NHPT PVTPR7JHELSEVIERJournal of Crystal Growth 230(200192-99Numerical inv estigati on of silic on melt ?ow in large diameter CZ-crystal growth un der the in?uence of steady and dyn amicmagn etic ?eldsJ. Virbulis a, *,Th. Wetzel b , A. Muiz ni eks b , B. Hanna a , E. Dorn berger a ,E. Tomzig a , A. M . uhlbauer b,W.v. Ammon aaWacker Siltro nic AG, P.O. Box 1140, Bur g hause n, D-84479, Germa nybInstitute for Electroheat, Uni v ersity of Hanno v er, Wilhelm-Busch str.4, D-30167, Hanno v er, Germa nyAbstractTurbule nt silic on melt ?ows are studied in large diameter Czochralski cruciblesun der the in?uence of alter nati ng, steady and comb ined magn etic ?elds. Thein vestigati ons are based on the experime ntally veri?ed tw-dime nsio nal axisymmetric mathematical models. The in?uence of steady, alter nat ing and comb ined magn etic ?elds on the ?ow pattern an dtemperature ?eldis in vestigated . Global heat tran sfer an dmelt ?ow calculati ons are coupleda ndthe in?uence of melt convection on the in terface shape is studied and compared with experime ntal data. r 2001Elsevier Scie nee B.V. All rights reserved.PACS:47.27.i; 47.65.+aKeywords:A1. Fluid ?ows; A1. Heat transfer; A1. Magnetic ?elds; A2. Czochralski method; B2. Semic on duct ing silic on1. In troducti onThe conversion to large silicon (Sisingle crystals of 300mm diameter requires larger batch sizes which gen erates turbule nt melt conv ecti on with Grashof nu mber up to 1010. Several e? orts of the crystal growth industry are dedicated to control the melt ?ow andthe temperature d is-tribution. In particular, its focus is on the correct prediction of the in terface shape and the related point defect distributio n in the crystal, of theoxyge n tran sport, of the crucible overheat ing and of the dislocati on free growth. Besides conven-tional means, electromagetic steady (DCand dynamic (AC?elds o? er new possibilities to meet the con ti nu ously in creas ing dema nds for crystal quality, yieldimprovement andcost red uction. A numerical simulation helps in investigating the wide ?eld of possible process con diti ons, tosave a lot of experime ntal costs for large diameter crystal growth an dto red uce the time to market.Global heat tran sfer calculati ons 143provide goodagreeme nt with temperature measureme nts in crystal andin sulati on 4a ndare established as a sta ndard tool for Czochralski (CZprocess developme nt.*Correspo ndin gauthor. Tel.:+49-8677-83-4227;fax:+49-8677-83-7303.E-mail address:janis.virbuliswacker.com(J.Virbulis. 0022-0248/01/$-see front matter r 2001Elsevier Science B.V. All rights reserved. PII:S 0022-0248(01 01321-5Several numerical studies are devoted to melt ?ow in CZ crucibles. Most of them are made for two-dime nsio nal (2Didealized cyli ndrical geo-metries with small crucible sizes andsimpli?ed thermal boundary conditions. In some cases, magptic ?eld e? ects have been studied, e.g. Ref. 5. Three-dimensional (3Ddirect numerical simula-tion without turbule nce models in idealized geometries show non-symmetric time-depe ndent?ow behavior in small 6andmed ium (Gr=108 7crucibles. Global heat transfer coupledwith 2D melt ?ow in large crucibles using low Re nu mber k 2e models has bee n calculated 8,9without the in?uence of magn etic ?elds.In this work, we prese nt nu merical in vestiga-ti ons of turbule nt Si-melt ?ows in large diameter CZ crucibles un der thein?uence of AC, DC and comb in edmag netic ?eld s. The in vestigati ons are basedo n the experime ntally veri?edsystem of a-symmetric mathematical models, where the melt conv ecti on an dthe global heat tran sfer are coupled. The in?uence of melt conv ecti on on thei nterface shape an dthermal grad ients in the crystal is studied and compared with experimental data. 2. Numerical models2.1. Coupli n g betwee n g lobal heat tran sferand melt con v ectionGlobal heat tran sfer in the whole axisymmetric CZ system is simulaidwith the ?n ite eleme nt cod e FEMAG, described in detail in Ref. 1.Heat tran sfer is modeled using quadratic ?nite elements in solids and view factors in radiative enclosures. Conductive and conv ective heat tran sfer in argo n gas is n eglectedd ue to low pressure. The growth process is assumedto be quasi-stead y an dthe release of late nt heat of fusi on at the crystallizatio n in terface is proporti onal to the imposedgrowth rate.Melt conv ecti on is simulatedwith the program package CFD-ACE 10.The coupli ng betwee n global thermal an dmelt ?ow simulati ons is realizedby excha nge of the heat ?uxes at the melt boundaries. The ?rst global simulation is carried out using the?eective heat transport co? cient including conductive and convective contributions in the melt with FEMAG. The calculatedheat ?uxes along the crucible an dmelt free surfaces are provided as thermal boun dary con diti ons for the melt ?ow simulati on with C