How to convert between different units of resistivity

Question

Some data sheets specify units of resistivity as Ω/sq/mil. How could I convert that to units of Ω-cm?

Some data sheets... what datasheets? Give links or names, please. — Rohat Kılıç, Oct 19 '23 at 20:56
I did not know what is policy of promoting company products, but a lot of silver conductive ink companies specify their ink resistivity with the above units in their data sheet — user510, Oct 20 '23 at 02:37

Dave Tweed · Answer 1 · 2023-10-20T01:13:05.080

4

There is no direct conversion. They are different concepts:

Ω - total resistance, as scalar quantity
Ω-<length> - bulk resistivity of a 3-D material
Ω/square - sheet resistivity of a 2-D material
Ω/<length> - linear resistivity of a 1-D wire
Ω-<area> - contact resistance

For example, you can convert between bulk resistivity and sheet resistivity if you know the thickness of the sheet.

edited Oct 20 '23 at 01:13

answered Oct 19 '23 at 21:20

Dave Tweed

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How does contact resistance work out as Ω/[L]²? – Hearth Oct 19 '23 at 23:56
@Hearth: It's resistance through a sheet (normal to the plane of the sheet) rather than along the surface. – Dave Tweed Oct 20 '23 at 00:36
Wouldn't that have units of Ω·[L]², not Ω/[L]²? – Hearth Oct 20 '23 at 00:49
@Hearth: OK, yes. That would be the correct units, given that you divide by area to get the total resistance. – Dave Tweed Oct 20 '23 at 01:14

Mattman944 · Answer 2 · 2023-10-20T13:22:11.367

Everything that Dave Tweed said is correct, but I still think that there is more to your question.

We need to see some example datasheets to fully understand the issue. I found these, two different datasheets for silver ink. Let's assume that their characteristics are similar.

The first has units of \$ \Omega /square/mil \$. Square has no units, so this can be simplified to \$ \Omega /mil \$. You would divide by the thickness to get resistance, so they are sloppy with their units, it should be \$ \Omega \text{-}mil \$

The second has units of \$ \Omega \text{-}cm \$. These are normal units for volume resistivity.

So, to convert the first to the second, divide by the number of mils in a cm (393.7).

\$ 0.005 \Omega\text{-}mil \frac{cm}{393.7 mil} = 12.7 \mu \Omega\text{-}cm\$

This is close, remember that these are not identical inks, just similar.

https://kayakuam.com/wp-content/uploads/2020/03/ag500a-silver-conductive-ink.pdf

https://www.sigmaaldrich.com/US/en/product/aldrich/791881

A good discussion about volume resistivity: What's a conceptual way to understand ohm-cm?

How to convert between different units of resistivity

2 Answers2