An Analytical Geometry Optimization Model for Current-Mode Cross-Like Hall Plates

This paper presents a new analytical geometry optimization model to depict the optimal current sensitivity and signal-to-noise ratio (SNR) for the current-mode Hall devices. The conformal mapping calculation is performed to study the influence of device geometry on the current sensitivity and SNR of the current-mode cross-like Hall plates. The analytical model indicates that a current-mode cross-like Hall plate can achieve optimal current sensitivity and SNR in the device length-to-width ratio (L/W) range of 0.4–0.5 when the thermal noise is taken into account. Three-dimensional (3D) technology computer aided design (TCAD) simulation validates the accuracy of the analytical model. The proposed analytical model provides a geometry design rule to achieve optimal sensitivity and SNR at the same time for the current-mode cross-like Hall plates.