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Erschienen in:
22.12.2015 | Original Paper
A method to compute the Hall-geometry factor at weak magnetic field in closed analytical form
Erschienen in: Electrical Engineering | Ausgabe 3/2016
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Abstract
The Hall-geometry factor describes how the output voltage of a Hall plate is affected by the shape of the plate and the size of its contacts. Closed analytical formulae are known only for degenerate or highly symmetric shapes of Hall plates. We present an approach which splits up the computation into a superposition of two electrostatic problems with simple scalar conductivity. This procedure is suited to prove various symmetry properties of Hall plates and to derive a number of formulae for the Hall-geometry factor. We apply it to rectangular Hall plates at weak magnetic field with arbitrarily large contacts having different input and output resistances. From this we deduce the case of Hall plates with \(90^{\circ }\) symmetry, for which a simple closed form approximation with an error of less than 0.02 % is given.