  Phonons-quantized vibrational modes in crystalline structures-govern
phenomena ranging from thermal and mechanical transport to quantum mechanics.
In recent years, a new class of artificial materials called phononic crystals
has emerged, aiming to control phononic properties. These materials are created
by introducing a superlattice structure on top of an already-existing atomic
lattice. Typically, phononic crystals are described using a continuous model,
in which effective elastic constants approximate potentials between atoms. This
approximation, however, assumes the wavelengths of vibrations to be
significantly greater than the interatomic distance. In this work, we
experimentally investigate the behavior of a honeycomb silicon phononic crystal
in the gigahertz range, where the continuum approximation holds, and in the
terahertz range, where the phonon wavelengths are comparable to interatomic
distances. Using Brillouin light scattering, we investigate the phonon
dispersion of the phononic crystal in the gigahertz range, finding a close
match with simulations based on the continuous model. Conversely, Raman
spectroscopy reveals no difference between the phononic crystal, an unpatterned
membrane, and a bulk silicon structure in the terahertz range, showing that the
continuous model no longer holds at these higher frequencies.
