Abstract
Silicon nanocrystals (Si-NC) in silicon oxide is a promising material for many applications in micro- and nanoelectronics. This article develops a theory of the kinetics of Si-NC formation when there are both diffusion and reaction mechanisms of their formation. The theoretical expressions obtained for changing the concentration of nanocrystals and silicon implanted in oxide and their sizes are consistent with experimental results and can be used to optimize the formation conditions of technological processes of Si-NC formation. An important modern problem is the doping of nanocrystals with impurities, which allows the creation of silicon Si-NC–emitting light, and are also objects for solar energy. We have shown that nanocrystals with sizes less than 5 nm are limited by the potential barrier that creates surface tension. Thermodynamic calculations showed that there is a critical size of the Si-NC and if it is smaller, then it is impossible to introduce an impurity into it. These calculations were performed for doping silicon with phosphorus and tin.
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References
Arduca E, Perego M (2017) Doping of silicon nanocrystals. Mater Sci Semicond Process 62:156–170. https://doi.org/10.1016/j.mssp.2016.10.054
Bisadi Z, Mancinelli M, Manna S, Tondini S, Bernard M, Samusenko A, Ghulinyan M, Fontana G, Bettotti P, Ramiro-Manzano F, Pucker G, Pavesi L (2015) Silicon nanocrystals for nonlinear optics and secure communications. Phys Status Solidi A 212(12):2659–2671. https://doi.org/10.1002/pssa.201532528
Brilliantov NV, Krapivskiy PL (1989) Kinetic models of point defects clustering in solids (Kineticheskie modeli klasterizacii tochechnyh defektov v tvyordom tele) [in Russian]. Phys Solid State (Fizika tvyordogo tela) 31(2):172–178
Bulyarskii SV, Oleinikov VP (1987) Thermodynamical evaluation of point defect density and impurity solubility in compound semiconductors. Phys Stat Sol A 141(1):K7–K10. https://doi.org/10.1002/pssb.2221410137
Bulyarskii SV, Oleinikov VP (1988) Thermodynamics of defect formation and defect interaction in compound semiconductors. Phys Stat Sol A 146(2):439–447. https://doi.org/10.1002/pssb.2221460204
Bulyarskii SV, Svetukhin VV, Prikhod’ko OV (1999) Spatially inhomogeneous oxygen precipitation in silicon. Semiconductors 33(11):1157–1162. https://doi.org/10.1134/1.1187839
Bulyarskiy S, Saurov A (2017) Doping of carbon nanotubes. NanoScience and Technology. https://doi.org/10.1007/978-3-319-55883-7
Chen X, Pi X, Yang D (2011) Critical role of dopant location for P-doped Si nanocrystals. J Phys Chem C 115(3):661–666. https://doi.org/10.1021/jp1102934
Claudio T, Stein N, Stroppa DG, Klobes B, Koza MM, Kudejova P, Petermann N, Wiggers H, Schierning G, Hermann RP (2014) Nanocrystalline silicon: lattice dynamics and enhanced thermoelectric properties. Phys Chem Chem Phys 16(47):25701–25709. https://doi.org/10.1039/c3cp53749h
Conibeer G, Green MA, König D, Perez-Wurfl I, Huang S, Hao X, Di D, Shi L et al (2011) Silicon quantum dot based solar cells: addressing the issues of doping, voltage and current transport. Prog Photovolt Res Appl 19(7):813–824. https://doi.org/10.1002/pip.1045
Daldosso N, Pavesi L (2009) Nanosilicon photonics. Laser Photon Rev 3(6):508–534. https://doi.org/10.1002/lpor.200810045
Dimitrakis P, Kapetanakis E, Tsoukalas D, Skarlatos D, Bonafos C, Ben Asssayag G, Claverie A, Perego M, Fanciulli M, Soncini V, Sotgiu R, Agarwal A, Ameen M, Sohl C, Normand P (2004) Silicon nanocrystal memory devices obtained by ultra-low-energy ion-beam synthesis. Solid State Electron 48(9):1511–1517. https://doi.org/10.1016/j.sse.2004.03.016
Dresselhaus MS, Chen G, Tang MY, Yang RG, Lee H, Wang DZ, Ren ZF, Fleurial J-P, Gogna P (2007) New directions for low-dimensional thermoelectric materials. Adv Mater 19(8):1043–1053. https://doi.org/10.1002/adma.200600527
Farooq U, Naz S, Xu H-G, Yang B, Xu X-L, Zheng W-J (2020) Recent progress in theoretical and experimental studies of metal-doped silicon clusters: trend among elements of periodic table. Coord Chem Rev 403:213095. https://doi.org/10.1016/j.ccr.2019.213095
Fistul VI (2004) Impurities in semiconductors. CRC Press, Boca Raton. https://doi.org/10.4324/9780203299258
Fistul’ VI (1977) Raspad peresyshchennykh poluprovodnikovykh tverdykh rastvorov (decomposition of supersaturated semiconductor solid solutions). Metallurgiya, Moscow
Glazov VM, Zemskov VS (1967) Fiziko-khimicheskiye osnovy legirovaniya poluprovodnikov (physicochemical principles of doping of semiconductors) (in Russian). Nauka, Moscow
Gnaser H, Gutsch S, Wahl M, Schiller R, Kopnarski M, Hiller D, Zacharias M (2014) Phosphorus doping of Si nanocrystals embedded in silicon oxynitride determined by atom probe tomography. J Appl Phys 115(3):34304. https://doi.org/10.1063/1.4862174
Gupta A, Khalil ASG, Offer M, Geller M, Winterer M, Lorke A, Wiggers H (2011) Synthesis and ink-jet printing of highly luminescing silicon nanoparticles for printable electronics. J Nanosci Nanotechnol 11(6):5028–5033. https://doi.org/10.1166/jnn.2011.4184
Ham FS (1958) Theory of diffusion-limited precipitation. J Phys Chem Solids 6(4):335–351. https://doi.org/10.1016/0022-3697(58)90053-2
Ham FS (1959a) Diffusion-limited growth of precipitate particles. J Appl Phys 30(10):1518–1525. https://doi.org/10.1063/1.1734993
Ham FS (1959b) Stress-assisted precipitation on dislocations. J Appl Phys 30(6):915–926. https://doi.org/10.1063/1.1735262
Ischenko AA, Fetisov GV, Aslanov LA (2015) Nanosilicon: properties, synthesis, applications, methods of analysis and control. CRC Press, Boca Raton
Kukushkin SA, Osipov AV (1998a) Kinetics of first-order phase transitions in the asymptotic stage. J Exp Theor Phys 86(6):1201–1208. https://doi.org/10.1134/1.558591
Kukushkin SA, Osipov AV (1998b) Thin-film condensation processes. Phys.-Usp. 41(10):983–1014. https://doi.org/10.1070/PU1998v041n10ABEH000461
Löper P, Canino M, López-Vidrier J, Schnabel M, Schindler F, Heinz F, Witzky A, Bellettato M, Allegrezza M, Hiller D, Hartel A, Gutsch S, Hernández S, Guerra R, Ossicini S, Garrido B, Janz S, Zacharias M (2013) Silicon nanocrystals from high-temperature annealing: characterization on device level. Phys Status Solidi A 210(4):669–675. https://doi.org/10.1002/pssa.201200824
Mangolini L (2013) Synthesis, properties, and applications of silicon nanocrystals. J Vac Sci Technol B Nanotechnol Microelectron Mater Process Meas Phenom 31(2):20801. https://doi.org/10.1116/1.4794789
Marri I, Degoli E, Ossicini S (2017) Doped and codoped silicon nanocrystals: the role of surfaces and interfaces. Prog Surf Sci 92(4):375–408. https://doi.org/10.1016/j.progsurf.2017.07.003
McVey BFP, Prabakar S, Gooding JJ, Tilley RD (2017) Solution synthesis, surface passivation, optical properties, biomedical applications, and cytotoxicity of silicon and germanium nanocrystals. ChemPlusChem 82(1):60–73. https://doi.org/10.1002/cplu.201600207
Nozik AJ (2010) Nanoscience and nanostructures for photovoltaics and solar fuels. Nano Lett 10(8):2735–2741. https://doi.org/10.1021/nl102122x
O'Farrell N, Houlton A, Horrocks BR (2006) Silicon nanoparticles: applications in cell biology and medicine. Int J Nanomedicine 1(4):451–472. https://doi.org/10.2147/nano.2006.1.4.451
Pi XD, Gresback R, Liptak RW, Campbell SA, Kortshagen U (2008) Doping efficiency, dopant location, and oxidation of Si nanocrystals. Appl Phys Lett 92(12):123102. https://doi.org/10.1063/1.2897291
Priolo F, Gregorkiewicz T, Galli M, Krauss TF (2014) Silicon nanostructures for photonics and photovoltaics. Nat Nanotechnol 9(1):19–32. https://doi.org/10.1038/nnano.2013.271
(2004) Silicon photonics. Topics in applied physics 94. Springer Berlin Heidelberg, Berlin, Heidelberg. https://doi.org/10.1007/b11504
Slezov VV, Schmelzer J (1994a) The initial stage of diffusion decomposition of solid solutions (Nachal'naya stadiya diffuzionnogo raspada tvyordogo rastvora) [in Russian]. Phys Solid State (Fizika tvyordogo tela) 36(2):353–362
Slezov VV, Schmelzer J (1994b) Kinetics of formation and growth of a new phase with a definite stoichiometric composition. J Phys Chem Solids 55(3):243–251. https://doi.org/10.1016/0022-3697(94)90139-2
Slezov VV, Schmelzer J (1997) Maximum number of new-phase particles nucleated during the decay of solid solutions. Phys Solid State 39(12):1971–1977. https://doi.org/10.1134/1.1130211
Song B, He Y (2019) Fluorescent silicon nanomaterials: from synthesis to functionalization and application. Nano Today 26:149–163. https://doi.org/10.1016/j.nantod.2019.03.005
Stegner AR, Pereira RN, Lechner R, Klein K, Wiggers H, Stutzmann M, Brandt MS (2009) Doping efficiency in freestanding silicon nanocrystals from the gas phase: phosphorus incorporation and defect-induced compensation. Phys Rev B 80:165526. https://doi.org/10.1103/PhysRevB.80.165326
Summonte C, Allegrezza M, Bellettato M, Liscio F, Canino M, Desalvo A, López-Vidrier J, Hernández S, López-Conesa L, Estradé S, Peiró F, Garrido B, Löper P, Schnabel M, Janz S, Guerra R, Ossicini S (2014) Silicon nanocrystals in carbide matrix. Sol Energy Mater Sol Cells 128:138–149. https://doi.org/10.1016/j.solmat.2014.05.003
Swalin RA (1972) Thermodynamics of solids. Wiley
Takahashi T, Fukatsu S, Itoh KM, Uematsu M, Fujiwara A, Kageshima H, Takahashi Y, Shiraishi K (2003) Self-diffusion of Si in thermally grown SiO2 under equilibrium conditions. J Appl Phys 93(6):3674–3676. https://doi.org/10.1063/1.1554487
Talapin DV, Lee JS, Kovalenko MV, Shevchenko EV (2010) Prospects of colloidal nanocrystals for electronic and optoelectronic applications. Chem Rev 110(1):389–458. https://doi.org/10.1021/cr900137k
Tang J, Wang H-T, Lee DH, Fardy M, Huo Z, Russell TP, Yang P (2010) Holey silicon as an efficient thermoelectric material. Nano Lett 10(10):4279–4283. https://doi.org/10.1021/nl102931z
Turnbull D (1953) The kinetics of precipitation of barium sulfate from aqueous solution. Acta Metall 1(6):684–691. https://doi.org/10.1016/0001-6160(53)90026-1
Turnbull D (1955) Theory of cellular precipitation. Acta Metall 3(1):55–63. https://doi.org/10.1016/0001-6160(55)90012-2
Volmer M (1939) Kinetik der Phasenbildung. Steinkopff, Dresden
Xu Q, Luo J-W, Li S-S, Xia J-B, Li J, Wei S-H (2007) Chemical trends of defect formation in Si quantum dots: the case of group-III and group-V dopants. Phys Rev B 75:235304. https://doi.org/10.1103/PhysRevB.75.235304
Yang P, Gwilliam RM, Crowe IF, Papachristodoulou N, Halsall MP, Hylton NP, Hulko O, Knights AP, Shah M, Kenyon AJ (2013) Size limit on the phosphorous doped silicon nanocrystals for dopant activation. Nucl Instrum Methods Phys Res, Sect B 307:456–458. https://doi.org/10.1016/j.nimb.2012.12.077
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The work was supported by the Ministry of Science and Higher Education of the Russian Federation, project No. 0004-2019-0001.
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All authors contributed to the study conception and design. The first draft of the manuscript was written by Sergey V. Bulyarskiy and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Bulyarskiy, S.V., Svetukhin, V.V. Kinetics of the formation and doping of silicon nanocrystals. J Nanopart Res 22, 361 (2020). https://doi.org/10.1007/s11051-020-05069-1
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DOI: https://doi.org/10.1007/s11051-020-05069-1