Exploring the synergic effect of thermal tuning and mode-coupling for frequency stabilization in micromechanical resonators

This work investigates the synergic effect of thermal tuning and mode-coupling on frequency stability in a dual-mode micromechanical resonator. Under dynamic input excitation, the signal in one mode induces the frequency shift of the other mode due to the self-heating and mode-coupling effects. We propose a method to stabilize frequency of the dual-mode resonator under dynamic piezoelectric excitation. The method leverages an on-chip micro-oven to thermally tune the resonator at different temperature coefficients of frequency (TCF) points, enabling the control of self-heating and mode-coupling induced resonant frequency shifts. In our experiment, the resonator is maintained at an appropriately selected TCF point, where the frequency shift caused by mode-coupling can be compensated by the self-heating effect. These findings provide valuable insights into the thermal and nonlinear dynamics of dual-mode resonators and offer a promising strategy for designing high-performance micromechanical resonators in timing and sensing applications.