晶体生长工艺之横向磁场直拉法

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1、GlobalSimulationofCzochralskiSiliconGrowthundertheEffectofaTransverseMagneticFieldFEMAGSoft©2013CzSigrowthunderaTMF晶体生长工艺之横向磁场直拉法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