Piezoelectrically Transduced Temperature-Compensated Flexural-Mode Silicon Resonators

In this paper, we explore the piezoelectric transduction of in-plane flexural-mode silicon resonators with a center frequency in the range of 1.3–1.6 MHz. A novel technique utilizing oxide-refilled trenches is implemented to achieve efficient temperature compensation. These trenches are encapsulated within the silicon resonator body so as to protect them during the device release process. By using this method, we demonstrate a high- $Q (>19,000)$ resonator having a low temperature coefficient of frequency of $< 2 \hbox {p\pm}/^{\circ}\hbox {C}$ and a turnover temperature of around 90 $^{\circ}\hbox {C}$ , ideally suited for use in an ovenized platform. Using electrostatic tuning, the temperature sensitivity of the resonator is compensated across a temperature range of $+50 ^{\circ}\hbox {C}$ to $+85 ^{\circ}\hbox {C}$ , demonstrating a frequency instability of less than 1 ppm. Using proportional feedback control on the applied electrostatic potential, the resonator frequency drift is reduced to less than 110 ppb during 1 h of continuous operation, indicating the ultimate stability that can be achieved for the resonator as a timing reference. The resonators show no visible distortion up to $-$ 1 dBm of input power, indicating their power handling capability. $\hfill$ [2012-0261]