Mechanical characterization and modelling of Lorentz force based MEMS magnetic field sensors

In this work we present experimental results from dynamic and static tests on miniature magnetic field sensors which are based on Micro Electro Mechanical Systems (MEMS) technologies. These MEMS magnetometers were fabricated on SOI wafers using Si bulk micromachining techniques and they operate at the first resonant frequency under the action of the Lorentz force which arises when a current flows through them in the presence of an external magnetic field. Sensing is based on piezoresistive principles and high sensitivity is expected from devices that show high total quality factors Qtot. We investigate here the energy loss mechanisms and the temperature rise due to Joule heating effects in the resonators of the magnetometers by performing tests both in air and under vacuum conditions. Testing was performed using laser Doppler Vibrometry and white light interferometry. At each pressure different driving currents have been applied and Qtot was extracted. It is found that Qtot varies with pressure between two limiting values: a low one in air which was between 17 and 500 for the tested devices and a high one in vacuum which in the case of one of our devices was equal to 2800. The amplitude of the applied current is also affecting the Q value at a certain pressure due to the rise of thermal stress in the resonating structures. The sensitivity of the sensors in air was experimentally measured using a Helmholtz coil and an oscilloscope and values between 72 mV T−1 and 513 mV T−1 were obtained from the tested devices. We further attempt to estimate the temperature rise in the devices due to Joule heating effects by combining the topography scans which were experimentally obtained with results from thermomechanical analysis of the sensors using Finite Element Modelling.