Enhancement of Frequency Stability in Injection Locked Bulk Mode MEMS Oscillators

This paper reports experimental results demonstrating significant gains in frequency stability for bulk acoustic wave (BAW) silicon disk resonator oscillators due to the locking of degenerate modes. The results show that when two degenerate modes are locked, the minimum Allan deviation is improved by a factor of more than two times in comparison with the minimum Allan deviation for oscillators locked to the individual degenerate modes. A shortterm stability of 48.3 μHz (51 ppt @ 0.27 s integration time) is recorded for a MEMS oscillator with an output of ~1 MHz which benchmarks favourably relative to the MEMS oscillator state-of-the-art and commercial crystal oscillators. The approach is applicable to the locking of oscillators based on degenerate modes generally and can be scaled to higher frequency axisymmetric resonators with the higher-order bulk modes also providing inherent immunity to shock and vibration.