Abstract
A phenomological model is described here to study the effect of size, shape and phonon scattering on the thermal conductivity of nanostructures. Using the classical model proposed by Guisbiers et al (Phys. Chem. Chem. Phys. 12, 7203 (2010), J. Phys. Chem. C 112, 4097 (2008)) in terms of the melting temperature of nanostructures, the expression for variation of thermal conductivity is obtained in terms of shape and size parameter. An additional term is included in the expression of thermal conductivity to consider the impact of phonon scattering due to the surface roughness with a decrease in size. The expression of thermal conductivity is obtained for spherical nanosolids, nanowires and nanofilms. The thermal conductivity is found to decrease in nanostructures in comparison with the counterpart bulk material. The values of thermal conductivity obtained from the present model are found to be close to the available experimental data for different values of roughness parameter which verifies the suitability of the model.
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References
C Weisbuch and B Vinter, Quantum semiconductor structures (Academic Press, San Diego, CA, 1991)
A Yariv, Quantum electronics, 3rd edn (Wiley, New York, 1989)
R J Moitsheki and C Harley, Pramana – J. Phys. 77, 519 (2011)
T Yao, Appl. Phys. Lett. 51(22), 1798 (1987)
W S Capinski and H J Maris, Physica B 219–220, 699 (1996)
E Ziambaras and P Hyldgaard, J. Appl. Phys. 99, 054303 (2006)
M Malligavathy, S Iyyapushpam, S T Nishanthi and D Pathinettam Paditan, Pramana – J. Phys. 90: 44 (2018)
Y He and G Galli, Phys. Rev. Lett. 108, 215901 (2012)
W Liu and M Asheghi, Appl. Phys. Lett. 84, 3819 (2004)
Z Wang and N Mingo, Appl. Phys. Lett. 97, 101903 (2010)
C Q Sun, L K Pan, C M Li and S Li, Phys. Rev. B 72, 134301 (2005)
A Malhotra and M Maldovan, J. Appl. Phys. 120, 204305 (2016)
L H Liang and B Li, Phys. Rev. B 73, 153303 (2006)
D G Cahill, P V Braun, G Chen, D R Clarke, S Fan, K E Goodson, P Keblinski, W P King, G D Mahan, A Majumdar, H J Maris, S R Phillpot, E Pop and L Shi, Appl. Phys. Rev. 1, 011305 (2014)
G Guisbiers, Nanoscale Res. Lett. 5, 1132 (2010)
G Guisbiers and L Buchaillot, Phys. Lett. A 374, 305 (2009)
G Guisbiers, D Liu, Q Jiang and L Buchaillot, Phys. Chem. Chem. Phys. 12, 7203 (2010)
G Guisbiers, M Kazan, O V Overschelde, M Wautelet and S Pereira, J. Phys. Chem. C 112, 4097 (2008)
M Wautelet, Phys. Lett. A 246, 341 (1998)
G Guisbiers and M José-Yacaman, Encyclopedia of interfacial chemistry: Surface science and electrochemistry, in: Reference module in chemistry, molecular sciences and chemical engineering (Elsevier, New York, 2018) pp. 875–885
J Ferrante, J H Rose and J R Smith, Appl. Phys. Lett. 44, 53 (1984)
F A Lindemann, Phys. Z. 11, 609 (1910)
J G Dash, Rev. Mod. Phys. 71, 1737 (1999)
J M Zimann, Electrons and phonons (Clarendon Press, Oxford, 1960), pp. 288, 58, 296, 456
E J Post, Can. J. Chem. 31, 112 (1953)
A R Regal and V M Glazov, Semiconductors 29(5), 405 (1995)
G Soyez, J A Eastman, L J Thompson, G R Bai, P M Baldo and A W McCormick, Appl. Phys. Lett. 77, 1155 (2000)
J Lim, K Hippalgaonkar, S C Andrews, A Majumdar and P Yang, Nano Lett. 12, 2475 (2012)
D Li, Y Wu, P Kim, L Shi, P Yang and A Majumdar, Appl. Phys. Lett. 83, 3186 (2003)
Y S Ju and K E Goodson, Appl. Phys. Lett. 74(20), 3005 (1999)
W S Capinski, H J Maris, T Ruf, M Cardona, K Ploog and D S Katzer, Phys. Rev. B 59, 8105 (1999)
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Goyal, M. Shape, size and phonon scattering effect on the thermal conductivity of nanostructures. Pramana - J Phys 91, 87 (2018). https://doi.org/10.1007/s12043-018-1660-8
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DOI: https://doi.org/10.1007/s12043-018-1660-8