DesignCon 2016

Effect of conductor profile structure

on propagation in transmission lines

Allen F. Horn III, Rogers Corporation

Associate Research Fellow,

Lurie R&D Center,

PO Box 157

Rogers, CT 06263 USA

al.horn@rogerscorp.com

Patricia A LaFrance, Rogers Corporation

Sr. Engineering Assistant

pat.lafrance@rogerscorp.com

Christopher J. Caisse, Rogers Corporation

Sr. Engineering Assistant

chris.caisse@rogerscorp.com

John P. Coonrod, Rogers Corporation

Technical Marketing Manager

john.coonrod@rogerscorp.com

Bruce B. Fitts, Rogers Corporation

Staff Development Engineer

bruce.fitts@rogerscorp.com

mailto:john.coonrod@rogerscorp.commailto:bruce.fitts@rogerscorp.com

2

Abstract

Designers of high frequency electrical devices have long known that conductor surface

roughness affects loss. Earlier correlations such as Morgan under predict insertion loss

by a large margin at higher frequencies and on narrower transmission lines where

conductor effects dominate. The present work experimentally demonstrates that the

recent Hall-Huray “snowball” model and the Sonnet conductor loss correlation correctly

predict the shape of the insertion loss versus frequency curve up to 110 GHz on treated

(nodulated) conductor surfaces. Quantitative agreement, however, requires empirical

adjustment of the surface area index (SAI), snowball radius or RMS roughness. It is also

shown that the untreated (not “nodulated”) surfaces of reverse-treated foils have little

effect on increasing conductor losses, even though they exhibit a significant RMS

roughness and SAI.

Authors’ Biographies

Allen F. Horn, III, Associate Research Fellow, received a BSChE from Syracuse

University in 1979, and a Ph. D. in Chemical Engineering from M.I.T. in 1984. Prior to

joining the Rogers Corporation Lurie R&D Center in 1987, he worked for Dow Corning

and ARCO Chemical. He is an inventor/co-inventor on 16 issued US patents in the area

of ceramic or mineral powder-filled polymer composites for electronic applications.

Patricia A. LaFrance, Engineering Assistant, has 25+ years’ experience in the formulation

and testing of composite materials for industrial and electronic applications. She joined

the Rogers R&D Center in 1997.

Christopher J. Caisse is a Senior Engineering Assistant at the Lurie R&D Center. Prior to

joining Rogers he worked at Lucent Technologies and OFS Optics. He has spent the past

12 years developing high frequency circuit materials, automated test software, and

electrical and thermal test methods. Chris is working towards a BSEE at UCONN.

John Coonrod is a Technical Marketing Manager for Rogers Corporation, Advanced

Connectivity Solutions. John has 26 years of experience in the PCB industry. The first

half of his career was spent on flexible circuit design, processing, and materials

engineering. The past 13 years he has worked on high frequency circuit fabrication,

application support, and conducting electrical characterization studies of Rogers HF

laminates. John has a BSEE degree from Arizona State University.

Bruce Fitts received a BS in Chemical Engineering from Northeastern University in

1972. He served as a member of the corporate R&D Group of the Rogers Corporation

from 1972 to 1993 formulating polymeric composite materials. From 1993 to 2002, he

was the product development manager for the Moldable Composites Division of Rogers

Corporation, and continued to work with Perstorp and Sumitomo after the sale of the

division. In 2006, Bruce re-joined the R&D staff at the Advanced Connectivity Solutions

division where he has worked on the development of polymer composite laminates for

advanced printed circuit applications.

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Introduction and Summary

As operating frequencies have increased and dielectric thickness has decreased for both

high speed digital and RF planar circuits, the effects of conductor profile on both

attenuation and propagation constant have become more evident. In the present work we

have characterized the roughness parameters Rq (RMS), Rz (peak-to-valley), and surface

area index (SAI) of both the treated and untreated side of copper foils by white light

interferometry. The SAI is the ratio of surface area of the structured surface to the

smooth base area. The nodule radius of the copper treatment was estimated by SEM

analysis. For the treated sides of the various foil samples, the measured Rq values ranged

from 0.2µ to 3.0µ, SAI values from 1.0 to 3.9, and nodule radii from zero to 0.9µ.

For the untreated (nodule-free) sides, the measured Rq values ranged from 0.2µ to 1.3µ

and SAI values from 1.0 to 2.2.

Microstrip fifty-ohm transmission lines were fabricated on 0.002” to 0.007” (0.05 mm to

0.2 mm) ultralow loss dielectric laminates. Standard laminates were made with the

treated (nodulated) side facing the dielectric. These materials exhibited an increase in

insertion loss with increasing profile, as measured by SAI and Rq.

A number of the reverse-treated foils exhibited sufficient adhesion on the untreated

(nodule-free) side to allow fabrication of test circuits with the untreated side facing the

dielectric. For this case, increasing Rq and SAI had little effect on the insertion loss. The

lack of nodules and relatively long range periodicity of thickness variation leads to much

lower energy dissipation. This is inherent in the Hall-Huray model.

Comparison modeled with measured data show very good agreement of the shape of the

insertion loss curve with Hall-Huray conductor model and the Sonnet correlation of

surface inductance to foil profile. Due to the ambiguity in measuring nodule diameter,

small adjustments to the parameters are required for quantitative agreement with

relatively low profile foils.

Quantitatively matching the insertion loss curves of the two high profile dendritic foils,

with a structure quite different than the nodulated foils requires larger adjustments for

quantitative agreement.

Background

It has been known since the early days of radar development using waveguides that rough

surfaces will increase the conductor loss. In 1949, S. P Morgan1 published the results of

numerically modelling the effect of rectangular and square grooves in a conductor with

an aspect ratio of about 1 to 1. For a signal traveling perpendicular to the groove

direction, the conductor loss would increase by a maximum of a factor of two with

increasing frequency as the skin depth approached and then became smaller than the

groove height. The increase in modelled conductor loss when the signal ran parallel to the

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grooves was much smaller. Similar results were obtained in 1996 by Groisse et al2. by a

finite element method

The Morgan correlation was adapted into an automated microstrip insertion loss and

impedance calculation described by Hammerstad and Jensen3 (H&J). The correlation is

incorporated as a multiplicative correction factor KSR to the attenuation constant

calculated for a smooth conductor.

α cond, rough = α cond, smooth · KSR (1)

where α cond, smooth is the attenuation constant calculated for a smooth conductor and

2

4.1arctan2

1 KRMS

SR

R (2)

where RRMS is the RMS value of the conductor roughness and δ is the skin depth. It

should be noted that both α cond, smooth and KSR are functions of frequency. When the

ratio of RRMS/ δ is small, as with a smooth conductor or at low frequencies where the skin

depth is large, the value of KSR is close to one. As the ratio becomes large with higher

profile conductors and higher frequencies, the value of KSR approaches two. This

correlation predicts a “saturation effect,” i.e., that the maximum effect of the conductor

roughness would be to double the conductor loss. This result also implies that the

conductor loss for a lower profile foil will eventually approach that of a rough foil as

frequency increases.

Over the years, the Morgan correlation has been used with a reasonable degree of success

and is standard text book knowledge4. However, as higher frequencies and thinner

circuits with narrow conductors have become more prevalent, inaccuracies in the model

have become evident.

Conductor loss models

In the last decade, a number of authors have examined the effect of conductor roughness

on the propagation of signals in PCD-based transmission lines.5-9

Brist et al5 and Liang

et al6 used the Morgan correlation (equation 2) to achieve a causal model of laminate

performance that agreed well with measured data up to 20 GHz. Hinaga et al7 used a

similar correlation to obtain more accurate dielectric loss values. Chen8 used numerical

EM modeling of a rough conductor with electroless nickel-immersion gold plating and

achieved good agreement with measured data. Tsang et al9 have performed numerical

and analytical simulations that show that for multi-scale rough surfaces (in contrast to the

periodic surfaces treated by Morgan), saturation does not occur and increases of greater

than a factor of two in conductor loss can occur.

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“Multi-GHz, causal transmission line modeling methodology with hemispherical surface

roughness approach” was proposed by Hall et al. “Fundamentals of a 3-D “snowball”

model for surface roughness power losses” by Huray et al describes the approach of

calculating the increase in attenuation factor due to the copper foil treatment modeled as

spheres and the model is described in greater detail in later work.

The simplified Hall-Huray model is applied as a roughness correction factor to the

calculated conductor attenuation factor for smooth foil.

α cond, HH rough = α cond, smooth · KHH (3)

where KHH is given by

(4)

and SAI is the surface area index and a is the nodule radius as described in detail by

Griesi et al. Griesi et al also discuss a number of methods of improving the

characterization of the foil surfaces with optical image analysis and mechanical

profilometer of the untreated surfaces of the base foil. The modeled data agreed very

well with measured on a microstrip TL with a relatively smooth copper foil exhibiting an

RMS surface roughness of 1.2µ, an effective nodule radius of 0.63 µ, and an SAI of 1.77.

Simonovich also discusses an alternative method of determining modeling parameters for

the Hall-Huray method. The predicted values of attenuation factor for the Hall-Huray

and H&J methods for three of the copper foils studied is shown in figure 1.

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A number of authors14-20

have observed an increase in the propagation constant, phase

length, and group delay that appears as an increase in extracted permittivity when the

substrate properties are calculated from circuit performance. Deutsch et al14

noted a 13%

increase in extracted permittivity for an unspecified high profile foil compared to a low

profile foil on 2.6 mil thick laminate from 250 MHz to 2 GHz. More recent work16

recorded an approximate 15% increase in the extracted permittivity of a 50 ohm TL on 5

mil very low loss laminate with 3µ RMS ED foil compared to that clad with 0.4 µ RMS

rolled foil. Other works have noted increases of 2 to 5% extracted permittivity on thicker

laminates with higher profile foils. The earlier models of conductor profile effects1-13

do

not address the observed increase in propagation constant and extracted permittivity.

A model based on correlating an increase in surface impedance with measured RMS

roughness has been incorporated into Sonnet Software and has been found to yield good

agreement between measured and modeled data for both attenuation and propagation

constants17-18

. Schlepnev et al19

proposes that the increase in extracted permittivity is

due to increased capacitance caused by the copper foil dendrites. Koledintseva et al20

propose an “effective roughness dielectric” where the local permittivity and DF are

effected by the copper foil dendrite structure. The values of the permittivity, DF, and

thickness of the “ERD” were extracted from measured foil roughness parameters and the

measured attenuation and phase constants of circuits made with the various foils. The

values of the ERD layer are the reinserted in a 3D EM model to calculate circuit

performance arriving at good agreement between modeled and measured values.

Current Work

In the current work, we have characterized the surface of a wide range of copper foils

using white light interferometry (WLI) and scanning electron microscopy (SEM). The

smoothest of surfaces were nearly perfectly smooth with surface area indices of less than

1.1 and no visible nodules. The untreated surfaces of reverse-treated (RT) foils, though

having no nodules, exhibited RMS roughness values of greater than 1µ and SAI values of

greater than two. The highest profile foils exhibited SAI values approaching 4 and a

range of nodule sizes from 0.3 to 1 microns.

The foils were laminated to several thin (0.05 to 0.2 mm) low loss dielectric materials.

Microstrip fifty ohm transmission lines were etched and the differential insertion loss

and phase length were measured to frequencies as high as 110 GHz. We were able to

fabricate and test a number of circuits with the untreated surface facing the dielectric, to

measure the effect of the different surfaces independently.

It is found that the RA foil behaves like perfectly smooth foil, in spite of having an SAI

value of greater than 2 and 0.3µ nodules that are clearly visible by SEM. The untreated

side of the RT foils also exhibit loss values approaching those of perfectly smooth foil,

again in spite of measured RMS roughness values greater than 1µ and SAI values of

greater than 2. It is implicit in the Hall-Huray model that these nodule-free surfaces

exhibit very low loss. We show experimentally that the Hall Huray model fits the shape

of insertion loss curves out to 100 GHz. However, with higher profile surfaces, the

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modeling parameters need to be adjusted significantly from what is measured by SEM

and WLI.

Experimental methods and results

Microstrip laminate samples

Fifty-ohm microstrip transmission lines were photo-lithographically etched onto thin low

loss high frequency circuit laminates. The majority of the samples ranged from 0.002” to

0.007” in thickness. Thin samples of low loss dielectric materials maximize the

contribution of the conductor to signal attenuation and propagation.

Rogers ULTRALAM® 3850HT LCP (liquid crystal polymer) makes an excellent test

vehicle for circuit properties. This material is a glass fabric-free, pure resin circuit

substrate that relies on the inherently low CTE of the oriented LCP film to achieve a good

in-plane CTE match to the copper foil. Since the ULTRALAM 3850HT substrate

consists of a single pure substance, the variation in the dielectric properties is inherently

low and there is no question of “glass to resin ratio” affecting the dielectric properties.

When tested by a variety of methods, the dielectric constant of the LCP is 3.05 and the

dissipation factor is 0.002 at 10 GHz.

Rogers RO3003™ laminate is a silica-filled PTFE composite exhibiting a dielectric

constant of 3.0 and DF of about 0.001 at 10 GHz. Rogers RO1200™ laminates are glass

fabric reinforced silica-PTFE composites targeted for ultralow loss digital applications,

with a dielectric constant of 3.0 and DF of about 0.0015 at 10 GHz.

The majority of our samples were electrically characterized up to 50 GHz using long and

short straight 50 –ohm transmission lines held in an Intercontinental W-7000

Intercontinental Universal Substrate Fixture. The system was SOLT calibrated to the

cable ends. Full S-parameter measurements were made with a 50 GHz Agilent PNA on

long and short TLs. Insertion loss was calculated from the difference in S21 of the long

and short TLs divided by the length difference. Differential phase length was calculated

similarly to yield the effective permittivity, Keff of the microstrip circuit and the substrate

permittivity, K’sub was extracted variously using Rogers’ impedance calculator, “MWI”

based on the method of H&J, HFSS, or Sonnet Software.

To obtain the 110 GHz data, we used 1mm Southwest Microwave model # 2492-04A-6

end launch connectors with a grounded co-planar launch to 50 Ω microstrip TL. The

lines were tapered in the launch area to improve the impedance match. Calibration was

done using a 1mm mechanical kit with offset shorts SOLT for a single sweep calibration

from 33 MHz to 110 GHz. S-parameter data were collected with a Keysight N5251A

mmWave PNA, with 3303 testing points, IF Bandwidth set uo 300 Hz, and the power

level at -5 dBm.

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Profile measurements

Planer organic composite circuit substrates are clad with one of three types of

commercially available copper foil specifically manufactured for that purpose: rolled

annealed, (RA), electrodeposited (ED) and reverse treated (RT). The foils are treated by

the foil manufacturers with different types of treatments to improve and preserve

adhesion to different types of circuit substrates. Historically, high profile (“rough”) foils

have been used to increase adhesion to the dielectric material while lower profile foils

are used to improve etch definition or reduce conductor loss.

The surface profiles in the current work have been characterized using a Veeco

Metrology Wyko® NT1100 optical profiling system. The instrument’s operation is

based on white light interferometry (WLI). This non-contact method generates a three

dimensional image of the surface topography with a resolution of about 1 nm in a 1 mm

square area. The profile can be characterized by a wide variety of different statistics,

including Rz, the peak-to-valley roughness, Rq (or RRMS), the root-mean-square

roughness, and the surface area index (SAI). RRMS is most widely used in characterizing

conductor roughness in high frequency electrical applications. However, Rz values based

on mechanical profilometers are still widely reported by foil manufacturers. A

representative WLI trace is shown in figure 2.

The SAI is the measure of visible surface area to the underlying flat smooth surface. It

should be noted that only the visible surface area is counted by the interferometry

method. A checkerboard square with side 2a will have an SAI of (π/2 + 0.215) when

covered by a hemisphere of radius a (the 0.215 due to the uncovered corners). The same

square would exhibit a true SAI of (π + 1) when covered by a perfect sphere, but only the

SAI of (π/2 + 0.215) would be visible when viewed head-on from above. Since the SAI

is an essential component of the Hall-Huray simplified calculation, we were hopeful

nonetheless, that this parameter could be helpful in calculating conductor loss.

Figure 2

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Copper foil cladding

RA (rolled annealed) foil is produced from an ingot of solid copper by successively

passing it though a rolling mill. After rolling, the foil itself is very smooth, with an RMS

profile Rq of 0.2 to 0.3μ. For printed circuit substrate applications, the foil manufacturer

additively treats the rolled foil, increasing the RRMS to 0.4 to 0.5 μ on the treated side, as

measured by WLI. The SAI value is 2.1 by WLI and the nodule radius was estimated as

0.3 based on SEM. The WLI SAI value for the untreated side of the RA foil is 1.1.

Currently, commercially available RA foil is limited to a width of 26” (0.66 m).

ED (electrodeposited) foil is produced by plating from a copper sulfate solution onto a

slowly rotating polished stainless steel drum. The “drum side” of ED foil exhibits an

RRMS of about 0.1 to 0.2μ, similar to untreated RA foil. The SAI of the untreated drum

side of ED foils are less than 1.2. The profile of the “bath side” of the plated foil is

controlled by the plating conditions, but is considerably higher in profile than the drum

side. The ED foil manufacturer generally applies a further plated treatment to the bath

side of the foil for improved adhesion and chemical compatibility with the intended

dielectric material. As observed by Griesi et al, the treatment nodules deposited on the

bath side of the foils tend to concentrate on the peaks of the underlying rough surface,

giving rise to a dendritic appearance. The cross section in figure 3 demonstrates just how

pronounced the dendrites can be. ED foils have historically been manufactured with

RRMS values in the range of 1 to 3μ. The SAI values of standard ED foils with high

profile range from 3 to 4 or even greater. These high values seem believable from simple

inspection of the scanning electron micrographs (fig. 6) and the cross section of figure 3.

Depending on the treatment type, we have observed nodules with radii ranging from 0.4

to 0.9 μ.

RT (reverse-treated) foil was developed to allow the manufacture of much lower profile

from an electro-deposited based foil. The plating conditions are adjusted to make the

bath side of the foil as smooth as possible. The adhesion promoting treatment is applied

to the drum side of the base foil can result in a nodular structure similar to the treatment

on RA foil. In our experience, the Rq values for treated side of RT foil are typically 0.7

to 1.2μ and the SAI values range from about 2.2 to 3. We have measured nodule radii

from 0.4 to 0.5μ on the RT samples.

The untreated bath side of the RT foils can exhibit RRMS and Rz values that are higher

than those of the treated side of the same foil. On the three RT foil types that we have

measured SAI of the untreated bath side is also rather high for an untreated surface, in the

range of 2.1 to 2.2. However, as is evident from comparing the SEM photos, the

structure of the surfaces of the RT-MP treated and untreated sides are very different

(figures 4 & 5). Even though the Rq of the untreated side is higher than the treated, its

effect on conductor loss is much lower due to the lack of nodulation.

Due to the growth of the lithium ion battery market, “battery foil” (BF) is now produced

in large quantities by ED foil suppliers. The battery foil is made to be a as smooth as

possible on both the bath and drum side. The two BF samples evaluated in the present

10

work were quite different from one another, with one exhibiting an extremely low profile

treatment (BF-ELP) and the other, a relatively high profile treatment (BF-HP2).

However, both exhibit low Rq and SAI on the untreated sides.

We also evaluated an experimental ED foil, EXP, that exhibits similar properties of a

measured SAI of 1.0 and Rq of 0.2µ on both sides. The structure is quite different than

any other foil (fig. 6).

The properties of the treated sides on 10 different foil samples are summarized in table 1

and those of the untreated sides in table 2. RT denotes a reverse-treated foil and ED is

for standard ED, treated on the bath side. LP and MP denote low and medium profile.

All samples are ½ oz./ft2 (17 μ thickness) with the exception of RT-MP-1.0 which is 1

oz./ft2. HP1 denotes one type of high profile treatment, and the HP2 treatment is a

different type of treatment. Note that the samples include three different base foils, an

RT, an ED, and a BF all with the same HP2 treatment.

Scanning electron micrographs at a magnification of 7000X of most of the above foils are

shown in figures 4-6. These photos were used to estimate the nodule radius. Not only is

there a fairly wide distribution of radii within each material as discussed in detail by

Greisi et al12

, but there is clearly some ambiguity as to how to define a radius, particularly

with the dendritic foils of figure 6.

Figure 3 - Cross section of ED-HP1 foil

Material Rq

(um) Rz

(um) SA

Index

Nodule Radius a (um)

EXP 0.2 1.3 1.0 --- BF-ELP 0.3 2.1 1.1 0.2 Rolled 0.4 3.7 2.1 0.3 RT-LP 0.8 5.2 2.2 0.5

RT-MP-0.5 0.8 4.2 2.3 0.5 RT-MP-1.0 0.9 4.1 2.3 0.5

BF-HP2 0.7 4.8 2.7 0.4 RT-HP2 1.2 8.7 3.0 0.4 ED-HP1 3.0 15.0 3.4 0.9 ED-HP2 2.2 13.1 3.9 0.4

Table 1 - Treated side

Material Rq (um) Rz (um) SA Index

EXP 0.2 1.3 1.0

BF-ELP 0.3 2.1 1.1

Rolled 0.3 2.1 1.1

RT-LP 0.5 3.7 1.7

RT-MP-0.5 0.8 5.8 2.2

RT-MP-1.0 1.3 8.8 2.2

BF-HP2 0.3 2.7 1.2

RT-HP2 0.9 6 2.1

ED-HP1 0.4 2.8 1.2

ED-HP2 0.4 2.8 1.2 Table 2 - Untreated side

11

Figure 4

Figure 5

12

Figure 6

Results and Discussion

An interesting characteristic of the insertion loss versus frequency curve for RO3003

laminate (figure 7) is that the loss of the Rolled foil matches the modeled value for

smooth foil, in spite of the fact that the Rolled foil exhibits significant nodular roughness,

with an Rq of 0.4µ, SAI of 2.1, and nodule radius of about 0.3 µ. The authors have

consistently observed this phenomenon over the last 20+ years.

The measured foil parameters for ED-HP2 (blue line in figure 7) are an Rq value of 2.2µ,

SAI of 3.9, and nodule radius of 0.4 µ. The Morgan/H&J correction calculated using an

Rq value of 2.2 µ clearly grossly under predicts the insertion loss beyond 25 GHz.

Sonnet, using the “thick metal” model, matches the data very well across the full range of

110 GHz, with an input Rq value of 2.6 µ, rather than the WLI-measured value of 2.2 µ.

Similarly, if the Hall-Huray model is an excellent fit across the full range, using the WLI-

measured SAI value of 3.9, but reducing the input value of nodule radius, a to 0.2 µ.

13

14

Similar results are obtained with the Rogers RO1200 laminate. The Rolled foil clad

sample nearly perfectly matches the values modeled for smooth foil up to 100 GHz. The

measured insertion loss of the RT-HP2 foil, with a measured Rq of 1.2µ, SAI of 3.0 and

nodule radius of 0.4µ matches the HH model well, using the SAI of 3.0, but adjusting the

input nodule radius to 0.15µ. Similarly, the Sonnet thick metal model fits the full range

of measured data well if the Rq value is adjusted to 2.0 µ.

The insertion loss versus frequency curve for 50 ohm transmission lines on 2, 4 and 7 mil

thick ULTRALAM 3850HT laminates (figure 9) further demonstrates that the insertion

loss with rolled foil matches that modeled for perfectly smooth with good accuracy.

In figure 10 we compare the measured and modeled insertion loss curves for the highest

profile (ED-HP1 and ED-HP2) foils. In this case, good agreement of the Hall-Huray

model was obtained using the SEM-measured values of the nodule radius for each foil

and adjusting the input value of SAI down to 2.0. Without this adjustment, the HH

model would predict substantially higher loss than was measured. Given that the

dendritic structure of these foils does deviate significantly from implied nodular structure

of the HH snowball model, this is not surprising.

15

The importance of the detail structure and not just a single parameter such as Rq is shown

by the difference in insertion loss of the treated (nodulated) and untreated RT-MP 1 oz/ft2

and ½ oz/ft2 foils (figure 11). It was our good fortune that the untreated sides of most of

the RT foils samples exhibited sufficient adhesion to make laminates and etch circuits to

compare the performance independently of the two sides. Comparing the WLI-measured

parameters in tables 1 and 2, it is seen that the Rq values of the untreated side is the same

as the treated side for the ½ oz/ft2 foil, with for the 1 oz. foil the untreated side exhibits a

higher Rq. However, the insertion loss values with the untreated sides facing the

dielectric are considerably lower than with the nodulated side facing the dielectric.

The comparatively small effect of Rq and SAI of the untreated, nodule-free side of the

foil facing the dielectric is demonstrated for five samples of RT foils by a plot of the

measured IL at 50 GHz versus Rq (figure 12). The measured IL increases from 1 dB/inch

to 1.75 dB/inch with the nodulated side facing the dielectric with a slope of 0.8 and R2 of

about 0.9 With the untreated side facing the dielectric, the IL at 50 GHz is flat, averaging

about 1.1 dB/inch, and slope and R2 value of 0.1

These results are implicit in the Hall-Huray model’s strong dependence of loss upon

nodule radius. In the absence of nodules, there is very little effect of the conductor

surface on conductor loss. An excellent simplified explanation of how the conductor

surface texture affects loss has recently been given by Loyer21`

.

16

17

The nodulated surfaces also show a greater effect on the phase constant, and the value of

the dielectric constant of the substrate that is extracted from the phase length. The details

of the differential phase length calculation are explained elsewhere17,18

.

A plot of the extracted K’ of the substrate from phase length data using the method of

H&J is shown for 50 ohm transmission lines on 0.004” LCP dielectric with RT-LP foil,

both with treated and untreated side facing the dielectric (figure 13). In this case the

nodulated side increases the value of extracted dielectric constant by about 0.1.

The effect of foil nodulation on the propagation constant on the ten foils included in this

study is shown in a plot of the value of the extracted K’ of the substrate versus Rq for

both the treated and untreated conductor sides facing the dielectric. When the

treated/modulated side is facing the dielectric, the extracted K’substrate value increases by

as much as 15% with increasing Rq (red squares). When the untreated side is facing the

dielectric, there is very little change in propagation constant with Rq (black diamonds).

18

Smooth foil options

As discussed earlier, we have observed that rolled foil exhibits conductor loss

approaching that of what is modeled for smooth foil at frequencies of up to 110 GHz. In

addition to the limitation of only exhibiting good adhesion to certain dielectric materials,

the use of rolled foil in laminate manufacture is limited by its maximum available width

of 26” (66 cm). While many copper clad laminates for RF applications are made in

relatively small formats, larger size laminates are required for lower cost applications.

Copper foil manufacturers are well aware of the market for lower loss foils. The profiles

of two of the ED foils included in this study, BF-ELP and EXP were lower than that of

the rolled foil. As shown in figure 15, the insertion loss up to 50 GHz is very close to

what is modeled for smooth foils. We are hopeful that smooth foil performance, with

reliably good adhesions and favorable economics will be achievable on larger laminates

19

Conclusion

In the present work, we have experimentally investigated the effects of

surface structure on ten copper foil samples with a wide range of properties.

In spite of exhibiting a SAI of 2.1 and a nodulated surface, rolled foils

exhibits conductor losses matching what is modeled for smooth foil at

frequencies of up to 110 GHz. ED foils with the lowest profiles exhibit

similar insertion loss characteristics.

Though the untreated (nodule-free) sides of reverse-treated copper foils can

exhibit Rq and SAI values higher than that of the treated sides, they exhibit

lower loss. As is implicit in the Hall-Huray model, the nodules are the

major contributor to excess conductor loss.

Foil nodules also affect the propagation constant, resulting in an increase in

the phase length and extracted dielectric constant. The nodule-free surfaces

exhibit much less of an effect.

20

References

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3. S. Groisse, I Bardi, O Biro, K Preis, & K. R. Richter, “Parameters of lossy cavity resonators calculated by the finite element method,” IEEE Transactions on

Magnetics, v. 32, n. 3, May 1996

4. D. M. Pozar, Microwave Engineering, 2nd Edtion, Wiley (1998) 5. G. Brist, S. Hall, S. Clouser, & T Liang, “Non-classical conductor losses due to

copper foil roughness and treatment,” 2005 IPC Electronic Circuits World

Convention, February 2005

6. T. Liang, S. Hall, H. Heck, & G. Brist, “A practical method for modeling PCB transmission lines with conductor roughness and wideband dielectric properties,”

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Acknowledgement

The authors thank Dr. Kristi Pance of the Rogers Innovation Center for many helpful

insights and Ms. Amie Tworzydlo for the skillfully executed cross-sectional photo of

figure 3.