The magnetic calibration of arbitrarily shaped Hall sensors in the absence of magnetic fields

Abstract

This paper presents a method to calibrate arbitrarily shaped planar Hall plates without the need for applying a magnetic field. Using the method of conformal mapping, it is shown that magnetic sensitivity parameters can be extracted from six independent resistance values measurable in the absence of a perpendicular magnetic field B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">perp</sub> . Remarkably, no prior knowledge of the device geometry is required. As a consequence, numerical simulations of Hall plate sensitivities can be performed by solving electrical conduction problems without magnetic effects, and using the appropriate value of the Hall mobility mu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> . Experimental data measured with CMOS sensors corroborate the theoretical findings.