Journal of Materials Science

, Volume 53, Issue 8, pp 5641–5683 | Cite as

A review of computational phononics: the bulk, interfaces, and surfaces

  • Francis VanGessel
  • Jie Peng
  • Peter W. Chung
Interface Behavior


Broad-based interest in microscale heat transport in novel materials, engineered phononic materials, metamaterials, and their relevant systems has created significant demand for computational approaches to aid in investigation and design of materials that support phonons. This review describes the significant improvements that have been made and new needs that have emerged for capabilities associated with the computability of phonons. The technical scope encompasses issues, especially relevant to bulk, interface, and surface effects. Traditional approaches such as molecular dynamics, lattice dynamics, and Boltzmann transport equation continue to advance the field but are frequently extended to the limits of their physical or numerical validity. New materials beyond traditional group-IV, III–V, and II–VI semiconductors, phenomena that critically depend on scattering, such as in low-dimensional nanostructures, materials with interior surfaces and defects, and in high-temperature environments, continue to push these limits. The basis for the traditional calculation methods shares their origins with the earliest theories for thermal transport, acoustic waves in solids, spectroscopy and dynamical crystal lattices. These will remain in wide use in the future. But computing methods and the accompanying advances in microprocessor technologies have enabled growth of phonon computing models and methods in sophistication, accuracy, fidelity and complexity that will lead to fundamental impacts beyond the classic types of problems for which they were developed. With their increasingly integrated use for design and research, the myriad developments that presently exist must be understood for their suitability for certain applications and their ability to aid in the pursuit of new technologies.



Support from the Army Research Office under Award W911NF-14-1-0330 is gratefully acknowledged.


  1. 1.
    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):793–818CrossRefGoogle Scholar
  2. 2.
    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 1:011305-1–011305-45CrossRefGoogle Scholar
  3. 3.
    Chernatynskiy A, Phillpot SR (2013) Phonon-mediated thermal transport: confronting theory and microscopic simulation with experiment. Curr Opin Solid State Mater Sci 17(1):1–9CrossRefGoogle Scholar
  4. 4.
    Lindsay L (2016) First principles Peierls–Boltzmann phonon thermal transport: a topical review. Nanoscale Microscale Thermophys Eng 20(2):67–84CrossRefGoogle Scholar
  5. 5.
    Pop E, Sinha S, Goodson KE (2006) Heat generation and transport in nanometer-scale transistors. Proc IEEE 94(8):1587–1601CrossRefGoogle Scholar
  6. 6.
    Dincer I, Zamfirescu C (2011) Sustainable Energy Systems and Applications. Springer, New YorkGoogle Scholar
  7. 7.
    Corporation Intel (2017) Intel Supports American Innovation with $7 Billion Investment in Next-Generation Semiconductor Factory in Arizona. Intel Corporation, Santa ClaraGoogle Scholar
  8. 8.
    International Technology Roadmap for Semiconductor (ITRS) (2014)
  9. 9.
    Ju YS, Goodson KE (1999) Phonon scattering in silicon films with thickness of order 100 nm. Appl Phys Lett 74(20):3005–3007CrossRefGoogle Scholar
  10. 10.
    Escobar RA, Ghai SS, Jhon MS, Amon CH (2006) Multi-length and time scale thermal transport using the lattice Boltzmann method with application to electronics cooling. Int J Heat Mass Transf 49(1):97–107CrossRefGoogle Scholar
  11. 11.
    Hussein MI, Leamy MJ, Ruzzene M (2014) Dynamics of phononic materials and structures: historical origins, recent progress, and future outlook. Appl Mech Rev 66(4):040802-1–040802-38Google Scholar
  12. 12.
    Ziman JM (2003) Electrons and Phonons. Clarendon Press, OxfordGoogle Scholar
  13. 13.
    Burnham AK, Weese RK, Wemhoff AP, Maienschein JL (2007) A historical and current perspective on predicting thermal cookoff behavior. J Therm Anal Calorim 89:407–415CrossRefGoogle Scholar
  14. 14.
    Coffey C (1985) Energy localization in rapidly deforming crystals. Phys Rev B 32:5335–5341CrossRefGoogle Scholar
  15. 15.
    Dlott DD, Fayer MD (1990) Shocked molecular solids: vibrational up pumping, defect hot spot formation, and the onset of chemistry. J Chem Phys 92:3798–3812CrossRefGoogle Scholar
  16. 16.
    Kraczek B, Chung PW (2013) Investigation of direct and indirect phonon-mediated bond excitation in alpha-RDX. J Chem Phys 138:074505-1–074505-10CrossRefGoogle Scholar
  17. 17.
    Rose JL (1999) Ultrasonic Waves in Solid Media. Cambridge University Press, CambridgeGoogle Scholar
  18. 18.
    Mandelis A (1987) Photoacoustic and Thermal Wave Phenomena in Semiconductors. North-Holland, New YorkGoogle Scholar
  19. 19.
    Meinhold L, Merzel F, Smith JC (2007) Lattice dynamics of a protein crystal. Phys Rev Lett 99:138101CrossRefGoogle Scholar
  20. 20.
    Baroni S, De Gironcoli S, Dal Corso A, Giannozzi P (2001) Phonons and related crystal properties from density-functional perturbation theory. Rev Mod Phys 73(2):515–562CrossRefGoogle Scholar
  21. 21.
    Wang Y, Shang S-L, Fang H, Liu Z-K, Chen L-Q (2016) First-principles calculations of lattice dynamics and thermal properties of polar solids. npj Comput Mater 2:1–10CrossRefGoogle Scholar
  22. 22.
    Luckyanova MN, Garg J, Esfarjani K, Jandl A, Bulsara MT, Schmidt AJ, Minnich AJ, Chen S, Dresselhaus MS, Ren Z, Fitzgerald EA, Chen G (2012) Coherent phonon heat conduction in superlattices. Science 338:936–939CrossRefGoogle Scholar
  23. 23.
    NW Ashcroft, ND Mermin (1976) Solid state physics, college edition. In: Crane DG (ed), Saunders College, PhiladelphiaGoogle Scholar
  24. 24.
    Meirovitch L (2001) Fundamentals of Vibrations, Long Grove. Waveland Press Inc, ILGoogle Scholar
  25. 25.
    Henry AS, Chen G (2008) Spectral phonon transport properties of silicon based on molecular dynamics simulations and lattice dynamics. J Comput Theor Nanosci 5(2):1–12CrossRefGoogle Scholar
  26. 26.
    Srivastava GP (1990) Physics of Phonons. IOP Publishing Ltd, New YorkGoogle Scholar
  27. 27.
    Gurevich VL (1988) Transport in phonon systems. In: Modern problems in condensed matter sciences. Elsevier Science Ltd, New YorkGoogle Scholar
  28. 28.
    Schelling PK, Philllpot SR, Keblinski P (2002) Phonon wave-packet dynamics at semiconductor interfaces by molecular-dynamics simulations. Appl Phys Lett 80(14):2484–2486CrossRefGoogle Scholar
  29. 29.
    Mazumder S, Majumdar A (2001) Monte Carlo study of phonon transport in solid thin films including dispersion and polarization. J Heat Transf 123(4):749–759CrossRefGoogle Scholar
  30. 30.
    Ali SA, Mazumder S (2015) Phonon heat conduction in multidimensional heterostructures: predictions using the Boltzmann transport equation. J Heat Transf 137(10):102401-1–102401-11CrossRefGoogle Scholar
  31. 31.
    Schelling PK, Phillpot P, Keblinski P (2004) Kapitza conductance and phonon scattering at grain boundaries by simulation. J Appl Phys 95(11):6082–6091CrossRefGoogle Scholar
  32. 32.
    Bottger H (1983) Principles of the theory of the lattice dynamics. Physik-Verlag, BerlinGoogle Scholar
  33. 33.
    Fritsch J, Schröder U (1999) Density functional calculation of semiconductor surface phonons. Phys Rep 309(4):209–331CrossRefGoogle Scholar
  34. 34.
    Harris FJ (1978) On the use of windows for harmonic analysis with the discrete Fourier transform. In: Proceedings of the IEEE, vol 66(1)Google Scholar
  35. 35.
    Izvekov S, Chung PW, Rice BM (2011) Non-equilibrium molecular dynamics simulation study of heat transport in hexahydro-1, 3, 5-trinitro-s-triazine (RDX). Int J Heat Mass Transf 54(25):5623–5632CrossRefGoogle Scholar
  36. 36.
    Jiang JW, Park HS, Rabczuk T (2013) Molecular dynamics simulations of single-layer molybdenum disulphide (MoS2): Stillinger-Weber parametrization, mechanical properties, and thermal conductivity. J Appl Phys 114(6):064307-1–064307-10CrossRefGoogle Scholar
  37. 37.
    Duan Y, Wu C, Chowdhury S, Lee MC, Xiong G, Zhang W, Caldwell J (2003) A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. J Comput Chem 24(16):1999–2012CrossRefGoogle Scholar
  38. 38.
    Li Y, Siegel DJ, Adams JB, Liu XY (2003) Embedded-atom-method tantalum potential developed by the force-matching method. Phys Rev B 67(12):125101-1–125101-8Google Scholar
  39. 39.
    Khakshouri S, Alfe D, Duffy DM (2008) Development of an electron-temperature-dependent interatomic potential for molecular dynamics simulation of tungsten under electronic excitation. Phys Rev B 78(22):224304-1–224304-11CrossRefGoogle Scholar
  40. 40.
    Peierls RE (1929) On the kinetic theory of thermal conduction in crystals. Ann D Physik 3:1055–1101CrossRefGoogle Scholar
  41. 41.
    Chen G (2005) Nanoscale Energy Transport and Conversion. Oxford University Press, New YorkGoogle Scholar
  42. 42.
    VanGessel FG, Chung PW (2017) An anisotropic full Brillouin zone model for the three dimensional phonon Boltzmann transport equation. Comput Methods Appl Mech Eng 317:1012–1036CrossRefGoogle Scholar
  43. 43.
    Turney JE, McGaughey AJH, Amon CH (2010) In-plane phonon transport in thin films. J Appl Phys 107(2):024317-1–024317-8CrossRefGoogle Scholar
  44. 44.
    Donmezer N, Graham S (2014) A multiscale thermal modeling appraoch for ballistic and diffusive heat transport in two dimensional domains. Int J Therm Sci 76(1):235–244CrossRefGoogle Scholar
  45. 45.
    Regner KT, McGaughey AJH, Malen JA (2014) Analytical interpretation of nondiffusive phonon transport in thermoreflectance thermal conductivity measurements. Phys Rev B 90(6):064302-1–064302-10CrossRefGoogle Scholar
  46. 46.
    Johnson JA, Maznev AA, Cuffe J, Eliason JK, Minnich AJ, Kehoe T, Torres CMS, Chen G, Nelson KA (2013) Direct measurement of room-temperature nondiffusive thermal transport over micron distances in a silicon membrane. Phys Rev Lett 110(2):025901-1–025901-5CrossRefGoogle Scholar
  47. 47.
    Yang F, Dames C (2013) Mean free path spectra as a tool to understand thermal conductivity in bulk and nanostructures. Phys Rev B 87(3):035437-1–035437-12CrossRefGoogle Scholar
  48. 48.
    Escobar RA, Amon CH (2008) Thin film phonon heat conduction by the dispersion lattice Boltzmann method. J Heat Transf 130(1):092402-1–092402-8Google Scholar
  49. 49.
    Guyver R, Krumhansl J (1966) Solution of the linearized phonon Boltzmann equation. Phys Rev 148(2):766–778CrossRefGoogle Scholar
  50. 50.
    Lee Y, Hwang GS (2012) Force-matching-based parameterization of the Stillinger–Weber potential for thermal conduction in silicon. Phys Rev B 85(12):125204-1–125204-5CrossRefGoogle Scholar
  51. 51.
    Ward A, Broido DA (2010) Intrinsic phonon relaxation times from first-principles studies of the thermal conductivities of Si and Ge. Phys Rev B 81(8):085205-1–085205-5CrossRefGoogle Scholar
  52. 52.
    Nabovati A, Sellan DP, Amon CH (2011) On the lattice Boltzmann method for phonon transport. J Comput Phys 230(15):5864–5876CrossRefGoogle Scholar
  53. 53.
    Sellan DP, Turney JE, McGaughey AJ, Amon CH (2010) Cross-plane phonon transport in thin films,”. J Appl Phys 108(11):113524-1–113524-8CrossRefGoogle Scholar
  54. 54.
    Modest MF (2013) Radiative heat transfer. Academic Press, LondonGoogle Scholar
  55. 55.
    Escobar RA, Amon CH (2007) Influence of phonon dispersion on transient thermal response of silicon-on_insulator transistors under self-heating conditions. J Heat Transf 129(1):790–797CrossRefGoogle Scholar
  56. 56.
    Heino P (2010) Lattice-Boltzmann finite-difference model with optical phonons for nanoscale thermal conduction. Comput Math Appl 59(1):2351–2359CrossRefGoogle Scholar
  57. 57.
    Christensen A, Graham S (2010) Multiscale lattice boltzmann modeling of phonon transport in crystalline semiconductor materials. Numer Heat Transf Part B Fundam 57(2):89–109CrossRefGoogle Scholar
  58. 58.
    Ali SA, Mazumder S (2017) Phonon Boltzmann Transport Equation based modeling of time domain thermo-reflectance experiments. Int J Heat Mass Transf 107:607–621CrossRefGoogle Scholar
  59. 59.
    Ali SAKG, Mazumder S, Sadayappan P, Mittal A (2014) Large-scale parallel computation of the phonon Boltzmann Transport Equation. Int J Therm Sci 86:341–351CrossRefGoogle Scholar
  60. 60.
    Guo Z, Xu K (2016) Discrete unified gas kinetic scheme for multiscale heat transfer based on the phonon Boltzmann transport equation. Int J Heat Mass Transf 102:944–958CrossRefGoogle Scholar
  61. 61.
    Murthy JY, Mathur SR (2003) An improved computational procedure for sub-micron heat conduction. J Heat Transf 125:904–910CrossRefGoogle Scholar
  62. 62.
    Narumanchi SVJ, Murthy JY, Amon CH (2006) Boltzmann transport equation-based thermal modeling approaches for hotspots in microelectronics. Heat Mass Transf 42(6):478–491CrossRefGoogle Scholar
  63. 63.
    Narumanchi SV, Murthy JY, Amon CH (2005) Comparison of different phonon transport models for predicting heat conduction in silicon-on-insulator transistors. J Heat Transf 127(7):713–723CrossRefGoogle Scholar
  64. 64.
    Murthy JY, Mathur SR (2002) Computation of sub-micron thermal transport using an unstructured finite volume method. J Heat Transf 124:1176–1184CrossRefGoogle Scholar
  65. 65.
    Ni C, Murthy JY (2009) Parallel computation of the phonon Boltzmann transport equation. Numer Heat Transf Part B Fundam 55(6):435–456CrossRefGoogle Scholar
  66. 66.
    Narumanchi SVJ, Murthy JY, Amon CH (2005) Submicron heat transport model in silicon accounting for phonon dispersion and polarization. J Heat Transf 126(6):946–955CrossRefGoogle Scholar
  67. 67.
    Ni C, Murthy JY (2012) Phonon transport modeling using Boltzmann transport equation with anisotropic relaxation times. J Heat Transf 134(8):082401-1–082401-12CrossRefGoogle Scholar
  68. 68.
    Zahiri S, Shao C, Shen Y, Bao H (2016) Collocation mesh-free method to solve the gray phonon Boltzmann transport equation. Numer Heat Transf Part B Fundam 70(5):459–471CrossRefGoogle Scholar
  69. 69.
    Hamian S, Yamada T, Faghri M, Park K (2015) Finite element analysis of transient ballistic–diffusive phonon heat transport in two-dimensional domains. Int J Heat Mass Transf 80:781–788CrossRefGoogle Scholar
  70. 70.
    Pisipati S, Chen C, Geer J, Sammakia B, Murray BT (2013) Multiscale thermal device modeling using diffusion in the Boltzmann transport equation. Int J Heat Mass Transf 64(1):286–303CrossRefGoogle Scholar
  71. 71.
    Allu P, Mazumder S (2016) Hybrid ballistic-diffusive solution to the frequency-dependent phonon Boltzmann Transport Equation. Int J Heat Mass Transf 100(1):165–177CrossRefGoogle Scholar
  72. 72.
    Chen G (2002) Ballistic-diffusive equations for transient heat conduction from nano to macroscales. J Heat Transf 124(1):320–328CrossRefGoogle Scholar
  73. 73.
    Loy JM, Murthy JY, Singh D (2013) A fast hybrid Fourier–Boltzmann transport equation solver for nongray phonon transport. J Heat Transf 135(1):011008-1–011008-12Google Scholar
  74. 74.
    Lin Z, Zhigilei LV, Celli V (2008) Electron–phonon coupling and electron heat capacity of metals under conditions of strong electron–phonon nonequilibrium. Phys Rev B 77(7):075133-1–075133-17CrossRefGoogle Scholar
  75. 75.
    Mittal A, Mazumder S (2010) Monte Carlo study of phonon heat conduction in silicon thin films including contributions of optical phonons. J Heat Transf 132(1):052402-1–052402-11Google Scholar
  76. 76.
    Peraud J-PM, Hadjiconstantinou NG (2011) Efficient simulation of multidimensional phonon transport using energy-based variance-reduced Monte Carlo formulations. Phys Rev B 84(20):205331-1–205331-15CrossRefGoogle Scholar
  77. 77.
    Shomali Z, Pedar B, Ghazanfarian J, Abbassi A (2017) Monte-Carlo parallel simulation of phonon transport for 3D silicon nano-devices. Int J Therm Sci 114:139–154CrossRefGoogle Scholar
  78. 78.
    Yang L, Minnich AJ (2017) Thermal transport in nanocrystalline Si and SiGe by ab initio based Monte Carlo simulation. Sci Rep 7(1):44254-1–44254-9Google Scholar
  79. 79.
    Lacroix D, Joulain K, Lemonnier D (2005) Monte Carlo transient phonon transport in silicon and germanium at nanoscales. Phys Rev B 72(6):064305-1–064305-11CrossRefGoogle Scholar
  80. 80.
    Klitsner T, VanCleve JE, Fischer HE, Pohl RO (1988) Phonon radiative heat transfer and surface scattering. Phys Rev B 38(11):7576–7594CrossRefGoogle Scholar
  81. 81.
    Majumdar A (1993) Microscale heat conduction in dielectric thin films. J Heat Transf 115:7–16CrossRefGoogle Scholar
  82. 82.
    Pop E, Dutton RW (2004) Analytic band Monte Carlo model for electron transport in SiSi including acoustic and optical phonon dispersion. J Appl Phys 96(9):4998–5005CrossRefGoogle Scholar
  83. 83.
    Chen G (1996) Nonlocal and nonequilibrium heat conduction in the vicinity of nanoparticles. J Heat Transf 118(1):539–545CrossRefGoogle Scholar
  84. 84.
    Sverdrup PG, Sinha S, Asheghi M, Uma S, Goodson KE (2001) Measurement of ballistic phonon conduction near hotspots in silicon. Appl Phys Lett 78(21):3331–3333CrossRefGoogle Scholar
  85. 85.
    Regner KT, Freedman JP, Malen JA (2015) Advances in studying phonon mean free path dependent contributions to thermal conductivity. Nanoscale Microscale Thermophys Eng 19(3):183–205CrossRefGoogle Scholar
  86. 86.
    Cuffe J, Eliason JK, Maznev AA, Collins KC, Johnson JA, Shchepetov A, Prunnila M, Ahopelto CMS, Torres G Chen, Nelson KA (2015) Reconstructing phonon mean-free-path contributions to thermal conductivity using nanoscale membranes. Phys Rev B 91(24):245423-1–245423-6CrossRefGoogle Scholar
  87. 87.
    Minnich AJ (2015) Advances in the measurement and computation of thermal phonon transport properties. J Phys Condens Matter 27(1):1–21Google Scholar
  88. 88.
    Callaway J (1959) Model for lattice thermal conductivity at low temperatures. Phys Rev 113(4):1046–1051CrossRefGoogle Scholar
  89. 89.
    Omini M, Sparavigna A (1995) An iterative approach to the phonon Boltzmann equation in the theory of thermal conductivity. Phys B 212(2):101–112CrossRefGoogle Scholar
  90. 90.
    Chernatynskiy A, Phillpot SR (2010) Evaluation of computational techniques for solving the Boltzmann transport equation for lattice thermal conductivity calculations. Phys Rev B 82(13):134301-1–134301-17CrossRefGoogle Scholar
  91. 91.
    Broido DA, Ward A, Mingo N (2005) Lattice thermal conductivity of silicon from empirical interatomic potentials. Phys Rev B 72(1):014308-1–014308-8CrossRefGoogle Scholar
  92. 92.
    Mingo N, Stewart DA, Broido DA, Lindsay L, Li W (2014) Ab initio thermal transport. In: Shindé S, Srivastava G (eds) Length-scale dependent phonon interactions. Topics in Applied Physics, vol 128. Springer, New YorkGoogle Scholar
  93. 93.
    Broido DA, Malorny M, Birner G, Mingo N, Stewart DA (2007) Intrinsic lattice thermal conductivity of semiconductors from first principles. Appl Phys Lett 91(23):231922-1–231922-3CrossRefGoogle Scholar
  94. 94.
    Omini M, Sparavigna A (1996) Beyond the isotropic-model approximation in the theory of thermal conductivity. Phys Rev B 53(14):9064–9073CrossRefGoogle Scholar
  95. 95.
    Omini M, Sparavigna A (1997) Heat transport in dielectric solids with diamond structure. NUOVO CIMENTO-SOCIETA ITALIANA DI FISICA SEZIONE D 19:1537–1564Google Scholar
  96. 96.
    Sparavigna A (2003) Role of nonpairwise interactions on phonon thermal transport. Phys Rev B 67(14):144305-1–144305-7CrossRefGoogle Scholar
  97. 97.
    Broido DA, Reinecke TL (2004) Lattice thermal conductivity of superlattice structures. Phys Rev B 70(8):081310-1–081310-4CrossRefGoogle Scholar
  98. 98.
    Lindsay L, Broido DA, Reinecke TL (2013) Ab initio thermal transport in compound semiconductors. Phys Rev B 87(16):165201-1–165201-15CrossRefGoogle Scholar
  99. 99.
    Ward A, Broido DA, Stewart DA, Deinzer G (2009) Ab initio theory of the lattice thermal conductivity in diamond. Phys Rev B 80(12):125203-1–125203-8CrossRefGoogle Scholar
  100. 100.
    Lindsay L, Broido DA, Mingo N (2010) Flexural phonons and thermal transport in graphene. Phys Rev B 82(11):115427-1–115427-6CrossRefGoogle Scholar
  101. 101.
    Tian Z, Garg J, Esfarjani K, Shiga T, Shiomi J, Chen G (2012) Phonon conduction in PbSe, PbTe, and PbTeSe from first principles calculations. Phys Rev B 85(18):184303-1–184303-7CrossRefGoogle Scholar
  102. 102.
    Delaire O, Ma J, Marty K, May AF, McGuire MA, Du MH, Singh DJ, Podlesnyak A, Ehlers G, Lumsden MD, Sales BC (2011) Giant anharmonic phonon scattering in PbTe. Nat Mater 10(1):614–619CrossRefGoogle Scholar
  103. 103.
    Kroonblawd MP, Sewell TD (2016) Anisotropic relaxation of idealized hot spots in crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB). J Phys Chem C 120(1):17214–17223CrossRefGoogle Scholar
  104. 104.
    Byrd EFC, Scuseria GE, Chabalowski CF (2004) An ab initio study of solid nitromethane, HMX, RDX, and CL20: successes and failures of DFT. J Chem Phys 108(35):13100–13106CrossRefGoogle Scholar
  105. 105.
    Joshi K, Losada M, Chaudhuri S (2016) Intermolecular energy transfer dynamics at a hot-spot interface in RDX crystals. J Phys Chem 120:477–489CrossRefGoogle Scholar
  106. 106.
    Long Y, Chen J (2017) Theoretical study of the phonon–phonon scattering mechanism and the thermal conductive coefficients for energetic materials. Phil Mag 97(28):2575–2595CrossRefGoogle Scholar
  107. 107.
    Sellan D, Landry E, Turney J, McGaughey A, Amon C (2010) Size effects in molecular dynamics thermal conductivity. Phys Rev B 81:214305-1–214305-10CrossRefGoogle Scholar
  108. 108.
    Kremer RK, Graf K, Cardona M, Devyatykh GG, Gusev AV, Gibin AM, Inyushkin AV, Taldenkov AN, Pohl HJ (2004) Thermal conductivity of isotopically enriched 28Si: revisited. Solid State Commun 131:499–503CrossRefGoogle Scholar
  109. 109.
    Klemens PG (1981) Theory of lattice thermal conductivity: role of low-frequency phonons. Int J Thermophys 2(1):55–62CrossRefGoogle Scholar
  110. 110.
    Picu RC (2002) The Peierls stress in non-local elasticity. J Mech Phys Solids 50:717–735CrossRefGoogle Scholar
  111. 111.
    Zbib H, Shehadeh M, Khan S, Karami G (2002) Multiscale dislocation dynamics plasticity. Washington State University, Pullman, WAGoogle Scholar
  112. 112.
    Garlick GFJ, Gibson AF (1948) The electron trap mechanism of luminescence in sulphide and silicate phophors. Proc Phys Soc 60(6):574–590CrossRefGoogle Scholar
  113. 113.
    Zhang Y, Brar V, Wang F, Girit C, Yayon Y, Panlasigui M, Zettl A, Crommie M (2008) Giant phonon-induced conductance in scanning tunnelling spectroscopy of gate-tunable graphene. Nat Phys 4:627–630CrossRefGoogle Scholar
  114. 114.
    Wolfe CM, Stillman GE, Lindley WT (1970) Electron mobility in high-purity GaAs. J Appl Phys 41(7):3088–3091CrossRefGoogle Scholar
  115. 115.
    Ishiwata S, Shiomi Y, Lee JS, Bahramy M, Suzuki T, Uchida M, Arita R, Taguchi Y, Tokura Y (2013) Extremely high electron mobility in a phonon-glass semimetal. Nat Mater 12:512–517CrossRefGoogle Scholar
  116. 116.
    Roy K, Mukhopadhyay S, Mahmoodi-Meimand H (2003) Leakage current mechanisms and leakage reduction techniques in deep-submicrometer CMOS circuits. Proc IEEE 91(2):305–327CrossRefGoogle Scholar
  117. 117.
    Hall RN, Racette JH, Ehrenreich H (1960) Direct observation of polarons and phonons during tunneling in group 3-5 semiconductor junctions. Phys Rev Lett 4(9):456–458CrossRefGoogle Scholar
  118. 118.
    Chen JK, Latham WP, Beraun JE (2005) The role of electron–phonon coupling in ultrafast laser heating. J Laser Appl 17(1):63–68CrossRefGoogle Scholar
  119. 119.
    Stevens RJ, Zhigilei LV, Norris PM (2007) Effects of temperature and disorder on thermal boundary conductance at solid-solid interfaces: nonequilibrium molecular dynamics simulations. Int J Heat Mass Transf 50(1):3977–3989CrossRefGoogle Scholar
  120. 120.
    Zhou XW, Jones RE, Kimmer CJ, Duda JC, Hopkins PE (2013) Relationship of thermal boundary conductance to structure from an analytical model plus molecular dynamics simulations. Phys Rev B 87(9):094303-1–094303-17CrossRefGoogle Scholar
  121. 121.
    Merabia S, Termentzidis K (2012) Thermal conductance at the interface between crystals using equilibrium and nonequilibrium molecular dynamics. Phys Rev B 86(9):094303-1–094303-16CrossRefGoogle Scholar
  122. 122.
    Merabia S, Termentzidis K (2014) Thermal boundary conductance across rough interfaces probed by molecular dynamics. Phys Rev B 89(5):054309-1–054309-9CrossRefGoogle Scholar
  123. 123.
    Prasher RS, Phelan PE (2001) A scattering-mediated acoustic mismatch model for the prediction of thermal boundary resistance. J Heat Transf 123(1):105–112CrossRefGoogle Scholar
  124. 124.
    Dames C, Chen G (2004) Theoretical phonon thermal conductivity of Si/Ge superlattice nanowires. J Appl Phys 95(2):682–693CrossRefGoogle Scholar
  125. 125.
    Reddy P, Castelino K, Majumdar A (2005) Diffuse mismatch model of thermal boundary conductance using exact phonon dispersion. Appl Phys Lett 87(21):211908-1–211908-3CrossRefGoogle Scholar
  126. 126.
    Hopkins PE (2009) Multiple phonon processes contributing to inelastic scattering during thermal boundary conductance at solid interfaces. J Appl Phys 106(1):013528-1–013528-9CrossRefGoogle Scholar
  127. 127.
    Duda JC, Beechem TE, Smoyer JL, Norris PM, Hopkins PE (2010) Role of dispersion on phononic thermal boundary conductance. J Appl Phys 108(7):073515-1–073515-10CrossRefGoogle Scholar
  128. 128.
    Beechem T, Hopkins PE (2009) Predictions of thermal boundary conductance for systems of disordered solids and interfaces. J Appl Phys 106(12):124301-1–124301-8CrossRefGoogle Scholar
  129. 129.
    Duda JC, Norris PM, Hopkins PE (2011) On the linear temperature dependence of phonon thermal boundary conductance in the classical limit. J Heat Transf 133(1):074501-1–074501-4Google Scholar
  130. 130.
    Kazan M (2011) Interpolation between the acoustic mismatch model and the diffuse mismatch model for the interface thermal conductance: application to InN/GaN superlattice. J Heat Transf 133(1):112401-1–112401-7Google Scholar
  131. 131.
    Little WA (1959) The transport of heat between dissimilar solids at low temperatures. Can J Phys 37(3):334–349CrossRefGoogle Scholar
  132. 132.
    Tien CL, Majumdar A, Gerner FM (1998) Microscale energy transport. Taylor & Francis, WashingtonGoogle Scholar
  133. 133.
    Swartz ET, Pohl RO (1989) Thermal boundary resistance. Rev Mod Phys 61(3):605–668CrossRefGoogle Scholar
  134. 134.
    Hopkins PE, Duda JC, Norris PM (2011) Anharmonic phonon interactions at interfaces and contributions to thermal boundary conductance. J Heat Transf 133(1):062401-1–062401-11Google Scholar
  135. 135.
    Saaskilahti K, Oksanen J, Tulkki J, Volz S (2014) Role of anharmonic phonon scattering in the spectrally decomposed thermal conductance at planar interfaces. Phys Rev B 90(13):134312-1–134312-8CrossRefGoogle Scholar
  136. 136.
    Duda JC, Hopkins PE, Smoyer JL, Bauer ML, English TS, Saltonstall CB, Norris PM (2010) On the assumption of detailed balance in prediction of diffusive transmission probability during interfacial transport. Nanoscale Microscale Thermophys Eng 14(1):21–33CrossRefGoogle Scholar
  137. 137.
    Beechem T, Graham S, Hopkins P, Norris P (2007) Role of interface disorder on thermal boundary conductance using a virtual crystal approach. Appl Phys Lett 90(5):054104-1–054104-3CrossRefGoogle Scholar
  138. 138.
    Young DA, Maris HJ (1989) Lattice-dynamical calculation of the Kapitza resistance between fcc lattices. Phys Rev B 40(6):3685–3693CrossRefGoogle Scholar
  139. 139.
    Stoner RJ, Maris HJ (1993) Kapitza conductance and heat flow between solids at temperatures from 50 to 300 K. Phys Rev B 48(22):373–387CrossRefGoogle Scholar
  140. 140.
    Singh D, Murthy JY, Fisher TS (2011) Effect of phonon dispersion on thermal conduction across Si/Ge interfaces. J Heat Transf 133(1):1–17Google Scholar
  141. 141.
    Minnich AJ, Chen G, Mansoor S, Yilbas BS (2011) Quasiballistic heat transfer studied using the frequency-dependent Boltzmann transport equation. Phys Rev B 84(23):235207-1–235207-8CrossRefGoogle Scholar
  142. 142.
    Hopkins PE, Beechem T, Duda JC, Khalid H, Hattar K, Ihlefeld J, Rodriguez MA, Piekos ES (2011) Influence of anisotropy on thermal boundary conductance at solid interfaces. Phys Rev B 84(12):125408-1–125408-7CrossRefGoogle Scholar
  143. 143.
    Duda JC, Smoyer JL, Norris PM, Hopkins PE (2009) Extension of the diffuse mismatch model for thermal boundary conductance between isotropic and anisotropic materials. Appl Phys Lett 95(3):031912-1–031912-3CrossRefGoogle Scholar
  144. 144.
    Su Z, Freedman JP, Leach JH, Preble EA, Davis RF, Malen JA (2013) The impact of film thickness and substrate surface roughness on the thermal resistance of aluminum nitride nucleation layers. J Appl Phys 113(21):213502-1–213502-5CrossRefGoogle Scholar
  145. 145.
    Baker CH, Jordan DA, Norris PM (2012) Application of the wavelet transform to nanoscale thermal transport. Phys Rev B 86(10):104306-1–104306-11CrossRefGoogle Scholar
  146. 146.
    Deng B, Chernatynskiy A, Khafizov M, Hurley DH, Phillpot SR (2014) Kapitza resistance of Si/SiO2 interface. J Appl Phys 115(8):084910-1–084910-7Google Scholar
  147. 147.
    Gordiz K, Henry A (2015) A formalism for calculating the modal contributions to thermal interface conductance. New J Phys 17(10):1–10CrossRefGoogle Scholar
  148. 148.
    Gordiz K, Henry A (2016) Phonon transport at interfaces: determining the correct modes of vibration. J Appl Phys 119(1):015101-1–015101-12CrossRefGoogle Scholar
  149. 149.
    Gordiz K, Henry A (2016) Phonon transport at crystalline Si/Ge interfaces: the role of interfacial modes of vibration. Sci Rep 6(1):23139-1–23139-9CrossRefGoogle Scholar
  150. 150.
    Termentzidis K, Chantrenne P, Keblinski P (2009) Nonequilibrium molecular dynamics simulation of the in-plane thermal conductivity of superlattices with rough interfaces. Phys Rev B 79(21):214307-1–214307-9CrossRefGoogle Scholar
  151. 151.
    Rajabpour A, Volz S (2010) Thermal boundary resistance from mode energy relaxation times: case study of argon-like crystals by molecular dynamics. J Appl Phys 108(9):094324-1–094324-8CrossRefGoogle Scholar
  152. 152.
    Huberman SC, Larkin JM, McGaughey AJH, Amon CH (2013) Disruption of superlattice phonons by interfacial mixing. Phys Rev B 88(15):155311-1–155311-12CrossRefGoogle Scholar
  153. 153.
    Li X, Yang R (2012) Effect of lattice mismatch on phonon transmission and interface thermal conductance across dissimilar material interfaces. Phys Rev B 86(5):054305-1–054305-13Google Scholar
  154. 154.
    Lu S, McGaughey AJH (2015) Thermal conductance of superlattice junctions. AIP Adv 5(5):053205-1–053205-12Google Scholar
  155. 155.
    Wallis RF (1994) Surface phonons: theoretical developments. Surf Sci 299:612–627CrossRefGoogle Scholar
  156. 156.
    Boukai AI, Bunimovich Y, Tahir-Kheli J, Yu JK, Goddard WA III, Heath JR (2008) Silicon nanowires as efficient thermoelectric materials. Nature 451(7175):168–171CrossRefGoogle Scholar
  157. 157.
    Balandin A, Wang KL (1998) Effect of phonon confinement on the thermoelectric figure of merit of quantum wells. J Appl Phys 84(11):6149–6153CrossRefGoogle Scholar
  158. 158.
    Hochbaum AI, Chen R, Delgado RD, Liang W, Garnett EC, Najarian M, Yang P (2008) Enhanced thermoelectric performance of rough silicon nanowires. Nature 451(7175):163–167CrossRefGoogle Scholar
  159. 159.
    Asheghi M, Leung YK, Wong SS, Goodson KE (1997) Phonon-boundary scattering in thin silicon layers. Appl Phys Lett 71(13):1798–1800CrossRefGoogle Scholar
  160. 160.
    Balandin A, Wang KL (1988) Significant decrease of the lattice thermal conductivity due to phonon confinement in a free-standing semiconductor quantum well. Phys Rev B 58(3):1544–1549CrossRefGoogle Scholar
  161. 161.
    Hopkins PE, Reinke CM, Su MF, Olsson RH III, Shaner EA, Leseman ZC, El-Kady I (2010) Reduction in the thermal conductivity of single crystalline silicon by phononic crystal patterning. Nano Lett 11(1):107–112CrossRefGoogle Scholar
  162. 162.
    Ruppin R, Englman R (1970) Optical phonons of small crystals. Rep Prog Phys 33(1):149–196CrossRefGoogle Scholar
  163. 163.
    Genzel L, Martin TP (1973) Infrared absorption by surface phonons and surface plasmons in small crystals. Surf Sci 34(1):33–49CrossRefGoogle Scholar
  164. 164.
    Dash WC, Newman R (1955) Intrinsic optical absorption in single-crystal germanium and silicon at 77 K and 300 K. Phys Rev 99(4):1151CrossRefGoogle Scholar
  165. 165.
    Schluter M, Lannoo M, Needels M, Baraff GA, Tomanek D (1992) Electron–phonon coupling and superconductivity in alkali-intercalated C60 solid. Phys Rev Lett 68(4):526–529CrossRefGoogle Scholar
  166. 166.
    Schlesinger Z, Collins RT, Kaiser DL, Holtzberg F (1987) Superconducting energy gap and normal-state reflectivity of single crystal Y–Ba–Cu–O. Phys Rev Lett 59(17):1958–1961CrossRefGoogle Scholar
  167. 167.
    Gaspar DJ, Hanbicki AT, Sibener SJ (1998) Inelastic multiphonon helium scattering from a stepped Ni(977) surface. J Chem Phys 109:6947–6955CrossRefGoogle Scholar
  168. 168.
    Niu L, Gaspar DJ, Sibener SJ (1995) Phonons localized at step edges: a Route to understanding forces at extended surface defects. Science 268:847–850CrossRefGoogle Scholar
  169. 169.
    Nave S, Jackson B (2007) Methane dissociation on Ni(111): the role of lattice reconstruction. Phys Rev Lett 98:173003-1–173003-4CrossRefGoogle Scholar
  170. 170.
    Kobayashi K (2002) Solid-state ionic reactions. In: Toda F (ed) Organic solid state reactions. Springer, Dordrecht, pp 69–108Google Scholar
  171. 171.
    Hurst WS, Frankl DR (1969) Thermal conductivity of silicon in the boundary scattering regime. Phys Rev 186(3):801–810CrossRefGoogle Scholar
  172. 172.
    Sadhu J, Sinha S (2011) Room-temperature phonon boundary scattering below the Casimir limit. Phys Rev B 84(11):115450-1–115450-6CrossRefGoogle Scholar
  173. 173.
    Bungaro C, de Gironcoli S, Baroni S (1996) Theory of the anomalous Rayleigh dispersion at H/W (110) surfaces. Phys Rev Lett 77(12):2491–2494CrossRefGoogle Scholar
  174. 174.
    Kohler B, Ruggerone P, Scheffler M (1997) Ab initio study of the anomalies in the He-atom-scattering spectra of H/Mo (110) and H/W (110). Phys Rev B 56(20):503–518CrossRefGoogle Scholar
  175. 175.
    Fritsch J, Eckert A, Pavone P, Schroder U (1995) Structure and dynamics of hydrogenated GaAs (110) and InP (110) surfaces. J Phys Condens Matter 7(40):7717–7728CrossRefGoogle Scholar
  176. 176.
    Bertoni CM, Shkrebtii AI, Di Felice R, Finocchi F (1993) Structural and dynamical properties of surfaces from ab initio molecular dynamics. Prog Surf Sci 42(1):319–330CrossRefGoogle Scholar
  177. 177.
    Fu CL, Freeman AJ, Wimmer E, Weinert M (1985) Frozen-phonon total-energy determination of structural surface phase transitions: W (001). Phys Rev Lett 54(20):2261–2264CrossRefGoogle Scholar
  178. 178.
    Grimes CC, Adams G (1979) Evidence for a liquid-to-crystal phase transition in a classical, two-dimensional sheet of electrons. Phys Rev Lett 42(12):795–798CrossRefGoogle Scholar
  179. 179.
    Daum W, Stuhlmann C, Ibach H (1988) Displacive phase transition and surface-phonon anomalies in fcc Fe films on Cu (100). Phys Rev Lett 60(26):2741–2744CrossRefGoogle Scholar
  180. 180.
    Shen S, Narayanaswamy A, Chen G (2009) Surface phonon polaritons mediated energy transfer between nanoscale gaps. Nano Lett 9(8):2909–2913CrossRefGoogle Scholar
  181. 181.
    Le Gall J, Olivier M, Greffet JJ (1997) Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton. Phys Rev B 55(15):10105–10114CrossRefGoogle Scholar
  182. 182.
    Chen DZA, Narayanaswamy A, Chen G (2005) Surface phonon-polariton mediated thermal conductivity enhancement of amorphous thin films. Phys Rev B 72(15):1–4Google Scholar
  183. 183.
    Dai S, Fei Z, Ma Q, Rodin AS, Wagner M, McLeod AS et al (2014) Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride. Science 343(6175):1125–1129CrossRefGoogle Scholar
  184. 184.
    Hellsing B, Eiguren A, Chulkov EV (2002) Electron–phonon coupling at metal surfaces. J Phys Condens Matter 14(24):5959–5977CrossRefGoogle Scholar
  185. 185.
    Cohen RE, Pickett WE, Krakauer H (1990) Theoretical determination of strong electron–phonon coupling in YBa2 Cu3O7. Phys Rev Lett 64(21):2575–2578CrossRefGoogle Scholar
  186. 186.
    Rayleigh L (1885) On waves propagated along the plane surface of an elastic solid. Proc Lond Math Soc 1(1):4–11CrossRefGoogle Scholar
  187. 187.
    Stoneley R (1955) The propagation of surface elastic waves in a cubic crystal. Proc R Soc Lond A Math Phys Eng Sci 232(1191):447–458Google Scholar
  188. 188.
    Gazis DC, Herman R, Wallis RF (1960) Surface elastic waves in cubic crystals. Phys Rev 119(2):533–544CrossRefGoogle Scholar
  189. 189.
    Lim TC, Farnell GW (1969) Character of pseudo surface waves on anisotropic crystals. J Acoust Soc Am 45(4):845–851CrossRefGoogle Scholar
  190. 190.
    Lim TC, Farnell GW (1968) Search for forbidden directions of elastic surface-wave propagation in anisotropic crystals. J Appl Phys 39(9):4319–4325CrossRefGoogle Scholar
  191. 191.
    Kliewer KL, Fuchs R (1996) Optical modes of vibration in an ionic crystal slab including retardation. I. Nonradiative region. Phys Rev 144(2):495–503CrossRefGoogle Scholar
  192. 192.
    Kliewer KL, Fuchs R (1996) Optical modes of vibration in an ionic crystal slab including retardation. II. Radiative region. Phys Rev 150(2):573–588CrossRefGoogle Scholar
  193. 193.
    Wallis RF (1957) Effect of free ends on the vibration frequencies of one-dimensional lattices. Phys Rev 105(2):540–545CrossRefGoogle Scholar
  194. 194.
    Eckl C, Fritsch J, Pavone P, Schro U (1997) Ab initio calculation of phonons in GaP (110) and InAs (110) and trends within III–V (110) surfaces. Surf Sci 394(1–3):47–59CrossRefGoogle Scholar
  195. 195.
    Fritsch J, Pavone P (1995) Ab initio calculation of the structure, electronic states, and the phonon dispersion of the Si (100) surface. Surf Sci 344(1–2):159–173CrossRefGoogle Scholar
  196. 196.
    Allan DC, Mele EJ (1984) Surface vibrational excitations on Si (001) 2 × 1. Phys Rev Lett 53(8):826–829CrossRefGoogle Scholar
  197. 197.
    Nelson JS, Daw MS, Sowa EC (1989) Cu (111) and Ag (111) surface-phonon spectrum: the importance of avoided crossings. Phys Rev B 40(3):1465–1480CrossRefGoogle Scholar
  198. 198.
    Dal Corso A (2001) Density-functional perturbation theory with ultrasoft pseudopotentials. Phys Rev B 64(23):1–17Google Scholar
  199. 199.
    Bortolani V, Franchini A, Santoro G, Toennies JP, Wöll C, Zhang G (1989) Surface phonons on the Pt (111) surface: a comparison of He-scattering experiments with lattice-dynamical calculations. Phys Rev B 40(6):3524–3545CrossRefGoogle Scholar
  200. 200.
    Allen RE, Alldredge GP, De Wette FW (1661) Studies of vibrational surface modes. II. Monatomic fcc crystals. Phys Rev B 4(6):1661–1681CrossRefGoogle Scholar
  201. 201.
    Allen RE, Alldredge GP, De Wette FW (1969) Surface modes of vibration in monatomic crystals. Phys Rev Lett 23(22):1285–1287CrossRefGoogle Scholar
  202. 202.
    Allen RE, Alldredge GP, De Wette FW (1971) Studies of vibrational surface modes. I. General formulation. Phys Rev B 4(6):1648–1660CrossRefGoogle Scholar
  203. 203.
    Tong SY, Maradudin AA (1969) Normal modes of a semi-infinite ionic crystal. Phys Rev 181(3):1318–1335CrossRefGoogle Scholar
  204. 204.
    Chen TS, Alldredge GP, De Wette FW, Allen RE (1971) Surface and pseudosurface modes in ionic crystals. Phys Rev Lett 26(25):1543–1546CrossRefGoogle Scholar
  205. 205.
    Chen TS, Alldredge GP, de Wette FW (1972) Distribution of surface phonon branches in RbF and RbCl. Solid State Commun 10(10):941–945CrossRefGoogle Scholar
  206. 206.
    Kress W, De Wette FW, Kulkarni AD, Schröder U (1987) Surface dynamics of relaxed (001) slabs of alkali halides and MgO. Phys Rev B 35(11):5783–5794CrossRefGoogle Scholar
  207. 207.
    Benedek G (1976) The Green function approach to the surface lattice dynamics of ionic crystals. Surf Sci 61(2):603–634CrossRefGoogle Scholar
  208. 208.
    Maradudin AA, Melngailis J (1964) Some dynamical properties of surface atoms. Phys Rev 133(4A):A1188–A1193CrossRefGoogle Scholar
  209. 209.
    Croitoru M, Grecu D (1973) Application of the Green’s function method to lattice vibrations in thin films. Surf Sci 38(1):60–76CrossRefGoogle Scholar
  210. 210.
    Musser SW, Rieder KH (1970) Influence of surface force-constant changes on surface-mode frequencies. Phys Rev B 2(8):3034–3039CrossRefGoogle Scholar
  211. 211.
    Weisburgh RE, Chung PW (2017) Parameterized and systematically assembled operators for lattice defect dynamics. Int J Solids Struct 110–111:178–191Google Scholar
  212. 212.
    Benedek G, Miglio L (1991) The Green’s function method in the surface lattice dynamics of ionic crystals. Springer, Berlin Heidelberg, pp 37–66Google Scholar
  213. 213.
    Manson R, Celli V (1971) Inelastic surface scattering of non-penetrating particles. Surf Sci 24(2):495–514CrossRefGoogle Scholar
  214. 214.
    Benedek G (1975) Van Hove singularities of the surface phonon density from inelastic reflection of atoms. Phys Rev Lett 35(4):234–237CrossRefGoogle Scholar
  215. 215.
    Ibach H (1970) Optical surface phonons in zinc oxide detected by slow-electron spectroscopy. Phys Rev Lett 24(25):1416–1418CrossRefGoogle Scholar
  216. 216.
    Lucas AA, Šunjić M (1972) Fast-electron spectroscopy of collective excitations in solids. Prog Surf Sci 2:75–137CrossRefGoogle Scholar
  217. 217.
    Mills DL, Maradudin AA, Burstein E (1968) Theory of the Raman effect in metals. Phys Rev Lett 21(16):1178–1182CrossRefGoogle Scholar
  218. 218.
    Martin TP, Genzel L (1973) Raman scattering in small crystals. Phys Rev B 8(4):1630–1635CrossRefGoogle Scholar
  219. 219.
    Heyes DM, Barber M, Clarke JHR (1977) Molecular dynamics computer simulation of surface properties of crystalline potassium chloride. J Chem Soc Faraday Trans Mol Chem Phys 73(7):1485–1496CrossRefGoogle Scholar
  220. 220.
    Yang L, Rahman TS, Daw MS (1991) Surface vibrations of Ag (100) and Cu (100): a molecular-dynamics study. Phys Rev B 44(24):13725–13733CrossRefGoogle Scholar
  221. 221.
    Gester M, Kleinhesselink D, Ruggerone P, Toennies JP (1994) Combined helium-atom-scattering and molecular-dynamics study of aluminum surface-phonon anharmonicities and linewidths. Phys Rev B 49(8):5777–5780CrossRefGoogle Scholar
  222. 222.
    Yang J, Hu W, Zhao D (2004) Temperature dependence of atomic relaxation and vibrations for the vicinal Ni (977) surface: a molecular dynamics study. Surf Sci 572(2):439–448CrossRefGoogle Scholar
  223. 223.
    Wang CZ, Fasolino A, Tosatti E (1988) Molecular-dynamics theory of the temperature-dependent surface phonons of W (001). Phys Rev B 37(4):2116–2122CrossRefGoogle Scholar
  224. 224.
    Ravelo R, El-Batanouny M (1989) Molecular-dynamics study of the reconstructed Au (111) surface: low temperature. Phys Rev B 40(14):9574–9589CrossRefGoogle Scholar
  225. 225.
    Yang L, Rahman TS (1991) Enhanced anharmonicity on Cu (110). Phys Rev Lett 67(17):2327–2330CrossRefGoogle Scholar
  226. 226.
    Raphuthi AM, Wang XQ, Ercolessi F, Adams JB (1995) Temperature dependence of surface phonons of Al (110). Phys Rev B 52(8):R5554–R5557CrossRefGoogle Scholar
  227. 227.
    Weakliem PC, Carter EA (1992) Constant temperature molecular dynamics simulations of Si (100) and Ge (100): equilibrium structure and short-time behavior. J Chem Phys 96(4):3240–3250CrossRefGoogle Scholar
  228. 228.
    Fuchs R, Kliewer KL (1965) Optical modes of vibration in an ionic crystal slab. Phys Rev 140(6A):A2076–A2088CrossRefGoogle Scholar
  229. 229.
    Kern K, David R, Palmer RL, Comsa G, Rahman TS (1986) Surface phonon dispersion of platinum (111). Phys Rev B 33(6):4334–4337CrossRefGoogle Scholar
  230. 230.
    Lehwald S, Wolf F, Ibach H, Hall BM, Mills DL (1987) Surface vibrations on Ni (110): the role of surface stress. Surf Sci 192(1):131–162CrossRefGoogle Scholar
  231. 231.
    Mohamed MH, Kesmodel LL, Hall BM, Mills DL (1988) Surface phonon dispersion on Cu (111). Phys Rev B 37(5):2763–2765CrossRefGoogle Scholar
  232. 232.
    Bortolani V, Santoro G, Harten U, Toennies JP (1984) Surface phonon calculations for noble metals: comparison with he-surface scattering experiments. Surf Sci 148(1):82–89CrossRefGoogle Scholar
  233. 233.
    Bortolani V, Franchini A, Nizzoli F, Santoro G (1984) Explanation of the anomalous peak observed in He-atom scattering from Ag (111). Phys Rev Lett 52(6):429–432CrossRefGoogle Scholar
  234. 234.
    Black JE, Franchini A, Bortolani V, Santoro G, Wallis RF (1987) Surface-phonon dispersion on Cu (110): a comparison of experiment and theory. Phys Rev B 36(6):2996–3001CrossRefGoogle Scholar
  235. 235.
    Daw MS, Baskes MI (1984) Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys Rev B 29(12):6443–6453CrossRefGoogle Scholar
  236. 236.
    Daw MS, Baskes MI (1983) Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals. Phys Rev Lett 50(17):1285–1288CrossRefGoogle Scholar
  237. 237.
    Foiles SM, Baskes MI, Daw MS (1986) Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B 33(12):7983–7991CrossRefGoogle Scholar
  238. 238.
    Ercolessi F, Tosatti E, Parrinello M (1986) Au (100) surface reconstruction. Phys Rev Lett 57(6):719–722CrossRefGoogle Scholar
  239. 239.
    Jacobsen KW, Norskov JK, Puska MJ (1987) Interatomic interactions in the effective-medium theory. Phys Rev B 35(14):7423–7442CrossRefGoogle Scholar
  240. 240.
    Ditlevsen PD, Stoltze P, No JK (1991) Anharmonicity and disorder on the Cu (110) surface. Phys Rev B 44(23):13002–13009CrossRefGoogle Scholar
  241. 241.
    Ditlevsen PD, Nørskov JK (1990) The surface phonons of Cu (111). J Electron Spectrosc Relat Phenom 54:237–244CrossRefGoogle Scholar
  242. 242.
    Hamad BA (2008) Structural and dynamical properties of Ru (0001) surface. Surf Sci 602(24):3654–3659CrossRefGoogle Scholar
  243. 243.
    Goldammer W, Ludwig W (1988) Surface phonons on Si (111) in comparison to EELS experiments. Phys Lett A 133(1–2):85–88CrossRefGoogle Scholar
  244. 244.
    Goldammer W, Ludwig W, Zierau W, Falter C (1984) Surface phonons and reconstruction of a silicon surface. Surf Sci 141(1):139–157CrossRefGoogle Scholar
  245. 245.
    Weber W (1974) New bond-charge model for the lattice dynamics of diamond-type semiconductors. Phys Rev Lett 33(6):371–374CrossRefGoogle Scholar
  246. 246.
    Tütüncü HM, Srivastava GP (1996) Phonon dispersion on a GaAs (110) surface studied using the adiabatic bond charge model. J Phys Condens Matter 8(10):1345–1358CrossRefGoogle Scholar
  247. 247.
    Tütüncü HM, Srivastava GP (1997) Theory of localized phonons on III–V (110) surfaces. J Phys Chem Solids 58(4):685–694CrossRefGoogle Scholar
  248. 248.
    Santini P, Miglio L, Benedek G, Ruggerone P (1991) Surface phonon dispersion curves in GaAs (110) and Ge (111) 2 × 1: a critical comparison. Surf Sci 241(3):346–352CrossRefGoogle Scholar
  249. 249.
    Miglio L, Santini P, Ruggerone P, Benedek G (1989) Dynamics of extensively reconstructed surfaces: Si (111) 2 × 1. Phys Rev Lett 62(26):3070–3073CrossRefGoogle Scholar
  250. 250.
    Chadi DJ (1978) Energy-minimization approach to the atomic geometry of semiconductor surfaces. Phys Rev Lett 41(15):1062–1065CrossRefGoogle Scholar
  251. 251.
    Alerhand OL, Mele EJ (1987) Surface reconstruction and vibrational excitations of Si (001). Phys Rev B 35(11):5533–5546CrossRefGoogle Scholar
  252. 252.
    Allan DC, Mele EJ (1985) Surface reconstruction and lattice dynamics of hydrogenated Si (001): 2 × 1. Phys Rev B 31(8):5565–5568CrossRefGoogle Scholar
  253. 253.
    Mazur A, Pollmann J (1990) Anisotropy of the mean-square displacements at the Si (001)-(2 × 1) surface. Surf Sci 225(1–2):72–80CrossRefGoogle Scholar
  254. 254.
    Ho KM, Bohnen KP (1986) First-principles calculation of surface phonons on the Al (110) surface. Phys Rev Lett 56(9):934–937CrossRefGoogle Scholar
  255. 255.
    Ho KM, Bohnen KP (1988) Surface-phonon calculations for the Al (110) surface. Phys Rev B 38(18):12897–12902CrossRefGoogle Scholar
  256. 256.
    Schöchlin J, Bohnen KP, Ho KM (1995) Structure and dynamics at the Al (111)-surface. Surf Sci 324(2–3):113–121CrossRefGoogle Scholar
  257. 257.
    Rodach T, Bohnen KP, Ho KM (1989) First-principles study of the Na (110) surface. Surf Sci 209(3):481–491CrossRefGoogle Scholar
  258. 258.
    Chen Y, Tong SY, Kim JS, Kesmodel LL, Rodach T, Bohnen KP, Ho KM (1991) Characterization of surface phonons on Cu (001) and Ag (001): first-principles phonon calculations with experimental and theoretical studies of high-resolution electron-energy-loss spectra. Phys Rev B 44(20):11394–11401CrossRefGoogle Scholar
  259. 259.
    Rodach T, Bohnen KP, Ho KM (1993) First principles calculations of lattice relaxation at low index surfaces of Cu. Surf Sci 286(1–2):66–72CrossRefGoogle Scholar
  260. 260.
    Lahee AM, Toennies JP, Wöll C, Bohnen KP, Ho KM (1989) Comparison of helium atom scattering surface phonon dispersion curves of the (1 × 2) reconstructed Au (110) surface with first-principle calculations. EPL (Europhys Lett) 10(3):261–268CrossRefGoogle Scholar
  261. 261.
    Bohnen KP, Eichler A, Hafner J (1996) First principles calculations of surface phonons on Rh (111). Surf Sci 368(1–3):222–225CrossRefGoogle Scholar
  262. 262.
    Yamamoto M, Chan CT, Ho KM, Naito S (1996) First-principles calculation of oxygen adsorption on Zr (0001) surface: possible site occupation between the second and the third layer. Phys Rev B 54(19):14111–14120CrossRefGoogle Scholar
  263. 263.
    Rodach T, Bohnen KP, Ho KM (1993) First principles calculations of surface phonons for Cu (110). Surf Sci 296(1):123–129CrossRefGoogle Scholar
  264. 264.
    Schmidt WG, Bechstedt F, Srivastava GP (1995) III–V (110) surface dynamics from an ab initio frozen-phonon approach. Phys Rev B 52(3):2001–2007CrossRefGoogle Scholar
  265. 265.
    Ho K-M, Fu CL, Harmon BN (1984) Vibrational frequencies via total-energy calculations. Applications to transition metals. Phys Rev B 29(4):1575–1587CrossRefGoogle Scholar
  266. 266.
    Eguiluz AG (1987) Lattice relaxation at an aluminum surface: self-consistent linear-electronic-response approach. Phys Rev B 35(11):5473–5486CrossRefGoogle Scholar
  267. 267.
    Gaspar JA, Eguiluz AG (1989) Microscopic theory of surface phonons in Al (100): mechanisms for the anomalous behavior of the dispersion curves for large wave vectors. Phys Rev B 40(17):11976–11979CrossRefGoogle Scholar
  268. 268.
    Giannozzi P, De Gironcoli S, Pavone P, Baroni S (1991) Ab initio calculation of phonon dispersions in semiconductors. Phys Rev B 43(9):7231–7242CrossRefGoogle Scholar
  269. 269.
    Zein NE (1992) Ab initio calculations of phonon dispersion curves. Application to Nb and Mo. Phys Lett A 161(6):526–530CrossRefGoogle Scholar
  270. 270.
    Xie J, de Gironcoli S, Baroni S, Scheffler M (1999) First-principles calculation of the thermal properties of silver. Phys Rev B 59(2):965–969CrossRefGoogle Scholar
  271. 271.
    Lazzeri M, de Gironcoli S (1998) Ab-initio dynamical properties of the Be (0001) surface. Surf Sci 402:715–718CrossRefGoogle Scholar
  272. 272.
    Lazzeri M, de Gironcoli S (2000) Ab initio study of Be (1010) surface dynamical properties. Surf Sci 454:442–446CrossRefGoogle Scholar
  273. 273.
    Hofmann P, Plummer EW, Bungaro C, Kress W (2000) Surface lattice dynamics of Mg (0001). Phys Rev B 62(24):17012–17019CrossRefGoogle Scholar
  274. 274.
    Fritsch J, Pavone P, Schröder U (1993) Ab initio calculation of surface phonons in GaAs (110). Phys Rev Lett 71(25):4194–4197CrossRefGoogle Scholar
  275. 275.
    Fritsch J, Pavone P, Schröder U (1995) Ab initio calculation of the phonon dispersion in bulk InP and in the InP (110) surface. Phys Rev B 52(15):11326–11334CrossRefGoogle Scholar
  276. 276.
    Eckl C, Honke R, Fritsch J, Pavone P, Schröder U (1997) Ab initio calculation of phonons in semiconductor surfaces. Zeitschrift für Physik B Condensed Matter 104(4):715–720CrossRefGoogle Scholar
  277. 277.
    Nardelli MB, Cvetko D, De Renzi V, Floreano L, Morgante A, Peloi M, Tommasini F (1995) Low-energy vibrations at the InSb (110) surface. Phys Rev B 52(23):16720–16726CrossRefGoogle Scholar
  278. 278.
    Stigler W, Pavone P, Schröder U, Fritsch J, Brusdeylins G, Wach T, Toennies JP (1997) Manifestation of the Dimer correlation in the phonon dispersion of Ge (001). Phys Rev Lett 79(6):1090–1093CrossRefGoogle Scholar
  279. 279.
    Shkrebtii AI, Di Felice R, Bertoni CM, Del Sole R (1995) Ab initio study of structure and dynamics of the Si (100) surface. Phys Rev B 51(16):11201–11204CrossRefGoogle Scholar
  280. 280.
    Casimir HBG (1938) Note on the conduction of heat in crystals. Physica 5(6):495–500CrossRefGoogle Scholar
  281. 281.
    Campisi GJ, Frankl DR (1974) Effects of etching and oxidation on the thermal conductivity of germanium. Phys Rev B 10(6):2644–2646CrossRefGoogle Scholar
  282. 282.
    Liu W, Asheghi M (2004) Phonon–boundary scattering in ultrathin single-crystal silicon layers. Appl Phys Lett 84(19):3819–3821CrossRefGoogle Scholar
  283. 283.
    Martin P, Aksamija Z, Pop E, Ravaioli U (2009) Impact of phonon-surface roughness scattering on thermal conductivity of thin Si nanowires. Phys Rev Lett 102(12):1–4CrossRefGoogle Scholar
  284. 284.
    Santamore DH, Cross MC (2001) Effect of surface roughness on the universal thermal conductance. Phys Rev B 63(18):1–6CrossRefGoogle Scholar
  285. 285.
    Carrillo-Nunez H, Rhyner R, Luisier M, Schenk A (2016) Effect of surface roughness and phonon scattering on extremely narrow InAs-Si Nanowire TFETs. In: Solid-state device research conference (ESSDERC), 2016 46th European, pp 188–191Google Scholar
  286. 286.
    Xie G, Guo Y, Li B, Yang L, Zhang K, Tang M, Zhang G (2013) Phonon surface scattering controlled length dependence of thermal conductivity of silicon nanowires. Phys Chem Chem Phys 15(35):14647–14652CrossRefGoogle Scholar
  287. 287.
    Ghossoub MGKVV, Seong M, Azeredo B, Hsu K, Sadhu JS, Singh PK, Sinha S (2013) Spectral phonon scattering from sub-10 nm surface roughness wavelengths in metal-assisted chemically etched Si nanowires. Nano Lett 13(4):1564–1571CrossRefGoogle Scholar
  288. 288.
    Lin I-T, Liu J-M (2013) Surface polar optical phonon scattering of carriers in graphene on various substrates. Appl Phys Lett 103(8):1–5Google Scholar
  289. 289.
    Yu J-K, Mitrovic S, Tham D, Varghese J, Heath JR (2010) Reduction of thermal conductivity in phononic nanomesh structures. Nat Nanotechnol 5(10):718–721CrossRefGoogle Scholar
  290. 290.
    Maire J, Anufriev R, Yanagisawa R, Ramiere A, Volz S, Nomura M (2017) Heat conduction tuning by wave nature of phonons. Sci Adv 3(8):1–6CrossRefGoogle Scholar
  291. 291.
    Van Hove MA, Somorjai GA (1980) A new microfacet notation for high-Miller-index surfaces of cubic materials with terrace, step and kink structures. Surf Sci 92(2–3):489–518CrossRefGoogle Scholar
  292. 292.
    Balden M, Lehwald S, Ibach H, Ormeci A, Mills DL (1992) Shear horizontal phonons on Ni (110). Phys Rev B 46(7):4172–4179CrossRefGoogle Scholar
  293. 293.
    Yater JE, Kulkarni AD, de Wette FW, Erskine JL (1990) Surface phonons of Ag (110): the importance of odd-symmetry modes in seeking accurate interaction models. J Electron Spectrosc Relat Phenom 54:395–404CrossRefGoogle Scholar
  294. 294.
    Zeppenfeld P, Kern K, David R, Kuhnke K, Comsa G (1988) Lattice dynamics of Cu (110): high-resolution He-scattering study. Phys Rev B 38(17):12329–12337CrossRefGoogle Scholar
  295. 295.
    Benedek G, Toennies JP (1994) Helium atom scattering spectroscopy of surface phonons: genesis and achievements. Surf Sci 299:587–611CrossRefGoogle Scholar
  296. 296.
    Lock A, Toennies JP, Wöll C, Bortolani V, Franchini A, Santoro G (1988) Phonons at the surface of the nearly-free-electron metal Al (111): realization of an ideal surface. Phys Rev B 37(12):7087–7090CrossRefGoogle Scholar
  297. 297.
    Armand G, Masri P (1983) Localized surface modes and resonances for vicinal surfaces: the (117) face of fcc crystals. Surf Sci 130(1):89–123CrossRefGoogle Scholar
  298. 298.
    Black JE, Bopp P (1984) The vibration of atoms at high miller index surfaces: face centred cubic metals. Surf Sci 140(2):275–293CrossRefGoogle Scholar
  299. 299.
    Tian ZJ, Black JE (1994) Phonon spectra and mean square displacements on Cu (11n) vicinal surfaces. Surf Sci 303(3):395–408CrossRefGoogle Scholar
  300. 300.
    Durukanog-Tildelu S, Kara A, Rahman TS (1997) Local structural and vibrational properties of stepped surfaces: Cu (211), Cu (511), and Cu (331). Phys Rev B 55(20):13894–13903CrossRefGoogle Scholar
  301. 301.
    Sklyadneva IY, Rusina GG, Chulkov EV (1998) Vibrational states on vicinal surfaces of Al, Ag, Cu and Pd. Surf Sci 416(1):17–36CrossRefGoogle Scholar
  302. 302.
    Kalla R, Pollmann J (1988) Bond-angle relaxation and electronic structure of Si and Ge overlayers on (110) surfaces of III–V semiconductors. Surf Sci 200(1):80–100CrossRefGoogle Scholar
  303. 303.
    Kitahara K, Metiu H, Ross J, Silbey R (1976) Dynamical theory of migration of an adsorbed atom on solid surfaces. J Chem Phys 65(7):2871–2882CrossRefGoogle Scholar
  304. 304.
    Shimada T, Ohtomo M, Suzuki T, Hasegawa T, Ueno K, Ikeda S, Saiki K, Sasaki M, Inaba K (2008) Step-bunched Bi-terminated Si (111) surfaces as a nanoscale orientation template for quasisingle crystalline epitaxial growth of thin film phase pentacene. Appl Phys Lett 93(22):1–3CrossRefGoogle Scholar
  305. 305.
    Ossó JO, Schreiber F, Kruppa V, Dosch H, Garriga M, Alonso MI, Cerdeira F (2002) Controlled molecular alignment in phthalocyanine thin films on stepped sapphire surfaces. Adv Func Mater 12(6–7):455–460CrossRefGoogle Scholar
  306. 306.
    Desai TV, Woll AR, Schreiber F, Engstrom JR (2010) Nucleation and growth of perfluoropentacene on self-assembled monolayers: significant changes in island density and shape with surface termination. J Phys Chem C 114(47):20120–20129CrossRefGoogle Scholar
  307. 307.
    Rivnay J, Jimison LH, Northrup JE, Toney MF, Noriega R, Lu S, Marks TJ, Facchetti A, Salleo A (2009) Large modulation of carrier transport by grain-boundary molecular packing and microstructure in organic thin films. Nat Mater 8(12):952–958CrossRefGoogle Scholar
  308. 308.
    Bertoni CM, Nardelli MB, Bernardini F, Finocchi F, Molinari E (1990) Chemisorption of H on GaAs (110): a first-principles calculation. EPL (Europhys Lett) 13(7):653–658CrossRefGoogle Scholar
  309. 309.
    Zhu X, Louie SG (1992) Anharmonicity of the hydrogen-carbon stretch mode on diamond (111)-1 × 1. Phys Rev B 45(7):3940–3943CrossRefGoogle Scholar
  310. 310.
    Ancilotto F, Selloni A (1992) Hydrogen-induced dereconstruction of Si (111) 2 × 1 from first-principles molecular dynamics. Phys Rev Lett 68(17):2640–2643CrossRefGoogle Scholar
  311. 311.
    Gai H, Voth GA (1994) First-principles molecular dynamics study of surface vibrations and vibrational mode coupling on the H/Si (111) 1 × 1 surface. J Chem Phys 101(2):1734–1737CrossRefGoogle Scholar
  312. 312.
    Honke R, Fritsch J, Pavone P, Schröder U (1996) Electronic, structural, and dynamical properties of the GaAs (110): Ge surface. Phys Rev B 53(15):9923–9929CrossRefGoogle Scholar
  313. 313.
    Godin TJ, LaFemina JP, Duke CB (1991) Dynamical strain at semiconductor interfaces: structure and surface-atom vibrations of GaAs (110) and GaAs (110)–p (1 × 1)–Sb. J Vac Sci Technol B Microelectron Nanometer Struct Process Meas Phenom 9(4):2282–2289CrossRefGoogle Scholar
  314. 314.
    Schmidt WG, Srivastava GP (1994) First principles calculations of interface phonons of an Epitaxial Sb monolayer on GaAs (110) and InP (110). Solid State Commun 89(4):345–348CrossRefGoogle Scholar
  315. 315.
    Schmidt WG, Srivastava GP (1995) III–V (110) Sb (1 ML): structural and dynamical properties. Surf Sci 331:540–545CrossRefGoogle Scholar
  316. 316.
    Podila R, Vedantam P, Ke PC, Brown JM, Rao AM (2012) Evidence for charge-transfer-induced conformational changes in carbon nanostructure–protein corona. J Phys Chem C 116(41):22098–22103CrossRefGoogle Scholar
  317. 317.
    Hajipour MJ, Akhavan O, Meidanchi A, Laurent S, Mahmoudi M (2014) Hyperthermia-induced protein corona improves the therapeutic effects of zinc ferrite spinel-graphene sheets against cancer. RSC Adv 4(107):62557–62565CrossRefGoogle Scholar
  318. 318.
    Wan S, Kelly PM, Mahon E, Stöckmann H, Rudd PM, Caruso F, Dawson KA, Yan Y, Monopol MP (2015) The “sweet” side of the protein corona: effects of glycosylation on nanoparticle–cell interactions. ACS Nano 9(2):2157–2166CrossRefGoogle Scholar
  319. 319.
    Mudalige TK, Qu H, Linder SW (2015) Asymmetric flow-field flow fractionation hyphenated ICP-MS as an alternative to cloud point extraction for quantification of silver nanoparticles and silver speciation: application for nanoparticles with a protein corona. Anal Chem 87(14):7395–7401CrossRefGoogle Scholar
  320. 320.
    Ritz S, Schöttler S, Kotman N, Baier G, Musyanovych A, Kuharev J, Landfester K, Schild H, Jahn O, Tenzer S, Mailänder V (2015) Protein corona of nanoparticles: distinct proteins regulate the cellular uptake. Biomacromol 16(4):1311–1321CrossRefGoogle Scholar
  321. 321.
    Lehman SE, Mudunkotuwa IA, Grassian VH, Larsen SC (2016) Nano-bio interactions of porous and nonporous silica nanoparticles of varied surface chemistry: a structural, kinetic, and thermodynamic study of protein adsorption from RPMI culture medium. Langmuir 32(3):731–742CrossRefGoogle Scholar
  322. 322.
    Zhou Y, Strachan A (2009) Thermal conduction in molecular materials using coarse grain dynamics: role of mass diffusion and quantum corrections for molecular dynamics simulations. J Chem Phys 131:1–9Google Scholar
  323. 323.
    Ferrari AC (2007) Raman spectroscopy of graphene and graphite: disorder, electron–phonon coupling, doping and nonadiabatic effects. Solid State Commun 143(1):47–57CrossRefGoogle Scholar
  324. 324.
    Majumdar A, Reddy P (2004) Role of electron–phonon coupling in thermal conductance of metal–nonmetal interfaces. Appl Phys Lett 84(23):4768–4770CrossRefGoogle Scholar
  325. 325.
    Hofmann P, Sklyadneva IY, Rienks EDL, Chulkov EV (2009) Electron–phonon coupling at surfaces and interfaces. New J Phys 11(12):1–29CrossRefGoogle Scholar
  326. 326.
    Eiguren A, Hellsing B, Chulkov EV, Echenique PM (2003) Phonon-mediated decay of metal surface states. Phys Rev B 67(23):1–17CrossRefGoogle Scholar
  327. 327.
    Eiguren A, Hellsing B, Reinert F, Nicolay G, Chulkov EV, Silkin VM, Echenique PM (2002) Role of bulk and surface phonons in the decay of metal surface states. Phys Rev Lett 88(6):1–4CrossRefGoogle Scholar
  328. 328.
    Guo Y, Zhang YF, Bao XY, Han TZ, Tang Z, Zhang LX, Jia JF (2004) Superconductivity modulated by quantum size effects. Science 306(5703):1915–1917CrossRefGoogle Scholar
  329. 329.
    Eiguren A, de Gironcoli S, Chulkov EV, Echenique PM, Tosatti E (2003) Electron–phonon interaction at the Be (0001) surface. Phys Rev Lett 91(16):1–4CrossRefGoogle Scholar
  330. 330.
    Sklyadneva IY, Chulkov EV, Echenique PM (2008) Electron–phonon interaction on an Al (001) surface. J Phys Condens Matter 20(16):1–6CrossRefGoogle Scholar
  331. 331.
    Leonardo A, Sklyadneva IY, Silkin VM, Echenique PM, Chulkov EV (2007) Ab initio calculation of the phonon-induced contribution to the electron-state linewidth on the Mg (0001) surface versus bulk Mg. Phys Rev B 76(3):1–7CrossRefGoogle Scholar
  332. 332.
    Giustino F (2017) Electron–phonon interactions from first principles. Rev Mod Phys 89(1):1–63CrossRefGoogle Scholar
  333. 333.
    Monserrat B, Drummond ND, Needs RJ (2013) Anharmonic vibrational properties in periodic systems: energy, electron–phonon coupling, and stress. Phys Rev B 87(14):1–10CrossRefGoogle Scholar
  334. 334.
    Monserrat B, Engel EA, Needs RJ (2015) Giant electron–phonon interactions in molecular crystals and the importance of nonquadratic coupling. Phys Rev B 92(14):1–6CrossRefGoogle Scholar
  335. 335.
    Gao HJ, Sohlberg K, Xue ZQ, Chen HY, Hou SM, Ma LP, Fang XW, Pang SJ, Pennycook SJ (2000) Reversible, nanometer-scale conductance transitions in an organic complex. Phys Rev Lett 84(8):1780–1783CrossRefGoogle Scholar
  336. 336.
    Chen J, Reed MA, Rawlett AM, Tour JM (1999) Large on-off ratios and negative differential resistance in a molecular electronic device. Science 286(5444):1550–1552CrossRefGoogle Scholar
  337. 337.
    Stipe BC, Rezaei MA, Ho W (1998) Single-molecule vibrational spectroscopy and microscopy. Science 280(5370):1732–1735CrossRefGoogle Scholar
  338. 338.
    Smit RHM, Noat Y, Untiedt C, Lang ND, van Hemert MV, Ruitenbeek JMV (2002) Measurement of the conductance of a hydrogen molecule. Nature 419(6910):906–909CrossRefGoogle Scholar
  339. 339.
    Radziemska E, Klugmann E (2002) Thermally affected parameters of the current–voltage characteristics of silicon photocell. Energy Convers Manag 43(14):1889–1900CrossRefGoogle Scholar
  340. 340.
    Madsen GKH, Singh DJ (2006) BoltzTraP: a code for calculating band-structure dependent quantities. Comput Phys Commun 175:67–71CrossRefGoogle Scholar
  341. 341.
    Li W, Carrete J, Katcho NA, Mingo N (2014) ShengBTE: a solver of the Boltzmann transport equation for phonons. Comput Phys Commun 185:1747–1758CrossRefGoogle Scholar
  342. 342.
    Chernatynskiy A, Phillpot SR (2015) Phonon transport simulator (PhonTS). Comput Phys Commun 192:196–204CrossRefGoogle Scholar
  343. 343.
    Beechem T, Duda JC, Hopkins PE, Norris PM (2010) Contribution of optical phonons to thermal boundary conductance. Appl Phys Lett 97(6):061907. doi: 10.1063/1.3478844 CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of Maryland at College ParkCollege ParkUSA

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