Symmetries of certain double integrals related to Hall effect devices

Producción CientíficaOne encounters iterated elliptic integrals in the study of Hall effect devices, as a result of conformal mappings of Schwarz–Christoffel type. Some of these double elliptic integrals possess amazing symmetries with regard to the physical parameters of the underlying Hall effect devices. We give a unified mathematical treatment of such symmetric double integrals, in the context of Hall effect devices with three and four contacts.Junta de Castilla y León (VA057U16) and MINECO (Project MTM2014-57129-C2-1-P)

Hall Effect Devices with Three Terminals: Their Magnetic Sensitivity and Offset Cancellation Scheme

This paper discusses properties of Hall effect sensors with only three terminals and compares them to conventional four-terminal devices. It covers both Horizontal and Vertical Hall effect devices. Their Hall-geometry factor is computed analytically. Several modes of operation are proposed and their signal-to-noise ratio is compared. A six-phase offset cancellation scheme is developed. All theoretical results are checked by measurements. The residual offset of Vertical Hall effect devices with three contacts is found to be smaller than the offset of conventional Vertical Hall effect devices with five contacts

An Analytical Theory of Piezoresistive Effects in Hall Plates with Large Contacts

Four-terminal transducers can be used to measure the magnetic field via the Hall effect or the mechanical stress via the piezoresistance effect. Both effects are described by an anisotropic conductivity tensor with small offdiagonal elements. This has led other authors to the conclusion that there is some kind of analogy. In both cases the output voltage depends on the geometry of the device and the size of the contacts. For Hall plates this influence is accounted for by the Hall-geometry factor. The alleged analogy proposes that the Hall-geometry factor also applies to four-terminal stress transducers. This paper shows that the analogy holds only for a limited class of devices. Moreover, it is shown that devices of different geometries may have identical magnetic field sensitivity but different mechanical stress sensitivities. Thus, shape optimization makes sense for mechanical stress sensors. In extreme cases the output voltages of vertical Hall-effect devices may have notable magnetic field sensitivity but zero mechanical stress sensitivity. As byproduct, exact analytical formulae for the equivalent resistor circuit of rectangular and circular devices with two perpendicular mirror symmetries are given. They allow for an accurate description of how mechanical stress and deformation affect the output offset voltage and the magnetic sensitivity of Hall-effect devices