晶体生长工艺之横向磁场直拉法.ppt

GlobalSimulationofCzochralskiSiliconGrowthundertheEffectofaTransverseMagneticField FEMAGSoft 2013 CzSigrowthunderaTMF 晶体生长工艺之横向磁场直拉法 MHDboundarylayers Hartmannlayers FEMAGSoft 2013 TheHartmannlayersdevelopalongthesurfaceswherethenormalcomponentofthemagneticfieldisnon negligible AnorderofmagnitudeofthethicknessofaHartmannlayerisdH LHa 1 L RsorRc TypicallydH 0 05 0 08mminindustrialfurnaces CzSigrowthunderaTMF cont d Transversemagneticfields FLETmethod Method Fourierdecompositionofallfields velocity pressure temperature Hypothesis Principalissue whichandhowmanymodes Objective global quasi steadyortime dependentcalculationsatareasonablecost FEMAGSoft 2013 CzSigrowthunderaTMF cont d FourierLimitedExpansionTechnique FLET FEMAGSoft 2013 ThefieldvariablesareexpandedasFourierseriesintheazimuthal q direction CzSigrowthunderaTMF cont d FourierLimitedExpansionTechnique FLET FEMAGSoft 2013 andwhilethenumberofmodesMisassmallaspossiblewithoutlossofaccuracy spectralconvergence whilethedifferentmodecoefficients are2DFiniteElementfunctionsofthemeridionalcoordinates r z Thisresultsinasystemwhosesizeisthatofthe2DsystemmultipliedbythenumberofFouriermodesconsideredandhenceinadramaticsystemsizereduction CzSigrowthunderaTMF cont d FEMAGSoft 2013 Radiationtransfer Couplingbetween3Dand2Daxisymmetricheattransferacrossaradiativeenclosure theviewedandhiddenpartsarecalculatedasaxisymmetricor equivalently eachsurfaceoftheenclosureisviewedasaxisymmetricfromtheothersurfaces Mainmodelinghypothesis generally3Dcomponentsarerotatingwithrespecttothe2Denvironment3Dcomponentsmostlyview2Dcomponentsbecauseofthepresenceofheatshields Thishypothesisissatisfactorybecause CzSigrowthunderaTMF cont d FEMAGSoft 2013 FlowandglobalheattransferinasiliconCzpullerundertheeffectofaTMF quasi steadysimulation CzSigrowthunderaTMF cont d FEMAGSoft 2013 Top topviewofthevelocitymagnitudeandstreamlines Bottom velocityfieldmagnitudeandcross sectionshowingasharpHartmannlayeralongthemelt crucibleinterface Growthofa300mmdiameterSicrystalundertheeffectofa0 5TTMF CzSigrowthunderaTMF cont d FEMAGSoft 2013 InatypicalTMFconfigurationextremelythinHartmannlayersof50 80mmdevelop Growthofa300mmdiameterSicrystalundertheeffectofa0 5TTMF CzSigrowthunderaTMF cont d FEMAGSoft 2013 DetailofthedeformingBoundaryLayerMesh BLM used FlowandglobalheattransferinasiliconCzpullerundertheeffectofaTMF CzSigrowthunderaTMF cont d FEMAGSoft 2013 Hartmannboundarylayersalongthemelt crystalandmelt crucibleinterfacesandassociatedboundarylayermeshes StrongHartmannbackflowsdevelop Growthofa300mmdiameterSicrystalundertheeffectofa0 5TTMF CzSigrowthunderaTMF cont d FEMAGSoft 2013 CzSigrowthunderaTMF cont d Czochralskigrowthofasiliconcrystalundera500mThorizontalmagneticfield Globalsimulationthegrowthof300mmand400mmcrystals FEMAGSoft 2013 CzSigrowthunderaTMF cont d Growthofa300mmcrystalundera500mTTMF Left meltsurfaceRight meridionalcross sectionsparallelandperpendiculartothemagneticfield Top velocityfieldBottom temperaturefield FEMAGSoft 2013 CzSigrowthunderaTMF cont d Growthofa400mmcrystalundera500mTTMF Left meltsurfaceRight meridionalcross sectionsparallelandperpendiculartothemagneticfield Top velocityfieldBottom temperaturefield FEMAGSoft 2013 Czochralskigrowthofasiliconcrystalundera3000or5000Ghorizontalmagneticfield Globalsimulationofthegrowthof300mmand400mmcrystals CzSigrowthunderaTMF cont d FEMAGSoft 2013 Geometryandoperatingconditions CzSigrowthunderaTMF cont d FEMAGSoft 2013 Descriptionofthesimulations CzSigrowthunderaTMF cont d FEMAGSoft 2013 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Temperaturefield K topleft parallelcrosssection bottomleft perpendicularcrosssection topright topview Case1 CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case1 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Velocityfield m s 1 topleft parallelcrosssection bottomleft perpendicularcrosssection CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case1 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Oxygenconcentration m 3 topleft parallelcrosssectioninmelt bottomleft perpendicularcrosssectioninmelt topright crystal CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case2 Crystaldiameter 300mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Temperaturefield K topleft parallelcrosssection bottomleft perpendicularcrosssection CzSigrowthunderaTMF cont d FEMAGSoft 2013 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Temperaturefield K topleft parallelcrosssection bottomleft perpendicularcrosssection Case1 CzSigrowthunderaTMF cont d FEMAGSoft 2013 Velocityfield m s 1 topleft parallelcrosssection bottomleft perpendicularcrosssection Case2 Crystaldiameter 300mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case1 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Velocityfield m s 1 topleft parallelcrosssection bottomleft perpendicularcrosssection CzSigrowthunderaTMF cont d FEMAGSoft 2013 Oxygenconcentration m 3 topleft parallelcrosssectioninmelt bottomleft perpendicularcrosssectioninmelt topright crystal Case2 Crystaldiameter 300mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case1 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Oxygenconcentration m 3 topleft parallelcrosssectioninmelt bottomleft perpendicularcrosssectioninmelt topright crystal CzSigrowthunderaTMF cont d FEMAGSoft 2013 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 5000GGasflow no Temperaturefield K topleft parallelcrosssection bottomleft perpendicularcrosssection topright topview Case3 CzSigrowthunderaTMF cont d FEMAGSoft 2013 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Temperaturefield K topleft parallelcrosssection bottomleft perpendicularcrosssection topright topview Case1 CzSigrowthunderaTMF cont d FEMAGSoft 2013 Velocityfield m s 1 topleft parallelcrosssection bottomleft perpendicularcrosssection Case3 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 5000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case1 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Velocityfield m s 1 topleft parallelcrosssection bottomleft perpendicularcrosssection CzSigrowthunderaTMF cont d FEMAGSoft 2013 Oxygenconcentration m 3 topleft parallelcrosssectioninmelt bottomleft perpendicularcrosssectioninmelt topright crystal Case3 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 5000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Oxygenconcentration m 3 topleft parallelcrosssectioninmelt bottomleft perpendicularcrosssectioninmelt topright crystal Case3 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 5000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case1 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Oxygenconcentration m 3 topleft parallelcrosssectioninmelt bottomleft perpendicularcrosssectioninmelt topright crystal CzSigrowthunderaTMF cont d FEMAGSoft 2013 Ovoidmagneticfield topleft sketchofthemagneticfield bottomleft sideview right topview Case4 CzSigrowthunderaTMF cont d FEMAGSoft 2013 Ovoidmagneticfield topleft sketchofthemagneticfield bottomleft sideview right topview Case4 CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case4 Temperaturefield K topleft parallelcrosssection bottomleft perpendicularcrosssection topright topview Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype ovoidMagneticfieldstrength 3000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Temperaturefield K topleft parallelcrosssection bottomleft perpendicularcrosssection topright topview Case1 CzSigrowthunderaTMF cont d FEMAGSoft 2013 Velocityfield m s 1 topleft parallelcrosssection bottomleft perpendicularcrosssection Case4 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype ovoidMagneticfieldstrength 3000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case1 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Velocityfield m s 1 topleft parallelcrosssection bottomleft perpendicularcrosssection CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case4 Oxygenconcentration m 3 topleft parallelcrosssectioninmelt bottomleft perpendicularcrosssectioninmelt topright crystal Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype ovoidMagneticfieldstrength 3000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case1 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow no Oxygenconcentration m 3 topleft parallelcrosssectioninmelt bottomleft perpendicularcrosssectioninmelt topright crystal CzSigrowthunderaTMF cont d FEMAGSoft 2013 Ovoidmagneticfield lifted topleft sketchofthemagneticfield bottomleft sideview right topview Case5 CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case5 Ovoidmagneticfield lifted topleft sketchofthemagneticfield bottomleft sideview right topview 2 CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case5 Temperaturefield K topleft parallelcrosssection bottomleft perpendicularcrosssection topright topview Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype ovoid lifted Magneticfieldstrength 3000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case4 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype ovoidMagneticfieldstrength 3000GGasflow no Temperaturefield K topleft parallelcrosssection bottomleft perpendicularcrosssection topright topview CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case5 Velocityfield m s 1 topleft parallelcrosssection bottomleft perpendicularcrosssection Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype ovoid lifted Magneticfieldstrength 3000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Velocityfield m s 1 topleft parallelcrosssection bottomleft perpendicularcrosssection Case4 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype ovoidMagneticfieldstrength 3000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case5 Oxygenconcentration m 3 topleft parallelcrosssectioninmelt bottomleft perpendicularcrosssectioninmelt topright crystal Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype ovoid lifted Magneticfieldstrength 3000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case4 Oxygenconcentration m 3 topleft parallelcrosssectioninmelt bottomleft perpendicularcrosssectioninmelt topright crystal Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype ovoidMagneticfieldstrength 3000GGasflow no CzSigrowthunderaTMF cont d FEMAGSoft 2013 Case7 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfieldtype horizontalMagneticfieldstrength 3000GGasflow yes Temperaturefield K topleft parallelcrosssection bottomleft perpendicularcrosssection CzSigrowthunderaTMF cont d FEMAGSoft 2013 Crystaldiameter 400mmPullingrate 0 45mm minCruciblerotationrate 5RPMMagneticfie