Geometrical Optimization of Resonant Cantilever Sensors

The influence of beam geometry on the quality factor Q of resonant cantilever sensors operated at atmospheric pressure has been investigated. The studied rectangular silicon cantilevers have lengths and widths ranging from 70-500 mum and 80-160 mum, respectively, and thicknesses of 5, 8, and 17 mum. Transverse cantilever vibrations are excited electromagnetically and the flexural resonance modes of the beams are detected on-chip by a piezoresistive Wheatstone bridge. Based on the experimental data, design guidelines for beam dimensions ensuring maximal Q-factors are established. In particular, an optimal length-to-thickness ratio of 15-20 is found; support loss limits the Q-factor for smaller length-to- thickness ratios, while air damping becomes dominant for larger ratios.