FEM simulation: Thermal properties of thin film quartz and silicon resonators

This semester project aimed at simulating two approaches for low temperature dependence of resonance frequency of resonators. The first one consists in using AT-cut quartz as the resonator’s material. The AT-cut quartz wafers are made using a 35° angle with respect to the z-axis and they show very low resonance frequency shift in the temperature range [-40, 100]°C for thickness shear modes. The second approach is based on adding a Lithium Niobate thin film on top of a silicon resonator to compensate for the resonance frequency shift (due to temperature) of the later. Initially, the change of material properties due to temperature were investigated through literature review and simulations on Matlab. Once those properties were defined, more detailed simulations were carried out using COMSOL Multiphysics. The minimum resonance frequency shift achieved for 0.35.82 (ZXZ Euler angles) rotated quartz was 0.36ppm/°C. A frequency shift of 2.7ppm/°C was obtained for a 2μm thick silicon resonator coated with 0.5μm thick, 0.38.90 rotated (ZXZ Euler angles) Lithium Niobate.