Designing sensors with tensioned silicon nitride micromechanical resonators

Mechanical resonators based on stressed silicon nitride have both exemplary optical and me-

chanical properties. Tensioning the silicon nitride enhances the mechanical properties of these

devices owing to the phenomenon of dissipation dilution. The effects of dissipation dilution can be

further enhanced through geometric engineering of the device, which has yielded devices that are

capable of quantum operation in ambient conditions. At the same time, interferometric detection

allows for a quantum-limited readout of the mechanical motion of such devices. The mechanical

motion of these devices can be selectively influenced by external perturbations by augmentation of

the mechanical resonator. In this work, we design a variety of sensors utilizing this combination

of low dissipation, precise motional readout, and a near-universal coupling to an external field of

interest. In this work, we study each of these elements, as well as their interplay, as they pertain to

tensioned silicon nitride mechanical resonators. We study the ramifications of functionalization for

force sensors, with a specific focus on developing probes for external magnetism, acceleration, and

gravity. Such sensors could enable high-resolution spin imaging or inertial navigation, and moti-

vate geometries and probes for fundamental physics in the context of larger-scale masses. My work

presents the development of specific design criteria pertaining to force sensors based on phononic

crystal membrane resonators. A deeper study of these resonators leads to a generalized formal-

ism to understand the effects of a general, spatially varying, thermal environment on the sensing

performance of such devices. This formalism is verified by direct measurement of an engineered

micromechanical resonator exposed to a spatially varying thermal bath. The work concludes by

considering the development of a micromechanical bolometer based on frequency-shift detection in

engineered tensioned silicon nitride resonators.