Prediction of thermal conductivity in dielectrics using fast, spectrally-resolved phonon transport simulations

Abstract

We present a new method for predicting effective thermal conductivity (κ eff ) in materials, informed by ab initio material property simulations. Using the Boltzmann transport equation in a Self-Adjoint Angular Flux formulation, we performed simulations in silicon at room temperatures over length scales varying from 10 nm to 10 µm and report temperature distributions, spectral heat flux and thermal conductivity. Our implementation utilizes a Richardson iteration on a modified version of the phonon scattering source. In this method, a closure term is introduced to the transport equation which acts as a redistribution kernel for the total energy bath of the system. This term is an effective indicator of the degree of disorder between the spectral phonon radiance and the angular phonon intensity of the transport system. We employ polarization, density of states and full dispersion spectra to resolve thermal conductivity with numerous angular and spatial discretizations.

Heat current anticorrelation effects leading to thermal conductivity reduction in nanoporous Si

“…Thermal transport in nanostructured geometries requires an understanding beyond what is achievable at a continuum level, and yet simulation domains larger than can be accommodated by first principles approaches. Methodologies available to study nanoporous morphologies are thus limited to classical molecular dynamics (MD) [24][25][26][27], or semi-classical approaches involving the numerical solution of the Boltzmann transport equation (BTE) [28][29][30][31][32], and, to some extent, lattice dynamics [24,33,34]. In this work, we use a combination of both equilibrium molecular dynamics (EMD) and wave packet simulations to evaluate thermal transport in Si nanoporous structures.…”

Mitigating the Effect of Nanoscale Porosity on Thermoelectric Power Factor of Si

“…In spite of the poor thermoelectric efficiency of bulk silicon due to its high thermal conductivity, it provides an excellent platform for studying the role of design parameters on transport properties, since its bulk properties are extremely well characterized. 9,10,11 We have validated the transport model against a set of phosphorous-doped Si based thermoelectrics. 12 The terms 𝐷(𝐸), and 𝜈(𝐸), in function 𝜒 for Si were derived from the conduction band of Si computed with density functional theory (DFT).…”

“…In spite of the poor TE efficiency of bulk silicon due to its high thermal conductivity, it provides an excellent platform for studying the role of design parameters on transport properties since its bulk properties are extremely well characterized. 22,25,26 Introducing pores into Si will not change the concentration of carrier concentration locally in the remaining Si (nor the Fermi energy), but it will change the volume averaged carrier concentration due to the reduction in the volume averaged density of states. This will impact the conductivity, and thus, the effective electrical conductivity of porous materials is modeled as σ eff = (1 − φ)σ np .…”

Enhanced Thermoelectric Performance of Polycrystalline Si0.8Ge0.2 Alloys through the Addition of Nanoscale Porosity

“…The effective lattice thermal conductivity, , of polycrystalline Si 0.8 Ge 0.2 containing nanoscale pores was computed by solving the frequency-dependent Boltzmann transport equation [ 28 ] to find the steady-state distribution of phonons moving between an array of pores under an imposed temperature gradient. The effective thermal conductivity of the material containing a given pore morphology is defined as the ratio of the heat flux carried by the phonon distribution divided by the imposed temperature gradient.…”