We demonstrate feedback and harmonic locking of chip-scale slot-type optomechanical oscillators to external low-noise reference clocks, with suppressed timing jitter by three orders of magnitude. The feedback and compensation techniques significantly reduce the close-to-carrier phase noise, especially within the locking bandwidth for the integral root-mean-square timing jitter. Harmonic locking via high-order carrier signals is also demonstrated with similar phase noise and integrated root-mean-square timing jitter reduction. The chip-scale optomechanical oscillators are tunable over an 80-kHz range by tracking the reference clock, with potential applications in tunable radio-frequency photonics platforms.

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