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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]
+ Show Author Affiliations
  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 Laboratory (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:
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.
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Hua, Chengyun, & Minnich, Austin J. Heat dissipation in the quasiballistic regime studied using the Boltzmann equation in the spatial frequency domain. United States. https://doi.org/10.1103/PhysRevB.97.014307
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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. https://doi.org/10.1103/PhysRevB.97.014307. https://www.osti.gov/servlets/purl/1427638.
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@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},
number = 1,
volume = 97,
place = {United States},
year = {Wed Jan 10 00:00:00 EST 2018},
month = {Wed Jan 10 00:00:00 EST 2018}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1103/PhysRevB.97.014307
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Cited by: 20 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
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Thermal Conductivity Spectroscopy Technique to Measure Phonon Mean Free Paths
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Disparate quasiballistic heat conduction regimes from periodic heat sources on a substrate
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Two-channel model for nonequilibrium thermal transport in pump-probe experiments
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Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films
journal, May 2015

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journal, December 2014

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journal, June 2015

  • Hu, Yongjie; Zeng, Lingping; Minnich, Austin J.
  • Nature Nanotechnology, Vol. 10, Issue 8
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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
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Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane
journal, January 2013

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journal, November 2011

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journal, March 2014

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journal, October 2014

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    Works referencing / citing this record:

    High-frequency measurements of thermophysical properties of thin films using a modified broad-band frequency domain thermoreflectance approach
    journal, August 2018

    • Shahzadeh, Mohammadreza; Rahman, Mizanur; Hellwig, Olav
    • Review of Scientific Instruments, Vol. 89, Issue 8
    • DOI: 10.1063/1.5037117

    Modeling ballistic phonon transport from a cylindrical electron beam heat source
    journal, September 2019

    • Wehmeyer, Geoff
    • Journal of Applied Physics, Vol. 126, Issue 12
    • DOI: 10.1063/1.5115165

    Simultaneous measurement of anisotropic thermal conductivity and thermal boundary conductance of 2-dimensional materials
    journal, November 2019

    • Rahman, Mizanur; Shahzadeh, Mohammadreza; Pisana, Simone
    • Journal of Applied Physics, Vol. 126, Issue 20
    • DOI: 10.1063/1.5118315
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      Figures / Tables found in this record:

      TABLE I (p. 5)table
      FIG. 1 (p. 6)figure
      FIG. 2 (p. 6)figure
      FIG. 3 (p. 8)figure
      FIG. 4 (p. 11)figure
      FIG. 5 (p. 11)figure
      FIG. 6 (p. 12)figure
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