Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit

Abstract

Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the small perturbation approach. In the limiting case of a large correlation length L compared with the acoustic wavelength, the The results indicate that thermal transport models using Ziman's formula are likely to overestimate the heat flux dissipation due to boundary scattering, whereas modeling interface roughness as atomic disorder is likely to underestimate scattering.

Rayleigh waves, surface disorder, and phonon localization in nanostructures

“…into longitudinal and transverse waves; there is no conversion from bulk into Rayleigh waves at a smooth surface [6,[11][12][13]15]. Wei et al [81] obtained similar results based on a molecular-dynamics simulation of mode conversion between bulk modes at smooth graphene surfaces.…”

“…Indeed, Ziman adapted the concept of a specularity parameter from electromagnetic waves, which do not undergo meaningful mode conversion [19]. Our results underscore the importance of the ongoing work to extend the specularity parameter model to account for mode conversion [112] and Rayleigh waves [11]. However, even with improvements, the specularity parameter concept only makes sense in the limit of weak roughness; all specularity parameter models have a "Casimir limit" when the specularity parameter is zero and all scattering is diffuse [3], yet in many three-dimensional nanostructures thermal conductivities far below that limit have been measured [1,2,113].…”

“…1) are a simple type of surface mode that occur only at free surfaces [5][6][7][8][9] and provide a good starting point for understanding surface modes in general. It has long been known that bulk waves (longitudinal and transverse) can be converted to Rayleigh waves at rough [10,11] or otherwise disordered [12][13][14] surfaces, but not at smooth ones [6,15]. So, early work on Rayleigh wave scattering focused on their decay into bulk waves in the presence of disorder [10,12,13,16,17], but did not address phonon transport.…”

“…Nakayama [14] identified Rayleigh-to-bulk mode conversion as a cause of diffuse phonon-surface scattering, which is important to many phonon transport models [18][19][20]. Maznev [11] investigated elastic wave scattering from a nearly smooth surface using a Green's-function technique and found that most energy from a normally incident longitudinal wave can be converted into Rayleigh waves, but conversion at other angles was not addressed. Kang and Estreicher [21] used molecular dynamics (MD) simulation to show that mode conversion between bulk modes and surface modes can lead to "phonon trapping," which can greatly reduce thermal conductivity.…”

“…Elastic materials are a simpler, long-wave-length limit of atomic materials [7,23], and elastic materials support longitudinal acoustic, transverse acoustic, Rayleigh [6][7][8][9], and structure-dependent modes (such as torsional modes for a wire [24]). The study of elastic continuum materials can provide important insights into phonon-surface scattering in atomic materials [7,11,[25][26][27][28], especially in nanostructures that are too large to treat directly using atomistic techniques, yet too small to be considered bulk [4,[29][30][31].…”