Effect of electron-phonon scattering in electron transport process

[weixiang]

Hello experts,
I am studying the e-ph interaction effect in graphene nanoribbon transistor device, and I have read through some Quantumwise case study page https://docs.quantumwise.com/tutorials/inelastic_current_in_si_pn_junction/inelastic_current_in_si_pn_junction.html
as well as the STD  case study for Si p-n junction in paper Phys. Rev. B 96, 161404(R). I got the idea that phonon will have the positive effect that increases the off-state current by several magnitudes (the phonon-assisted tunneling), while unchanging the on state current.
However other papers speak otherwise. In paper  PhysRevB.80.155430, they studied Si nanowire and their simulation shows an opposite result that the off-state current is rather unchanged, but the on-state current is reduced because of the phonon scattering. Some other paper also indicates so. For example in a paper named " Role of phonon scattering in graphene nanoribbon transistors: Nonequilibrium Green’s function method with real space approach" They also give a similar result for GNR transistor.

I just wonder why does the STD method give an opposite result than others? Is there anything that I misunderstand here?

Thanks!

[weixiang]

I am actually mentioning the difference between the following two figures. In the left figure, the top branch is in log scale and the bottom branch is in linear scale.
 

Ref: Left PhysRevB.80.155430
         Right Phys. Rev. B 96, 161404(R)

[Petr Khomyakov]

You are comparing studies done for two different material systems: nanowire vs thin film.

Moreover, one study is done using semi-empirical tight-binding model, whereas the other one is based on ab-initio density functional theory.

In addition, the tight-binding study is likely using electron-phonon coupling constants obtained from bulk 3D calculations unlike the DFT study in which the electron-phonon coupling is computed for the actual low-dimensional system, taking into account surface phonons.

Also, the DFT-based calculations in the QuantumATK were done with two rather different methods (special thermal displacement and LOE) to account for electron-phonon interaction, and these two methods give similar results. So, I would question the reliability of the tight-binding-based calculations in the other paper.

You may consider carefully reading the two papers and try to understand what are the approximations used in these two rather different works for describing the electronic structure and the electron-phonon interaction of Si nanostructures.

[weixiang]

Thanks for the reply! That clarifies a lot!

[Kim_W]

Dear Petr Khomyakov,
  I am still confused about your explainations. The effects of phonon on the transport properties of ML MoS2 FET have been checked in an SE calculation with inclusion of acoustic phonon scattering (both transverse acoustic and longitudinal acoustic phonons), zero-order longitudinal optical phonon scattering, zero-order homopolar phonon (HP) scattering, and Fröhlich interaction.[IEEE Trans. Electron Devices 2013, 60, 4133] The off-state current is nearly unchanged, but the on-state current is affected. The shorter the channel length is, the smaller the phonon scattering effects on the on-state current. In addition, According to an ab initio quantum transport simulation with inclusion of electron−phonon interaction, the on-state currents reach about 90% of their ballistic limit in ML BP MOSFETs at Lg = 10.5 nm [IEEE Int. Electron Devices Meeting 2015, 12.1.1−12.1.4.].

[Petr Khomyakov]

  I am still confused about your explainations. The effects of phonon on the transport properties of ML MoS2 FET ...

The original post by weixiang, as well as my reply to it, is about Si, not MoS2. These are two very different semiconductor materials. So, which explanations of mine are you referring to?

[weixiang]

Dear Petr Khomyakov and Wang Jin,
You can also check this paper IEEE Transactions on Electron Devices 65.6 (2018): 2654-2659. It treats a GNR transistor with EPC considered, using self-consistent NEGF via TB Hamiltonian. The materials system and method might be different (or might possibly be similar)  from that in  IEEE Trans. Electron Devices 2013, 60, 4133 but it gives very similar phonon effect on the ON state and OFF state current.  I wonder if the calculation method rather than the materials system dominate the results here?

[Petr Khomyakov]

I wonder if the calculation method rather than the materials system dominate the results here?

It can be both.

MoS2 is a polar material in which there exists the electron-optical polar phonon scattering that might be the dominate scattering channel in some temperature range similarly to III-V semiconductors such as InAs and GaAs at room temperature, unlike non-polar Si in which there exist no polar optical phonons.   One can investigate it by explicit calculations with and without the electron-polar optical phonon included.

Another thing is that there is no guarantee that the tight-binding approach reproduces supposedly more accurate calculations based on density functional  theory.