Modelling of a magnetic sensor based on vacuum field emission

A model is developed in order to analyse a magnetic sensor based on vacuum field emission. The operation of the sensor is based on the deflection of the electron current obtained through cold emission due to the Lorentz force. The electronsʹ velocities obtained in vacuum are higher than in a semiconductor, being not limited by scattering processes. They allow for higher electron deviations and sensor sensitivities to be obtained. The sensor based on cold emission is less sensitive to environmental conditions (temperature and radiation) compared with semiconductor based sensors. The field emission diode model considered comprises two co-axial metallic cylinders placed in vacuum. The spacing between cylinders is d and the diode difference of potential is Va. The inner cylinder acts as emitter. The outer cylinder acts as split-anode with two active parts of equal angular aperture. The differential signal from the two anodes is a function of the applied magnetic field B, which is parallel to the cylindersʹ axis. The trajectory of the emitted electrons is obtained both in analytical and numerical form. The sensor relative sensitivity S and magnetic field measuring range Bm are defined and computed. It is shown that Bm increases linearly with Va and 1d, whilst S varies in the opposite way, decreasing with Va and linearly increasing with d. High sensor relative sensitivities are obtained, in the range several hundred to thousand %/T. These values compare well with experimental data.