MEMS resonators that are robust to process-induced feature width variations

In this paper, a frequency stability analysis and design method for MEMS resonators is presented. The frequency characteristics of a laterally vibrating resonator are analyzed. With the fabrication error on the sidewall of the structure being considered, the first and second order frequency sensitivities to the fabrication error are derived. A simple relationship between the proof mass area and perimeter, and the beam width, is developed for single material structures, which expresses that the proof mass perimeter times the beam width should equal six times the area of the proof mass. Design examples are given for the single material and multi-layer structures. The results and principles presented in the paper can be used to analyze and design other MEMS resonators