# Bandstructure of W shape Silicon

Silicon W_bandstructure.fsp (737.1 KB) Silicon W_bandstructure.lsf (1.3 KB)

Hello, I met a problem when I want to simulate the bandstructure of W shape Silicon substrate. the dispersion curve is a straight line parallel to k axis always. Could you help me check it?

Hello @tingting.zhai,

Thank you for the question. It looks like you’re basing your simulation on the Square 2D bandstructure example. This is a good approach, but you also need to make sure that your model setup script works with your new simulation. We can see here that the script encounters an error because there is no object named rect_pc in your simulation, so the rest of the script doesn’t run.

You need to make sure that your simulation objects are designed such that the setup scripts in your structure and analysis groups run properly. In particular, you will have to make some modifications due to the fact that the original example is periodic in the y direction and your simulation is not. You will probably have to go through each of the analysis groups and make sure they are set up for a simulation that is only periodic in the x direction.

For example, notice in the above image that the model setup script sets the y span of the FDTD region to be ay, the periodicity in the y direction. This doesn’t make sense for your simulation, so you should remove this line.

I hope this helps. Let me know if you have any questions.

1 Like

Hello Kjohnson,

Thank you very much for your detailed explanation. I changed the script as you told me. I attached the files, and the result behaves like below. Do you think it’s correct ? Could you give me some explanations from the result I get?

I also attached a file to simulate the bandstructure of graphene, but the result seems not correct.

Also I read the example Simple Glass-Silver-Air Slab https://apps.lumerical.com/sp_spr_2d.html , the following two files, the y span is 1 nm. However , if I use a larger y span, the dispersion curve totally changed. Could you tell me the reason.
sp_film_dispersion.fsp

sp_film_dispersion.lsf

Best regards,

Tingting

Silicon W_bandstructure.lsf (1.27 KB)

Silicon W_bandstructure.fsp (1.48 MB)

Silicon W_bandstructure.lsf (1.27 KB)

I attached the files, and the result behaves like below. Do you think it’s correct ? Could you give me some explanations from the result I get?

Yes, those results seem reasonable to me. You can see the dispersion of the band as well as the light line.

I also attached a file to simulate the bandstructure of graphene, but the result seems not correct.

The 2D graphene material can be complicated to use. I believe it is not possible to use it in a 2D simulation where the FDTD region and the graphene are parallel (for example, when both are y-normal). I would recommend you take a look at some of our graphene examples (and in particular the TM surface plasmon example) to see how to use this material in your simulations.

Also I read the example Simple Glass-Silver-Air Slab https://apps.lumerical.com/sp_spr_2d.html , the following two files, the y span is 1 nm. However , if I use a larger y span, the dispersion curve totally changed. Could you tell me the reason.

Here is the original bandstructure:

I ran the simulation with a y span of 100 nm. Here are the results:

You can see that this is the same as the original bandstructure with a second set of bands, same as the first, that is reflected across the y axis and shifted to the right. This are the bands of the second Brillouin zone.

Because this is a planar 1D structure that is infinite in the y direction, when we use periodic boundary conditions we are imposing an artificial periodicity on the structure. Varying the y span changes the “periodicity”, which changes the size of the Brillouin zone. With a periodicity of 100 nm, the Brillouin zone has a half width of

$$\pi/100\textrm{ nm} = 31.4 \times 10^6 \textrm{ m}^{-1}$$

We can see that this is approximately where the plane of reflection is located on the x axis in the bandstructure of the simulation with a y span of 100 nm, indicating this is the edge of the first Brillouin zone.

These secondary bands are not physical, they are only created by the periodic BCs. For a 1D planar structure, you should use small simulation region in order to have a large Brillouin zone to avoid seeing these extra bands.

I should add that I am not sure what results you should be expecting for this structure. It is possible that these results are just the light lines of air and silicon, especially because there doesn’t seem to be a large bandgap. You should make sure these results agrees with what you expect to see.

Hello Kjohnson,

Thank you with your reply! The graphene is perpendicular to the FDTD area, the same as TM surface plasmon example.

Could you further check it?

Best regards,

Tingting

I’m not sure what the issue is with the graphene example you sent me. I made a new file based on the surface plasmon example from this page.

Here are the results:

Here are the files I used:
graphene_film_dispersion.fsp (1.3 MB)
sp_film_dispersion_171125_s.lsf (1.4 KB)

I would recommend you use these files as a starting point for your simulations. Let me know if you have any further questions.

Hi Kyle Johnson,

Thank you very much, I also want to ask, if I use the symmetric boundary conditions to get the bandstructure in another simulation, should I put all the time monitors on one side?

if I use the symmetric boundary conditions to get the bandstructure in another simulation, should I put all the time monitors on one side?

Yes, the time monitors placed on the side of the simulation region that is shaded blue/green by the boundary conditions will not be included in the simulation. You should place your monitors on the side that is not shaded.

I tried to simulate the bandstructure with 3D FDTD and 2.5D FDTD as the following pictures.Why did I get totally different results?

[ https://kx.lumerical.com/u/kjohnson | kjohnson ] Lumerical Team
March 2

if I use the symmetric boundary conditions to get the bandstructure in another simulation, should I put all the time monitors on one side?

Yes, the time monitors placed on the side of the simulation region that is shaded blue/green by the boundary conditions will not be included in the simulation. You should place your monitors on the side that is not shaded.

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I don’t think that this is a good application for varFDTD because there is large amount of light propagating in the vertical direction. Usually varFDTD is used for planar integrated devices, for example with SOI waveguide structures, where there is minimal coupling between slab modes… I would recommend you use either 2D (for your initial simulations) or 3D FDTD for this application.

Let me know if you have any more questions.