Coupled Multiscale Simulation and Optimization in Nanoelectronics PDF
Preview Coupled Multiscale Simulation and Optimization in Nanoelectronics
Mathematics in Industry 21 The European Consortium for Mathematics in Industry Michael Günther E ditor Coupled Multiscale Simulation and Optimization in Nanoelectronics MATHEMATICS IN INDUSTRY 21 Editors Hans-GeorgBock FrankdeHoog AvnerFriedman ArvindGupta AndréNachbin HelmutNeunzert WilliamR.Pulleyblank TorgeirRusten FadilSantosa Anna-KarinTornberg THEEUROPEANCONSORTIUM FORMATHEMATICSININDUSTRY SUBSERIES ManagingEditor VincenzoCapasso Editors LuisL.Bonilla MichaelGünther RobertMattheij HelmutNeunzert OtmarScherzer WilH.A.Schilders Moreinformationaboutthisseriesat http://www.springer.com/series/4650 Michael GuRnther Editor Coupled Multiscale Simulation and Optimization in Nanoelectronics 123 Editor MichaelGuRnther LehrstuhlfuRrAngewandte Mathematik/NumerischeAnalysis BergischeUniversitaRtWuppertal Wuppertal Germany ISSN1612-3956 ISSN2198-3283 (electronic) MathematicsinIndustry ISBN978-3-662-46671-1 ISBN978-3-662-46672-8 (eBook) DOI10.1007/978-3-662-46672-8 LibraryofCongressControlNumber:2015941321 MathematicsSubjectClassificationNumbers(2010):65M20,65L80,68N30,78M34,93A30,97U50 SpringerHeidelbergNewYorkDordrechtLondon ©Springer-VerlagBerlinHeidelberg2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper Springer-VerlagGmbHBerlinHeidelbergispartofSpringerScience+Business Media(www.springer. com) AngeloMarcelloAnile(1948–2007) DedicatedtoAngelo MarcelloAnile, thescientist,colleague,anddear friend. Withouthisenthusiasm,mediativeattitude, andextensiveknowledge, COMSONwould neverhavebeen possible. Preface Circuit design based on numerical simulation relies heavily on mathematical methods. As a result, relations have long since been established between the microelectronics industry and university groups specializing in simulations for semiconductor processes and devices, electromagnetics and electronic circuits. State-of-the-artmethodsfromthefieldsofappliedandnumericalanalysis,aswell as newly developed dedicated algorithms, have facilitated the large-scale use of simulations,therebyenablingtheindustrytoreachitscurrenthighstateoftheart. Designingcomplexintegratedcircuitscallsforadequatesimulationandoptimi- sation tools. The current design approach involves simulations and optimizations in different physical domains (device, circuit, thermal, electromagnetic) and in electrical engineering disciplines (logic, timing, power, crosstalk, signal integrity, system functionality). The physical aspects are essential to characterizing circuit behaviorfromanelectricalengineeringandsystem-orientedstandpoint. Accordingly, the main scientific objectives of the COMSON (COupled Multi- scaleSimulationandOptimizationinNanoelectronics)projectwereasfollows: (cid:129) To develop new descriptive models that take these mutual dependencies into account (cid:129) To combine these models with existing circuit descriptions in new simulation strategies (cid:129) Todevelopnewoptimizationtechniquesthatwillaccommodatenewdesigns COMSON was a Marie Curie Research Training Network supported by the EuropeanCommissionintheprogrammeStructuringtheEuropeanResearchArea, partoftheEU’sSixthFrameworkResearchProgramme.Theprojectwasinitiated by the three major European semiconductor companies – Infineon Technologies AG,laterreplacedbyitsspin-offQimondaAGofNeubiberg,Germany;Koninklijke PhilipsN.V., later replacedby its spin-offNXP SemiconductorsNetherlandsN.V. of Eindhoven, the Netherlands; and STMicroelectronics of Catania, Italy – who worked in cooperation with five European academic partners in Applied Mathe- matics and Electrical Engineering with considerable experience in the simulation and optimization of integrated circuits – the University of Wuppertal, Germany vii viii Preface (coordinator);EindhovenUniversityofTechnology,theNetherlands;Universityof Catania,Italy;UniversityofCalabria,Italy;andUniversityPolitehnicaofBucharest, Romania.Therationalebehindtheprojectandthisbookwasdescribedasfollows: Performing the step from micro- to nanoelectronics, the semiconductor industry is con- fronted with very high levels of integration, introducing coupling effects that were not observedbefore.Currently,thecomplexityofthisproblemisbeyondthecapabilitiesofany industrial software and design environment. Furthermore, in the near future, researchers mustunderstandallaspectsoftheproblemsfacedbyindustry. Tomeetthesenewscientificandtrainingchallenges,theCOMSONprojecton“COupled MultiscaleSimulationandOptimizationinNanoelectronics”mergestheknow-howofthe threemajorEuropeansemiconductorcompanieswiththecombinedexpertiseofuniversity groupsspecializedindevelopingadequatemathematicalmodels,numericalschemes,and e-learning facilities, covering all relevant fields of interest. In COMSON, academia and industry jointheirefforts torealize acommon Demonstrator Platform: ontheone hand, to test mathematical methods and approaches, so as to assess whether they are capable of addressing the industry’s problems; on the other hand, to adequately educate young researchersbyprovidinghands-onexperiencewithstate-of-the-artproblems,andbeyond. The editor thanks his colleagues for their valued contributions in the different chapters of this handbook: Roland Pulch of Greifswald, Germany (PDAE mod- elling);AndreasBartelofWuppertal,Germany,andSebastianSchöpsofDarmstadt, Germany (dynamic iteration); E.J.W. ter Maten of Eindhoven, the Netherlands (MOR);SalvatoreRinaudoofCatania,Italy(optimization);GeorgDenkofMunich, Germany(demonstratorplatform);andGiuseppeAlìofCosenza,Italy(e-learning). Wuppertal,Germany MichaelGünther September2014 Contents PartI Introduction 1 TheCOMSONProject ...................................................... 3 MichaelGüntherandUweFeldmann 1.1 TrendsinMicroelectronics............................................. 3 1.2 ScopeoftheCOMSONProject........................................ 4 1.3 Methodology............................................................ 5 1.3.1 TheDemonstratorPlatform................................... 6 1.3.2 E-Learning..................................................... 9 1.4 Modelling,SimulationandOptimisation .............................. 9 1.4.1 PartialDifferentialAlgebraicEquations ..................... 10 1.4.2 DynamicIteration............................................. 10 1.4.3 ModelOrderReduction....................................... 11 1.4.4 Optimisation................................................... 11 References..................................................................... 12 PartII PartialDifferentialAlgebraicEquations 2 PDAEModelingandDiscretization........................................ 15 GiuseppeAlì,MassimilianoCulpo,RolandPulch, VittorioRomano,andSebastianSchöps 2.1 IntroductiononModelingandPDAEs................................. 15 2.1.1 MathematicalModelinginNanoelectronics................. 16 2.1.2 ClassificationofPDAEModels............................... 18 2.2 Modeling,AnalysisandDiscretizationofCoupledProblems........ 21 2.2.1 RefinedModelingofNetworkswithDevices................ 21 2.2.2 Electro-ThermalEffectsattheSystemLevel................ 45 2.2.3 MultiphysicsModelingviaMaxwell’sEquations ........... 64 2.2.4 ThermalandQuantumEffectsinSemiconductors........... 78 References..................................................................... 99 ix
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