Guidelines for the mechanical design of resonant beam force transducers are developed. By considering the effects of beam dimensions on the force sensitivity, it is shown that thin, narrow beams are optimal for resonant sensing. Sensitivity is also shown to be inversely dependent on the amplitude of oscillation, and linear with the resonance quality (Q) of the oscillator. Based on this analysis, an axial resonant force detector was developed for use in atomic force microscopy. Initial measured results in air with a Q of 15 and 60nm oscillations give 33nN force resolution in a 1 kHz bandwidth. The Q improves to 1200 in moderate vacuum, yielding an expected force resolution of 10pN in a 1 kHz bandwidth. Due to its high axial spring constant (∼200N/m) and vertical orientation, this force probe has the added benefit for surface force measurements that it is not susceptible to snap-down or other force instability.

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