Frequency Stabilization of Nanomechanical Resonators Using Thermally Invariant Strain Engineering

Microfabricated mechanical resonators enable precision measurement techniques from atomic force microscopy to emerging quantum applications. The resonance frequency-based physical sensing combines high precision with long-term stability. However, widely used Si₃N₄ resonators suffer from frequency sensitivity to temperature due to the differential thermal expansion vs the Si substrates. Here we experimentally demonstrate temperature- and residual stress-insensitive 16.51 MHz tuning fork nanobeam resonators with nonlinear clamps defining the stress and frequency by design, achieving a low fractional frequency sensitivity of (2.5 ± 0.8) × 10^-6 K^-1, a 72× reduction. On-chip optical readout of resonator thermomechanical fluctuations allows precision frequency measurement without any external excitation at the thermodynamically limited frequency Allan deviation of ≈7 Hz/Hz^1/2 and (relative) bias stability of ≈10 Hz (≈ 0.6 × 10^-6) above 1 s averaging, remarkably, on par with state-of-the-art driven devices of similar mass. Both the resonator stabilization and the passive frequency readout can benefit a wide variety of micromechanical sensors.