Van der Pauw

The van der Pauw method is a technique commonly used to measure the resistivity and the Hall coefficient of a sample. Its power lies in its ability to accurately measure the properties of a sample of arbitrary shape, providing that the sample:

• Is approximately two-dimensional (i.e. it is much thinner than it is other dimensions)
• Has no isolated holes
• Is homogeneous and isotropic
• Has all four contacts located at the edges of the sample
• Has contacts with the area at least an order of magnitude smaller than the area of the entire sample

Resistivity then:

$$\rho =\frac{1}{q{n}_m{\mu }_m}$$

• $\rho$ is the resistivity. $[\rho ]=\Omega \cdot m$
• $q$ is the elementary charge. $q=1.602\times 10^{-19}$ C
• $n_m$ is the majority carrier concentration. $[n_m]=m^{-3}$
• ${\mu }_m$ is the majority carrier mobility. $[{\mu }_m]=m^2/(V\cdot s)$

The product $q{n}_m{\mu }_m$ is the conductivity $\sigma$, so this is just $\rho =1/\sigma$. Van der Pauw gives you $\rho$ (and with a Hall measurement on the same structure, you can separately extract $n_m$ and ${\mu }_m$). Knowing two of the three lets you determine the third.