Mobility and carrier density in materials with anisotropic conductivity revealed by van der Pauw measurements

The validity of four-contact van der Pauw--Hall measurements of rectangularly shaped semiconductors with anisotropic transport properties is investigated analytically, numerically, and experimentally. We show that the carrier concentration is correctly measured using the van der Pauw technique without corrections. Furthermore, the asymmetry in the resistance of the van der Pauw sample is related to the real transport asymmetry through an analytically obtained formula. Thus, the mobility in both principal directions as well as the carrier density can be obtained from van der Pauw data. Measurements of electron concentration and mobility using both the Hall-bar and van der Pauw geometries in semiconductor coupled quantum-wire structures confirm this expectation for different anisotropies.