Simulation of nanoparticle has unexpected absorption peak


I am attempting to simulate the absorption characteristics of a single indium nanoparticle on a silicon substrate. I have followed the advice on how to properly define an absorption simulation here as well as more specifics on adjusting material fits and mesh overrides. I have then adapted the script found in the Mie 3D page to analyze my simulation region.

This is the absorption spectra that I obtained:

However, from other experimental results, I anticipated that the peak mie efficiency would occur at around 210 nm as opposed to ~180 nm.

I have checked that my simulation is defined in accordance with the above recommendations, and the absorptive peak is still at 180 nm. One thing that is slightly off is the material fit, though I do not believe it is so imprecise as to shift the peak in such a significant manner.

I would greatly appreciate it if someone could look through my .fsp file to see if I did overlook something when defining my simulation regions that might cause this difference.

Thanks in advance.

mie_analysis_3d_modified.lsf (6.8 KB)
1x1x1_In_on_Si_20_nm_rad_test.fsp (468.5 KB)

Dear @eelu

Thanks for very detailed question as always!

Recalling from our previous discussion in here, and before discussing simulation details, did you have a chance to check your results with analytical results obtained from mie3d? More specifically, based on material index obtained from getfdtdindex command, does analytical results predict a peak at 180 nm or 210 nm?


Hello @bkhanaliloo

Thank you very much for reminding me about the getfdtdindex command. Here is the result when I analyzed my simulation, where indeed, the absorptive peak occurs at a wavelength of ~ 210 nm :

However, the result from Mie theory is for a sphere in a constant dielectric medium. That is not exactly what I am simulating, though I do expect an absorptive peak at a similar wavelength.

Consequently, beyond my initial inquiry, I have a few remaining questions:

  1. On the page describing how to properly use a TFSF source, it states that scatterer must be completely inside of the source. How then, should a substrate be treated? Can it extend through the TFSF boundaries and beyond without impacting the analysis?

  2. From my understanding, Mie theory is applicable to spheres enclosed by one dielectric medium. If I have a substrate enclosing half of the sphere, then I essentially have two media surrounding a hemisphere. Would mie theory and the mie3d command still apply in this case? If not, is there a way to computationally confirm the absorption results of such structures?

Note: I defined my simulation structures to be a custom structure (hemisphere) on top of a substrate. It dawned on me later that I simply could have used the properties of mesh order found here to implement the same design using a sphere. Regardless, I do not believe that this impacts the simulation result, but please correct me if I am mistaken.

Thanks in advance for your help.

Dear @eelu

Thank you for providing additional information.

I doubled the simulation region to have at least half wavelength between sphere and PML layer (0.2um on all three directions) and then ran simulations for different mesh sizes. Results were converging and show a peak at ~180 nm. Since simulation take a long time to run at finer mesh, I could not make time to repeat the simulation for different PML and perform more convergence testing. Below is my results and show the absorption cross section for different mesh accuracies:

The simulations make sense, and I still do not know why it does not match the experimental results.

Yes, the substrate should be extended through TFSF source region. TFSF source runs two simulation, one with and one without substrate. If you do not extend substrate through TFSF source region, substrate will be considered as an scatterer.

Also, substrate needs to be extended through PML layer as well for best PML performance. You can read more about the importance of extending structure through PML here.

Mie3d will only apply to cases where the sphere is embedded in a dielectric medium. As you have noticed, mie3d only requires the ratio of indices (n_sphere/n_background). This means that you can not use this theory for cases of half sphere, or if the background material is air + substrate. For example, you could not use mie3d command in your case even if you had a full sphere (because substrate covers only part of the sphere). I haven’t tried to come up with other ways to calculate scattering in slightly complicated cases, and I do not have any shortcut to recommend you. Let me know if you had any ideas and we can discuss it further.

I checked results for the second case, and was almost identical to first case. So this should not be a problem.

Your simulation look reasonable to me. As next practices, you can try more convergence test. You can also try to modify the material fit and see if there was any change in results. If not, I guess we should look into why experimental results are different than simulation results, and if there is any difference in experiment compared to what we are simulating.

I hope this was helpful.