VanderPauwMethode

The VanderPauw method, often written Van der Pauw method or VanderPauwMethode in Dutch, is a technique for determining the resistivity or sheet resistance of thin films of arbitrary shape. It was developed by Leendert J. van der Pauw in 1958 and applies to flat, homogeneous samples of uniform thickness with four small ohmic contacts placed on the periphery. The method assumes the film is simply connected, the contacts are ideal, and the thickness is uniform and much smaller than the lateral dimensions.

In the standard procedure, four contacts are placed on the sample’s edge, labeled 1 through 4 in a clockwise order. A current I is passed between adjacent contacts (for example 1 and 2), and the resulting voltage V is measured across the opposite pair (3 and 4), giving R12,34 = V34 / I12. A second measurement is made with current between contacts 2 and 3 and voltage between 4 and 1, yielding R23,41 = V41 / I23.

The sheet resistance Rs is obtained from the van der Pauw equation: exp(-π R12,34 / Rs) + exp(-π R23,41 / Rs) = 1. The equation is solved numerically. If the two resistances are nearly equal, a convenient approximation is Rs ≈ (π / ln 2) × R12,34 ≈ 4.532 × R12,34. The film resistivity is ρ = Rs × t, where t is the film thickness.

The method is widely used for characterizing thin films of metals, semiconductors, and two-dimensional materials. Limitations include sensitivity to contact size and placement, thickness nonuniformity, and sample geometry. Extensions allow measurement of the Hall coefficient by applying a magnetic field and using additional configurations.