graphene complex conductivity model

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I am trying to simulate a nanoantenna with a layer of graphene, but I don´t have the complex conductivity model for graphene in cst and hfss and the other problem is that the layer of graphene is only one atom thick (2D).
has anyone done similar simulation in cst or hfss?
 

Hi!

I haven't done anything similar but have an idea how to do it in CST:

Represent graphene by a layer that is d_g=0.34nm thick. For material, choose 'Normal' type, leave 'Epsilon' and 'Mue' to be 1 and set the electric conductivity to be e^2/(4*hbar*d_g). Here e^2 is the electron charge and hbar is the reduced Planck's constant h/(2*pi).
 
Dear goran

your proposed technique is very good when the material conductivity is real!
by the adjusting the tan loss, the graphene layer can be simulated easily.
 

I am interested in going one step further and want to get the dielectric constant of the graphene. I could get the plot of conductivity real and imaginary parts in the units of e^2/h-bar as shown in the paper by Falkovsky (from above link by Moshik Cohen). But now while modeling the dielectric constant what relation could be used ?
 

You should use Kubo formula to calculate the graphene conductivity as function of frequency, then you can import the results inside the HFSS as a frequency dependent material ... this will help you to model the graphene ... Note, this model is usefull when the graphene is not biased with a magnetic field ... in the presence of the magnetic field you will have a hall conductivity ... this hall conductivity is not modelable with HFSS ... in this case you should you COMSOL ...

good luck
 
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Thank you for the help a.mal. Actually I don't have access to this commercial software HFSS. Could you suggest some alternative way for this.
I have access to one FDTD simulation software but it takes the refractive index/dielectric constant data as input to model the materials.
 

what about the conductivity ... it should ask for conductivity as well ...
 

No it doesn't. It takes inputs of either dielectric constant or refractive index alone to model a material.

Anyone has idea about how good is the estimates made by "Optical constants of graphene layers in the visible range",M. Bruna and S. Borini, DOI: 10.1063/1.3073717
 

hi!
I want to simulate a nanoantenna with graphene, but I am beginner in Comsol,
can you help me to model graphene in Comsol?
thanks,
 

I think it is time to MEASURE graphene complex permittivity at frequencies of interest. Modeling offers quite limited answers based on no knowledge at all. I would expect the permittivity is an interesting function of the frequency like in many other materials.
 

I have seen in many papers that Kubo formula was used to model graphene conductivity at microwave frequencies in CST, but I am not sure how to enter the values into CST. Can anyone please help me with a quick explanation?


 

Hi! Could you please make me clear, what simulation package can be used for working with the 2d conductive materials (such as 2d electron gas, graphene and metallic carbon nanotubes)? For example, one can see in the paper by Tamagnone et al (https://infoscience.epfl.ch/record/182204/files/JApplPhys_112_114915.pdf), that it is possible to use HFSS for this purpose by some way. But how can I assign graphene conductive properties to some given flat or maybe curved surface? As I see the realization of this task, one needs to set a bulk material with small finite thickness and set the conductivity tensor with normal to surface component equal to zero. But it is too complex and leading to big errors solution from my point of view. Maybe in some packages it is possible to set conductive surfaces with zero thickness?
 


hello，I am doing the simulation of the graphene in HFSS recently,I can obtain the complex conductivity of the graphene through the Kubo formula,but how about the permittivity?How to set the value of permittivity?And there is an other question that as you say,import the complex conductivity inside the HFSS as a frequency dependent material,but the complex number is not available here,how to solve the problem?
 


You can get permittivity through conductivity. Just look up the formula that relates real/imag part of permittivity with real/imag part of conductivity. The formula is available in the advance electromagnetics book by Balanis. Otherwise, you may also find some thesis work on graphene simulation for that formula.

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Did you try to get a 3D conductivity and then use a finite thickness? I did that before and it gave me reasonable result, but I guess it's really depend on the application. If you have to use 2D conductivity, you probably need some feature like Surface Impedance Boundary Condition. I heard CST has a feature (maybe called PBA or something BA) that might be similar, but I didn't look into it, so don't take my words
 

There is a finite conductivity when assign the boundary in HFSS, I think maybe it can help you~
 

Hi a.mal !
I know how to set frequency dependent material form your post here but I am still confued that how to set thickness of graphene ? when I set 0.34nm as the thickness of graphene, the box wil become a sheet and it can't be set as some special materials. How did you solve this problem ?
 

hello
I want to model graphen in HFSS but when I import the data of conductivity it gives error because of imaginary conductivity. how can I give imaginary data for conductivity?
thanks for your help
 

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