Generalized Fourier's law for nondiffusive thermal transport: Theory and experiment

Hua, Chengyun; Lindsay, Lucas; Chen, Xiangwen; Minnich, Austin J.

doi:10.1103/physrevb.100.085203

Cited by 33 publications

(29 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Heat conduction in bulk materials at room temperature is usually described by the Fourier's law of thermal conduction, which implies that the heat carriers (phonons) undergo a diffusive process [1][2][3]. However, as the system size or dimension decreases, the phonons no longer transport diffusively [4][5][6][7][8][9][10][11][12][13][14] due to the existence of the ballistic [15,16] or hydrodynamic [17][18][19][20][21][22][23][24][25] phonon transport.…”

Section: Introductionmentioning

confidence: 99%

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

Shang

Zhang

Guo

et al. 2020

Sci Rep

View full text Add to dashboard Cite

In this work, the heat vortexes in two-dimensional porous or ribbon structures are investigated based on the phonon Boltzmann transport equation (BTE) under the Callaway model. First, the separate thermal effects of normal (N) scattering and resistive (R) scattering are investigated with frequency-independent assumptions. And then the heat vortexes in graphene are studied as a specific example. It is found that the heat vortexes can appear in both ballistic (rare R/N scattering) and hydrodynamic (N scattering dominates) regimes but disappear in the diffusive (R scattering dominates) regime. As long as there is not sufficient R scattering, the heat vortexes can appear in present simulations.

show abstract

Section: Introductionmentioning

confidence: 99%

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

Shang

Zhang

Guo

et al. 2020

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Among the different studies, the one of non-diffusive and quasiballistic phonon transport in SC and dielectric crystals including the transition between the ballistic and diffusive regimes has attracted a growing interest in the last decade. 10,12,[14][15][16][17][57][58][59][60][61][62][63]65,[68][69][70][71] In fact, some recent works have shown that the average MFP of phonons in SC crystals can be up to two orders of magnitude longer than the prediction of the kinetic theory at room temperature. 5,6 This has raised the fundamental question about the real contribution of low frequency phonons to the effective thermal conductivity of SC crystals that has been measured by several photothermal methods, mainly time domain thermoreflectance (TDTR), 10,16,21,29,30,59,60,62,70 frequency domain thermoreflectance (FDTR), 22,25 and transient thermal grating (TTG) 17,20,31,35,41,45 techniques.…”

Section: Introductionmentioning

confidence: 99%

“…10,12,[14][15][16][17][57][58][59][60][61][62][63]65,[68][69][70][71] In fact, some recent works have shown that the average MFP of phonons in SC crystals can be up to two orders of magnitude longer than the prediction of the kinetic theory at room temperature. 5,6 This has raised the fundamental question about the real contribution of low frequency phonons to the effective thermal conductivity of SC crystals that has been measured by several photothermal methods, mainly time domain thermoreflectance (TDTR), 10,16,21,29,30,59,60,62,70 frequency domain thermoreflectance (FDTR), 22,25 and transient thermal grating (TTG) 17,20,31,35,41,45 techniques. The exploitation of these techniques has allowed obtaining the key and relevant information about the phonon MFP spectral distribution in SC crystals, especially at room temperature.…”

Section: Introductionmentioning

confidence: 99%

Heat transport in semiconductor crystals: Beyond the local-linear approximation

Ezzahri

Joulain

Ordoñez-Miranda

2020

Journal of Applied Physics

View full text Add to dashboard Cite

We extend the application of the nonlocal theory of Mahan and Claro [Phys. Rev. B 38, 1963 (1988)] to solve the steady-state Boltzmann-Peierls transport equation within the framework of the single mode relaxation time approximation using the modified Debye-Callaway model. We consider the case of a semi-infinite semiconductor (SC) crystal with a boundary condition at its top surface that can be considered reasonably representative of time domain thermoreflectance (TDTR) and frequency domain thermoreflectance (FDTR) techniques. The approach allows us to obtain three different contributions to the heat flux density current that shed further light on the fundamental role of nonlocality and nonlinearity in heat transport by phonons in SC crystals. Through their intrinsic and implicit shuffling effect of the crystal momentum, phonon-phonon Normal scattering processes play a key role in the onset of thermal conduction as they introduce the temperature Laplacian as a second driving potential force for the heat flux density current in addition to the conventional Fourier's temperature gradient. The developed model suits quite fairly to interpret the frequency behavior of the reduced effective thermal conductivity of SC crystals that is observed in TDTR and FDTR experiments. We obtain an expression of the effective thermal conductivity of the SC crystal that is characterized with a universal spectral suppression function that captures and describes the role, the weight, and the contribution of quasi-ballistic and non-diffusive phonons. The spectral suppression function only depends on the ratio between the phonon mean free path and the thermal penetration depth as defined based on the diffusive Fourier's law.

show abstract

“…More recently, nonthermal source heating distributions have been studied to see their effect on the temperature and effective conductivity in the nano/micro scale regime through artificially created heat sources [20] or through phonon transmission through an interface [21][22][23]. We had suggested that nonequilibrium phonon distributions in a grating geometry can actually lead to an effective thermal conductivity higher than the regular macroscale conductivity [20].…”

mentioning

confidence: 99%

“…We had suggested that nonequilibrium phonon distributions in a grating geometry can actually lead to an effective thermal conductivity higher than the regular macroscale conductivity [20]. Enhancement of the effective thermal conductivity beyond the regular macroscopic value was also recently seen in the solution of the BTE for the pump-probe geometry when interfacial phonon transmission led to a nonthermal phonon distribution in the substrate [23]. Here, we formalize our previous work [20] and show how the heat source distribution can affect affect nondiffusive thermal transport.…”

mentioning

confidence: 99%

Thermal transport exceeding bulk heat conduction due to nonthermal micro/nanoscale phonon populations

Chiloyan

Huberman

Maznev

et al. 2020

Applied Physics Letters

View full text Add to dashboard Cite

While classical size effects usually lead to a reduced effective thermal conductivity, we report here that nonthermal phonon populations produced by a micro/nanoscale heat source can lead to enhanced heat conduction exceeding the prediction from Fourier's law. We study nondiffusive thermal transport by phonons at small distances within the framework of the Boltzmann transport equation (BTE) and demonstrate that the transport is significantly affected by the distribution of phonons emitted by the source. We discuss analytical solutions of the steady-state BTE for a source with a sinusoidal spatial profile, as well as for a three-dimensional Gaussian "hot spot," and provide numerical results for single crystal silicon at room temperature. If a micro/nanoscale heat source produces a thermal phonon distribution, it gets hotter than predicted by the heat diffusion equation; however, if the source predominantly produces low-frequency acoustic phonons with long mean free paths, it may get significantly cooler than predicted by the heat equation, yielding an enhanced heat transport beyond bulk heat conduction.

show abstract

Generalized Fourier's law for nondiffusive thermal transport: Theory and experiment

Cited by 33 publications

References 62 publications

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

Heat transport in semiconductor crystals: Beyond the local-linear approximation

Thermal transport exceeding bulk heat conduction due to nonthermal micro/nanoscale phonon populations

Contact Info

Product

Resources

About