A computationally efficient numerical model of the offset of CMOS-integrated vertical Hall devices

This paper describes a computationally efficient numerical model to study effects determining the offset of five-contact vertical Hall sensors (VHS). It applies a two-dimensional finite element model implemented in COMSOL Multiphysics and allows to take into account the junction field effect (JFE) altering the depletion layer width between n-well and p-doped regions as well as resistive asymmetries due to contact shifts. Doping profiles of realistic devices were extracted using SYNOPSYS TCAD simulations based on three sets of process parameters with different doping doses of the n-well and p+-diffusions. The VHS offset was compared with experimental results obtained using complementary metal oxide semiconductor (CMOS)-based VHS and analyzed as a function of the input voltage. It was shown that the linear offset components are modeled adequately by resistive imbalances caused by lateral contact shifts in the nanometer range. The JFE in turn is responsible for the nonlinear effects of dominantly quadratic dependence on the input voltage. Both effects contribute additively to the overall offset. According to the simulations, the nonlinear contribution is strongly reduced at higher n-well doping concentrations.