An Analytical Theory of the Signal-to-Noise Ratio of Hall Plates with Four Contacts and a Single Mirror Symmetry

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DOI: 10.4236/jamp.2018.610174    870 Downloads   1,932 Views  Citations
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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.

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Ausserlechner, U. (2018) An Analytical Theory of the Signal-to-Noise Ratio of Hall Plates with Four Contacts and a Single Mirror Symmetry. Journal of Applied Mathematics and Physics, 6, 2032-2066. doi: 10.4236/jamp.2018.610174.
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