The incorporation of electronic compasses in smart phones and tablets provides an easy access to navigation and location based services. Magnetometers are the key element to such electronic compasses in multi degree of freedom (DOF) inertial measurement units (IMUs) embedded in consumer electronic products. A typical 10 DOF IMU combines a three-axis accelerometer, a three-axis gyroscope, a three-axis magnetometer, and a barometric pressure sensor. Out of these four sensors, only the magnetometer remains to be a microelectromechanical systems (MEMS) device. As such, there has been interest to develop MEMS magnetometers towards highly integrated IMUs. The most common approach has been to use capacitive resonators actuated by a Lorentz force resulting from an external magnetic field. These devices typically require vacuum to operate. This thesis presents an attractive approach by using Thin-film Piezoelectric-on-Silicon (TPoS) MEMS resonators. The electromechanical coupling from piezoelectric transduction compensates the lower quality (Q) factor while operating the device in air, thus overcoming the restriction of requiring vacuum. The thesis presents the design, modeling and experimental validation of both out-of-plane (i.e. along z-axis) and lateral field (i.e. along xy-plane) magnetometers to build a three-axis on a chip TPoS Lorentz force magnetometer (LFM).

Various lateral mode resonators are explored for z-axis field detection. We begin with a one-dimensional (1D) mode; the width-extensional (WE) mode. Operating the WE mode MEMS LFM at its 18 MHz resonant frequency, the device yields a measured responsivity of 4.84 ppm/mT with an associated Q factor of 1500 under ambient conditions in air. The responsivity is defined as the ratio of output motional current to the external magnetic field, normalized over the input alternating (AC) drive current.
Given that the WE mode offers stresses along only one axis (i.e. either x-axis or y-axis), the thesis next demonstrates a LFM based on TPoS square-extensional (SE) mode MEMS resonator. The SE mode benefits from having a two-dimensional (2D) stress profile along both x- and y-axes. Such a 2D stress profile contributes to an enhanced responsivity of 6.95 ppm/mT (to z-axis magnetic field), despite having a possibly lower Q factor of 1056 in air under ambient conditions.

Increasing the effective area for piezoelectric transduction improves the electromechanical coupling as well as the responsivity of the LFM. But such an increase in the effective area of the resonator reduces the resonant frequency of the device. To address such trade-off, two single disk resonators were mechanically coupled. Chapter 4 shows that the mechanically coupled disk resonators achieved a responsivity of 21.20 ppm/mT (to z-axis magnetic field) compared to a responsivity of 12.55 ppm/mT (to z-axis magnetic field) for a single disk LFM, while both the resonators were operated at nearly 6.3 MHz resonant frequency.

As a step towards the on-chip integration for a complete three-axis magnetic field detection, the thesis, then, describes an amplitude-modulated lateral field (for x-/y-axis magnetic field) LFM based on mechanically coupled clamped-clamped beam resonator array. In addition to a measured responsivity of 0.33 ppm/mT with a substantially lower Q factor of 30, the coupled clamped-clamped beam based lateral field magnetometerattained ameasured bandwidth of 1.36 kHz.

To address the problem related to viscous damping limited lower Q factor and the associated reduction in responsivity, the thesis, finally, demonstrates two amplitude-modulated lateral field (for x-/y-axis magnetic field) LFMs based on classic cantilever and corner-flapping square plate. The corner flapping topology yielded a measured responsivity of 12.02 ppm/mT, despite having a suboptimal Q factor of 508 in air.