Optimization of Piezoresistive Cantilevers for Static and Dynamic Sensing Applications

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. While the presented optimizations for the static mode specifically targets the force sensitivity of piezoresistive cantilevers, the results and findings for the dynamic mode can be used for improving the resonance quality of rectangular cantilevers in general, regardless of the implemented sensing schemes. 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. Through simulation and measurement, the effect of the stress concentrating elements on the force sensitivity and stiffness of cantilevers is studied and it is found that decreasing the size of these elements results in an improved sensitivity. 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 mum and lengths and widths ranging from 70 to 1050 mum and 80 to 230 mum, 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, which is applicable even for cases where the noise and signal powers are equal. 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 ppmC-1 and from 0.7 to -0.03 ppm%RH -1, respectively. To apply the compensation technique, the cantilever-based resonator must be tuned in two distinct frequency overtones. Thus, the last part of the work is aimed on techniques to enhance or suppress the vibration amplitude in desired overtones, either by optimizing the location of piezoresistive detectors, or by selectively actuating the cantilever.