Phononic crystals are artificial periodic structures engineered to manipulate mechanical vibrations, sound, and heat through phonon interference. However, the spatial and spectral limits at which phonons still sense the periodicity and experience interference remain unclear, as does the nature of their transition into an incoherent state.
In this work, we use Brillouin-Mandelstam light scattering (BMLS) and Raman spectroscopy to experimentally probe phonon dispersion relations in two-dimensional silicon phononic crystals. We measured the dispersion relations of six phononic crystals with periods ranging from 150 to 4000 nm, with 0.7 diameter-to-period ratio. Our findings reveal distinct interference regimes: at nanoscale dimensions, phonons exhibit in-plane interference consistent with elasticity theory up to at least 35 GHz. However, at larger scales and higher frequencies, phonons transition into an out-of-plane interference regime dominated by the out-of-plane phonon confinement, with the dispersion relation similar to that of plain membrane. This transition occurs approximately at the phonon wavelength twice shorter that the period of phononic crystals. Beyond these regimes, interference ceases altogether and phonon transport transitions into incoherent regime, as evidenced by the Raman spectroscopy data.
These results challenge the prevailing assumption that phonon transport transitions directly from a coherent to an incoherent state at a critical frequency or size. Instead, we identify an intermediate out-of-plane interference regime that persists up to much higher frequencies. This refined understanding of phonon transport establishes a framework for the applications of phononic crystals in quantum computing, sensing, and microelectronics.
Acknowledgments:
This work has been partially funded by the CNRS Energy unit (Cellule Energie) through the project SEGMENT.