Thermal characterization of nanoscale phononic crystals using supercell lattice dynamics

Abstract

The concept of a phononic crystal can in principle be realized at the nanoscale whenever the conditions for coherent phonon transport exist. Under such conditions, the dispersion characteristics of both the constitutive material lattice (defined by a primitive cell) and the phononic crystal lattice (defined by a supercell) contribute to the value of the thermal conductivity. It is therefore necessary in this emerging class of phononic materials to treat the lattice dynamics at both periodicity levels. Here we demonstrate the utility of using supercell lattice dynamics to investigate the thermal transport behavior of three-dimensional nanoscale phononic crystals formed from silicon and cubic voids of vacuum. The periodicity of the voids follows a simple cubic arrangement with a lattice constant that is around an order of magnitude larger than that of the bulk crystalline silicon primitive cell. We consider an atomic-scale supercell which incorporates all the details of the silicon atomic locations and the void geometry. For this supercell, we compute the phonon band structure and subsequently predict the thermal conductivity following the Callaway-Holland model. Our findings dictate that for an analysis based on supercell lattice dynamics to be representative of the properties of the underlying lattice model, a minimum supercell size is needed along with a minimum wave vector sampling resolution. Below these minimum values, a thermal conductivity prediction of a bulk material based on a supercell will not adequately recover the value obtained based on a primitive cell. Furthermore, our results show that for the relatively small voids and void spacings we consider (where boundary scattering is dominant), dispersion at the phononic crystal unit cell level plays a noticeable role in determining the thermal conductivity

Phonon Scattering in One-Dimensional Anharmonic Crystals and Superlattices: Analytical and Numerical Study

“…They have shown a decrease of thermal conductivity by several orders of magnitude due to the periodic structure of the system. Davis and Hussein [15] have considered three-dimensional nanoscale phononic crystals formed from silicon and cubic voids of vacuum. The voids are arranged on a simple cubic lattice with a lattice constant an order of magnitude larger than that of the bulk crystalline silicon primitive cell.…”

Angular Band Gaps in Sonic Crystals: Evanescent Waves and Spatial Complex Dispersion Relation

“…Then, both the propagating (real part of the complex relation dispersion) and the evanescent (imaginary part) properties of these systems are necessary to explain the control of the diffraction and the diffusion of acoustic waves with periodic structures. Finally, the properties of these systems are independent of the spatial scale of the structure, and as a consequence the control of phonons by means of periodic systems could be a promising area [54][55][56][57]. Therefore, in principle all phenomena could be observed in micro-or nano-scale phononic (so called hypersonic [58]) crystals, and evanescent waves can play an important role.…”

Thermal Conductivity Reduction in a Nanophononic Metamaterial versus a Nanophononic Crystal: A Review and Comparative Analysis

“…Downsizing a phononic crystal to the nanoscale brings rise to the notion of a nanophononic crystal. NPCs were first studied in the context of 1D layered materials, also known as superlattices, but quickly were generalized to materials with 2D and 3D periodicities …”

“…The in‐plane thermal conductivity of this system is also obtained by Equation keeping in consideration that the phonon dispersion now is that of an NPC unit cell such as the one depicted in Figure b, and V is the volume of the NPC unit cell. While the interest in macroscopic phononic crystals is dominated by the presence of bandgaps, at the nanoscale (when a 3D crystal structure is modeled atomistically), a complete bandgap is unlikely to form . This, however, is not a deterrent because the focus is primarily in the flattening of the dispersion curves.…”