Derivation of a hydrodynamic heat equation from the phonon Boltzmann equation for general semiconductors

Sendra, Lluc; Beardo, Albert; Torres, Pol; Bafaluy, J.; Álvarez, F. X.; Camacho, J.

doi:10.1103/physrevb.103.l140301

Cited by 37 publications

(35 citation statements)

References 45 publications

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“…The value of the non-local length ( ) rises towards a converged value as the ribbon becomes wider (see Fig. 11), in agreement with what is expected from a microscopic description of the value [55]. The observed differences between RTA and the higher beyond-RTA values, especially for larger widths, can be easily interpreted by keeping in mind that in RTA all scattering processes are deemed as resistive and introduce artifactual modifications of the heat flux.…”

Section: Nanoribbonssupporting

confidence: 80%

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BTE-Barna: An extension of almaBTE for thermal simulation of devices based on 2D materials

Raya-Moreno¹,

Cartoixà²,

Carrete³

2022

Preprint

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We present BTE-Barna (Boltzmann Transport Equation -Beyond the Rta for NAnosystems), a software package that extends the Monte Carlo (MC) module of the almaBTE solver of the Peierls-Boltzmann transport equation for phonons (PBTE) to work with nanosystems based on 2D materials with complex geometries. To properly capture how the phonon occupations evolve in momentum space as a result of scattering, we have supplemented the relaxation-time approximation with an implementation of the propagator for the full linearized version of the PBTE. The code can now find solutions for finite and extended devices under the effect of a thermal gradient, with isothermal reservoirs or with an arbitrary initial temperature distribution in space and time, writing out the temperature and heat flux distributions as well as their spectral decompositions. Besides the full deviational MC solver, a number of useful approximations for highly symmetric devices are also included.

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Section: Nanoribbonssupporting

confidence: 80%

“…where W is the nanoribbon width, x is the distance from the center of the nanoribbon, is the non-local length [55] and C is related to wall properties, taking a value of 2 in our case because we have assumed completely diffusive walls.…”

Section: Nanoribbonsmentioning

confidence: 99%

BTE-Barna: An extension of almaBTE for thermal simulation of devices based on 2D materials

Raya-Moreno¹,

Cartoixà²,

Carrete³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Although the present effective MFP analysis is based on a gray phonon hydrodynamic model, it captures the crucial point and predicts the correct general trend. This paper thus also demonstrates the power of macroscopic hydrodynamic equations [5] in understanding non-Fourier heat transport, which have followed appreciable progress in recent years [6][7][8][9]58].…”

Section: B End Effect On Phonon Knudsen Minimummentioning

confidence: 59%

“…The investigation of phonon hydrodynamics was motivated by the exploration of second sound (wavelike heat transport) in solids at low temperatures [4,5]. On the other hand, it has significantly promoted the development of macroscopic hydrodynamic equations for non-Fourier heat transport [5][6][7][8][9]. There is a renewed interest in hydrodynamic heat transport in graphitic materials in recent years due to its occurrence at relatively high temperatures [10][11][12], which shows great potential for thermal management applications [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Size effect on phonon hydrodynamics in graphite microstructures and nanostructures

et al. 2021

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The understanding of hydrodynamic heat transport in finite-sized graphitic materials remains elusive due to the lack of an efficient methodology. In this paper, we develop a computational framework enabling an accurate description of heat transport in anisotropic graphite ribbons by a kinetic theory approach with full quantum mechanical first-principles input. A unified analysis of the size scaling of the thermal conductivity in the longitudinal and transverse directions of the system is made within the computational framework complemented with a macroscopic hydrodynamic approach. As a result, we demonstrate a strong end effect on the phonon Knudsen minimum, as a hallmark of the transition from ballistic to hydrodynamic heat transports, along a rectangular graphite ribbon with finite length and width. The phonon Knudsen minimum is found to take place only when the ribbon length is ∼5-10 times the upper limit of the width range in the hydrodynamic regime. This paper contributes to a unique methodology with high efficiency and a deeper understanding of the size effect on phonon hydrodynamics, which would open opportunities for its theoretical and experimental investigation in graphitic micro-and nanostructures.

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“…The concept of the kinetic theory of relaxons to characterize phonon hydrodynamics have been introduced by Cepellotti and Marzari [14]. Very recently, Sendra et al [15] introduced a framework to use hydrodynamic heat equations from phonon Boltzmann equation to study the hydrodynamic effects in semiconductors.…”

Section: Introductionmentioning

confidence: 99%

Effect of characteristic size on the collective phonon transport in crystalline GeTe

Ghosh

Kusiak

Battaglia

2021

Phys. Rev. Materials

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We study the effect of characteristic size variation on the phonon thermal transport in crystalline GeTe for a wide range of temperatures using the first-principles density-functional method coupled with the kinetic collective model approach. The characteristic size dependence of phonon thermal transport reveals an intriguing collective phonon transport regime, located in between the ballistic and the diffusive transport regimes. Therefore, systematic investigations have been carried out to describe the signatures of phonon hydrodynamics via the competitive effects between grain size and temperature. A characteristic nonlocal length associated with phonon hydrodynamics and a heat wave propagation length has been extracted. The connections between phonon hydrodynamics and these length scales are discussed in terms of the Knudsen number. Further, the scaling relation of thermal conductivity as a function of characteristic size in the intermediate size range emerges as a crucial indicator of the strength of the hydrodynamic behavior. A ratio concerning normal and resistive scattering rates has been employed to understand these different scaling relations, which seems to control the strength and prominent visibility of the collective phonon transport in GeTe. This systematic investigation emphasizes the importance of the competitive effects between temperature and characteristic size on phonon hydrodynamics in GeTe, which can lead to a better understanding of the generic behavior and consequences of the phonon hydrodynamics and its controlling parameters in low-thermal conductivity materials.

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Derivation of a hydrodynamic heat equation from the phonon Boltzmann equation for general semiconductors

Cited by 37 publications

References 45 publications

BTE-Barna: An extension of almaBTE for thermal simulation of devices based on 2D materials

BTE-Barna: An extension of almaBTE for thermal simulation of devices based on 2D materials

Size effect on phonon hydrodynamics in graphite microstructures and nanostructures

Effect of characteristic size on the collective phonon transport in crystalline GeTe

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