  Implementing microelectromechanical system (MEMS) resonators calls for
detailed microscopic understanding of the devices, such as energy dissipation
channels, spurious modes, and imperfections from microfabrication. Here, we
report the nanoscale imaging of a freestanding super-high-frequency (3 ~ 30
GHz) lateral overtone bulk acoustic resonator with unprecedented spatial
resolution and displacement sensitivity. Using transmission-mode microwave
impedance microscopy, we have visualized mode profiles of individual overtones
and analyzed higher-order transverse spurious modes and anchor loss. The
integrated TMIM signals are in good agreement with the stored mechanical energy
in the resonator. Quantitative analysis with finite-element modeling shows that
the noise floor is equivalent to an in-plane displacement of 10 fm/sqrt(Hz) at
room temperatures, which can be further improved under cryogenic environments.
Our work contributes to the design and characterization of MEMS resonators with
better performance for telecommunication, sensing, and quantum information
science applications.
