plasmon resonance and experiment

fdtd
plasmonics

#1

front.fsp (313.3 KB)

Hi ,
i attached a simulation of a hole array (unit cell) . The sample consists in a GaAs substrate with the hole array (Ti/Au). The experimental data of a similar fabricated sample is also attached. I am trying to understand the big difference in the simulation/experiment in terms of the resonances and their shapes.
I have some ideas of the problem but haven’t succeeded to make a good simulation and this is the reason i ask you for help:

-material fitting

-mesh (i tried to run with mesh =3) but it takes 4 hours simulation, so attached is the mesh =2 example.

-difference between plane wave simulated and the measurement setup. i am measuring the transmission of the sample in normal incidence using an FTIR spectrometer and normalized by the substrate.

Thanks


#2

Hi,

I have made a modified version of your simulation file: modified_front.fsp (311.0 KB)

Using this file, I was able to get the following plot of the transmission spectrum where there are peaks near 8.5 and 12 um which is similar to where there are peaks in the experimental data:

I made the assumption that the metal can be modelled as PEC (perfect electrical conductors) which behave ideally with 100% reflection. This assumption would be valid if the skin depth of the metal is much smaller than the wavelength of light, and it allows you to use a much courser mesh to model the metal which will require substantially less memory and simulation time.

I also made the following changes:

  1. I increased the simulation time to allow enough time for the fields to propagate through the simulation region and fully decay - I think that having too short of a simulation time is likely a main cause for the results not matching the experimental results. The effect of having too short of a simulation time is discussed in more detail here: https://kb.lumerical.com/en/index.html?ref_sim_obj_frequency_monitors_simulation_time.html
  2. I changed the PML profile from “Standard” to “Steep angle”, and I increased the number of PML layers to 64 to help absorb light which may be diffracted to grating orders which travel at steep angles away from normal.
  3. I added a mesh override region over the metal layers to set the dz mesh step size to make sure the thickness of the metal is properly resolved
  4. I changed the mesh refinement method from conformal variant 2 to conformal variant 0 since conformal variant 2 can sometimes lead to numerical artifacts if the mesh step size is not fine enough

I think it would be a good idea to do some further convergence testing of the settings, like described on the simulation methodology page here:
https://kb.lumerical.com/en/index.html?sp_common_simulation_consideratio.html

You may also want to check the assumption that the metal can be represented as PEC by simulating the Au and Ti materials instead of PEC. Since this would require a finer mesh, and increased simulation time and memory requirements, you may consider running 2 separate simulations with 1 source in each and summing the results to get the result for circular polarization as shown in the example here:
https://kb.lumerical.com/en/index.html?ref_sim_obj_planewave_circular_polarization.html

The advantage of this method is that you can use symmetry in the boundary conditions when you have only 1 source in the simulation which will allow you to reduce the memory and simulation time required for the simulation.

Hopefully this helps!


#3

Thanks for the response.

I continue doing some testing on this simulation. I haven’t check the PEC assumption yet (i see that the simulation runs very fast). I am trying to deal with plasmonics in the interface between metal and semiconductor so in my opinion is very important to simulate the most real metals that are used in the experiment.
I am doing different simulations all around the same plasmonics - metamaterials ( different types of antennas). Specifically using AlGaN and GaN thin films (which i need to import manually their material dielectric constants into database). I will try to finish them and probably have more specific questions.

Regarding:

  1. May i use this almost always in these type of simulations ? How can i check that it yields better results.
  2. and 4) Why not to use the STAIRCASE refinement method that is less consuming resources , and add very fine override meshing in all the metals and interfaces between different materials? what do you think about it ?

thanks in advance


#4

When using the real material data, you can perform convergence testing to get accurate results. For example to find the required mesh step size for accurate results, you can decrease the mesh step size until the results converge and stop changing when you further decrease the mesh step size.

Using PEC does make an assumption that the metal is ideal so if this assumption isn’t valid it won’t give the same results as the real material data, however it is much faster to run the simulation using PEC, so you can compare the results between using PEC and the real material data to see if they match. If they do match, you may decide to use PEC in future simulations of the device (when optimizing the design of the device) in order to be able to run the simulations much faster.

We do have examples of metamaterials simulations which use the PEC assumption such as the one here:
https://kb.lumerical.com/en/index.html?metamaterials_thz_chen.html

Regarding the question about using staircase mesh refinement method with a finer mesh compared to using the conformal meshing method, the advantage is that when using the conformal meshing method, although it does take slightly longer to mesh the simulation, this is much less than the decrease in simulation running time in order to achieve the same level of accuracy. This is because a finer mesh is required to achieve the same level of accuracy when using the staircase mesh refinement method and the simulation running time increases exponentially as you decrease the mesh step size. The relationship between simulation running time and mesh step size for 2D and 3D simulations is given on the chart here:
https://kb.lumerical.com/en/ref_sim_obj_mesh_refinement.html#sim_time