Abstract
A phenomenological model based on thermodynamical variables is used to analyze the optical properties of nanomaterials. The expression of cohesive energy given by Qi and Wang model is extended to study the variation of the energy band gap, vibrational frequency, and static dielectric constant with size for nanoparticles, nanowires, and nanofilms. The energy bandgap is observed to increase in nanostructures with a reduction in size while the reduction in the vibrational frequency of nanostructures is found with a decrease in size from model calculations. The dielectric constant is also found decreasing with the size reduction of the nanostructure to the nanoscale. As the number of surface atoms changes with change in the shape of the nanomaterial, the shape effect on optical properties is also studied. The size and shape effect are found prominent in nanostructures up to the size limit of approximately 30 nm; however, the effect of size and shape becomes less significant as the size is more than 30 nm. The model predictions are consistent with the available experimental and simulated trend which supports the validity of the model theory.
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References
A. Pierret, C. Bougerol, S. Murcia-Mascaros, A. Cros, H. Renevier, B. Gayral, B. Daudin, Nanotechnology 24, 115704 (2013)
A.S. Edelstein, R.C. Cammarata, Nanomaterials: synthesis, properties and applications (Institute of Physics, Bristol, 1996)
B. Bonham, G. Guisbiers, Nanotechnology 28, 245702 (2017)
L. Huang, Z.L. Wei, F.M. Zhang, X.S. Wu, J Alloys Compd 648, 591 (2015)
J.A. Van Vechten, M. Wautelet, Phys Rev B 23, 5543 (1981)
G. Guisbiers, M. Kazan, O.V. Overschelde, M. Wautelet, S. Pereira, J Phys Chem C 112, 4097 (2008)
G. Guisbiers, Adv Phys X 4, 1668299 (2019)
C.C. Yang, Y.-W. Mai, Mater Sci Eng R Rep 79, 1 (2014)
M. Goyal, B.R.K. Gupta, Pramana J Phys 90(6), 80 (2018)
M. Singh, M. Goyal, K. Devlal, J Taibah Univ Sci 12, 470 (2018)
M. Li, H. Li, IEEE Trans Nanotechnol 11, 1004 (2012)
C. Delerue, M. Lannoo, G. Allan, Phys Rev B 68, 115411 (2003)
H. Li, H.J. Xiao, T.S. Zhu, H.C. Xuan, M. Li, J Phys Chem 119, 12002 (2015)
A. Biswas, A. Corani, A. Kathiravan, Y. Infahsaeng, A. Yartsev, V. Sundstrom, Nanotechnology 24, 195601 (2013)
W.H. Qi, M.P. Wang, Mater Chem Phys 88, 280 (2004)
J. Shanker, M. Kumar, Phys Status Solid B 158, 11 (1990)
R. Kumar, G. Sharma, M. Kumar, J Thermodyn 328051, 1 (2013)
C. Kittel, Introduction to solid state physics, 7th edn. (Wiley, New York, 1996)
M. Li, J.C. Li, Mater Lett 60, 2526 (2006)
R. Zallen, The physics of amorphous solids (Wiley, New York, 1983)
C.Q. Sun, X.W. Sun, B.K. Tay, S.P. Lau, H.T. Huang, S. Li, J Phys D Appl Phys 34, 2359 (2001)
H.M. Lu, X.K. Meng, Sci Rep 5, 16939 (2015)
D.R. Penn, Phys Rev 128, 2093 (1962)
W.H. Qi, M.P. Wang, Q.H. Liu, J Mater Sci 40, 2737 (2005)
W.H. Qi, B.Y. Huang, M.P. Wang, Z.M. Yin, J. Li, Phys B 403, 2386 (2008)
W.H. Qi, Phys B 368, 46 (2005)
D.D.D. Ma, C.S. Lee, F.C.K. Au, S.Y. Tong, S.T. Lee, Science 299, 1874 (2003)
H. Yu, J. Li, R.A. Loomis, L.W. Wang, W.E. Buhro, Nat Mat 21, 517 (2003)
J. Li, L.W. Wang, Phys Rev 72, 125325 (2005)
G.X. Cheng, H. Xia, K.J. Chen, W. Zhang, X.K. Zhang, Phys Stat Sol 118, K51 (1990)
Ch. Ossadnik, S. Veprek, I. Gregora, Thin Solid Films 337, 148 (1999)
Y. Feng, Y. Liu, B. Wang, Acta Mech 217, 149 (2011)
H.M. Cheng, K.F. Lin, H.C. Hsu, C.J. Lin, L.J. Lin, W.F. Heish, J Phys Chem B 109, 18385 (2005)
M.J. Seong, O.I. Micic, A.J. Nozik, A.M. Ascarenhas, H.M. Cheong, Appl Phys Lett 82, 185 (2003)
H.G. Yoo, P.M. Fauchet, Phys Rev B 77, 115355 (2008)
R. Tsu, D. Babic, Appl Phys Lett 64, 1806 (1994)
R. Tsu, L. Ioriatti, J.F. Harvey, H. Shen, R.A. Lux, Mater Res Soc Symp Proc 283, 437 (1993)
M. Li, J.C. Li, Q. Jiang, Int J Mod Phys B 24, 2297 (2010)
C.C. Yang, Q. Jiang, Mater Sci Eng B 131, 191 (2006)
C.C. Yang, S. Li, J Phys Chem C 112, 14193 (2008)
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Goyal, M., Singh, M. Size and shape dependence of optical properties of nanostructures. Appl. Phys. A 126, 176 (2020). https://doi.org/10.1007/s00339-020-3327-9
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DOI: https://doi.org/10.1007/s00339-020-3327-9