Temperature-insensitive nanomechanical resonators in CMOS oxides.

For nearly a century, quartz has been the material of choice for stable clock generation due to its uniquely temperature-insensitive stiffness, enabling frequency variations of only a few parts per million across wide temperature ranges. However, quartz cannot be monolithically integrated with silicon, and sub-part-per-million or parts-per-billion-class quartz modules require discrete packaging together with temperature sensing and compensation circuitry, or oven-controlled crystal oscillator implementations, adding package volume, assembly complexity, and power overhead. These limitations restrict scalability for distributed energy-efficient clocks in computing, wireless communication, and navigation under Global Positioning System-denied conditions. Here, we introduce a complementary-metal-oxide-semiconductor-compatible resonator platform that achieves a temperature-insensitive mechanical response by combining hafnium-zirconium oxide, which exhibits phase-transformation-induced anomalous elasticity, with silicon dioxide. This combination enables simultaneous compensation of the first- and second-order temperature coefficients of frequency, together with electric-field-controlled stiffness tuning for frequency stabilization and parametric effective quality factor amplification. The resulting resonators exhibit approximately 9 parts per million under passive compensation and 7 parts per billion under active compensation over a 120 °C range (-40 °C to 80 °C), offering a pathway toward monolithically integrated, thermally robust frequency references.