Turnover Temperature Point Adjustment in Mechanically Coupled Single-Crystal Silicon MEMS Resonators

This paper presents an effective approach for adjusting the zero temperature coefficient of frequency (turnover point) in mechanically coupled single-crystal silicon (SCS) microelectromechanical system (MEMS) resonators. The mechanically coupled MEMS resonators are fabricated on a heavily n-type doped SCS with a phosphorus doping concentration of around $1.0\times 10^{20}$ cm $^ - 3 $ for achieving high turnover points. A turnover point tuning prediction model is derived, showing that the turnover point of mechanically coupled resonators can be represented as the weighted average sum of the product of the effective mass and the second order TCF of each individual resonator, along with its corresponding turnover point. By leveraging mechanical coupling between breathing-ring (BR) mode resonators and length-extensional (LE) or width-extensional (WE) mode resonators, the turnover point of mechanically coupled resonator can be purposely manipulated to above industrial temperature ranges by adjusting the dimensions of the coupled components. Such turnover temperatures can be employed in micro-oven-controlled MEMS oscillators (OCMOs) to achieve excellent frequency stability. The results offer valuable insights into optimizing the frequency-temperature characteristic of MEMS resonators in high-end timing field.[2024-0184]