Orientation dependence of nonlinearity and TCf in high-Q shear-modes of silicon MEMS resonators

This paper reports the first results that correlate nonlinear Duffing behavior and the temperature coefficient of frequency (TCf) in single-crystal-silicon (SCS) micromechanical resonators vibrating in lateral shear-dominant bulk modes, i.e. face shear (FS) and Lamé modes. Based on the anisotropic material property of SCS, we have derived a model to capture the nonlinear responses and the TCf for these devices in different orientations. The model predicts a clear orientation dependence of nonlinearity and temperature stability in SCS microresonators. These results suggest the possibility of reducing both nonlinearity and TCf by engineering the material properties (e.g. doping).