Four-Point Probe Method - Engineering Physics


Four-Point Probe Method

The Four-Point Probe method is used to measure the resistivity of a material. This method involves four equally spaced probes as shown in Figure which is in contact with the material of unknown resistance. The current is passing through the outer probes and voltage induces through the inner probes. 

This method can be used either in bulk or thin specimen.

For Bulk -

Consider the material of thickness 't' when . Then the differential resistance due to the current through the outer probe is given by


 ...(1)

As we know the current flow through two probes so resistance can be written as


 ...(2)

So from eq. (1) and (2), we get


 ...(3)
For Thin Sheet - 

Consider thin sheet of thickness . Here we have current rings instead of sphere. So area is 
 

So in this case the deferential resistance is given by 
 ...(4)
So from eq. (4) and (2), we get
 ...(5)
It is independent of probe spacing.
The Hall mobility is given as 
Where  is Hall Coefficient and n is the carrier density. So from above data we can find out the resistivity, carrier concentration and Hall mobility.

For Van der Pauw Method - Click Here

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