Effect of thermomechanical stress on resonant frequency shift of a silicon MEMS resonator

In this study, finite element modelling (FEM) is used to estimate the stresses induced by the package on a high precision silicon resonator. A link between the induced stresses and strains at different temperatures and the shift in the resonance frequency is presented. In order to accentuate the effects of the package on the resonance frequency of the resonators a double clamped beam vibrating in a flexural mode was designed. The resonance frequency can be shifted dramatically by the mechanical stress induced by the package; however, those stresses can be used to compensate the shift in resonance frequency due to the intrinsic temperature dependence of silicon. In order to prove the package design, a full 3D FEM of a O-level package containing a square Lame mode resonator is studied. Modelling results show that this resonator and package design is almost insensitive to the package deformation.