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1、GlobalSimulationofCzochralskiSiliconGrowthundertheEffectofaTransverseMagneticFieldFEMAGSoft?2013CzSigrowthunderaTMF晶體生長工藝之橫向磁場直拉法MHDboundarylayers:HartmannlayersFEMAGSoft?2013TheHartmannlayersdevelopalongthesurfaceswherethenormalcomponentofthemagneticfieldisnon-negligible.Anorderofmagnitudeof
2、thethicknessofaHartmannlayerisdH=LHa-1(L=RsorRc).TypicallydH=0.05-0.08mminindustrialfurnaces.CzSigrowthunderaTMF(cont’d)Transversemagneticfields: FLETmethodMethod:Fourierdecompositionofallfields(velocity,pressure,temperature)Hypothesis:Principalissue:whichandhowmanymodes?Objective:global,quas
3、i-steadyortime-dependentcalculationsatareasonablecostFEMAGSoft?2013CzSigrowthunderaTMF(cont’d)FourierLimitedExpansionTechnique(FLET)FEMAGSoft?2013ThefieldvariablesareexpandedasFourierseriesintheazimuthal(q)direction:CzSigrowthunderaTMF(cont’d)FourierLimitedExpansionTechnique(FLET)FEMAGSoft?20
4、13andwhilethenumberofmodesMisassmallaspossiblewithoutlossofaccuracy(spectralconvergence).whilethedifferentmodecoefficients:are2DFiniteElementfunctionsofthemeridionalcoordinates(r,z)Thisresultsinasystemwhosesizeisthatofthe2DsystemmultipliedbythenumberofFouriermodesconsideredandhenceinadramatic
5、systemsizereduction.CzSigrowthunderaTMF(cont’d)FEMAGSoft?2013RadiationtransferCouplingbetween3Dand2Daxisymmetricheattransferacrossaradiativeenclosuretheviewedandhiddenpartsarecalculatedasaxisymmetricor,equivalently,eachsurfaceoftheenclosureisviewedasaxisymmetricfromtheothersurfacesMainmodelin
6、ghypothesis:generally3Dcomponentsarerotatingwithrespecttothe2Denvironment3Dcomponentsmostlyview2DcomponentsbecauseofthepresenceofheatshieldsThishypothesisissatisfactorybecause:CzSigrowthunderaTMF(cont’d)FEMAGSoft?2013FlowandglobalheattransferinasiliconCzpullerundertheeffectofaTMF(quasi-steady
7、simulation)CzSigrowthunderaTMF(cont’d)FEMAGSoft?2013Top:topviewofthevelocitymagnitudeandstreamlines.Bottom:velocityfieldmagnitudeandcross-sectionshowingasharpHartmannlayeralongthemelt-crucibleinterface.Growthofa300mmdiameterSicrystalunderthee
