Optimization of qPlus sensor geometry and circuit for high-speed atomic force microscopy in liquid environments

Atomic force microscopy (AFM) using qPlus sensors is a powerful tool for high-resolution analysis in various liquids, including high-viscosity or opaque environments. However, the relatively high displacement sensor noise density (n_{ds}), combined with the high spring constant and the low resonance frequency, limits force sensitivity and has hindered high-speed imaging. In this paper, we clarify the dominant factors governing n_{ds} and the minimum detectable force gradient (F'_{min}) through a comprehensive analysis of sensor geometry and circuit theory. Based on these findings, we developed a low-noise qPlus sensor that achieves an n_{ds} of 9.3 fm Hz^{-1/2}, which is approximately one-third that of conventional sensors, and reduces F'_{min} by half. Using this sensor, we demonstrated high-speed, atomic-resolution imaging of a molten gallium interface at a frame rate of 6.6 s frame^{-1} (39 lines s^{-1}), proving its advantage for analyzing fast interfacial dynamics in liquid environments.