Van der Pauw Method

The Van-der Pauw technique is employed to determine the resistivity and Hall coefficient of a material. It can accurately measure the sample properties having any shape if the sample is 2-dimensional. It uses a four-point probe position around the perimeter of the sample rather than in a straight line. Therefore the average resistivity of the sample measured by this method while the linear arrangement measures the resistivity only in the measuring direction.

Following properties of a material can be measured by this method - 

  • Resistivity
  • Doping type (whether it is p-type or n-type) 
  • The density of majority carrier
  • Mobility of the majority carrier

The following conditions must be met in order to apply this method -

  • The sample must be flat shaped and uniformly thick 
  • The sample should not possess isolated holes 
  • The sample should be isotropic and homogeneous 
  • The contacts should be placed at sample edges 
  • The contact area of individual contacts must be smaller  
Van-der Pauw method to determine the resistivity of a uniform sample - 

This technique was invented by Van-der Pauw and is extensively employed in the semiconductor industry for the determination of resistivity of uniform samples. This technique requires an arbitrarily shaped thin-plate sample having four very small ohmic contacts placed on the periphery, usually at the corners of the plate.
In order to determine the resistivity of a uniform sample, the sheet resistanceneeds to be determined. As demonstrated by Van-der Pauw, two characteristics resistancesare associated with the corresponding terminals as depicted in Fig. A.
These characteristic resistancesandare related to the sheet resistancethrough the Van der Pauw equation, as -
 ...(1)
The above equation can be solved to obtain. 
Thus, the bulk resistivity ρ is obtained fromas - 
 ...(2)
For determiningand, dc current (I) is applied across contact 1 and contact 2 and the voltageis measured across contact 4 and contact 3, as depicted in Fig. A. 
Similarly, voltageis measured across contact 1 and contact 4 by applying current I across contacts 2 and contact 3. and  can be obtained as follows - 
 and 

For Hot-Point Probe Method - Click Here 
For Four Point Probe Method - Click Here