An Analytical Theory of Hall-Effect Devices with Three Contacts

Abstract

Object:Vertical Hall-effect devices (VHalls) and split-drain MAG-FETs often have three contacts and a single mirror symmetry. We discuss the Equivalent Resistor Circuit (ERC) at small magnetic field, relate it to the electrical degrees of freedom, and compare it to traditional Hall plates with four contacts.Methods:In contrast to devices with four contacts, it is not possible to determine the sheet resistance of devices with three contacts by electrical measurements like the one of van der Pauw. However, for both types of devices, the output voltage over input current depends only on resistances of the ERC, the sheet resistance, and the Hall angle, irrespective of the exact shape of the devices and the size of the contacts.Result:This allows one to explore the maximum Signal-to-Noise Ratio (SNR) in a very general sense without consideration of any specific device geometry. It is shown how VHalls with all three contacts on the top face of the Hall tub can have electrical symmetry with maximum SNR.