Generally, the resistance depends upon the resistivity, length and cross section area of the specimen. Because the resistance is proportional to length of the sample. As we decreases the thickness of the sample then obviously its length for charge transport will be changed therefore the resistance would declined.
In general, the material’s sheet resistivity, r, can be calculated by the relation
r=RCF(V measured /I measured).
The resistivity correction factor RCF takes the size of the test structure, the thickness of the material, the size of the electrodes, and the position of the electrodes with respect to the boundary of the test structure into account. So, if the thickness is more charge transport will change, which will affect resistivity.
Dear Nancy,
to your question :
1. the 4-probe measurements of dc resistance are only precise enough for materials with resistivities bellow 800 Ohm.cm (given a typical dimensions like thickness < 1-3 mm and probe separation ~5 mm.
2. if the separation between the electrodes is >> thickness of the material, then in the first approximation, the resistance should increase by a factor of two, whent the thickness is decreased by a factor of two. The resistance of your sample in this approximation is R~resitivity. (voltage probes separation)/(thickness of the pellet).
3. Please consult the following :
Semiconductor Material Device Characterisation by D.K.Schroder (Wiley 1998)
Look at correction factors in particular (p.8).
With bets regards
Petr
Conductivity measurements by :
1) which method[1] ?
2) 4-point[2] contacts ?
3) if the method you follow is the Van der Pauw, then what is the (range[3] of the) sample(s) thickness[4] ?
1. Electrical Conductivity and Resistivity https://www.academia.edu/29112469/Electrical_Conductivity_and_Resistivity
2. a)VdP method https://en.wikipedia.org/wiki/Van_der_Pauw_method b)VdP (orig.) http://www.extra.research.philips.com/hera/people/aarts/_Philips%20Bound%20Archive/PRRep/PRRep-13-1958-001.pdf c)Van der Pauw Method http://www.academia.edu/1747742/Van_der_Pauw_Method d)Modified van der Pauw method... https://arxiv.org/pdf/1204.0085.pdf
3. The range of the thickness, among the (your) samples.
4. Effects of sample thickness on the van der Pauw technique for resistivity measurements http://aip.scitation.org/doi/full/10.1063/1.1866232
by decreasing the thickness, cross section area will be reduced. Therefor resistance increases.
Dear Nancy,
The four point probe is used to measure the sheet resistance rohs of a a relatively thin semiconductor layer on an insulating substrate.
If the thickness of the layer d is smaller than s/2 of the probes,
Then there is simple relation between rohs and and the ratio of the V/I of the four probes. Specifically rohs = roh/d= 4.44 V/I,
In case of increasing the thickness beyond of pellet than S/2, the V/I will decrease and the above formula will no longer valid.
For the exact formula please refer to the link: http://www.pveducation.org/pvcdrom/four-point-probe-resistivity-measurementswelcome-to-pvcdrom
Best wishes
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