Application Note AP8155 

Surface roughness of copper in core layers

The thermal stability (and hence the reliability) of a PCB structure will relate to the mechanical strength of the bond between dielectric and copper layers. In order to provide good adhesion between copper and dielectric materials in core layers PCB materials vendors control the roughness of the associated copper layers (typically by chemical treatment). Since the roughness is a random quantity it is commonly specified in terms of the rms (root-mean-square) height h of the surface unevenness. 

The surface roughness of the copper layers will have no effect on current at low frequencies as, at low frequencies, the depth of current penetration will exceed the value of h. At high frequencies, however (i.e. in the GHz region), the skin effect (see below) will be significant as, at high frequencies, most current  flows in the outside of the conductor (in a very narrow skin on the conductor — hence the name). 

The skin effect 

Skin effect refers to the phenomenon where electromagnetic fields (and hence the current) decay rapidly with depth inside a conductor.

The diagram above graphs the amplitude of magnetic field against depth (z) into a conductor and shows the variation of the amplitude of magnetic field H_y in the z-direction where H₀ is the amplitude at the conductor surface. As a consequence of Ampere's Law in a conductor, a conduction current is associated with H_y. This current will be perpendicular to H_y. Thus there is a conduction current of density Jx, (where J₀ is the current density at the surface) whose amplitude will vary in the same manner as that for H_y. The distance d is the value of z at which |Jx| = J_0/e. This is also the same value at which the rectangular area dJ₀ in the diagram equals the area under the exponential curve. d is known as the Skin Depth. 

Surface roughness effects

At very high frequencies (where skin depth d is less than h, i.e even smaller than the conductor surface roughness) current follows the contours of the surface of the copper, effectively increasing the distance over which current must flow and hence the resistance of the copper. Chemical treatments producing roughness heights of several microns are typical with FR-4 dielectrics resulting in signal attenuation at high frequencies. Attenuation factor variations with frequency for different roughness values (in µm) are shown as shown in the graph below. From the chart it can be seen that as the surface roughness increases attenuation occurs at lower frequencies; at low values of roughness attenuation is insignificant below 1GHz, at higher values attenuation can begin at frequencies in the low hundreds of MHz.

Conductor losses in PCBs

Losses that need to be considered by the PCB designer/fabricator can be summarised as conductor and dielectric losses. Conductor losses include DC, skin effect and surface roughness losses and the designer will need to balance the trade-off associated with foil roughness and conductor loss with the requirement for robust packaging — the challenge is to optimize conductor loss while ensuring good dielectric/foil adhesion. Designers and fabricators will need to discuss with the PCB vendor the surface treatments and dielectric materials available.

Graphing loss due to surface roughness with the Si9000

The Si9000 versions 9.10 and above allow the user optionally to include the RMS value for surface roughness in frequency dependent calculations and chart dielectric losses along with conductor losses and attenuation values that include compensation for surface roughness.

Values for surface roughness (obtainable in consultation with the board manufacturer) are specified in the currently chosen units.

Typical values for RMS roughness could be 0.8 µm (0.03mils) for stripline, 1.6µm (0.06mils) for surface microstrip. The Si9000 assumes losses on both sides of a copper trace.

The Si9000 graph above charts all losses, the dielectric loss and the significant increase in the overall loss due to surface roughness, allowing the materials supplier to isolate the contributions of the different loss mechanisms. For designer and supplier the Si9000 will prove invaluable in recording such data to guarantee product consistency and in developing improved material behaviour.