Transport regimes in quasiballistic heat conduction

Hua, Chengyun; Minnich, Austin J.

doi:10.1103/physrevb.89.094302

Cited by 91 publications

(143 citation statements)

References 18 publications

(32 reference statements)

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“…A variaty of studies [6,7,11,12,15,16,18,21,24] have reconstructed the 'MFP spectrum' (cumulative conductivity function) κ Σ (Λ) from effective conductivities κ eff (χ) measured as a function of a controllable parameter χ. Although the κ Σ curve reveals the spatial extent of distinct transport regimes [23], it holds insufficient information for computing the actual quasiballistic heat dynamics.…”

Section: Propagator Functions As Thermal Blueprintmentioning

confidence: 99%

“…This might raise conceptual concerns towards thermal modelling, since phonons propagate at well defined group velocities. In practice, however, most experimental observations operate within the so called weakly quasiballistic regime t/τ 1 ↔ |s|τ 1 in which the Green's function G(ξ, t) of the 1D BTE is known to obey an exponential time decay with ξ-dependent rate [18]. From a stochastic viewpoint, G thus conforms precisely to the characteristic signature (2) of a Poissonian flight process, as we also pointed out in prior first-principles work [23].…”

Section: Note Regarding Transition Velocitymentioning

confidence: 99%

“…The essential physics that underpin the quasiballistic heat flow observations have been theoretically explained by a variety of works [14][15][16][17][18][19][20][21][22][23][24] largely indebted to the Boltzmann transport equation (BTE). However, BTE solutions are formulated in terms of a wide spectrum of phonon modes and as such are too intricate and inflexible for direct processing of experimental data.…”

Section: Introductionmentioning

confidence: 99%

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Compact stochastic models for multidimensional quasiballistic thermal transport

Vermeersch

2016

Journal of Applied Physics

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The Boltzmann transport equation (BTE) has proven indispensable in elucidating quasiballistic heat dynamics. Experimental observations of nondiffusive thermal transients, however, are interpreted almost exclusively through purely diffusive formalisms that merely extract 'effective' Fourier conductivities. Here, we build upon stochastic transport theory to provide a characterisation framework that blends the rich physics contained within BTE solutions with the convenience of conventional analyses. The multidimensional phonon dynamics are described in terms of an isotropic Poissonian flight process with rigorous Fourier-Laplace single pulse response P ( ξ, s) = 1/[s+ψ( ξ )]. The spatial propagator ψ( ξ ), unlike commonly reconstructed mean free path spectra κΣ(Λ), serves as a genuine thermal blueprint of the medium that can be identified in compact form directly from raw measurement signals. Practical illustrations for transient thermal grating (TTG) and time domain thermoreflectance (TDTR) experiments on respectively GaAs and InGaAs are provided.

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Section: Propagator Functions As Thermal Blueprintmentioning

confidence: 99%

Section: Note Regarding Transition Velocitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Compact stochastic models for multidimensional quasiballistic thermal transport

Vermeersch

2016

Journal of Applied Physics

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“…This assumption allows one to obtain effective thermal conductivities by solving for the suppression function from the gray BTE, i.e., the BTE equation with a single MFP [24]. This assumption has been shown to be not strictly valid in the past [24,25] and will be further shown in this work, with an approach that addresses this shortcoming.The BTE is notoriously difficult to solve, especially for complex geometries, which presents difficulty in calculating the effective thermal conductivity of materials in a given experimental geometry. So far almost exclusively, numerical solutions are implemented that directly attempt to solve the BTE and are then fitted to the Fourier heat conduction solution to extract the effective thermal conductivity and corresponding suppression function for the experimental geometry.…”

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confidence: 95%

Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation

et al. 2016

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The phonon Boltzmann transport equation (BTE) is a powerful tool for studying nondiffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring nondiffusive transport. By utilizing the known Fourier heat conduction solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating experiment, which is a useful tool for studying nondiffusive thermal transport and probing the MFP distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the nonuniversality of the suppression function used in the past, while providing a general approach to studying thermal properties in the nondiffusive regime. DOI: 10.1103/PhysRevB.93.155201 The Boltzmann transport equation (BTE) is widely used in analyzing heat transfer at length scales and time scales for which Fourier's law breaks down. In particular, there has been a growing interest recently in developing numerical and analytical solutions to the BTE to model thermal transport in phonon spectroscopy experiments [1-12] to extract phonon mean free path (MFP) distribution. The thermal conductivity accumulation function has been utilized as an elegant metric for understanding which MFP phonons contribute predominantly to thermal transport in a material [13][14][15]. Various experimental tools such as time-domain thermoreflectance (TDTR) [4,6,8,12,16,17], frequency-domain thermoreflectance (FDTR) [18,19], and transient thermal grating (TTG) [3,5,7,20] techniques have been extensively utilized recently in order to probe and observe nondiffusive transport by using ultrafast time scales or ultrashort length scales and gain key insight into the material's MFP spectrum.When the length scales in a system become comparable to the MFPs in a material, the effective thermal conductivity is reduced compared to its bulk, diffusive limit value [21,22]. A suppression function S ω is used to quantify this reduction or suppression of thermal conductivity, defined asThe variables C ω ,v ω , ω are the volumetric spectral heat capacity, the group velocity, and the MFP, respectively. The suppression function provides the ability to extend the notion of thermal conductivity beyond the diffusive regime in which it is defined from Fourier's law [21,23]. By utilizing the suppression function for a given experimental geometry, one can obtain the material's phonon MFP distribution from the experimentally measured thermal conductivity [5,6,12,23]. To obtain the effective thermal conductivity, the thermal signal from the experiment is fitted to the results of the Fourier law. The suppression function is calculated through modeling of the given experimental geometry with the BTE. However, one key assumption in this method is the universality of the suppression function, i.e....

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“…Hua et al 28 analytically solved the BTE for transient thermal grating. Regner et al 29 obtained analytical solutions to the BTE for time-periodic surface heating in both planar and spherical geometries.…”

Section: Introductionmentioning

confidence: 99%

Heating-frequency-dependent thermal conductivity: An analytical solution from diffusive to ballistic regime and its relevance to phonon scattering measurements

Yang

Dames

2015

Phys. Rev. B

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The heating frequency dependence of the apparent thermal conductivity in a semi-infinite body with periodic planar surface heating is explained by an analytical solution to the Boltzmann transport equation. This solution is obtained using a two-flux model and gray mean free time approximation, and verified numerically with a lattice Boltzmann method and numerical results from the literature. Extending the gray solution to the non-gray regime leads to an integral transform and accumulation-function representation of the phonon scattering spectrum, where the natural variable is mean free time, rather than mean free path as often used in previous work. The derivation leads to an approximate cutoff conduction similar in spirit to that of Koh and Cahill [Phys. Rev. B 76, 075207 (2007)] except that the most appropriate criterion involves the heater frequency rather than thermal diffusion length. The non-gray calculations are consistent with Koh and Cahill's experimental observation that the apparent thermal conductivity shows a stronger heater-frequency dependence in a SiGe alloy than in natural Si. Finally these results are demonstrated using a virtual experiment, which fits the phase lag between surface temperature and heat flux to obtain the apparent thermal conductivity and accumulation function.

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Transport regimes in quasiballistic heat conduction

Cited by 91 publications

References 18 publications

Compact stochastic models for multidimensional quasiballistic thermal transport

Compact stochastic models for multidimensional quasiballistic thermal transport

Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation

Heating-frequency-dependent thermal conductivity: An analytical solution from diffusive to ballistic regime and its relevance to phonon scattering measurements

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