全球半导体晶体生长建模著名商业软件FEMAG-横向磁场直拉硅晶体生长的全局模拟

全球半导体晶体生长建模著名商业软件FEMAGGlobalSimulationofCzochralskiSiliconGrowthundertheEffectofaTransverseMagneticFieldFEMAGSoft©2013CzSigrowthunderaTMFMHDboundarylayers:HartmannlayersFEMAGSoft©2013TheHartmannlayersdevelopalongthesurfaceswherethenormalcomponentofthemagneticfieldisnon-negligible.AnorderofmagnitudeofthethicknessofaHartmannlayerisdH=LHa-1(L=RsorRc).TypicallydH=0.05-0.08mminindustrialfurnaces.CzSigrowthunderaTMF(cont’d)Transversemagneticfields:FLETmethodMethod:Fourierdecompositionofallfields(velocity,pressure,temperature)Hypothesis:Principalissue:whichandhowmanymodes?Objective:global,quasi-steadyortime-dependentcalculationsatareasonablecostFEMAGSoft©2013CzSigrowthunderaTMF(cont’d)FourierLimitedExpansionTechnique(FLET)FEMAGSoft©2013ThefieldvariablesareexpandedasFourierseriesintheazimuthal(q)direction:CzSigrowthunderaTMF(cont’d)FourierLimitedExpansionTechnique(FLET)FEMAGSoft©2013andwhilethenumberofmodesMisassmallaspossiblewithoutlossofaccuracy(spectralconvergence).whilethedifferentmodecoefficients:are2DFiniteElementfunctionsofthemeridionalcoordinates(r,z)Thisresultsinasystemwhosesizeisthatofthe2DsystemmultipliedbythenumberofFouriermodesconsideredandhenceinadramaticsystemsizereduction.CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013RadiationtransferCouplingbetween3Dand2Daxisymmetricheattransferacrossaradiativeenclosure-theviewedandhiddenpartsarecalculatedasaxisymmetric-or,equivalently,eachsurfaceoftheenclosureisviewedasaxisymmetricfromtheothersurfacesMainmodelinghypothesis:-generally3Dcomponentsarerotatingwithrespecttothe2Denvironment-3Dcomponentsmostlyview2DcomponentsbecauseofthepresenceofheatshieldsThishypothesisissatisfactorybecause:CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013FlowandglobalheattransferinasiliconCzpullerundertheeffectofaTMF(quasi-steadysimulation)CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Top:topviewofthevelocitymagnitudeandstreamlines.Bottom:velocityfieldmagnitudeandcross-sectionshowingasharpHartmannlayeralongthemelt-crucibleinterface.Growthofa300mmdiameterSicrystalundertheeffectofa0.5TTMF.CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013InatypicalTMFconfigurationextremelythinHartmannlayersof50-80mmdevelopGrowthofa300mmdiameterSicrystalundertheeffectofa0.5TTMF.CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013DetailofthedeformingBoundaryLayerMesh(BLM)usedFlowandglobalheattransferinasiliconCzpullerundertheeffectofaTMFCzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Hartmannboundarylayersalongthemelt-crystalandmelt-crucibleinterfacesandassociatedboundarylayermeshes.StrongHartmannbackflowsdevelop.Growthofa300mmdiameterSicrystalundertheeffectofa0.5TTMF.CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013CzSigrowthunderaTMF(cont’d)Czochralskigrowthofasiliconcrystalundera500mThorizontalmagneticfieldGlobalsimulationthegrowthof300mmand400mmcrystalsFEMAGSoft©2013CzSigrowthunderaTMF(cont’d)Growthofa300mmcrystalundera500mTTMFLeft:meltsurfaceRight:meridionalcross-sectionsparallelandperpendiculartothemagneticfieldTop:velocityfieldBottom:temperaturefieldFEMAGSoft©2013CzSigrowthunderaTMF(cont’d)Growthofa400mmcrystalundera500mTTMFLeft:meltsurfaceRight:meridionalcross-sectionsparallelandperpendiculartothemagneticfieldTop:velocityfieldBottom:temperaturefieldFEMAGSoft©2013Czochralskigrowthofasiliconcrystalundera3000or5000GhorizontalmagneticfieldGlobalsimulationofthegrowthof300mmand400mmcrystalsCzSigrowthunderaTMF(cont’d)Geometryissuedfromfollowingpublications:K.Takano&al.Mat.Sc.&Eng.,B73(2000)30-35Y.Shiraisho&al.,JCG229(2001)17-21Parametersforthereferencesimulation:CrystalDiameter=0.4[m]CrucibleDiameter=0.9[m]CrystalRotationrate=-10[RPM]CrucibleRotationrate=+5[RPM]Totalcharge=400[kg]PullRate=0.45[mm/min]HorizontalMagneticField=3000Gauss(inxdirection)FEMAGSoft©2013.52[m]1.3[m].78[m]SiliconGraphiteQuartzInsulatorGeometryandoperatingconditionsCzSigrowthunderaTMF(cont’d)FEMAGSoft©2013IDCrucibleRotationrateCrystaldiameterTypeofmagneticfieldMagneticstrengthTotalchargeVerticalpositionoftheTMFCrystallengthArgasflow[mm][Gauss][kg][m][mm]15400horizontal3000400/+/-500nogas25300horizontal3000400/+/-500nogas35400horizontal5000400/+/-500nogas45400ovoid+/-3000400h1=1.2+/-500nogas55400ovoid+/-3000400h2=1.37+/-500nogas65400horizontal3000400/+/-400nogas75400horizontal3000400/+/-500withgas85400--400/+/-500nogas90.2400horizontal3000400/+/-500nogasDescriptionofthesimulationsCzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:noTemperaturefield(K):topleft:parallelcrosssection;bottomleft:perpendicularcrosssection;topright:topviewCase1CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case1Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:noVelocityfield(m.s-1):topleft:parallelcrosssection;bottomleft:perpendicularcrosssectionCzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case1Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasf