Copper Foil Roughness And High Frequency Loss

At low frequencies the resistance of a trace is set by its cross section, and the surface of the copper can be rough or smooth without consequence. As the frequency rises, the current stops using the whole conductor and crowds into a thin layer at the surface, and at that point the texture of that surface becomes part of the electrical design. A foil that was perfectly adequate for a microcontroller board becomes a measurable loss on a 10 gigabit link.

This article explains why copper foil roughness matters, how the effect is measured and quoted, what the different foil types offer, and what a designer can do about it within a normal stackup.

Why The Surface Enters The Circuit

Copper foil is bonded to the laminate by pressing it against a resin that has to adhere to it. Adhesion is produced by a treatment on the foil surface, and the treatment works by making the surface rough, both chemically and physically. The result is a surface with a profile of a few microns, which is small compared with the width of a typical trace and large compared with the depth of the current layer at microwave frequencies.

The consequence is that the current path is longer than the geometric length of the trace. The current follows the contours of the treated surface rather than a flat plane, so the effective resistance rises and the loss per unit length rises with it. The effect grows as the frequency rises, because the current layer becomes thinner and follows the profile more closely, until at the highest frequencies the whole of the current is travelling over the texture.

Skin Effect And Where The Current Flows

Skin depth is the depth at which the current density has fallen to about 37 percent of its value at the surface, and it falls as the square root of frequency. At 1 MHz it is about 66 microns in copper, which is thicker than any foil; at 1 GHz it is about 2 microns, which is comparable with the roughness of a standard foil; at 10 GHz it is under a micron. The transition from a smooth conductor to a rough one is therefore a matter of frequency and of foil treatment rather than of trace geometry.

Two consequences follow. The first is that the loss of a transmission line is not simply resistive, because the roughness also changes the phase velocity slightly and therefore the delay. The second is that a circuit that was modelled with a smooth conductor will show more loss and more dispersion when it is built, and the difference is largest on the long routes, where the accumulated length multiplies the per unit figure.

How Roughness Is Described

The profile is quoted in several ways, and the numbers are not interchangeable. The arithmetic mean roughness and the root mean square roughness describe the average deviation from a mean line, while the maximum peak to valley figure describes the extreme. A manufacturer may also quote the tooth profile from a cross section, since the shape of the teeth matters as much as their height when the current is following them.

Measurement is made with a profilometer on a sample of the foil, or from a cross section examined at magnification. Because the figures depend on the stylus, on the evaluation length and on the filtering, a roughness number without its method is of limited use in a comparison. The practical approach is to compare offers in terms of the foil type and the measured loss on a test coupon rather than in terms of a single roughness figure.

Foil Types And Their Trade-Offs

Standard electrodeposited foil has the highest profile and the best adhesion, and it is the default for general purpose boards. Reverse treated foil is deposited with a smooth matte side and a rough treated side, so the smooth face can be laminated against the dielectric on the layer where the signal runs, while the rough face grips the prepreg on the other side. Very low profile and hyper very low profile foils reduce the treatment further, at a cost premium and with a narrower lamination window.

Rolled annealed foil is made by rolling rather than by deposition, and it is smoother and more ductile than any electrodeposited product. It is used on flexible circuits and on the most demanding high frequency designs, where its smooth surface and predictable grain structure are worth the extra cost. The choice is a trade between loss, adhesion and price, and it is made per layer rather than per board.

Design And Stackup Consequences

The most effective action is to put the sensitive signals on the layer that carries the smooth foil face, and to keep the reference plane on a layer whose roughness does not matter, since return current in a plane is spread over a wide area and is less affected. Layer ordering for this purpose is discussed under layer stackup from one to eight layers and multilayer PCB advantages at high speed.

The geometry of the route matters as well. Wider traces have proportionally less surface per unit of cross section, so a wide trace on a thin dielectric is more efficient than a narrow one on a thick dielectric, and short routes are obviously better than long ones. The transmission line forms themselves are described under microstrip and stripline routing.

Modelling, Verification And Acceptance

Field solvers accept a roughness parameter and apply a correction to the conductor loss, most commonly a model that multiplies the smooth conductor loss by a factor derived from the profile and the skin depth. The correction is an approximation, and its accuracy depends on the parameter being fed to it, so the model should be checked against measurement rather than trusted on its own.

Verification is done on a coupon that is built as part of the panel and measured with a vector network analyser. The result is compared with the specification and with the model, and the difference is attributed to the foil, to the dielectric or to the geometry. Acceptance is then written into the fabrication drawing as a foil type and a loss limit rather than as a roughness number, because that is what both the shop and the designer can actually control.

Additional Considerations for This Build

Practical attention to insertion loss pays for itself here, because it decides whether the finished board behaves as the drawing intended. Where the requirement is not stated on the fabrication drawing or in the assembly notes, the shop has to assume a default, and that default is rarely the value the design was simulated with. Stating insertion loss explicitly, together with the tolerance that applies, removes the assumption and keeps the result predictable from batch to batch.

Process Control and Verification

On a design of this kind, conductor loss is the item that decides how the rest of the board is arranged. Where the requirement is not written down, the shop supplies its own default, and the default is chosen for the process rather than for the design. The measurements that matter are the repeatable ones: conductor width and spacing, annular ring, finished hole size, plating thickness and surface finish are all verifiable on a coupon that travels with the panel.

FAQ

Does roughness matter at 1 GHz? It does, though the effect is modest. At 1 GHz the skin depth is about 2 microns, which is the order of the profile of a standard foil, so a very low profile foil will show a measurable but not dramatic reduction in loss.

Can a smooth foil be substituted without requalification? A change of foil type changes the loss and the impedance of every transmission line on the affected layers. It requires a new set of coupons and, on a high speed design, a new simulation run.

Is the dielectric loss or the conductor loss dominant? Above a few gigahertz the dielectric loss usually dominates on ordinary FR-4, so a change of foil alone will not rescue a design that is limited by the laminate.