Geometry optimization of a Lorentz force, resonating MEMS magnetometer

In this paper, we propose a multiphysics-based optimization of the geometry of a microbeam, which represents the sensing part of a Lorentz force, resonating, MEMS magnetometer. The optimization problem is framed by accounting for a (weak) electro-thermo-mechanical coupling, which induces a state of residual stresses in the microbeam, clamped at both its ends. Nonlinearities caused by the aforementioned residual stresses and by the electrostatic sensing are taken into account up to second order. In the optimization procedure, two objective functions are handled, as linked to the sensitivity (to be maximized) and to the power consumption (to be minimized) of the system; a constraint is also accounted for to ensure the sensor to work within a required frequency regime. By considering the microbeam width and length as design parameters, we show that a set of possible optimal designs can be obtained by tuning the weighting factors mixing the two aforementioned objective functions.