Learning Forum

[Greg Baethge]

The 2D surface conductivity model of graphene used in Lumerical’s optical solvers (FDTD and MODE) requires the user to specify the scattering rate for graphene in units of energy (eV), which is a common way to quote this parameter in the literature.

[Yevh]

Dear Greg,
Regarding your last sentence in the post, could you please specify where I can look up the relationship between the scattering rate and the carrier mobility (in order to connect the "C (graphene)" model with "C (graphene) - Falkovsky (mid-IR)" model? In addition, page https://support.lumerical.com/hc/en-us/articles/360043797833 describes only eight parameters (x1 to x8), however one can see ten parameters (from x1 to x10) in Lumerical. What do x9 and x10 stand for in Lumerical's "C (graphene) - Falkovsky (mid-IR)" model? And how I can define the temperature value in "C (graphene) - Falkovsky (mid-IR)" model?

Thank you for your time and consideration.

Best wishes,
Yevhenii.

[Greg Baethge]

Hi Yevhenii,
Thanks for posting your question. Actually, in the "C (graphene) - Falkovsky (mid-IR)" model, we only use the 8 parameters listed in the documentation. It happens that we used our analytical material model, where we can use up to 10 parameters. As x9 and x10 are not used, their values are set to 0 (default value).
You can check that in the expressions
Real part: x6-x1^2*x3/(pi*x2^2)/(w^2+((x1*x4^2)/(x5*x3))^2)*w/(x8*w*x7)
Imaginary part: x1^2*x3/(pi*x2^2)/(w^2+((x1*x4^2)/(x5*x3))^2)*((x1*x4^2)/(x5*x3))/(x8*w*x7)
This model is not temperature dependent. I guess you could include the effect of the temperature by modifying some of the relevant coefficient. I'm not familiar enough with the model to really comment further on this.

[Yevh]

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Hi Greg,

Thanks for the reply.

As well, you cannot specify where I can look up the relationship between the scattering rate and the carrier mobility, right?

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[Greg Baethge]

Unfortunately, no. I had a look at the publications we referenced, but couldn't find any information about this.

[Yevh]

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The relationship between the scattering rate and the carrier mobility can be found in [Luo, X., (2013). Plasmons in graphene - Recent progress and applications. Materials Science and Engineering - R - Reports, 74(11), 351–376] on Page 354.

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[Greg Baethge]

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Thanks for the information, Yevh :)

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