Interference, scattering, and transmission of acoustic phonons in Si phononic crystals

Metamaterials are diverse synthetic materials possessing precisely constructed periodicity. Their microstructure can be manipulated to achieve superior physical properties. The artificial periodicity of these materials changes the dynamics of wave propagation in the structures, suggesting a close relationship between the wave propagation and the interaction of the materials with their mechanical, thermal, optical, light, sound, and heat properties. To this end, the characteristics of periodically structured metamaterials can be well understood when their properties are studied based on their wave dynamics: transmission, scattering, and interference.

From previous studies, artificial periodicity has been theoretically observed to lead to Brillouin-zone folding, resulting in folded acoustic phonons. This concept has been used to interpret phononic crystal properties, including sound control and heat transportation by manipulating the phonons. Specifically, Si phononic crystals with periodically arranged holes have attracted growing research attention owing to their potential application in harvesting and managing thermal energy. However, Si phononic crystals exhibit ultralow thermal conductivity, which has remained a challenge to explain. The size of acoustic metamaterials or phonic crystals typically ranges from tens of nanometers to a few microns. Such a wide range of length scales is challenging for existing atomistic methods to simulate and investigate the nature of phonon transport in the structures.

Herein, researchers at the University of Florida: Dr. Yang Li, Dr. Adrian Diaz, Professor Xiang Chen and Professor Youping Chen together with Professor David McDowell from Georgia Institute of Technology studied the processes of phonon scattering, interference, and transmission in micro-sized Si phonon crystals. A space- and time-resolved multiscale simulation tool, called Concurrent Atomistic-Continuum (CAC), was employed in this study. CAC addresses the length scale challenge for atomistic methods by reducing the degrees of freedom of an atomistic system through using the continuum description of the structure and dynamics of crystals at the lattice level, while preserving the discrete atomic structure and motion within each lattice cell. A series of CAC simulations were employed to simulate the dynamic phonon transport processes so as to establish the role of structural parameters and to understand the nature of phonon transport. Two distinct phononic structures were investigated: one was a homogenous structure with periodically arranged pores one, while the other had a single crystal heater at the center. Their work is currently published in the journal, Acta Materialia.

The research team showed that phonon transport was primarily dependent on the relation between the structural parameters of the phononic crystals (i.e., periodic length, p, and neck width, n) and phonon wavelength. The nature of the transport was described using three different regimes. First, the transportation of phonons with wavelength equal to or exceeding 2.9p was characterized by predominantly ballistic propagation. The phononic crystals behaved like homogenous and harmonic systems. The properties of these long-wavelength phonons were consistent with the phonon dispersion relations of the phononic crystal under the harmonic assumption. These phonons exhibited the highest energy transmission, contributing the most to energy flux for the Si phononic crystals.

Second, the transport of phonons with wavelength smaller than the neck size was partly diffusive due to the reflections by the pore boundaries and partly ballistic in the solid neck regions. Two vibrational modes were identified in this regime: the single-crystal Si phonon modes and those resulting from the scattering at the internal surfaces, which may be called surface-related phonons. The third regime revealed that the transport of phonons with wavelengths close to the period length was most strongly scattered and the transport was dominated by the internal surface-related phonon modes, which generally had the lowest energy transmission and slowest group velocities. Furthermore, for phononic crystals with a single crystal heater at the center, the interference between the phononic structure and the heater provided strong resistance to phonons with short wavelengths, resulting in predominantly diffusive phonon transport and an average energy flux that was two orders of magnitude lower than a same-sized single crystal specimen.

In summary, this is the first study to provide a detailed understanding of the multiscale transient processes of phonon transmission, interference and scattering in Si photonic crystals. As such, it provides more knowledge on the nature of phonon transport and how it is affected by different parameters of the phononic crystal structures. In a statement to Advances in Engineering, first author Dr. Yang Li said their findings will advance the study of the dynamics of waves in periodically structured metamaterials.