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Title: Heat dissipation in the quasiballistic regime studied using the Boltzmann equation in the spatial frequency domain

Abstract

Quasiballistic heat conduction, in which some phonons propagate ballistically over a thermal gradient, has recently become of intense interest. Most works report that the thermal resistance associated with nanoscale heat sources is far larger than predicted by Fourier's law; however, recent experiments show that in certain cases the difference is negligible despite the heaters being far smaller than phonon mean-free paths. In this work, we examine how thermal resistance depends on the heater geometry using analytical solutions of the Boltzmann equation. We show that the spatial frequencies of the heater pattern play the key role in setting the thermal resistance rather than any single geometric parameter, and that for many geometries the thermal resistance in the quasiballistic regime is no different than the Fourier prediction. We further demonstrate that the spectral distribution of the heat source also plays a major role in the resulting transport, unlike in the diffusion regime. Our work provides an intuitive link between the heater geometry, spectral heating distribution, and the effective thermal resistance in the quasiballistic regime, a finding that could impact strategies for thermal management in electronics and other applications.

Authors:
ORCiD logo [1];  [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1427638
Alternate Identifier(s):
OSTI ID: 1416419
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 97; Journal Issue: 1; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
77 NANOSCIENCE AND NANOTECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Phonons; thermal conductivity; transport phenomena; Boltzmann theory

Citation Formats

Hua, Chengyun, and Minnich, Austin J. Heat dissipation in the quasiballistic regime studied using the Boltzmann equation in the spatial frequency domain. United States: N. p., 2018. Web. doi:10.1103/PhysRevB.97.014307.
Hua, Chengyun, & Minnich, Austin J. Heat dissipation in the quasiballistic regime studied using the Boltzmann equation in the spatial frequency domain. United States. doi:10.1103/PhysRevB.97.014307.
Hua, Chengyun, and Minnich, Austin J. Wed . "Heat dissipation in the quasiballistic regime studied using the Boltzmann equation in the spatial frequency domain". United States. doi:10.1103/PhysRevB.97.014307. https://www.osti.gov/servlets/purl/1427638.
@article{osti_1427638,
title = {Heat dissipation in the quasiballistic regime studied using the Boltzmann equation in the spatial frequency domain},
author = {Hua, Chengyun and Minnich, Austin J.},
abstractNote = {Quasiballistic heat conduction, in which some phonons propagate ballistically over a thermal gradient, has recently become of intense interest. Most works report that the thermal resistance associated with nanoscale heat sources is far larger than predicted by Fourier's law; however, recent experiments show that in certain cases the difference is negligible despite the heaters being far smaller than phonon mean-free paths. In this work, we examine how thermal resistance depends on the heater geometry using analytical solutions of the Boltzmann equation. We show that the spatial frequencies of the heater pattern play the key role in setting the thermal resistance rather than any single geometric parameter, and that for many geometries the thermal resistance in the quasiballistic regime is no different than the Fourier prediction. We further demonstrate that the spectral distribution of the heat source also plays a major role in the resulting transport, unlike in the diffusion regime. Our work provides an intuitive link between the heater geometry, spectral heating distribution, and the effective thermal resistance in the quasiballistic regime, a finding that could impact strategies for thermal management in electronics and other applications.},
doi = {10.1103/PhysRevB.97.014307},
journal = {Physical Review B},
issn = {2469-9950},
number = 1,
volume = 97,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
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Citation Metrics:
Cited by: 6 works
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Figures / Tables:

TABLE I TABLE I: Input function Q̄ in Fourier space for Gaussian spot heating, nanoline array heating, and nanodot array heating. For the Gaussian heater, D is the 1/e2 width of a Gaussian distribution, also called the Gaussian diameter. In the nanoline and nanodot array heating patterns, the ratio of the linewidthmore » or dot width w and the period $L, w/L$, is defined as duty cycle. The heating is assumed to be periodic in time with frequency η0 and exponentially decaying in the cross-plane direction with a decay depth $d$ = 10 nm, which mimics an optical penetration depth in silicon by a laser source at a 400 nm wavelength.« less

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Works referenced in this record:

Measuring Phonon Mean Free Path Distributions by Probing Quasiballistic Phonon Transport in Grating Nanostructures
journal, November 2015

  • Zeng, Lingping; Collins, Kimberlee C.; Hu, Yongjie
  • Scientific Reports, Vol. 5, Issue 1
  • DOI: 10.1038/srep17131

Experimental metrology to obtain thermal phonon transmission coefficients at solid interfaces
journal, May 2017


Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams
journal, November 2009

  • Siemens, Mark E.; Li, Qing; Yang, Ronggui
  • Nature Materials, Vol. 9, Issue 1
  • DOI: 10.1038/nmat2568

Ab initio thermal transport in compound semiconductors
journal, April 2013


Thermal Conductivity Spectroscopy Technique to Measure Phonon Mean Free Paths
journal, August 2011


Disparate quasiballistic heat conduction regimes from periodic heat sources on a substrate
journal, August 2014

  • Zeng, Lingping; Chen, Gang
  • Journal of Applied Physics, Vol. 116, Issue 6
  • DOI: 10.1063/1.4893299

Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation
journal, September 2013

  • Collins, Kimberlee C.; Maznev, Alexei A.; Tian, Zhiting
  • Journal of Applied Physics, Vol. 114, Issue 10
  • DOI: 10.1063/1.4820572

Two-channel model for nonequilibrium thermal transport in pump-probe experiments
journal, October 2013


Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films
journal, May 2015

  • Hua, Chengyun; Minnich, Austin J.
  • Journal of Applied Physics, Vol. 117, Issue 17
  • DOI: 10.1063/1.4919432

Nanoscale thermal transport. II. 2003–2012
journal, March 2014

  • Cahill, David G.; Braun, Paul V.; Chen, Gang
  • Applied Physics Reviews, Vol. 1, Issue 1
  • DOI: 10.1063/1.4832615

Steady-state heat transport: Ballistic-to-diffusive with Fourier's law
journal, January 2015

  • Maassen, Jesse; Lundstrom, Mark
  • Journal of Applied Physics, Vol. 117, Issue 3
  • DOI: 10.1063/1.4905590

Superdiffusive heat conduction in semiconductor alloys. II. Truncated Lévy formalism for experimental analysis
journal, February 2015


Superdiffusive heat conduction in semiconductor alloys. I. Theoretical foundations
journal, February 2015


Analytical interpretation of nondiffusive phonon transport in thermoreflectance thermal conductivity measurements
journal, August 2014


Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations
journal, April 2014

  • Ding, D.; Chen, X.; Minnich, A. J.
  • Applied Physics Letters, Vol. 104, Issue 14
  • DOI: 10.1063/1.4870811

Analytical Green's function of the multidimensional frequency-dependent phonon Boltzmann equation
journal, December 2014


Spectral mapping of thermal conductivity through nanoscale ballistic transport
journal, June 2015

  • Hu, Yongjie; Zeng, Lingping; Minnich, Austin J.
  • Nature Nanotechnology, Vol. 10, Issue 8
  • DOI: 10.1038/nnano.2015.109

A new regime of nanoscale thermal transport: Collective diffusion increases dissipation efficiency
journal, March 2015

  • Hoogeboom-Pot, Kathleen M.; Hernandez-Charpak, Jorge N.; Gu, Xiaokun
  • Proceedings of the National Academy of Sciences, Vol. 112, Issue 16
  • DOI: 10.1073/pnas.1503449112

Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane
journal, January 2013


Onset of nondiffusive phonon transport in transient thermal grating decay
journal, November 2011


Frequency dependence of the thermal conductivity of semiconductor alloys
journal, August 2007


Transport regimes in quasiballistic heat conduction
journal, March 2014


Microscale Heat Conduction in Dielectric Thin Films
journal, February 1993


Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments
journal, October 2014

  • Wilson, R. B.; Cahill, David G.
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms6075

    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.