Ansys Insight: Scattering rate in surface conductivity of graphene

greg_baethgegreg_baethge Ansys Employee Posts: 13

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.

However, this can be confusing when looking at the expressions for the surface conductivity:

In these expressions the scattering rate parameter Γ should have units of inverse time. How is Γ related to the “scattering rate (eV)” parameter in the material database? The answer is simple: Γ is just the result of dividing the “scattering rate (eV)” parameter by hbar, ℏ, in appropriate units.

Another common parameter found in the literature is the electron relaxation time, τ, which is typically deduced from a comparison with the Drude model and is related to Γ by τ=1/(2Γ). In some references they also relate the scattering rate to the electron mobility.

Comments

  • YevhYevh Posts: 6Member

    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_baethgegreg_baethge Posts: 153Ansys Employee

    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.

  • YevhYevh Posts: 6Member

    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?

  • greg_baethgegreg_baethge Posts: 153Ansys Employee

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

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