band structure under electric field with LCAO basis

[jchang]

Hi,

I have a question about band structure calculation under electric field.
Basically, I am trying to do the same thing shown in tutorial below
http://quantumwise.com/applications/item/512-opening-a-band-gap-in-silicene-and-bilayer-graphene-with-an-electric-field

I am trying the same approach to other material with LCAO basis, not with EH parameters.
What I found is that band gap does not change much with LCAO basis and it is highly affected by the number for variable 'solvent_dielectric_constant'.

Does anyone know if band gap calculation under electric field with LCAO basis is possible in ATK?
And anyone can explain me how to set up 'solvent_dielectric_constant' for band structure under e-field with LCAO?

Thanks.
jiwon

[Jess Wellendorff]

It should certainly be possible to use LCAO for this. The electric field is set up by applying an electrostatic field between 2 electrostatic gates above and below the structure. The field will be screened according to the dielectric constant of the material (vacuum in the tutorial).

[jchang]

Thanks Jess.

Then, 'solvent_dielectric_constant' is for material?
For example, if I have MoS2, then, I need to set  dielectric constant of MoS2 to 'solvent_dielectric_constant'?

And if I use plane wave basis set instead of LCAO, I found that I cannot modify variable 'solvent_dielectric_constant'.
Then, default dielectric constant 1 is used if I use plane wave basis set?

One more question is if I want to do device simulation to get IV in monolayer MoS2 MOSFET, how do I set the dielectric constant for monolayer MoS2?
Device characteristic should be affected by dielectric constant of channel material MoS2.

jiwon

[Daniele Stradi]

Hello,

Then, 'solvent_dielectric_constant' is for material?

Yes, it is.

For example, if I have MoS2, then, I need to set  dielectric constant of MoS2 to 'solvent_dielectric_constant'?

You should set the value of the dielectric constant according to that of the solvent, not that of the material you want to simulate.
If the solvent_dielectric_constant = 1, it means that the region around the material you simulate is vacuum.

And if I use plane wave basis set instead of LCAO, I found that I cannot modify variable 'solvent_dielectric_constant'.

To enable the use of a solvent dielectric constant, you should use a Possion solver other than FFT and FFT2D, for example "Multi-Grid"

One more question is if I want to do device simulation to get IV in monolayer MoS2 MOSFET, how do I set the dielectric constant for monolayer MoS2?
Device characteristic should be affected by dielectric constant of channel material MoS2.

In a device calculation in ATK, the channel material is treated at the atomistic level, so it is not necessary to set any dielectric constant.

Regards,
Daniele.

[jchang]

Thanks Daniele. Appreciate  your response.

Let me confirm my understanding.

So, band structure under electric field using LCAO basis,  I have structure of  'electrode-solvent-my material-solvent-electrode'.
'Solvent_dielectric_constant' sets up dielectric constant for two solvent regions in my above structure, right?
And dielectric constant for 'my material' is atomistically treated (don't need to set up by user) as same as in device simulation you mentioned.

Is my understanding right?

Thanks.
jiwon

[Kim_W]

I cannot repeat the results with below script (A=14). The value of band gap under electric field is much bigger than below picture.

[Petr Khomyakov]

Please describe the problem in more detail. I guess the results depend on the system geometry, H-passivation and the computational method adopted for calculating  for band gap calculation, so you have to make sure that you are using the same procedure as in the reference work. Actually, you have not cited the work you are trying to reproduce, and have not given any of your results. 

I have also noticed that most of your parameters are given by default, so you may need to check the convergence of the band gap with respect to computational settings.

I would also perhaps use the default boundary conditions for this bulk configuration calculations:

 poisson_solver = MultigridSolver(
    boundary_conditions=[[PeriodicBoundaryCondition(),PeriodicBoundaryCondition()],
                         [PeriodicBoundaryCondition(),PeriodicBoundaryCondition()],
                         [PeriodicBoundaryCondition(),PeriodicBoundaryCondition()]],
    solvent_dielectric_constant=1.0
    )

But that might also depend on what is done in the reference paper.

[Kim_W]

Which parameter should I have to change? I did it according to this tutorials: https://docs.quantumwise.com/tutorials/opening_a_band_gap/opening_a_band_gap.html.
I also changed  boundary conditions according to your advice, but the band gap does not change much.
I obtained an indirect bandgap about 1.8eV with A12 at the electric field 4 V/nm, which is much larger than the value in the reference (~0.2eV). The results is line with the reference when I didn't add the electric field.
Reference paper: http://dx.doi.org/10.1016/j.physe.2017.07.020
Thank you very much!

[Petr Khomyakov]

Assuming that the results obtained in the paper are converged with respect to the computational settings, you have to adopt those settings such as the basis set, k-point sampling, mesh cut-off and so on. The tutorial is done for a different system, whereas the computational settings depend on a particular system of study, and have to be systematically adjusted to converge a physical quantity of interest, e.g., band gap value.

I would suggest you first try to reproduce the paper's result for the band gap value at zero field.  I did not get what you meant saying "The results is line with the reference ... ".

You also have to make sure that the potential difference between the metal regions gives you the external electric field (i.e., the field in the vacuum) consistent with that in the reference paper. I would calculate this macroscopic field in the out-of-plane direction using the ElectrostaticDifferencePotential analysis object. This also shows whether you have any field in the vacuum.

 Another thing is to make sure that the structure you have built is exactly the same as in the paper.

[Kim_W]

Thank you very much. I have calculated the band gap value at zero field, which is close to that reference.