Assessment of phonon boundary scattering from light scattering standpoint

In the present study, we have applied the light scattering theory to investigate the phonon boundary scattering from one-dimensional rough surfaces. It has been shown that Ziman's model for the specularity is only applicable to a slightly rough surface at normal incidence. For relatively rougher Gaussian surfaces, the specularity is insufficient to properly describe the phonon scattering characteristics. Instead, the bidirectional reflectance distribution function must be fully incorporated into the analysis. We also showed that the phonon scattering from a sawtooth-like rough surface is quite different from that from a Gaussian rough surface, even though the roughness parameters are comparable. It was revealed that the multiple scattering from sawtooth-like rough surfaces can cause the confinement of phonons, which is responsible for the reduction of the thermal conductivity of rough Si nanowire below the Casimir limit.