Trying to understand the Inelastic Transmission Spectrum Analyzer

[weixiang]

Dear Quantumwise experts,
I am trying to under the  Inelastic Transmission Spectrum Analyzing result in this tutorial page https://docs.quantumwise.com/tutorials/inelastic_current_in_si_pn_junction/inelastic_current_in_si_pn_junction.html.
(1)Particularly,  in the following left figure, it shows " that the phonon that contributes the most to the current is that with index 66, and energy ℏω=63.01meV."
Since the analysis is conducted at the Γ point, does this means that this phonon mode corresponds to the red-circled point in the right figure of the phonon band structure of Si? Which is roughly of the same energy.

(2) In addition, in the phonon band structure, I can see that at the Γpoint there are only two possible energy for phonons to occupy, either 0eV or ~63meV. However, in the lower window of the left figure, there are many blue points represent phonon occupied energy ranges almost continuously from 0eV to 70meV.  This is contradictory of my understanding of the phonon band structure. Can you explain it a little on this?
Many thanks!

[Petr Khomyakov]

(1)Particularly,  in the following left figure, it shows " that the phonon that contributes the most to the current is that with index 66, and energy ℏω=63.01meV."
Since the analysis is conducted at the Γ point, does this means that this phonon mode corresponds to the red-circled point in the right figure of the phonon band structure of Si? Which is roughly of the same energy.

Yes, it roughly corresponds to that point if you think in terms of phonon band structure of bulk Si described with a primitive cell.

(2) In addition, in the phonon band structure, I can see that at the Γpoint there are only two possible energy for phonons to occupy, either 0eV or ~63meV. However, in the lower window of the left figure, there are many blue points represent phonon occupied energy ranges almost continuously from 0eV to 70meV.  This is contradictory of my understanding of the phonon band structure. Can you explain it a little on this?

I do not see any contradiction because your device is not described with a single primitive cell of Si, but rather with a structure comprised of many cells, meaning that there exist many phonon modes folded onto the Gamma point of the supercell, compared to the number of modes at the Gamma point of the corresponding primitive cell. 

[weixiang]

Thank you for replying!
So can we think these phonon modes in the supercell at Gamma point as the linear combinations of the two phonons modes in the primitive cell at gamma point, with 0meV and 65meV energy, respectively? i.e. q = aq₁ + bq₂., and q₁ and q₂ are the two phonon modes in the primitive cell at gamma point.
So that they have so many possible energy?
Is my understanding here correct?

[Petr Khomyakov]

To really understand this, please read the notes in the manual https://docs.quantumwise.com/manual/Types/InelasticTransmissionSpectrum/InelasticTransmissionSpectrum.html, as well as the reference papers  cited in the manual. There is also plenty of the literature about the effect of electron-phonon scattering on the electron transport.