  # Calculating scattering in a Plasmonic solar cell

I want to calculate the fraction of light scattered into the substrate, in the case of a plasmonic photovoltaic, I want to get this curve: I tried this geometry but it didn’t work:

This curve is from Plasmonics for improved photovoltaic devices , Atwater and Polman.

Here is my simulation:
Project-small.fsp (314.0 KB)

Thank you!

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I’m guessing you want to extract the fraction of a forward scattering to a total scattering in respect of the particle geometries and sizes on the substrate. A TFSF (total-field scattered-field) source is suitable for a particle scattering. You can extract the absorption cross-sections from the total-field monitor (incident field + scattered field) and scattering cross-section from the scattered-field monitor (ONLY scattered field) for the particle on a substrate system. For more detailed information, you can consult “Particle on a surface at non-normal incidence” section from the TFSF example. I have some questions regarding your project file.

Q1) Do you want to simulate the portion of the forward or backward scattering from the total scattering of the particle on a substrate? Is the scattering into the substrate meaing the back scattering?

Q2) Are you considering peirodic particles array or a standalone particle for the scattering cross-section simulation?

There is a more simpler appoach that implements 2D power monitor rather than a “scatt_ff” box monitor to catch a scattering cross-section from the scatter on a substrate system; please refer to this KX site.

I hope it could be giving you some guideline.

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Dear,
Thanks so much for answering the question.

The problem I face is: I want to calculate the scattered light into substrate , not just the whole scattered light !

I tried using two cross section scattering analysis groups, the first covers only the particle, the second one covers the particle and the substrate and then substract both to get only the scattered light inside the substate, something weird happened , Sigma in the first case is bigger than the second case! Project-EDITED.fsp (312.3 KB)

I don’t understand the difference, I used periodic BC in the FDTD and selected only one particle.

Thank you

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Sorry for the delayed response.I had taken a look at your reference paper about a scatter on a substrate. I’ve made some modification from your model file based on this paper.

• A 10 nm-thick SiO2 is added on the Si substrate
• A spherical Ag NP with d = 150 nm is selected instead on that with r = 150 nm
• I guessed “Single” Ag NP on a Si substrate is considered in this article.
• I’ve built three candidates based on structure (single or periodic) and source (plane-wave or TFSF).
1. A periodic NPs with a plane-wave source
2. A single NP with a plane-wave source
3. A single NP with a TFSF source
• The T and R 2D power monitors are set to catch the forward scattering (into a substrate) and backward scattering light in the model, respectively.
• The fraction of a scattering into the substrate can be evaluated by (forward scattering / (forward scattering + backward scattering)).
• The location and the size of the of Ag NPs, Si substrate, FDTD region are adjusted as follow (please refer to the attached files)
1. for a periodic AgNPs array, the pitch between neighboring Ag NPs is assumed to be 300 nm (150 nm X 2).
2. for a single Ag NP, the size “x, y, and z spans” of and the FDTD region are all “2,000 nm” (large than the maximum wavelength)
• In the next step, we can set up the scattering analysis (scatt_ff) for calculating an angular field pattern after the clarification of your model.
• In the reference paper, the electrical dipole source in used, but in the model the plane-wave or TFSF source is implemented, focusing a particle scattering effect. 1) the periodic NPs with a plane-wave source
The FDTD model for a periodic NPs with a plane-wave source is shown in the following image. The plane-wave source is more suitable source for a periodic array with PBCs than the TFSF source. I set the R and T monitors to record the forward scattering into the substrate (the propagation direction of plane-wave) and back scattering, respectively.

Here is the result graph from the simulation. As you can see the result, the fraction of the scattered into the substrate is much higher than the result in FIG. 1 of the reference paper. I guessed that the “Single” Ag NP is considered in the reference simulation, on the other hand, “Periodic” Ag NPs array is studied in this simulation. In the periodic Ag NPs array, much amount of light would be back-scattered owing to the large density of the Ag NPs compared to the single Ag NP. Here are the project and script files for this model.
Project_Periodic_AgNPs_Array_Plane-wave_v3a.lsf (384 바이트)
Project_Periodic_AgNPs_Array_Plane-wave_v3a.fsp (255.5 KB)

2) The single NP with a plane-wave source
I had made “a single NP with a plane-wave source” model to compare the effect of Ag NP scatters. The FDTD region were extended in x, y-axes to consider the “Single Ag NP” on the Si substrate by implementing PML BCs. As the structure and the source have a symmetric nature, the anti-symmetric (E-field) and symmetric (H-field) BCs are applied to the model. In the following figure, you can see the trend and value of the “fraction of the scattering into a substrate” in this model is similar to that in the reference paper. But the edge effect of the plane-wave source to the PML in x, y-axes could be a limitation in the approach. Here are the project and script files for this model.
Project_Single_AgNP_Plane-wave_v3b.lsf (397 바이트)
Project_Single_AgNP_Plane-wave_v3b.fsp (256.4 KB)

3) The single NP with a TFSF source
The last model is the “Single” Ag NP on the Si substrate with a TFSF source. The volumetric TFSF source (500 nm X 500 nm X 500 nm) is injected in the downward z-direction. We also applied the anti-symmetric (E-field) and symmetric (H-field) BCs to the model as the symmetric nature of the structure and the source in order to reduce the simulation time. As seen in the figure, the trend and value of the “fraction of the scattering into a substrate” in this model is similar to that in the previous simulation and in the reference paper. Only small portion of the substrate is encompassed to the TFSF in xy plane compared to the plane-wave source, transmitted back and forward scattering light could be different from two simulations. Here are the project and script files for this model.
Project_Single_AgNP_TFSF_v3c.lsf (381 바이트)
Project_Single_AgNP_TFSF_v3c.fsp (257.5 KB)

If you are considering the infinite “Periodic” Ag NPs array on the substrate, the simulation model 1) the periodic NPs with a plane-wave source is applicable to your purpose. On the other hand, if you are interested in the “Single” Ag NP on the substrate, 3) the single NP with a TFSF source model is appropriate for you. But it is the important to keep in mind, the parallel (or vertical) electrical dipole source was used in the reference paper. There exists a slight difference of the “fraction of the scattering into a substrate” between the simulation models 2), 3) and referece paper might be due which source is used in the model.

I hope this could be a helpful guidline for you. 3 Likes

Wow ! Thank you dear for that great answer Are you ignoring the side scattering in this case? Shouldn’t we add Vertical power monitors also?

Does that mean we should use a Dipole source for more accurate results?

Thank you for the great answer. I am grateful 