When capacitive transduction meets the thermomechanical limit: Towards femto-newton force sensors at very high frequency

Abstract

We show that the capacitive transduction of a MEMS device using a setup based on a microwave detection scheme achieves the measurement of the thermomechanical noise spectrum of a high-frequency (>10 MHz) highstiffness (>10 5 N/m) resonator, reaching the outstanding displacement resolution of 1 fm/√Hz. This result paves the way for vibrating sensors with exquisite force resolution in the fN/√Hz range, enabling large-bandwidth measurements of mechanical interactions at small scale and rheology of fluids at very high frequency. An example of application is given and concerns atomic force microscopy images of biomolecular assemblies.

Thermomechanical Noise Characterization in Fully Monolithic CMOS-MEMS Resonators

“…Similarly, the outcomes also improve the results obtained for piezoresistive monolithic systems in terms of [ 12 , 13 ] by . Finally, our results also improve by 10 the outcomes achieved by opto-mechanical systems, both the optical readout and the microwave cavity solution [ 16 , 17 ], with the exception of the works by Ding [ 14 ] and Zhang [ 15 ] that provide a that is better than our result. These two-latter works exploit the advantages of the optical readout system that allows operation at very-high frequency, with the limitation of not being easily integrated as a monolithic solution.…”

“…These results are similar to the best solutions achieved for the transduction of displacement in the micro and even nanomechanical world, that is constantly under progress [ 7 ]. Both, the and , are more than four orders of magnitude below state-of-the-art capacitive alternatives [ 8 , 9 , 10 , 11 ] and piezoresistive ones [ 12 , 13 ], being similar to optical and microwave cavity systems [ 14 , 15 , 16 , 17 ]. In addition, measurements in vacuum conditions show a performance increase, achieving a for CC-Beam resonator, and a minimum detectable change in capacitance , becoming closer to the state-of-the-art optical solutions [ 14 , 15 , 16 , 17 ].…”

Multi-MHz micro-electro-mechanical sensors for atomic force microscopy

“…Therefore, microwave parts of the circuit have to be selected for very low-noise and low-loss operation. A displacement resolution of 1 fm/√Hz was achieved with such a detection method [26]. Finally, using Eq.1, Eq.2 and the AFM resonator mechanical equation, the electrical transfer function H(f) of the MEMS AFM probe can be written in harmonic regime as: 3)…”

“…Further works demonstrated that such probes are sensitive to mechanical interactions with surface forces [23] and can be successfully used for AFM imaging [24]. Recent advances in signal processing gave access to the detection the thermomechanical displacement noise of the probes, paving the way for exquisite sensitivity and force resolution [25,26]. In the present study, AFM results obtained with 13.6 MHz MEMS AFM probes are presented.…”

Atomic force microscope based on vertical silicon probes

“…Previously, we demonstrated the use of MEMS resonators at very high frequencies 15 that were used in an AFM setup with resonant amplitudes in the range 10-20 pm and stiffness constant above 100 kN/m. 16 Here, we present a family of vertical probes that enable to combine much lower stiffness constants to high amplitude dynamic range, together with low impedance electrical transducers and optimized aspect ratio for the tip. The architecture of these vertical probes (Vprobes) is described in Fig.…”