Interfacial Phonon Scattering and Transmission Loss in >1 um Thick Silicon-on-insulator Thin Films

Scattering of phonons at boundaries of a crystal (grains, surfaces, or solid/solid interfaces) is characterized by the phonon wavelength, the angle of incidence, and the interface roughness, as historically evaluated using a specularity parameter p formulated by Ziman [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. This parameter was initially defined to determine the probability of a phonon specularly reflecting or diffusely scattering from the rough surface of a material. The validity of Ziman's theory as extended to solid/solid interfaces has not been previously validated. To better understand the interfacial scattering of phonons and to test the validity of Ziman's theory, we precisely measured the in-plane thermal conductivity of a series of Si films in silicon-on-insulator (SOI) wafers by time-domain thermoreflectance (TDTR) for a Si film thickness range of 1 - 10 {\mu}m and a temperature range of 100 - 300 K. The Si/SiO2 interface roughness was determined to be 0.11+/-0.04 nm using transmission electron microscopy (TEM). Furthermore, we compared our in-plane thermal conductivity measurements to theoretical calculations that combine first-principles phonon transport with Ziman's theory. Calculations using Ziman's specularity parameter significantly overestimate values from the TDTR measurements. We attribute this discrepancy to phonon transmission through the solid/solid interface into the substrate, which is not accounted for by Ziman's theory for surfaces. We derive a simple expression for the specularity parameter at solid/amorphous interfaces and achieve good agreement between calculations and measurement values.