First principles kinetic-collective thermal conductivity of semiconductors

Torres, Pol; Torelló, Àlvar; Bafaluy, J.; Camacho, J.; Cartoixà, Xavier; Álvarez, F. X.

doi:10.1103/physrevb.95.165407

Cited by 60 publications

(82 citation statements)

References 57 publications

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“…To further interpret this transition from ballistic to normal behavior, a recent proposed kinetic-collective model [16] based on different phonon-phonon scattering physics might be worthwhile, from which a wide range of temperature-and size-dependent thermal conductivity can be predicted quite well [16][17][18]. However, obviously such a theoretical model does not involve the effects of other nonlinear excitations, such as solitons [19] and discrete breathers (DBs) [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Crossover from ballistic to normal heat transport in theϕ4lattice: If nonconservation of momentum is the reason, what is the mechanism?

2017

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Anomalous (non-Fourier's) heat transport is no longer just a theoretical issue since it has been observed experimentally in a number of low-dimensional nanomaterials, such as SiGe nanowires, carbon nanotubes, and others. To understand these anomalous behaviors, exploring the microscopic origin of normal (Fourier's) heat transport is a fascinating theoretical topic. However, this issue has not yet been fully understood even for one-dimensional (1D) model chains, in spite of a great amount of thorough studies done to date. From those studies it has been widely accepted that the conservation of momentum is a key ingredient to induce anomalous heat transport, while momentumnonconserving systems usually support normal heat transport where Fourier's law is valid. But if the nonconservation of momentum is the reason, what is the underlying microscopic mechanism for the observed normal heat transport? Here we carefully revisit a typical 1D momentum-nonconserving φ 4 model and present evidence that the mobile discrete breathers or, in other words, the moving intrinsic localized modes with frequency components above the linear phonon band can be responsible for that.

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Section: Introductionmentioning

confidence: 99%

Crossover from ballistic to normal heat transport in theϕ4lattice: If nonconservation of momentum is the reason, what is the mechanism?

2017

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“…Other researchers have proposed alternative definitions for * , such as the geometric mean of the bulk MFP and a local MFP, the latter of which decreases near a boundary [12]. We take * to be the non-local length computed from the Kinetic Collective Model (KCM), which is an accurate approach for predicting the thermal conductivity in a number of materials [30]. We refer to A for a more detailed description of how * is obtained from the KCM.…”

Section: Governing Equationsmentioning

confidence: 99%

Effective thermal conductivity of rectangular nanowires based on phonon hydrodynamics

Calvo-Schwarzwälder

Hennessy

Torres

et al. 2018

International Journal of Heat and Mass Transfer

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A mathematical model is presented for thermal transport in nanowires with rectangular cross sections. Expressions for the effective thermal conductivity of the nanowire across a range of temperatures and cross-sectional aspect ratios are obtained by solving the Guyer-Krumhansl hydrodynamic equation for the thermal flux with a slip boundary condition. Our results show that square nanowires transport thermal energy more efficiently than rectangular nanowires due to optimal separation between the boundaries. However, circular nanowires are found to be even more efficient than square nanowires due to the lack of corners in the cross section, which locally reduce the thermal flux and inhibit the conduction of heat. By using a temperature-dependent slip coefficient, we show that the model is able to accurately capture experimental data of the effective thermal conductivity obtained from Si nanowires, demonstrating that phonon hydrodynamics is a powerful framework that can be applied in nanosystems even at room temperature.

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“…Thermophysical parameters for Silicon at 1000 K[26,27].k * [W/m·K] c * [J/kg·K] ρ * [kg/m 3 ] L * m [kJ/kg] T *…”

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confidence: 99%

Non-local effects and size-dependent properties in Stefan problems with Newton cooling

Calvo-Schwarzwälder

2019

Applied Mathematical Modelling

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We model the growth of a one-dimensional solid by considering a modified Fourier law with a size-dependent effective thermal conductivity and a Newton cooling condition at the interface between the solid and the cold environment. In the limit of a large Biot number, this condition becomes the commonly used fixed-temperature condition. It is shown that in practice the size of this non-dimensional number is very small. We study the effect of a small Biot number on the solidification process with numerical and asymptotic solution methods. The study indicates that non-local effects become less important as the Biot number decreases.

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First principles kinetic-collective thermal conductivity of semiconductors

Cited by 60 publications

References 57 publications

Crossover from ballistic to normal heat transport in theϕ4lattice: If nonconservation of momentum is the reason, what is the mechanism?

Crossover from ballistic to normal heat transport in theϕ4lattice: If nonconservation of momentum is the reason, what is the mechanism?

Effective thermal conductivity of rectangular nanowires based on phonon hydrodynamics

Non-local effects and size-dependent properties in Stefan problems with Newton cooling

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