A force sensor based on three weakly coupled resonators with ultrahigh sensitivity

• Ultrahigh sensitive MEMS resonator force sensor.
• Novel 3 degree-of-freedom resonator sensor structure.
• Theoretically calculated the noise floor of the sensor.
• Discussed dynamic range and nonlinearity of the sensor.
• Theoretically calculated the mechanical noise of the coupled resonator system using transfer function models.

A proof-of-concept force sensor based on three degree-of-freedom (DoF) weakly coupled resonators was fabricated using a silicon-on-insulator (SOI) process and electrically tested in 20 μTorr vacuum. Compared to the conventional single resonator force sensor with frequency shift as output, by measuring the amplitude ratio of two of the three resonators, the measured force sensitivity of the 3DoF sensor was 4.9 × 106/N, which was improved by two orders magnitude. A bias stiffness perturbation was applied to avoid mode aliasing effect and improve the linearity of the sensor. The noise floor of the amplitude ratio output of the sensor was theoretically analyzed for the first time, using the transfer function model of the 3DoF weakly coupled resonator system. It was shown based on measurement results that the output noise was mainly due to the thermal–electrical noise of the interface electronics. The output noise spectral density was measured, and agreed well with theoretical estimations. The noise floor of the force sensor output was estimated to be approximately 1.39nN for an assumed 10 Hz bandwidth of the output signal, resulting in a dynamic range of 74.8 dB.