Geometrical optimization of resonant cantilevers vibrating in in-plane flexural modes

The influence of the beam geometry on the quality factor and resonance frequency of resonant silicon cantilever beams vibrating in their fundamental in-plane flexural mode has been investigated in air and water. Compared to cantilevers vibrating in their out-of-plane flexural mode, utilizing the in plane mode results in reduced damping and reduced mass loading by the surrounding fluid. Quality factors as high as 4,300 in air and 67 in water have been measured for cantilevers with a 12 μm thick silicon layer. This is in comparison to Q factors up to 1,500 in air and up to 20 in water for cantilevers vibrating in their fundamental out-of-plane bending mode. Based on the experimental data, design guidelines are established for beam dimensions that ensure maximal Q-factors and minimal mass loading by the surrounding fluid.