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2020 | OriginalPaper | Chapter

7. Nonequilibrium Energy Transfer in Nanostructures

Author : Zhuomin M. Zhang

Published in: Nano/Microscale Heat Transfer

Publisher: Springer International Publishing

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Abstract

This chapter begins with a description of the phenomenological theories in which the energy transport processes are represented by a single differential equation or a set of differential equations that can be solved with appropriate initial and boundary conditions. These equations are often called non-Fourier heat equations, which can be considered as extensions of the conventional heat diffusion equation based on Fourier’s law. The limitations of the phenomenological theories are discussed. While the BTE, Monte Carlo method, and MD simulations have been presented in previous chapters, this chapter stresses the application in solid nanostructures, including thermal boundary resistance (TBR) and multilayer structures. The equation of phonon radiative transfer (EPRT) is introduced and used to delineate the diffusive and ballistic heat conduction regimes in thin films. A heat conduction regime with respect to length and time scale is presented, followed by a summary of the contemporary methods for measuring thermal transport properties of solids, thin films, and nanostructures.

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Appendix
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Literature
1.
go back to reference H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, 2nd edn. (Clarendon Press, Oxford, 1959)MATH H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, 2nd edn. (Clarendon Press, Oxford, 1959)MATH
2.
go back to reference M.N. Özişik, Heat Conduction, 2nd ed., Wiley, New York, 1993; also D.W. Hahn and M.N. Özişik, Heat Conduction, 3rd ed., Wiley, New York, 2012 M.N. Özişik, Heat Conduction, 2nd ed., Wiley, New York, 1993; also D.W. Hahn and M.N. Özişik, Heat Conduction, 3rd ed., Wiley, New York, 2012
3.
go back to reference T.J. Bright, Z.M. Zhang, Common misperceptions of the hyperbolic heat equation. J. Thermophys. Heat Transfer 23, 601–607 (2009) T.J. Bright, Z.M. Zhang, Common misperceptions of the hyperbolic heat equation. J. Thermophys. Heat Transfer 23, 601–607 (2009)
4.
go back to reference D. D. Joseph, L. Preziosi, Heat waves. Rev. Mod. Phys., 61, 41–73 (1989) D. D. Joseph, L. Preziosi, Heat waves. Rev. Mod. Phys., 61, 41–73 (1989)
5.
go back to reference D.D. Joseph, L. Preziosi, Addendum to the paper ‘heat waves’. Rev. Mod. Phys. 62, 375–391 (1990) D.D. Joseph, L. Preziosi, Addendum to the paper ‘heat waves’. Rev. Mod. Phys. 62, 375–391 (1990)
6.
go back to reference D.Y. Tzou, Macro- to Microscale Heat Transfer: The Lagging Behavior, 2nd edn. (Wiley, New York, 2015) D.Y. Tzou, Macro- to Microscale Heat Transfer: The Lagging Behavior, 2nd edn. (Wiley, New York, 2015)
7.
go back to reference M.N. Özişik, D.Y. Tzou, On the wave theory in heat conduction. J. Heat Transfer 116, 526–535 (1994) M.N. Özişik, D.Y. Tzou, On the wave theory in heat conduction. J. Heat Transfer 116, 526–535 (1994)
8.
go back to reference W.K. Yeung, T.T. Lam, A numerical scheme for non-Fourier heat conduction, Part I: one-dimensional problem formulation and applications. Numer. Heat Transfer B 33, 215–233 (1998) W.K. Yeung, T.T. Lam, A numerical scheme for non-Fourier heat conduction, Part I: one-dimensional problem formulation and applications. Numer. Heat Transfer B 33, 215–233 (1998)
9.
go back to reference A. Haji-Sheikh, W.J. Minkowycz, E.M. Sparrow, Certain anomalies in the analysis of hyperbolic heat conduction. J. Heat Transfer 124, 307–319 (2002) A. Haji-Sheikh, W.J. Minkowycz, E.M. Sparrow, Certain anomalies in the analysis of hyperbolic heat conduction. J. Heat Transfer 124, 307–319 (2002)
10.
go back to reference J. Gembarovic, J. Gembarovic Jr., Non-Fourier heat conduction modeling in a finite medium. Int. J. Thermophys. 25, 1261–1268 (2004)MATH J. Gembarovic, J. Gembarovic Jr., Non-Fourier heat conduction modeling in a finite medium. Int. J. Thermophys. 25, 1261–1268 (2004)MATH
11.
go back to reference C.A. Bennett, R.R. Patty, Thermal wave interferometry: a potential application of the photoacoustic effect. Appl. Opt. 21, 49–54 (1982) C.A. Bennett, R.R. Patty, Thermal wave interferometry: a potential application of the photoacoustic effect. Appl. Opt. 21, 49–54 (1982)
12.
go back to reference A. Mandelis (ed.), Photoacoustic and Thermal Wave Phenomena in Semiconductors (Elsevier, Amsterdam, 1987) A. Mandelis (ed.), Photoacoustic and Thermal Wave Phenomena in Semiconductors (Elsevier, Amsterdam, 1987)
13.
go back to reference M.B. Rubin, Hyperbolic heat conduction and the second law. Int. J. Eng. Sci. 30, 1665–1676 (1992)MathSciNetMATH M.B. Rubin, Hyperbolic heat conduction and the second law. Int. J. Eng. Sci. 30, 1665–1676 (1992)MathSciNetMATH
14.
go back to reference C. Bai, A.S. Lavine, On hyperbolic heat conduction and the second law of thermodynamics. J. Heat Transfer 117, 256–263 (1995) C. Bai, A.S. Lavine, On hyperbolic heat conduction and the second law of thermodynamics. J. Heat Transfer 117, 256–263 (1995)
15.
go back to reference A. Barletta, E. Zanchini, Hyperbolic heat conduction and local equilibrium: a second law analysis. Int. J. Heat Mass Transfer 40, 1007–1016 (1997)MATH A. Barletta, E. Zanchini, Hyperbolic heat conduction and local equilibrium: a second law analysis. Int. J. Heat Mass Transfer 40, 1007–1016 (1997)MATH
16.
go back to reference D. Jou, G. Lebon, J. Casas-Vázquez, Extended Irreversible Thermodynamics, 4th edn. (Springer, Berlin, 2010)MATH D. Jou, G. Lebon, J. Casas-Vázquez, Extended Irreversible Thermodynamics, 4th edn. (Springer, Berlin, 2010)MATH
17.
go back to reference Z.M. Zhang, T.J. Bright, G.P. Peterson, Reexamination of the statistical derivations of Fourier’s law and Cattaneo’s equation. Nanoscale Microscale Thermophys. Eng. 15, 220–228 (2011) Z.M. Zhang, T.J. Bright, G.P. Peterson, Reexamination of the statistical derivations of Fourier’s law and Cattaneo’s equation. Nanoscale Microscale Thermophys. Eng. 15, 220–228 (2011)
18.
go back to reference J. Tavernier, Sur l’équation de conduction de la chaleur. Comptes Rendus Acad. Sci. 254, 69–71 (1962)MathSciNet J. Tavernier, Sur l’équation de conduction de la chaleur. Comptes Rendus Acad. Sci. 254, 69–71 (1962)MathSciNet
19.
go back to reference A. Majumdar, Microscale heat conduction in dielectric thin films. J. Heat Transfer 115, 7–16 (1993) A. Majumdar, Microscale heat conduction in dielectric thin films. J. Heat Transfer 115, 7–16 (1993)
20.
go back to reference A.A. Joshi, A. Majumdar, Transient ballistic and diffusive phonon heat transport in thin films. J. Appl. Phys. 74, 31–39 (1993) A.A. Joshi, A. Majumdar, Transient ballistic and diffusive phonon heat transport in thin films. J. Appl. Phys. 74, 31–39 (1993)
21.
go back to reference S. Volz, J.-B. Saulnier, M. Lallemand, B. Perrin, P. Depondt, M. Mareschal, Transient Fourier-law deviation by molecular dynamics in solid argon. Phys. Rev. B 54, 340–347 (1996) S. Volz, J.-B. Saulnier, M. Lallemand, B. Perrin, P. Depondt, M. Mareschal, Transient Fourier-law deviation by molecular dynamics in solid argon. Phys. Rev. B 54, 340–347 (1996)
22.
go back to reference J. Xu, X.W. Wang, Simulation of ballistic and non-Fourier thermal transport in ultra-fast laser heating. Phys. B 351, 213–226 (2004) J. Xu, X.W. Wang, Simulation of ballistic and non-Fourier thermal transport in ultra-fast laser heating. Phys. B 351, 213–226 (2004)
23.
go back to reference M. Chester, Second sound in solids. Phys. Rev. 131, 2013–2015 (1963) M. Chester, Second sound in solids. Phys. Rev. 131, 2013–2015 (1963)
24.
go back to reference M.E. Gurtin, A.C. Pipkin, A general theory of heat conduction with finite wave speeds. Arch. Ration. Mech. Anal. 31, 113–126 (1968)MathSciNetMATH M.E. Gurtin, A.C. Pipkin, A general theory of heat conduction with finite wave speeds. Arch. Ration. Mech. Anal. 31, 113–126 (1968)MathSciNetMATH
25.
go back to reference P.J. Antaki, Solution for non-Fourier dual phase lag heat conduction in a semi-infinite slab with surface heat flux. Int. J. Heat Mass Transfer 41, 2253–2258 (1998)MATH P.J. Antaki, Solution for non-Fourier dual phase lag heat conduction in a semi-infinite slab with surface heat flux. Int. J. Heat Mass Transfer 41, 2253–2258 (1998)MATH
26.
go back to reference D.W. Tang, N. Araki, Wavy, wavelike, diffusive thermal responses of finite rigid slabs to high-speed heating of laser-pulses. Int. J. Heat Mass Transfer 42, 855–860 (1999)MATH D.W. Tang, N. Araki, Wavy, wavelike, diffusive thermal responses of finite rigid slabs to high-speed heating of laser-pulses. Int. J. Heat Mass Transfer 42, 855–860 (1999)MATH
27.
go back to reference D.Y. Tzou, K.S. Chiu, Temperature-dependent thermal lagging in ultrafast laser heating. Int. J. Heat Mass Transfer 44, 1725–1734 (2001)MATH D.Y. Tzou, K.S. Chiu, Temperature-dependent thermal lagging in ultrafast laser heating. Int. J. Heat Mass Transfer 44, 1725–1734 (2001)MATH
28.
go back to reference L.Q. Wang, X.S. Zhou, X.H. Wei, Heat Conduction: Mathematical Models and Analytical Solutions (Springer-Verlag, Berlin, 2008)MATH L.Q. Wang, X.S. Zhou, X.H. Wei, Heat Conduction: Mathematical Models and Analytical Solutions (Springer-Verlag, Berlin, 2008)MATH
29.
go back to reference W.J. Minkowycz, A. Haji-Sheikh, K. Vafai, On departure from local thermal equilibrium in porous media due to a rapid changing heat source: the Sparrow number. Int. J. Heat Mass Transfer 42, 3373–3385 (1999)MATH W.J. Minkowycz, A. Haji-Sheikh, K. Vafai, On departure from local thermal equilibrium in porous media due to a rapid changing heat source: the Sparrow number. Int. J. Heat Mass Transfer 42, 3373–3385 (1999)MATH
30.
go back to reference W. Kaminski, Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure. J. Heat Transfer 112, 555–560 (1990) W. Kaminski, Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure. J. Heat Transfer 112, 555–560 (1990)
31.
go back to reference J. Callaway, Model for lattice thermal conductivity at low temperatures. Phys. Rev. 113, 1046–1951 (1959)MATH J. Callaway, Model for lattice thermal conductivity at low temperatures. Phys. Rev. 113, 1046–1951 (1959)MATH
32.
go back to reference R. A. Guyer, J. A. Krumhansl, Solution of the linearized phonon Boltzmann equation. Phys. Rev. 148, 766–778 (1966); Thermal conductivity, second sound, and phonon hydrodynamic phenomena in nonmetallic crystals. Phys. Rev. 148, 778–788 (1966) R. A. Guyer, J. A. Krumhansl, Solution of the linearized phonon Boltzmann equation. Phys. Rev. 148, 766–778 (1966); Thermal conductivity, second sound, and phonon hydrodynamic phenomena in nonmetallic crystals. Phys. Rev. 148, 778–788 (1966)
33.
go back to reference J. Shiomi, S. Maruyama, Non-Fourier heat conduction in a single-walled carbon nanotube: Classical molecular dynamics simulations. Phys. Rev. B 73, 205420 (2006) J. Shiomi, S. Maruyama, Non-Fourier heat conduction in a single-walled carbon nanotube: Classical molecular dynamics simulations. Phys. Rev. B 73, 205420 (2006)
34.
go back to reference D.H. Tsai, R.A. MacDonald, Molecular-dynamics study of second sound in a solid excited by a strong heat pulse. Phys. Rev. B 14, 4714–4723 (1976) D.H. Tsai, R.A. MacDonald, Molecular-dynamics study of second sound in a solid excited by a strong heat pulse. Phys. Rev. B 14, 4714–4723 (1976)
35.
go back to reference X.W. Wang, X. Xu, Thermoelastic wave induced by pulsed laser heating. Appl. Phys. A 73, 107–114 (2001) X.W. Wang, X. Xu, Thermoelastic wave induced by pulsed laser heating. Appl. Phys. A 73, 107–114 (2001)
36.
go back to reference X.W. Wang, Thermal and thermomechanical phenomena in picosecond laser copper interaction. J. Heat Transfer 126, 355–364 (2004) X.W. Wang, Thermal and thermomechanical phenomena in picosecond laser copper interaction. J. Heat Transfer 126, 355–364 (2004)
37.
go back to reference S.I. Anisimov, B.L. Kapeliovich, T.L. Perel’man, Electron emission from metal surfaces exposed to ultrashort laser pulses. Sov. Phys. JETP 39, 375–377 (1974) S.I. Anisimov, B.L. Kapeliovich, T.L. Perel’man, Electron emission from metal surfaces exposed to ultrashort laser pulses. Sov. Phys. JETP 39, 375–377 (1974)
38.
go back to reference J.G. Fujimoto, J.M. Liu, E.P. Ippen, N. Bloembergen, Femtosecond laser interaction with metallic tungsten and nonequilibrium electron and lattice temperatures. Phys. Rev. Lett. 53, 1837–1840 (1984) J.G. Fujimoto, J.M. Liu, E.P. Ippen, N. Bloembergen, Femtosecond laser interaction with metallic tungsten and nonequilibrium electron and lattice temperatures. Phys. Rev. Lett. 53, 1837–1840 (1984)
39.
go back to reference S.D. Brorson, J.G. Fujimoto, E.P. Ippen, Femtosecond electronic heat-transport dynamics in thin gold films. Phys. Rev. Lett. 59, 1962–1965 (1987) S.D. Brorson, J.G. Fujimoto, E.P. Ippen, Femtosecond electronic heat-transport dynamics in thin gold films. Phys. Rev. Lett. 59, 1962–1965 (1987)
40.
go back to reference T.Q. Qiu, C.L. Tien, Short-pulse laser heating on metals. Int. J. Heat Mass Transfer 35, 719–726 (1992) T.Q. Qiu, C.L. Tien, Short-pulse laser heating on metals. Int. J. Heat Mass Transfer 35, 719–726 (1992)
41.
go back to reference T.Q. Qiu, C.L. Tien, Size effect on nonequilibrium laser heating of metal films. J. Heat Transfer 115, 842–847 (1993) T.Q. Qiu, C.L. Tien, Size effect on nonequilibrium laser heating of metal films. J. Heat Transfer 115, 842–847 (1993)
42.
go back to reference T.Q. Qiu, T. Juhasz, C. Suarez, W.E. Bron, C.L. Tien, Femtosecond laser heating of multi-layer metals—II. Experiments. Int. J. Heat Mass Transfer 37, 2799–2808 (1994) T.Q. Qiu, T. Juhasz, C. Suarez, W.E. Bron, C.L. Tien, Femtosecond laser heating of multi-layer metals—II. Experiments. Int. J. Heat Mass Transfer 37, 2799–2808 (1994)
43.
go back to reference J.L. Hostetler, A.N. Smith, D.M. Czajkowsky, P.M. Norris, Measurement of the electron-phonon coupling factor dependence on film thickness and grain size in Au, Cr, and Al. Appl. Opt. 38, 3614–3620 (1999) J.L. Hostetler, A.N. Smith, D.M. Czajkowsky, P.M. Norris, Measurement of the electron-phonon coupling factor dependence on film thickness and grain size in Au, Cr, and Al. Appl. Opt. 38, 3614–3620 (1999)
44.
go back to reference S. Link, C. Burda, Z.L. Wang, M.A. El-Sayed, Electron dynamics in gold and gold-silver alloy nanoparticles: The influence of a nonequilibrium electron distribution and the size dependence of the electron-phonon relaxation. J. Chem. Phys. 111, 1255–1264 (1999) S. Link, C. Burda, Z.L. Wang, M.A. El-Sayed, Electron dynamics in gold and gold-silver alloy nanoparticles: The influence of a nonequilibrium electron distribution and the size dependence of the electron-phonon relaxation. J. Chem. Phys. 111, 1255–1264 (1999)
45.
go back to reference A.N. Smith, P.M. Norris, Influence of intraband transition on the electron thermoreflectance response of metals. Appl. Phys. Lett. 78, 1240–1242 (2001) A.N. Smith, P.M. Norris, Influence of intraband transition on the electron thermoreflectance response of metals. Appl. Phys. Lett. 78, 1240–1242 (2001)
46.
go back to reference R.J. Stevens, A.N. Smith, P.M. Norris, Measurement of thermal boundary conductance of a series of metal-dielectric interfaces by the transient thermoreflectance techniques. J. Heat Transfer 127, 315–322 (2005) R.J. Stevens, A.N. Smith, P.M. Norris, Measurement of thermal boundary conductance of a series of metal-dielectric interfaces by the transient thermoreflectance techniques. J. Heat Transfer 127, 315–322 (2005)
47.
go back to reference D.G. Cahill, K.E. Goodson, A. Majumdar, Thermometry and thermal transport in micro/nanoscale solid-state devices and structures. J. Heat Transfer 124, 223–241 (2002) D.G. Cahill, K.E. Goodson, A. Majumdar, Thermometry and thermal transport in micro/nanoscale solid-state devices and structures. J. Heat Transfer 124, 223–241 (2002)
48.
go back to reference D.G. Cahill, W.K. Ford, K.E. Goodson et al., Nanoscale thermal transport. J. Appl. Phys. 93, 793–818 (2003) D.G. Cahill, W.K. Ford, K.E. Goodson et al., Nanoscale thermal transport. J. Appl. Phys. 93, 793–818 (2003)
49.
go back to reference J. Zhu, D.W. Tang, W. Wang, J. Liu, K.W. Holub, R. Yang, Ultrafast thermoreflectance techniques for measuring thermal conductivity and interface thermal conductance of thin films. J. Appl. Phys. 108, 094315 (2010) J. Zhu, D.W. Tang, W. Wang, J. Liu, K.W. Holub, R. Yang, Ultrafast thermoreflectance techniques for measuring thermal conductivity and interface thermal conductance of thin films. J. Appl. Phys. 108, 094315 (2010)
50.
go back to reference D.M. Riffe, X.Y. Wang, M.C. Downer et al., Femtosecond thermionic emission from metals in the space-charge-limited regime. J. Opt. Soc. Am. B 10, 1424–1435 (1993) D.M. Riffe, X.Y. Wang, M.C. Downer et al., Femtosecond thermionic emission from metals in the space-charge-limited regime. J. Opt. Soc. Am. B 10, 1424–1435 (1993)
51.
go back to reference A.N. Smith, J.L. Hostetler, P.M. Norris, Nonequilibrium heating in metal films: An analytical and numerical analysis. Numer. Heat Transfer A 35, 859–874 (1999) A.N. Smith, J.L. Hostetler, P.M. Norris, Nonequilibrium heating in metal films: An analytical and numerical analysis. Numer. Heat Transfer A 35, 859–874 (1999)
52.
go back to reference M. Li, S. Menon, J.P. Nibarger, G.N. Gibson, Ultrafast electron dynamics in femtosecond optical breakdown of dielectrics. Phys. Rev. Lett. 82, 2394–2397 (1999) M. Li, S. Menon, J.P. Nibarger, G.N. Gibson, Ultrafast electron dynamics in femtosecond optical breakdown of dielectrics. Phys. Rev. Lett. 82, 2394–2397 (1999)
53.
go back to reference L. Jiang, H.-L. Tsai, Energy transport and nanostructuring of dielectrics by femtosecond laser pulse trains. J. Heat Transfer 128, 926–933 (2006) L. Jiang, H.-L. Tsai, Energy transport and nanostructuring of dielectrics by femtosecond laser pulse trains. J. Heat Transfer 128, 926–933 (2006)
54.
go back to reference L. Jiang, H.-L. Tsai, Plasma modeling for ultrashort pulse laser ablation of dielectrics. J. Appl. Phys. 100, 023116 (2006) L. Jiang, H.-L. Tsai, Plasma modeling for ultrashort pulse laser ablation of dielectrics. J. Appl. Phys. 100, 023116 (2006)
55.
go back to reference Y. Ma, A two-parameter nondiffusive heat conduction model for data analysis in pump-probe experiments. J. Appl. Phys. 116, 243505 (2014); ibid, Hotspot size-dependent thermal boundary conductance in nondiffusive heat conduction. J. Heat Transfer 137, 082401 (2015) Y. Ma, A two-parameter nondiffusive heat conduction model for data analysis in pump-probe experiments. J. Appl. Phys. 116, 243505 (2014); ibid, Hotspot size-dependent thermal boundary conductance in nondiffusive heat conduction. J. Heat Transfer 137, 082401 (2015)
56.
go back to reference G. Chen, Ballistic-diffusion heat-conduction equations. Phys. Rev. Lett. 86, 2297–2300 (2001); ibid, Ballistic-diffusive equations for transient heat conduction from nano to macroscales. J. Heat Transfer 124, 320–328 (2002) G. Chen, Ballistic-diffusion heat-conduction equations. Phys. Rev. Lett. 86, 2297–2300 (2001); ibid, Ballistic-diffusive equations for transient heat conduction from nano to macroscales. J. Heat Transfer 124, 320–328 (2002)
57.
go back to reference T. Klitsner, J.E. VanCleve, H.E. Fischer, R.O. Pohl, Phonon radiative heat transfer and surface scattering. Phys. Rev. B 38, 7576–7594 (1988) T. Klitsner, J.E. VanCleve, H.E. Fischer, R.O. Pohl, Phonon radiative heat transfer and surface scattering. Phys. Rev. B 38, 7576–7594 (1988)
58.
go back to reference R.B. Peterson, Direct simulation of phonon-mediated heat transfer in a Debye crystal. J. Heat Transfer 116, 815–822 (1994) R.B. Peterson, Direct simulation of phonon-mediated heat transfer in a Debye crystal. J. Heat Transfer 116, 815–822 (1994)
59.
go back to reference E.T. Swartz, P.O. Pohl, Thermal boundary resistance. Rev. Mod. Phys. 61, 605–668 (1989) E.T. Swartz, P.O. Pohl, Thermal boundary resistance. Rev. Mod. Phys. 61, 605–668 (1989)
60.
go back to reference W.A. Little, The transport of heat between dissimilar solids at low temperatures. Can. J. Phys. 37, 334–349 (1959) W.A. Little, The transport of heat between dissimilar solids at low temperatures. Can. J. Phys. 37, 334–349 (1959)
61.
go back to reference G. Chen and C.L. Tien, “Thermal conductivity of quantum well structures,” J. Thermophys. Heat Transfer, 7, 311–318, 1993 G. Chen and C.L. Tien, “Thermal conductivity of quantum well structures,” J. Thermophys. Heat Transfer, 7, 311–318, 1993
62.
go back to reference G. Chen, Size and interface effects on thermal conductivity of superlattices and periodic thin-film structures. J. Heat Transfer 119, 220–229 (1997) G. Chen, Size and interface effects on thermal conductivity of superlattices and periodic thin-film structures. J. Heat Transfer 119, 220–229 (1997)
63.
go back to reference G. Chen, Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices. Phys. Rev. B 57, 14958–14973 (1998) G. Chen, Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices. Phys. Rev. B 57, 14958–14973 (1998)
64.
go back to reference G. Chen, T. Zeng, Nonequilibrium phonon and electron transport in heterostructures and superlattices. Microscale Thermophys. Eng. 5, 71–88 (2001) G. Chen, T. Zeng, Nonequilibrium phonon and electron transport in heterostructures and superlattices. Microscale Thermophys. Eng. 5, 71–88 (2001)
65.
go back to reference T. Zeng, G. Chen, Phonon heat conduction in thin films: impacts of thermal boundary resistance and internal heat generation. J. Heat Transfer 123, 340–347 (2001) T. Zeng, G. Chen, Phonon heat conduction in thin films: impacts of thermal boundary resistance and internal heat generation. J. Heat Transfer 123, 340–347 (2001)
66.
go back to reference S. Sinha, K.E. Goodson, Review: multiscale thermal modeling in nanoelectronics. Int. J. Multiscale Comp. Eng. 3, 107–133 (2005) S. Sinha, K.E. Goodson, Review: multiscale thermal modeling in nanoelectronics. Int. J. Multiscale Comp. Eng. 3, 107–133 (2005)
67.
go back to reference R.A. Escobar, S.S. Ghai, M.S. Jhon, C.H. Amon, Multi-length and time scale thermal transport using the lattice Boltzmann method with application to electronics cooling. Int. J. Heat Mass Transfer 49, 97–107 (2006)MATH R.A. Escobar, S.S. Ghai, M.S. Jhon, C.H. Amon, Multi-length and time scale thermal transport using the lattice Boltzmann method with application to electronics cooling. Int. J. Heat Mass Transfer 49, 97–107 (2006)MATH
68.
go back to reference E.M. Sparrow, R.D. Cess, Radiation Heat Transfer, Augmented edn. (McGraw-Hill, New York, 1978) E.M. Sparrow, R.D. Cess, Radiation Heat Transfer, Augmented edn. (McGraw-Hill, New York, 1978)
69.
go back to reference M.F. Modest, Radiative Heat Transfer, 3rd edn. (Academic Press, New York, 2013) M.F. Modest, Radiative Heat Transfer, 3rd edn. (Academic Press, New York, 2013)
70.
go back to reference T.J. Bright, Z.M. Zhang, Entropy generation in thin films evaluated from phonon radiative transport. J. Heat Transfer 132, 101301 (2010) T.J. Bright, Z.M. Zhang, Entropy generation in thin films evaluated from phonon radiative transport. J. Heat Transfer 132, 101301 (2010)
71.
go back to reference H.B.G. Casimir, Note on the conduction of heat in crystal. Physica 5, 495–500 (1938) H.B.G. Casimir, Note on the conduction of heat in crystal. Physica 5, 495–500 (1938)
72.
go back to reference R.G. Deissler, Diffusion approximation for thermal radiation in gasses with jump boundary condition. J. Heat Transfer 86, 240–245 (1964) R.G. Deissler, Diffusion approximation for thermal radiation in gasses with jump boundary condition. J. Heat Transfer 86, 240–245 (1964)
73.
go back to reference A. Malhotra, K. Kothari, M. Maldovan, Cross-plane thermal conduction in superlattices: Impact of multiple length scales on phonon transport. J. Appl. Phys. 125, 044304 (2019) A. Malhotra, K. Kothari, M. Maldovan, Cross-plane thermal conduction in superlattices: Impact of multiple length scales on phonon transport. J. Appl. Phys. 125, 044304 (2019)
74.
go back to reference K. Kothari, A. Malhotra, M. Maldovan, Cross-plane heat conduction in III–V semiconductor superlattices. J. Phys. Condens. Matter 31, 345301 (2019) K. Kothari, A. Malhotra, M. Maldovan, Cross-plane heat conduction in III–V semiconductor superlattices. J. Phys. Condens. Matter 31, 345301 (2019)
75.
go back to reference M.M. Yovanovich, Four decades of research on thermal contact, gap, and joint resistance in microelectronics. IEEE Trans. Compon. Packag. Technol. 28, 182–206 (2005) M.M. Yovanovich, Four decades of research on thermal contact, gap, and joint resistance in microelectronics. IEEE Trans. Compon. Packag. Technol. 28, 182–206 (2005)
76.
go back to reference R.J. Stoner, H.J. Maris, Kapitza conductance and heat flow between solids at temperatures from 50 to 300 K. Phys. Rev. B 48, 16373–16387 (1993) R.J. Stoner, H.J. Maris, Kapitza conductance and heat flow between solids at temperatures from 50 to 300 K. Phys. Rev. B 48, 16373–16387 (1993)
77.
go back to reference R.S. Prasher and P.E. Phelan, “Review of thermal boundary resistance of high-temperature superconductors,” J. Supercond., 10, 473–484, 1997 R.S. Prasher and P.E. Phelan, “Review of thermal boundary resistance of high-temperature superconductors,” J. Supercond., 10, 473–484, 1997
78.
go back to reference P.E. Phelan, Application of diffuse mismatch theory to the prediction of thermal boundary resistance in thin-film high-Tc superconductors. J. Heat Transfer 120, 37–43 (1998) P.E. Phelan, Application of diffuse mismatch theory to the prediction of thermal boundary resistance in thin-film high-Tc superconductors. J. Heat Transfer 120, 37–43 (1998)
79.
go back to reference L. De Bellis, P.E. Phelan, R.S. Prasher, Variations of acoustic and diffuse mismatch models in predicting thermal-boundary resistance. J. Thermophys. Heat Transfer 14, 144–150 (2000) L. De Bellis, P.E. Phelan, R.S. Prasher, Variations of acoustic and diffuse mismatch models in predicting thermal-boundary resistance. J. Thermophys. Heat Transfer 14, 144–150 (2000)
80.
go back to reference A. Majumdar, Effect of interfacial roughness on phonon radiative heat conduction. J. Heat Transfer 113, 797–805 (1991) A. Majumdar, Effect of interfacial roughness on phonon radiative heat conduction. J. Heat Transfer 113, 797–805 (1991)
81.
go back to reference A. Majumdar, P. Reddy, Role of electron–phonon coupling in thermal conductance of metal–nonmetal interfaces. Appl. Phys. Lett. 84, 4768–4770 (2004) A. Majumdar, P. Reddy, Role of electron–phonon coupling in thermal conductance of metal–nonmetal interfaces. Appl. Phys. Lett. 84, 4768–4770 (2004)
82.
go back to reference A. Giri, P.E. Hopkins, A review of experimental and computational advances in thermal boundary conductance and nanoscale thermal transport across solid interfaces. Adv. Func. Mater. 2019, 1903857 (2019) A. Giri, P.E. Hopkins, A review of experimental and computational advances in thermal boundary conductance and nanoscale thermal transport across solid interfaces. Adv. Func. Mater. 2019, 1903857 (2019)
83.
go back to reference S. Mazumdar, A. Majumdar, Monte Carlo study of phonon transport in solid thin films including dispersion and polarization. J. Heat Transfer 123, 749–759 (2001) S. Mazumdar, A. Majumdar, Monte Carlo study of phonon transport in solid thin films including dispersion and polarization. J. Heat Transfer 123, 749–759 (2001)
84.
go back to reference Q. Hao, G. Chen, M.-S. Jeng, Frequency-dependent Monte Carlo simulations of phonon transport in two-dimensional porous silicon with aligned pores. J. Appl. Phys. 106, 114321 (2009) Q. Hao, G. Chen, M.-S. Jeng, Frequency-dependent Monte Carlo simulations of phonon transport in two-dimensional porous silicon with aligned pores. J. Appl. Phys. 106, 114321 (2009)
85.
go back to reference J.-P.M. Péraud, C.D. Landon, N.G. Hadjiconstantinou, Monte Carlo methods for solving the Boltzmann transport equation. Annu. Rev. Heat Transfer 17, 205–265 (2014) J.-P.M. Péraud, C.D. Landon, N.G. Hadjiconstantinou, Monte Carlo methods for solving the Boltzmann transport equation. Annu. Rev. Heat Transfer 17, 205–265 (2014)
86.
go back to reference A. Nabovati, D.P. Sellan, C.H. Amon, On the lattice Boltzmann method for phonon transport. J. Comput. Phys. 230, 5864–5876 (2011)MathSciNetMATH A. Nabovati, D.P. Sellan, C.H. Amon, On the lattice Boltzmann method for phonon transport. J. Comput. Phys. 230, 5864–5876 (2011)MathSciNetMATH
87.
go back to reference S.R. Phillpot, P.K. Schelling, P. Keblinski, Phonon wave-packet dynamics at semiconductor interfaces by molecular-dynamics simulation. Appl. Phys. Lett. 80, 2484–2486 (2002); ibid, Interfacial thermal conductivity: Insights from atomic level simulation. J. Mater. Sci. 40, 3143–3148 (2005) S.R. Phillpot, P.K. Schelling, P. Keblinski, Phonon wave-packet dynamics at semiconductor interfaces by molecular-dynamics simulation. Appl. Phys. Lett. 80, 2484–2486 (2002); ibid, Interfacial thermal conductivity: Insights from atomic level simulation. J. Mater. Sci. 40, 3143–3148 (2005)
88.
go back to reference C.-J. Twu, J.-R. Ho, Molecular-dynamics study of energy flow and the Kapitza conductance across an interface with imperfection formed by two dielectric thin films. Phys. Rev. B 67, 205422 (2003) C.-J. Twu, J.-R. Ho, Molecular-dynamics study of energy flow and the Kapitza conductance across an interface with imperfection formed by two dielectric thin films. Phys. Rev. B 67, 205422 (2003)
89.
go back to reference H. Zhong, J.R. Lukes, Interfacial thermal resistance between carbon nanotubes: Molecular dynamics simulations and analytical thermal modeling. Phys. Rev. B 74, 125403 (2006) H. Zhong, J.R. Lukes, Interfacial thermal resistance between carbon nanotubes: Molecular dynamics simulations and analytical thermal modeling. Phys. Rev. B 74, 125403 (2006)
90.
go back to reference R.J. Stevens, L.V. Zhigilei, P.M. Norris, Effects of temperature and disorder on thermal boundary conductance at solid-solid interfaces: non-equilibrium molecular dynamics simulations. Int. J. Heat Mass Transfer 50, 3977–3989 (2007)MATH R.J. Stevens, L.V. Zhigilei, P.M. Norris, Effects of temperature and disorder on thermal boundary conductance at solid-solid interfaces: non-equilibrium molecular dynamics simulations. Int. J. Heat Mass Transfer 50, 3977–3989 (2007)MATH
91.
go back to reference E.S. Landry, A.J.H. McGaughey, Thermal boundary resistance predictions from molecular dynamics simulations and theoretical calculations. Phys. Rev. B 80, 165304 (2009) E.S. Landry, A.J.H. McGaughey, Thermal boundary resistance predictions from molecular dynamics simulations and theoretical calculations. Phys. Rev. B 80, 165304 (2009)
92.
go back to reference Y. Chalopin, K. Esfarjani, A. Henry, S. Volz, G. Chen, Thermal interface conductance in Si/Ge superlattices by equilibrium molecular dynamics. Phys. Rev. B 85, 195302 (2012) Y. Chalopin, K. Esfarjani, A. Henry, S. Volz, G. Chen, Thermal interface conductance in Si/Ge superlattices by equilibrium molecular dynamics. Phys. Rev. B 85, 195302 (2012)
93.
go back to reference S. Merabia, K. Termentzidis, Thermal conductance at the interface between crystals using equilibrium and nonequilibrium molecular dynamics. Phys. Rev. B 86, 094303 (2012) S. Merabia, K. Termentzidis, Thermal conductance at the interface between crystals using equilibrium and nonequilibrium molecular dynamics. Phys. Rev. B 86, 094303 (2012)
94.
go back to reference Z. Liang, M. Hu, Tutorial: Determination of thermal boundary resistance by molecular dynamics simulations. J. Appl. Phys. 123, 191101 (2018) Z. Liang, M. Hu, Tutorial: Determination of thermal boundary resistance by molecular dynamics simulations. J. Appl. Phys. 123, 191101 (2018)
95.
go back to reference F. VanGessel, J. Peng, P.W. Chung, A review of computational phononics: the bulk, interfaces, and surfaces. J. Mater. Sci. 53, 5641–5683 (2018) F. VanGessel, J. Peng, P.W. Chung, A review of computational phononics: the bulk, interfaces, and surfaces. J. Mater. Sci. 53, 5641–5683 (2018)
96.
go back to reference S. Datta, Nanoscale device modeling: the Green’s function method. Superlattices Microstruct. 28, 253–278 (2000) S. Datta, Nanoscale device modeling: the Green’s function method. Superlattices Microstruct. 28, 253–278 (2000)
97.
go back to reference N. Mingo, L. Yang, Phonon transport in nanowires coated with an amorphous material: an atomistic Green’s function approach. Phys. Rev. B 68, 245406 (2003) N. Mingo, L. Yang, Phonon transport in nanowires coated with an amorphous material: an atomistic Green’s function approach. Phys. Rev. B 68, 245406 (2003)
98.
go back to reference W. Zhang, T.S. Fisher, N. Mingo, Simulation of interfacial phonon transport in Si–Ge heterostructures using an atomistic Green’s function method. J. Heat Transfer 129, 483–491 (2007); ibid, The atomistic Green’s function method: an efficient simulation approach for nanoscale phonon transport. Numerical Heat Transfer B 51, 333–349 (2007) W. Zhang, T.S. Fisher, N. Mingo, Simulation of interfacial phonon transport in Si–Ge heterostructures using an atomistic Green’s function method. J. Heat Transfer 129, 483–491 (2007); ibid, The atomistic Green’s function method: an efficient simulation approach for nanoscale phonon transport. Numerical Heat Transfer B 51, 333–349 (2007)
99.
go back to reference S. Sadasivam, Y. Che, Z. Huang, L. Chen, S. Kumar, T.S. Fisher, The atomistic Green’s function method for interfacial phonon transport. Annu. Rev. Heat Transfer 17, 89–145 (2014) S. Sadasivam, Y. Che, Z. Huang, L. Chen, S. Kumar, T.S. Fisher, The atomistic Green’s function method for interfacial phonon transport. Annu. Rev. Heat Transfer 17, 89–145 (2014)
100.
go back to reference A. Ozpineci, S. Ciraci, Quantum effects of thermal conductance through atomic chains. Phys. Rev. B 63, 125415 (2001) A. Ozpineci, S. Ciraci, Quantum effects of thermal conductance through atomic chains. Phys. Rev. B 63, 125415 (2001)
101.
go back to reference Z.-Y. Ong, G. Zhang, Efficient approach for modeling phonon transmission probability in nanoscale interfacial thermal transport. Phys. Rev. B 91, 174302 (2015) Z.-Y. Ong, G. Zhang, Efficient approach for modeling phonon transmission probability in nanoscale interfacial thermal transport. Phys. Rev. B 91, 174302 (2015)
102.
go back to reference L. Yang, B. Latour, A.J. Minnich, Phonon transmission at crystalline-amorphous interfaces studied using mode-resolved atomistic Green’s functions. Phys. Rev. B 97, 205306 (2018) L. Yang, B. Latour, A.J. Minnich, Phonon transmission at crystalline-amorphous interfaces studied using mode-resolved atomistic Green’s functions. Phys. Rev. B 97, 205306 (2018)
103.
go back to reference D.A. Young, H.J. Maris, Lattice-dynamical calculation of the Kapitza resistance between fcc lattices. Phys. Rev. B 40, 3685–3693 (1989) D.A. Young, H.J. Maris, Lattice-dynamical calculation of the Kapitza resistance between fcc lattices. Phys. Rev. B 40, 3685–3693 (1989)
104.
go back to reference H. Zhao, J.B. Freund, Lattice-dynamical calculation of phonon scattering at ideal Si–Ge interfaces. J. Appl. Phys. 97, 024903 (2005) H. Zhao, J.B. Freund, Lattice-dynamical calculation of phonon scattering at ideal Si–Ge interfaces. J. Appl. Phys. 97, 024903 (2005)
105.
go back to reference S. Sadasivam, N. Ye, J.P. Feser, J. Charles, K. Miao, T. Kubis, T.S. Fisher, Thermal transport across metal silicide-silicon interfaces: First-principles calculations and Green’s function transport simulations. Phys. Rev. B 95, 085310 (2017) S. Sadasivam, N. Ye, J.P. Feser, J. Charles, K. Miao, T. Kubis, T.S. Fisher, Thermal transport across metal silicide-silicon interfaces: First-principles calculations and Green’s function transport simulations. Phys. Rev. B 95, 085310 (2017)
106.
go back to reference Z. Tian, K. Esfarjani, G. Chen, Green’s function studies of phonon transport across Si/Ge superlattices. Phys. Rev. B 89, 235307 (2014) Z. Tian, K. Esfarjani, G. Chen, Green’s function studies of phonon transport across Si/Ge superlattices. Phys. Rev. B 89, 235307 (2014)
107.
go back to reference Z. Yan, L. Chen, M. Yoon, S. Kumar, Phonon transport at the interfaces of vertically stacked graphene and hexagonal boron nitride heterostructures. Nanoscale 8, 4037 (2016) Z. Yan, L. Chen, M. Yoon, S. Kumar, Phonon transport at the interfaces of vertically stacked graphene and hexagonal boron nitride heterostructures. Nanoscale 8, 4037 (2016)
108.
go back to reference J. Lai, A. Majumdar, Concurrent thermal and electrical modeling of sub-micrometer silicon devices. J. Appl. Phys. 79, 7353–7361 (1996) J. Lai, A. Majumdar, Concurrent thermal and electrical modeling of sub-micrometer silicon devices. J. Appl. Phys. 79, 7353–7361 (1996)
109.
go back to reference P.G. Sverdrup, Y.S. Ju, K.E. Goodson, Sub-continuum simulation of heat conduction in silicon-on-insulator transistors. J. Heat Transfer 123, 130–137 (2001) P.G. Sverdrup, Y.S. Ju, K.E. Goodson, Sub-continuum simulation of heat conduction in silicon-on-insulator transistors. J. Heat Transfer 123, 130–137 (2001)
110.
go back to reference S. Sinha, E. Pop, R.W. Dutton, K.E. Goodson, Non-equilibrium phonon distribution in sub-100 nm silicon transistors. J. Heat Transfer 128, 638–647 (2006) S. Sinha, E. Pop, R.W. Dutton, K.E. Goodson, Non-equilibrium phonon distribution in sub-100 nm silicon transistors. J. Heat Transfer 128, 638–647 (2006)
111.
go back to reference C.D.S. Brites, P.P. Lima, N.J.O. Silva, A. Millán, V.S. Amaral, F. Palacio, L.D. Carlos, Thermometry at the nanoscale. Nanoscale 4, 4799–4829 (2012) C.D.S. Brites, P.P. Lima, N.J.O. Silva, A. Millán, V.S. Amaral, F. Palacio, L.D. Carlos, Thermometry at the nanoscale. Nanoscale 4, 4799–4829 (2012)
112.
go back to reference X.W. Wang, Experimental Micro/Nanoscale Thermal Transport (Wiley, New York, 2012) X.W. Wang, Experimental Micro/Nanoscale Thermal Transport (Wiley, New York, 2012)
113.
go back to reference A.J. McNamara, Y. Joshi, Z.M. Zhang, Characterization of nanostructured thermal interface materials—a review. Int. J. Thermal Sci. 62, 2–11 (2012) A.J. McNamara, Y. Joshi, Z.M. Zhang, Characterization of nanostructured thermal interface materials—a review. Int. J. Thermal Sci. 62, 2–11 (2012)
114.
go back to reference G. Chen, Probing nanoscale heat transfer phenomena. Annu. Rev. Heat Transfer 16, 1–8 (2013) G. Chen, Probing nanoscale heat transfer phenomena. Annu. Rev. Heat Transfer 16, 1–8 (2013)
115.
go back to reference D. Zhao, X. Qian, X. Gu, S.A. Jajja, R. Yang, Measurement techniques for thermal conductivity and interfacial thermal conductance of bulk and thin film materials. J. Electron. Package 138, 040802 (2016) D. Zhao, X. Qian, X. Gu, S.A. Jajja, R. Yang, Measurement techniques for thermal conductivity and interfacial thermal conductance of bulk and thin film materials. J. Electron. Package 138, 040802 (2016)
116.
go back to reference Z.M. Zhang, Surface temperature measurement using optical techniques. Annu. Rev. Heat Transfer 11, 351–411 (2000) Z.M. Zhang, Surface temperature measurement using optical techniques. Annu. Rev. Heat Transfer 11, 351–411 (2000)
117.
go back to reference B. Abad, D.-A. Borca-Tasciuc, M.S. Martin-Gonzalez, Non-contact methods for thermal properties measurement. Renew. Sustain. Energy Rev. 76, 1348–1370 (2017) B. Abad, D.-A. Borca-Tasciuc, M.S. Martin-Gonzalez, Non-contact methods for thermal properties measurement. Renew. Sustain. Energy Rev. 76, 1348–1370 (2017)
118.
go back to reference A.C. Jones, B.T. O’Callahan, H.U. Yang, M.B. Raschke, The thermal near-field: coherence, spectroscopy, heat-transfer, and optical forces. Prog. Sur. Sci. 88, 349–392 (2013) A.C. Jones, B.T. O’Callahan, H.U. Yang, M.B. Raschke, The thermal near-field: coherence, spectroscopy, heat-transfer, and optical forces. Prog. Sur. Sci. 88, 349–392 (2013)
119.
go back to reference K.E. Goodson, Y.S. Ju, Heat conduction in novel electronic films. Annu. Rev. Mater. Sci. 29, 261–293 (1999) K.E. Goodson, Y.S. Ju, Heat conduction in novel electronic films. Annu. Rev. Mater. Sci. 29, 261–293 (1999)
120.
go back to reference K. Park, G.L.W. Cross, Z.M. Zhang, W.P. King, Experimental investigation on the heat transfer between a heated microcantilever and a substrate. J. Heat Transfer 130, 102401 (2008) K. Park, G.L.W. Cross, Z.M. Zhang, W.P. King, Experimental investigation on the heat transfer between a heated microcantilever and a substrate. J. Heat Transfer 130, 102401 (2008)
121.
go back to reference D. G. Cahill and R. O. Pohl, “Thermal conductivity of amorphous solids above the plateau,” Phys. Rev. B, 35, 4067–4073, 1987 D. G. Cahill and R. O. Pohl, “Thermal conductivity of amorphous solids above the plateau,” Phys. Rev. B, 35, 4067–4073, 1987
122.
go back to reference D.G. Cahill, H.E. Fischer, T. Klitsner, E.T. Swartz, R.O. Pohl, Thermal conductivity of thin films: measurements and understanding. J. Vac. Sci. Technol. A 7, 1259–1266 (1989) D.G. Cahill, H.E. Fischer, T. Klitsner, E.T. Swartz, R.O. Pohl, Thermal conductivity of thin films: measurements and understanding. J. Vac. Sci. Technol. A 7, 1259–1266 (1989)
123.
go back to reference D.G. Cahill, Thermal conductivity measurement from 30 K to 750 K: the 3-omega method. Rev. Sci. Instrum. 61, 802–808 (1990) D.G. Cahill, Thermal conductivity measurement from 30 K to 750 K: the 3-omega method. Rev. Sci. Instrum. 61, 802–808 (1990)
124.
go back to reference C. Dames, Measuring the thermal conductivity of thin films: 3 omega and related electrothermal methods. Annu. Rev. Heat Transfer 16, 7–49 (2013) C. Dames, Measuring the thermal conductivity of thin films: 3 omega and related electrothermal methods. Annu. Rev. Heat Transfer 16, 7–49 (2013)
125.
go back to reference S. Kommandur, S.K. Yee, A suspended 3-omega technique to measure the anisotropic thermal conductivity of semiconducting polymers. Rev. Sci. Instrum. 89, 114905 (2018) S. Kommandur, S.K. Yee, A suspended 3-omega technique to measure the anisotropic thermal conductivity of semiconducting polymers. Rev. Sci. Instrum. 89, 114905 (2018)
126.
go back to reference L. Shi, D. Li, C. Yu, W. Jang, D. Kim, Z. Yao, P. Kim, A. Majumdar, Measuring thermal and thermoelectric properties of one-dimensional nanostructures using a microfabricated device. J. Heat Transfer 125, 881–888 (2003) L. Shi, D. Li, C. Yu, W. Jang, D. Kim, Z. Yao, P. Kim, A. Majumdar, Measuring thermal and thermoelectric properties of one-dimensional nanostructures using a microfabricated device. J. Heat Transfer 125, 881–888 (2003)
127.
go back to reference P. Kim, L. Shi, A. Majumdar, P.L. McEuen, Thermal transport measurements of individual multiwalled nanotubes. Phys. Rev. Lett. 87, 215502 (2001) P. Kim, L. Shi, A. Majumdar, P.L. McEuen, Thermal transport measurements of individual multiwalled nanotubes. Phys. Rev. Lett. 87, 215502 (2001)
128.
go back to reference C. Yu, L. Shi, Z. Yao, D. Li, A. Majumdar, Thermal conductance and thermopower of an individual single-wall carbon nanotube. Nano Lett. 5, 1842–1846 (2005) C. Yu, L. Shi, Z. Yao, D. Li, A. Majumdar, Thermal conductance and thermopower of an individual single-wall carbon nanotube. Nano Lett. 5, 1842–1846 (2005)
129.
go back to reference A. Mavrokefalos, M.T. Pettes, F. Zhou, L. Shi, Four-probe measurements of the in-plane thermoelectric properties of nanofilms. Rev. Sci. Instrum. 78, 034901 (2007) A. Mavrokefalos, M.T. Pettes, F. Zhou, L. Shi, Four-probe measurements of the in-plane thermoelectric properties of nanofilms. Rev. Sci. Instrum. 78, 034901 (2007)
130.
go back to reference A. Weathers, L. Shi, Thermal transport measurement techniques for nanowires and nanotubes. Annu. Rev. Heat Transfer 16, 101–134 (2013) A. Weathers, L. Shi, Thermal transport measurement techniques for nanowires and nanotubes. Annu. Rev. Heat Transfer 16, 101–134 (2013)
131.
go back to reference M. Fujii, X. Zhang, H. Xie, H. Ago, K. Takahashi, T. Ikuta, H. Abe, T. Shimizu, Measuring the thermal conductivity of a single carbon nanotube. Phys. Rev. Lett. 95, 065502 (2005) M. Fujii, X. Zhang, H. Xie, H. Ago, K. Takahashi, T. Ikuta, H. Abe, T. Shimizu, Measuring the thermal conductivity of a single carbon nanotube. Phys. Rev. Lett. 95, 065502 (2005)
132.
go back to reference J. Kim, E. Ou, D.P. Sellan, L. Shi, A four-probe thermal transport measurement method for nanostructures. Rev. Sci. Instrum. 86, 044901 (2015) J. Kim, E. Ou, D.P. Sellan, L. Shi, A four-probe thermal transport measurement method for nanostructures. Rev. Sci. Instrum. 86, 044901 (2015)
133.
go back to reference J. Kim, D.A. Evans, D.P. Sellan, O.M. Williams, E. Ou, A.H. Cowley, L. Shi, Thermal and thermoelectric transport measurements of an individual boron arsenide microstructure. Appl. Phys. Lett. 108, 201905 (2016) J. Kim, D.A. Evans, D.P. Sellan, O.M. Williams, E. Ou, A.H. Cowley, L. Shi, Thermal and thermoelectric transport measurements of an individual boron arsenide microstructure. Appl. Phys. Lett. 108, 201905 (2016)
134.
go back to reference A. Majumdar, Scanning thermal microscopy. Annu. Rev. Mater. Sci. 29, 505–585 (1999) A. Majumdar, Scanning thermal microscopy. Annu. Rev. Mater. Sci. 29, 505–585 (1999)
135.
go back to reference A. Majumdar, J. P. Carrejo, J. Lai, Thermal imaging using the atomic force microscope. Appl. Phys. Lett. 62, 2501–2503 (1993) A. Majumdar, J. P. Carrejo, J. Lai, Thermal imaging using the atomic force microscope. Appl. Phys. Lett. 62, 2501–2503 (1993)
136.
go back to reference A. Majumdar, J. Lai, M. Chandrachood, O. Nakabeppu, Y. Wu, J. Shi, Thermal imaging by atomic force microscopy using thermocouple cantilever probes. Rev. Sci. Instrum. 66, 3584–3592 (1995) A. Majumdar, J. Lai, M. Chandrachood, O. Nakabeppu, Y. Wu, J. Shi, Thermal imaging by atomic force microscopy using thermocouple cantilever probes. Rev. Sci. Instrum. 66, 3584–3592 (1995)
137.
go back to reference C.C. Williams, H.K. Wickramasinghe, Scanning thermal profiler. Appl. Phys. Lett. 49, 1587–1589 (1986) C.C. Williams, H.K. Wickramasinghe, Scanning thermal profiler. Appl. Phys. Lett. 49, 1587–1589 (1986)
138.
go back to reference A. Majumdar, J. Varesi, Nanoscale temperature distribution measured by scanning Joule expansion microscopy. J. Heat Transfer 120, 297–305 (1998) A. Majumdar, J. Varesi, Nanoscale temperature distribution measured by scanning Joule expansion microscopy. J. Heat Transfer 120, 297–305 (1998)
139.
go back to reference S.P. Gurrum, W.P. King, Y.K. Joshi, K. Ramakrishna, Size effect on the thermal conductivity of thin metallic films investigated by scanning Joule expansion microscopy. J. Heat Transfer 130, 082403 (2008) S.P. Gurrum, W.P. King, Y.K. Joshi, K. Ramakrishna, Size effect on the thermal conductivity of thin metallic films investigated by scanning Joule expansion microscopy. J. Heat Transfer 130, 082403 (2008)
140.
go back to reference K.L. Grosse, M.-H. Bae, F. Lian, E. Pop, W.P. King, Nanoscale Joule heating, Peltier cooling and current crowding at graphene-metal contacts. Nat. Nanotech. 6, 287–290 (2011) K.L. Grosse, M.-H. Bae, F. Lian, E. Pop, W.P. King, Nanoscale Joule heating, Peltier cooling and current crowding at graphene-metal contacts. Nat. Nanotech. 6, 287–290 (2011)
141.
go back to reference T. Borca-Tasciuc, Scanning probe methods for thermal and thermoelectric property measurements. Annu. Rev. Heat Transfer 16, 211–258 (2013) T. Borca-Tasciuc, Scanning probe methods for thermal and thermoelectric property measurements. Annu. Rev. Heat Transfer 16, 211–258 (2013)
142.
go back to reference S. Gomès, A. Assy, P.-O. Chapuis, Scanning thermal microscopy: a review. Phys. Status Solidi A 212, 477–494 (2015) S. Gomès, A. Assy, P.-O. Chapuis, Scanning thermal microscopy: a review. Phys. Status Solidi A 212, 477–494 (2015)
143.
go back to reference K. Kim, J. Chung, G. Hwang, O. Kwon, J.S. Lee, Quantitative measurement with scanning thermal microscope by preventing the distortion due to the heat transfer through the air. ACS Nano 11, 8700–8709 (2011) K. Kim, J. Chung, G. Hwang, O. Kwon, J.S. Lee, Quantitative measurement with scanning thermal microscope by preventing the distortion due to the heat transfer through the air. ACS Nano 11, 8700–8709 (2011)
144.
go back to reference H.F. Hamann, Y.C. Martin, H.K. Wickramasinghe, Thermally assisted recording beyond traditional limits. Appl. Phys. Lett. 84, 810–812 (2004) H.F. Hamann, Y.C. Martin, H.K. Wickramasinghe, Thermally assisted recording beyond traditional limits. Appl. Phys. Lett. 84, 810–812 (2004)
145.
go back to reference W.P. King, T.W. Kenny, K.E. Goodson et al., Atomic force microscope cantilevers for combined thermomechanical data writing and reading. Appl. Phys. Lett. 78, 1300–1302 (2001) W.P. King, T.W. Kenny, K.E. Goodson et al., Atomic force microscope cantilevers for combined thermomechanical data writing and reading. Appl. Phys. Lett. 78, 1300–1302 (2001)
146.
go back to reference J. Lee, T. Beechem, T. L. Wright, B. A. Nelson, S. Graham, W. P. King, Electrical, thermal, and, mechanical characterization of silicon microcantilever heaters. J. Microelectromech. Syst. 15, 1644 (2007) J. Lee, T. Beechem, T. L. Wright, B. A. Nelson, S. Graham, W. P. King, Electrical, thermal, and, mechanical characterization of silicon microcantilever heaters. J. Microelectromech. Syst. 15, 1644 (2007)
147.
go back to reference J. Lee, T.L. Wright, M.R. Abel et al., Thermal conduction from microcantilever heaters in partial vacuum. J. Appl. Phys. 101, 014906 (2007) J. Lee, T.L. Wright, M.R. Abel et al., Thermal conduction from microcantilever heaters in partial vacuum. J. Appl. Phys. 101, 014906 (2007)
148.
go back to reference K. Park, J. Lee, Z.M. Zhang, W.P. King, Frequency-dependent electrical and thermal response of heated atomic force microscope cantilevers. J. Microelectromech. Syst. 16, 213–222 (2007) K. Park, J. Lee, Z.M. Zhang, W.P. King, Frequency-dependent electrical and thermal response of heated atomic force microscope cantilevers. J. Microelectromech. Syst. 16, 213–222 (2007)
149.
go back to reference K. Park, A. Marchenkov, Z.M. Zhang, W.P. King, Low temperature characterization of heated microcantilevers. J. Appl. Phys. 101, 094504 (2007) K. Park, A. Marchenkov, Z.M. Zhang, W.P. King, Low temperature characterization of heated microcantilevers. J. Appl. Phys. 101, 094504 (2007)
150.
go back to reference W.P. King, B. Bhatia, J.R. Felts, H.J. Kim, B. Kwon, B. Lee, S. Somnath, M. Rosenberger, Heated atomic force microscope cantilevers and their applications. Annu. Rev. Heat Transfer 16, 287–326 (2013) W.P. King, B. Bhatia, J.R. Felts, H.J. Kim, B. Kwon, B. Lee, S. Somnath, M. Rosenberger, Heated atomic force microscope cantilevers and their applications. Annu. Rev. Heat Transfer 16, 287–326 (2013)
151.
go back to reference A.J. Schmidt, X. Chen, G. Chen, Pulse accumulation, radial heat conduction, and anisotropic thermal conductivity in pump-probe transient thermoreflectance. Rev. Sci. Instrum. 79, 114802 (2008) A.J. Schmidt, X. Chen, G. Chen, Pulse accumulation, radial heat conduction, and anisotropic thermal conductivity in pump-probe transient thermoreflectance. Rev. Sci. Instrum. 79, 114802 (2008)
152.
go back to reference A.J. Minnich, Measuring phonon mean free paths using thermal conductivity spectroscopy. Annu. Rev. Heat Transfer 16, 183–210 (2013) A.J. Minnich, Measuring phonon mean free paths using thermal conductivity spectroscopy. Annu. Rev. Heat Transfer 16, 183–210 (2013)
153.
go back to reference J. Zhu, H. Park, J.-Y. Chen et al., Revealing the origins of 3D anisotropic thermal conductivities of black phosphorus. Adv. Electron. Mater. 2, 1600040 (2016) J. Zhu, H. Park, J.-Y. Chen et al., Revealing the origins of 3D anisotropic thermal conductivities of black phosphorus. Adv. Electron. Mater. 2, 1600040 (2016)
154.
go back to reference P. Jiang, X. Qian, R. Yang, Tutorial: time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials. J. Appl. Phys. 124, 161103 (2018) P. Jiang, X. Qian, R. Yang, Tutorial: time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials. J. Appl. Phys. 124, 161103 (2018)
155.
go back to reference Z. Cheng, T. Bougher, T. Bai et al., Probing growth-induced anisotropic thermal transport in high-quality CVD diamond membranes by multifrequency and multiple-spot-size time-domain thermoreflectance. ACS Appl. Mater. Interfaces. 10, 4808–4815 (2018) Z. Cheng, T. Bougher, T. Bai et al., Probing growth-induced anisotropic thermal transport in high-quality CVD diamond membranes by multifrequency and multiple-spot-size time-domain thermoreflectance. ACS Appl. Mater. Interfaces. 10, 4808–4815 (2018)
156.
go back to reference S. Huxtable, D.G. Cahill, V. Fauconnier, J.O. White, J.-C. Zhao, Thermal conductivity imaging at micrometrescale resolution for combinatorial studies of materials. Nat. Mater. 3, 298–301 (2004) S. Huxtable, D.G. Cahill, V. Fauconnier, J.O. White, J.-C. Zhao, Thermal conductivity imaging at micrometrescale resolution for combinatorial studies of materials. Nat. Mater. 3, 298–301 (2004)
157.
go back to reference D.G. Cahill, Analysis of heat flow in layered structures for time-domain thermoreflectance. Rev. Sci. Instrum. 75, 5119–5122 (2004) D.G. Cahill, Analysis of heat flow in layered structures for time-domain thermoreflectance. Rev. Sci. Instrum. 75, 5119–5122 (2004)
158.
go back to reference J. Jeong, X. Meng, A. K. Rockwell et al., Picosecond transient thermoreflectance for thermal conductivity characterization. Nanoscale Microscale Thermophys. Eng. 23, 211−221 (2019) J. Jeong, X. Meng, A. K. Rockwell et al., Picosecond transient thermoreflectance for thermal conductivity characterization. Nanoscale Microscale Thermophys. Eng. 23, 211−221 (2019)
159.
go back to reference P.M. Norris, A.P. Caffrey, R.J. Stevens, J.M. Klopf, J.T. McLeskey, A.N. Smith, Femtosecond pump–probe nondestructive examination of materials. Rev. Sci. Instrum. 74, 400–406 (2003) P.M. Norris, A.P. Caffrey, R.J. Stevens, J.M. Klopf, J.T. McLeskey, A.N. Smith, Femtosecond pump–probe nondestructive examination of materials. Rev. Sci. Instrum. 74, 400–406 (2003)
160.
go back to reference K.E. Goodson, M. Asheghi, Near-field optical thermometry. Microscale Thermophys. Eng. 1, 225–235 (1997) K.E. Goodson, M. Asheghi, Near-field optical thermometry. Microscale Thermophys. Eng. 1, 225–235 (1997)
161.
go back to reference D. Seto, R. Nikka, S. Nishio, Y. Taguchi, T. Saiki, Y. Nagasaka, Nanoscale optical thermometry using a time-correlated single-photon counting in an illumination-collection mode. Appl. Phys. Lett. 110, 033109 (2017) D. Seto, R. Nikka, S. Nishio, Y. Taguchi, T. Saiki, Y. Nagasaka, Nanoscale optical thermometry using a time-correlated single-photon counting in an illumination-collection mode. Appl. Phys. Lett. 110, 033109 (2017)
162.
go back to reference M.E. Siemens, Q. Li, R. Yang, 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, 26–30 (2010) M.E. Siemens, Q. Li, R. Yang, 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, 26–30 (2010)
163.
go back to reference T. Favaloro, J.-H. Bahk, A. Shakouri, Characterization of the temperature dependence of the thermoreflectance coefficient for conductive thin films. Rev. Sci. Instrum. 86, 024903 (2015) T. Favaloro, J.-H. Bahk, A. Shakouri, Characterization of the temperature dependence of the thermoreflectance coefficient for conductive thin films. Rev. Sci. Instrum. 86, 024903 (2015)
164.
go back to reference C. Wei, X. Zheng, D.G. Cahill, J.-C. Zhao, Invited article: Micron resolution spatially resolved measurement of heat capacity using dual-frequency time-domain thermoreflectance. Rev. Sci. Instrum. 84, 071301 (2013) C. Wei, X. Zheng, D.G. Cahill, J.-C. Zhao, Invited article: Micron resolution spatially resolved measurement of heat capacity using dual-frequency time-domain thermoreflectance. Rev. Sci. Instrum. 84, 071301 (2013)
165.
go back to reference P.E. Hopkins, C.M. Reinke, M.F. Su, R.H. Olsson III, E.A. Shaner, Z.C. Leseman, J.R. Serrano, L.M. Phinney, I. El-Kady, Reduction in the thermal conductivity of single crystalline silicon by phononic crystal patterning. Nano Lett. 11, 107–112 (2011) P.E. Hopkins, C.M. Reinke, M.F. Su, R.H. Olsson III, E.A. Shaner, Z.C. Leseman, J.R. Serrano, L.M. Phinney, I. El-Kady, Reduction in the thermal conductivity of single crystalline silicon by phononic crystal patterning. Nano Lett. 11, 107–112 (2011)
166.
go back to reference M.R. Wagner, B. Graczykowski, J.S. Reparaz et al., Two-dimensional photonic crystals: Disorder matters. Nano Lett. 16, 5661–5668 (2016) M.R. Wagner, B. Graczykowski, J.S. Reparaz et al., Two-dimensional photonic crystals: Disorder matters. Nano Lett. 16, 5661–5668 (2016)
167.
go back to reference X. Wang, T. Mori, I. Kuzmych-Ianchuk, Y. Michiue, K. Yubuta, T. Shishido, Y. Grin, S. Okada, D.G. Cahill, Thermal conductivity of layered borides: The effect of building defects on the thermal conductivity of TmAlB4 and the anisotropic thermal conductivity of AlB2. APL Mater. 2, 046113 (2014) X. Wang, T. Mori, I. Kuzmych-Ianchuk, Y. Michiue, K. Yubuta, T. Shishido, Y. Grin, S. Okada, D.G. Cahill, Thermal conductivity of layered borides: The effect of building defects on the thermal conductivity of TmAlB4 and the anisotropic thermal conductivity of AlB2. APL Mater. 2, 046113 (2014)
168.
go back to reference J. Liu, G.-M. Choi, D.G. Cahill, Measurement of the anisotropic thermal conductivity of molybdenum disulfide by the time-resolved magneto-optic Kerr effect. J. Appl. Phys. 116, 233107 (2014) J. Liu, G.-M. Choi, D.G. Cahill, Measurement of the anisotropic thermal conductivity of molybdenum disulfide by the time-resolved magneto-optic Kerr effect. J. Appl. Phys. 116, 233107 (2014)
169.
go back to reference A. J. Schmidt, R. Cheaito, M. Chiesa, A frequency-domain thermoreflectance method for the characterization of thermal properties. Rev. Sci. Instrum. 80, 094901 (2009); ibid, Characterization of thin metal films via frequency-domain thermoreflectance. J. Appl. Phys. 107, 024908 (2010) A. J. Schmidt, R. Cheaito, M. Chiesa, A frequency-domain thermoreflectance method for the characterization of thermal properties. Rev. Sci. Instrum. 80, 094901 (2009); ibid, Characterization of thin metal films via frequency-domain thermoreflectance. J. Appl. Phys. 107, 024908 (2010)
170.
go back to reference K.T. Regner, D.P. Sellan, Z. Su, C.H. Amon, A.J.H. McGaughey, J.A. Malen, Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance. Nat. Commun. 4, 1640 (2013) K.T. Regner, D.P. Sellan, Z. Su, C.H. Amon, A.J.H. McGaughey, J.A. Malen, Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance. Nat. Commun. 4, 1640 (2013)
171.
go back to reference D. Rodin, S.K. Yee, Simultaneous measurement of in-plane and through-plane thermal conductivity using beam-offset frequency domain thermoreflectance. Rev. Sci. Instrum. 88, 014902 (2017) D. Rodin, S.K. Yee, Simultaneous measurement of in-plane and through-plane thermal conductivity using beam-offset frequency domain thermoreflectance. Rev. Sci. Instrum. 88, 014902 (2017)
172.
go back to reference J. Johnson, A. A. Maznev, J. Cuffe, J. K. Eliason, A. J. Minnich, T. Kehoe, C. M. Sotomayor 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) J. Johnson, A. A. Maznev, J. Cuffe, J. K. Eliason, A. J. Minnich, T. Kehoe, C. M. Sotomayor 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)
173.
go back to reference J. Cuffe, J.K. Eliason, A.A. Maznev et al., Reconstructing phonon mean-free-path contributions to thermal conductivity using nanoscale membranes. Phys. Rev. B 91, 245423 (2015) J. Cuffe, J.K. Eliason, A.A. Maznev et al., Reconstructing phonon mean-free-path contributions to thermal conductivity using nanoscale membranes. Phys. Rev. B 91, 245423 (2015)
174.
go back to reference A. Vega-Flick, R.A. Duncan, J.K. Eliason et al., Thermal transport in suspended silicon membranes measured by laser-induced transient gratings. AIP Adv. 6, 120903 (2016) A. Vega-Flick, R.A. Duncan, J.K. Eliason et al., Thermal transport in suspended silicon membranes measured by laser-induced transient gratings. AIP Adv. 6, 120903 (2016)
Metadata
Title
Nonequilibrium Energy Transfer in Nanostructures
Author
Zhuomin M. Zhang
Copyright Year
2020
DOI
https://doi.org/10.1007/978-3-030-45039-7_7

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