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Numerical study of the infl uence of different types of magnetic fi elds on the interface shape in directional solidifi cation of multi-crystalline silicon ingots C. Tanasie a, D. Vizmana,n, J. Friedrichb aPhysics Faculty, West University of Timisoara, Bd. V. Parvan 4, 300223 Timisoara, Romania bDepartment of Crystal Growth, Fraunhofer Institute IISB Erlangen, Schottkystrasse 10, 91058 Erlangen, Germany a r t i c l e i n f o Available online 2 December 2010 Keywords: A1. Computer simulation A1. Fluid fl ow A2. Ingot casting method B2. Multi-crystalline silicon a b s t r a c t Numerical simulations were carried out in order to study the effect of various types of magnetic fi elds (steadyverticalandhorizontalmagneticfi eldsandacombinationofasteadyfi eldandDCelectriccurrent) onmeltconvectionandinterfaceshapeduringdirectionalsolidifi cationofmulti-crystallinesiliconingots. It is shown that steady magnetic fi elds can decrease the interface defl ection. The electromagnetic fi eld produced by the combination of DC current through the melt and a steady magnetic fi eld can produce a stirringeffectinthemeltforarelativelysmallvalueofmagneticfi eldandelectricalcurrent.Consequently, a more uniform distribution of dopants and impurities can be obtained in the silicon crystals. The melt rotation rate can be easily controlled by the intensity of the electrical current. . C. Tanasie et al. / Journal of Crystal Growth 318 (2011) 293297295 from 4 mm/s without a magnetic fi eld down to 0.4 mm/s with magneticfi elds.Ifwelookatparticletracking(Fig.3aandb)itcanbe easily observed that in the case of VMF the very low intensity of convectionwillnotcontributetothemeltmixingatall.Ontheother hand the HMF can doa better mixing, of course after a longer period oftimebecauseofsmallmeltvelocities.BothHMFandVMFdecrease theinterfacedefl ectionascanbeseeninFig.4.InthecaseofHMFthe interface shape is slightly asymmetric, which is a result of the asymmetric fl ow pattern in the melt fl ow as can be seen in Fig. 3b. In order to obtain a homogeneous distribution of impurities, a meltstirringcanbeasolutionforbettermixing.Anelegantsolution for rotating the melt without mechanical elements was proposed by Wang et al. 10 for the Czochraski method. We analyzed the same confi guration for the directional solidifi cation method. The mould is placed in a vertical magnetic fi eld and an electrical DC current passes from the bottom of the growing crystal to a small diameter electrode attached to the melt surface in the center (Fig. 1). Along the crystal bottom a uniform distribution of the electric current was considered. The effects of the electrode on the thermal and velocity fi elds at the free surface were ignored due to the small size of the electrode. Because of the Lorentz force, generated by the VMF and the radial components of the electrical current,themeltwillspontaneouslyrotateascanbeseeninFig.3c. The scalar potential distribution in a central vertical section is Fig. 6. Interface shape in xOz plane, for EMF with B100 mT and different intensities of electrical current I. Fig. 7. Interface shape in xOz plane, for EMF with B200 mT and different intensities of electrical current I. C. Tanasie et al. / Journal of Crystal Growth 318 (2011) 293297296 presented in Fig. 5. In order to understand the infl uence of EMF parameters on the melt fl ow both, intensity of electrical current I and magnetic fi eld induction B, were varied. Their infl uence on interface shape and defl ection and on melt rotation rate was studied. Two values for induction B of the magnetic fi eld were considered100 and 200 mT. It can be observed in Figs. 6 and 7 that in the case of EMF the defl ection of the interface shape increases. For higher intensities of electrical current I the interface shape in the central part has a w-form. This effect on the interface shape is much higher for B200 mT than for B100 mT. For B100 mT and for small values of the electrical current (3 A) the interface defl ection increases only slightly and deformation in the central part is not very signifi cant (Fig. 6). Concerning the melt rotation rate (w), Fig. 8 shows that for B100 mT, w increases with intensityofelectricalcurrentI.ItcanbeobservedthatforI3 Athe rotation rate is about 4 rpm, and for I10 A, w is around 9 rpm, which is the same order as in EMCZ 16. For B200 mT the rotation rate increases with the intensity of electrical current till I10 A and then slightly decreases (Fig. 8). 4. Conclusion The obtained results show that magnetic fi elds can be an option for controllingthe melt convection, interfaceshape, and impurities distribution in the directional solidifi cation of multi-crystalline silicon. Horizontal and vertical magnetic fi elds damp the fl ow therefore do not mix the melt but reduce the bending of the interface. These facts let us conclude that they will fi nd less application unless additional ways for mixing are used. The combination of vertical magnetic fi eld and electrical current (EMF) has the potential to control the melt fl ow, interface shape, and interface defl ection. Relatively small values of the magnetic fi eld (100 mT) and the electrical current (35 A) can lead to a melt stirring effect, where the melt rotates with a rotation speed of 48 rpm.Thebendingofthe interfaceshapeincreasesslightly.This effect has to be compensated by e.g. heater adjustments. Although the EMF seems to have potential for improving the directional solidifi cation process, the experimental proof of the numerical results seems to be diffi cult. A technological solution has to be developedfi rsttorealizetheelectricalcontactsformeltandcrystal. Then, one still has to deal with the additional and not negligible costs especially for the magnet. Acknowledgements The authors would like to acknowledge the European Social Fund through the Sectoral Operational Program for Human Resources Development 20072013 for fi nancial support under the project POSDRU/88/1.5/S/49516 coordinated by West Univer- sity of Timisoara in partnership with the University of Craiova and Fraunhofer Institute IISB, Erlangen. References 1 D. Vizman, J. Friedrich, G. Mueller, J. Cryst. Growth 303 (2007) 231235. 2 H. Miyazawa, L. Liu, S. Hisamatsu, K. Kakimoto, J. Cryst. Growth 310 (2008) 10341039. 3 B. Gao,S. Nakano, K. Kakimoto, J.Electrochem. Soc. 157 (2) (2010)H153H159. 4 C. Reimann, M. Trempa, T. Jung, J. Friedrich, G. Mueller, J. Cryst. Growth 312 (2010) 878885. 5 Y. Teng, J. Chen, C. Lu, C. Chen, J. Cryst. Growth 312 (2010) 12821290. 6 D. Vizman, J. Friedrich, G. Mueller, J. Cryst. Growth 230 (2001) 7380. 7 A. Muiznieks, A. Krauze, B. Nacke, J. Cryst. Growth 303 (2007) 211220. 8 P. Rudolph, J. Cryst. Growth 310 (2008) 12981306. 9 L. Liu, K. Kakimoto, J. Cryst. Growth 310 (2008) 306312. 10 W. Wang, M. Watanabe, T. Hibiya, T. Tanahashi, Jpn. J. Appl. Phys. 39 (2000) 372377. 11 K.Dadzis,M.Zschorsch,U.Wunderwald,T.Jung,J.Friedrich,Proceedingsofthe Sixth Conference on Electromagnetic Processing of Materia