This thesis presents the first demonstration of a liquid-gated graphene field-effect biosensor transduced by a microwave cavity. To achieve this, a microwave cavity was developed to measure the sheet resistance of graphene with low uncertainty and high stability over extended periods. Specifically, the Allan variance in the Q-factor of ~10^4 was found to be ~0.1 over an averaging time of 1 s, and ~0.5 over an averaging time of 2000 s. The biosensor was demonstrated to detect bovine serum albumin in 0.01 × PBS with a limit of detection below 10^-12 M, which is competitive with other sensors reported in the literature. The adsorption dynamics at different concentrations of BSA were investigated, and detection of the clinically relevant CA 15-3 breast cancer antigen was demonstrated. This study establishes a proof-of-concept for a novel graphene biosensor that may be further explored in future research.

This thesis also presents analytical and finite element modelling using COMSOL to demonstrate and assess the feasibility of a system for molecular mass detection that employs a graphene drum, with its frequency transduced by near-field scanning microwave microscopy (NSMM). It was established that the frequency of the graphene drum modes could be measured using an NSMM, and that if the frequency could be determined with a resolution of 100 Hz, a mass resolution of ~10^-22 kg could be achieved. If the frequency could be determined with a resolution of 1 Hz, a mass resolution of ~10^-24 kg could be achieved. Such a system, if demonstrated experimentally, would offer a molecular mass resolution exceeding that of the best silicon beam resonators reported to date.