Modeling Size and Dimension Dependence of Electrical and Optical Properties of Semiconductor Materials at Nanoscale

Madan Singh¹ , Sekhants’o Lara² , Naleli Jubert Matjelo³ , Limakatso Lepekola⁴ , Moruti Kao⁵ , Mampesi Thato Matobako⁶

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.3 , pp.21-28, Jun-2023

Online published on Jun 30, 2023

Copyright © Madan Singh, Sekhants’o Lara, Naleli Jubert Matjelo, Limakatso Lepekola, Moruti Kao, Mampesi Thato Matobako . 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 :
Semiconductor nanomaterials show changing behavior when the size of materials decreases from bulk to nanoscale. Inspired by this, we developed a model free from adjustable parameters to calculate the optoelectrical properties of CdSe, CdS, ZnSe, Si, and ZnO semiconductor nanosolids. Cohesive energy varies by reducing the particle size, based on this we established a model to calculate the dielectric constant, phonon frequency, and energy band gap of semiconductor nanomaterials. In our calculations, we incorporated the shape factor, which changes from a spherical shape to an octahedral shape. It is reported that the energy band gap increases on decreasing the size of the particle and the effect is more when the shape changes from spherical to tetrahedral to octahedral on the same size. Also, it is observed that there is an appreciable change in the properties of the semiconductors materials when the size is near 10 nm. Our results are compared with the existing experimental and simulation data. It is reported that the model prediction agrees well with the experimental data, which validates the theory developed.

Key-Words / Index Term :
Dangling bonds, Cohesive energy, Bandgap, Phonon frequency, Nanomaterials, Shape factor.

References :
[1] A. D. Yoffe, “Semiconductor Quantum Dots and related Systems: Electronic, Optical, Luminescence and related Properties of low Dimensional Systems,” Advances in Physics, Vol. 50, No. 1, pp. 1-208, 2001.
[2] C.Q. Sun, “Oxidation Electronics: Bond–Band–Barrier Correlation and its Applications,” Progress in Materials Science, Vol. 48, No. 6, pp. 521-68, 2003.
[3] A.A. Sonkamble, S.M. Dongarge, M. Malathi, U.V. Biradar, "Dielectric Relaxation Study of Lipids in the Microwave Frequency Region Using TDR," International Journal of Scientific Research in Physics and Applied Sciences, Vol.9, Issue.5, pp.16-22, 2021.
[4] H.I. Ikeri, A.I. Onyia, P.U. Asogwa, "Theoretical Modeling and Simulation of Electronic Band Structure and Properties of InAs/GaAs Superlattice," International Journal of Scientific Research in Physics and Applied Sciences, Vol.8, Issue.5, pp.28-37, 2020.
[5] G.R. Patel, T.C. Pandya, "Effect of Size and Shape on Static Refractive Index, Dielectric constant and Band gap of Nano solids," International Journal of Scientific Research in Physics and Applied Sciences, Vol.6, Issue.1, pp.37-42, 2018.
[6] D. Segets, J.M. Lucas, R.N. Klupp Taylor, M. Scheele, H. Zheng, A.P. Alivisatos, W. Peukert, “Determination of the Quantum Dot Band Gap Dependence on Particle Size from Optical Absorbance and Transmission Electron Microscopy Measurements,” ACS. Nano, Vol. 6, No. 10, pp. 9021-32, 2012.
[7] M. Singh, S. Lara, S. Tlali, “Effects of Size and Shape on the Specific Heat, Melting Entropy and Enthalpy of Nanomaterials,” Journal of Taibah University for Science, Vol. 11, No. 6, pp. 922-929, 2016.
[8] Y. Kayanuma, “Quantum-Size Effects of Interacting Electrons and Holes in Semiconductor Microcrystals with Spherical Shape,” Physical Review B, Vol. 38, No. 14, pp. 9797-9805, 1988.
[9] R. Viswanatha, S. Sapra, T. Saha-Dasgupta, D. Sarma, “Electronic Structure of and Quantum Size Effect in III-V and II-VI Semiconducting Nanocrystals using a Realistic Tight Binding Approach,” Physical Review B, Vol. 72, No 4, pp. 045333, 2005.
[10] G. Guisbiers, O. Van Overschelde, M. “Wautelet, Theoretical Investigation of Size and Shape Effects on the Melting Temperature and Energy Bandgap of TiO2 Nanostructures,” Applied Physics Letters, Vol. 92, No. 10, pp. 103121, 2008.
[11] A.S. Barnard, “Shape-Dependent Confinement of the Nanodiamond Band Gap,” Crystal Growth & Design, Vol. 9, No. 11, pp. 4860-4863, 2009.
[12] M. Singh, M. Goyal, K Devlal, “Size and Shape Effects on the Band Gap of Semiconductor Compound Nanomaterials,” Journal of Taibah University for Science, Vol. 12, No. 4, pp. 470-475, 2018
[13] G. Guisbiers, “Advances in Thermodynamic Modelling of Nanoparticles,” Advances in Physics: X, Vol. 4, No. 1, pp. 1668299, 2019.
[14] M. Goyal, B.R.K. Gupta, “Temperature Dependent Equation of State for Solids,” Oriental Journal of Chemistry, Vol. 32, No. 4, pp. 2193-2198, 2016.
[15] M. Goyal, M. Singh, “Size and Shape Dependence of Optical Properties of Nanostructures,” Applied Physics A, Vol. 126, No. 3, pp. 1, 2020.
[16] Z. Iqbal, S. Veprek, “Raman Scattering from Hydrogenated Microcrystalline and Amorphous Silicon,” Journal of Physics C: Solid State Physics, Vol. 15, No..2, pp. 377-392, 1982.
[17] G. X. Cheng, H. Xia, K.J. Chen, W. Zhang, X. K. Zhang, “Raman Measurement of the Grain Size for Silicon Crystallites,” Physica Status Solidi A, Vol. 118, No. 1, pp. K51-K54, 1990.
[18] C. Ossadnik, S. Vepr?ek, I. Gregora, “Applicability of Raman Scattering for the Characterization of Nanocrystalline Silicon,” Thin Solid Films, Vol. 337, No. 1-2, pp. 148-151, 1999.
[19] A. Tanaka, S. Onari, T. Arai, “Raman Scattering from CdSe Microcrystals Embedded in a Sermanate Glass Matrix,” Physical Review B, Vol. 45, No. 12 pp. 6587-6592, 1992.
[20] H.M. Cheng, K.F. Lin, H.C. Hsu, C.J. Lin, L.J. Lin, W.F. Hsieh, “Enhanced Resonant Raman Scattering and Electron-Phonon Coupling from Self-Assembled Secondary ZnO Nanoparticles,” The Journal of Physical Chemistry B, Vol. 109, No. 39, pp. 18385-18390, 2005.
[21] J.A. Van Vechten, M. Wautelet, “Variation of Semiconductor Band Gaps with Lattice Temperature and with Carrier Temperature when these are not Equal,” Physical Review B, Vol. 23, No. 10, pp. 5543-5550, 1981.
[22] G. Guisbiers, M. Kazan, O. Van Overschelde, M. Wautelet, S. Pereira, “Mechanical and Thermal Properties of Metallic and Semiconductive Nanostructures,” The Journal of Physical Chemistry C, Vol. 112, No. 11, pp. 4097-4103, 2008.
[23] Q. Jiang, H. Shi, M. Zhao, “Melting Thermodynamics of Organic Nanocrystals,” The Journal of Chemical Physics, Vol. 111, No. 5, pp. 2176-2180, 1999.
[24] G. Patel, M. Singh, T. Pandya, “Effect of Size and Shape on Refractive Index, Dielectric Constant and Band Gap of Semiconducting Nanowire,” Nanoscience & Nanotechnology-Asia, Vol. 10, No. 3, pp. 279-285, 2020.
[25] C.C. Yang, Q. Jiang, “Size Effect on the Bandgap of II–VI Semiconductor Nanocrystals,” Materials Science and Engineering: B, Vol. 131, No 1-3 pp. 191-194, 2006.
[26] T.T.M. Palstra, B. Batlogg, R.B. Van Dover, L.F. Schneemeyer, J.V. Waszczak, “Dissipative Flux Motion in High-Temperature Superconductors,” Physical Review B, Vol. 41, No. 10, pp. 6621-6632, 1990.
[27] M. Li, J.C. Li, “Size Effects on the Band-Gap of Semiconductor Compounds,” Materials Letters, Vol. 60, No. 20, pp. 2526-2529, 2006.
[28] R. Zallen, “The Physics of Amorphous Solids,” Wiley, New York, 1983.
[29] H.M. Lu, P.Y. Li, Z.H. Cao, S.K. Meng, “Size-, Shape-, and Dimensionality-Dependent Melting Temperatures of Nanocrystals, “The Journal of Physical Chemistry C, Vol. 113, No. 18, pp. 7598-7602, 2009.
[30] J.H. Rose, J. Ferrant, J.R. Smith, “Universal Binding Energy Curves for Metals and Bimetallic Interfaces,” Physical Review Letters, Vol. 47, No. 9, pp. 675-678, 1981.
[31] C.Q. Sun, X.W. Sun, B.K. Tay, S.P. Lau, H.T. Huang, S.J. Li, “Dielectric Suppression and its Effect on Photo absorption of Nanometric Semiconductors,” Journal of Physics D: Applied Physics, Vol. 34, No. 15, pp. 2359-2362, 2001.
[32] C.C. Yang, S. Li, “Size-Dependent Raman Red Shifts of Semiconductor Nanocrystals” The Journal of Physical Chemistry B, Vol. 112, No. 45, pp. 14193-14197, 2008.
[33] C. Kittle, Introduction to Solid State Physics, 7th edition, John Wiley & sons, New York, 1996.
[34] M. Mi, H. Li, “Modeling Dielectric Constant of Semiconductor Nanocrystals,” IEEE Transactions on Nanotechnology Vol. 11, No. 5, pp. 1004-1008 , 2012.
[35] R.C. Weast, CRC Handbook of Chemistry and Physics, Boca Raton, FL: CRC Press, 69th ed., E-112, 1988.
[36] C.C. Yang, Q. Jiang, “Size effect on the bandgap of semiconductor nanocrystals,” Solid State Phenomena, Vol. 121, pp 1069-1072, 2007.
[37] N. Arora, D.P. Joshi, “Band Gap Dependence of Semiconducting Nano-Wires on Cross-Sectional Shape and Size,” Indian Journal of Physics, Vol. 91, No. 12, 1493-1501, 2017.
[38] C.Q. Sun, S. Li, B.K. Tay, T.P. Chen, “Upper Limit of Blue Shift in the Photoluminescence of CdSe and CdS Nanosolids,” Acta Materialia Vol. 50, No. 18, 4687-4693, 2002.
[39] W.H. Qi, M.P. Wang, Q.H. Liu, “Shape Factor of Nonspherical Nanoparticles,” Journal of materials Science, Vol. 40, No. 9-10, pp. 2327-2739, 2005.
[40] W.H. Qi, B.Y. Huang, M.P. Wang, Z.M. Yin, J. Li, “Shape Factor for Non-Cylindrical Nanowires,” Physica B: Condensed Matter, Vol. 403, No. 13-16, pp. 2386-2389, 2008.
[41] H. Yu, J. Li, R.A. Loomis, L.W. Wang, W.E. Buhro, “Two- Versus Three-Dimensional Quantum Confinement in Indium Phosphide Wires and Dots,” Nature Materials, Vol. 2, No. 8, pp.517-520, 2003.
[42] J. Li, W. Wang, “Band-Structure-orrected Local Density Approximation Study of Semiconductor Quantum Dots and Wires,” Physical Review B, Vol. 72, No. 12, pp. 125325, 2005.
[43] B.F. Levine, d-Electron Effects on Bond Susceptibilities and Ionicities, Physical Review B, Vol. 7, No. 6, pp. 2591-2600, 1973.
[44] C.B. Murray, D.J. Norris, M.G. Bawendi, “Synthesis and Characterization of Nearly Monodisperse CdE (E = S, Se, Te) Semiconductor Nanocrystallites,” Journal of the American Chemical Society, Vol 115, No. 19, pp. 8706-8715, 1993.
[45] C. Delerue, M. Lannoo, G. Allan, “Concept of Dielectric Constant for Nanosized Systems,” Physical Review B, Vol. 68, No. 11, pp. 115411, 2003.
[46] C.C. Yang, S. Li, “Investigation of Cohesive Energy Effects on Size-Dependent Physical and Chemical Properties of Nanocrystals,” Physical Review B, Vol. 75, No. 16, pp. 165413, 2007.