Abstract
Control and modelling of thermal transport at the nanoscale has emerged either as a key issue in modern nanoscience or as a compelling demand for the ever-increasing miniaturization process in information technologies: here the thermal budget of nanodevices is basically ruled over by heat exchanges across interfaces, and the relevant physics is cast in terms of a thermal boundary resistance. In this chapter, we present a unified discussion about the fundamental knowledge developed in this framework. Starting from the most general thermodynamical description of an interface, where the driving force for heat transport is identified together with the actual location and thickness of the interface itself, we define what the thermal boundary resistance is in fact. We then delve into the most successful modelling approaches, based either on the phonon picture or on the atomistic picture. Adopting different assumptions and employing different implementation strategies, they offer a complementary description of the physical mechanisms underlying thermal boundary resistance, and they provide useful computational protocols to predict its value in realistic systems.
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References
Balandin AA (2002) Nanoscale thermal management. IEEE Potentials 21(1):11–15. https://doi.org/10.1109/45.985321
Cahill DG, Ford WK, Goodson KE, Mahan GD, Majumdar A, Maris HJ, Merlin R, Phillpot SR (2003) Nanoscale thermal transport. J Appl Phys 93(2):793–818. https://doi.org/10.1063/1.1524305
Cahill DG, Braun PV, Chen G, Clarke DR, Fan S, Goodson KE, Keblinski P, King WP, Mahan GD, Majumdar A, Maris HJ, Phillpot SR, Pop E, Shi L (2014) Nanoscale thermal transport. II. 2003–2012. Appl Phys Rev 1(1):011305. https://doi.org/10.1063/1.4832615
Chen G (2005) Nanoscale energy transport and conversion: a parallel treatment of electrons, molecules, phonons, and photons. MIT-Pappalardo series in mechanical engineering. Oxford University Press. https://books.google.it/books?id=M3n3lUJpYDYC
Chen J, Zhang G, Li B (2012) Thermal contact resistance across nanoscale silicon dioxide and silicon interface. J Appl Phys 112(6):064319. https://doi.org/10.1063/1.4754513
Dames C (2009) Solid-state thermal rectification with existing bulk materials. J Heat Trans 131(6):061301
Dresselhaus M, Chen G, Tang M, Yang R, Lee H, Wang D, Ren Z, Fleurial JP, Gogna P (2007) New directions for low-dimensional thermoelectric materials. Adv Mater 19(8):1043–1053. https://doi.org/10.1002/adma.200600527
Fan Z, Pereira LFC, Wang HQ, Zheng JC, Donadio D, Harju A (2015) Force and heat current formulas for many-body potentials in molecular dynamics simulations with applications to thermal conductivity calculations. Phys Rev B 92:094301. https://link.aps.org/doi/10.1103/PhysRevB.92.094301
Finnis M (2003) Interatomic forces in condensed matter. EBSCO ebook academic collection. Oxford University Press. https://books.google.it/books?id=RNFmvsWQmZoC
Frenkel D, Smit B (eds) (1996) Understanding molecular simulation: from algorithms to applications, 1st edn. Academic Press, Orlando
Hardy RJ (1963) Energy-flux operator for a lattice. Phys Rev 132:168–177. https://link.aps.org/doi/10.1103/PhysRev.132.168
He Y, Savic I, Donadio D, Galli G (2012) Lattice thermal conductivity of semiconducting bulk materials: atomistic simulations. Phys Chem Chem Phys 14:16209–16222. https://doi.org/10.1039/C2CP42394D
Hopkins PE (2013) Thermal transport across solid interfaces with nanoscale imperfections: effects of roughness, disorder, dislocations, and bonding on thermal boundary conductance. ISRN Mech Eng 2013, 682586. https://doi.org/10.1155/2/682586
Kapitza PL (1941) Heat transfer and superfluidity of helium II. Phys Rev 60:354–355. https://link.aps.org/doi/10.1103/PhysRev.60.354
Kinaci A, Haskins JB, Cagin T (2012) On calculation of thermal conductivity from Einstein relation in equilibrium molecular dynamics. J Chem Phys 137(1):014106. https://doi.org/10.1063/1.4731450
Kittel C, Kroemer H (1980) Thermal physics. W. H. Freeman. https://books.google.it/books?id=c0R79nyOoNMC
Kjelstrup S, Bedeaux D (2008) Non-equilibrium thermodynamics of heterogeneous systems. Series on advances in statistical mechanics. World Scientific. https://books.google.it/books?id=yAUxz6tQKl0C
Lienhard IV J, Lienhard V J (2017) A heat transfer textbook, 4th edn. Phlogiston Press, Cambridge. http://ahtt.mit.edu, version 2.11
Maasilta I, Minnich AJ (2014) Heat under the microscope. Phys Today 67(8):27–32. https://doi.org/10.1063/PT.3.2479
McGaughey A, Kaviany M (2006) Phonon transport in molecular dynamics simulations: formulation and thermal conductivity prediction. Adv Heat Tran 39(C):169–255. https://doi.org/10.1016/S0065-2717(06)39002-8
Minnich AJ, Dresselhaus MS, Ren ZF, Chen G (2009) Bulk nanostructured thermoelectric materials: current research and future prospects. Energy Environ Sci 2:466–479. https://doi.org/10.1039/B822664B
M\(\ddot {\mathrm {u}}\)ller-Plathe F (1997) A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity. J Chem Phys 106(14):6082–6085. https://doi.org/10.1063/1.473271
Pollack G (1969) Kapitza resistance. Rev Mod Phys 41:48–81. https://link.aps.org/doi/10.1103/RevModPhys.41.48
Rurali R, Colombo L, Cartoixa X, Wilhelmsen O, Trinh TT, Bedeaux D, Kjelstrup S (2016) Heat transport through a solid-solid junction: the interface as an autonomous thermodynamic system. Phys Chem Chem Phys 18:13741–13745. https://doi.org/10.1039/C6CP01872F
Schelling PK, Phillpot SR, Keblinski P (2002) Comparison of atomic-level simulation methods for computing thermal conductivity. Phys Rev B 65:144306. https://link.aps.org/doi/10.1103/PhysRevB.65.144306
Sellan DP, Landry ES, Turney JE, McGaughey AJH, Amon CH (2010) Size effects in molecular dynamics thermal conductivity predictions. Phys Rev B 81:214305. https://link.aps.org/doi/10.1103/PhysRevB.81.214305
Stoner RJ, Maris HJ (1993) Kapitza conductance and heat flow between solids at temperatures from 50 to 300 k. Phys Rev B 48:16373–16387. https://link.aps.org/doi/10.1103/PhysRevB.48.16373
Swartz ET, Pohl RO (1987) Thermal resistance at interfaces. Appl Phys Lett 51(26):2200–2202. https://doi.org/10.1063/1.98939
Swartz ET, Pohl RO (1989) Thermal boundary resistance. Rev Mod Phys 61:605–668. https://link.aps.org/doi/10.1103/RevModPhys.61.605
Volz S, Ordonez-Miranda J, Shchepetov A, Prunnila M, Ahopelto J, Pezeril T, Vaudel G, Gusev V, Ruello P, Weig EM, Schubert M, Hettich M, Grossman M, Dekorsy T, Alzina F, Graczykowski B, Chavez-Angel E, Sebastian Reparaz J, Wagner MR, Sotomayor-Torres CM, Xiong S, Neogi S, Donadio D (2016) Nanophononics: state of the art and perspectives. European Phys J B 89(1):15. https://doi.org/10.1140/epjb/e2015-60727-7
Acknowledgements
The work by LC is supported in part by the Progetto biennale di Ateneo UniCA funded by Fondazione di Sardegna titled “Multiphysics theoretical approach to thermoelectricity.” The work by AA is funded by Regione Autonoma della Sardegna (RAS) under the basic research project CRP78744 “Energy Applications with Porous Silicon (ENAPSi).” Finally, computational support by CINECA (Italy) under several ISCRA projects is acknowledged.
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Antidormi, A., Colombo, L. (2018). Lattice Thermal Boundary Resistance. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-50257-1_15-1
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DOI: https://doi.org/10.1007/978-3-319-50257-1_15-1
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