Very High Frequency Stability of Single-Crystal Silicon Thermal-Piezoresistive Resonators with Phase-Locked Loop

This paper reports on a single-crystal silicon (Si) thermal-piezoresistive resonator (TPR) achieving very high frequency stability in phase-locked loop (PLL) measurements. A pair of resonators operating in a balanced-bridge configuration is presented, with one device being driven at resonance and the other used to null the background response. The resonance frequency of the single TPR is collected over 40 hours with closed-loop tracking by PLL and yields Allan deviation σ
A
≈ 2.66ppb for an averaging time τ ≈ 4.95 seconds, which is the lowest reported value among all Si TPRs studied to date. This result is significant as it suggests that such TPRs can potentially achieve frequency stabilities comparable to, or better than, existing state-of-the-art resonators used in oscillator circuits, with significantly reduced external thermal control requirements and power demands.