Hall effect FEM modeling using FreeFEM++: Illustration on a cross-shaped graphene sensor

The Hall effect, which occurs in metals and semiconductors, is used in numerous applications, particularly in the fabrication of magnetic field sensors. This phenomenon is influenced by the physical properties of the material (electron mobility, doping), the geometry of the device, and the size and position of the metallic contacts. The analytical model has limitations in accurately capturing all these phenomena. Therefore, in this work, we propose a finite element model using FreeFEM++ to accurately model the Hall effect. The validity of this model is assessed by comparing it to analytical ones. The effect of physical defects on the electrical measurements, which cannot be analytically calculated, is explored to illustrate the usefulness of this model under realistic conditions. These simulations can be used both as teaching tools, to illustrate this physical effect and as research tools, as demonstrated in the case of a graphene-based transistor. The reported simulation script is openly shared.