This work aims to provide guidelines for designing rectangular silicon cantilever beams to achieve maximum quality factors for the fundamental flexural resonance at atmospheric pressure. The methodology of this work is based on experimental data acquisition of resonance characteristics of silicon cantilevers, combined with modification of analytical damping models to match the captured data. For this purpose, rectangular silicon cantilever beams with thicknesses of 5, 7, 8, 11, and 17 μm and lengths and widths ranging from 70 to 1050 μm and 80 to 230 μm, respectively, have been fabricated and tested. Combining the three dominant damping mechanisms, i.e., the air damping, support loss, and thermoelastic damping, the variation in the measured Q-factors with the cantilever geometrical dimensions is predicted. Also to better describe the experimental data, modified models for air damping have been developed. These modified models can predict the optimum length and thickness of a resonant cantilever to achieve the maximum quality factor at the fundamental flexural resonance mode in air.

A new method for eliminating the noise effect in interpreting the measured magnitude transfer characteristic of a resonator, in particular in extracting the Q-factor, is proposed and successfully tested. In this method the noise contribution to the measured power spectral density of resonator is iteratively excluded through a sequence of least-square curve fittings. The advantage of the presented method becomes more tangible when the signal to noise power ratio (SNR) is close to unity. A set of experiments for a resonant cantilever vibrating at different amplitudes has shown that when SNR is less than 10, the calculation results of conventional methods in extracting the Q-factor, i.e., the 3 dB bandwidth and single least-square curve fit, exhibit significant deviations from the actual Q-factor, while the result of the proposed iterative method remains in 5% margin of error even for a SNR of unity. This method is especially useful when no specific data is available about the measurement noise, except the assumption that the noise spectral density is constant over the measured bandwidth.

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A novel approach for enhancing the sensitivity of piezoresistive cantilever sensors is presented. Thin piezoresistive clamped-clamped silicon beams are released on the surface of the cantilever by a micromachining process sequence combining deep-reactive ion etching and anisotropic wet etching of silicon. A deflection of the cantilever sensor yields a stress concentration in these micromachined piezoresistive structures. Finite element simulations indicate an increase in both force and displacement sensitivity compared to a conventional cantilever beam with the same thickness. Devices have been fabricated and initial characterization has been performed. Under constant tip deflection of the cantilever, the new piezoresistor design shows an increase in the relative resistance change by a factor of 5.2 compared to a cantilever with the same thickness and conventional piezoresistor design.