Radial periodic instability of whiskers in a growth model controlled by a heterogeneous chemical reaction

   The purpose – paper analyzes the phenomenon of radial periodic instability that occurs during the growth of silicon whiskers using model representations of the growth processes that accompany the formation of whiskers during a chemical reaction at the gas-melt interface that leads to its growth.

   Methods. Gas phase deposition in an open SiCl4 + H2system. Mathematical modeling of the silicon separation process during the growth of filamentous crystals, taking into account the metal etching reaction at the gas-melt interface at the crystal tip.

   Results. Within the framework of the model of growth of nanowhiskers controlled by the chemical reaction of silicon separation at the gas-melt interface, the balance of the flows of the heterogeneous reaction of silicon separation and etching of metal from the melt drop at the crystal top is considered. The presence of a chemical metal compound in the gas phase leads to a dependence of the etching flow on the temperature, which has a maximum in the negative region. With the growth of a filamentous crystal on a substrate of limited size, the dependence of the temperature of the crystal-
substrate system on the magnitude of the crystallizing matter and metal fluxes is considered. In the growing section of the curve, the dependence of the metal etching flux on temperature increases, as the temperature increases as a result of heating during crystallization, the influx of metal into the melt drop at the top of the crystal is replaced by etching and a drop in temperature, which leads to the development of an oscillatory process, a periodic change in the radius of the crystal over time.

   Conclusion. A system of kinetic equations has been obtained that explains the occurrence of radial periodic instability in filamentous crystals. A numerical evaluation conducted using the obtained system of kinetic equations confirmed the possibility of developing radial periodic instability in filamentous crystals.

1. Antipov S.A., Drozhzhin A.I., Roshhupkin A.M. Relaxation phenomena in filamentous semiconductor crystals. Voronezh: VGU; 1987. 192 р. (In Russ.)

2. Drozhzhin A.I. P-Si <111> filament crystal transducers. Voronezh: Voronezh. Politekhn. in-t; 1984. Dep. v VINITI 29.06.84. 241 p. No 6606-84. (In Russ.)

3. Vagner R. Single crystal fibers and materials reinforced with them. Moscow: Mir; 1973. 464 p. (In Russ.)

4. Givargizov E.I. Growth of filamentous and lamellar crystals from steam. Moscow: Nauka; 1977. 304 p. (In Russ.)

5. Nebol'sin V.A., Shchetinin A.A. Growth of filamentous crystals. Voronezh: VGU; 2003. 620 p. (In Russ.)

6. Dubrovskii V.G., Tsyrlin G.E., Ustinov V.M. Kinetics of spontaneous formation of the core-shell structure in filamentous nanocrystals (In,Ga)As. Fizika i tekhnika poluprovodnikov = Physics and technology of semiconductors. 2009;43(12):1585-1628. (In Russ.)

7. Kozenkov O.D., Zhukalin D.A., Baklanov I.O. A model of the growth of filamentous crystals controlled by a heterogeneous chemical reaction, taking into account the dimensional effect. Kondensirovannye sredy i mezhfaznye granicy = Condensed media and interphase boundaries. 2019;21(4):579-589. (In Russ.)

8. Kozenkov O.D., Sychev I.V., Zhuravleva E.V. A model of the growth of a filamentous crystal during physical vapor deposition. Vestnik Voronezhskogo instituta MVD Rossii = Proceedigs of Voronezh Institute of the Ministry of Internal Affairs of Russia. 2019;(2):101-112. (In Russ.)

9. Kozenkov O.D., Sychev I.V., Baklanov I.O. Experimental confirmation of the growth model of a filamentous crystal limited by a heterogeneous chemical reaction. Vestnik Voronezhskogo instituta FSIN Rossii = Proceedings of Voronezh Institute of the Federal Penitentiary Service of Russia. 2021;(2):44-51. (In Russ.)

10. Kozenkov O.D., Kozyakov A.B., Shchetinin A.A. Dependence of the growth rate of a filamentous crystal limited by a heterogeneous chemical reaction on the composition of the gas phase at high concentrations of silicon tetrachloride. Izvestiya vuzov. Fizika. 1986;29(9):115-117. (In Russ.)

11. Darinskii B.M., Kozenkov O.D., Shchetinin A.A. On the dependence of the growth rate of filamentous crystals on their diameter. Izvestiya vuzov. Fizika. 1986; 32(12):18-22. (In Russ.)

12. Kozenkov O.D., Shchetinin A.A., Kosyreva L.G. Formation of the crystallization front of a filamentous crystal. Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta = Bulletin of the Voronezh State Technical University. 2011;7(4):31-35. (In Russ.)

13. Kozenkov O.D., Boldyreva Ya.A., Sannikov V.G. Temperature dependence of the growth rate of a filamentous silicon crystal controlled by a heterogeneous chemical reaction. Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika = Bulletin of the Voronezh State University. Series: Physics. Mathematics. 2023;(4):30-42. (In Russ.)

14. Kozenkov O.D., Gorbunov V.V., Kosyreva L.G., Zhilyakov D.G. Estimation of the temperature at the tip of a conical filamentous crystal at the transition point to cylindrical growth. Vestnik Voronezhskogo gosudarstvennogo universiteta = Bulletin of the Voronezh State University. 2017;13(4):125-130. (In Russ.)

15. Kozenkov O.D., Baklanov I.O., Sychev I.V. A model of the thermal balance of a filamentous crystal growing on a thick substrate. Vestnik Voronezhskogo instituta MVD Rossii = Proceedigs of Voronezh Institute of the Ministry of Internal Affairs of Russia. 2021;(4):34-42. (In Russ.)

16. Kozenkov O.D., Boldyreva Ya.A., Sannikov V.G. A model of growth limited by a heterogeneous chemical reaction of nanoscale filamentous silicon crystals at a high density of their location on a substrate. Vestnik Voronezhskogо University. Seriya: Fizika. Matematika = Bulletin of the Voronezh State University. Series: Physics. Mathematics 2023;(3):5-17. (In Russ.)

17. Kozenkov O.D., Baklanov I.O., Sychev I.V. A model of the growth, limited by a heterogeneous chemical reaction, of filamentous silicon crystals at a high density of their location on a substrate. Vestnik Voronezhskogo instituta MVD Rossii = Proceedigs of Voronezh Institute of the Ministry of Internal Affairs of Russia. 2024;(1):60-67. (In Russ.)

18. Kozenkov O.D. Taper of a filamentous crystal caused by a heterogeneous chemical reaction. Neorganicheskie materialy = Inorganic materials. 2016;52(3):279-284. (In Russ.)

19. Glinka N.L. General chemistry. Moscow: KnoRus; 2016. 746 p. (In Russ.)

20. Ugai Ya.A. General and inorganic chemistry. Moscow: Vysshaya skola; 1997. 527 p. (In Russ.)

21. Nekrasov V.B. Fundamentals of general chemistry. Moscow: Khimiya; 1993. 255 p. (In Russ.)

22. Nikolsky B.P. Chemist's Handbook. Leningrad: Chemistry, Leningr. otd-nie; 1971. 600 p. (In Russ.)

23. Kozenkov O.D., Kosyreva L.G. Dependence of the growth rate of a whisker crystal limited by a heterogeneous chemical reaction on the composition of the gas phase. Neorganicheskie materialy = Inorganic materials. 2015;51(11):1255-1259. (In Russ.)