TITLE:
An Analytical Theory of the Signal-to-Noise Ratio of Hall Plates with Four Contacts and a Single Mirror Symmetry
AUTHORS:
Udo Ausserlechner
KEYWORDS:
Hall Plate, Vertical Hall Effect Device, Geometry Factor, Conformal Mapping, Signal to Noise Ratio, Single Mirror Symmetry, Equivalent Resistor Circuit, Common Mode Potential
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.10,
October
24,
2018
ABSTRACT: This work gives an analytical theory of the signal-to-thermal-noise
ratio (SNR) of classical Hall plates with four contacts at small magnetic
field. In contrast to previous works, the symmetry of the Hall plates is reduced to only a single mirror axis,
whereby the average of potentials of the two output contacts off this mirror
axis differs from the average of potentials at the two supply contacts on the
mirror axis, i.e. the output common
mode differs from 50%. Surprisingly, at fixed power dissipated in the Hall
plate, the maximum achievable SNR is only 9% smaller for output common modes of
30% and 70% when compared to the overall optimum at output common modes of 50%.
The theory is applied to Vertical Hall effect devices with three contacts on
the top surface and one contact being the buried layer in a silicon BiCMOS
process. Geometries are found with large contacts and only a moderate loss in
SNR.