Improved design of micromachined lateral suspensions using intermediate frames

A complete analysis of the translational and rotational modes of a model lateral suspension is presented. The derived formulae quantify spurious-mode resonant frequencies for cross-axis translation and rotation, and on-axis translation, and can provide very simple expressions for the rejection ratios in terms of the geometry of the suspensions. It is shown that the introduction of intermediate frames, coupling equivalent points of the lateral suspension either side of the suspended mass, can provide much improved dynamics. To investigate the derived relationships, suspensions have been fabricated using through-wafer deep reactive-ion etching (DRIE). Using analysis of the suspension dynamics under the rastered beam of a scanning electron microscope, the various modes of the suspension have been visualized and quantified. These observations are in good agreement with the derived formulae, taking into account the actual profile of the beams fabricated in DRIE. Further finite element analysis across a broad range of suspensions is consistent with the derived formulae. A design heuristic is provided for rapidly optimizing micromachined lateral suspensions by incorporating intermediate frames.