Graphene is a 2D material with very particular dielectric properties. For different wave ranges and different doping dielectric permittivity (depends on frequency) can be negative (i.e. graphene behaves itself like a metal) or positive (i.e dielectric) with low damping (2.3%). The dielectric permittivity can be calculated from conductivity through relation ε = 1 +i*σ/(δωε0), where δ is a thickness of the graphene layer. Conductivity σ is calculated using random phase approximation and final formula can be found in a lot of sources.

Most of Dielectric Constant requires when you use the material as insulator between channel and gate. As much as I know, Graphene can't be used for that if it has zero band gap. Silicon Dioxide, Hofnium Dioxides, Boron etc are used for that.

I would like to know why you need this value.

I am very sorry, if my answer doesnt help you much. By the way the attachments might help you. 

i want to know this parameter so that can used in aasimulation of graphene based device

mostly you may not find the correct answer because grapehen dependent on the frequency so its value is still unknown best of my knowledge.

If you can say on what devices and which software you are using then we may help you in better way..,

i am using silvaco TCAD

Graphene is a 2D material with very particular dielectric properties. For different wave ranges and different doping dielectric permittivity (depends on frequency) can be negative (i.e. graphene behaves itself like a metal) or positive (i.e dielectric) with low damping (2.3%). The dielectric permittivity can be calculated from conductivity through relation ε = 1 +i*σ/(δωε0), where δ is a thickness of the graphene layer. Conductivity σ is calculated using random phase approximation and final formula can be found in a lot of sources.

Hi Gopi,

I am not sure  you still need this information. Anyway check this following link. In this work, they showed field dependence of dielectric constant. Hoping this might help. 

http://scholar.harvard.edu/files/efthimios_kaxiras/files/nanolett_13_898-902_2013.pdf

Let me know if you have trouble in downloading from this link.

Thanks. 

Hi Gopi,

I recently did some work on revealing the static and spatially-resolved dielectric constant of graphene and graphene nanoribbons. My original intention is also trying to provide the dielectric constant when simulating graphene devices. 

http://dx.doi.org/10.1103/PhysRevB.94.045318

Hi, Everyone. I want to use Graphene as a material in MEEP. Can you help me how I can use it.

For this I need its complex permittivity

or complex refractive index?

Hi Jingtian,

From your paper mentioned above (Phys. Rev. B 94, 045318), I suppose DIC of wide area graphene can be taken as 6.9.

Hi Gana,

You are right that the relative dielectric constant of graphene can be taken as 6.9 with a effective dielectric thickness of 0.22 nm.

Jingtian

Hi Gopi,

you can use these values : e=6.9, t=0.22 nm and the following paper can answer you well.

https://doi.org/10.1103/PhysRevB.94.045318

B.R

Khalil

these information are truly helpful. i am looking to apply the material in my design of antenna. does the thickness have to be 0.22nm?

@ V. A. Shaidiuk

Dear Dr.

I have question, in Terahertz frequency below far infrared, when we consider just intraband transition, is real part of Graphene permittivity negative or positive?

I see two different Kubo formula in the papers, one of them reach to negative and another to positive real part of permittivity.

Could you clarify this for me?

those formula are in the attachment.

thank you.

@ Ali Ghajar

It really depends on the features of your Graphene such as Fermi level and the thickness, for instance , for the Fermi level equal to zero and the thickness less than 1 micro is for sure negative.

is it possible to fabricate such small thickness 0.22nm by chemical vapor deposition technique?

Jingtian Fang

Hi Jingtian,

Could you tell me what the static dielectric constant( I use it to solve the electrostatics problem) of graphene is ?

Thanks so much!

Xingdong

Hi Xingdong,

You can use a static relative dielectric constant of 6.9 with the graphene thickness being 0.22 nm. These numbers are provided in my PRB paper.

Best,

Jingtian

Jingtian Fang

Thanks so much, Jingtian. I am also wondering if this quantity of dielectric constant is appropriate for both of the perpendicular and parallel cases? I mean whether there would be some significant differences when considering longitudinal electric field and Transverse electric field within graphene?

I am thinking because the density of states of graphene is approaching to zero near Dirac point,which is extremely small compared to that of common semi-conductors, the fermi surface can be tuned easily through charge doping. Thus, the dielectric permittivity has a strong dependence with carrier density. So, when applying bias to graphene, what the static dielectric permittivity could change into?

Hi Xingdong,

I am actually now working on a method trying to resolve the dielectric screening when the electric field is applied parallel to the atomic plane for 2D materials and when the electric field is applied along the periodic direction for 1D materials. It should come up in the coming half a year. I have already gotten some good results. Regarding the effect of carrier density on the dielectric permittivity, I am not sure I understand your arguments. In my opinion, the carrier density should not affect the permittivity. The dielectric matrix depends on the whole details of the band structure and wavefunctions, instead of only the values around the Dirac points. I will update here once I have the results for in-plane screening published.

Jingtian

Jingtian Fang

Thanks again,Jingtian. Iam looking forward to your good results!

Xingdong

Jingtian Fang

Hi Jingtian,

Have you already gotten the static transverse dielectric function of graphene?

Xingdong

Luo Xingdong

Hi Xingdong,

You can refer to this article for now: "First-principles theory of nonlocal screening in graphene", PHYSICAL REVIEW B 83, 081409(R) (2011). Although it did not present the position dependence, it presents the q-dependence of the transverse dielectric function. I think this can be useful for you.

Jingtian

Jingtian Fang

Thanks a lot, Jingtian.

Xingdong