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

TL;DR

This study measures in-plane thermal conductivity of thick silicon films in SOI wafers to test Ziman's phonon scattering theory, finding that transmission effects at interfaces cause discrepancies with traditional models.

Contribution

The paper provides experimental validation of phonon boundary scattering models in thick silicon films and introduces a modified specularity parameter accounting for interface transmission.

Findings

Ziman's theory overestimates phonon scattering at solid/solid interfaces.

Transmission of phonons into the substrate significantly affects thermal conductivity.

A new expression for the specularity parameter at solid/amorphous interfaces improves model accuracy.

Abstract

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.