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Copper Roughness and Si9000e
1 Copyright © Polar Instruments 2017 polarinstruments.com
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Copper Roughness and how to account for itMartyn Gaudion– October 2017 (Rev 1)
Copyright © Polar Instruments 2017 polarinstruments.com
Presented for Altium PCB2020
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Copper Roughness and Si9000e
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Acknowledgments
Alan Staniforth
Bert Simonovich
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Copper Roughness and Si9000e
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"All models are wrong
but some are useful"
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Copper Roughness and Si9000e
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George E. P. Box
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Copper Roughness and Si9000e
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Introducing Polar Instruments
Welcome to a presentation that will cover the following topics:
1. Overview and significance of copper roughness
2. Methods for calculating insertion loss with roughness
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Copper Roughness and Si9000e
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Overview of Copper Roughness
Current Distribution Through a Conductor
DC current is uniform through cross-sectional area of
conductor
AC current above ~10MHz flows mainly along “skin” of the
conductor
[1] Simonovich 2015, pg 5
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Copper Roughness and Si9000e
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Overview of Copper Roughness
Skin Depth Vs Frequency
μ0 = Permeability of free space in H/m
σ = Conductivity in S/m.
AC current above ~10MHz flows mainly along “skin” of the
conductor [2] Simonovich 2015, Slide 9
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Copper Roughness and Si9000e
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Overview of Copper Roughness
Copper is Roughened for Various Reasons
Roughness is always applied to promote adhesion to the dielectric
material
No such thing as a perfectly smooth PCB conductor surface
[2] Simonovich 2015, Slide 17
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Copper Roughness and Si9000e
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Overview of Copper Roughness
[2] Simonovich 2015, Slide 18
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Copper Roughness and Si9000e
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Overview of Copper Roughness
[2] Simonovich 2015, Slide 19
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Copper Roughness and Si9000e
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Overview of Copper Roughness
[2] Simonovich 2015, Slide 20
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Copper Roughness and Si9000e
13 Copyright © Polar Instruments 2017 polarinstruments.com
Overview of Copper Roughness
[2] Simonovich 2015, Slide 21
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Copper Roughness and Si9000e
14 Copyright © Polar Instruments 2017 polarinstruments.com
Overview of Copper Roughness
[2] Simonovich 2015, Slide 22
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Copper Roughness and Si9000e
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Overview of Copper Roughness
Profilometers Used to Measure Surface Roughness
[2] Simonovich 2015, Slide 23-24
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Copper Roughness and Si9000e
16 Copyright © Polar Instruments 2017 polarinstruments.com
Methods for Calculating Insertion Loss with Roughness
• Smooth Conductor
• Morgan-Hammerstad
• Groisse Method
• Huray “Snowball” Method
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Copper Roughness and Si9000e
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Methods for Calculating Insertion Loss with Roughness
Garbage In = Garbage Out
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Copper Roughness and Si9000e
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Which is correct?
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Copper Roughness and Si9000e
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Measured or
modelled?
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Copper Roughness and Si9000e
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Methods for Calculating Insertion Loss with Roughness
Loss Calculations
Total Loss = Insertion Loss of Dielectric +
Surface Roughness Coefficient X Insertion Loss of Conductor
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Copper Roughness and Si9000e
21 Copyright © Polar Instruments 2017 polarinstruments.com[3] Bogatin et al., Pg. 5
Based on scratches on conductor surfaces
Methods for Calculating Insertion Loss with Roughness
Morgan-Hammerstad
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Copper Roughness and Si9000e
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Methods for Calculating Insertion Loss with Roughness
Morgan-Hammerstad
• Based on scratches on conductor surfaces
• First developed in 1949. Republished in 1975 by Hammerstad
• Saturates for rough conductor at low frequencies to a value of 2221 arc tan 1.4rough
smooth
αα π δ
∆ = +
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Copper Roughness and Si9000e
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Methods for Calculating Insertion Loss with Roughness
Groisse
Also Saturates as the Ksr approaches 2.
Depending on Conductor roughness, predictions can go to higher frequencies than Hammerstad
Groisse Equation:1.6
1 exp2
rough
smooth
PP
δ = + − ∆
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Copper Roughness and Si9000e
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Methods for Calculating Insertion Loss with Roughness
Huray
• The surface can be modelled using a pyramid of metal spheres called “snowballs”
[4] Huray, Paul G
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Copper Roughness and Si9000e
25 Copyright © Polar Instruments 2017 polarinstruments.com
Methods for Calculating Insertion Loss with Roughness
Huray• The theory starts with a single snowball between conductors with
an electromagnetic wave incident on it.• The wave is both reflected (scattered) and absorbed
Cross Section Longitudinal View
[4] Huray, Paul G
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Copper Roughness and Si9000e
26 Copyright © Polar Instruments 2017 polarinstruments.com
Methods for Calculating Insertion Loss with Roughness
Huray
• In the pyramid of snowballs, multiple scattering and absorption occurs. However, It is found that absorption dominates over scattering at the frequencies of interest
[5] Griesi G. et al.
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Copper Roughness and Si9000e
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Methods for Calculating Insertion Loss with Roughness
Huray
• Equation12 2
216 1
2
is thepower lostis theareais thenumber of snowballsin area
is thedistribution of snowballsis theskin depth
jrough smooth i ii
smooth rough smooth i i
P A N aP A A a a
PAN Aj
π δ δ
δ
−
=
= + + +
∑
[4] Huray, Paul G
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Copper Roughness and Si9000e
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Methods for Calculating Insertion Loss with Roughness
Huray
• In order to simplify the formula for practical use simulations, using different ball radii have been conducted.
[4] Huray, Paul G
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Copper Roughness and Si9000e
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Methods for Calculating Insertion Loss with Roughness
Huray
• Simplification of the formula for a single effective ball radius
( ) 2
2
3 12 11
2
4is the Hall-Huray Surface Ratio
is the radius of all snowballsN is the number of snowballs in area
rough rough
smooth smooth
smooth
P ASR
P Aa a
NaSRA
aA
δ δ
π
= + + +
=
effective
[4] Huray, Paul G
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Copper Roughness and Si9000e
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Methods for Calculating Insertion Loss with Roughness
Comparisons with Si9000e
-4,0E+02
-3,5E+02
-3,0E+02
-2,5E+02
-2,0E+02
-1,5E+02
-1,0E+02
-5,0E+01
0,0E+000,0E+00 2,0E+10 4,0E+10 6,0E+10 8,0E+10 1,0E+11
Att
enua
tion
(dB
/m)
Frequency (Hz)
Smooth
Hamm
Goisse
Huray
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Copper Roughness and Si9000e
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Copper Roughness and Si9000e
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Methods for Calculating Insertion Loss with Roughness
Practically How Do I do this?
?
?
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Copper Roughness and Si9000e
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References[1] Lambert (Bert) Simonovich, Practical Method for Modeling Conductor Surface Roughness Using Close Packing of Equal Spheres, DesignCon 2015[2] Lambert (Bert) Simonovich, Practical Method for Modeling Conductor Surface Roughness Using Close Packing of Equal Spheres Presentation, DesignCon 2015[3] Bogatin et al. Which one is better? Comparing Options to Describe Frequency Dependent Losses, DesignCon 2013[4] Huray, Paul G. The Foundations of Signal Integrity, pub. Wiley, 2010[5] Griesi G. et al. Electrodeposited Copper Foil Surface Characterisation for Accurate Conductor Loss Modelling DesignCon 2015.
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Copper Roughness and Si9000e
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“Si9000e insertion loss solver"
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Copper Roughness and Si9000e
35 Copyright © Polar Instruments 2017 polarinstruments.com
“Si9000e insertion loss solver"
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Copper Roughness and Si9000e
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“Si9000e insertion loss solver"
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Copper Roughness and Si9000e
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“Si9000e insertion loss solver"
Images courtesy of Circuit foil Luxembourg
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Copper Roughness and Si9000e
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Copper Roughness and Si9000e
39 Copyright © Polar Instruments 2017 polarinstruments.com
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Thank you
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