Equivalent Capacitance Approach to Calculate Effective Roughness Dielectric Parameters for Copper Foils on Printed Circuit Boards

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 (pe...