Modelling and design of planar Hall effect bridge sensors for low-frequency applications

The applicability of miniaturized magnetic field sensors is being explored in several areas of magnetic field detection due to their integratability, low mass, and potentially low cost. In this respect, different thin-film technologies, especially those employing magnetoresistance, show great potential, being compatible with batch micro- and nanofabrication techniques. For low-frequency magnetic field detection, sensors based on the planar Hall effect, especially planar Hall effect bridge (PHEB) sensors, show promising performance given their inherent low-field linearity, limited hysteresis and moderate noise figure. In this work, the applicability of such PHEB sensors to different areas is investigated. An analytical model is constructed to estimate the performance of an arbitrary PHEB sensor geometry in terms of, e.g., sensitivity and detectivity. The model is valid for an ideal case, e.g., disregarding shape anisotropy effects, and also incorporates some approximations. To validate the results, modelled data was compared to measurements on actual PHEBs and was found to predict the measured values within 13% for the investigated geometries. Subsequently, the model was used to establish a design process for optimizing a PHEB to a particular set of requirements on the bandwidth, detectivity, compliance voltage and amplified signal-to-noise ratio. By applying this design process, the size, sensitivity, resistance, bias current and power consumption of the PHEB can be estimated. The model indicates that PHEBs can be applicable to several different areas within science including satellite attitude determination and magnetic bead detection in lab-on-a-chip applications, where detectivities down towards 1 nT Hz -0.5 at 1 Hz are required, and maybe even magnetic field measurements in scientific space missions and archaeological surveying, where the detectivity has to be less than 100 pT Hz-0.5 at 1 Hz.