bandstructure of InAs slab

[skg]

Hi,
We calculated the bandstructure of InAs slab (same as the example given on ATK tutorial). We found that the X valley is lower than the L valley, while in the bulk, it's the reverse. Existing literature (e.g. 2.6nm thick slab[1], 3nm and 5nm thick slab[2]), report using TB calculations, that the L valley is lower than the X valley, similar to the bulk case. Could you please explain this difference? Is it due to a different nomenclature used by ATK?

Best Regards,


[1] Y. Liu et al., “Band-structure effects on the performance of III-V ultrathin-body SOI MOSFETs,” IEEE Trans. Electron Devices, vol. 55, no. 5, pp. 1116–1122, 2008.
[2] Mugny, G., et al. "Band structure of III-V thin films: An atomistic study of non-parabolic effects in confinement direction,"  Joint International EUROSOI Workshop and International Conference on Ultimate Integration on Silicon ((EUROSOI-ULIS) 2015.

[zh]

Yes, it may due to the different structures used in the simulations. The  InAs slab in the tutorial example contains only one atomic layer.

[skg]

So, do you mean different nomenclature than others?

The example (http://quantumwise.com/documents/tutorials/latest/InAs-2D/index.html/chap.slab.html) is for 8 layers (and not 1 layer), and we found that the relative positions of “L” and “X” valleys don't change on changing the number of layers from 4 to 40 layers.

So  my question remains the same.
Here are some snapshots to further clarify the question (Note the X valley in ATK is called L valley in existing literature)

Image1 : Bandstructure of 2.43 nm thick slab (8 layers)
Image2: Bandstructure of 3 and 5 nm thick InAs slab. Taken from[2]

[zh]

Yes, the example in the posted link contains 8 atomic layers.  Just by looking at the two band structures, it seems that the definition of L and X points in them are different.  So you have to check what kind of in-plane lattice vectors are used to describe the 2D thin film of AlAs as well as the corresponding Brillouin zone.  Are they form a rectangular box?

[Anders Blom]

Ok, lots of confusion here. I haven't had time to look at the specifics of your model, but whether a specific minimum is lower or higher than another one is strongly dependent on the method of calculation. A tight-binding calculation may give quite different results than DFT, depending on the parameters used.

Moreover, the L point in ATK is of course the L point, as in the literature - same for X. However, the "L" point in a 2D slab needs to be carefully specified, since you can't use the 3D fcc Brillouin zone anymore.

[skg]

Hi,
  Thanks for quick reply. As you asked earlier about the BZ, when we cleave along [1 0 0], we get a square shaped BZ. The coordinates of L points in reciprocal vectors is (0.5, 0.5, 0.5) as given in ATK for the same BZ. We also plotted band structure along G- C , the co-ordinate of C being (0.5, 0.5, 0.0), which seems more logical in a 2D slab system and it wasn't much different from what we got along G-L. We are also attaching the BZ for clarification. I just want to know that are we doing correctly or is there anything wrong with the method, in which case please tell us the correct way to do so.
 

[Anders Blom]

As I mentioned above, you can't just translate the fcc L point to the slab by the same fractional coordinates, since the symmery changes. If you do the math, you find that the L point in the 100 supercell (4 atoms, not 2 anymore) is actually located at (0.0,0.5,0.5) in units of the new reciprocal lattice vectors. This point is labeled A in ATK, but this is a somewhat arbitrary notation (the name is chosen for kA=0), which we use for the generic "UnitCell" lattice class. There are no "standard" labels for a generic unit cell since the underlying crystal can have any symmetry. The true symmetry of the 100 cell is for instance actually SimpleTetragonal and the fcc L point maps over to its R point.

The easiest way to see this is to run a band structure calculation for bulk Si (fcc) and Si 100, using a nonselfconsistent tight-binding model, the calculation takes seconds only. If you compare the L-G-X fcc band structure to that for the cleaved system, you see that the points A and B in the 100 case (they are degenerate) will have the same energy as the L point in the fcc bulk. And, the same for the SimpleTetragonal representation.

So, if you want to compare to the literature, it's probably best to use the SimpleTetragonal lattice class and just use the R point as L, and the M point as X (the Delta valley in along G-M).