# Material Conductivity Models

Materials specified using a conductive model can be specified for 2D rectangle and polygon objects.

### Behavior of Material Explorer, meshing algorithm and index monitor

The material explorer will display the surface conductivity. The surface conductivity can be displayed by a refractive index monitor, or in the FDE solver it can be displayed in the modal analysis tab. The meshing algorithm will attempt to automatically place a mesh cell on the boundaries of each planar structure (2D rectangle or 2D polygon), yet there will be situations where it is not possible to align the mesh with all 2D objects. In this situations any planar objects which are not aligned with the mesh will be snapped the nearest mesh cell.

## Conductive 2D

### Parameters and units

- Layer thickness: physical thickness of the sheet which will be represented as a 2D sheet in the simulation [m]
- Conductivity: bulk conductivity of the material [S/m]

The surface conductivity that will be simulated will be the multiplication of conductivity and layer thickness.

## Conductive 3D

This material is implemented as a 3D permittivity. For additional details about this model see the Conductive 3D section in Material permittivity models.

## Graphene

This material employs the surface conductivity to model the optical properties of a graphene sheet. No base material is needed.

### Parameters and units

- Scattering Rate: the scattering rate is related to the sample purity of the graphene sheet. This parameter may be available from the graphene manufacturer, other literature or users' own requirement for this parameter. [eV]
- Chemical potential: chemical potential [eV]
- Temperature: temperature [K]
- Conductivity scaling: This number is typically 1, for a layer of graphene. Under some circumstances, this model can also be used to represent multiple layers by scaling the total conductivity by the number of layers, for example, 2 for two layers of graphene.

### Examples and more information

Graphene material approach

## PEC

A Perfect Electrical Conductor (PEC). The Electric field within this material must be zero. It will have 100% reflection and 0% absorption. There are no parameters for this model.

### Index monitor results

The conductivity of this material is infinite, however since an infinite number cannot be represented in an index monitor plot, index monitors will report a finite but high value of refractive index and surface conductivity.

## RLC

The RLC material is used to specify a lumped element with a given resistance (R), inductance (L), and capacitance (C). The material is implemented as a distributed surface conductivity is calculated based on the lumped R, L, C values and the length of the object along the current flow direction.

The RLC material is defined from the Materials tab of a 2D rectangle object when the material selected for the object is <RLC>. RLC materials will not appear in the Material Database or Material Explorer.

Any combination of R, L, and C can be enabled by selecting the check boxes next to the R, L, and C parameters. If multiple options are selected, the R, L, and C components are added in parallel.

### Parameters and units

- R: resistance [ohm]
- L: impedance [H]
- C: capacitance [F]
- current flow direction: the direction of current flow in the plane of the sheet (x, y, or z)

## Sampled 2D data

The Sampled data material definition uses an automatic fitting routine to generate a multi-coefficient material model of the experimental data over the frequency range specified by the source. The fits can be checked and adjusted in the Material Explorer.

### Parameters and units

- Conductivity or resistivity: Bulk conductivity [S/m] or resistivity [Ωm] of the material.
- Layer thickness: Thickness of the physical sheet which will be represented as a 2D sheet in the simulation. [m]
- Tolerance: The desired RMS error between the surface conductivity of the experimental data and the material fit. The fitting routine will use the least number of coefficients that produce a fit with an RMS error less than the tolerance.
- Max coefficients: The maximum number of coefficients allowed to be used in the material fit. More coefficients can produce a more accurate fit, but will make the simulation slower.

The following advanced options can be set in the Material Explorer:

- MAKE FIT PASSIVE: Set to be true to prevent the fit from having gain at any frequency. By default this is true in order to prevent diverging simulations.
- IMPROVE STABILITY: If this setting is true, the fitting routine restricts the range of coefficients in the fit in order to reduce numerical instabilities which cause simulations to diverge.
- IMAGINARY WEIGHT: Increasing the weight increases the importance of the imaginary part of the conductivity when calculating a fit. A weight of 1 gives equal weight to the imaginary and real parts of the conductivity.
- SPECIFY FIT RANGE: Set to true to decouple the bandwidth used to generate the material fit and the source bandwidth. This option is used in parameter sweeps where the source frequency is changed, and where it is important to keep the material parameters constant over the whole parameter sweep. The fit range should cover the simulation bandwidth.
- BANDWIDTH RANGE: Bandwidth to be used for the fit when Specify Fit Range is true.

### Examples and more information

For an example showing how 2D conductivity models can be generated from 3D material permittivity data.

Tutorial on creating sampled data materials from the graphical user interface and from the script: