Layered Impedance Boundary Condition
The Layered Impedance Boundary Condition is an extension of the Impedance Boundary Condition that allows to model a sequence of geometrically thin layers on top of a substrate. It is used on exterior boundaries where the field is known to penetrate only a short distance outside the boundary. In brief, this feature combines a Layered Transition Boundary Condition with an Impedance Boundary Condition of the type:
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The layer stack is built using a Layered Material. For each layer in the Layered Material, the transfer and surface impedances are obtained from the layer thickness and the material properties. The impedances are then used to relate the discontinuity in the tangential electric field to the current flowing on the surface of either side (up/down) of the corresponding layer. The mathematical details relative to the field propagation in the layer stack can be found in the Layered Transition Boundary Condition section.
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See Layered Material, Layered Material Link, Layered Material Stack, Layered Material Link (Subnode), and Single Layer Materials in the COMSOL Multiphysics Reference Manual for details on the definition of layered materials.
The Layered Impedance Boundary Condition is based on the assumption that in the thin layers and in the substrate the wave propagates essentially in the normal direction. Thus, the wave could be incident in the normal direction or the wave could be refracted to propagate in a direction close to the normal direction. The latter condition is fulfilled for a good conductor.
The thickness of the layer should be less than the radius of curvature for the boundary and the material properties are assumed to be isotropic.
Shell properties
The Shell Properties section displays which Layered Material is coupled to the Layered Impedance Boundary Condition.
Clear the Use all layers check box in order to select a specific Layered Material from the list. The Layered Impedance Boundary Condition feature is then applicable only on the boundaries where the chosen Layered Material is defined.
You can visualize the selected Layered Material and the layers that constitute it by clicking the Layer Cross Section Preview and Layer 3D Preview buttons.
The thickness of the Layered Material should be set as follows, depending on the type of material:
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For a general Layered Material, added through a Layered Material Link or a Layered Material Stack, the Thickness is set in the Layer Definition section of the Settings window. Several layers may be defined in the table, and the Thickness should be defined for each of them. The total thickness of the Layered Material is the sum of all the layers thicknesses.
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When the Layered Material is a Single Layer Material, the Thickness is set in the Material Contents section in the Settings window. Alternatively it can be set in the Layer Definition section of the Shell property group Settings window.
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In a Material node, the layer Thickness is set in the Material Contents section by adding a Shell property group from the Material Properties section in the material Settings window. This automatically adds a Shell subnode under the Material node, transforming it into a Layered Material.
Layer Properties
The Layer Properties section specifies the material properties of the thin layers constituting the stack located on top of the substrate. Select an Electric displacement field model — Relative permittivity (the default), Refractive index, Loss tangent, loss angle, Loss tangent, dissipation factor, Dielectric loss, Drude-Lorentz dispersion model, or Debye dispersion model. See the Wave Equation, Electric node, Electric Displacement Field section, for all settings. However, notice that only isotropic (scalar) material parameters are supported for this boundary condition.
The defaults use the values From material. In this case, the material properties are taken layer by layer from the Layered Material existing on those boundaries where the Layered Impedance Boundary Condition feature is enabled. Otherwise, choose User defined and enter a value or an expression. In the latter case all layers constituting the chosen Layered Material will take on the same given value for the selected material property.
Substrate Properties
The Substrate Properties section specifies the material properties of the thick domain that is not included in the model, being approximated by an Impedance Boundary Condition.
Select a Surface impedance definition — From material properties (the default) or User defined.
Select a Substrate Material from the list of materials that have been introduced in the model previously. Select an Electric displacement field model — Relative permittivity (the default), Refractive index, Loss tangent, loss angle, Loss tangent, dissipation factor, Dielectric loss, Drude-Lorentz dispersion model, or Debye dispersion model. See the Wave Equation, Electric node, Electric Displacement Field section, for all settings. The defaults use the values From material. In this case, the material properties are taken from the specified Substrate Material. Otherwise, choose User defined and enter a value or an expression.
Enter a Surface impedance for User defined (SI unit: Ω) in the Surface impedance definition. The default is Z0_const that is the predefined COMSOL constant for the wave impedance of free space.
See Skin Depth Calculator to evaluate the skin depth of a homogeneous material.