TITLE:
The Classical Hall Effect in Multiply-Connected Plane Regions Part I: Topologies with Stream Function
AUTHORS:
Udo Ausserlechner
KEYWORDS:
Anti-Hall Bar, Doubly Connected, Geometry Factor, Hall Plate, Multiply Connected, Non-Peripheral Contacts, Reverse Magnetic Field Reciprocity, Stream Function
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.9,
September
9,
2019
ABSTRACT: Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. They are commonly called offset and Hall voltage. Contemporary smart Hall sensor circuits extract the Hall voltage via spinning current Hall probe schemes, thereby cancelling out the offset very efficiently. The magnetic field response of such Hall plates can be computed via the electric potential or via the stream function. Conversely, Hall plates with holes show new phenomena: 1) the stream function exists only for a limited class of multiply-connected domains, and 2) a sub-class of 1) behaves like a Hall/Anti-Hall bar configuration, i.e., no Hall voltage appears between any two points on the hole boundary if current contacts are on their outer boundary. The paper studies the requirements under which these effects occur. Canonical cases of simply and doubly connected domains are computed analytically. The focus is on 2D multiply-connected Hall plates where all boundaries are insulating and where all current contacts are point sized.