femag晶体生长计算软件横向磁场直拉硅晶体生长的全局模拟

FEMAG晶体生长计算软件GlobalSimulationofCzochralskiSiliconGrowthundertheEffectofaTransverseMagneticFieldFEMAGSoft©2013CzSigrowthunderaTMFMHDboundarylayers:HartmannlayersFEMAGSoft©2013TheHartmannlayersdevelopalongthesurfaceswherethenormalcomponentofthemagneticfieldisnon-negligible.AnorderofmagnitudeofthethicknessofaHartmannlayerisdH=LHa-1(L=RsorRc).Typically

dH=0.05-0.08mminindustrialfurnaces.

CzSigrowthunderaTMF(cont’d)Transversemagneticfields:

FLETmethodMethod:Fourierdecompositionofallfields(velocity,pressure,temperature)Hypothesis:Principalissue:whichandhowmanymodes?Objective:global,quasi-steadyortime-dependent calculationsatareasonablecostFEMAGSoft©2013

CzSigrowthunderaTMF(cont’d)FourierLimitedExpansionTechnique(FLET)FEMAGSoft©2013ThefieldvariablesareexpandedasFourierseriesintheazimuthal(q)direction:CzSigrowthunderaTMF(cont’d)FourierLimitedExpansionTechnique(FLET)FEMAGSoft©2013andwhilethenumberofmodesMis

assmallaspossiblewithoutlossofaccuracy(spectralconvergence).whilethedifferentmodecoefficients:are2DFiniteElementfunctionsofthemeridionalcoordinates(r,z)Thisresultsinasystemwhosesizeisthatofthe2DsystemmultipliedbythenumberofFouriermodesconsideredandhenceinadramaticsystemsizereduction.CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013RadiationtransferCouplingbetween3Dand2Daxisymmetricheattransferacrossaradiativeenclosuretheviewedandhiddenpartsarecalculatedasaxisymmetricor,equivalently,eachsurfaceoftheenclosureisviewedasaxisymmetricfromtheothersurfacesMainmodelinghypothesis:generally3Dcomponentsarerotatingwithrespecttothe2Denvironment3Dcomponentsmostlyview2DcomponentsbecauseofthepresenceofheatshieldsThishypothesisissatisfactorybecause:CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013FlowandglobalheattransferinasiliconCzpullerundertheeffectofaTMF(quasi-steadysimulation)CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Top:

topviewofthevelocitymagnitudeandstreamlines.Bottom:

velocityfieldmagnitudeandcross-sectionshowingasharpHartmannlayeralongthemelt-crucibleinterface.Growthofa300mmdiameterSicrystalundertheeffectofa0.5TTMF.

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013InatypicalTMFconfigurationextremelythinHartmannlayers

of50-80mmdevelopGrowthofa300mmdiameterSicrystalundertheeffectofa0.5TTMF.

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)FEMAGSoft©2013GeometryandoperatingconditionsCzSigrowthunderaTMF(cont’d)FEMAGSoft©2013DescriptionofthesimulationsCzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Temperaturefield

(K):topleft:parallelcrosssection;bottomleft:perpendicularcrosssection;topright:topviewCase1CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case1Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Velocityfield

(m.s-1):topleft:parallelcrosssection;bottomleft:perpendicularcrosssectionCzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case1Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Oxygenconcentration

(m-3):topleft:parallelcrosssectioninmelt;bottomleft:perpendicularcrosssectioninmelt;topright:crystal

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case2Crystaldiameter:

300mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Temperaturefield

(K):topleft:parallelcrosssection;bottomleft:perpendicularcrosssection

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Temperaturefield

(K):topleft:parallelcrosssection;bottomleft:perpendicularcrosssectionCase1

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Velocityfield

(m.s-1):topleft:parallelcrosssection;bottomleft:perpendicularcrosssectionCase2Crystaldiameter:

300mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case1Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Velocityfield

(m.s-1):topleft:parallelcrosssection;bottomleft:perpendicularcrosssection

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Oxygenconcentration

(m-3):topleft:parallelcrosssectioninmelt;bottomleft:perpendicularcrosssectioninmelt;topright:crystalCase2Crystaldiameter:

300mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case1Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Oxygenconcentration

(m-3):topleft:parallelcrosssectioninmelt;bottomleft:perpendicularcrosssectioninmelt;topright:crystal

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:5000GGasflow:no

Temperaturefield

(K):topleft:parallelcrosssection;bottomleft:perpendicularcrosssection;topright:topviewCase3

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Temperaturefield

(K):topleft:parallelcrosssection;bottomleft:perpendicularcrosssection;topright:topviewCase1

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Velocityfield

(m.s-1):topleft:parallelcrosssection;bottomleft:perpendicularcrosssectionCase3Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:5000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case1Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Velocityfield

(m.s-1):topleft:parallelcrosssection;bottomleft:perpendicularcrosssection

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Oxygenconcentration

(m-3):topleft:parallelcrosssectioninmelt;bottomleft:perpendicularcrosssectioninmelt;topright:crystalCase3Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:5000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Oxygenconcentration

(m-3):topleft:parallelcrosssectioninmelt;bottomleft:perpendicularcrosssectioninmelt;topright:crystalCase3Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:5000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case1Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Oxygenconcentration

(m-3):topleft:parallelcrosssectioninmelt;bottomleft:perpendicularcrosssectioninmelt;topright:crystalCzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Ovoidmagneticfield:topleft:sketchofthemagneticfield;bottomleft:sideview;right:topviewCase4CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Ovoidmagneticfield:topleft:sketchofthemagneticfield;bottomleft:sideview;right:topviewCase4

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case4Temperaturefield

(K):topleft:parallelcrosssection;bottomleft:perpendicularcrosssection;topright:topviewCrystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:ovoidMagneticfieldstrength:±3000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Temperaturefield

(K):topleft:parallelcrosssection;bottomleft:perpendicularcrosssection;topright:topviewCase1

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Velocityfield

(m.s-1):topleft:parallelcrosssection;bottomleft:perpendicularcrosssectionCase4Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:ovoidMagneticfieldstrength:±3000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case1Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Velocityfield

(m.s-1):topleft:parallelcrosssection;bottomleft:perpendicularcrosssectionCzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case4Oxygenconcentration

(m-3):topleft:parallelcrosssectioninmelt;bottomleft:perpendicularcrosssectioninmelt;topright:crystalCrystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:ovoidMagneticfieldstrength:±3000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case1Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:no

Oxygenconcentration

(m-3):topleft:parallelcrosssectioninmelt;bottomleft:perpendicularcrosssectioninmelt;topright:crystal

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Ovoidmagneticfield(lifted):topleft:sketchofthemagneticfield;bottomleft:sideview;right:topviewCase5

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case5Ovoidmagneticfield(lifted):topleft:sketchofthemagneticfield;bottomleft:sideview;right:topview2.CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case5Temperaturefield

(K):topleft:parallelcrosssection;bottomleft:perpendicularcrosssection;topright:topviewCrystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:ovoid(lifted)Magneticfieldstrength:±3000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case4Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:ovoidMagneticfieldstrength:±3000GGasflow:no

Temperaturefield

(K):topleft:parallelcrosssection;bottomleft:perpendicularcrosssection;topright:topviewCzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case5Velocityfield

(m.s-1):topleft:parallelcrosssection;bottomleft:perpendicularcrosssectionCrystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:ovoid(lifted)Magneticfieldstrength:±3000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Velocityfield

(m.s-1):topleft:parallelcrosssection;bottomleft:perpendicularcrosssectionCase4Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:ovoidMagneticfieldstrength:±3000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case5Oxygenconcentration

(m-3):topleft:parallelcrosssectioninmelt;bottomleft:perpendicularcrosssectioninmelt;topright:crystalCrystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:ovoid(lifted)Magneticfieldstrength:±3000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case4Oxygenconcentration

(m-3):topleft:parallelcrosssectioninmelt;bottomleft:perpendicularcrosssectioninmelt;topright:crystalCrystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:ovoidMagneticfieldstrength:±3000GGasflow:no

CzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Case7Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneticfieldtype:horizontalMagneticfieldstrength:3000GGasflow:yes

Temperaturefield

(K):topleft:parallelcrosssection;bottomleft:perpendicularcrosssectionCzSigrowthunderaTMF(cont’d)FEMAGSoft©2013Crystaldiameter:400mmPullingrate:0.45mm/minCruciblerotationrate:5RPMMagneti