Contact Impedance
Use the Contact Impedance node on interior boundaries to model a thin layer of resistive material. It can also be added as a pair using a Pair Contact Impedance node. The feature allows specifying the contact impedance either by entering the properties of the material together with the layer thickness, or by entering the impedance properties of the thin layer directly.
The feature, in stationary studies, applies the following conditions that relate the normal electric current density with the jump in the electric potential:
The first two equations refer to a layer impedance specified using the bulk material conductivity σs and the layer thickness ds, while the last two equations refer to the case in which the surface resistance ρs is specified. The indices 1 and 2 refer to the two sides of the boundary. These parameters work the same as with Distributed Impedance.
For the frequency domain and Time Dependent study types, this boundary condition is slightly more sophisticated and accounts also for capacitive coupling. The bulk material relative permittivity εr or the layer capacitance Cs can be specified.
The equations used in Frequency Domain studies are:
In Time Dependent studies:
Contact Impedance
Select a potentially complex-valued Layer specification—Thin layer (the default) or Surface impedance.
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For Thin layer, enter values or expressions for the:
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Surface thickness ds (SI unit: m). The default is 5·10−3 m (5 mm).
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Electrical conductivity σ (SI unit: S/m) and Relative permittivity εr (dimensionless). The defaults take values From material. For User defined, enter different values or expressions. The default electrical conductivity is 1 × 10−2 S/m and the default relative permittivity is 1.
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For Surface impedance, enter values or expressions for the Surface resistance ρs (SI unit: Ω ·m2) and the Surface capacitance Cs (SI unit:  F/m2). The default surface impedance is 1 × 10−8 Ω ·m2 and the default surface capacitance is 0 F/m2.
Thin-Film Resistance: Application Library path COMSOL_Multiphysics/Electromagnetics/thin_film_resistance