The Hall probe measurement system is not working well, so I was thinking to measure the sheet resistance of the graphene layer with multimeter. The thickness of the graphene layer is around 0.35nm. How can I precisely measure the sheet resistance?
The easiest way to measure the sheet resistance with multimeter is that first just measure the resistance of the deposited material with the multimeter and note it down. Then measure the dimensions (Length and Width) of the deposited material. Then use the following formula
Rsh = R*W / L
An easy but effective method is to use a four point probe.
You will just need two mutimeters:
Arrange them as shown in the following image:
http://upload.wikimedia.org/wikipedia/commons/thumb/0/08/Fourpointprobe_GMR.png/800px-Fourpointprobe_GMR.png
To clarify: over the two outer probe heads, you will have a current I, while you measure the voltage U with the two inner probe heads.
Make sure that the probe heads are as far away from the edges of the surface you want to probe as possible.
To calculate the sheet resistance Rs you have to use the following equation:
Rs = PI/ln(2) * U/I with Rs = R/d (which is the sheet resistance, if I'm not mistaken)
Make several different measurements, to make sure that you get similar results.
The easiest way to measure the sheet resistance with multimeter is that first just measure the resistance of the deposited material with the multimeter and note it down. Then measure the dimensions (Length and Width) of the deposited material. Then use the following formula
Rsh = R*W / L
Well, you may pay attention to what you want to measure, surface resistivity or volume resistivity.
Surface resisitivity can be measured up to BS 6524:1984 standard
surface and volume resisitvities can be measured by ASTM D 257-61 standard as well.
Contacting methods like four-point-probes will always be harmful to the sensitive graphene layer. Non-contact sheet resistance of graphene can be well measured with high frequency eddy-current. https://en.wikipedia.org/wiki/Sheet_resistance#measurement
Is this considering a dc circuit? what happen if you have AC circuit?For example you have a square mesh , will this sheet resistance change with function of frequency? and If so, what will happen to that mesh electromagnetically ?
When using two probe method to measure the resistivity of a thin film you have to take into consideration the flowing precautions:
- The probes must make low resistance ohmic contact with the film
- the geometry of the electrodes must be well defined. The most easier geometry is the stripe geometry comprising the width of the specimen say w.
- Then the thickness and the length L must be known. It is advantageous to make L>> w to make the resistance of the film much greater than the contact resistance with electrodes.
Then one can use the expression for determining the film resistivity roh :
Rf= roh L/ wt
where Rf is the film resistance between the two electrodes and t is the thickness of the film. Rf is directly measured by the ohmeter
It is also assumed that the substrate must insulating.
In order to avoid all these precautions one uses four point probe or the Van der Paw method provided also that the substrate must be insulating.
In case of using four point probe:
If you have the sheet resistance of the film measured by the 4-point probe provided you satisfy all the assumptions of the simplified expression:
Rs= sheet resistance = 4.44 V/I where V is the four point probe voltage and I is it current. The sheet resistance = the resistivity roh/ t the thickness of the film.
To get roh= Rs.t , which is the expression brought by Zainab.
The most important requirement for the validity of the above expression:
-The substrate must insulating
- The extention of the film must be much greater than s the probe spacing
- The probe spacing must be much greater than the film thickness
- The material is homogeneous
For the four point probe measurement you need a known current source and a voltmeter.
Best wishes
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