Surface roughness can increase electric field strength and capacitance.

Conductor surface roughness directly interferes with conduction in high-frequency circuits. How is this? Surface conductivity (or RF resistivity) of a metal film is a function of frequency, as conduction decreases exponentially from the surface into the film. But it’s a Catch-22; the “roughness rule” states the rougher the interface between metal and substrate, the better the adhesion, but the higher the attenuation. 

Scientists have long studied the effect of grooves present on the surface of a conductor, having noted the additional losses through the conductors caused by them. In worst-case scenarios, the grooves cause losses that sometimes reach a factor of two. The explanation proposed was electromagnetic (EM) waves travel mostly along the surface of a conductor; e.g., the copper signal trace. The grooves effectively cause the signal paths to become longer, as the EM waves, while traveling along the surface, enter in and then exit from the grooved shapes.

But it isn’t as simple as integrating the conductivity of remaining “non-rough” metal. RF currents seem to find a way up and down the hills and valleys. It’s possible to observe the attenuation of like structures of various roughness levels and come up with an empirical formula for the increase in attenuation.

Let's say, for example, we were to make a table of the incremental conductivity versus skin depth. At the surface, conductivity is 100%; at one skin depth, it is decreased to 36.8%, and so forth, until at five, 0.7%. Thus, if you have five skin depths of metal, you have more or less captured all the conduction you can.

Skin effect. The surface roughness of a conductor thus creates a longer mean path, resulting in additional losses. Effectively, the higher the degree of conductor surface roughness, the higher the resistance from skin-depth effects. When an EM wave propagates through a conductor, this skin effect tends to change the current distribution of the EM wave to concentrate more toward the surface of the conductor, rather than remaining deep within the conductor material.

When designing an RF circuit, one must choose the most appropriate PCB material for the application. In this context, modern CAE simulation tools help predict the electrical performance of circuits on different types of PCB materials. These tools use material parameters in their calculations, with relative Dk being one of the most important. But most such tools often overlook a critical material parameter; i.e., the surface roughness of the conductor. Contrary to popular opinion, the conductor surface is never perfectly smooth, and this has real consequences in high-frequency circuit design.

When using EM simulators or other commercial CAE tools, designers account for the effects of conductor surface roughness by relying on the traditional Morgan Correlation. They do this by applying a surface-roughness correction factor, Kr, which is a numerical factor based on the ratio of a smooth surface to a rough one. While calculating the loss of high-frequency microstrip lines, using the Kr factor does a good job of closely matching the measured results for conductor losses. Nevertheless, there are cases in which both predictions and measurements fail to match as closely as one might wish.

Such deviations between the calculated and measured values can be expensive at the design stage, especially since achieving the desired performance specifications can lead to additional design iterations. Avoiding such delays in design might mean considering carefully the RF PCB laminate in terms of its conductor surface roughness.

Copper cladding types. Manufacturers must use some form of a copper cladding on the PCB substrate. Three types are most common: rolled-annealed (RA) copper, electrodeposited (ED) copper and reverse-treated (RT) copper.

Forming RA copper foils involves rolling the copper ingot through a rolling mill, where subsequent passes through the rollers results in a thin copper foil with good thickness consistency.

ED copper formation requires depositing copper onto a slowly-rotating, polished stainless-steel drum, within a bath containing a solution of copper sulfate. While the surface roughness of the copper where it meets the stainless-steel drum is similar to that of RA copper, the copper surface of the deposition side facing the solution is much rougher.

RT foil production begins by plating the ED copper foil on the drum side, when the foil on the bath side is still low profile.

Since the copper foil must adhere to the dielectric material, which might range from FR-4 to polytetrafluoroethylene (PTFE) substrates, the copper surface must be treated to increase its adhesion. This is because a perfectly smooth copper surface does not adhere ideally to the dielectric. Whether formed by RA or ED processes, an untreated copper film has a surface typically covered with tiny tooth-like imperfections, and the jagged surface is ideal for forming a strong bond between the copper and dielectric.

Yet this is in direct contrast with the requirements of a good transmission line, since the rough surface is then less-than-ideal for transmission of high-frequency EM waves. Conversely, a surface with a mirror-like finish on a perfectly smooth copper foil is inadequate for foil-to-dielectric adhesion.

Ultimately, fabricating PCBs with low-loss conductors, while maintaining good adhesion between the dielectric material and copper, depends on achieving a compromise in the surface composition of the copper foil.

Effect on Dk. Another important factor is the relative permittivity of the dielectric material, commonly referred to as its dielectric constant, or Dk. In reality, Dk varies with frequency, rather than being a constant.

The value of Dk is often assumed to be an intrinsic property of the material. However, manufacturers generate the effective Dk using a specific test method, sandwiching the dielectric material between two copper plates. When comparing simulation against measurements, there is often a discrepancy in insertion loss caused by increased phase delay, resulting from surface roughness.

The explanation is simply surface roughness decreases the effective separation between the parallel plates, thereby increasing the electric field strength, leading to an increase in capacitance. This accounts for the increase in effective Dk.

Laminate suppliers commonly use the clamped stripline resonator test to measure the effective Dk of a material. The test is defined by IPC-TM-650 2.5.5.5C, which was widely adopted by industry because it is repeatable, accurate and fast. As the measurement is highly dependent on the test apparatus and measuring conditions, it does not guarantee the values are accurate for design applications. This is primarily because copper foils used for the test are not physically bonded to the laminate, leaving small air gaps in between the layers, affecting the results. Designers avoid this mismatch during simulations by using a multiplication factor for the Dk for their impedance calculations, rather than using the Dk factor directly.

Commercial laminates. Recognizing the effect of surface roughness on performance at high frequencies, suppliers offer commercial laminates with copper foils in numerous profiles. They produce these laminates with different levels of copper treatment. For instance, they offer low-profile (LP) copper conductors that provide excellent adhesion of the copper to the dielectric material, while the smooth conductor surface improves etch definition and reduces conductor losses.

Other suppliers offer materials with low-profile, reverse-treated copper foils, ideal for high-frequency analog and digital circuits. They come in a variety of panel sizes and standard dielectric thicknesses, with 0.5 or 1-oz. low-profile, reverse-treated ED copper cladding.

Although special materials can help overcome the effects of conductor surface roughness at high frequencies, selecting a PCB material that minimizes the effects of surface roughness is not a simple task. When seeking to minimize the effects of surface roughness, materials with low-profile copper foils will perform better with low conductor losses at higher frequencies than materials with foils that feature higher profiles.

Akber Roy is chief executive officer of Rush PCB Inc., a printed circuit design, fabrication and assembly company (rushpcb.com); roy@rushpcb.com.