Dear ATK-experts,
I calculated the band structure of a couple of silicon nanowires (SiNWs) using DFT and the meta-GGA potential by Tran and Blaha with ATK 15.1.
For one single SiNW I observed that the Fermi energy E_F is not located in the center of the band gap. I tried to change some settings and finally realized that this depends on the k-point sampling.
Attached you can find the band structures for 51, 52, and 53 k-points in the direction of the wire (1 k-point in the other directions). For 52 k-points, E_F is located in the center. For 51 k-points it is close to the valence band and for 53 k-points it is close to the conduction band. I tried 31 k-points and 61 k-points and for those values, E_F is also in the middle of the band gap. (*)
I did not observe this behavior for the GGA functional (51 k-points). But when using the meta-GGA potential, E_F is also not centered for different tolerance values in the IterationControlParameters or different c-parameters (I varied these values for 51 k-points). The non-centered E_F also appeared before and after the relaxation of the SiNW. For all other SiNW under study, E_F was centered in the band gap.
Any idea what could be the reason of this? It is probably not very critical, because the band structure itself does not change at all for 50+ k-points. But it is still very puzzling.
The corresponding python-script is attached.
Thank you very much.
(*) I similar problem was discussed in
http://quantumwise.com/forum/index.php?topic=3006.0 (even though they used ATK 14) and the problem could be solved with an odd number of k-points. In my case however, the problem seems to appear mainly for odd k-points.
