Simulation of MHD-influence on silicon melt flow in Czochralski process
https://doi.org/10.17073/1609-3577j.met202310.603
Abstract
The applications of rotating magnetic field (RMF) in semiconductor crystals growth technology from a melt by Czochralski method (Cz) are discussed, including the known data of physical modeling of an electrically conductive KOH solution flows in a cylindrical crucible under RMF are considered and verified. Mathematical model of hydrodynamic processes is considered in relation to silicon single crystal growth in 100 mm diameter on Redmet-30 furnace equipped by RMF-magnet. The test results of calculated azimuth velocity profile with the measured data in KOH solution are presented. The results of parametric studies of melt flows stability in depending on the frequency and magnitude of RMF induction are summarized in the stability diagram.
Supporting agencies: The work was carried out on the topic of the state assignment of the Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences (No. 123021700045-7).
About the Authors
N. A. Verezub
Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Russian Federation
Russian Federation
101-1 Vernadskii Ave., Moscow 119526
Nataliya A. Verezub — Cand. Sci. (Phys.-Math.), Senior Researcher
A. I. Prostomolotov
Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Russian Federation
Russian Federation
101-1 Vernadskii Ave., Moscow 119526
Anatoly I. Prostomolotov — Dr. Sci. (Eng.), Leading Researcher
References
1. Shashkov Yu.M. Methods for growing single crystals and films of solid-state electronics materials. In: Results of science and technology. Electronics. Moscow: VINITI; 1988. Vol. 18. P. 184—216. (In Russ.)
2. Arkhipova L.V., Keskula V.F., Kilk A.O. Experimental determination of the melt rotation speed in a rotating magnetic field. In: Proceed. of the Tallinn Polytechnic Institute. Tallinn: TPI; 1983. No. 655. P. 18—25. (In Russ.)
3. Gorbachev L.P., Nikitin N.V., Ustinov A.L. On MHD rotation of an electrically conductive liquid in a cylindrical vessel of finite dimension. Magnitnaya gidrodinamika = Magnetohydrodynamics. 1974; (4): 32—42. (In Russ.)
4. Zibol'd A.F., Kapusta A.B., Keskyula V.F., Petrov G.N., Remizov O.A. Hydrodynamic phenomena arising when growing single crystals using the Czochralski method in a rotating magnetic field. Magnitnaya gidrodinamika = Magnetohydrodynamics. 1986; (2): 100—104. (In Russ.)
5. Kapusta A.B. One simple energy estimate of the stability of flows excited by a rotating magnetic field. Magnitnaya gidrodinamika = Magnetohydrodynamics. 1984; (1): 63—65. (In Russ.)
6. Kapusta A.B., Zibol'd A.F. Stationary instability of an axisymmetric flow excited by a high-frequency rotating magnetic field. Magnitnaya gidrodinamika = Magnetohydrodynamics. 1983; (1): 77—81. (In Russ.)
7. Kapusta A.B., Shamota V.P. Rotational flow of a conducting fluid in an alternating electromagnetic field. Magnitnaya gidrodinamika = Magnetohydrodynamics. 1991; (4): 116—119. (In Russ.)
8. Boyarevich A.V., Gorbunov L.A., Lyumkis E.D. Physical and numerical modeling of the influence of a vertical magnetic field on forced convection in the processes of growing single crystals using the Czochralski method. Magnitnaya gidrodinamika = Magnetohydrodynamics. 1983; (2): 81—87. (In Russ.)
9. Abricka M., Krumins J., Gelfgat Yu. Numerical simulation of MHD rotator action on hydrodynamics and heat transfer in single crystal growth processes. Journal of Crystal Growth. 1997; 180(3–4): 388—400.
10. Gelfgat Yu.M., Abriska M., Krumins J. Influence of alternating magnetic field on the hydrodynamics and heat/mass transfer in the processes of bulk single crystal growth. In: Ginkin V.P. (ed.). Proc. of 4th Int. conf. ICSC-2001. Obninsk, Russia, September 24–28, 2001. Obninsk: IPhPE; 2001. P. 68—79.
11. Barz R.U., Gerbeth G., Wunderwald U. Buhrig E., Gelfgat Y.M. Modelling of the isotermal melt flow due to rotating magnetic fields in crystal growth. Journal of Crystal Growth. 1997; 180: 410—421.
12. Virbus J., Wetzel Th., Muiznieks A., Hanna B., Dornberger E., Tomzig E., Mühlbauer A., von Ammon W. Numerical investigation of silicon melt flow in large diameter CZ-crystal growth under the influence of steady and dynamic magnetic fields. Journal of Crystal Growth. 2001; 230(1–2): 92—99.
13. Goncharov A.L., Devdariani M., Beritashvili I., Prostomolotov A.I., Fryazinov I.V. Approximation and a numerical method for the solution of three-dimensional Navier—Stokes equations on orthogonal grids. Matematicheskoe modelirovanie. 1991; 3(5): 89—109. (In Russ.)
14. Pat. No 2022067C1 (RU). Kachalov R.M., Pelevin O.V., Rubinraut A.M., Bochkarev E.P. Process of production of crystalline semiconductor material and device to implement it. Appl.: 29.01.1991; publ.: 30.10.1994. (In Russ.)
15. Kakimoto K. Effects of rotating magnetic fields on temperature and oxygen distributions in silicon melt. Journal of Crystal Growth. 2002; 237–239: 1785—1790. https://doi.org/10.1016/S0022-0248(01)02341-7
16. Kartavykh A.V., Kopeliovich E.S., Milvidskii M.G., Rakov V.V., Yurova E.S. Formation of inhomogeneous impurity distribution in germanium single crystals grown under conditions of microgravity. Crystallography Reports. 1997; 42(4): 755—761.
Review
For citations:
Verezub N.A., Prostomolotov A.I. Simulation of MHD-influence on silicon melt flow in Czochralski process. Izvestiya Vysshikh Uchebnykh Zavedenii. Materialy Elektronnoi Tekhniki = Materials of Electronics Engineering. 2024;27(2):132-139. (In Russ.) https://doi.org/10.17073/1609-3577j.met202310.603
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