Coherent phononic frequency combs in ferroelectric CMOS oxides

Abstract

Modern electronic systems require tens of clock and carrier frequencies, each synthesized by a dedicated phase-locked loop from a shared reference, imposing routing, power and synchronization burdens that grow with every domain. Optical frequency combs solved this problem in photonics, whereas electronics has lacked an equivalent source in its native radiofrequency domain. Here we report broadband phononic frequency combs in ferroelectric hafnia-zirconia nanoelectromechanical resonators built from complementary metal-oxide-semiconductor (CMOS) oxides. Lithographically defined detuning of a 2:1 internal resonance selects the generation mechanism: two-tone-seeded wave mixing yields more than 170 lines distributed over two octaves, with mutual coherence verified for representative pump and generated lines, whereas an autonomous Hopf route yields hierarchical combs of more than 200 lines through torus and period-doubling dynamics, in agreement with slow-flow bifurcation theory. Geometric scaling extends comb generation across 0.44 GHz to 2.1 GHz. Heterodyne measurements, analyzed using the modified Allan deviation (MDEV), establish a two-timescale law. The mechanism governs short-term stability: seeded combs inherit the white-phase-noise scaling of their pumps, whereas autonomous combs acquire the phase diffusion of a free-running oscillator, with the one-second MDEV increasing from 1e-11 to 1e-8. The material governs long-term stability: in air and without active thermal control, the temperature-compensated stack suppresses the random-walk drift that dominates uncompensated resonators. These results establish mechanism- and material-level design rules for operating a single resonator as chip-scale frequency infrastructure, from multi-clock generation to radiofrequency parallel processing.