Crystallographic effects in modeling fundamental behavior of MEMS silicon resonators

This paper presents the effects of silicon crystal properties on fundamental behavior of MEMS resonators. MEMS resonators are commonly built from single crystal silicon with proven long-term stability. Frequency and quality factor (Q) of silicon resonators, however, depend on the silicon crystal orientation and its interplay with the resonance mode. It is experimentally shown that Q of resonators can vary up to 25% with change in crystal orientation. Anisotropy also causes a split in frequencies of degenerate mode pairs of disk resonators, splitting also occurs in nominally isotropic polysilicon devices where theoretically not expected. In this paper, we model resonators based on crystallographic properties to predict and explain these experimental results. Tuning forks quality factor dependence on orientation in (100) and (111) wafers as well as frequency splitting of disk resonators is examined. Incorporating appropriate silicon crystal elasticity into finite-element modeling and accounting for geometric implications of these resonators we demonstrate that the frequency splitting and quality factor of those devices can be accurately predicted.