near the valence band maximum, then the electron must lose some momentum (change its $k$ value) in making this transition. In order for the electron to change its momentum another particle must be involved for energy and momentum conservation. This 'particle' is called a phonon and it is in fact just a lattice vibration. At any finite temperature the lattice atoms will be vibrating about their mean positions and these vibrations lead to the propagation of vibrational waves, phonons, throughout the crystal. The momentum change required for the electron to recombine with the hole in the indirect band-gap semiconductor comes from the interaction of the electron with a phonon.

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My question relates to this part:

At any finite temperature the lattice atoms will be vibrating about their mean positions and these vibrations lead to the propagation of vibrational waves, phonons, throughout the crystal. The momentum change required for the electron to recombine with the hole in the indirect band-gap semiconductor comes from the interaction of the electron with a phonon.

Here, the author depicts vibrational waves as something that is just being propagated randomly all the time, due to the constant vibrations of the lattice atoms. But this doesn't really explain the process for how the electron and phonon interact for recombination to occur.

So how exactly do the electron and phonon interact for the process of recombination to occur? I would greatly appreciate it if people would please take the time to explain this.


EDIT

I found PM2RING's comment helpful:

Does this help? physics.stackexchange.com/q/240514/123208 Also see physics.stackexchange.com/q/78442/123208 & physics.stackexchange.com/q/280678/123208 The answers to those two questions mostly require a fair amount of familiarity with quantum mechanics, but you can just skim over the stuff that's too technical. ;)

So, to put it in rudimentary terms, would it be accurate to say that electrons and phonons interact by the phonon "wave" essentially transferring its energy/momentum (in the indirect band-gap case, since the phonon possess such small amounts of energy compared to the photon (at least, in GaAs), it seems that the transfer of momentum is of primary relevance) to the electron, as it propagates throughout the crystal (through the ions in the crystal)?

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    $\begingroup$ Does this help? physics.stackexchange.com/q/240514/123208 Also see physics.stackexchange.com/q/78442/123208 & physics.stackexchange.com/q/280678/123208 The answers to those two questions mostly require a fair amount of familiarity with quantum mechanics, but you can just skim over the stuff that's too technical. ;) $\endgroup$ – PM 2Ring Jun 10 '20 at 3:45
  • $\begingroup$ @PM2Ring That helps a lot. So, to put it in rudimentary terms, would it be accurate to say that electrons and phonons interact by the phonon "wave" essentially transferring its energy/momentum to the electron, as it propagates throughout the crystal (through the ions in the crystal)? $\endgroup$ – The Pointer Jun 10 '20 at 15:46
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A rigorous theory tells you how exactly it occurs. The rest is a qualiataitve picture.

P.S. It happens not instantly, but it takes a time - for the frequency (energy) to be a meaningful quantity.

Lack of time make the pictue flue.

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