  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.

Mesoscale and Nanoscale Physics