Van der Pauw's method of measuring resistivities on lamellae of non-uniform resistivity

Abstract

When the resistivity of a lamella of non-uniform resistivity is measured by Van der Pauw's method, an average value for the resistivity is found. It is shown here that, for circular lamellae and a simple resistivity distribution ρ=ρ 0+Mr 2 (Mr 2 ▪ρ 0) , the result obtained by Van der Pauw's method is, in a first-order approximation, the same as that obtained by an actual integration of the resistivity over the surface of the lamella. It is also essential, for the above result to be true, that the four contacts are not too close to each other. This result is probably true for lamellae of other shapes and resistivity distributions, if the perimeter is a line of constant resistivity.