Combining traditional modelling, model order reduction and ...
Transcript of Combining traditional modelling, model order reduction and ...
Combiningtraditionalmodelling,modelorderreductionandbigdata
WilSchilders,TUEindhoven(Netherlands)
4TU.AMIsymposium,June8,2018
Aimoftalk
• Sketchaglobalpicture− Relationsbetweenphysical
modeling,modelorderreductionandtheuseofdata
• Startwithaspecificexamplefromtheelectronicsindustry,owingtotheworkthatwasdoneatPhilipsandNXPSemiconductors
• Discusssomemajorchallengesanddevelopments
• Presentthewayforward
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Semiconductordevices
• Semiconductordevicesarethebuildingblocksofallelectronicsproducts
− Resistors,Capacitors,Inductors,Diodes
− Bipolartransistors− MOStransistors(metaloxidesemiconductor)
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SemiconductordevicesimulationatPhilipsResearch• Semiconductordevicesaredescribedbyusing2typesofparticles:electronsandholes(=“absenceofelectron”)
• StartingpointforthemodellingistheBoltzmannTransportEquation(BTE),forbothparticles(“n”referringtoelectrons,“p”toholes):
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The BTE need to be solved, in 6-dimensional phase space, for the density functions f
àvery time consuming…alternative?
Themethodofmoments
• MomentsoftheBTEhaveaphysicalmeaning:thezeroordermomentrelatestotheconcentrationofparticles
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• Thefirstordermomentrelatestothecurrentdensity:
Usingthemethodofmomentsuptoorder1,wearriveatthedrift-diffusionmodel
• Thedrift-diffusionmodelconsistsofthePoissonequationfortheelectricpotential:
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• Plusthecontinuityequationsforholesandelectrons:
• Andconstitutiverelationsforthecurrentdensities:
Usingthemethodofmomentsuptoorder1,wearriveatthedrift-diffusionmodel
• Thedrift-diffusionmodelconsistsofthePoissonequationfortheelectricpotential:
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• Plusthecontinuityequationsforholesandelectrons:
• Andconstitutiverelationsforthecurrentdensities:
D is the doping profile, specific for the device
Usingthemethodofmomentsuptoorder1,wearriveatthedrift-diffusionmodel
• Thedrift-diffusionmodelconsistsofthePoissonequationfortheelectricpotential:
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• Plusthecontinuityequationsforholesandelectrons:
• Andconstitutiverelationsforthecurrentdensities:
The recombination R and the mobilities μare parameters to be determined/given
Modelsformobilityandrecombination
• AtPhilipsResearch,therewasagroupofphysicistsandelectronicengineersworkingconstantlyonnewmodelsformobilityandrecombination
• Alsoatothercompanies,suchgroupsexisted,andtheywerecompetingonaworldwidescale
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Howwerethesemodelsconstructed?
• ThePhilipsgroupperformedmanyexperimentsandmanysimulations
• Thenusedphysical/electronicinsight,curve-fitting,interpolationandothermethodstocomeupwithamodelthat
− Hadincreasedfunctionality− Improvedtheaccuracyofsimulations− Broughtexperimentalresultsandsimulationsclosertogetherintheprocessofon-goingminiaturizationofsemiconductordevices
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Hierarchyofmodelsformobility
• Simpleinitialsimulationsusingconstantmobilities• Modelsdescribinglatticescattering(particlesinteractwiththeatomsinthesemiconductorlattice)
• Ionizedimpurityscattering(interactionswiththeionizedimpuritiesà doping)
• Carrier-carrierscattering(electronsandholeswitheachotherandwiththedifferentspecies)
• Effectsofultra-highconcentration• Velocitysaturation,fielddependence,…
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Similar story for the recombination R
Electroniccircuits
• Semiconductordevicesmaybethebasicbuildingblocks,alevelhigherwefindtheelectroniccircuitsthatconsistofhundreds,thousandsandoftenmillionsofsemiconductordevices
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Electroniccircuitsimulation
• Simulatingthebehaviorofanelectroniccircuitbyusing(coupled)semiconductordevicesimulationforalldevicesinthecircuitisanimpossibletask
• Fortunately,notalldevicesaredifferent,oftenonlyafewtypesoftransistorsareused
• Forthesedevices,so-calledcompactdevicemodelsareconstructed,inawaythatisverysimilartoconstructingmodelsformobilityandrecombination:
− Performmanymeasurementsandsimulations− Usephysical/electronicinsight,discardcertainphenomena
• Bigdifference/complication:− Themodelmustbeparameterized!− ModelslikeMEXTRAMcontain50parameters
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Developmentsinlast15years
• Besidesthetransistormodelsdevelopedinthemajorsemiconductorcompanies,theso-calledBSIMmodelsweredevelopedatBerkeley
• Thesemodelsareconstructedinanautomaticway,byusingalsomanyexperimentalresultsaswellasresultsfromsimulations
• Majorquestions:− cantheworkdonebythespecializedgroupsbereplacedbyautomaticproceduresgeneratingadvancedmobilityandrecombinationmodels,orevencompletedevicemodels?
− Can“insight”beincorporatedinsomeway?
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Robin Bornoff
Delphi4LEDTask 2.5 – Model Calibration
Market Development ManagerMechanical Analysis Division
January, 2018
Restricted © 2017 Mentor Graphics Corporation
Summary of Calibration Studies –Royal Bluen Cost Function a
quantification of the difference between measured and simulated SFs
Your Initials, Presentation Title, Month Year18
Restricted © 2017 Mentor Graphics Corporation
Summary of Calibration Studies –Royal Bluen 100 (Computational) Design of
Experiments set and solved
Your Initials, Presentation Title, Month Year19
Restricted © 2017 Mentor Graphics Corporation
Summary of Calibration Studies –Royal Bluen Global minima
identified from the cost function response surface— Simulated for
verification
Your Initials, Presentation Title, Month Year20
Lessonslearnedintheelectronicsindustry
• Modellingofsemiconductordevicesandelectroniccircuitsisdoneinamixedway:
− Usingphysical/electronicinsight,severaleffectsaredescribedbypartialandordinarydifferentialequations,aswellasbyalgebraicrelationsthatmimicthephysicaleffects
− Manymeasurementsandsimulationsareperformedinordertoproducetablesofvaluesforparametersinthemodels
− Compactdevicemodelsareneededtoperformelectroniccircuitsimulationinanefficientway– thesemodelsarealsoconstructedasacombinationofphysicaleffectsandparameterextraction
• Physicalinsightmustbeusedtoreducethecomplexityofmodels,butdataarenecessarytomakesuchmodelsaccuratedescriptionsofreality
PAGE 21Automatic via MOR?
Theparticularapproachdependsupontheexistingstateofsimulationand/orproxymodelimplementation
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Importanttostart/joinnewinitiatives
• WerecentlygotourMSCAEIDproposalBIGMATHfunded:“BigDataChallengesforMathematics”(4years,7PhDstudents,8academic/industrypartners)
• NWA(NationaleWetenschapsAgenda):callwaspublishedbyNWOonMay24
− 2-stepprocedure,1st proposalinSeptember
• NWOCross-Over:calltobepublishedsoon• WeproposedatopicforFETProactive:“DigitalTwinsforIndustryandInnovation”,outcomeexpectedsoon
− Ifsuccessful,~20Meuroavailableforcallsin2020PAGE 3622 March 2011