Hi. I'm using ITO coated PET sheets , in which the sheet resistance informed by the manufacturer is 60 Ω/sq and with a ITO film thickness of 130nm.
I performed 4-point measurements on rectangular pieces of (2cm x 1cm) and obtained resistivity of 6.11x10-4 Ωcm, which according to the literature are acceptable values. But I would like to calculate the sheet resistance using the values obtained from experiments and then apply it to new measurements in modified ITO rectangles from an experimental procedure that I am carrying out and obtaining other resistivity values.
If anyone can help me with some material to understand how to calculate or to help understand some concept that I am confusing I would appreciate it.
Start from the definition of sheet resistance:
you must consider your film as formed by a grid of squares of length=width=unit-lenght used in the resistivity measurement (if you want to use Ohm-cm, the side of each square will be 1 cm). Then just consider that in the film all the current proceeds parallel to the surface... and apply the super-simple Resistance definition R=rho x lenght / transverse area, where lenght is 1 unit lenght (1 cm in our example), cross section area is width x film thickness. In case of conduction through a single 1x1 cm2 square of the film, the cross section area is 1 cm x thickness (in cm).
It is easy to see that resistance R-square of the square is just given by pho/thickness...
in few words Sheet resistance = resistivity / thickness (using the correct unit lenghts for the thickness)
In your case your meaurement of rho 6.11x10-4 Ohm cm, divided by the film thickness (130 x10-7 cm) gives 47 Ohm-square that is not 60 as stated by the manufacturer, but you should verify the measured value is within the tolerance range provided by the same manufacturer (if provided in the datasheet)..
The resistivity value you measured (supposing it as reproducible in various regions of the film and in various directions in case of linear 4-point probe) suggest a film thickness of about 100 nm... not 130.
Isuggest you perform more measurements changing position and direction of the probe on the 1x2 cm2 sample and take the average resistivity.
Dear Mateus Siraque,
I agree with the answer mentioned by Giuseppe Curro, you could repeat the resistivity measurements several times in several directions. Then, you could calculate the average.
Actually, if the film was prepared by the manufacture in good quality, you should get the resistivity with low tolerance.
What a nice answer! Giuseppe Curro
Best Wishes
Try seeing this
http://four-point-probes.com/sheet-resistance-and-the-calculation-of-resistivity-or-thickness-relative-to-semiconductor-applications/
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