Nanoscale imaging of super-high-frequency microelectromechanical resonators with femtometer sensitivity

Microelectromechanical system (MEMS) resonators, converting electrical energy into mechanical vibrations, are crucial for various applications, including frequency references, RF filters, and quantum information processing. Super high-frequency (SHF, 3–30 GHz) resonators, particularly those with densely packed resonances, are highly desirable for advanced functionalities. However, conventional electrical readouts often overlook microscopic details like mode profiles, energy dissipation, spurious modes, and fabrication imperfections, hindering the design of efficient devices. Direct visualization of SHF acoustic mode profiles is challenging due to the need for sub-100 nm spatial resolution, sensitivity below 1 pm, and the capability to detect in-plane oscillations. Existing techniques like SEM, AFM, and X-ray imaging have limitations in spatial resolution, sensitivity, or the ability to measure in-plane displacements. Optical methods, such as interferometry and pump-probe techniques, are diffraction-limited and only detect vertical displacements. Therefore, a new method capable of imaging laterally polarized SHF acoustic waves with high sensitivity and resolution is needed.

The authors review existing microscopy techniques for probing GHz acoustic fields. Scanning electron microscopy (SEM) is limited to sub-GHz frequencies due to charging effects. Atomic force microscopy (AFM) relies on nonlinear effects, unsuitable for low signal levels. Stroboscopic X-ray imaging requires highly coherent sources and has limited sensitivity. Laser-based techniques like interferometry and pump-probe methods have diffraction-limited spatial resolution and only detect vertical displacement. These limitations highlight the need for a new approach to image laterally polarized SHF acoustic waves with high sensitivity and spatial resolution.

The researchers used transmission-mode microwave impedance microscopy (TMIM) to image acoustic waves in a freestanding LiNbO3 thin-film lateral overtone bulk acoustic resonator (LOBAR). The LOBAR, with electrodes covering a small section of the acoustic cavity, exhibits high Q-factors due to low acoustic and thermoelastic damping. The TMIM setup utilizes an atomic force microscopy (AFM)-based system capable of operating in a broad frequency range (0.1–18 GHz). The TMIM tip acts as a microwave receiver, picking up the GHz piezoelectric potential. The signal is demodulated using an I/Q mixer, providing phase-sensitive measurement of the electric potential proportional to the piezoelectric coefficient and local displacement field. Fast Fourier transformation (FFT) of the real-space TMIM images provides information in k-space. Broadband TMIM imaging was performed on the LOBAR to obtain spatially resolved information on various overtones. The mixer phase was adjusted to optimize signal capture in one TMIM channel. The researchers also performed impedance matching to enhance sensitivity. Noise power analysis was conducted on the TMIM data to determine the instrument's sensitivity.

TMIM successfully visualized the A1 Lamb waves in the LiNbO3 LOBAR, revealing standing waves within the resonator and acoustic leakage through the anchor. The FFT images confirmed the standing wave nature of the resonator. The acoustic leakage was two orders of magnitude lower than the signal inside the resonator, indicating that anchor loss was not the primary energy dissipation mechanism. The spatial resolution of the TMIM was on the order of 100 nm. Broadband imaging showed that the spacing between adjacent fringes decreased with increasing mode index, correlating with the acoustic wavelength. The phase velocity decreased with increasing frequency. TMIM images revealed higher-order transverse modes near the main resonance, which agree with finite-element analysis (FEA) simulations. The integrated TMIM-Mod² signals correlated well with the measured Y² (square of admittance), both proportional to the acoustic power. Sensitivity analysis showed that the TMIM could detect 5 GHz in-plane oscillations down to 10 fm/√Hz at room temperature, limited by power-line noise. Noise analysis indicated an ultimate sensitivity floor of 3-5 fm/√Hz, which is significantly better than that of optical methods. Cryogenic operation is predicted to further improve sensitivity to below 1 fm/√Hz.

The high sensitivity and spatial resolution of the TMIM technique successfully addressed the challenge of visualizing nanoscale acoustic wave phenomena in SHF MEMS resonators. The ability to directly image mode profiles, anchor loss, and spurious modes provides valuable insights for optimizing resonator design. The good agreement between TMIM measurements and FEA simulations validates the accuracy of the method. The femtometer-level sensitivity achieved opens up new possibilities for studying low-energy acoustic phenomena, such as those relevant to quantum acoustics. The observed correlation between integrated TMIM signals and stored mechanical energy provides a powerful tool for characterizing the performance of these devices.

This study demonstrates the successful nanoscale imaging of a freestanding overtone resonator with unprecedented femtometer-level sensitivity using TMIM. The technique provides direct visualization of acoustic wave profiles, anchor leakage, and spurious modes. The sensitivity achieved opens new possibilities for studying low-energy acoustic phenomena and optimizing MEMS resonator design. Future research could focus on cryogenic implementation of the TMIM to further improve sensitivity and explore applications in quantum acoustics.

The current sensitivity is limited by power-line noise. Further improvements could be achieved by operating the TMIM under cryogenic conditions to reduce thermal noise. The study focused on a specific type of resonator; the generalizability of the findings to other MEMS resonator designs requires further investigation. The analysis assumes a linear response of the resonator. Non-linear effects that might occur at high power levels were not investigated.