晶体生长模拟软件FEMAG之DynamicSimulationoftheEntireCrystalGrowthProcess:Multi-ScaleAnalysisofMeltFlowTransientsV.Regnier,L.Wu,B.Delsaute,F.Bioul,N.VandenBogaert,F.DupretCESAME,UniversitécatholiquedeLouvain,E-mail:fd@mema.ucl.ac.beAbstractThispaperinvestigatesthetransientmeltflowevolutionduringacompleteCzochralskicrystalgrowthprocess.Twobasictimescalesareconsidered.Theshortscaleconcernsthebasictransientsassociatedwithflowoscillationsatdifferentprocessstages.Accurateunderstandingoftheflowmechanismsatthisscaleisrequiredtodevelopanaverageaxisymmetricflowmodelforcompletedynamicsimulations.Thelongtimescaleisassociatedwiththetransientscausedbytheslowersystemevolutionoccurringduringthecompletegrowthprocess.Inordertofocusonthefundamentaleffectsgoverningtheflow,amodelproblemisconsideredwheretheliquidisplacedintoapossiblyrotatingcontainerwhileadiskofsmallerdiameterrotatesonitstopsurface.Boththecontainerandthediskareisothermal.Severaltransienteffectsareinvestigatedincludingtheeffectofdiskradiusincreaseordecrease,andabruptchangesofdiskorcontainertemperatureorrotationrate.Introduction:dynamicmodelingofcrystalgrowthbymeansoftheFEMAGsoftwareThereisincreasingdemandtodayforrobust,reliableanduser-friendlysoftwaretomodelbulkgrowthtechniquessuchastheCzochralski(Cz),LiquidEncapsulatedCzochralski(LEC),FloatingZone(FZ)andVerticalBridgman(VB)processes.Theaimistohelppredict,designandcontrolthegrowthprocesses,andtobetterunderstandthefactorsaffectingcrystalquality.However,thegrowthtechniquesaremoreandmorecomplex,andoptimizationcanbeachievedonlybyuseofsuitablenumericalmodelingthataccountsfortheseverelynon-linearphysicalphenomenainvolvedaswellasforthehighsystemthermalinertia.Theresultingproblemiscoupled,global,nonlinearanddynamic.Ontheotherhand,accuratepredictionofcrystalqualityrequiresbothappropriatemodelingofthegoverningphysics,andhighlyaccuratedynamicnumericalmethodsforcomputingtheevolutionofthesolid-liquidinterfaceshapeandthetemperaturefieldgradientinitsvicinity.TheFEMAGsimulationsoftwaredevelopedintheCESAMEcenteroftheUniversityofLouvainiscurrentlyusedbymajorcrystalgrowthcompanies.Thenumericalmodelisbothglobalanddynamic,andtakestheeffectofmeltconvectionintoaccount.Diffusesurfaceradiationisconsidered.Geometricalunknownsaredynamicallycoupledtotheotherunknowns,i.e.temperaturefield,velocityfield,electricalpotential,etc.,leadingtoacomplexnon-linearsystemofequationswhosesolutionisfoundbyuseofadecoupledschemeateverytimestepofthesimulation.WhereasinitsfirstgenerationFEMAGalreadyperformedglobalquasi-steadyortime-dependentsimulations,applicationswererestrictedtotopcone,shoulderingandbodygrowthstages.Bothlaminarandnon-laminarflowmodelswereconsidered,includingornottheeffectofaxisymmetricmagneticfields.TheobjectiveoflaunchingtheFEMAG-2softwaregenerationhasbeentoprovideafullyautomaticsimulatorpredictingtheentiregrowthprocesswhilehandlingcorrectlytheswitchesbetweenthegrowthstages,togetherwithcouplingdynamiccalculationswithaccuratemeltflowprediction.Asignificantdifficultylayintheimportantevolutionofthesystemgeometryduringacompletegrowthprocess.Indeed,thesolidifiedregionisverysmallduringseedingandsubsequentlybecomeslargerandlarger,whilethevolumeofthemoltenregiondecreasescontinuallyandcantakeacomplexshapeduringtail-endstage.Thesolutionadoptedcombinesseveralapproachesbasedonarepresentationofthefurnacebymeansofdef...