Extracting the full conductivity tensor in a rectangular sample

Abstract

Electrical transport measurements reveal that many 2D materials exhibit anisotropic conductivity. However, current methodologies for rectangular geometries can only extract a partial conductivity tensor or are difficult to execute experimentally. Here, we propose a simple experimental procedure to extract the full conductivity tensor (or the resistivity tensor by inversion) including the principal axes angle. Our procedure is developed by using a conformal mapping approach to obtain an analytical expression for the potential with a point source and drain on the perimeter. Our solution agrees very well with numerical simulations using COMSOL and the known limiting case where the principal axes angle vanishes. Finite source/drains can be modeled using superposition.