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

Abstract

The transient processes of phonon scattering and transmission in Si phononic crystals with periodic pores are simulated using the concurrent atomistic-continuum method. The nature of phonon transport is demonstrated to be dependent on the relation between the phonon wavelength, λ, the period length, p, and the neck width, n, of the phononic crystal. Three distinct regimes have been observed: (1) phonons with wavelengths equal to 2.9p or larger propagate predominantly ballistically, which is accompanied by specular reflection of varying extents, depending on the wavelength of the phonons; the properties of these phonons are consistent with the phonon dispersion relations of the phononic crystal modelled as a homogenous and harmonic system; (2) phonons with wavelengths < n are partly reflected by the pore boundaries and partly propagate ballistically in the solid regions of the necks; two types of vibrational modes are identified: the single crystal Si phonon modes, and the vibrational modes resulting from internal surface scattering; (3) phonons with wavelength close to p are most strongly scattered, and the internal surface-related modes dominate the transport; these modes have the slowest group velocities and lowest energy transmission, and the transport is predominantly diffusive even for specimens originally at zero temperature. For phononic crystals that contain a single crystal heater at their center, the interface between the single crystal heater and the phononic structure provides a strong resistance to short wavelength phonons, leading to predominantly diffusive phonon transport and an average energy flux that is two orders of magnitude lower than a same-sized single crystal specimen.