How Do Phonon-Related IR-Absorption Processes Differ Between Ge and GaAs?

[Tapasito]

Homework Statement

Discuss the difference between phonon related ir-absorption processes in Ge and GaAs. For instance, excitation of TO-phonon by photon.

Homework Equations

The Attempt at a Solution

I really don't know how I should phrase my answer. Thoughts that I have include:
Since GaAs is polar and Ge isn't, it should have an influence of the absorption process. So perhaps the process is more likely to occur in Ge? For example, you can easily observe two-phonon absorption induced by a photon (k = 0) in Ge, since there is no TO-phonon absorption.
Another attempt could be to reason about the dielectric constant that is higher in Ge, 16.2, compared to GaAs, 12.9. And that the TO-phonon frequencies are higher in Ge.
Am I on my way to get the solution perhaps?

 

[Jhero]

Good start! The difference in polarizability between Ge and GaAs, as indicated by their dielectric constants, does indeed play a role in their phonon-related ir-absorption processes.

One key difference between Ge and GaAs is their crystal structure. Ge has a diamond structure, while GaAs has a zincblende structure. This results in different phonon modes and frequencies for each material. In Ge, the TO-phonon frequency is higher compared to GaAs, which makes it more likely to be excited by a photon.

Additionally, the strength of the electron-phonon coupling in each material can also affect the absorption process. In Ge, the electron-phonon coupling is stronger, which leads to a higher absorption coefficient compared to GaAs.

Another important factor to consider is the band structure of each material. In Ge, the conduction band minimum and valence band maximum are located at different points in the Brillouin zone, resulting in a larger energy difference between them. This means that the energy of the photon must be closer to the energy of the TO-phonon in order to excite it. In contrast, in GaAs, the conduction band minimum and valence band maximum are located at the same point in the Brillouin zone, resulting in a smaller energy difference and making it easier to excite the TO-phonon.

Overall, the combination of crystal structure, phonon frequencies, electron-phonon coupling, and band structure all contribute to the differences in phonon-related ir-absorption processes between Ge and GaAs.