Phonon dispersion of nanoscale honeycomb phononic crystal: gigahertz and terahertz spectroscopy comparison

TL;DR

This study compares phonon dispersion in nanoscale honeycomb phononic crystals using gigahertz and terahertz spectroscopy, revealing the limits of the continuous model at high frequencies where atomic-scale effects dominate.

Contribution

It experimentally demonstrates the breakdown of the continuum approximation in phononic crystals at terahertz frequencies, highlighting the need for atomic-scale modeling.

Findings

Gigahertz phonon dispersion matches continuous model simulations.

Terahertz measurements show no phononic crystal effects, indicating model failure.

Continuum approximation is valid only at lower frequencies.

Abstract

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.