全球半导体晶体生长计算商业软件FEMAGSimulationoftheCrystalGrowthProcessAnalysisofMeltFlow.doc

全球半导体晶体生长计算著名的商业软件FEMAG之DynamicSimulationoftheEntireCrystalGrowthProcess:Multi-ScaleAnalysisofMeltFlowTransientsV. Regnier, L. Wu, B. Delsaute,F. Bioul, N. Van den Bogaert, F. DupretCESAME, Université catholiquedeLouvain, E-mail: fdmema.ucl.ac.beAbstractThispaperinvestigatesthetransientmeltflowevolutionduringapleteCzochralskicrystalgrowth process. Twobasictimescalesareconsidered.The short scaleconcernsthe basictransientsassociatedwith flow oscillationsatdifferentprocessstages.Accurateunderstanding oftheflowmechanismsatthisscaleisrequired todevelopanaveragea*isymmetricflowmodelforpletedynamicsimulations. Thelongtimescaleis associatedwiththetransientscausedbytheslowersystem evolution occurring during theplete growth process.Inordertofocusonthefundamentaleffectsgoverningtheflow,amodelproblemisconsideredwhere theliquidisplacedintoapossiblyrotatingcontainerwhileadiskofsmallerdiameterrotatesonitstopsurface. Boththecontainerandthediskareisothermal. Severaltransienteffectsareinvestigated including theeffectof diskradiusincreaseordecrease,andabruptchangesofdiskorcontainertemperatureorrotationrate.Introduction: dynamic modeling of crystal growth by means of the FEMAG softwareThereisincreasingdemandtodayforrobust,reliableanduser-friendlysoftwaretomodelbulkgrowthtechniquessuchastheCzochralski (Cz),LiquidEncapsulatedCzochralski (LEC),FloatingZone(FZ)and VerticalBridgman (VB)processes.Theaimistohelppredict,designandcontrolthegrowth processes, andto betterunderstandthefactorsaffecting crystalquality.However,thegrowthtechniques aremoreandmore ple*,andoptimizationcanbeachievedonlybyuseofsuitablenumericalmodelingthataccountsforthe severelynon-linearphysicalphenomenainvolvedaswellasforthehighsystem thermalinertia.Theresulting problemiscoupled,global,nonlinearanddynamic.Ontheotherhand,accuratepredictionofcrystalquality requiresbothappropriatemodelingofthegoverningphysics,andhighlyaccuratedynamiumericalmethods forputingtheevolutionofthe solid-liquidinterfaceshapeandthetemperaturefieldgradientinitsvicinity.The FEMAGsimulationsoftwaredevelopedin the CESAMEcenterof the Universityof Louvainis currently usedbymajorcrystalgrowthpanies.Thenumericalmodelisbothglobalanddynamic,andtakes theeffectofmeltconvectionintoaccount.Diffusesurfaceradiationisconsidered.Geometrical unknownsare dynamicallycoupledtotheotherunknowns,i.e.temperaturefield,velocityfield,electricalpotential,etc., leadingtoaple*non-linearsystem ofequationswhosesolutionisfoundbyuseofadecoupledschemeat everytimestepofthesimulation.WhereasinitsfirstgenerationFEMAGalreadyperformedglobalquasi-steadyortime-dependentsimulations,applicationswererestrictedtotopcone,shoulderingandbodygrowthstages.Bothlaminarandnon-laminarflowmodelswere considered,includingor not the effectofa*isymmetric magneticfields.TheobjectiveoflaunchingtheFEMAG-2softwaregeneration hasbeentoprovideafully automaticsimulatorpredictingtheentiregrowthprocesswhilehandlingcorrectly theswitchesbetweenthe growthstages,togetherwithcouplingdynamiccalculationswithaccuratemeltflowprediction.Asignificantdifficultylayintheimportantevolutionofthesystemgeometryduringapletegrowth process.Indeed,thesolidifiedregionisverysmallduringseedingandsubsequentlybeeslargerandlarger, whilethevolume ofthemoltenregiondecreasescontinuallyandcantakeaple*shapeduringtail-endstage. Thesolutionadoptedbinesseveralapproachesbasedonarepresentation ofthefurnacebymeansof deformingunstructuredmeshestogetherwithautomaticmeshgeneration.Newgeometrical methodswere designedtoalloweasycalculationofthedifferentsystemfreesurfaces(solidificationfront,melt/gasinterfaceincludingcrystal/meltandcrucible/melt menisci,andcrystal/gassurface).Thesemethodsallowperformingeasytime-dependentsimulationsevenfor stagesoftheprocesswhereimportantgeometricalchangesoccur.Another important difficultyto address in FEMAG-2 developmentwas related to the ple*ityof dynamicmeltflowmodeling.Severalproblemsmustbesolvedtoaccurately couplemeltflowpredictionswith crystalgrowthprocesssimulation.First,insemi-conductorgrowth,themeltflowistime-dependent,3Dand weakly turbulent,whereasitcane*hibit3Dazimuthalandtemporalstructuredoscillations. Theuseofan a*isymmetricquasi-steady flowmodelisdevotedtoaveragetheeffectoftheseoscillations,andtheprincipal issueistodeterminereliableaverageflowmodels,withthecorrespondingboundaryconditions,abovethe steadylaminarregime.Secondly,duetohighnonlinearities, thesolutionofnon-laminarflowproblemscanbe quitedifficultwhile,inmostcases,theseproblemse*hibitthenumericalstabilityandconvergenceissuesof transport-dominatedsystems. To this end, appropriateiterative schemes and stabilization techniques were introduced into the FEMAG-2 flow module. Thirdly,inordertoachievecoupling withglobalthermal calculations,themeltflowproblemissolvedinFEMAG-2atseveralstagesofthesimulation byusingaquasi- steady model,whilelongtermthermaltransientsaretreatedbyincluding appropriate sourcetermsintothe momentum andenergyequations.Interpolationbetweenthecollectedresultsp。