Effective roughness dielectric (ERD) is a homogeneous lossy dielectric layer of certain thickness with effective (averaged) dielectric parameters. The ERD layer is used to model copper foil roughness in printed circuit board interconnects by being placed on a smooth conductor surface to substitute an inhomogeneous transition layer between a conductor and laminate substrate dielectric. This work derives the ERD parameters based on the understanding that there is a gradual variation of concentration of metallic inclusions in the transition layer between the dielectric and foil. The gradual variation can be structured as thin layers that are obtained using the equivalent capacitance approach. The concentration profile is extracted from scanning electron microscopy or high-resolution optical microscopy. As the concentration of metallic particles increases along the axis normal to the laminate dielectric and foil boundary, two regions can be discerned: an insulating (prepercolation) region and a conducting (percolation) region. The rates of increase in effective loss (or corresponding conductivity) in these two regions differ significantly. The proposed model of equivalent capacitance with gradient dielectric is applied to a number of different types of copper foils. The frequency-dependent dielectric parameters of the homogenized ERD are calculated from the equivalent capacitance. The results are validated using 3D numerical electromagnetic simulations. There are two types of numerical models: with homogeneous ERD parameters and layered. Both models show excellent agreement with measurements.


Electrical and Computer Engineering

Keywords and Phrases

Complex permittivity; Copper foil; Dielectric constant; Dissipation factor; Electric percolation; Loss constant; Numerical electromagnetic simulations; Phase constant; printed circuit board; Roughness; S-parameters; Signal integrity; Stripline

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Document Type

Article - Conference proceedings

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Publication Date

01 Apr 2018