Monte Carlo simulations of phonon transport in nanoporous silicon and germanium

Abstract

International audienceHeat conduction of nanoporous silicon and germanium thin films is studied thanks to a statistical approach. Resolution of phonon Boltzmann transport equation is performed with a Monte Carlo technique in order to assess thermal conductivity. Sensitivity of this latter property with respect to parameters such as phonon mean free path and characteristics of the pores ( distribution, size, porosity) is discussed and compared to predictions from analytical models. Results point out that thermal properties might be tailored through the design of the porosity and more specifically by the adjustment of the phonon-pore mean free path. Finally, an effective medium technique is used to extend our work to multilayered crystalline-nanoporous structures. Results show that ought to pore scattering, a diffusive Fourier regime can be recovered even when the film thickness is below the bulk limit

Size and porosity effects on thermal conductivity of nanoporous material with an extension to nanoporous particles embedded in a host matrix

“…3 and 4 depict the dependence of the effective thermal conductivities of the nano composite p-Si/Ge versus the volume fraction of the p-Si particles for several porosities , pore radii and particle radii . Note that = 0 corresponds to bulk silicon nanoparticles embedded in germanium as studied in [12], whereas = 1 describes nanoporous Ge samples [6]. than 0.1 is necessary to reach the same result, though the thermal conductivity still remains rather insensitive to the porosity.…”

“…The validity of our approach will be checked by comparing our results with experimental data and five different models [6,8,23,24] briefly described below. The comparison with the aforementioned models will also allow better understanding the underlying difficulties in modeling thermal conductivity of nano-porous materials.…”

“…The comparison with the aforementioned models will also allow better understanding the underlying difficulties in modeling thermal conductivity of nano-porous materials. The first model, referred to as Eucken's formula (e.g [6]), is a simplification of expression (1) wherein is replaced by the bulk value , whereas is neglected:…”

“…3 with Λ , designating the mean free path in the bulk and Λ , the supplementary contribution due to the interactions at the nanopore-medium interface [6,17] given by…”

“…It has therefore fostered an increasing interest during the last decade. Thermal properties of nanoporous media are generally investigated by referring to, for instance, kinetic theory of phonons [3], molecular simulations [5], Monte Carlo simulations [6], two-component materials [7] or hydrodynamic models [8]. In this work, we take a different route and prefer a thermodynamic approach.…”