InSb bandgap problem with MBJ including SOC

[ralf_tonner1]

Dear Admin,
I am trying to calculate the bandgap of InSb using MBJ functional in vasp5.4.4. The experimental bandgap value of InSb is 0.24 eV at 0K (Vurgaftman et al. J. Appl. Phys. 89 5815 2001) and it is direct bandgap at the gamma point.

Problem:
My calculated bandgap value at the gamma point is 0.25 eV when no spin-orbit coupling (SOC) is considered, which agrees well with experiment. But with SOC the bandgap value at the gamma point almost vanished (0.03 eV). The standard In and Sb potcar files were used.
I then checked with 'In_d_GW' and 'Sb_d_GW' potcars. The bandgap value decrease to 0.12 eV without SOC and 0.0 eV with SOC.

o I used PBE-D3(BJ) optimized structure.
o The bandstructure of InSb, calculated using MBJ and SOC is attached.
o All the calculations are attached (folder names are self explanatory).

Any suggestions?

Thank you

[fabien_tran1]

Hi,

I had a look at your input files and did not see any problems with them. The parameters (ENCUT, etc.) that you used seem to be fairly reasonable.

The disagreement with experiment is simply due to the fact that density functional theory is an approximate method and is unlikely to provide the exact answer. It is just by chance that the MBJ band gap was in perfect agreement with experiment when SOC is not included. If for some reason you really need very good agreement with experiment, then you may try hybrid functionals, but they are more expensive than MBJ.

Also, note that the lattice constant has an influence on the band gap. You used the PBE-D3(BJ) geometry, but what would be the band gap if the experimental geometry is used instead?

[ralf_tonner1]

Dear Fabien,

Also, note that the lattice constant has an influence on the band gap. You used the PBE-D3(BJ) geometry, but what would be the band gap if the experimental geometry is used instead?

I agree with you on the effect of lattice constant on the band gap. This article exactly performed this study (effect of strain on band gap of III-V materials). PBE-D3(BJ) geometry optimization, MBJ+SOC band gap.
This github page summarizes the results from that paper.
1. https://bmondal94.github.io/Bandgap-Pha ... Table.html
2. https://bmondal94.github.io/Bandgap-Pha ... Plots.html

According to Table 1 of the article the experimental lattice constant of InSb is about 1.3% smaller than the calculated value. And according to Figure S11g (figure is based on calculated lattice parameters and band gaps), at 1.3% compressive strain the band gap value is about 0.27 eV, which matches quite well with experiment. Apparent conclusion, the deviation in equilibrium/unstrained MBJ band gap value is because of the deviation in equilibrium/unstrained lattice constant from PBE-D3(BJ).

If we apply the same strategy for other compounds, let say InAs, we see that (table 1) the calculated lattice parameter is about 1.4% smaller than experiment. But the calculated unstrained band gap value agree well with experiment (error=0.05 eV). And if we take the band gap at 1.4% compressive strain then the error is about 0.2 eV. And this is true for other compounds as well. Therefore, the deviation in equilibrium/unstrained MBJ band gap value is most likely not because of the deviation in equilibrium/unstrained lattice constant from PBE-D3(BJ). In fact from Table 1, one can see that the antimonide compounds (GaSb, InSb) consistently produce the large disagreement in band gap value (error~0.2 eV). We have also seen this same problem in ternary antimonide III-V materials (e.g. PRB108, 035202 (2023)) and other materials containing Sb, In atoms.

Comment: Did not check with LMBJ and hybrid functional yet.

Thank you

[fabien_tran1]

Hi,

Thank you for making us aware of your very interesting results. Yes sure, since DFT is approximate, the geometry can not be the only reason for the disagreement with the experimental band gap, but it can play a role. Including SOC may also be necessary if heavy atoms are present.

For bulk systems, MBJ and LMBJ are basically the same methods and should provide the same band gap. Besides, GW is considered as state-of-the-art, but is even more expensive than hybrid functionals.

Note that I moved the topic to "From Users for Users".

[ralf_tonner1]

Dear Fabien,
Thank you very much for looking into the issue so far. I completely agree with you on all the three points.
1.

Yes sure, since DFT is approximate, the geometry can not be the only reason for the disagreement with the experimental band gap, but it can play a role. Including SOC may also be necessary if heavy atoms are present.

I agree and I see that I missed a word in the last message. I wanted to write "Therefore, the deviation in equilibrium/unstrained MBJ band gap value is most likely not only because of the deviation in equilibrium/unstrained lattice constant from PBE-D3(BJ)."

2.

For bulk systems, MBJ and LMBJ are basically the same methods and should provide the same band gap. Besides, GW is considered as state-of-the-art, but is even more expensive than hybrid functionals.

Thank you very much for this information.

3. Just for the future reference (forgot to mention this in the previous message): this article (Kim et al. PBR 82 205212 2010) summarizes the bandgap of III-V materials direct bandgap at experimental lattice parameter.

Thank you again so far.