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2004 | 2 | 1 | 183-203
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Industrial challenges for numerical simulation of crystal growth

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Numerical simulation of industrial crystal growth is difficult due to its multidisciplinary nature and the complex geometry of the real-life growth equipment. An attempt is made to itemize physical phenomena dominant in the different methods for growth of bulk crystals from the melt and the vapor phase as well as to review corresponding numerical approaches. Academic research and industrial applications are compared. Development of a computational engine and a graphic user interface of the industry-oriented codes is discussed. A simulator for the entire growth process of bulk crystals by sublimation method is described.
Słowa kluczowe
Wydawca

Czasopismo
Rocznik
Tom
2
Numer
1
Strony
183-203
Opis fizyczny
Daty
wydano
2004-03-01
online
2004-03-01
Twórcy
autor
autor
Bibliografia
  • [1] D.M. Anderson, G.B. McFadden, A.A. Wheeler: “A phase-field model of solidification with convection”, Physica D, Vol. 135, (2000), pp. 175–194. http://dx.doi.org/10.1016/S0167-2789(99)00109-8[Crossref]
  • [2] C. Barat, T. Duffar, P. Dusserre, J.P. Garandet: “Chemical segregation in vertical Bridgman growth of GaInSb alloys”, Crystal Res. Technol., Vol. 34, (1999), pp. 449–456. http://dx.doi.org/10.1002/(SICI)1521-4079(199904)34:4<449::AID-CRAT449>3.0.CO;2-2[Crossref]
  • [3] S.V. Batill, J.E. Renand, X. Gu: “Modeling and simulation uncertainty in multidisciplinary design optimization”, In: AIAA Multidisciplinary Analysis and Optimization Conference and Exhibit, Long Beach (USA), 2000, AIAA Paper 2000-4803 pp. 11.
  • [4] M. Beneś: “Mathematical and computational aspects of solidification of pure substances”, Acta Math. Univ. Comenianae, Vol. LXX, (2001), pp. 123–151.
  • [5] M.V. Bogdanov, A.O. Galyukov, S.Yu. Karpov, A.V. Kulik, S.K. Kochuguev, D.Kh. Ofengeim, A.V. Tsirulnikov, I.A. Zhmakin, A.E. Komissarov, O.V. Bord, M.S. Ramm, A.I. Zhmakin, Yu.N. Makarov: “Virtual reactor: a new tool for SiC bulk crystal growth study and optimization”, Mat. Sci. Forum, Vol. 353–356, (2001), pp. 57–60. http://dx.doi.org/10.4028/www.scientific.net/MSF.353-356.57[Crossref]
  • [6] Yu.A. Borovlev, N.V. Ivannikova, V.N. Shlegel, Ya.V. Vasiliev, V.A. Gusev: “Progress in growth of large sized BGO crystals by the low-thermal-gradient Czochralski technique”, J. Crystal Growth, Vol. 229, (2001), pp. 305–311. http://dx.doi.org/10.1016/S0022-0248(01)01162-9[Crossref]
  • [7] G. Butlin, C. Stops: “CAD data repair”, 5th International Meshing Roundtable, Sandia National Laboratories, (1996), pp. 7–12.
  • [8] Cape Simulation, Engineering Solutions Through Computer Simulations, 2002, http://www.capesim.com/simulators.htm.
  • [9] W. Christopher, CFD codes list, ICEM CFD Engineering, 2002, http://www.icemcfd.com/cfd/CFD-codes.html.
  • [10] Welcome to the Crystal Growth Laboratory, Crystal Growth Laboratory, 2003, http://www.cgl-erlangen.com/.
  • [11] PHOENICS Overview, CHAM Technical Report TR 001, http://www.cham.co.uk/phoenics/d-polis/d-info/phover.htm.
  • [12] F. Dupret, P. Nicodeme, Y. Ryckmans, M.J. Crochet: “Global modeling of heat transfer in crystal growth furnaces”, Int. J. Heat Mass Transfer, Vol. 33, (1990), pp. 1849–1871. http://dx.doi.org/10.1016/0017-9310(90)90218-J[Crossref]
  • [13] P.S. Dutta, A.G. Ostrogorski: “Suppression of cracks inIn x Ga 1−x Sb crystals through forced convection in the melt”, J. Crystal Growth, Vol. 194, (1998), pp. 1–7. http://dx.doi.org/10.1016/S0022-0248(98)00621-6[Crossref]
  • [14] Yu.E. Egorov, Yu.N. Makarov, E.A. Rudinsky, E.M. Smirnov, A.I. Zhmakin: “Modelling analysis of oxygen transport during Czochralski growth of silicon crystals”, Mat. Res. Soc. Proc., Vol. 490, (1998), pp. 181–186.
  • [15] Yu.E. Egorov, A.I. Zhmakin: “Numerical simulation of low-Mach number gas mixture flows with heat and mass transfer using unstructured grid”, Comput. Mater. Sci., Vol. 11, (1998), pp. 204–220. http://dx.doi.org/10.1016/S0927-0256(98)00005-6[Crossref]
  • [16] M.S. Eldred, W.E. Hart, W.J. Bohnhoff, V.J. Romero, S.A. Hutchinson, A.G. Salinger: “Utilizing Object-Oriented Design to Build Advanced Optimization Strategies with Generic Implementation”, (1996), pp. 16.
  • [17] I.Yu. Evstratov, V.V. Kalaev, V.N. Nabokov, A.I. Zhmakin, Yu.N. Makarov, A.G. Abramov, N.G. Ivanov, E.A. Rudinsky, E.M. Smirnov, S.A. Lowry, E. Dornberger, J. Virbulis, E. Tomzig, W. von Ammon: “Global model of Czochralski silicon growth to predict oxygen content and thermal fluctuations at the melt-crystal interface”, Microelectronic Engineering, Vol. 56, (2001), pp. 139–142. http://dx.doi.org/10.1016/S0167-9317(00)00516-5[Crossref]
  • [18] I.Yu. Evstratov, V.V. Kalaev, A.I. Zhmakin, Yu.N. Makarov, A.G. Abramov, N.G. Ivanov, E.M. Smirnov, E. Dornberger, J. Virbulis, E. Tomzig, W. von Ammon: “Modeling analysis of unsteady three-dimensional turbulent melt flow during Czochralski growth of Si crystals”, J. Crystal Growth, Vol. 230, (2001), pp. 22–29. http://dx.doi.org/10.1016/S0022-0248(01)01314-8[Crossref]
  • [19] F. Dupret: FEMAG. The Software for Bulk Crystal Growth Simulation, http://www.meca.ucl.ac.be/femag.
  • [20] J.P. Giesing, J.-F.M. Barthelemy: “A Summary of Industry MDO Applications and Needs”, In: AIAA 98-4737, 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis (USA), 1998, pp. 20.
  • [21] John W. Slater: Glossary of Verification and Validation Terms, http://www.grc.nasa.gov/WWW/wind/valid/tutorial/glossary.html.
  • [22] V.D. Golyshev, M.A. Gonik, V.B. Tsvetovsky: “In situ measurement ofBi 4Ge 3O 12 interface supercooling during melt crystal growth”, J. Crystal Growth, Vol. 237–239, (2002), pp. 735–739. http://dx.doi.org/10.1016/S0022-0248(01)01990-X[Crossref]
  • [23] Guide for the Vertification and Validation of Computational Fluid Dynamixcs (G-077-1998), AIAA Standards Series, 1998.
  • [24] Ch. Hirsh: “The QNET-CFD project”, Network Bulletin, Vol. 1, (2001), pp. 4–5. (http://www.qnet-cfd.net/newsletter/1st/newsletter-1.pdf)
  • [25] I. Hooks: “Writing Good Requirements”, In: NCOSE-93, 3rd Int. Symposium NCOSE, Washington, (USA), 1993, INCOSE, 1993, http://www.incose.org./rwg/writing.html.
  • [26] D.T.J. Hurle (Ed.): Handbook of Crystal Growth. Bulk Crystal Growth, Elsevier, North-Holland, 1994.
  • [27] V.V. Kalaev, I.Yu. Evstratov, Yu.N. Makarov: “Gas flow effect on global heat transport and melt convection in Czochralski silicon growth”, J. Crystal Growth, Vol. 249, (2003), pp. 87–99. http://dx.doi.org/10.1016/S0022-0248(02)02109-7[Crossref]
  • [28] V.V. Kalaev, A.I. Zhmakin, E.M. Smirnov: Modeling of turbulent melt convection during Czochralski bulk crystal growth, J. of Turbulence, Vol. 3, (2002), pp. 13. (http://jot.iop.org)
  • [29] V.V. Kalaev, A.I. Zhmakin: “Large Eddy Simulation of melt convection during Czochralski crystal growth”, Proc. 9th European Turbulence Conf, (2002), pp. 207–210.
  • [30] Y. Kaneda, T. Ishihara, M. Yokokawa, K. Itakura, A. Uno: “Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box”, Phys. Fluids, Vol. 15, (2003), pp. L21-L24. http://dx.doi.org/10.1063/1.1539855[Crossref]
  • [31] S. Kochuguev, D. Ofengeim, A. Zhmakin, A. Galyukov: “Ray tracing method for axisymmetrical global heat transfer simulation”, CFD Journal, Vol. II–33, (2001), pp. 440–448.
  • [32] A.V. Kulik, M.V. Bogdanov, D.Kh. Ofengeim, S.K. Kochuguev, S.E. Demina, S.Yu. Karpov, A.I. Zhmakin, M.S. Ramm, Yu.N. Makarov: “Modeling and optimization of SiC bulk crystal growth by sublimation technique”, Proc. 4th Int. Conf. Single Crystal Growth and Heat Mass Transfer, (2001), pp. 698–705.
  • [33] C.W. Lan: “Three-dimensional simulation of floating-zone crystal growth of oxide crystals”, J. Crystal Growth, Vol. 247, (2003), pp. 597–612. http://dx.doi.org/10.1016/S0022-0248(02)02056-0[Crossref]
  • [34] A. Lipchin, R.A. Brown: “Hybrid finite-volume/finite-element simulation of heat transfer and melt turbulence in Czochralski crystal growth of silicon”, J. Crystal Growth, Vol. 216, (2000), pp. 192–203. http://dx.doi.org/10.1016/S0022-0248(00)00428-0[Crossref]
  • [35] Yu.N. Makarov, A.I. Zhmakin: “On flow regimes in VPE reactors”, J. Crystal Growth, Vol. 94, (1989), pp. 537–551. http://dx.doi.org/10.1016/0022-0248(89)90032-8[Crossref]
  • [36] D. Maroudas, R.A. Brown: “On the prediction of dislocation formation in semiconductor crystals grown from the melt: analysis of the haasen model for plastic deformation dynamics”, J. Crystal Growth, Vol. 108, (1991), pp. 399–415. http://dx.doi.org/10.1016/0022-0248(91)90388-L[Crossref]
  • [37] S. Maruyama, T. Aihira: “Radiation heat transfer of arbitrary three-dimensional absorbing, emitting and scattering media and specular and diffuse surfaces”, J. Heat Transfer, Vol. 119, (1997), pp. 129–136.
  • [38] M. Meyappan (Ed.): Computational Modeling in Semiconductor Processing, The Artech House, Norwood, 1994.
  • [39] N. Miyazaki: “Development of a thermal stress analysis system for anisotropic single crystal growth”, J. Crystal Growth, Vol. 236, (2002), pp. 455–465. http://dx.doi.org/10.1016/S0022-0248(01)02193-5[Crossref]
  • [40] A. Muehlbauer, A. Muiznieks, G. Raming: “System of mathematical models for the analysis of industrial FZ-Si-Crystal Growth Processes”, Cryst. Res. Technol., Vol. 34, (1999), pp. 217–226. http://dx.doi.org/10.1002/(SICI)1521-4079(199902)34:2<217::AID-CRAT217>3.0.CO;2-1[Crossref]
  • [41] G. Müller: “Experimental analysis and modeling of melt growth processes”, J. Crystal Growth, Vol. 237–239, (2002), pp. 1628–1637. http://dx.doi.org/10.1016/S0022-0248(01)02356-9[Crossref]
  • [42] J.T. Oden: “The promise of Computational Engineering and Science: will it be kept?”, IACM Express, Vol. 12, (2002), pp. 12–15.
  • [43] T. Ozawa, Y. Hayakawa, K. Balakrishnan, M. Kumagawa: “Numerical simulation of effect of ampoule rotation for the growth of InGaSb by rotational Bridgman method”, J. Crystal Growth, Vol. 237–239, (2002), pp. 1692–1696. http://dx.doi.org/10.1016/S0022-0248(01)02332-6[Crossref]
  • [44] P.Y. Papllambros: “Extending the optimization paradigm in engineering design”, In: Proc. 3rd Int. Symp. Tools Meth. Compet. Engineer., Delft (Netherlands), 2000, pp. 14.
  • [45] Welcome to Crosslight Software, Crosslight Software, Inc., 2003, http://www.crosslight.com.
  • [46] S. Prudhomme, J. T. Oden, T. Westermann, J. Bass, M.E. Botkin: “Practical Methods for a posteriori Error Estimation in Engineering Applications”, Int. J. Num. Meth. Engineer., Vol. 56, (2003), pp. 1193–1224. http://dx.doi.org/10.1002/nme.609[Crossref]
  • [47] D. Reid, B. Lent, T. Bryskiewicz, P. Singer, E. Mortimer, W.A. Bonner: “Cellular structure in LEC ternaryGa x In 1−x As crystals”, J. Crystal Growth, Vol. 174, (1997), pp. 250–255. http://dx.doi.org/10.1016/S0022-0248(96)01113-X[Crossref]
  • [48] Ch. Renner, J. Peinke, R. Friedrich, O. Chanal, B. Chaubad: “On the universality of small scale turbulence”, arXiv.org e-Print archive, http://arxiv.org/pdf/physics/0109052
  • [49] P.J. Roache: Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Albuquerque, New Mexico, 1998.
  • [50] S.A. Rukolaine, M.G. Vasilyev, V.S. Yuferev, A.O. Galyukov: “Numerical solution of axisymmetric radiative transfer problems in arbitrary domains using the characteristic method”, J. Quant. Spectr. Radiat. Transfer, Vol. 73, (2002), pp. 205–217. http://dx.doi.org/10.1016/S0022-4073(01)00204-7[Crossref]
  • [51] W. Schönauer: “Numerical engineering: design of PDE black-box solvers”, Math. Comput. Simul., Vol. 54, (2000), pp. 269–277. http://dx.doi.org/10.1016/S0378-4754(00)00188-9[Crossref]
  • [52] Products, semiconductor Technology Research, Inc., 2002, http://www.semitech.us/products/.
  • [53] Computational Fluid Dynamics Modeling for Semiconductor Industry, Soft-Impact Ltd., 2002, http://www.softimpact.ru/main-engl.html
  • [54] J.P. Steinbrenner, N.J. Wyman, J.R. Chawner: “Fast Surface Meshing on Imperfect CAD Models”, In: Proceedings, 9th International Meshing Roundtable, Jew Orleans (USA), 2000, Sandia National Laboratories, pp. 33–41.
  • [55] M. Suezawa, K. Sumino, N. Yonenaga: “Dislocation dynamics in the plastic deformation of silicon crystals”, Phys. Stat. Sol., Vol. A 51, (1979), pp. 217–233.
  • [56] A. N. Tihnnov, V.Ya. Arsenin: Solution of Ill-posed problems, Wiley, New York, 1977.
  • [57] Transcen Data, transcendata Europe Ltd., 2001–2003, http://www.fegs.co.uk/.
  • [58] C.T. Tsai: “On the finite element modeling of dislocation dynamics during semiconductorcrystal growth”, J. Cryst. Growth, Vol. 113, (1991), pp. 499–507. http://dx.doi.org/10.1016/0022-0248(91)90085-J[Crossref]
  • [59] A. Virozub, S. Brandon: “Selecting finite element basis functions for computation of partially facetted melt/crystal interfaces appearing during the directional growth of large-scale single crystals”, Model. Simul. Mater. Sci. Eng. Vol. 10, (2002), pp. 57–72. http://dx.doi.org/10.1088/0965-0393/10/1/305[Crossref]
  • [60] D. Vizman, O. Grabner, G. Müller: “Three-dimensional numerical simulation of thermal convection in an industrial Czochralski melt: comparison to experimental results”, J. Cryst. Growth, Vol. 233, (2001), pp. 687–698. http://dx.doi.org/10.1016/S0022-0248(01)01633-5[Crossref]
  • [61] V.V. Voronkov, R. Falster: “Intrinsic point defects and impurities in silicon crystal growth”, J. Electrochem. Soc., Vol. 149, (2002), pp. G167-G174. http://dx.doi.org/10.1149/1.1435361[Crossref]
  • [62] K. Weihe, Th. Willhalm: “Why CAD data repair requires discrete algorithmic techniques”, Konstanzer Schrift. Math. Inform., N 61, (1998), pp. 12.
  • [63] W.R. Wilcox, L.L. Regel, W.A. Arnold: “Convection and segregation during vertical Bridgman growth with centrifugation”, J. Crystal Growth, Vol. 187, (1998), pp. 543–558. http://dx.doi.org/10.1016/S0022-0248(97)00885-3[Crossref]
  • [64] M. Yokokawa, K. Itakura, A. Uno, T. Ishihara, Y. Kaneda: 16.4 TFlops direct numerical simulation of turbulence by a Fourier spectral method on the Earth simulator, http://www.sc-2002.org/paperpdfs/pap.pap273.pdf
  • [65] V.S. Yuferev, O.N. Budenkova, M.G. Vasiliev, S.A. Rukolaine, V.N. Shlegel, Ya.V. Vasiliev, A.I. Zhmakin: “Variations of solid-liquid interface in BGO low thermal gradients Cz growth for diffuse and specular crystal side surface”, J. Crystal Growth, Vol. 253, (2003), pp. 383–397. http://dx.doi.org/10.1016/S0022-0248(03)01110-2[Crossref]
  • [66] N. Zabaras: “Adjoint methods for inverse free convection problems with application to solidification processes”, In: J. Borggaard, E. Cliff, S. Schreck and J. Burns (Eds.): Computational Methods for Optimal Design and Control, Birkhauser Series in Progress in Systems and Control Theory, Birkhauser, 1998, pp. 391–426.
  • [67] A.I. Zhmakin: “A memory-efficient unstructured grid refinement algorithm for computation of 3d steady viscous flows”, Comm. Num. Meth. Eng., Vol. 13, (1997), pp. 219–228. http://dx.doi.org/10.1002/(SICI)1099-0887(199704)13:4<219::AID-CNM41>3.0.CO;2-9[Crossref]
  • [68] I.A. Zhmakin, A.V. Kulik, S. Yu. Karpov, S.E. Demina, M.S. Ramm, Yu. N. Makarov: “Evolution of thermoelastic strain and dislocation density during sublimation growth of silicon carbide”, Dimond and Related Materials, Vol. 9, (2000), pp. 446–451. http://dx.doi.org/10.1016/S0925-9635(99)00307-6[Crossref]
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_BF02476280
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