combining traditional modelling, model order reduction and
TRANSCRIPT
Combiningtraditionalmodelling,modelorderreductionandbigdata
WilSchilders,TUEindhoven(Netherlands)
4TU.AMIsymposium,June8,2018
Aimoftalk
• Sketchaglobalpicture− Relationsbetweenphysical
modeling,modelorderreductionandtheuseofdata
• Startwithaspecificexamplefromtheelectronicsindustry,owingtotheworkthatwasdoneatPhilipsandNXPSemiconductors
• Discusssomemajorchallengesanddevelopments
• Presentthewayforward
PAGE 2
GOINGBACKINTIME30YEARS
PAGE 3
Semiconductordevices
• Semiconductordevicesarethebuildingblocksofallelectronicsproducts
− Resistors,Capacitors,Inductors,Diodes
− Bipolartransistors− MOStransistors(metaloxidesemiconductor)
PAGE 4
SemiconductordevicesimulationatPhilipsResearch• Semiconductordevicesaredescribedbyusing2typesofparticles:electronsandholes(=“absenceofelectron”)
• StartingpointforthemodellingistheBoltzmannTransportEquation(BTE),forbothparticles(“n”referringtoelectrons,“p”toholes):
PAGE 5
The BTE need to be solved, in 6-dimensional phase space, for the density functions f
àvery time consuming…alternative?
Themethodofmoments
• MomentsoftheBTEhaveaphysicalmeaning:thezeroordermomentrelatestotheconcentrationofparticles
PAGE 6
• Thefirstordermomentrelatestothecurrentdensity:
Usingthemethodofmomentsuptoorder1,wearriveatthedrift-diffusionmodel
• Thedrift-diffusionmodelconsistsofthePoissonequationfortheelectricpotential:
PAGE 7
• Plusthecontinuityequationsforholesandelectrons:
• Andconstitutiverelationsforthecurrentdensities:
Usingthemethodofmomentsuptoorder1,wearriveatthedrift-diffusionmodel
• Thedrift-diffusionmodelconsistsofthePoissonequationfortheelectricpotential:
PAGE 8
• Plusthecontinuityequationsforholesandelectrons:
• Andconstitutiverelationsforthecurrentdensities:
D is the doping profile, specific for the device
Usingthemethodofmomentsuptoorder1,wearriveatthedrift-diffusionmodel
• Thedrift-diffusionmodelconsistsofthePoissonequationfortheelectricpotential:
PAGE 9
• Plusthecontinuityequationsforholesandelectrons:
• Andconstitutiverelationsforthecurrentdensities:
The recombination R and the mobilities μare parameters to be determined/given
Modelsformobilityandrecombination
• AtPhilipsResearch,therewasagroupofphysicistsandelectronicengineersworkingconstantlyonnewmodelsformobilityandrecombination
• Alsoatothercompanies,suchgroupsexisted,andtheywerecompetingonaworldwidescale
PAGE 10
Howwerethesemodelsconstructed?
• ThePhilipsgroupperformedmanyexperimentsandmanysimulations
• Thenusedphysical/electronicinsight,curve-fitting,interpolationandothermethodstocomeupwithamodelthat
− Hadincreasedfunctionality− Improvedtheaccuracyofsimulations− Broughtexperimentalresultsandsimulationsclosertogetherintheprocessofon-goingminiaturizationofsemiconductordevices
PAGE 11
Hierarchyofmodelsformobility
• Simpleinitialsimulationsusingconstantmobilities• Modelsdescribinglatticescattering(particlesinteractwiththeatomsinthesemiconductorlattice)
• Ionizedimpurityscattering(interactionswiththeionizedimpuritiesà doping)
• Carrier-carrierscattering(electronsandholeswitheachotherandwiththedifferentspecies)
• Effectsofultra-highconcentration• Velocitysaturation,fielddependence,…
PAGE 12
Similar story for the recombination R
Electroniccircuits
• Semiconductordevicesmaybethebasicbuildingblocks,alevelhigherwefindtheelectroniccircuitsthatconsistofhundreds,thousandsandoftenmillionsofsemiconductordevices
PAGE 13
Electroniccircuitsimulation
• Simulatingthebehaviorofanelectroniccircuitbyusing(coupled)semiconductordevicesimulationforalldevicesinthecircuitisanimpossibletask
• Fortunately,notalldevicesaredifferent,oftenonlyafewtypesoftransistorsareused
• Forthesedevices,so-calledcompactdevicemodelsareconstructed,inawaythatisverysimilartoconstructingmodelsformobilityandrecombination:
− Performmanymeasurementsandsimulations− Usephysical/electronicinsight,discardcertainphenomena
• Bigdifference/complication:− Themodelmustbeparameterized!− ModelslikeMEXTRAMcontain50parameters
PAGE 14
PAGE 1522 March 2011
Developmentsinlast15years
• Besidesthetransistormodelsdevelopedinthemajorsemiconductorcompanies,theso-calledBSIMmodelsweredevelopedatBerkeley
• Thesemodelsareconstructedinanautomaticway,byusingalsomanyexperimentalresultsaswellasresultsfromsimulations
• Majorquestions:− cantheworkdonebythespecializedgroupsbereplacedbyautomaticproceduresgeneratingadvancedmobilityandrecombinationmodels,orevencompletedevicemodels?
− Can“insight”beincorporatedinsomeway?
PAGE 16
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?
RECENTDEVELOPMENTS
PAGE 22
PAGE 23January 2010
PAGE 24January 2010
Product Lifecycle Management
PAGE 25January 2010
PAGE 26January 2010
PAGE 27January 2010
PAGE 28January 2010
PAGE 29January 2010
PAGE 30January 2010
PAGE 31January 2010
PAGE 32January 2010
PAGE 33January 2010
CONCLUSION
PAGE 34
Theparticularapproachdependsupontheexistingstateofsimulationand/orproxymodelimplementation
PAGE 35January 2010
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