Basic relationships for Hall half-plane structures with multiple extended contacts on the boundary: Applications to the extraction of physical parameters and optimization of graphene and vertical Hall devices

Abstract

The basic relationships for a Hall plate with N non-symmetric contacts placed in an arbitrary magnetic field are a set of N-1 relationships that are necessary and sufficient for the existence of a complex electrostatic potential function. By the application of the boundary conditions, they turn into a linear system of N-1 compatibility conditions involving the terminal voltages and currents. The construction of the basic relationships requires the positions of the contact extremities on the real axis of the canonical domain (the upper half-plane) as well as the electric and magnetic parameters of the Hall device. The conduction and resistance matrices can be obtained easily from the basic relationships. They give an effective method for predicting the performance of both horizontal and vertical Hall effect devices and provide a useful method for designing these types of planar devices.