Abstract
The lattice thermal conductivity (LTC) of silicon nanowires (NWs) with diameters of 115, 56, 37 and 22 nm in the temperature range of 2–300 K for different pressures ranging from 0 to 10 GPa, was calculated by employing a modified Callaway model. Both longitudinal and transverse modes were explicitly considered within the model. A strategy is utilized to calculate the Debye and phonon group velocity in addition to the bulk modulus and it is derivative for different NW diameters from their related melting temperature under different pressures. The influence of the Gruneisen parameter, surface roughness and dislocation as structurally dependent parameters are successfully exploited to correlate the calculated values of LTC to that of the experimentally measured curves at various pressures including zero. The respective application of the Murnghan and Clapeyron equations for pressure-dependent lattice volume and melting temperature in the Callaway model produces results that tend to be systematically applicable by this model. The confinement and size effects of phonons and the role of pressure in the reduction of LTC are investigated. The peak value of LTC decreases with the increase of pressure for both bulk and its nanowires.
Similar content being viewed by others
References
Laurent S, Bridot J L, Elst L V and Muller R 2010 Future Med. Chem. 2 427
Callaway J 1959 Phys. Rev. 113 1046
Omar M S and Taha H T 2010 Sadhana 35 177
Hieu H K, Hung V V and Hung N V 2011 Commun. Phys. 21 245
Duclos S J, Vohra Y K and Ruoff A L 1990 Phys. Rev. B 41 12021
Durandurdu M and Drabold D A 2003 Phys. Rev. B 67 212101
John S and Tse 2019 Engineering 5 421
Tang X and Dong J 2010 Proc. Natl. Acad. Sci. USA 107 4539
Kinaci A, Haskins J B and Cagin T 2012 J. Chem. Phys. 137 01406
Yang J, Fan Q, Yu Y and Zhang W 2018 Materials 11 2370
Zou J 2010 J. Appl. Phys. 108 034324
Zou J and Balandin A 2001 J. Appl. Phys. 89 2932
Balandin A and Wang K L 1998 Phys. Rev. B 58 1544
Khitun A, Balandin A and Wag K L 1999 Superlatt. Microstruct. 26 181
Asen-Palmer M, Bartvoski K, Gmelin E and Cardona M 1997 Phys. Rev. B 56 9431
Morell D T, Heremans J P and Slack G A 2002 Phys. Rev. B 66 195304
Mamand S M, Omar M S and Muhamad A J 2012 Mater. Res. Bull. 47 1264
Mingo N 2003 Phys. Rev. B 68 113308
Li D 2002 PhD Thesis (Berkeley: University of California)
Qader I N and Omar M S 2017 Bull. Mater. Sci. 40 599
Omar M S 2012 Mater. Res. Bull. 47 3518
Murnaghan F D 1944 Proc. Natl. Acad. Sci. USA 30 244
Magomedov M 2017 Phys. Solid State 59 1085
Abdulla B J, Omar M S and Jiang Q 2018 Sadhana 48 174
Abdulla B J, Jiang Q and Omar M S 2016 Bull. Mater. Sci. 39 1295
Magomedov M N 2010 Study of interatomic interaction, vacancy formation and self-diffusion in crystals (Moscow: Fizmatlit) (in Russian)
Kotchetkov D, Zou J, Balandin A, Florescu D I and Pollak F H 2001 Appl. Phys. Lett. 79 4316
Laing L H and Li B 2006 Phys. Rev. B 73 53303
Dash J G 1999 Rev. Mod. Phys. 71 1737
Post E J and Can J 1953 Canadian J. Phys. 31 112
Zhang Z, Zhao M and Jiang Q 2001 Semicond. Sci. Technol. 16 33
Lobo L Q and Ferreria A G M 2001 J. Chem. Thermodyn. 33 1597
Yang C C and Jiang Q 2004 ScienceDirect 51 1081
R C Weast 1988-1989 CRC Handbook of Chemistry and Physics, 69th edn (CRC Press, Inc., Boca Raton, Florida), p B-219, B-217, F-12, F-27 and F-23
Soler J M, Beltran M R, Michaelian K, Garzon I L, Ordejon P, Sanchez-Portal D et al 2000 Phys. Rev. B 61 5771
Jiang Q, Liang L H and Zhao D S 2001 J. Phys. Chem. B 105 6275
Jiang Q, Shi H X and Zhao M 1999 ScienceDirect 47 2109
Mott N F 1934 Proc. Royal Soc. A 146 465
Jiang Q, Zhou X H and Zhao M 2002 J. Chem. Phys. 117 10269
Jiang Q and Yang C C 2008 Curr. Nanosci. 4 179
Sargent-Welch Scientific Company Skokie: Illinois 1980 Table of Periodic properties of the elements p 1
Yang C C, Li G and Jiang Q 2003 J. Phys. Condens. Matter 15 49619
Yang C C, Li G and Jiang Q 2003 Solid State Commun. 129 437
Magomedov M N 2019 J. Phys. Conf. Ser. 1348 012013
Qader I N, Abdulla B J and Omar M S 2020 Aksaray Univ. J. Sci. Eng. 4 30
Acknowledgements
This work is part of a PhD research program supervised by Prof. M.S. Omer in the Department of Physics, College of Science at Salahaddin University-Erbil, Kurdistan region, Iraq. Their financial support is acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hamarashid, M.M., Omar, M.S. Hydrostatic pressure effects on the processes of lattice thermal conductivity of bulk Silicon and nanowires. Bull Mater Sci 44, 201 (2021). https://doi.org/10.1007/s12034-021-02467-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12034-021-02467-6