# Calculating the band structure with different unit cell

I have to do a electronic band structure calculation on a heterostructure using DFT calculation. First I do the calculation on each phase separately. I use a primitive unit cell to do the calculation and the band structure was assumed to be the band from the bulk. Since I have to change the unit cell when I do the calculation on my heterostructure, I try to use another unit cell with different shape to do the calculation again on each phase separately. I found that the band structure differ from the previous one which was done with primitive cell. I know that the band structure must be different, because the reciprocal space spanned by reciprocal vector become different and the Brillouin zone become different too. But the band gap of the system was changed. How can I understand it ? I did the calculation on SnTe with a primitive cell and a large cell. And the band structure was shown in below, for the left one it was done in primitive cell and calculate along the High symmetry point. Another one was done in a larger unit cell. • I don't quite follow how you plan to combine band structure calculations from separate bulk calculations into a heterostructure, but I think you are asking about doing two calculations for the same structure, simply using different cells. The BZ will be different in the two, so you will get band folding and the band structures will appear different. However, the band gap should be the same. This suggests that in the calculation with the larger band gap you haven't really found the fundamental gap? Perhaps the VBM or CBM are at a k-point you haven't explored? Oct 24, 2020 at 7:38
• @ProfM Thank you for your answering. but when I change the shape of unit cell, I found that the the band gap become smaller. I can update my post. In fact Im calculating the SnTe structure. I try to use a primitive cell to do the calculation and a bigger cubic unit to do it again. You can see my post – Oct 28, 2020 at 3:25
• The bands that are present at the Gamma point for the primitive cell must also be present for any supercell. In the primitive cell you have a valence band at Gamma at about -2 eV which is not there for the supercell. This convinces me that the two calculations are not consistent, but it is impossible to decide why. Perhaps you should share the input files? Oct 28, 2020 at 7:24
• @ProfM But I was told that if I want to verify the figure on the right hand side. I can do a transformation on the left figure to the one on the right to see whether they are match with my calculation or not. How can I find this transformation ? Oct 29, 2020 at 5:11
• You can see that they don't match without a transformation in this case. The bands that you get for the primitive cell should be present in all supercells. What happens in a supercell is that you get "extra" bands (band folding), and what you would generally do is to "unfold" the bands from the supercell calculation to remove the extra bands and recover those of the primitive cell. But in your case you are missing bands from the primitive cell in the supercell (e.g. the band at -2eV at Gamma), so we can see straight-away that the calcualtions aren't consistent. Oct 29, 2020 at 7:07

The electronic band structure is a concept for periodic system. Heterostructures are not periodic system (in the direction of heterostructure grow). What is done is an approximation where the bulk's band of each bulk system is combined using the band off-sets.

Some reference about how to calculate band off-sets are:

• Theoretical calculations of heterojunction discontinuities in the Si/Ge systems. Chris G. Van de Walle et al., PHYSICAL REVIEW B 34, 5621 (1986)
• First-principles calculation of the band offset at BaO/BaTiO3 and SrO/SrTiO3 interfaces. J. Junquera et al., PHYSICAL REVIEW B 67, 155327 (2003)
• Band alignment at metal/ferroelectric interfaces: Insights and artifacts from first principles. M. Stengel, et al., PHYSICAL REVIEW B 83, 235112 (2011)

This is widely used studying semiconductor lasers, for example.

• Thank you Camps, now I can get a more sense in understanding how to start !! Oct 27, 2020 at 11:39

I think Camps gives a mostly correct answer for this. I will say though, it may be possible in some cases to generate a band structure in the direction of the heterostructure by making a periodic bulk heterojunction. By layering two materials with minimal (or large if intended) strain in a bulk system with bulk crystal structure, you may get some interesting effects.

You may also see some effects in a 2D surface band structure, but I am unsure what you should expect there.