FEMAG块晶体生长数值模拟-如何将直拉法模拟技术拓展到区熔法生长

,FEMAGSoft2013,HowtoextendCzmodelingtechniquestoFZgrowth?,ModelingofFZgrowth,FEMAGSoft2013,Globaltemperaturefield(left),meltflow(right),andalternatingmagneticfield(bottom),Quasi-steadysimulationoftheFloatingZone(FZ)growthofa100mmsiliconcrystal(1mm/minpullrate),ModelingofFZgrowth(contd),Turbulentviscosityislowandthemeltflowcanbecomputedbymeansofalaminarmodel.,FEMAGSoft2013,ModelingofFZgrowth(contd),Inductionheating,FEMAGSoft2013,ModelingofFZgrowth(contd),InductionHeatinginFZsemi-conductorgrowth,FEMAGSoft2013,JcurrentdensityJsourceimposedbyexternalsourceJeddyinducedbytime-dependentmagneticfield,inductor,susceptor,ModelingofFZgrowth(contd),Slottedinductor,TopviewSectionS-S,S,S,Jsource,N:numberofslits,FEMAGSoft2013,ModelingofFZgrowth(contd),Numericalresults,Non-slottedinductor,Slottedinductor,z,r,susceptor,inductor,z,r,susceptor,inductor,FEMAGSoft2013,ModelingofFZgrowth(contd),Realpartofmagneticflux,FEMAGSoft2013,Imaginarypartofmagneticflux,ModelingofFZgrowth(contd),Difficulties,FEMAGSoft2013,melt-atmosphereinterfaceshape(magneticpressure),openmeltingfront(thinfluidfilm),tangentialstressexertedontothemeltfreesurface:-generallyundesiredresultingshearflow-potentiallyusefuleffecttocontroltheflow.,InductionHeatinginFZsemi-conductorgrowth,ModelingofFZgrowth(contd),FEMAGSoft2013,InductionHeatinginFZsemi-conductorgrowth,Bmagneticinductionm0magneticpermeabilityofvacuumselectricconductivitywangularfrequency,Dissipatedpower:Forcedensity:,Heatflux2)Normalstress3)Tangentialstress,Alternatingmagneticfieldeffects:,Inductor,Susceptor,ModelingofFZgrowth(contd),Developmentofamathematicalmodeloftheelectromagneticfielddistributioninplanarandaxisymmetricconfigurations,Hypothesis:lowvalueofthemagneticskindepth,FEMAGSoft2013,Modelbasedonusing:-amatchedasymptoticexpansiontechniquetoapproximatetheelectromagneticfieldinsidetheconductors-aFiniteElementnumericalrepresentationoftheelectromagneticfieldoutsidetheconductors.,ModelingofFZgrowth(contd),Meandissipatedpower:,Meanbodyforcedensity:,Equivalentnormalheatfluxqneq:,Equivalentsurfacestressteq:,FEMAGSoft2006,Equivalentmagneticstressesandheatflux,ModelingofFZgrowth(contd),Flowandtemperaturecalculationsareperformedwitha200mmdiametercrystal.Themeltviscosityissetto5timestheactualsiliconviscositytoobtainsteadyresults.,RePolycrystal=7460ReCrystal=3730Pe=261Gr=2.7x107Ma=6116,FloatingZoneSiliconGrowthSimulation,FEMAGSoft2013,ModelingofFZgrowth(contd),Temperaturefieldandisolinesofthenormofthemagneticfluxfunction.,FEMAG-FZquasi-steadysimulationofthegrowthofa200mmsiliconcrystal,FEMAGSoft2013,ModelingofFZgrowth(contd),Withequivalentmagnetictangentialstress.,Withoutequivalentmagnetictangentialstress.,Temperaturefield(left)andStokesstreamfunction(right)inthemelt,FEMAGSoft2013,6.ModelingofFZgrowth(contd),FEMAG-FZquasi-steadysimulationofthegrowthofa200mmsiliconcrystal,FEMAGSoft2013,(right)Temperaturefieldandisolinesofthenormofthemagneticfluxfunction.(bottom)Streamfunctionisolinesinthemelt,ModelingofFZgrowth(contd),Modelvalidation,FEMAGSoft2013,ModelingofFZgrowth(contd),Crystalradius:51mmFeedrotationrate:15RPMCrystalrotationrate:(a)5RPM,(b)10RPM,(c)15RPMMarangonicoefficient:1.010-4N/mK,(a),(b),(c),Goodcorrespondencebetweenpredictedandexperimentalresults,Effectofcrystalrotationrateonthemeltflow(FZgrowth),FEMAGSoft2013,WiththecourtesyofIKZ,Berlin,ModelingofFZgrowth(contd),FEMAGSoft2013,CalculationofpointdefectsinagrowingFZcrystal,ModelingofFZgrowth(contd),FEMAGSoft2013,Globaltemperaturefield(left),meltflow(right),andalternatingmagneticfield(bottom),Quasi-steadysimulationoftheFloatingZone(FZ)growthofa100mmsiliconcrystal(1mm/minpullrate),ModelingofFZgrowth(contd),FEMAGSoft2013,Growthofa100mmsiliconcrystal(1mm/minpullrate),Predicteddefectdelta-(CI-CV)distributionbymeansofaquasi-steadysimulation,ModelingofFZgrowth(contd),FEMAGSoft2013,Secondexample,ModelingofFZgrowth(contd),FEMAGSoft2013,Rs=5.1cm,Rf=4.7cm,Ws=10rpm,Wf=-15rpmvpul=3.4mm/min,Temperaturefield,ModelingofFZgrowth(contd),FEMAGSoft2013,Rs=5.1cm,Rf=4.7cm,Ws=10rpm,Wf=-15rpmvpul=3.4mm/min,Streamlines,ModelingofFZgrowth(contd),FEMAGSoft2013,Rs=5.1cm,Rf=4.7cm,Ws=10rpm,Wf=-15rpmvpul=3.4mm/min,Differenceofinterstitialandvacancyconcentrations(CI-CV),ModelingofFZgrowth(contd),FEMAGSoft2013,Rs=5.1cm,Rf=4.7cm,Ws=10rpm,Wf=-15rpmvpul=3.4mm/min,Differenceofinterstitialandvacancyconcentrations(CI-CV)(detail),ModelingofFZgrowth(contd),FEMAGSoft2013,vonMisesinvariant:globalviewanddetail,RatioofthevonMisesinvariantovertheCRSS,ModelingofFZgrowth(contd),FEMAGSoft2013,CalculationofthermalstressesinagrowingFZcrystalwithoutconvection,ModelingofFZgrowth(contd),FEMAGSoft2013,Effectofaheatshield:temperaturefield,Noconvection,Rs=5.1cm,Rf=4.7cm,vpul=3.4mm/min,a)Withoutheatshieldb)Withaheatshield,ModelingofFZgrowth(contd),FEMAGSoft2013,Effectofaheatshield:vonMisesstress,a),b),growthorientation,ModelingofFZgrowth(contd),FEMAGSoft2013,a),b),growthorientation,Effectofaheatshield:vonMisesstress,ModelingofFZgrowth(contd),TypicalFEMAG-FZglobalunstructuredmeshforheattransferandinductionheating,FEMAGSoft2013,ModelingofFZgrowth(contd),FEMAGSoft2013,FEMAG-FZtime-dependentsimulationofthegrowthofasiliconcrystalUseofanequivalentthermalconductivity,ModelingofFZgrowth(contd),Freeinterfaceconstrainingloci(secondarymesh)inFZgrowth,FEMAGSoft2013,ModelingofFZgrowth(contd),FEMAGSoft2013,InversemodelinginFZgrowthmuchmoredifficultproblemthaninCzgrowthcanleadtomisleadinginterpretationsofthesimulationresultssincecompletelyinversemodelsresultinthecalculationofthemeltvolumeandhenceparametricstudiesaredifficulttointerpretwithclassicalsimplifiedmodels,theopenmeltingfront(OMF)isimposedandthemeltingfrontiseitherimposedorcalculated(asanisotherm),ModelingofFZgrowth(contd),FEMAGSoft2013,OpenMeltingFrontafterextractionofthesinglecrystal,ModelingofFZgrowth(contd),FEMAGSoft2013,Mainissue:modelingoftheOpenMeltingFront(OMF),Physicalproblem:theflowofthemoltensiliconalongtheOMFandtheangleatwhichthemelt-gasinterfacedetachesfromtheOMFrequireaccuratemodelinginviewoftheirdirectimpactontheradiationtransfertotheOMFandonthemelt-gasinterfaceshape,Numericalproblem:thecoupledsolutionofaproblemwith4interfaces(solidificationfront,meltingfront,melt-gasinterface,andOMF)and3tri-junctionsrepresentsadifficultproblemofcomputationalgeometry.,ModelingofFZgrowth(contd),FEMAGSoft2013,Otherkeyissues:,Speciestransport(dopantandimpurities):theproblemissimilartospeciestransportinCzgrowth,butmuchmoredifficultsincealmostnoturbulentmixingispresentinFZgrowth,Oscillationsofthecrystaland/orfeed-rodrotationrates:thistechniqueisoftenusedtobettermixthemeltandcanbesimulatedbyuseofaquasi-dynamicmodel,3Deffects:non-axisymmetriceffectsaregenerated(i)bytheinductorshapeandpossibly(ii)bytheuseofnon-alignedcrystalandfeed-rodrotationaxes,ModelingofFZgrowth(contd),FEMAGSoft2013,InvestigationofACRTtechnique,ModelingofFZgrowth(contd),InvestigationofACRTtechnique,FEMAGSoft2013,ModelingofFZgrowth(contd),FEMAGSoft2013,Quasi-steadysimulation:globaltemperaturefield,Quasi-steadysimulation:localtemperaturefield,ModelingofFZgrowth(contd),FEMAGSoft2013,Quasi-steadysimulation:globaltemperaturefield,Quasi-steadysimulation:localtemperaturefieldandmeridionalvelocityvectors,ModelingofFZgrowth(contd),FEMAGSoft2013,Quasi-dynamicsimulations,Temperaturefieldandmeridionalvelocity,ModelingofFZgrowth(contd),FEMAGSoft2013,Quasi-dynamicsimulations,Azimuthalvelocity,ModelingofFZgrowth(contd),FEMAGSoft2013,Topright:temperaturefieldandmeridionalvelocityBottomleft:azimuthalvelocity,Quasi-dynamicsimulations,ModelingofFZgrowth(contd),FEMAGSoft2013,Definitionofanaverageflowforspeciestransportinversesimulation,Averageflow:quasi-dynamicresultsarefurthertime-averagedinordertoprovidemeanvelocity,viscosity,andheatandspeciesdiffusivityfields,Inversesimulations:time-averagedfieldsareusedinquasi-steadyorinversedynamicsimulationsinordertopredictspeciestransportinthemeltandincorporationintothecrystal,Ultimategoal:topredicttheresistivitydistributioninthecrystal.,ModelingofFZgrowth(contd),FEMAGSoft2013,Quasi-steadyandquasi-dynamic“ACRT”simulation:localtemperaturefieldandaveragemeridionalvelocityvectors,Quasi-steadysimulation:localtemperaturefielda