Universal Effective Medium Theory to Predict the Thermal Conductivity in Nanostructured Materials

TL;DR

This paper introduces the Ballistic Correction Model (BCM), an effective medium theory that accurately predicts thermal conductivity in nanostructured materials by incorporating mean-free-path distribution and boundary effects, validated against full BTE simulations.

Contribution

The paper presents a novel, computationally efficient model (BCM) that accounts for complex boundary effects and MFP distribution, filling gaps left by previous simplified models.

Findings

BCM shows excellent agreement with full BTE simulations.

The model effectively captures boundary and size effects on thermal conductivity.

Parameters derived can be used for various materials and geometries.

Abstract

Nanostructured materials enable high thermal transport tunability, holding promises for thermal management and heat harvesting applications. Predicting the effect that nanostructuring has on thermal conductivity requires models, such as the Boltzmann transport equation (BTE), that capture the non-diffusive transport of phonons. Although the BTE has been well validated against several key experiments, notably those on nanoporous materials, its applicability is computationally expensive. Several effective model theories have been put forward to estimate the effective thermal conductivity; however, most of them are either based on simple geometries, e.g., thin films, or simplified material descriptions such as the gray-model approximation. To fill this gap, we propose a model that takes into account the whole mean-free-path (MFP) distribution as well as the complexity of the material's boundaries in infinitely thick films with extruded porosity using uniparameter logistic regression. We validate our approach, which is called the "Ballistic Correction Model" (BCM), against full BTE simulations of a selection of three base materials (GaAs, InAs, and Si) with nanoscale porosity, obtaining excellent agreement. While the key parameters of our method, associated with the geometry of the bulk material, are obtained from the BTE, they can be decoupled and used in arbitrary combinations and scales. We tabulated these parameters for a few cases, enabling the exploration of systems that are beyond those considered in this work. Providing a simple yet accurate estimation of thermal transport in nanostructures, our work sets out to accelerate the discovery of materials for thermal-related applications.