# Define material with surface conductivity

#1

How can I define a material based on frequency dependent surface conductivity data that is different than Graphene? A good example of such a material would be a 2-dimensional electron gas (2DEG).

#2

Dear @hasantahir

My knowledge of electron gas properties is limited but if you have the surface conductivity values you can use sampled 2D data:

and then click on import data.

These pages and scripts might be useful for you to review as well:

https://kb.lumerical.com/en/materials_creating_sampled_data_material.html
https://kb.lumerical.com/en/index.html?materials_create-2d-conductivity.html

#3

I have a related question regarding implementing a dielectric function out of surface conductivity data. In the tutorial video/slides showing how to model graphene, a dielectric function is generated out of the surface conductivity data through the equation:

ε W = ε r ε 0 + i σ ω ω Δ

Can you please share any reasoning behind using this approach?

#4

Dear @hasantahir

Please take a look at the lossy medium section of this Wikipedia article which extracts the relation between permittivity and surface conductivity:

in which it explains for the lossy mediums we have:
ε(w) = ε(r)ε + i σ/ω;

where σ is the 3D surface conductivity. Now to move from 3D surface conductivity to 2D surface conductivity, please see the 5th post in this KX page.

σ(2D) = σ(3D)*Δ;

This post might be also useful for you to read: