3D modeling and simulation of the triple junction line movement in Czochralski crystal growth
Final Report Abstract
Numerical simulations of the Czochralski process use the assumption of a quasi-steady state of the crystal growth, which neglects the change of the crystal geometry with time. This denotes that transient phenomena of the crystallization process such as diameter changes of the crystal cannot be predicted. In this project, a method was developed to overcome the restrictions due to the quasi-steady state assumption. For that purpose, an iterative algorithm was designed, which integrates the computation of the Stefan condition for the crystallization and the simulation of the melt free surface, which both determine the movement of the three-phase junction. These new features completing realistic predictions of the CZ crystals growth process were combined with the numerical simulation of the turbulent flow and heat transfer in the melt using LES. In a test case, this algorithm was successfully applied. It could be shown that under certain process conditions, diameter variations occur during the crystal growth process. However, beside the successful simulations of the entire process for several seconds of physical time on the one hand the algorithm turned out to be sensitive towards perturbations on the other hand. This is due to the complexity of the problem and the large number of degrees of freedom. Potentially resulting problems of stability are always connected to severe grid deformations in the free surface region. To improve the algorithm, on the one hand the elliptic grid smoothing algorithm showed promising results for the inner grid points. Here, code optimization is still necessary to reduce computational time. On the other hand, in addition to the work plan, the TSE scheme was implemented and tested to maintain the order of accuracy on deformed grids. Here, initial tests showed very promising results. In future research, the algorithm can be used for the optimization of the process parameters in Czochralski crystal growth, especially for the development of new diameter control strategies.
Publications
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Analysis of turbulent structures in a Czochralski system using DNS and LES predictions. In: High Performance Computing in Science and Engineering ' 07, Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2007, Hrsg.: W. E. Nagel; D.B. Kröner; M.M. Resch, Berlin: Springer, 2008, 371-386
Raufeisen, A.; Breuer, M.; Botsch, T.; Durst, F.
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DNS of rotating buoyancy- and surface tension-driven flow. Int Journal of Heat and Mass Transfer 51(2008), 6219-6234
Raufeisen, A.; Breuer, M.; Botsch, T.; Delgado, A.
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Einfluss der Lage der Tripelllnie auf die Phasengrenze bei der numerischen Simulation der Einkristallzüchtung nach dem Czochralski-Verfahren. DGKK-Jahrestagung, München, 5.-7. März 2008
Raufeisen, A.; Breuer, M.; Botsch, T.; Delgado, A.
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Transient 3D simulation of Czochralski crystal growth considering diameter variations. 4th Asian Conference on Crystal Growth and Crystal Technology (CGCT-4), Sendai, Japan, 21.-24. Mai 2008
Raufeisen, A.; Breuer, M.; Botsch, T.; Delgado, A.
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Beitrag zur Bestimmung der Dreiphasengrenzlinie bei der Simulation des Czochralski-Prozesses. DGKK Arbeitskreistreffen "Angewandte Simulation in der Kristallzüchtung", Potsdam. 1.-3. April 2009
Raufeisen, A.; Breuer, M.; Botsch, T.; Delgado, A.
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LES validation of turbulent rotating buoyancy- and surface tension-driven flow against DNS. Computers and Fluids 38(2009), 1549-1565
Raufeisen, A.; Breuer, M.; Botsch, T.; Delgado, A.
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Prediction of the three-phase boundary movement in Czochralski crystal growth. 6th International Workshop on Modeling in Crystal Growth (lWMCG-6), Lake Geneva, WI, USA, 9.-14. Aug. 2009
Raufeisen, A.; Breuer, M.; Botsch, T.; Delgado, A.
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Transient 3D simulation of Czoct)ratski crystal growth considering diameter variations. Journal of Crystal Growth 311 (2009), 695-697
Raufeisen, A.; Breuer, M.; Botsch, T.; Delgado, A.
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3D modelling and simulation of the triple junction line movement in Czochralski crystal growth. KFBT-Tagung, Berlin, 16.-17. Sept. 2010
Hirt, M.; Raufeisen, A.; Botsch, T.; Franz, E.; Breuer, M.; Delgado, A.
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Prediction of the three-phase boundary movement in Czochralski crystal growth. Journal of Crystal Growth 312(2010), 2297-2299
Raufeisen, A.; Breuer, M.; Botsch, T.; Delgado, A.
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Time-dependent three-dimensional simulation of the turbulent flow and heat transfer in Czochralski crystal growth including the three-phase boundary movement. Iin: High Performance Computing in Science and Engineering '10, Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2010, Hrsg.: W. E. Nagel; D.B. Kröner; M.M. Resch, Berlin: Springer, 2011, 353-367
Raufeisen, A.; Breuer, M.; Botsch, T.; Durst, F.
