Ultra-wideband phononic frequency combs in AlScN-on-Si via Duffing-enhanced four-wave mixing

Abstract

This work reports the generation of an ultra-wideband phononic frequency comb in aluminum scandium nitride (AlScN)-on-silicon resonators by single-tone excitation. The generated comb spans a bandwidth from 100 kHz to 1 MHz, exhibiting a normalized spectral width of 1.4 and comprising over 1000 discrete, equally spaced comb lines. Comb formation is enabled by nonlinear intermodal coupling, including combination resonance and a 2:1 internal resonance among an out-of-plane width flexural mode, torsional mode, and length flexural modes. These interactions give rise to multiple comb sets that are qualitatively captured by a three-mode Fermi–Pasta–Ulam model. Under appropriate frequency-detuning conditions, additional modes become involved, and the system subsequently transitions into a strongly nonlinear multimode regime, in which the combs merge into a dense, ultra-wideband spectrum. We attribute this transition to the combined effects of geometric nonlinearity and the intrinsic elastic nonlinearity of heavily doped silicon, which enhance the effective Duffing-type response and facilitate the emergence of slow-timescale dynamics. Digital holographic microscopy is employed to visualize the nonlinear mode evolution, revealing the participation of coupled flexural and torsional motion. This compact, single-tone-driven mechanism provides a potential pathway toward dense mechanical frequency grids for multi-channel sensing, spectral synthesis, and compact frequency referencing.