Design criteria for MEMS magnetometers resonating in free-molecule flow and out of the acoustic bandwidth

Theoretical and measured performance of Lorentz-force-based vibratory MEMS magnetometers for consumer applications are reported. A detailed analysis of the mechanical sensitivity and of the signal to noise ratio in case the dominating noise contribution is thermomechanical, reveals new design criteria for these devices. In particular, it is shown that it is in principle advantageous to design magnetometers with a reduced number of parallel plate-sensing cells as the loss in capacitance variation per unit displacement is counterbalanced by the gain in displacement at resonance due to the reduced damping coefficient. The results obtained on a device built using an industrial process and packaging, reveal a mechanical sensitivity around 0.6 aF/μT and a minimum measurable field around 1 μT, for a device driven with a 140 μA_rms AC current. Linearity and temperature dependence are finally discussed.