Heat pulse experiments revisited

Dreyer, Wolfgang; Struchtrup, Henning

doi:10.1007/bf01135371

Cited by 311 publications

(266 citation statements)

References 35 publications

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“…The above choice involves the minimal number of moments necessary for describing the thermal energy transport, but this number, if required by the physical problem under study, can be easily extended to cover, for example, an arbitrary number of scalar and vector moments both for carriers and phonons, by taking into account, e.g., higher microscopic energy powers in the functions ψ [7,26].…”

Section: The 3d Semiclassical Macroscopic Modelsmentioning

confidence: 99%

“…However, these various closure assumptions are, at best, only phenomenological and often a consistent physical and mathematical justification is lacking. Lately, a closure assumption based on the Maximum Entropy Principle of extended thermodynamics [6,7] has been successfully applied, both in the parabolic and non-parabolic band approximation, to various types of semiconductors [8][9][10][11][12][13]. The resulting models, which differ for the choice of the moments to assume as field variables, are, in fact, able to describe charge transport due both to electrons and holes and also heat transport due to phonons.…”

Section: Introductionmentioning

confidence: 99%

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Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Mascali

Romano

2017

Entropy

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Abstract:In the last two decades, the Maximum Entropy Principle (MEP) has been successfully employed to construct macroscopic models able to describe the charge and heat transport in semiconductor devices. These models are obtained, starting from the Boltzmann transport equations, for the charge and the phonon distribution functions, by taking-as macroscopic variables-suitable moments of the distributions and exploiting MEP in order to close the evolution equations for the chosen moments. Important results have also been obtained for the description of charge transport in devices made both of elemental and compound semiconductors, in cases where charge confinement is present and the carrier flow is two-or one-dimensional.

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Section: The 3d Semiclassical Macroscopic Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Mascali

Romano

2017

Entropy

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“…where is the wavenumber vector and the mean free path associated with the heat flux of order n. We now select the latter as given path ln of order n in terms of n as = ( + 1) /(4( + 1) − 1), with l identified as the mean free path independent of the order of approximation, this being a natural choice in phonon's kinetic theory [18]. By identifying k (which becomes a scalar in our one-dimensional case) as = 2 / and using the definition (9) of the Knudsen number in expression (10) has the asymptotic limit [19] …”

Section: Heat Conductivity Of Nano-porous Si Devicesmentioning

confidence: 99%

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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“…This represents a nonlinear evolution equation for the heat flux which allows to consider in a simple way some nonlocal, nonlinear and memory effects, beside to study the propagation of heat waves, which is a well-known topic in current nonequilibrium thermodynamics [22,30,[46][47][48].…”

Section: Higher-order Fluxes and Hierarchy Of Nonlinear Transport Equmentioning

confidence: 99%

Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

Jou¹,

Cimmelli

2016

Communications in Applied and Industrial Mathematics

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Heat pulse experiments revisited

Cited by 311 publications

References 35 publications

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

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

Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

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