Thermodynamic Bases for Obtaining Crystalline Perfect Silicon from Tin-silicon Solution

Year 2022, Volume: 25 Issue: 2, 1 - 6, 01.06.2022

Alijon Razzokov Khushnudbek Eshchanov

Abstract

Silicon epitaxial layers were grown on a silicon (Si<111>) substrate in the range of 1323÷1073 K with initial crystallization temperatures from the silicon-tin (Si-Sn) solution. To determine the forces acting between the silicon nanoclusters in solution and the tin (Sn) particles and the silicon (Si) surface, the dielectric constant values of silicon, tin at selected temperatures were found experimentally. Given the Gibbs energy of the system to obtain the perfect epitaxial layers and structures of the crystal, optimal technological growth conditions are given.

Keywords

epitaxy, nanocluster, crystallization, solution-melt, dislocation, dielectric constant

References

• A. Nikiforov, V. Timofeev, V. Mashanov, T. Gavrilova and D. Gulyaev, "Elastically stressed pseudomorphic SiSn island array formation with a pedestal on the Si(100) substrate using Sn as a growth catalyst", Journal of Crystal Growth, vol. 518, pp. 103-107, 2019. Available: https://doi.org/10.1016/j.jcrysgro.2019.04.021.
• K. Fujiwara, "Crystal Growth Behaviors of Silicon during Melt Growth Processes", International Journal of Photoenergy, pp. 1-16, 2012. Available: https://doi.org/10.1155/2012/169829.
• Gaskell, D.R., & Laughlin, D.E. Introduction to the Thermodynamics of Materials, 6th Ed. CRC Press, 2017. Available: https://doi.org/10.1201/9781315119038. Arthur D. Pelton. Phase Diagrams and Thermodynamic Modeling of Solutions, Elsevier. 2019. Available: https://doi.org/10.1016/C2013-0-19504-9.
• Kaufman Myron, Principles of Thermodynamics, CRC Press, p. 213, 2002. ISBN 978-0-8247-0692-0
• Guggenheim, E.A. "The Conceptions of Electrical Potential Difference between Two Phases and the Individual Activities of Ions". Journal Physcal Chemistry, vol. 33, (6), pp. 842–849, 1929. Available: https://doi.org/10.1021/j150300a003.
• J. Safarian, L. Kolbeinsen, and M. Tangstad, “Thermodynamic activities in silicon binary melts,” Journal of Materials Science, vol. 47, no. 14, pp. 5561–5580, 2012. Available: https://doi.org/10.1007/s10853-012-6449-4.
• Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey. Fundamentals of Engineering Thermodynamics, 3rd Ed. Michael J., Wiley –Interscience, 2010. ISBN 0-471-07681-3
• L. S. Darken, “Application of the Gibbs-duhem equation to ternary and multicomponent systems,” Journal of the American Chemical Society, vol. 72, no. 7, pp. 2909–2914, 1950. Available: https://doi.org/10.1021/ja01163a030.
• S. Uda, X. Huang, S.Koh. Journal of Crystal Growth, vol. 281, pp. 481–491, 2005.
• P. Rudolph, in: Crystal growth Technology, H.J. Scheel and T. fukuda (eds.) Wiley –Interscience, 2003.
• E. D. Shukin, A. V. Persov, E.A. Ameline. Colloid chemistry, -M.: Higher. sch., 2004.
• Ivan Markov. Crystal Growth For Beginners: Fundamentals of Nucleation, Crystal Growth And Epitaxy, 3th Ed. Singapore: World Scientific, 2016. Available: https://doi.org/10.1142/10127.
• Burton, W. K.; Cabrera, N. "Crystal growth and surface structure. Part I". Discussions of the Faraday Society, 1949. Available: https://doi.org/10.1039/DF9490500033.
• Burton, W.K.; Cabrera, N. "Crystal growth and surface structure. Part II". Discussions of the Faraday Society, 1949. Available: https://doi.org/10.1039/DF9490500040.
• Razzokov, A.Sh., Khakimov, N.Z., Davletov, I.Y., Eshchanov, Kh.O. and Matnazarov, A.R. "Obtaining a structurally perfect semiconductor solid solution Si1-xGex with electrophysical and photoelectric properties," Scientific-technical journal, vol. 24, iss. 5, pp. 11, 2020. Available: https://uzjournals.edu.uz/ferpi/vol24/iss5/11.
• Saidov, A.S., Razzokov, A. Sh. “Obtaining and morphological studies of epitaxial layers of the Si1-x Gex solid solution”, Siberian Physical Journal, vol. 15, no. 2, pp. 84–91, 2020. Available: https://doi.org/10.25205/2541-9447-2020-15-2-84-91.
• Lennard-Jones, J.E. "Cohesion". Proceedings of the Physical Society, vol. 43 no. 5, pp. 461–482, 1931. Available: https://doi.org/10.1088/0959-5309/43/5/301.
• Simon Stephan, Martin T. Horsch, Jadran Vrabec & Hans Hasse. MolMod–an open access database of force fields for molecular simulations of fluids, Molecular Simulation, vol. 45, no. 10, pp. 806-814, 2019. Available: https://doi.org/10.1080/08927022.2019.1601191.
• N. Tchipev, S. Seckler, M. Heinen, J. Vrabec, F. Gratl, M. Horsch, M. Bernreuther, C. W. Glass, C. Niethammer, N. Hammer, B. Krischok, M. Resch, D. Kranzlmüller, H. Hasse, H.-J. Bungartz, and P. Neumann, “Twetris: Twenty trillion-atom simulation,” The International Journal of High Performance Computing Applications, vol. 33, no. 5, pp. 838–854, 2019. Available: https://doi.org/10.1177/1094342018819741.
• Jones, J. E. "On the determination of molecular fields. —II. From the equation of state of a gas". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 106 no. 738, pp. 463–477, 1924. Available: https://doi.org/10.1098/rspa.1924.0082.
• Wood, W. W.; Parker, F. R. "Monte Carlo Equation of State of Molecules Interacting with the Lennard-Jones Potential. I. A Supercritical Isotherm at about Twice the Critical Temperature". The Journal of Chemical Physics, vol. 27, no. 3, pp. 720–733, 1957. Available: https://doi.org/10.1063/1.1743822.
• S. Dubrovskiy and K. Gareev, “Measurement method for detecting magnetic and dielectric properties of composite materials at microwave frequencies”, 2015 IEEE NW Russia Young Researchers in Electrical and Electronic Engineering Conference, St. Petersburg, pp. 24-26, 2015. Available: https://doi.org/10.1109/EIConRusNW.2015.7102223.
• Grove, Timothy & Masters, Mark & Meirs, Richard. Determining Dielectric Constants Using a Parallel Plate Capacitor. Physics Faculty Publications, 2005. Available: https://doi.org/10.1119/1.1794757.
• Boltaev, A.P., Pudonin, F.A. & Sherstnev, I.A. “Low-frequency giant effective permittivity of island metal films”, Physics of the Solid State, vol. 57, pp. 2099–2105, 2015. Available: https://doi.org/10.1134/S1063783415100066.
• Costa, F., Amabile, C., Monorchio, A., Prati, E. "Waveguide Dielectric Permittivity Measurement Technique Based on Resonant FSS Filters", IEEE Microwave and Wireless Components Letters. vol. 21, no. 5, pp. 273, 2011. Available: https://doi.org/10.1109/LMWC.2011.2122303.