Well, resistivity is dependent on the current pathway, which will depend at least in some way on thickness. The best way to measure the resistivity is to have some independent thickness data, and then use a four electrode setup. Here, sourcing current across the outer two contacts, and then measuring the voltage drop across the center two contacts can be used to get resistivity values (a standard four point probe method).

And yes, the spacing of the electrodes is critical since Rho = (R*(A/l), where Rho is resistivity, A is cross sectional area, and l is the length over which the current flows and voltage is applied. Note that strictly speaking, in order to apply such basic equations, the current flow must be very well-defined, and in real samples a shape factor is needed to correct for the actual shape of the current path in real samples.

Most four point probes come pre-calibrated for probe spacing and various shape factors (for the most common sample geometries). If you don't have access to one of these, then you would want to do the measurement using well-defined probe spacing. Also, getting an idea of the thickness can at least give you a range of Rho values.

Thank you for that info. I guess this method can only measure electronic conductivity. My sample is an electroceramic where am interested in the ionic conductivity. The four point probe seems to only measure electronic conductivity but cant resolve to ionic +electronic.

how can i go round that challenge

Ah, that helps. What exactly is the sample, and what parameters are you attempting to measure?

The sample is NASICON.......Na3Zr2Si2PO12. I am only interested in the conductivity but of course I got to measure its resistance.

If you have some standards with "known" resitivity you could use eddy currents. Since you are interested in ionic conductivity, the results may well be frequency dependent

Not my work, but try this:

http://jes.ecsdl.org/content/143/4/1254.short

If you need a full text, let me know.

Thanks Adam, will go through it. Your help is well treasured. Peter, how do I go about it using eddy currents. Any article or book I can read through.

I thought about this a bit and it would depend on whether your film was unsupported or not and what the conductivity of the substrate was like relative to the film. Basically the idea is that you put a coil up against the film and pass a sinusoidally varying current through it to produce a sinsusoidally varying magentic field. The time varying field produces eddy currents in the sample. the skin depth is prportional to 1/sqrt(f*conductivity*permeability). So by making f high enough you can make the depth of penetration as small as you like. One advantage of this approach is that you can do it dry (don't know if that is an advantage for you). Obviously you would like the substrate to have a conductivity of zero. The way this is normally done, you you measure the relative impedance difference in the drive coil due to standards spanning the range of conductivity you are interested in and your unknown and interpolate to get the conductivity. The result will be sensitive to any variation in lift-off (distance between your coil and the sample). Sensitivty can be improved using secondary pick-up coils and differential configurations. I think the biggest question for you is whether or not your conductivity shows a huge frequency difference. Sensitivity to you film is improved by making the frequency very high. If you think this is still worth pursuing, I can try and give you some more details

Thanks Peter. Details please. This is really interesting

Wihout knowing something of the details of your films and the substrates they are on, its hard to give specifics. I did a quick search using "conductivity" & "eddy current" & "thin flm" and came up with a number of interesting hits including

Sub surface material characterization using high frequency eddy current spectroscopy

Heuer, Henning (Fraunhofer Institute for Non-Destructive Testing, Dresden, Germany); Hillmann, Susanne; Klein, Marcus; Meyendorf, Norbert Source: Materials Research Society Symposium Proceedings, v 1195, p 253-258, 2010, Reliability and Materials Issues of Semiconductor Optical and Electrical Devices and Materials

The folk at the Fraunhofer Institute do some clever stuff with eddy currents.

Thanks mate!

best way is 4 point measurement but with 2 contacts and a rectangular sample I think from memory that an approximate measurement can be obtained using the contacts in opposite corners - but check this is true.

thanks Driss. But I want to measure ionic conductivity. This measures electronic conducticity

In fact, the 4 point method measures total conductivity as it has no way of distinguishing what the current is. It can go from DC to any frequency. Typically, if there is any electronic conduction at all, it will dominate because the mobility of electrons is typically much higher than that of ions. The other problem in this case is that the substrate needs to have a conductivity orders of magnitude less than the film or else it will dominate the measurement. As a question, I don't see how you can have a DC ionic current unless there is some source of ions to replenish the source. Am I wrong?

You can use Van der Pauw method. See with google. It is a technique used for semi conductor films. It works also with metals, we tried.