Three-Dimensional Ballistic-Diffusive Heat Transport in Silicon: Transient Response and Thermal Conductivity

  • 1 Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Kingdom of Saudi Arabia
Saad Bin Mansoor
  • Corresponding author
  • Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Kingdom of Saudi Arabia
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and Bekir S. YilbasORCID iD: https://orcid.org/0000-0003-0670-6306

Abstract

Phonons are the main contributors to thermal energy transfer in thin films. The size dependence of the thermal transport characteristics alters the film properties such as thermal conductivity. Hence, in the present study, three-dimensional, transient phonon transport in dielectric material is studied through the Equation of Phonon Radiative Transport (EPRT) to assess the size dependence of thermal conductivity. The numerical scheme is introduced solving the EPRT in three dimensions and the governing algorithm is described in detail. A parametric study is carried out examining the effect of the Kn number on the thermal energy transport characteristics in three-dimensional thermally excited film. The formulation and estimation of the effective thermal conductivity tensor is presented and discussed, thereby extending, to some extent, the one-dimensional results obtained earlier. We demonstrate that thermal conductivity changes in all directions, depending on the size effect. In addition, the directions of the temperature gradient and heat flux vectors differ as the Kn number approaches unity.

  • [1]

    A. Majumdar, Microscale heat conduction in dielectric thin films, ASME J. Heat Transfer 115 (1993), 7–16.

    • Crossref
    • Export Citation
  • [2]

    S. Bin Mansoor and B. S. Yilbas, Temperature distribution in silicon-aluminum thin films with presence of thermal boundary resistance, Transp. Theory Stat. Phys. 40 (2011), no. 3, 153–181.

    • Crossref
    • Export Citation
  • [3]

    S. Bin Mansoor and B. S. Yilbas, Phonon transport in silicon–silicon and silicon–diamond thin films: Consideration of thermal boundary resistance at interface, Transp. Theory Stat. Phys. 406 (2011), 2186–2195.

  • [4]

    B. S. Yilbas, R. S. M. Alassar, A. Y. Al-Dweik and S. B. Mansoor, A new approach for semi-analytical solution of cross-plane phonon transport in silicon–diamond thin films, J. Non-Equilib. Thermodyn. 43 (2018), no. 4, 359–372.

    • Crossref
    • Export Citation
  • [5]

    H. Ali and B. S. Yilbas, Microscale thermal energy transfer between thin films with vacuum gap at interface, J. Non-Equilib. Thermodyn. 44 (2019), no. 2, 123–142.

    • Crossref
    • Export Citation
  • [6]

    H. Ali and B. S. Yilbas, Energy transport across the thin films pair with presence of minute vacuum gap at interface, J. Non-Equilib. Thermodyn. 42 (2016), no. 2, 113–131.

  • [7]

    G. Chen, Size and interface effects on thermal conductivity of superlattices and periodic thin-film structures, ASME J. Heat Transfer 119 (1997), 220–229.

    • Crossref
    • Export Citation
  • [8]

    G. Chen, Thermal conductivity and ballistic phonon transport in cross-plane direction of superlattices, Phys. Rev. B 57 (1998), 14958–14973.

    • Crossref
    • Export Citation
  • [9]

    K. E. Goodson, Thermal conductivity in nonhomgeneous CVD diamond layers in electronic microstructures, ASME J. Heat Transfer 118 (1996), 279–336.

    • Crossref
    • Export Citation
  • [10]

    A. A. Joshi and A. Majumdar, Transient ballistic and diffusive heat transport in thin films, J. Appl. Phys. 74 (1993), 31–39.

    • Crossref
    • Export Citation
  • [11]

    A. J. Minnich, G. Chen, S. Mansoor and B. S. Yilbas, Quasiballistic heat transfer studied using the frequency-dependent Boltzmann transport equation, Phys. Rev. B 84 (2011), 235207.

  • [12]

    S. Bin Mansoor and B. S. Yilbas, Phonon radiative transport in siliconealuminum thin films: Frequency dependent case, Int. J. Therm. Sci. 57 (2012), 54–62.

    • Crossref
    • Export Citation
  • [13]

    R. G. Yang and G. Chen, Two-dimensional nanoscale heat conduction using ballistic-diffusive equations, in: Proc. of Int. Mechanical Engineering Conference and Exhibition, New York 369 (2001), 363–366.

  • [14]

    R. G. Yang, G. Chen and Y. Taur, Ballistic-dIFFUSIVE eQUATIONS FOR mULTIDIMENSIONAL nANOSCALE hEAT cONDUction, in: Proc. of International Heat Transfer Conference, Grenoble, France, Elsevier, Paris 1 (2002), 579–584.

  • [15]

    R. Yang, G. Chen, M. Laroche and Y. Taur, Simulation of nanoscale multidimensional transient heat conduction problems using ballistic-diffusive equations and phonon Boltzmann equation, Trans. Am. Soc. Mech. Eng. 127 (2005), 298–306.

  • [16]

    B. S. Yilbas and S. Bin Mansoor, Phonon transport in two-dimensional silicon thin film: influence of film width and boundary conditions on temperature distribution, Eur. Phys. J. B (2012), 85. 243.

  • [17]

    B. S. Yilbas and S. Bin Mansoor, Frequency dependent phonon transport in two-dimensional Silicon and Diamond thin films, Mod. Phys. Lett. B 26 (2012), 17.

  • [18]

    Saad B. Mansoor and Bekir S. Yilbas, Phonon transport across nano-scale curved thin films, Physica B 503 (2016), 130–140.

    • Crossref
    • Export Citation
  • [19]

    B. S. Yilbas and S. Bin Mansoor, Transient effects of phonon transport in two-dimensional silicon film, Numer. Heat Transf., Part A, Appl. 62 (2012), no. 9, 742–760.

    • Crossref
    • Export Citation
  • [20]

    H. Ya-Fen, L. Hai-Dong and C. Xue, Numerical simulation for thermal conductivity of nanograin within three dimensions, Therm. Sci. 22 (2018), no. 2, 449–457.

    • Crossref
    • Export Citation
  • [21]

    D. E. Khalili, R. Afrasiab and G. Behzad, Numerical study of 3-D microscale heat transfer of a thin diamond slab under fix and moving laser heating, Therm. Sci. 23 (2019), no. 5B, 3035–3045.

    • Crossref
    • Export Citation
  • [22]

    B. S. Yilbas and S. Bin Mansour, Phonon transport and equivalent equilibrium temperature in thin silicon films, J. Non-Equilib. Thermodyn. 38 (2013), no. 2, 153–174.

  • [23]

    H. Ali and B. S. Yilbas, Influence of heat source size and film thickness on phonon transport in a two-dimensional thin film, J. Non-Equilib. Thermodyn. 39 (2014), no. 2, 79–91.

  • [24]

    B. S. Yilbas, S. B. Mansoor and H. Ali, Heat Transport in Micro- and Nanoscale Thin Films, Elsevier, New York, 2017.

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The Journal of Non-Equilibrium Thermodynamics serves as an international publication organ for new ideas, insights and results on non-equilibrium phenomena in science, engineering and related natural systems. The central aim of the journal is to provide a bridge between science and engineering and to promote scientific exchange on non-equilibrium phenomena and on analytic or numeric modeling for their interpretation.

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