Meaning
Geometric interaction between the microscopic profile of a conductor and the region where current flows at high frequencies determines the total resistance. This surface roughness skin depth effect becomes noticeable when the average height of surface peaks is equal to or greater than the depth of the current layer. As frequency increases, the current is forced into a thinner layer near the surface.
If the surface is rough, the electrons must follow a longer and more tortuous path.
High Frequency
High frequency signals concentrate at the outer edges of a wire or trace. This concentration increases the effective resistance of the conductor.
Resistive Penalty
Surface peaks and valleys effectively increase the distance a signal must travel along a trace. This surface roughness skin depth relationship causes an increase in attenuation that is not accounted for by standard bulk resistivity calculations. For example, at 10 GHz in copper, the current flows in a layer only 660 nanometers thick.
If the surface roughness (Ra) is also 600 nanometers, the losses can double compared to a perfectly smooth surface. High-speed circuit board designers specify low-profile copper foils to mitigate this problem. Smooth foils are treated with chemical bonding agents to maintain adhesion to the dielectric substrate without increasing the signal path length.
Impact Assessment
Impact of the surface profile grows as the operating frequency moves into the millimeter-wave range. Modeling software uses Hammerstad or Huray models to predict these losses during the design phase. Accurate measurements of the surface topography are required to calibrate these models for specific manufacturing processes.
