Band gap InAs

[sabine]

Hello,

I would like to calculated the band gap of InAs. Since it is known that standard DFT underestimates the band gap, I am running GW calculations (LDA, FHI psps, screened exchange). Nevertheless, the band gap is still too small compared to literature data: 0.091 eV (300 eV, 4x4x4 k-point grid) vs. 0.418 eV (exp.).

I have also tried to use a 13-electron semicore pseudopotential for In, but the result does not improve (0.068 eV).

Using the 13-electron psp, I obtain also a strange message:
Number of electrons calculated from density = 15.4078; Expected = 18.0000

Does anyone know what might be wrong? My input file is attached.

I would be very grateful for any help!

Best regards,
Sabine

[jzwanzig]

Hi,
first, have you carefully checked convergence? If 300 eV is your ecut, it seems very small (11 Ha), I would have suspected something more like 25 or 30. Second, your 4x4x4 kpt mesh seems very small, what is kptrlen for this mesh? I think your grid should be dense enough to get kptrlen more like 60, but this needs to be checked by a convergence study.

[sabine]

Dear Professor Zwanziger,

Thank you very much for your quick response!

I had performed some convergence studies indeed:

1. Increasing ecut to ~22 H (600 eV) or ~33 H (900 eV) had only minor influence on the band gap:
0.068 eV (11 H) vs. 0.075 eV (for both 22 H and 33 H).
However, concerning the absolut total energy, you are right that ecut is too small. To reach convergence for etotal, you need a cutoff of around 44 H, but the 4x4x4 mesh should be reasonable.

2. I had also carried out GW calculations using a 8x8x8 mesh, but this did not much change the result:
0.068 eV (4x4x4, kptrlen ~45) vs 0.047 eV (8x8x8, kptrlen ~90).
By the way, I get fairly good results when using a 2x2x2 mesh (band gap = 0.204 eV with ecut = 900 eV). I am wondering if this is just by chance.

Do you have any suggestions what else I could check?

Thanks again and best regards,
Sabine

[david.waroquiers]

Hi,

I would advice you these :

1. Generate your KSS file with the number of bands you want for the calculation of the screening and sigma :
nbandkss 100
(I suspect that you have only 8 bands in your kss file ... but not sure, check that in your output file)
2. Use also kssform 3
3. Remove the ecutwfn's, => use the same as your "normal" ecut
4. Same for ecutsigx, you could even go further for ecutsigx (like 2*ecut)
5. Check the convergence with respect to ecuteps, it might not be high enough (when doing this, be aware that this strongly increases the computer time)

David

[sabine]

Dear David,

Thanks a lot for your helpful comments!

I have done some test calculations and would like to ask now a few questions. Please see below.

1. Generate your KSS file with the number of bands you want for the calculation of the screening and sigma :
nbandkss 100
(I suspect that you have only 8 bands in your kss file ... but not sure, check that in your output file)

As far as I could see, the KSS file was created with a number of bands of 609. So, this should not have been the problem, I think.

2. Use also kssform 3

I have done this, but now the number of bands for generating the KSS file seems to be taken from the keyword nband2 and no longer from nbandkss, which a bit confuses me. Has nbandkss any influence when kssform is set to 3?

3. Remove the ecutwfn's, => use the same as your "normal" ecut

This solved my problem with the missing electrons. Thanks!

When comparing the results for kssform=1 and =3, the absolute energies are somewhat different (e.g. E = 8.504 vs E = 8.466 for a certain band). Is this deviation due to the different algorithms (digonalization vs cojugate gradient)?

4. Same for ecutsigx, you could even go further for ecutsigx (like 2*ecut)[
5. Check the convergence with respect to ecuteps, it might not be high enough (when doing this, be aware that this strongly increases the computer time)

The energies are converged within 0.01 eV using ecuteps = 7 H (had to increase by 2). However, the band gap is still not in the range of the experimental data. Do you have any idea what might be the reason or what else I could try?

Thanks,
Sabine

[david.waroquiers]

Hi

I forgot to say also, I think you should use nband2 100 (the same number as nbandkss2) for your second dataset

I hope it will solve your problem

David

[sabine]

Hello,

Thanks for your comment, David.

Unfortunately, I have still some problems and would be very grateful for any comments or suggestions:

• kssform:
  I have difficulties to understand why I do not obtain the same results for kssform=1 and kssform=3.
  
  In case of InAs, the deviations are rather small, but for another system I obtain unconvincing results when using kssform=3:
  E^GW_gap = 2.016 eV (kssform=1) and
  E^GW_gap= -1.784 eV (kssform=3).
  (The experimental band gap is 1.7 eV.)
  
  I thought that increasing nbands2/nbandkss2 might help, but the result is the same.
  
  
• Concerning InAs: The calculated (GW corrected) band gap of InAs is too small. I know that DFT underestimates the band gap, but when applying the GW approximation to GaAs, for instance, I obtain quite reasonable results for the band gap. I have tried to find something in literature, but couldn't find anything helpful.

I would greatly appreciate if anyone could help.

Sabine

[david.waroquiers]

Hi Sabine,


In your DFT calculation, when you produce your KSS file (dataset 2), have you checked that all the states are converged ? The negative bandgap with kssform 3 is very strange ...

I would also recommend you using tolvrs as a convergence criterium for the SCF calculation (dataset 1) instead of the energy. Something like tolvrs 1.0d-15 should be ok.

Here is what I would do for the second dataset :

# kss file
tolwfr2 1.0d-16
iscf2 -2
getden2 -1
nband2 110
nbdbuf2 10
nbandkss2 100

David

[sabine]

Hello David,

Many thanks for your help!

I have used the options you suggested, but nevertheless I obtain a negative band gap when using cg instead of the diagonlization. The only difference in the input is the kssform option.

Do you have any idea what could go wrong?

Thanks again,
Sabine

[julienvidal]

Sabine,

Some general comments about InAs:
- DFT band gap of InAs is inverted i.e. similar to what happens with topological insulator such as HgTe except in the case of InAs, it is an artifact of DFT...
- Spin orbit coupling is the main contribution to the observed band gap (0.47 eV) and when comparing your GW results to experiment, you should make sure to include SO in some ways.

Finally, you should also question the validity of the perturbative approach you are using for InAs, when your starting point is as bad as DFT.

hope it helps

julien

[sabine]

Hello Julien,

Thank you very much for your insightful comments.

What would you consider a better starting point - would LDA+U be an option?

As far as I know, LDA+U works in Abinit with PAW potentials. If this would actually be the method of choice, do you know if there are any PAW potentials available which are suited for GW calculations? Or do you have any advice how to generate appropriate PAWs? I tried atompaw, but I had difficulties to get all criterions that are stated in the documentation/tutoral fulfilled.

Any comments would be highly appreciated.

Thanks again and best regards,
Sabine

[carsten.fortmann]

hi sabine,
i'm working on the same problem. did you get any further with it? if yes, what was your solution?

appreciating your reply,

carsten

[sabine]

Hello Carsten,

I didn't get much further. However, as I have seen, the latest Abinit version supports PAWs prepared for GPAW, which might be very helpful in this context, but I did not yet have the time to test it. If you have any tips, it would be great, if you could share it.

Thanks and best regards,
Sabine