全球半导体晶体生长仿真著名商业软件FEMAG-建模策略

全球半导体晶体生长仿真著名商业软件FEMAG-建模策略FrançoisDupret1,2,RomanRolinsky2,BrieucDelsaute2,RajeshRamaya2,NathalieVandenBogaert21UniversitécatholiquedeLouvain,Louvain-la-Neuve,Belgium2FEMAGSoftS.A.company,Louvain-la-Neuve,BelgiumFEMAGSoft©2013Howtoimprovethegrowthprocessintermsof:-crystalquality?-processyield?-energyconsumption?-productionrate?IntroductionMaindifficulties:FEMAGSoft©2013–Multi-physics:heatandmasstransportinthemeltandthegas,turbulence,radiationtransfer,etc.,allinteractandstronglyaffectspeciesincorporationanddefectformationinthecrystal–Multiplespacescales:sharpdiffusive,viscous,radiativeandthermalboundarylayersarepresentinthemeltandthegas,togetherwithcomplexdefectboundarylayersinthecrystal–Multipletimescales:typicallythegrowthprocessisveryslowwhilethemeltflowisgovernedbymuchshortertimeconstantsIntroduction(cont’d)FEMAGSoft©2013Solvingtheseproblemsrequires…•Toresorttoappropriateandup-to-datenumericalsimulationtechniquestocoupleandsolvethesemodels→quasi-steadyanddynamicmodels•Todevelopasoundphysicalmodelforeachseparateeffect→globalandtime-dependentmodelingofheattransfer,turbulencemodeling,defectmodeling,…Introduction(cont’d)FEMAGSoft©2013•Principalobjectivehasbeentocompletetheplatform•FEMAG-2→FEMAG-3softwaregenerationtransitiontakingplacefrom2008-2009GeneralobjectiveofFEMAGSoft→stronglyimprovedplatformintermsofcomputationtime,memory,etc.Introduction(cont’d)FEMAGSoft©2013•b)Time-dependentmodeling:useofvarioussimulationmodes(ex:quasi-steady,quasi-dynamic,inverseordirectdynamicmodelsinCzgrowth)•c)FEMdiscretization:useof2D,Spectral3D,Cartesian3D,…models(highgeometricalflexibility,simpleassemblingtechnique)•a)Globalmodeling:subdivisionofthefurnaceinto“macro-elements”(solidorliquidconstituents,radiationenclosures,“cement”elements...)•d)Geometricalmodeling:toaccuratelyhandlestronglydeformingbodiesandinterfaceandwell-capturealltheboundarylayers•e)Solutiontechnique:coupledNewton-RaphsoniterationsbyuseofahighlyeffectivelinearsolverIntroduction(cont’d)FEMAGsoftwaredevelopmentstrategy1.NumericalstrategyFEMAGSoft©2013NumericalstrategyFEMAGSoft©2013Quasi-steady–thermalequilibrium–adaptedheaterpowertogettheprescribedcrystaldiameter–heatsourceonthesolidificationfrontinproportiontothepullrateInversedynamic–adaptedheaterpowertogrowtheprescribedcrystalshape–effectofpullrateandsolid-liquidinterfacedeformationonthesolidificationheatDirectdynamic–calculatedcrystalshape–precribedheaterpowerhistory–effectofpullrateandsolid-liquidinterfacedeformationonthesolidificationheatTimedependentQuasi-steadyQuasi-dynamic–frozengeometry(exceptthesolid-liquidinterface)–adaptedheaterpowertogettheprescribedcrystaldiameter–effectofpullrateandsolid-liquidinterfacedeformationonthesolidificationheatDifferentsimulationmodes1.Numericalstrategy(cont’d)GlobaltemperaturefieldStreamfunctionFEMAGSoft©2013psi7.4E-057.1E-056.8E-056.5E-056.2E-055.8E-055.5E-055.2E-054.9E-054.6E-054.3E-054.0E-053.6E-053.3E-053.0E-052.7E-052.4E-052.1E-051.7E-051.4E-051.1E-058.0E-064.8E-061.7E-06-1.5E-06-4.7E-06t18001740168016201560150014401380132012601200114010801020960900840780720660600540480420360300InverseQSandTDsimulationofthegrowthofa300mmsiliconcrystalAnalysisofconicalgrowthandshoulderingstagesm=8.22510-4kg/m.sWc=3.82rpm(0.4s-1)Ws=-3.82rpm(-0.4s-1)Vpul=1.8cm/h(5.10-6m/s)1.Numericalstrategy(cont’d)FEMAGSoft©2013TemperaturefieldStreamfunctionNumericalstrategy(cont’d)FEMAGSoft©2013FEMAG-1time-dependentsimulationofCzochralskiGegrowthInversedynamicsimulation(imposedcrystalshape,calculatedheaterpower):poweroscillationsresultingfrominversemodeling,andsmoothedpowerNumericalstrategy(cont’d)FEMAGSoft©2013Directdynamicsimulation(imposedstepwisedecreaseofheaterpower,calculatedcrystalshape):evolutionofthetemperaturefieldFEMAG-1time-dependentsimulationofCzochralskiGegrowthNumericalstrategy(cont’d)Inversedynamic–oftenmorereliablethanquasi-steadymodel–highlyattractivetopredictcrystalqualityQuasi-steady–frequentlyused–cheap,butnotalwaysvalid–doesnotallowcrystalqualitypredictionDirectdynamic–simulationofthesystemresponsetoperturbationsoftheinputparameters–veryusefulforcontrollerdesignQuasi-dynamic–maycapturethedetailedsystemdynamicsatvariousstages–veryusefulforcontrollerdesignFEMAGSoft©2013DifferentsimulationtechniquesNumericalstrategy(cont’d)TypicalFEMAG-CZglobalunstructuredmeshFEMAGSoft©2013HeatshieldcomponentsNumericalstrategy(cont’d)FEMAG-CZglobalunstructuredmeshdeformationFEMAGSoft©2013Numericalstrategy(cont’d)DetailFEMAGSoft©2013Numericalstrategy(cont’d)YUseofspecialCAGDtechniquesformeniscuscalculationduringtail-endstage:-Secondarymesh(constrainingloci)anddeformedmelt-crystalandmelt-gasinterfaces(right)-Generated1Dand2Dmeshes(left)FEMAGSoft©2013Numericalstrategy(cont’d)SmootheffectofremeshingFEMAGSoft©2013Numericalstrategy(cont’d)t0t1t2t3t4t5t6timet7ConegrowthBodygrowthTail-endstageMeshre-generationMeshdeformationMeshgenerationGeneralgeometricalstrategyFEMAGSoft©2013Numericalstrategy(cont’d)FEMAGSoft©2013TheFEMAG-3platformFEMAG-1FEMAG-2FEMAG-3199020081984Numericalstrategy(cont’d)FEMAGSoft©