Coherent Acoustic Phonons in Supported and Suspended MoS ₂ Nanocavities

Nanoacoustic cavities made with van der Waals materials offer unique opportunities for optomechanics, quantum information, and nanoscale sensing. Here, we present a comprehensive study of coherent acoustic phonons in mechanically exfoliated MoS 2 nanocavities under both supported and suspended configurations, covering an unprecedented frequency range from 5 to 300 GHz. We show that, as the flake thickness increases from 10 to 500 nm, the vibrational spectrum extends beyond the fundamental breathing mode to include higher harmonics up to N = 7, low-frequency Lamb waves, and an out-of-plane propagating acoustic mode that yields Brillouin oscillations. A detailed analysis of dissipation mechanisms reveals that, at intermediate frequencies, radiative energy leakage into the substrate reduces lifetimes of supported flakes by up to an order of magnitude. Suspended flakes, instead, are limited by surface roughness at high frequencies and Lamb wave conversion at low frequencies. Strikingly, the higher harmonics in supported flakes achieve lifetimes that approach those of suspended samples, enabling efficient energy transmission without the need for substrate decoupling. We further analyze the frequency–thickness relationship, which is accurately described by a spring-model treatment of imperfect interfaces that accounts for surface roughness. Altogether, these findings provide a unified understanding of coherent acoustic phonon dynamics in MoS 2, and suggest that substrate decoupling, surface engineering, and harmonic mode utilization are promising strategies for enhancing quality factors in optomechanical and quantum nanodevices.