Generic placeholder image

Nanoscience & Nanotechnology-Asia

Editor-in-Chief

ISSN (Print): 2210-6812
ISSN (Online): 2210-6820

Research Article

Lattice Thermal Conductivity Modelling of a Diatomic Nanoscale Material

Author(s): Adil H. Awad*

Volume 10, Issue 5, 2020

Page: [602 - 609] Pages: 8

DOI: 10.2174/2210681209666190423142040

Price: $65

Abstract

Introduction: A new approach for expressing the lattice thermal conductivity of diatomic nanoscale materials is developed.

Methods: The lattice thermal conductivity of two samples of GaAs nanobeam at 4-100K is calculated on the basis of monatomic dispersion relation. Phonons are scattered by nanobeam boundaries, point defects and other phonons via normal and Umklapp processes.

Results: A comparative study of the results of the present analysis and those obtained using Callaway formula is performed. We clearly demonstrate the importance of the utilised scattering mechanisms in lattice thermal conductivity by addressing the separate role of the phonon scattering relaxation rate. The formulas derived from the correction term are also presented, and their difference from Callaway model is evident. Furthermore their percentage contribution is sufficiently small to be neglected in calculating lattice thermal conductivity.

Conclusion: Our model is successfully used to correlate the predicted lattice thermal conductivity with that of the experimental observation.

Keywords: Thermal conductivity, GaAs nanobeam, dispersion relation, diatomic nanostructure, scattering mechanisms.

Graphical Abstract

[1]
Klemens, P.G. Solid State Physics,F; Seitz, D., ; Turnbull, , Eds.; Academic Press: New York, 1958, Vol. 7, p. 1.
[2]
Carruthers, P. Theory of thermal conductivity of solids at low temperatures. Rev. Mod. Phys., 1961, 33(1), 92-138.
[3]
Callaway, J. Model for lattice thermal conductivity at low temperatures. Phys. Rev., 1959, 113(4), 1046-1051.
[4]
Holland, M.G. Analysis of lattice thermal conductivity. Phys. Rev., 1963, 132, 2461-2471.
[5]
Dubey, K.S.G.S.; Verma, G.S. Phonon conductivity of InSb and GaAs in the temperature range 2-300°K. Phys. Rev., 1971, B4, 4491-4531.
[6]
Hunt, D.R. Ph. D. Thesis, College of Science - Swansea University, U.K.. 1974.
[7]
Dubey, K.S. Analysis of lattice thermal conductivity of GaAs at high temperatures. J. Therma. Anal., 1978, 14, 213-219.
[8]
Al-Edani, M.C.; M., Sc Thesis, University of Basrah, Basrah (Iraq). 1978.
[9]
Awad, A.H.; Hussain, W.A. Phonon conductivity of Gallium Arsenide. Dirasat, Nat. Eng. Sci., 1998, 25(1), 167-174.
[10]
Ansari, M.A.; Ashokan, V.; Indu, B.D.; Kumar, R. Lattice thermal conductivity of GaAs. Acta Pys.Polonica, 2012, A121(3), 639-646.
[11]
Morkoc, H. Nitride semiconductors and devices; Springer-Verlag: Berlin, 1999.
[12]
Majumdar, A. Microscale heat conduction in dielectric thin films. J. Heat Trans, 1993, 115, 7-16.
[13]
Asheghi, M.; Leung, Y.K.; Wong, S.S.; Goodson, K.E. Phonon-boundary scattering in thin silicon layers. Appl. Phys. Lett., 1997, 71(13), 1798-1800.
[14]
Balandin, A.; Wang, K.L. Significant decrease of the lattice thermal conductivity due to phonon confinement in a free-standing semiconductor quantum well. Phys. Rev., 1998, B58, 1544-1549.
[15]
Balandin, A.; Wang, K.L. Effect of phonon confinement on the thermoelectric figure of merit of quantum wells. J. Appl. Phys., 1998, 84, 6149-6153.
[16]
Li, D.; Wu, Y.; Fan, R.; Yang, P.; Majumdara, A. Thermal conductivity of Si/SiGe superlattice nanowires. Appl. Phys. Lett., 2003, 83(15), 3186-3188.
[17]
Mingo, N. Calculation of nanowire thermal conductivity using complete phonon dispersion relations. Phys. Rev., 2003, B68, 113308-113311.
[18]
Mingo, N.; Yang, L.; Li, D.; Majumdar, A. Predicting the thermal conductivity of Si and Ge nanowires. Nano Lett., 2003, 3, 1713-1716.
[19]
Pokatilov, E.P.; Nika, D.L.; Balandin, A.A. Acoustic-phonon propagation in rectangular semiconductor nanowires with elastically dissimilar barriers. Phys. Rev., 2005, B72113311
[20]
Hochbaum, A.I.; Chen, R.; Delgado, R.D.; Liang, W.; Garnett, E.C.; Najarian, M.; Majumdar, A.; Yang, P. Enhanced thermoelectric performance of rough silicon nanowires. Nature, 2008, 451, 163-167.
[21]
Martin, P.; Aksamija, Z.; Pop, E.; Ravaioli, U. Impact of phonon-surface roughness scattering on thermal conductivity of thin Si nanowires. Phys. Rev. Lett., 2009, 102, 125503-4.
[22]
Sellan, D.P.; Turney, J.E.; McGaughey, A.J.H.; Amon, C.H. Cross-plane phonon transport in thin films. J. Appl. Phys., 2010, 108(11)113524
[23]
Turney, J.E.; McGaughey, A.J.H.; Amon, C.H. In-plane phonon transport in thin films. J. Appl. Phys., 2010, 107, 024317-8.
[24]
McGaughey, A.J.H.; Landry, E.S.; Sellan, D.P.; Amon, C.H. Size-dependent model for thin film and nanowire thermal conductivity. Appl. Phys. Lett., 2011, 99, 131904-3.
[25]
Tian, Z.; Esfarjani, K.; Shiomi, J.; Henry, A.S.; Chen, G. On the importance of optical phonons to thermal conductivity in nanostructures. Appl. Phys. Lett., 2011, 99, 053122-6.
[26]
Hopkins, P.E.; Reinke, C.M.; Su, M.F.; Olsson, R.H.; Shaner, E.A.; Leseman, Z.C.; Serrano, J.R.; Phinney, L.M.; El-Kady, I. Reduction in the thermal conductivity of single crystalline silicon by phononic crystal patterning. Nano Lett., 2011, 11(1), 107-112.
[27]
McGaughey, A.J.H.; Jain, A. Nanostructure thermal conductivity prediction by Monte Carlo sampling of phonon free paths. Appl. Phys. Lett., 2012, 100, 061911-061913.
[28]
Shi, L.; Hao, Q.; Yu, C.; Mingo, N.; Kong, X.; Wang, Z.L. Thermal conductivities of individual tin dioxide nanobelts. Appl. Phys. Lett., 2004, 84, 2638-2640.
[29]
Mingo, N.; Broido, D.A. Carbon nanotube ballistic thermal conductance and its limits. Phys. Rev. Lett., 2005, 95, 096105-4.
[30]
Mingo, N.; Broido, D.A. Length dependence of carbon nanotube thermal conductivity and the “Problem of Long Waves”. Nano Lett., 2005, 5(7), 1221-1225.
[31]
Fon, W.; Schwab, K.C.; Warlock, J.M.; Roukes, M.L. Phonon scattering mechanisms in suspended nanostructures from 4 to 40 K. Phys. Rev., 2002, B66, 045302-045305.
[32]
Barman, S.; Srivastava, G.P. Thermal conductivity of suspended GaAs nanostructures: Theoretical study. Phys. Rev., 2007, B73, 205308-205306.
[33]
Mamand, S.M.; Omar, M.S.; Muhammed, A.J. Calculation of lattice thermal conductivity of suspended GaAs nanobeams: Effect of size dependent parameters. Adv. Mat. Lett, 2012, 3(6), 449-458.
[34]
Kittel, C. Introduction to Solid State Physics, 7th ed; John Wiley and Sons, Inc.: New York, 1996.
[35]
Awad, A.H. Modeling nanostructure lattice thermal conductivity: The dispersion relation role. J. Therm. Anal. Calor., 2015, 119(2), 1459-1467.
[36]
Herring, C. Role of low energy phonons in thermal conduction. Phys. Rev., 1954, 95, 954-960.
[37]
Driscoll, C.M.H.; Willoughby, A.F.W.; Mullin, J.B.; Straughan, B.W. Gallium Arsenide and Related Compounds 1974; Bok, J., Ed.; Institute of Physics: London, and Bristol, 1975.
[38]
Kaplan, H.; Sullivan, J.J. Lattice vibrations of zinc-blende structure crystals. Phys. Rev., 1969, 130, 120.
[39]
Awad, A.H.; Dubey, K.S. Analysis of the lattice thermal conductivity and phonon–phonon scattering relaxation rate: Application to Mg2Ge and Mg2Si. J. Therm. Anal., 1982, 24, 233-2360.
[40]
Awad, A.H. Debye temperature dependent lattice thermal conductivity of silicon. J. Therm. Anal. Calor., 1999, 55, 187-196.
[41]
Awad, A.H. Contribution to the lattice thermal conductivity due to the three phonon normal processes in the presence of core dislocations in the frame of the Callaway integral. Acta Phys. Hungar., 1990, 67(1-2), 211-216.
[42]
Li, D.; Wu, Y.; Kim, P.; Shi, L.; Yang, P.; Majumdar, A. Thermal conductivity of individual silicon nanowires. Appl. Phys. Lett., 2003, 83(14), 2934-2944.
[43]
Kazan, M.; Guisbiers, G.; Pereira, S.; Correia, M.R.; Masri, P.; Bruyant, A.; Volz, S.; Royer, P. Thermal conductivity of silicon bulk and nanowires: Effects of isotopic composition, phonon confinement, and surface roughness. J. Appl. Phys., 2010, 107, 083503-14.
[44]
Chen, K.Q.; Li, W.X.; Duan, W.; Shuai, Z.; Gu, B.L. Effect of defects on the thermal conductivity in a nanowire. Phys. Rev., 2005, B72, 045422-5.
[45]
Santamore, D.H.; Cross, M.C. Effect of Phonon scattering by surface roughness on the universal thermal conductance. Phys. Rev. Lett., 2001, 87115502

Rights & Permissions Print Cite
© 2024 Bentham Science Publishers | Privacy Policy