Quantitative analysis of Hall effect in two-dimensional materials

Abstract

Two-dimensional (2D) materials are a promising class of materials due to their exotic properties, including flexibility, atomically thin layer, and tunability. While Hall measurements are widely used to investigate promising and conductive materials, 2D material devices often exhibit non-uniform current flows due to the difficulty of fabrication, particularly in bottom-contact or via-contact geometries, complicating quantitative analysis. Here, we demonstrate numerical simulation by incorporating non-diagonal terms in the conductivity tensor, enabling accurate estimation of Hall voltages under arbitrary device geometry. The simulation reproduces device resistance and Hall voltage in Hall bar geometry as a function of resistivity tensor, consistent with analytic solutions derived in another study. We estimate Hall voltages in two geometries—bottom-contact and via-contact— and demonstrate how much the device configuration can suppress the Hall voltage depending on the location of probes. This work provides an extendable framework for analyzing transport properties quantitatively in 2D materials and semiconductors.