What does mΩ/sq/25 μm mean?

Question

I came across this specification on Saralon.com where they mentioned for one of their products

"Stretchable silver ink for stretchable electrical connections. Specially designed for bending applications such as TPU or bendable plastics with a good sheet resistance (30 mΩ/sq/25 μm)."

So, does this mean the Sheet resistance is 30 mΩ/sq for thickness(sheet) 25 μm?

Answer 1

What does mΩ/sq/25 μm mean?

Surface resistance is measured in resistance units per square. This is because the resistance between two opposite sides of a square of some approximately 2 dimensional material is (approximately) a constant, regardless of the size of the square! The larger the size of the square, the more distance between the opposite sides, but also the wider the path for current to flow. The two effects cancel each other.

This explains the unit \$m\Omega/sq\$.

Now, the resistance of a 3 dimensional approximation of a two dimensional square will also depend on the thickness of the material. In this case ink. The thicker the material, the lower the resistance. So, for this ink, we have a resistance per square that depends on the thickness of the ink layer. What you should have (thanks Hearth) is

$$m\Omega/sq \cdot \mu m$$

or just

$$m\Omega\cdot\mu m$$

The unit \$m\Omega/sq/\mu m\$ used by the vendor is in error.

Answer 2

It's wrong.

What they're trying to say is that the sheet resistivity of the material is 30 mΩ/⬜ for a sheet thickness of 25 μm. However, that wouldn't be expressed the way they wrote it--it should be 30·25 mΩ·μm/⬜, or a bulk resistivity of 750 nΩ·m, or 75·10⁻⁸ Ω·m*. This seems reasonable for silver ink, as it's a little worse than most metals (between about 1·10⁻⁸ and 20·10⁻⁸ Ω·m), but substantially better than semiconductors (graphite, for instance, is very roughly 20000·10⁻⁸ Ω·m).

You can divide this number by the sheet thickness to get the sheet resistivity.

Footnotes:
_{*The reason I use 10⁻⁸ Ω·m, rather than μΩ·m or nΩ·m, as a unit here is because this is what metal resistivities are usually quoted in in the literature. It works out to small numbers greater than 1 for most metals, and makes it easy to compare without having to move decimal places around. I think nΩ·m would have been a better unit to use overall, being a standard SI prefix, but the decision to use 10⁻⁸ Ω·m was likely made well over a century ago, before SI prefixes went smaller than μ.}

_{⁻⁸ No, this is an exponent, not a footnote. What are you doing down here?}