Influence of the Size Reduction on the Thermal Conductivity of Bismuth Nanowires

Authors: Ibrahim Nazem Qader1 & Botan Jawdat Abdullah2 & Muhammad Abdullah Hassan1 & Peshawa H.Mahmood3
1Department of Physics, College of Science, Raparin University, Sulaimani, Iraq
2Department of Physics, College of Science, Salahaddin University, Erbil, Iraq
3Department of Chemistry, College of Science, Raparin University, Sulaimani, Iraq

Abstract:  Theoretical calculations on the lattice thermal conductivity (LTC) of the bulk bismuth (Bi) and nanowires (NWs) have been studied with diameters 98 nm, 115 nm and 327 nm in the 〈110〉 direction from temperature range of 0 to 300 K. Several size dependent parameters are estimated to correlate the value of LTC using the modified Morelli-Callaway model, including mass density, Umklapp, normal, boundary impurity, dislocation, and phonon-electron scattering rate. In a particular range of temperature, their effects are varied on the bell-shaped LTC. In accordance, Grüneisen parameter has been calculated for each case and the obtained values fitted with the experimental data of LTC. The result indicates that the impact of increasing the surface area to volume ratio is satisfied on the LTC for some Bi NWs. At a specific temperature, the LTC drops with the reduction of size of NWs. The effects of the variation in size on LTC are calculated and the obtained results are in good agreement with the experimental data.

Keywords: Lattice Thermal Conductivity, Bismuth, Nanowires, Mass Density, Morelli-Callaway Model
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doi: 10.23918/eajse.v4i3sip55


Abdullah, B. J. (2010). Effect of size on lattice thermal conductivity in Si and Ge nanowires from 2K to room temperatures. Physics of Aero Dispersed Systems, 47, 67-80.

Abdullah, B. J., Jiang, Q., & Omar, M. S. (2016). Effects of size on mass density and its influence on mechanical and thermal properties of ZrO2 nanoparticles in different structures. Bulletin of Materials Science, 39(5), 1295-1302.

Abdullah, B. J., Omar, M. S., & Jiang, Q. J. (2016). Grüneisen Parameter and Its Related Thermodynamic Parameters Dependence on Size of Si Nanoparticles. ZANCO Journal of Pure and Applied Sciences, 28(4), 126-132.

Asen-Palmer, M., Bartkowski, K., Gmelin, E., & Cardona, M. (1997). AP Zhernov, AV Inyushkin, A. Taldenkov, and VI Ozhogin, KM Itoh and EE Haller. Phys. Rev. B, 56, 9431-9447.

Callaway, J. (1959). Model for lattice thermal conductivity at low temperatures. Physical Review, 113(4), 1046.

Caylor J, C. K., Stuart J, Colpitts T, Venkatasubramanian R. (2005). Enhanced thermoelectric performance in PbTe-based superlattice structures from reduction of lattice thermal conductivity. Applied Physics Letters, 87.

Choi, S., Wang, K., Leung, M., Stupian, G., Presser, N., Morgan, B., . . . & Tueling, M. (2000). Fabrication of bismuth nanowires with a silver nanocrystal shadowmask. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, 18(4), 1326-1328.

Cornelius, T., Brötz, J., Chtanko, N., Dobrev, D., Miehe, G., Neumann, R., & Molares, M. T. (2005). Controlled fabrication of poly-and single-crystalline bismuth nanowires. Nanotechnology, 16(5), S246.

Gupta, I., & Trikha, S. (1978). Lattice Thermal Conductivity of Solid Neon in the Temperature Range 0.5 to 10 K. Physica Status Solidi (b), 88(2), 815-818.

Herring, C. (1954). Role of low-energy phonons in thermal conduction. Physical Review, 95(4), 954.

Holland, M. (1963). Analysis of lattice thermal conductivity. Physical Review, 132(6), 2461.

Kamatagi, M., Vaidya, R., Sankeshwar, N., & Mulimani, B. (2009). Low-temperature lattice thermal conductivity in free-standing GaN thin films. International Journal of Heat and Mass Transfer, 52(11-12), 2885-2892.

Klemens, P. (1955). The scattering of low-frequency lattice waves by static imperfections. Proceedings of the Physical Society Section A, 68(12), 1113.

Li, L., Yang, Y., Fang, X., Kong, M., Li, G., & Zhang, L. (2007). Diameter-dependent electrical transport properties of bismuth nanowire arrays. Solid State Communications, 141(9), 492-496.

Liang, L., & Li, B. (2006). Size-dependent thermal conductivity of nanoscale semiconducting systems. Physical Review B, 73(15), 153303.

Lin, Y.-M., Cronin, S. B., Ying, J. Y., Dresselhaus, M., & Heremans, J. P. (2000). Transport properties of Bi nanowire arrays. Applied Physics Letters, 76(26), 3944-3946.

Liu, K., Chien, C., Searson, P., & Yu-Zhang, K. (1998). Structural and magneto-transport properties of electrodeposited bismuth nanowires. Applied Physics Letters, 73(10), 1436-1438.

Lü, X., Chu, J., & Shen, W. (2003). Modification of the lattice thermal conductivity in semiconductor rectangular nanowires. Journal of Applied Physics, 93(2), 1219-1229.

Madelung, O. (2012). Semiconductors: Data handbook. Springer Science & Business Media.

Mamand, S., & Omar, M. (2014). Effect of Parameters on Lattice Thermal Conductivity in Germanium Nanowires. Paper presented at the Advanced Materials Research.

Mamand, S., Omar, M., & Muhammad, A. (2012). Nanoscale size dependence parameters on lattice thermal conductivity of Wurtzite GaN nanowires. Materials Research Bulletin, 47(5), 1264-1272.

Moore, A. L., Pettes, M. T., Zhou, F., & Shi, L. (2009). Thermal conductivity suppression in bismuth nanowires. Journal of Applied Physics, 106(3), 034310.

Morelli, D., Heremans, J., & Slack, G. (2002). Estimation of the isotope effect on the lattice thermal conductivity of group IV and group III-V semiconductors. Physical Review B, 66(19), 195304.

Nabarro, F. (1951). The interaction of screw dislocations and sound waves. Paper presented at the Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences.

Omar, M. (2012). Models for mean bonding length, melting point and lattice thermal expansion of nanoparticle materials. Materials Research Bulletin, 47(11), 3518-3522.

Post, E. (1953). On the characteristic temperatures of single crystals and the dispersion of the “debye heat waves”. Canadian Journal of Physics, 31(1), 112-119.

Qader, I. N., Abdullah, B. J., & Karim, H. H. (2017). Lattice Thermal Conductivity of Wurtzite Bulk and Zinc Blende CdSe Nanowires and Nanoplayer. Eurasian Journal of Science & Engineering, 3(1), 9-26.

Qader, I. N., & Omar, M. (2017). Carrier concentration effect and other structure-related parameters on lattice thermal conductivity of Si nanowires. Bulletin of Materials Science, 40(3), 599-607.

Roh, J. W., Hippalgaonkar, K., Ham, J. H., Chen, R., Li, M. Z., Ercius, P., . . . Lee, W. (2011). Observation of anisotropy in thermal conductivity of individual single-crystalline bismuth nanowires. ACS Nano, 5(5), 3954-3960.

Simon, S. H. (2013). The Oxford solid state basics. OUP Oxford.

Wang, X., Zhang, J., Shi, H., Wang, Y., Meng, G., Peng, X., . . . Fang, J. (2001). Fabrication and temperature dependence of the resistance of single-crystalline Bi nanowires. Journal of Applied Physics, 89(7), 3847-3851.

Wingert, M. C., Chen, Z. C., Dechaumphai, E., Moon, J., Kim, J.-H., Xiang, J., & Chen, R. (2011). Thermal conductivity of Ge and Ge–Si core–shell nanowires in the phonon confinement regime. Nano Letters, 11(12), 5507-5513.

Xu, Y., Ren, Z., Ren, W., Cao, G., Deng, K., & Zhong, Y. (2008). Magnetic-field-assisted solvothermal growth of single-crystalline bismuth nanowires. Nanotechnology, 19(11), 115602.

Yang, F., Liu, K., Chien, C., & Searson, P. (1999). Large magnetoresistance and finite-size effects in electrodeposited single-crystal Bi thin films. Physical Review Letters, 82(16), 3328.