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.
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.
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.