Effect of Size and Shape on Static Refractive Index, Dielectric constant and Band gap of Nano solids

G.R. Patel¹ , T.C. Pandya²

1. Physics Department, Government Science College, Gandhinagar, Gujarat, India.
2. Physics Department, St. Xaviers College, Navrangpura, Ahmedabad, Gujarat, India.

Correspondence should be addressed to: grpalp94@gmail.com.

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.37-42, Feb-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrpas/v6i1.3742

Online published on Feb 28, 2018

Copyright © G.R. Patel, T.C. Pandya . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In the present study, a simple theoretical model has been proposed for computation of optical properties such as static refractive index, static dielectric constant and band gap for nanosolids having different nanostructures of different shape based on size dependent atomic cohesive energy. We have computed size dependent static dielectric constant for silicon nanofilm and deviation in band gap for Si nanowire and nanofilm for different size. We have also computed size dependent bandgap of Ge nanowire having square cross section. We have also found that band gap increases as particle size decreases. Our results are compared with the available experimental and simulated data. A close agreement of the computed results with available experimental and simulated data validates the present theoretical model. The present relationships of Static Refractive Index, Dielectric constant and Band gap of Nano solids are potentially applicable for those materials whose experimental data are not available.

Key-Words / Index Term :
Band-gap, refractive index, dielectric constant, size and shape dependent, Si, Ge

References :
[1] H.Lu, X.Meng, “Correlation between bandgap, dielectric constant, young modulus and melting temperature of GaN nanocrystals and their size and shape dependence”, Scientific Reports 5: 16939, 2015.
[2] M. Li, J.C. Li, Q. Jiang, “Size-Dependent Band-Gap and Dielectric Constant of Si Nanocrystals, International Journal of Modern Physics B Vol.24, Issue 15 & 16, pp. 2297–2301, 2010.
[3] K. K. Nanda, S. N. Sahu, S. N. Behera, “Liquid drop-model for size-dependent melting of low-dimensional system”, PHYSICAL REVIEW A Vol. 66, pp. 013208,2002.
[4] K. K. Nanda, “A simple classical approach for the melting temperature of inert-gas nanoparticles", Chem. Phys. Lett., Vol. 419, pp. 195–200, 2006.
[5] W.H.Qi., Physica B, “Size effect on melting temperature of nanosolids”, Vol.368, pp.46–50, 2005.
[6] Q. Jiang, J. C. Li, and B. Q. Chi, “Size-dependent cohesive energy of nanocrystals”, Chem. Phys. Lett., Vol. 366, pp. 551–554, 2002.
[7] W. H. Qi, M. P. Wang, and G. Y. Xu, “The particle size dependence of cohesive energy of metallic nanoparticles”, Chem. Phys. Lett., Vol.372, pp. 632–634, 2003.
[8] A. D. Yoffe, “Semiconductor quantum dots and related systems: electronic, optical, luminescence and related properties of low dimensional systems”, Adv. Phys. Vol.50, pp. 1–208, 2001.
[9] C. Delerue, M. Lannoo, and G. Allan, “Concept of dielectric constant for nanosized systems”. Phys. Rev. B, Vol.68, pp. 115411, 2003.
[10] G. Guisbiers, Di Liu, Q. Jiang, and L. Buchaillot, “Theoretical predictions of wurtzite III-nitride nano-materials properties”. Phys. Chem. Chem. Phys., Vol.12, pp. 7203–7210, 2010.
[11] J. Zhang, “Small-scale effect on the piezoelectric potential of gallium nitride nanowires”. Appl. Phys. Lett., Vol.104, pp. 253110, 2014.
[12] G. Guisbiers, “Size-dependent materials properties toward a universal Equation. Nanoscale” Res. Lett., Vol.5, pp. 1132–1136, 2010.
[13] Feynman, Leighton, Sands, “The Feynman lectures on physics”, California Institute of Technology, Vol.1, Ch.31.
[14] C kittle,” Introduction to solid state physics” Wiley India Pvt. Ltd., 2015.
[15] Li. Lihong, Ma. Hansong, and Wei.Yueguang, “Size- dependent elastic modulus and vibration frequency of nanocrystals”, Journal of Nanomaterials, 2011.
[16] W.H. Qi, M. P. Wang, “Size and shape dependent melting temperature of metallic nanoparticles”, Materials Chemistry and Physics, Issue 16, Vol.88, pp. 280-284, 2004.
[17] W.H. Qi et al., “Shape factor for non-cylindrical nanowires”, physica B, vol.403, Issue 13-16, pp. 2386-2389, 2008.
[18] G. R. Patel, N.A. Thakar, T.C. Pandya,” Size and shape dependent melting temperature and thermal expansivity of metallic semiconductor nanoparticles” in the 60th DAESSPS, AIP Conference Proceedings. 1731, 050042, 2015.
[19] N.M. Ravindra, P. Ganapathy, Jinsoo Choi, “Energy gap-refractive index relations in semiconductors” –An overview Infrared Physics & Technology, Vol. 50, pp. 21–29, 2007.
[20] R. Zallen, “The Physics of Amorphous Solids”, Wily, New York, 1983.
[21] C. Delerue, M. Lannoo and G. Allan, “concept of dielectric constant for nanosized systems”, Phys. Rev. B Vol.68, pp. 115411, 2003.
[22] H. G. Yoo and P. M. Fauchet, “Dielectric constant reduction in silicon nanostructure”, Phys. Rev. B, Vol.77, pp. 115355, 2008.
[23] L. Dorigoni, O. Bisi, F. Bernardini and S. Ossicini, “Electron states and luminescence transition in porous silicon”, Phys Rev B, Vol. 53, pp. 4557, 1996.
[24] D. D. D. Ma, C.S.Lee, F.C.K.Au, S.Y.Tong, S.T.Lee, “Small-diameter silicon nanowire, surface Science”, Vol. 299, pp.1874, 2003.
[25] X. Y. Zhao, C. M. Wei, L. Yang, and M. Y. Chou, “Quantum confinement and electronic properties of silicon nanowires” Phys. Rev. Lett., Vol.92, pp. 236805, 2004.
[26] Y. Kanemitsu, H. Uto and Y. Masumoto, “Microstructure and optical properties of free standing porous silicone films: size dependence of absorption spectra in Si nanometer sized – crystallites” Phys. Rev. B, Vol.48, pp. 2827, 1993.
[27] C. Y. Yeh, S. B. Zhang and A. Zunger, “Confinement, surface, and chemisorption effects on the optical properties of Si quantum wires”, Phys Rev, Vol.40, pp. 14405, 1994.
[28] T.Van Buuren, L. N. Dinh, L. L. Chase., W. J. Siekhaus and L. J. Terminello “Changes in the electronic properties of Si Nanocrystals as a function of particle size”, Phys. Rev. Lett., Vol.80, pp. 3803, 1998.
[29] P. Alfaro, A. Miranda, A.E Ramos., and M. Cruz-Irisson, “Hydrogenated Ge nanocrystals: band gap evolution with increasing size”, Brazilian Journal of Physics, Vol.36, no.2A, 2006.
[30] R.K.Das “optical and electrical properties of Zno nanorods at different temperatures” International journal of scientific research in physics and applied sciences, Vol.5,Issue 6,pp.9-12,2017.