Micromechanical resonators are used in a variety of sensing and filtering applications. In these applications, the accurate performance of micro resonators depends on the sensitivity of these devices to a particular resonance frequency. This sensitivity is measured using the quality factor Q, which is the ratio of the total input energy into the device to the energy dissipated within a vibration cycle. A higher quality factor indicates a smaller resonance bandwidth, which makes the micro-resonator more effective in identifying a desired signal. Higher Q values result from reductions in dissipation losses. Dissipation losses occur through damping by the ambient fluid, anchor losses, thermoelastic damping, and other sources. The squeeze-film effect is of particular interest in micro-resonators as the fluid enclosed between the resonating components can provide significant dissipation. This work covers investigations into the air damping of oscillating micromachined resonators that operate near a fixed wall, which is parallel to the oscillating surface. The main portion of this work focuses on the theoretical and numerical investigation of the air damping of micromachined resonators when the surrounding gas (air) is in the Free-Molecule regime. Errors and limitations of previous theoretical models have been found and corrected. A molecular dynamics simulation code that is suitable to handle a more general class of resonators has been developed. This code has been used to find the quality factor of a microbeam resonator. The results from the code were compared to existing experimental results, and were found to have very good agreement in the free molecular regime. The simulation was then used to investigate the effects of the oscillation mechanics on the energy dissipation and quality factor. The second part of this work focuses on the region between the bottom surface of a laterally-oscillating disk resonator and the substrate. The compressibility effects of a 1 micron thick film of air on a laterally-oscillating disk resonator were investigated. The pressure perturbation for this case was found to be minimal, which means that the compressibility effects of the fluid film will negligible.

The presented work aims to optimize the performance of piezoresistive cantilevers in cases where the output signal originates either from a static deflection of the cantilever or from the dynamic (resonance) characteristic of the beam. Based on a new stress concentration technique, which utilizes silicon beams and wires embedded in the cantilever, the force sensitivity of the cantilever is increased up to 8 fold with only about a 15% decrease in the cantilever stiffness. Moreover, the developed stress-concentrating cantilevers show almost the same resonance characteristic as conventional cantilevers. The focus of the second part of the present work is to provide guidelines for designing rectangular silicon cantilever beams to achieve maximum quality factors for the fundamental and higher flexural resonance at atmospheric pressure. The applied methodology is based on experimental data acquisition of resonance characteristics of silicon cantilevers, combined with modification of analytical damping models to match the measurement data. To this end, rectangular silicon cantilever beams with thicknesses of 5, 7, 8, 11 and 17 um and lengths and widths ranging from 70 to 1050 um and 80 to 230 um, respectively, have been fabricated and tested. To better describe the experimental data, modified models for air damping have been developed. Moreover, to better understand the damping mechanisms in a resonant cantilever system, analytical models have been developed to describe the cantilever effective mass in any flexural resonance mode. To be able to extract reliable Q-factor data for low signal-to-noise ratios, a new iterative curve fitting technique is developed and implemented. To address the challenge of frequency drift in (mass-sensitive) resonant sensors, and especially cantilever-based devices, the last part of the research deals with a novel compensation technique to cancel the unwanted environmental effects (e.g., temperature and humidity). This technique is based on exploring the resonance frequency difference of two flexural modes. Experimental data show improvements in temperature and humidity coefficients of frequency from -19.5 to 0.2 ppm/˚C and from 0.7 to -0.03 ppm/%RH, respectively. The last part of the work also aims on techniques to enhance or suppress the flexural vibration amplitude in desired overtones.