Importance of frequency-dependent grain boundary scattering in nanocrystalline silicon and silicon-germanium thermoelectrics

TL;DR

This paper investigates how frequency-dependent phonon scattering at grain boundaries affects thermal conductivity in nanocrystalline silicon and silicon-germanium, revealing that low-frequency phonons can carry significant heat, which impacts thermoelectric efficiency.

Contribution

It introduces a realistic 3D simulation approach to study frequency-dependent grain boundary scattering, challenging the assumptions of the gray model and providing new insights for thermoelectric material design.

Findings

Low frequency phonons are less scattered by grain boundaries.

Significant heat is carried by phonons with long mean free paths.

Frequency dependence influences the effectiveness of grain boundary scattering.

Abstract

Nanocrystalline silicon and silicon-germanium alloys are promising thermoelectric materials that have achieved substantially improved figure of merits compared to their bulk counterparts. This enhancement is typically attributed to a reduction in lattice thermal conductivity by phonon scattering at grain boundaries. However, further improvements are difficult to achieve because grain boundary scattering is poorly understood, with recent experimental observations suggesting that the phonon transmissivity may depend on phonon frequency rather than being constant as in the commonly used gray model. Here, we examine the impact of frequency-dependent grain boundary scattering in nanocrystalline silicon and silicon-germanium alloys in a realistic 3D geometry using frequency-dependent variance-reduced Monte Carlo simulations. We find that the grain boundary may not be as effective as predicted by the gray model in scattering certain phonons, with a substantial amount of heat being carried by low frequency phonons with mean free paths longer than the grain size. Our result will help guide the design of more efficient thermoelectrics.