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Phonon Spectrum and Transient Regimes in the KCM

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Abstract

The goal of reduce the device sizes and obtain faster performance has caused that recent experiments are moving the focus to measurements at short length and time scales [1–7]. This makes it necessary to have a model which is able to work in the transient regime between diffusive and ballistic heat transport. Such models would depend strongly on the phonon mean free paths (MFP) and mean free times (MFT). For that reason, models able to provide a deeper insight on the different transport phenomena would become a suitable tool for such experiments. Works along this line have demonstrated that pure kinetic models are not enough to understand thermal conductivity at short length and time scales [5, 7]. A collective or hydrodynamic flow has been used to explain the origin of the non-monotonous dependence of the thermal boundary resistance as a function of the size of the heating source arising from ultrafast laser heating experiments  [7]. Also theoretically, collective transport has been successfully used to understand first principles results on graphene thermal transport [8, 9], where normal (N) scattering plays an important role. All seems to point out that models including collective effects will be necessary in next years in order to analyze these new experiments.

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References

  1. J.A. Johnson, A.A. Maznev, J. Cuffe, J.K. Eliason, A.J. Minnich, T. Kehoe, C.M.S. Torres, G. Chen, K.A. Nelson, Direct measurement of room-temperature nondiffusive thermal transport over micron distances in a silicon membrane. Phys. Rev. Lett. 110, 025901 (2013)

    Article  ADS  Google Scholar 

  2. M.E. Siemens, Q. Li, R. Yang, K.K.A. Nelson, E.H. Anderson, M.M. Murnane, H.C. Kapteyn, Quasi-Ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams. Nat. Mater. 9, 26 (2010)

    Article  ADS  Google Scholar 

  3. A.J. Minnich, J.A. Johnson, A.J. Schmidt, K. Esfarjani, M.S. Dresselhaus, K.A. Nelson, G. Chen, Thermal conductivity spectroscopy technique to measure phonon mean free paths. Phys. Rev. Lett. 107 (2011)

    Google Scholar 

  4. K.T. Regner, D.P. Sellan, Z. Su, C.H. Amon, A.J.H. McGaughey, J. Malen, Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance. Nat. Commun. 4, 1640 (2013)

    Google Scholar 

  5. R.B. Wilson, D.G. Cahill, Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments. Nat. Commun. 5, 5075 (2014)

    Article  ADS  Google Scholar 

  6. Y. Hu, L. Zeng, A.J. Minnich, M.S. Dresselhaus, G. Chen, Spectral mapping of thermal conductivity through nanoscale ballistic transport. Nat. Nanotechnol. 10, 701 (2015)

    Article  ADS  Google Scholar 

  7. K.M. Hoogeboom-Pot, J.N. Hernandez-Charpak, X. Gu, T.D. Frazer, E.H. Anderson, W. Chao, R.W. Falcone, R. Yang, M.M. Murnane, H.C. Kapteyn, D. Nardi, A new regime of nanoscale thermal transport: collective diffusion increases dissipation efficiency. Proc. Natl. Acad. Sci. 112, 201503449 (2015)

    Article  Google Scholar 

  8. A. Cepellotti, G. Fugallo, L. Paulatto, M. Lazzeri, F. Mauri, N. Marzari, Phonon hydrodynamics in two-dimensional materials. Nat. Commun. 6, 1 (2015)

    Article  Google Scholar 

  9. S. Lee, D. Broido, K. Esfarjani, G. Chen, Hydrodynamic phonon transport in suspended graphene. Nat. Commun. 6, 6290 (2015)

    Google Scholar 

  10. A. Jain, A.J.H. McGaughey, Effect of exchange-correlation on first-principles-driven lattice thermal conductivity predictions of crystalline silicon. Comput. Mater. Sci 110, 115 (2015)

    Article  Google Scholar 

  11. P. Jiang, L. Lindsay, Y.K. Koh, Role of low-energy phonons with mean-free-paths >0.8 \(\mu \)m in heat conduction in silicon. J. Appl. Phys. 119 (2016)

    Article  ADS  Google Scholar 

  12. C. De Tomas, A. Cantarero, A.F. Lopeandia, F.X. Alvarez, Enhancing of optic phonon contribution in hydrodynamic phonon transport. J. Appl. Phys 118 (2015)

    Google Scholar 

  13. R.A. Guyer, J.A. Krumhansl, Thermal conductivity, second sound, and phonon hydrodynamic phenomena in nonmetallic crystals. Phys. Rev. 148, 778 (1966)

    Article  ADS  Google Scholar 

  14. W. Li, N. Mingo, L. Lindsay, D.A. Broido, D.A. Stewart, N.A. Katcho, Thermal conductivity of diamond nanowires from first principles. Phys. Rev. B 85, 195436 (2012)

    Google Scholar 

  15. Y.J. Han, P.G. Klemens, Anharmonic thermal resistivity of dielectric crystals at low temperatures. Phys. Rev. B 48, 6033 (1993)

    Article  ADS  Google Scholar 

  16. A. Jain, Y.J. Yu, A.J.H. McGaughey, Phonon transport in periodic silicon nanoporous films with feature sizes greater than 100 nm. Phys. Rev. B 87, 1 (2013)

    Google Scholar 

  17. B. Vermeersch, J. Carrete, N. Mingo, A. Shakouri, Superdiffusive heat conduction in semiconductor alloys. I. Theoretical foundations. Phys. Rev. B 91, 085202 (2015)

    Article  ADS  Google Scholar 

  18. B. Vermeersch, A.M.S. Mohammed, G. Pernot, Y.R. Koh, A. Shakouri, Superdiffusive heat conduction in semiconductor alloys. II. Truncated Lévy formalism for experimental analysis. Phys. Rev. B 91, 085203 (2015)

    Article  ADS  Google Scholar 

  19. R. Cheaito, J.C. Duda, T.E. Beechem, K. Hattar, J.F. Ihlefeld, D.L. Medlin, M.A. Rodriguez, M.J. Campion, E.S. Piekos, P.E. Hopkins, Experimental investigation of size effects on the thermal conductivity of silicon-germanium alloy thin films. Phys. Rev. Lett. 109, 195901 (2012)

    Google Scholar 

  20. C. De Tomas, A. Cantarero, A.F. Lopeandia, F.X. Alvarez, From kinetic to collective behavior in thermal transport on semiconductors and semiconductor nanostructures. J. Appl. Phys 115 (2014)

    Article  ADS  Google Scholar 

  21. P. Torres, A. Torello, J. Bafaluy, J. Camacho, X. Cartoixà, F.X. Alvarez, First principles Kinetic-Collective thermal conductivity of semiconductors. Phys. Rev. B 95, 165407 (2017)

    Article  ADS  Google Scholar 

  22. C. Herring, Role of low-energy phonons in thermal conduction. Phys. Rev. 95, 954 (1954)

    Article  ADS  Google Scholar 

  23. J.C. Maxwell, On the dynamical theory of gases, The London, Edinburgh, and Dublin. Philos. Mag. J. Sci. 35, 49 (1868)

    Google Scholar 

  24. Y.-J. Han, Intrinsic thermal-resistive process of crystals: Umklapp processes at low and high temperatures. Phys. Rev. B 54, 8977 (1996)

    Article  ADS  Google Scholar 

  25. A. Togo, L. Chaput, I. Tanaka, Distributions of phonon lifetimes in Brillouin zones. Phys. Rev. B 91 (2015)

    Google Scholar 

  26. A. Cepellotti, N. Marzari, Thermal transport in crystals as a kinetic theory of relaxons. Phys. Rev. X 6, 041013 (2016)

    Google Scholar 

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Correspondence to Pol Torres Alvarez .

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Torres Alvarez, P. (2018). Phonon Spectrum and Transient Regimes in the KCM. In: Thermal Transport in Semiconductors. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-94983-3_6

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