Practical Method for Modeling Conductor

Surface Roughness Using Close Packing

of Equal Spheres

Bert Simonovich Lamsim Enterprises Inc. lsimonovich@lamsimenterprises.com

2

Acknowledgements

David Dunham, Molex Inc.

Scott McMorrow, Teraspeed Consulting. -A Division of Samtec

Dr. Yuriy Shlepnev, Simberian Software Corp.

Dr. Alexandre Guterman

3

Outline

Overview

Conductor loss

Copper foil fabrication

Modeling roughness

Hexagonal Close-packing of Equal Spheres Model

Practical method to determine rough conductor loss

Case study

With just -3.5dB delta @12.5 GHz => ½ the eye height with rough copper

4

Failure To Model Roughness Can Ruin You Day

Rough Copper Smooth Copper

Simulated with Keysight ADS

25Gb/s

Current distribution at DC is uniform through cross-sectional area of conductor

5

DC Current Distribution Through a Rectangular Conductor

t

w

DC resistance is proportional resistivity and inversely proportional to the cross sectional area

6

DC Resistance

t

w

_ / mDC condRt w

ρ = Bulk resistivity of the material in Ω-m

X-sectional Area

Above ~10MHz current flows mainly along “skin” of the conductor

7

Skin Effect

δ

Skin depth (δ) is effective thickness where AC current flows

8

Skin Depth

9

Skin Depth vs Frequency

μ0 = Permeability of free space in H/m σ = Conductivity in S/m.

0

1

f

δ

Skin depth inversely proportional to 𝑓

10

AC Resistance

δ

w

_ / m2

AC condRw

Effective X-sectional Area

Reduced cross-sectional area causes AC resistance to increase proportional to 𝑓

High frequency currents concentrated mostly along surface facing reference plane due to proximity effect

11

Current Distribution Microstrip

Reference Plane

12

Current Distribution Stripline

Reference Plane

Symmetrical

Reference Plane

Reference Plane

Asymmetrical

Reference Plane

Return current on respective reference plane ≈ +/-3H from signal conductor center

13

Return Current Distribution

H

3H 3H

H2

H1

3H1

3H2 3H2

3H1

RAC_microstrip = RAC_trace + RAC_ref

14

AC Resistance Microstrip

H

w

t

2

0_ 2

1 1 40.94 0.132 0.0062 ln /m ; when 0.5 10

5.8 0.03AC microstrip

wf w w w wHR f

w Hw H H t H

H w

Reference [1]

1. Determine RAC_microstrip1

2. Determine RAC_microstrip2

3. Combine both in parallel

4. Determine Insertion Loss:

15

Stripline Conductor Loss

_ 1 _ 2

_ 1 _ 2

_ /mAC microstrip AC microstrip

AC microstrip AC

AC str

microstrip

ipline

R f RR

f

R Rf

f f

_

10( ) 20log dB/m( )

AC stripline

smooth

R fIL f e

Zo f

H2

H1

w2

w1

t

16

Conductor Loss Model Validation

4 in

Excellent correlation!

_

10( ) 20log dB/m( )

AC stripline

smooth

R fIL f e

Zo f

VS

Keysight ADS Momentum

No such thing as a perfectly smooth PCB conductor surface

Roughness is always applied to promote adhesion to the dielectric material

17

Conductor Roughness

18

Copper Foil Manufacturing Processes

VS

Rolled Electro-deposited (ED)

Lower Cost Smoother

Copper bar fed through a series of progressively smaller rollers to achieve final thickness

Roller smoothness determines final smoothness of foil

19

Rolled Copper Foil Fabrication Process

Copper Foil

Reducing Rollers

Copper Bar

Drum speed controls foil thickness

Matte side always rougher than drum side

20

Electrodeposited Copper Foil Fabrication Process

Cathode

Drum Side

Matte Side

Anode

Drum

Untreated Foil

Cu Sulfate

21

Common Roughness Profiles

IPC Standard Profile IPC Very Low Profile(VLP) Ultra Low Profile (ULP)Class

SEM Photos Courtesy [6]

No min/max spec < 5.2 μm max -Other names: HVLP, VSP -No IPC spec -Typically < 2 μm max

22

Electro-deposited Copper Foil Nodulation Treatment

Drum Side Untreated

Matte Side Untreated

Drum Side Treated

Matte Side Treated

Untreated Foil

Nodulation Treatment

Treated Foil

Drum Side

Matte Side Matte Side

Drum Side

SEM Photos Courtesy [2]

Profilometers are often used to measure surface roughness

23

Measuring Surface Roughness

Stylus Tip

Surface Profile

Stylus Sample

Motor Drive and Processing Unit

Measured Profile

Stylus Pickup Unit

3D Scan Profile

Faster

More reliable

More accurate

24

Optical Profilometer

Sample

Measured Profile

Optics

CCD

Processing Unit

Average roughness (Ra) typically specified for drum side on data sheet

Ra = Arithmetic average of the absolute values of deviations Yi

25

Average Roughness Parameter

N

a i

i

R YN

1

1

Ten-point mean roughness (Rz) typically specified for matte side on data sheet

Rz= Sum of the average of the five highest peaks and the five lowest valleys over the sample length

26

Ten-point Mean Roughness Parameter

z Pi Vi

i i

R Y Y

5 5

1 1

1 1

5 5

27

Modeling Copper Roughness

Assumes 2D corrugated surface

Based on mathematical fit to S.P. Morgan Power Loss Data (1948)

Lose accuracy above 5GHz for rough copper

28

Hamerstad & Jenson Model

22

1 arctan 1.4rough

HJ

flat

PK

P

RMS tooth height in meters

SF = scaling factor representing the ratio of the length of the rough surface (Lrough )to the spatial length (Lspatial) –Ref [2]

Impractical from first principles perspective – Lrough not published in data sheets

29

Modified Hamerstad & Jenson Model

2

21 arctan 1.4 1

rough

HJM

flat

PK SF

P

Lspatial

Lrough

𝐴𝑚𝑎𝑡𝑡𝑒

𝐴𝑓𝑙𝑎𝑡 = relative area of the matte base compared to a flat surface

ai = radius of the copper sphere (snowball) of the ith size, in meters

𝑁𝑖

𝐴𝑓𝑙𝑎𝑡 = number of copper spheres of the ith size per unit flat area in

sq. meters

δ (f) = skin-depth, as a function of frequency, in meters

30

Huray “snowball” Model

SEM Photo Courtesy [3]

1

2 2

21

43 ( ) ( )1

2 2

jrough matte i i

SRH

iflat flat flat i i

P A N a f fK f

P A A a a

Reference [2]

31

Huray Model Prior Art

11 spheres min; 38 spheres max of radius 1μm to fit within hex tile area and height of 5.8μm

Fit equation parameters to measured data

Assumes stacked “snowballs” arranged in hexagonal lattice

SEM Photo Courtesy [3] Plot Courtesy [2]

VNA Measurement

Model

Benefits:

Practical

Accurate

Issues:

Expertise Required

Time

Money

32

Design Feedback Method*

*Reference [2]

Design Product Channel Simulation

Dk

Df

Roughness

Extract Parameters

Fit

Model Test Design Coupon

X-section Data

Fab

Hexagonal Close-packing of Equal Spheres (HCPES) Model

33

34

Why Bother?

Helps make informed decision sooner - “Sometimes an OK answer NOW! is more important than a good answer late” – Eric Bogatin

Fast simulation time - Practical for what-if spreadsheet analysis

Minimal expertise required

Useful to sanitize CAD tools

Useful to gain intuition on what to expect with measurements and help determine root cause of differences

Similar to Huray Model

Based on close-packing of 11 equal sized spheres

Does not require SEM analysis to determine stack height (HRMS ) or hexagonal tile area

35

HCPES Model

Reference [5]

Hexagonal Tile Area

Assumes nodule treatment applied

to perfect flat surface

Sphere radius and hex tile area

determined solely on published

roughness parameters from

manufacturer’s data sheet

36

HCPES Correction Factor

2

2

2

1 66( ) ( )

12

rough Hex

HCPES

flat

r

P AK f

P f f

r r

HCPES lattice structure loosely resembles the actual SEM photo

37

HCPES Model Lattice Structure

SEM Photo Courtesy [3]

Lattice structure scales inversely to the square of the height

38

HCPES Model Scalability

H H/2

Total of 11 equal sized spheres

HRMS = height of 2 tetrahedrons plus 2 sphere radii

Hexagonal tile perimeter surrounds 7 base spheres exactly

39

HCPES Model Anatomy

Hexagonal Tile

Determine Height of Single Tetrahedron

40

H

41

1. Determine DE

Given: Each side of the tetrahedron = 2r Using Pythagorean theorem:

2

3DE DF

2 2

2 2

2

3

22

3

23

3

DE DB BF

r r

r

A

D

B

F

C E

42

2. Determine Height (AE)

Therefore:

2 2

22 2

2 33

26

3

AE AD DE

r r

r

A

D

B

F

C E

Since HRMS = height of 2 tetrahedrons + sphere dia.

Therefore sphere radius is:

43

Determine HCPES Sphere Radius

2 2

22 6 1

3

RMSH AE r

r

22 6 1

3

RMSHr

r

r

A

E

HRMS

AHex = 6 x area of equilateral triangle ADG

44

Determine Hexagonal Tile Area

2

2

6

1 16 1 3 1

3 3

16 3 1

3

HexA DF AF

r r

r

Hexagonal Tile Area

45

Method to Determine Rough Conductor Loss

Typically:

Must consider roughness of each side when determining AC resistance

Matte sides bonded to core

Drum sides bonded to prepreg

Drum sides roughened with oxide or etch treatment prior to lamination

46

Stripline Geometry with Surface Roughness Example

47

Dual Triangular Sawtooth Profile (DTSP) Model

Used to approximate RMS height of matte and drum side

2 3

aRMSa

RH

2 3

zRMSz

RH

Matte Side Rz

Drum Side Ra

PCB Conductor DTSP

Mean

Mean

Not to Scale

Ra

Rz

48

1. Determine RMS Tooth Height of Matte and Drum Sides

_2 3

zRMS matte

RH

_2 3

aRMS drum

RH

*Use Micro-etch Roughness for Drum Side

*

49

2. Determine HCPES Matte & Drum Correction Factors

_

22 6 1

3

RMS matte

matte

Hr

2

2

_

16 3 1

3Hex matte matteA r

_

22 6 1

3

RMS drum

drum

Hr

2

2

_

16 3 1

3Hex drum drumA r

2

_

_2

2

1 66( ) ( )

12

matte

Hex matte

HCPES matte

matte matte

r

AK f

f f

r r

2

_

_2

2

1 66( ) ( )

12

drum

Hex drum

HCPES drum

drum drum

r

AK f

f f

r r

50

3. Determine AC Resistances of Each Surface

Reference [1]

1

2

0 1 1 1_ 2

1 1 1

41 1ln 0.94 0.132 0.0062 /mAC w

f w w wR f

w t H H

2

2

0 2 2 2_ 2

2 2 2

41 1ln 0.94 0.132 0.0062 /mAC w

f w w wR f

w t H H

1

0 1_ _1

1 1 1

1 1

/m

5.8 0.03

AC ret

w

f HR f

w w H

H w

2

0 2_ _ 2

2 2 2

2 2

/m

5.8 0.03

AC ret

w

f HR f

w w H

H w

* when 0.5 10n

n

w

H

*

*

51

4. Determine Stripline Rough Conductor Loss

2 2_ _ _ _ /mAC drum HCPES drum AC w AC retR f K f R f R f

1 1_ _ _ _ /mAC matte HCPES matte AC w AC retR f K f R f R f

_ _

_ _

_ _

/mAC matte AC drum

AC stripline rough

AC matte AC drum

R f R fR f

R f R f

_ _

10( ) 20log dB/m( )

AC stripline rough

rough

o

R fIL f e

Z f

Case Study

52

53

Test Platform

Case 1 Megtron-6

HVLP Cu

Case 2 N4000-13EP

VLP Cu

Photos courtesy [2]

12 Layer test boards designed, built and tested by Molex Inc., courtesy of David Dunham

Generalized Modal S-parameters (GMS) data courtesy Scott McMorrow, Teraspeed Consulting Group

Generalized Modal S-parameters (GMS) data courtesy Yuriy Shlepnev, Simberian Software Corp

Parameter Case 1 Megtron-6 Case 2 N4000-13EP

Dk 3.62 @50GHz 3.6-3.7 @10GHz[i]

Df 0.006 @ 50GHz 0.008-0.009 @ 10GHz[ii]

Rz HVLP 1.50 μm -

Rz VLP - 2.50 μm

Ra w/Micro-etch [iii] 1.44 μm 1.44 μm

Trace Thickness, t 15.23 μm 15.23 μm

Trace Widths w1, w2 251 μm, 236 μm 251 μm, 236 μm

Dielectric Heights, H1,H2 249 μm, 231 μm 249 μm, 231 μm

GMS trace length 10.15 cm (4.00 in) 10.15 cm (4.00 in)

Zo(fo) ohms [iv] 52.29 @ 50GHz 52.07 @ 10GHz

[i] Dk = 3.65 used [ii] Df = 0.0085 used [iii] CO-BRA BOND® SM is an example of a hydrogen peroxide/sulfuric acid micro-etch treatment often used by PCB

fabricators to improve the adhesion of copper surface to dielectric materials. [iv] Zo(fo) = Characteristic impedance determined by 2D field solver at frequency fo

54

Board Parameters From Data Sheets and Design

Stripline Geometry Reference

Determining Total Insertion Loss

55

_ Total diel cond roughIL f IL f IL f

Keysight ADS

• Svensson/Djordjevic wideband Debye model used to ensure causality for dielectric loss

• Conductivity parameter set to a value much-much greater than the normal conductivity of copper ensures the conductor is lossless for the simulation

_ _

10( ) 20log dB/m( )

AC stripline rough

rough

o

R fIL f e

Z f

Simulation Correlation Results

56

Excellent correlation!

VLP HVLP

Model Comparisons

57

2

2

2

1 66( ) ( )

12

rough Hex

HCPES

flat

r

P AK f

P f f

r r

HCPES HJ

22

1 arctan 1.4rough

HJ

flat

PK

P

HJM

2

21 arctan 1.4 1

rough

HJM

flat

PK SF

P

Tuned SF=1.65

Correction Factor Comparisons (Ra = 1.44μm; Rz =2.5 μm)

58 KHJM SF = 1.65 KHJM SF = 1.65

59

Summary and Conclusions

1. Using the concept of hexagonal close-packing of equal spheres, a novel method to accurately calculate sphere size and hexagonal tile area was devised for use in the Huray model.

2. By using published roughness parameters and dielectric properties from manufacturers’ data sheets, we show the need for further SEM analysis or experimental curve fitting, may no longer be required for preliminary design and analysis.

3. HCPES model looks promising as a practical alternative to previous modeling methods.

60

Ongoing Research

Test the HCPES model to see how well this method applies to other material and copper roughness

61

References [1] S. Hall, H. Heck, “Advanced Signal Integrity for High-Speed Digital Design”, John Wiley & Sons, Inc., Hoboken, NJ, USA., 2009.

[2] E. Bogatin, D. DeGroot, P. G. Huray, Y. Shlepnev, “Which one is better? Comparing Options to Describe Frequency Dependent Losses”, DesignCon2013 Proceedings, Santa Clara, CA, 2013.

[3] Huray, P.G.; Hall, S.; Pytel, S.; Oluwafemi, F.; Mellitz, R.; Hua, D.; Peng Ye, "Fundamentals of a 3-D “snowball” model for surface roughness power losses," Signal Propagation on Interconnects, 2007. SPI 2007. IEEE Workshop on , vol., no., pp.121,124, 13-16 May 2007 doi: 10.1109/SPI.2007.4512227.

[4] Huray, P. G. (2009) “The Foundations of Signal Integrity”, Chapter 6, John Wiley & Sons, Inc., Hoboken, NJ, USA., 2009

[5] L. Simonovich, “Method for Modeling Conductor Surface Roughness”, Provisional Patent Application # US 61/977,138

[6] ISOLA-Group, “Copper Foil 102 Presentation”, 2012

62

Thank You!

www.lamsimenterprises.com