Measuring anisotropic resistivity of single crystals using the van der Pauw technique

Abstract

Anisotropy in properties of materials is important in materials science and solid-state physics. Measurement of the full resistivity tensor of crystals using the standard four-point method with bar shaped samples requires many measurements and may be inaccurate due to misalignment of the bars along crystallographic directions. Here an approach to extracting the resistivity tensor using van der Pauw measurements is presented. This reduces the number of required measurements. The theory of the van der Pauw method is extended to extract the tensor from parallelogram shaped samples with known geometry. Methods to extract the tensor for both known and unknown principal axis orientation are presented for broad applicability to single crystals. Numerical simulations of errors are presented to quantify error sources. Several benchmark experiments are performed on isotropic graphite samples to verify the internal consistency of the developed theory, test experimental precision, and characterize error sources. The presented methods are applied to a RuSb_2 single crystal at room temperature and the results are discussed based on the error source analysis. Temperature resolved resistivities along the a and b directions are finally reported and briefly discussed.