Nanoscale Imaging of Super-High-Frequency Microelectromechanical Resonators with Femtometer Sensitivity*

The implementation of microelectromechanical system (MEMS) resonators calls for detailed microscopic understanding of the devices, such as energy dissipation channels, spurious modes, and imperfections from microfabrication. Unfortunately, such features are mostly overlooked by conventional transducer-based electrical readouts, which becomes the major bottleneck for designing efficient acoustic or cross-domain microsystems. Using transmission-mode microwave impedance microscopy (TMIM), we report the nanoscale imaging of a freestanding super-high-frequency (3 – 30 GHz) lateral overtone bulk acoustic resonator (LOBAR) with a spatial resolution of ~ 100 nm and an equivalent in-plane displacement sensitivity of ~ 10 fm/ÖHz. We have visualized acoustic mode profiles of individual overtones and quantitatively analyzed higher-order transverse spurious modes and anchor loss. Our work provides insightful guidance for designing and optimizing future MEMS resonator and contribute to broad areas from electromechanical device applications to advanced quantum information research.