Ballistic transport of long wavelength phonons and thermal conductivity accumulation in nanograined silicon-germanium alloys

TL;DR

This paper introduces a frequency-dependent effective medium model to accurately predict thermal conductivity in nanostructured silicon-germanium alloys, revealing that long wavelength phonons are less affected by grain boundaries than previously thought.

Contribution

The work presents a novel modeling approach that accounts for long wavelength phonons, challenging traditional assumptions about grain boundary scattering effects in nanostructured materials.

Findings

Long wavelength phonons are less impacted by grain boundaries.

The model accurately predicts thermal conductivity reduction in nanostructured SiGe.

Experimental TDR measurements support the model's predictions.

Abstract

Computationally efficient modeling of the thermal conductivity of materials is crucial to thorough experimental planning and theoretical understanding of thermal properties. We present a modeling approach in this work that utilizes frequency-dependent effective medium to calculate lattice thermal conductivity of nanostructured solids. The method accurately predicts a significant reduction in the thermal conductivity of nanostructured Si80Ge20 systems, along with previous reported thermal conductivities in nanowires and nanoparticles-in-matrix materials. We use our model to gain insight into the role of long wavelength phonons on the thermal conductivity of nanograined silicon-germanium alloys. Through thermal conductivity accumulation calculations with our modified effective medium model, we show that phonons with wavelengths much greater than the average grain size will not be impacted by grain boundary scattering, counter to the traditionally assumed notion that grain boundaries in solids will act as diffusive interfaces that will limit long wavelength phonon transport. This is further supported through a modulation frequency dependent thermal conductivity as measured with time-domain thermoreflectance.