Exploiting nonlinear amplitude-frequency dependence for temperature compensation in silicon micromechanical resonators

Resonators used in frequency-reference oscillators must maintain a stable frequency output even when subjected to temperature variations. The traditional solution is to construct the resonator from a material with a low temperature coefficient, such as AT-cut quartz, which can achieve absolute frequency stability on the order of ±25 ppm over commercial temperature ranges. In comparison, Si microresonators suffer from the disadvantage that silicon's temperature coefficient of frequency (TCF) is approximately two orders of magnitude greater than that of AT-cut quartz. In this paper, we present an in situ passive temperature compensation scheme for Si microresonators based on nonlinear amplitude-frequency coupling which reduces the TCF to a level comparable with that of an AT-quartz resonator. The implementation of this passive technique is generic to a variety of Si microresonators and can be applied to a number of frequency control and timing applications.