Principles of nonlinear MEMS-resonators regarding magnetic-field detection and the interaction with a capacitive read-out system

This paper presents a magnetic field sensor with capacitive read-out, whose active element is a micromachined mechanical resonator. The MEMS magnetic field sensor exploits the Lorentz force to detect external magnetic flux density through the displacement of the resonant structure, which can be measured with optical and capacitive sensing techniques. The micromachined U-shaped cantilever features a length of 2 mm, a base width of 90 μm and a thickness of 20 μm, and is manufactured in SOI technology. The designed sensor has a measured resonant frequency of 4.359 kHz for the fundamental mode and a calculated mass of the flexible structure of 24.5 ng. A quality factor in the order of 10⁴ at an ambient pressure of 0.3 Pa has been measured where a magnetic field resolution of 15 nT can be achieved. Although these arrangements are well suited to capacitively sense the vibrations caused by the Lorentz force on the current lead on the silicon part, care has to be taken to avoid undesired mutual interferences. A serious interference was observed in case of a DC bias voltage at the readout capacitance and a significant voltage drop caused by the current needed for the generation of the Lorentz force. This work investigates in detail this phenomenon as well as the complete physical transduction chain and improves the understanding of such microelectromechanical systems significantly. An analytical model of the electrostatic system is established including all relevant components and their interactions as well as the motion of the MEMS part. The importance of electrostatic back-action for a feasible detection limit for magnetic fields was recognized for the first time.