# Electrial Conductivity of Thin Metal Films

What is the best way to find specific/electric conductivity which is dependent of very thin film thickness?

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How thin? Few atoms? Few million atoms? –  Steve B Aug 1 '12 at 21:17
Like 250nm thin. –  Syed Samiul Elahi Aug 2 '12 at 18:51

One way to do this is either a two point or four point measurement - the four point will be more accurate if you have significant contact resistance. If not, a simpler two point setup will be sufficient.

One basic setup is to pass a known current between two probes which lie on the outside of two other probes, which you are trying to measure the voltage difference across. Using the known current and measured voltage (and a known geometry), you can deduce the sheet resistance in Ohms (per square). From that, you can then multiply by the film thickness to get resistivity.

http://en.wikipedia.org/wiki/Sheet_resistance#section_2

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Your problem is that the conductivity depends on the film structure. Back in the dawn of time (mid 1980s!) I spent a happy three years studying reactions of silver films, and one of the techniques used was to measure the resistance of the film. As the silver reacted the film thickness went down and the resistance went up.

However once the film thickness forms below around 400$\mathring{A}$ the film is no longer solid metal. As the thickness falls you get voids, then a reticulate structure and finally isolated islands of metal. You'll also find that annealing films can reduce the resistance by a factor of two. I found that if you control the film preparation very carefully you can get reproducible resistances, but it does take some work. For example the substrate cleanliness was very important and I had to plasma etch my glass substrates before growing the films. With careful preparation you can construct a resistivity vs thickness curve for your films (but note this curve will probably differ from researchers using different preparation methods).

Actually measuring the resistance is dead easy. I just used scored a track in the film then measured the resistance as a function of track length, and one linear regression later I had the resistance. You don't need any special techniques to get measurements more accurate than the natural variability in the films.

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If the film is thick enough to be more-or-less smooth and contiguous, then

$$(\text{sheet resistance}) = (\text{resistivity}) / (\text{thickness}).$$

How thick? It differs from metal to metal. John Rennie's answer says that 40nm is roughly the threshold for silver to be contiguous. I know that gold is very susceptible to dewetting when you deposit too thin a film. It depends on the substrate too. But I think most if not all metals would be "more-or-less smooth and contiguous" if they are as thick as 250nm.

Surface scattering or surface disorder can also cause the above equation to be inaccurate. But for metals, I doubt that would be noticeable except for films thinner than maybe 10nm.

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