Frequency stabilization of nanomechanical resonators using thermally invariant strain engineering
Mingkang Wang, Rui Zhang, Bojan R. Ilic, Vladimir A. Aksyuk, Yuxiang Liu
Microfabricated mechanical resonators enable precision measurement and transduction techniques from atomic force microscopy and inertial sensing to magnetometry and emerging quantum applications. Coupling the resonator frequency to specific physical processes permits their low-noise detection with high long-term stability. Although doubly-clamped tensile Si3N4 resonator structures are broadly used, their stress and frequency are temperature sensitive due to differential thermal expansion relative to the Si substrates, necessitating temperature control or differential sensing. Here we experimentally demonstrate temperature and residual stress insensitive tuning fork nanobeam resonators with nonlinear compensating clamps, which determine the tuning fork stress and frequency by the design. The temperature sensitivity of a 16.51 MHz mode is reduced by 72 times, achieving a fractional frequency sensitivity of (2.5 ± 0.8)x10-6 K-1. Remarkably, the resonator thermal motion without excitation, measured via an integrated cavity optomechanical readout, shows a frequency Allan deviation at the thermodynamic limit of ≈ 7 Hz/Hz0.5 below 0.1 s and (relative) bias stability of ≈ 10 Hz (≈ 0.60×10-6) above 1 s averaging. The nonlinear clamp and the resonator are fabricated simultaneously form the same film, making the stabilization approach readily accessible and broadly appealing. The resonator stabilization scheme and the passive frequency readout technique can benefit a wide variety of micromechanical sensors.