I agree with Yuriy with respect to the first and second uncertainties of
measuring the DC resistance and using the cross-sectional area of the trace
segment. Last summer I did experiments on some test coupons with
cross-sections I had, using 4-wire (Kelvin) measurement and I found that a
variation of just 2.5um (100uin) in measuring the thickness (worst case) was
the difference between having a conductivity of 5.844E7 S/m (1.711E-8
ohm-m)and 5.067E7 S/m (1.973E-08 ohm-m). Like Yuriy said it is sometimes
hard to decide where to draw the boundary between copper and dielectric,
especially with rough copper.
With respect to insertion loss method, depending on what method you use to
determine a roughness correction co-efficient, you might come up with an
"effective roughness" that gives good correlation to measured data, as Yuriy
said, but that does not necessarily prove the actual resistivity is higher.
It just means that was the factor needed for that model for good
correlation.
The roughness model I presented at this year's DesignCon2015 using
close-packing of equal spheres (
http://lamsimenterprises.com/5-WE4Paper_PracticalMethodForModelingConductor_
Final_Submitted.pdf ), and my more recent White Paper (
http://lamsimenterprises.com/White_Paper-Practical_Method_for_Modeling_Condu
ctor_Surface_Roughness_Using_The_Cannonball_Stack-Principle-v2.0.pdf )
applied to the Huray model gives excellent correlation to GMS-parameters
with the published conductivity for annealed copper of 5.8E8 S/m to ~50GHz.
Best regards,
Bert Simonovich
Signal Integrity | Backplane Specialist | Founder
LAMSIM Enterprises Inc.
Web Site: http://lamsimenterprises.com
Blog: http://blog.lamsimenterprises.com/
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Yuriy Shlepnev
Sent: July-02-15 5:29 PM
To: jeff.loyer.si@xxxxxxxxxxx; 'Lee Ritchey'; 'SI-LIST'
Subject: [SI-LIST] Re: Resistivity of copper
Lee, I agree with Jeff that the doubling the resistivity may be way too
pessimistic.
The key in apparent increase of the resistivity in how you measure it.
It can be done at DC with measurement of resistance and use of cross-section
geometry of a trace segment.
The first uncertainty is that the cross-section is usually assumed to be the
same along a segment - there are some variations along due to manufacturing
tolerances (that is probably minor effect for wider traces).
The second uncertainty is that the cross-section is not well defined due to
the roughness and etching. There is a layer between copper and dielectric
that contains mixture or copper and dielectric (see more at this paper
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6991529). Where
to draw the boundary of the cross-section? - the identified resistivity will
depend on that. The etching can also produce complicated shapes.
Another way to identify resistivity is to match measured and computed
reflection-less insertion loss (GMS-parameters) or attenuation at
frequencies below 40-50 MHz (for PCBs). Though, it suffers from the same
uncertainties in the geometry definition in the model. We usually observe up
to 10% increase in the bulk resistivity identified with the GMS-parameters.
Note that with the Effective Roughness Dielectric (ERD) model (suggested in
http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6351795), the bulk
resistivity of the conductor core can be same as for annealed copper and
additional ERD layers on surfaces of strips and planes will increase the
overall resistivity. The increase of resistivity may be needed only with the
use of roughness correction coefficients (commonly used model).
Best regards,
Yuriy
Yuriy Shlepnev, Ph.D.
President, Simberian Inc.
3030 S Torrey Pines Dr. Las Vegas, NV 89146, USA Office +1-702-876-2882; Fax
+1-702-482-7903 Cell +1-206-409-2368; Virtual +1-408-627-7706
Skype: shlepnev
www.simberian.com
Simbeor - Accurate, Productive and Cost-Effective Electromagnetic Signal
Integrity Software 2010 and 2011 DesignVision Award Winner, 2015 Best In
Design&Test Finalist
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Jeff Loyer SI
Sent: Thursday, July 2, 2015 1:28 PM
To: 'Lee Ritchey'; 'SI-LIST'
Subject: [SI-LIST] Re: Resistivity of copper
Sorry, Lee, but I disagree. I don't think that's where the discrepancy
comes from (impure copper from the ED vendors). My understanding from the
ED copper foil vendors I've spoken with is that they measure the
conductivity to be very close to that of copper. IPC spec. 4562A section
3.8.1 is also very clear about the purity and resistivity of incoming
copper. Something happens after it's received by the laminate vendors, I
believe.
The values below represent data I've measured and gathered from other
sources. Doubling the resistivity of copper seems overly conservative.
Jeff Loyer
Signal Integrity Consulting
-----Original Message-----
From: Lee Ritchey [mailto:leeritchey@xxxxxxxxxxxxx]
Sent: Thursday, July 2, 2015 12:24 PM
To: jeff.loyer.si@xxxxxxxxxxx; dbrooks9@xxxxxxxxxxxxxxx; 'SI-LIST'
Subject: RE: [SI-LIST] Re: Resistivity of copper
Most foil copper used in PCBs is plated on a drum using scrap wire copper.
You can guess how impure that might be! Because of this, I take a
pessimistic view of its conductivity, doubling what pure copper is. Yes,
that is a guess, but so is the foil data you get.
Some world we live in! That's what you get when you drive the system with
price instead of cost!
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Jeff Loyer SI
Sent: Wednesday, July 1, 2015 9:45 PM
To: dbrooks9@xxxxxxxxxxxxxxx; 'SI-LIST'
Subject: [SI-LIST] Re: Resistivity of copper
Hi Doug,
FYI, my experience (and others') agrees with Gert's, that PCB "copper" isn't
pure. Our measured conductivities were:
2.1uohm-cm (4.76e7 ohm-m conductivity) for stripline
2.4uohm-cm for microstrip
Copper = 1.7uohm-cm (5.88e7 ohm-m)
We measured the temperature coefficient as 0.35%/degree C (interestingly
there was a difference between U.S. domestic and foreign vendors').
Coming from the copper foil vendors, IPC specs. ensure it is very "pure",
with conductivity specified. It appears the processing of the laminate
suppliers affects the conductivity significantly, though we've never
understood exactly what part of the process does that. I suspect treatments
diffuse into the copper, reducing its conductivity.
The data I've seen indicates packages' copper behaves more like copper.
Jeff Loyer
Signal Integrity Consulting
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Doug Brooks
Sent: Wednesday, July 1, 2015 8:44 PM
To: SI-LIST
Subject: [SI-LIST] Re: Resistivity of copper
Thank you all for your help.
Turns out I was on the wrong track! First, I have been under the assumption
that the resistivity curve was non-linear over this wide a range. Turns out
that the normal equation still works here. ( Rho-subT
= Rho-sub20*(1 + Alpha-sub20*(T-20)) This leads to about 5.3 or 5.1
depending on what assumptions you make. My 4.3 number, it turns out, was
irrelevant!
So, I apologize for the exercise. But thanks for the support.
Doug Brooks
Doug Brooks wrote:
I would like to know the resistivity of copper at 540 degrees C,
assuming it is 1.72 * 10^-8 Ohm*m^2/m at 20 degrees C. The temp
coefficient of resistivity is .00393 at 20 degrees C but using this I
get a result of around 5.31 at 540 degrees. But a problem I am solving
says it is closer to 4.30. I am having trouble resolving the difference.
Can anyone confirm the (approx.) 4.3 number for me?
Thanks for any help.
Doug Brooks
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