Finite-Element Models for Planar Hall Probes of Arbitrary Shape and Composition

Previous numerical models of planar Hall probes using finite-difference and finite-element methods were limited to open boundaries parallel to the coordinate axes. This paper derives the finite-element equations on a conformal triangular mesh directly from the law of current conservation. The treatment shows that the Hall condition for general curved boundaries is inherent in the equations and can be implemented in numerical programs with little effort. Results are presented from a code that can handle spatial variations of magnetic field, layer thickness, volume resistivity, and the Hall coefficient in probes of any shape.