TITLE:
Relations between Hall Plates with Complementary Contact Geometries
AUTHORS:
Udo Ausserlechner
KEYWORDS:
Complementary Hall Plate, Conformal Mapping, Hall Plate, Reverse Magnetic Field on Complementary Device, Resistance Matrix, Reverse Magnetic Field Reciprocity, Stream Function, Calculus of Residues
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.11,
November
20,
2019
ABSTRACT: Singly connected Hall plates with N peripheral contacts can be mapped onto the upper half of the z-plane by a conformal transformation. Recently, Homentcovschi and Bercia derived the General Formula for the electric field in this region. We present an alternative intuitive derivation based on conformal mapping arguments. Then we apply the General Formula to complementary Hall plates, where contacts and insulating boundaries are swapped. The resistance matrix of the complementary device at reverse magnetic field is expressed in terms of the conductance matrix of the original device at non-reverse magnetic field. These findings are used to prove several symmetry properties of Hall plates and their complementary counterparts at arbitrary magnetic field.