Pore-size dependence of the thermal conductivity of porous silicon: A phonon hydrodynamic approach

Álvarez, F. X.; Jou, David; Sellitto, A.

doi:10.1063/1.3462936

Cited by 127 publications

(107 citation statements)

References 37 publications

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“…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.…”

Section: Results and Comparison With Other Modelsmentioning

confidence: 99%

“…A more sophisticated formalism, was developed by Alvarez et al [8] and also used by Criado-Sancho et al [3,4]. It is based on a phonon hydrodynamic version of Stokes resistance force exerted on a sphere in an infinite medium.…”

Section: Results and Comparison With Other Modelsmentioning

confidence: 99%

“…2(b), but instead of the hydrodynamic model, we compare with the Lysenko model. [1,7] and, in dashed lines, the hydrodynamic model [8] (Fig. 2a) and the Lysenko model [23] (Fig.…”

Section: Results and Comparison With Other Modelsmentioning

confidence: 99%

“…The role of porosity and size of the nanopores has been examined. The model has been validated against experimental data and compared to other theoretical models, being those of Stokes [8] and Eucken [6], two models presented recently by Lysenko et al [23] and Sumirat et al [24] and finally the simplified percolation model. It is shown that our model fits better the experimental values than the other models.…”

Section: Discussionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Machrafi

Lebon

2015

Physics Letters A

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Abstract.A formula for the effective thermal conductivity of nanoporous media is derived, following a thermodynamic approach. An extension to nanocomposites composed of a homogeneous matrix wherein porous nanoparticles are dispersed is proposed as well. The originality of the model is that it is based on extended irreversible thermodynamics, a theory specifically designed for sub-scaled systems. Two different situations are discussed, in the first one, nanoporous silicon with spherical porous inclusions of micro, meso and macro-dimension respectively is considered. The description is validated by comparison with experimental data and five other models. Analysis of the results shows an excellent agreement of our theoretical approach with experiments in the whole range of porous radii, from 2 to 100 nm. In the second part of the work, thermal conductivity of porous silicon nanoparticles embedded in a germanium host matrix is investigated. The coupled influence of the pore and nanoparticles sizes is emphasized.Keywords: nanoporous media, thermal conductivity, phonon scattering, extended thermodynamics IntroductionThe effect of porosity is to decrease considerably the thermal conductivity of crystalline materials, as is observed, for instance, in nanoporous silicon [1][2][3][4][5]. This lowering property has been widely exploited with the objective to reinforce thermal insulation in several systems as microsensors, integrated circuits, semiconductor devices. 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. To be explicit, we will base our study on extended irreversible thermodynamics (EIT) [9,10], which is a formalism specifically dedicated to the treatment of micro and nano systems and highfrequency processes. For the sake of completeness, the present analysis will be compared to other theoretical models and experimental data.Nanoporous materials are generally made out of a homogeneous matrix wherein nanopores are dispersed. In that respect, such systems are similar to nanocomposites, wherein nanoparticles are embedded in a matrix, the difference being that nanoparticles are replaced by nanopores. A great deal of papers have been devoted to the problem of heat transport in nanofluids and nanocomposites, see for instance the review paper by Michaeledis [11]. In particular, the problem of the overall heat conductivity of the system as a function of the volume fraction of the nanoparticles and their size has drawn much attention. Our purpose in the present work is twofold. Firstly, it is the purpose to study the role of porosity and the size of the pores on the heat conductivity of porous systems, like nanoporous silicon, via our thermodynamic formalism. Secondly, we examine, using t...

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Section: Results and Comparison With Other Modelsmentioning

confidence: 99%

Section: Results and Comparison With Other Modelsmentioning

confidence: 99%

“…2(b), but instead of the hydrodynamic model, we compare with the Lysenko model. [1,7] and, in dashed lines, the hydrodynamic model [8] (Fig. 2a) and the Lysenko model [23] (Fig.…”

Section: Results and Comparison With Other Modelsmentioning

confidence: 99%