# changing graphene chemical potential for different frequencies?

#1

Hi, I am trying to simulate a structure consists of graphene.
In my simulation i need to change graphene chemical potential and scattering for each frequency.

actually, i do have their corresponding value versus frequency in a MATLAB m-file.

how can i do that in lumerical?
is it necessary to write a script file for that?

best regards
Mehdi

#2

Hi Mehdi,
I am not sure but I don’t think this is possible. Because the surface conductivity model used treats the Chemical potential and Scattering rates as constants in the integral as in this page:
https://kb.lumerical.com/en/other_application_graphene_simulation_tips.html#surface_conductivity_approach
So, even if you write a script that sweeps over the frequency and changes the material properties each run, it would not make much sense.

#3

Hi,

Thanks for your reply, @aya_zaki. The Kubo formula used for the 2D graphene model assumes a chemical potential and scattering rate to be independent of frequency, but in principle the integrals (2) and (3) in the page that @aya_zaki mentioned can be calculated without this assumption because the integration does not involve frequency. However, it is important to check if the frequency-dependent chemical potential and scattering rate are meant to be used in the Kubo-formula conductivity implemented in Lumerical’s optical solvers. If that is the case then there are two approaches you can use:

1. run a sweep over single frequency simulations, changing the material properties, as @aya_zaki suggested, or
2. calculate the conductivity as a function of frequency and use the sampled 2D data conductivity model, which can be used with 2D rectangles, just like the regular 2D graphene material.

The second method has the advantage that you can run broadband simulations so you can get many frequencies from one simulation. Furthermore, if you need to use a conductivity formula that is not the same as Kubo’s, you can still do it; you just need to calculate the conductivity for a bunch of frequency points and use it as sampled 2D data.