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Quantitative Modeling of Total Ionizing Dose Reliability Effects in Device SiO2 Layers

Permanent Link: http://ufdc.ufl.edu/UFE0044042/00001

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Title: Quantitative Modeling of Total Ionizing Dose Reliability Effects in Device SiO2 Layers
Physical Description: 1 online resource (2 p.)
Language: english
Creator: Rowsey, Nicole L
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: charge -- defect -- dose -- eldrs -- enhanced -- fixed -- floods -- flooxs -- glpnp -- interface -- ionizing -- low -- mediated -- nit -- not -- oxide -- rate -- sensitivity -- simulation -- tcad -- tid -- total -- transport -- traps
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The electrical breakdown of oxides and oxide/semiconductor interfaces is one of the main reasons for device failure in integrated circuits, especially devices under high-stress conditions. One high-stress environment of interest is the space environment. All electronics are vulnerable to ionizing radiation; any high-energy particle that passes through an insulating layer will deposit unwanted charge there, causing shifts in device characteristics. Designing electronics for use in space can be a challenge, because much more energetic radiation exits in space than on Earth, as there is no atmosphere in space to collide with, and thereby reduce the energy of, energetic particles. Although oxide charging due to ionizing radiation creates well-known changes in device characteristics, or total ionizing dose effects, it is still poorly-understood exactly how these changes come about. There are many theories that draw upon a large body of both experimental work and, more recently, quantum-mechanical first principles calculations at the molecular level. This work uses FLOODS, a 3D object-oriented device simulator with multi-physics capability, to investigate these theories, by simulating oxide degradation in realistic device geometries, and comparing the subsequent degradation in device characteristics to experimental measurements. The charge trapping and defect-modulated transport models developed and implemented here have resulted in the first quantitative account of the enhanced low-dose-rate sensitivity effect, and are applicable in a comprehensive range of hydrogen environments. Measurements show that devices exposed to ionizing radiation at high dose rates exhibit less degradation that those exposed at low dose rates. Furthermore, the observed trend differs depending on the amount of hydrogen available before, during, and after irradiation. It is therefore important to understand and take into account the effects of dose rate and hydrogen when developing accelerated testing procedures for devices which have been exposed to various levels of hydrogen during processing and packaging, and which must be deployed in the low-dose-rate space environment. Thus, this work represents a substantial increase in the state-of-the-art, since a quantitative model has not previously been available. The success of the model is due in great part to the use of first-principles calculations of defect and hydrogen bond energies. Vanderbilt collaborators provided the results of these calculations as input to the FLOODS simulations. Using these physical insights, a sensitivity analysis in FLOODS yielded insights into key controlling parameters.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Nicole L Rowsey.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Law, Mark E.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044042:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044042/00001

Material Information

Title: Quantitative Modeling of Total Ionizing Dose Reliability Effects in Device SiO2 Layers
Physical Description: 1 online resource (2 p.)
Language: english
Creator: Rowsey, Nicole L
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: charge -- defect -- dose -- eldrs -- enhanced -- fixed -- floods -- flooxs -- glpnp -- interface -- ionizing -- low -- mediated -- nit -- not -- oxide -- rate -- sensitivity -- simulation -- tcad -- tid -- total -- transport -- traps
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The electrical breakdown of oxides and oxide/semiconductor interfaces is one of the main reasons for device failure in integrated circuits, especially devices under high-stress conditions. One high-stress environment of interest is the space environment. All electronics are vulnerable to ionizing radiation; any high-energy particle that passes through an insulating layer will deposit unwanted charge there, causing shifts in device characteristics. Designing electronics for use in space can be a challenge, because much more energetic radiation exits in space than on Earth, as there is no atmosphere in space to collide with, and thereby reduce the energy of, energetic particles. Although oxide charging due to ionizing radiation creates well-known changes in device characteristics, or total ionizing dose effects, it is still poorly-understood exactly how these changes come about. There are many theories that draw upon a large body of both experimental work and, more recently, quantum-mechanical first principles calculations at the molecular level. This work uses FLOODS, a 3D object-oriented device simulator with multi-physics capability, to investigate these theories, by simulating oxide degradation in realistic device geometries, and comparing the subsequent degradation in device characteristics to experimental measurements. The charge trapping and defect-modulated transport models developed and implemented here have resulted in the first quantitative account of the enhanced low-dose-rate sensitivity effect, and are applicable in a comprehensive range of hydrogen environments. Measurements show that devices exposed to ionizing radiation at high dose rates exhibit less degradation that those exposed at low dose rates. Furthermore, the observed trend differs depending on the amount of hydrogen available before, during, and after irradiation. It is therefore important to understand and take into account the effects of dose rate and hydrogen when developing accelerated testing procedures for devices which have been exposed to various levels of hydrogen during processing and packaging, and which must be deployed in the low-dose-rate space environment. Thus, this work represents a substantial increase in the state-of-the-art, since a quantitative model has not previously been available. The success of the model is due in great part to the use of first-principles calculations of defect and hydrogen bond energies. Vanderbilt collaborators provided the results of these calculations as input to the FLOODS simulations. Using these physical insights, a sensitivity analysis in FLOODS yielded insights into key controlling parameters.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Nicole L Rowsey.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Law, Mark E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044042:00001


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QUANTITATIVEMODELINGOFTOTALIONIZINGDOSERELIABILITYEFFECTSINDEVICESIO2LAYERSByNICOLEL.ROWSEYADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSPHYUNIVERSITYOFFLORIDA2012

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c2012NicoleL.Rowsey 2

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ACKNOWLEDGMENTS Thankstomyadvisor,ProfessorMarkLawforhisguidanceandtomycomitteemembers,ProfessorsNishida,Fossum,andGilaforhelpingmecompletethiswork.ThankstotheISDEgroupatVanderbilt,especiallyProfessorsSchrimpf,Fleetwood,andPantelides.AlsothankstoProfessorBlairTuttleatU.Penn.ErieforDFTcalculationsandinsightsintothenestructureofSiO2.ThankstoSRC,MURI,andAFOSRforfundingmeandthiswork,andthankstomycolleaguesinlabfordiscussionandfriendship:SaurabhMorarka,DanCummings,DavidHorton,AshishKumar,BenGilstad,ErinPatrick,SrivatsanParthasarathy,AndyKoeler,AmitGupta,MinChu,OnurBaykan,andTonyAcosta. 3

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 3 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 11 CHAPTER 1TIDEFFECTSOVERVIEWANDMOTIVATIONFORPROPOSEDWORK ... 13 1.1Motivation:DesigningfortheSpaceEnvironment .............. 15 1.1.1CharacterizingRadiationforSpacecraftDesignandTIDStudies 16 1.1.1.1Neartheearth:trappedradiation .............. 17 1.1.1.2Otherradiationsources ................... 19 1.1.2On-OrbitAnomaliesduetoTID .................... 20 1.1.2.1Telstarexample ....................... 21 1.1.2.2HIPPARCOSexample .................... 21 1.1.2.3Galileoprobeexample .................... 21 1.2Motivation:UnderstandingTIDRadiationEffectsinDevices ........ 22 1.2.1IonizingRadiationinSiO2 ....................... 22 1.2.1.160Co-raysinduceComptonscatteringinSiO2-on-Sistructures ........................... 24 1.2.1.2Equivalencyof60Co-raysandhighenergyelectronsources ............................ 24 1.2.1.3ConductionbandEHPgenerationandrecombination .. 25 1.2.2TIDEffectsinCMOS .......................... 26 1.2.3TIDEffectsinBipolarDevices ..................... 28 1.2.4ELDRSinTesting,Prediction,andHardnessAssurance ...... 34 1.3ChapterSummary ............................... 37 2UNDERSTANDINGANDMODELINGA-SIO2PHYSICS ............. 39 2.1OxygenVacancyComplexesinSiO2 ..................... 39 2.2ChargeTrappingandHydrogenReactionsinThermalSiO2 ........ 43 2.3ExistingDeviceDegradationModels ..................... 46 2.3.1RecombinationMechanisms ...................... 47 2.3.2TheImportanceoftheCrackingReaction .............. 48 2.3.3Pre-ExistingDefectDensityandLocation .............. 50 2.4ChapterSummary ............................... 52 4

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3FLOODSIMPLEMENTATION ............................ 53 3.1PhysicalStructure ............................... 53 3.2BulkPhysics .................................. 54 3.2.1Drift-DiffusionModeling ........................ 55 3.2.1.1Bulksilicon .......................... 55 3.2.1.2BulkSiO2 ........................... 57 3.2.1.3FLOODSscriptingandautomation ............. 59 3.2.2RadiationModel ............................ 61 3.2.3RecombinationandGenerationDuetoChargeTrapping ...... 63 3.2.3.1RGterms ........................... 64 3.2.3.2Formulationofthereactionrates .............. 65 3.3BoundaryConditions .............................. 67 3.3.1ElectronandHoleTransportfromSiO2toSiandAl ......... 67 3.3.2InterfaceTrapReaction ......................... 69 3.4InitialConditions ................................ 70 3.4.1GeneralAssumedQuantities ..................... 70 3.4.2Oxygen-PoorInterfaceTransitionRegion ............... 70 3.5Solving ..................................... 72 3.5.1PreliminaryPoisson-OnlySolution .................. 73 3.5.2DCandTransientCalculations .................... 74 3.6SensitivityAnalysisMethod .......................... 75 4INTERFACETRAPGENERATION:H2ANDELDRSEFFECTS ......... 77 4.1BackgroundInformation ............................ 77 4.2ModelingSummary .............................. 78 4.2.1Drift-DiffusionModeling ........................ 78 4.2.2TrappingSpeciesandReactions ................... 81 4.3SimulationResults ............................... 83 4.3.1IndividualContributionsofEachTrapSpecies ............ 86 4.3.2DefectConcentration .......................... 89 4.3.3DefectLocation ............................. 91 4.3.4SensitivityAnalysis ........................... 93 4.3.4.1H2trend ............................ 95 4.3.4.2ELDRStrend ......................... 96 4.3.4.3Holecaptureandrelease .................. 97 4.3.4.4Directprotonrelease .................... 99 4.3.4.5Electronrecombination ................... 100 4.3.4.6ParameterfortheELDRStransitionregion ........ 100 4.4ChapterSummary ............................... 100 5RADIATIONINDUCEDOXIDECHARGEBUILDUP ............... 102 5.1BackgroundInformation ............................ 102 5.2ModelingSummary .............................. 104 5

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5.3OxideChargeBuildup ............................. 106 5.3.1FixedOxideChargeTypes ....................... 107 5.3.2InterfaceTrapRateandProtonConcentration ............ 112 5.4ChapterSummary ............................... 116 6SEPARATINGTIMEDEPENDENTANDTRUEDOSERATEEFFECTS .... 117 6.1BackgroundInformation ............................ 117 6.2ModelingSummary .............................. 118 6.3HydrogenDimerizationandElectronRecombination ............ 121 6.4TDEandTDREEffects ............................ 127 6.5ChapterSummary ............................... 131 7CONCLUSIONSANDFUTUREWORK ...................... 132 7.1Conclusions ................................... 132 7.2FutureWork ................................... 133 7.2.1LocalElectricFieldDependencies .................. 134 7.2.1.1Initialrecombinationandyield ............... 134 7.2.1.2Simulationsundernon-zerobiasingconditions ...... 135 7.2.2Application:STIOxidesinModernCMOS .............. 136 7.3FinalSummary ................................. 138 APPENDIX:SENSITIVITYANALYSISRESULTSSUMMARY ............. 139 LISTOFREFERENCES .................................. 141 BIOGRAPHICALSKETCH ................................ 150 6

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LISTOFTABLES Table page 3-1Diffusivity ....................................... 61 3-2Mobility ........................................ 61 3-3Radiationparameters ................................ 63 3-4Reactionenergiesandresultantkvalues ..................... 68 3-5Numericaleffectofasampleofenergies ...................... 68 3-6Criticallength ..................................... 68 3-7Attempttoescapefrequency ............................ 69 3-8Initialconditions:well-knownICs .......................... 71 3-9Initialconditions:bulkpre-existingdefectconcentrations ............. 71 A-1ResultsofSensitivityAnalysis ............................ 140 7

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LISTOFFIGURES Figure page 1-1Illustrationofionizingdose. ............................. 14 1-2CalculationofenergeticelectronssurroundingEarth. ............... 18 1-3SatellitedataofenergeticelectronssurroundingEarth. ............. 18 1-4Thesolarirradiancespectrum. ........................... 19 1-5Photon-matterinteractiontypes. .......................... 23 1-6Holeyieldsfromtworadiationsourcesandgeminatecalculation ........ 25 1-7Illustrationofoxidetrappedcharge. ......................... 27 1-8Illustrationofinterfacetrapcharge. ......................... 27 1-9Effectofinterfacetrapsonbipolarbasecurrent. .................. 29 1-10GLPNPteststructure. ................................ 30 1-11BasecurrentofGLPNPduringagatesweep. ................... 31 1-12Time-dependentandtruedoserateeffectsdata. ................. 33 1-13NitandNotmeasurementsvs.H2concentration. ................. 35 1-14Nitmeasurementsvs.doserate(ELDRScurves). ................ 36 1-15Totaldose,doserate,andH2measurementsshowingTDEsandTDREs. ... 37 2-1Banddiagramindicatingholeinteractionwithshallowanddeeptraps. ..... 41 2-2DFTrepresentationofVo. ............................. 41 2-3DFTrepresentationofVo. ............................. 42 2-4Qualitativetrap-assistedelectronrecombinationmodelforELDRS. ....... 47 2-5ELDRSdataindifferentH2ambients. ....................... 48 2-6Qualitative,hand-calculateddirectelectronrecombinationmodelforELDRS. 49 2-7QualitativeTCADmodelcalculationsforELDRS,withoutDFTcalculations. .. 50 2-8LimitedTCADmodelwithuncontrolledttingparameters. ............ 51 3-12DrepresentationoftheGLPNPteststructure. .................. 54 3-2Energydiagramforchargetrappinganddetrapping. ............... 66 8

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3-3Oxygen/siliconrationeartheinterface. ....................... 72 4-1DFTrepresentationofVo. ............................. 80 4-2DFTrepresentationofVo. ............................. 80 4-3FLOODSquantitativematchforNitvs.H2atHDR. ................ 83 4-4FLOODSquantitativematchtoELDRSdataindifferentH2ambients. ...... 84 4-5SimulationsdecouplingthetwodominantH2mechanisms. ........... 85 4-6Simulationsdecouplingthetwodominantdoseratemechanisms. ........ 87 4-7FLOODSresultsshowingextremeH2sensitivityatLDR. ............. 88 4-8FLOODSresultsshowingsensitivityofinitialdefectconcentrations. ....... 90 4-9FLOODSresultsshowingthesensitivityofinitialdefectlocationathighH2. .. 92 4-10FLOODSresultsshowingthesensitivityofinitialdefectlocationatlowH2. ... 93 4-11SensitivityoftheH2crackingbarrier. ........................ 95 4-12Sensitivityanalysisofshallowtrapdepth,lowH2. ................. 98 4-13Sensitivityanalysisofshallowtrapdepth,highH2. ................ 99 5-1SimultaneousquantitativematchtoNitandNot. .................. 105 5-2Simulatedoxidechargedensity,brokendownbytype. .............. 107 5-3Calculatedprotonconcentrationneartheinterfaceforintermediatekint. .... 111 5-4Protonconcentrationneartheinterfaceforhighkint. ............... 113 6-1FLOODSquantitativematchtoELDRStrendsindifferentH2ambients. .... 119 6-2FLOODSbreakdownofprotoncreationmechanisms. .............. 120 6-3EffectofinterfacereactionrateonELDRS. .................... 123 6-4Protonconcentrationvs.oxidedepth. ....................... 124 6-5CalculatedELDRStrendassuminguniforminitialdefectdistribution. ...... 125 6-6Electron,V+o,andVoH+2concentrationvs.oxidedepth. ............. 127 6-7FLOODSquantitativematchtoexpandeddoseratedataset. .......... 128 6-8ChangeinELDRStrendovertimefor100%H2case. .............. 129 6-9ChangeinELDRStrendovertimeforaircase. .................. 130 9

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7-1ModernCMOScross-section. ............................ 136 7-2Worst-caseCVresponseforirradiatedSTIregion. ................ 137 10

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosphyQUANTITATIVEMODELINGOFTOTALIONIZINGDOSERELIABILITYEFFECTSINDEVICESIO2LAYERSByNicoleL.RowseyMay2012Chair:MarkE.LawMajor:ElectricalEngineeringTheelectricalbreakdownofoxidesandoxide/semiconductorinterfacesisoneofthemainreasonsfordevicefailureinintegratedcircuits,especiallydevicesunderhigh-stressconditions.Onehigh-stressenvironmentofinterestisthespaceenvironment.Allelectronicsarevulnerabletoionizingradiation;anyhigh-energyparticlethatpassesthroughaninsulatinglayerwilldepositunwantedchargethere,causingshiftsindevicecharacteristics.Designingelectronicsforuseinspacecanbeachallenge,becausemuchmoreenergeticradiationexitsinspacethanonEarth,asthereisnoatmosphereinspacetocollidewith,andtherebyreducetheenergyof,energeticparticles.Althoughoxidechargingduetoionizingradiationcreateswell-knownchangesindevicecharacteristics,ortotalionizingdoseeffects,itisstillpoorly-understoodexactlyhowthesechangescomeabout.Therearemanytheoriesthatdrawuponalargebodyofbothexperimentalworkand,morerecently,quantum-mechanicalrstprinciplescalculationsatthemolecularlevel.ThisworkusesFLOODS,a3Dobject-orienteddevicesimulatorwithmulti-physicscapability,toinvestigatethesetheories,bysimulatingoxidedegradationinrealisticdevicegeometries,andcomparingthesubsequentdegradationindevicecharacteristicstoexperimentalmeasurements.Thechargetrappinganddefect-modulatedtransportmodelsdevelopedandimplementedherehaveresultedintherstquantitativeaccountoftheenhanced 11

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low-dose-ratesensitivityeffect,andareapplicableinacomprehensiverangeofhydrogenenvironments.Measurementsshowthatdevicesexposedtoionizingradiationathighdoseratesexhibitlessdegradationthatthoseexposedatlowdoserates.Furthermore,theobservedtrenddiffersdependingontheamountofhydrogenavailablebefore,during,andafterirradiation.Itisthereforeimportanttounderstandandtakeintoaccounttheeffectsofdoserateandhydrogenwhendevelopingacceleratedtestingproceduresfordeviceswhichhavebeenexposedtovariouslevelsofhydrogenduringprocessingandpackaging,andwhichmustbedeployedinthelow-dose-ratespaceenvironment.Thus,thisworkrepresentsasubstantialincreaseinthestate-of-the-art,sinceaquantitativemodelhasnotpreviouslybeenavailable.Thesuccessofthemodelisdueingreatparttotheuseofrst-principlescalculationsofdefectandhydrogenbondenergies.VanderbiltcollaboratorsprovidedtheresultsofthesecalculationsasinputtotheFLOODSsimulations.Usingthesephysicalinsights,asensitivityanalysisinFLOODSyieldedinsightsintokeycontrollingparameters. 12

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CHAPTER1TIDEFFECTSOVERVIEWANDMOTIVATIONFORPROPOSEDWORKIonizingradiationgenerateschargeinmaterials,includingtheisolationlayersusedinsemiconductorelectronicdevices.Eventhehighestqualityoxidesusedintheintegratedcircuit(IC)industryarenotperfect,containingirregularitiesintheirmolecularstructure,andforeignchemicalspecies.Materialinterfacesareregionsofespeciallyhighdefectdensities,evenforSiO2-on-Sisystems,whereSiO2isanativeoxideandwell-matchedtoSi.Bulkoxideandinterfacedefectscanactaschargetrappingsites,someofwhichtrapchargeforlongtimes,ontheorderofyears.Thestudyofthisbuildupofchargeindeviceoxidelayersandthechanges,oftendegradation,indeviceandcircuitcharacteristicsthatresultisknownastotalionizingdose(TID)effects.TIDeffectsareconsideredseparatelyfromsingleeventeffects,whichincontrastdescribetransientchargegenerationanddissipationonmuchshortertimescales,andgenerallyonlyinSi.Fig. 1-1 summarizestheconceptofTIDinanSiO2-on-Sistructure.Oncechargeisdepositedinanoxide,varioussubsequentphysicalmechanismscanoccur,dependingonthelocalenvironmentoftheoxide.Forexample,temperature,electriceld,ambienthydrogenconcentration,depositionorgrowthtemperatureandmethod,andpackagingmethodallplayaroleinwhathappenstothegeneratedcharge,andthusthenalstateofindividualtransistorsandwholecircuits.Empiricalornon-physicalmodelscanbeusedtounderstandindividualmechanismsinspecicdevices,circuitsandcircumstances,butaretypicallyonlyapplicableinthekindofenvironmenttowhichtheyhavebeentted.However,ICdeploymentenvironmentsandmissioncriteriavarywidely.Forexample,on-Earthserverfarms,Earth-orbitingcommercialcommunicationssatellites,militarycommunicationsatellites,andMarsroverswillallcontainICswhichwillbeaffectedbyTIDradiation,buteachofthesemissionswillbeexposedtoaverydifferentenvironmentandwillhaveverydifferentoperationaltimeframes,performance 13

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requirements,andbudgets.Becausesomanyphysicalmechanismscontroldevicedegradationduringthesemissions,havingornothavinganaccurateunderstandingofwhatisgoingoninsidetheonboardelectronicdevicescanhaveimplicationsfortesting,prediction,andhardnessassuranceofICs. Figure1-1. AnillustrationsummarizingionizingdoseinSiO2-on-Sistructures.Energeticparticles,forexampleelectrons,protons,orotherparticles,ionizeSiO2,creatingchargewhichmaybetrappedforlongtimes.TIDeffectsareconsideredseparatelyfromsingleeventeffects,whichincontrastdescribetransientchargegenerationanddissipationonmuchshortertimescales,andgenerallyonlyinSi. ThegoalofthisworkistoincreasetheunderstandingofthebasicchargetransportandtrappingmechanismsindeviceSiO2layersusedinspaceapplications.WewillbeconcernedmainlywiththeenergeticelectronsthatsurroundtheEarthandotherplanets,andthroughwhichpracticalorbitsmustpass.Section 1.1 ofthischapterprovidesanoverviewofthespaceenvironment,concentratingontheelectronstrappedinplanetaryradiationbelts.Section 1.2 ofthischapterprovidesanoverviewofthebasicTIDeffectsinMOSandbipolardevices,aswellasanintroductiontothecombinedMOSandbipolarteststructureofinteresttothiswork.Chapter 2 givesanoverviewofexperimentalandtheoreticalinvestigationsintothenestructureofSiO2,and,basedonthemostcurrentunderstanding,developsamodelofdefectinteractionandchargetransportthatcanquantitativelyaccountfortheoxidecharge(Not)andinterfacetrap(Nit)buildupobserved 14

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inbipolardevices.Chapter 3 describeshowthismodelisimplementedinFLOODS,a3Dobject-orienteddevicesimulatorwithmulti-physicscapability.Chapters 4 6 showthequantitativeresultsachievedbythemodel,anddiscusstheinsightsgainedfromthemodelingeffort.Finally,Chapter 7 concludes,summarizingthemaincontributionsofthiswork,anddiscussingtheimplicationsforcurrenttestingcriteriaforTIDeffects. 1.1Motivation:DesigningfortheSpaceEnvironmentAsofDecember9,2011,CelesTrak,asatellite-trackingwebsitemaintainedbyAnalyticalGraphics,Inc.,reported1,099activeman-madesatellitesorbitingtheEarth,including389ownedbytheUnitedStates[ 1 ].Communicationanddefensesatellitesareanintegralparttomanypeople'severydaylife.Inaddition,specializedsatellitesandotherspacecraftareusedforscienticpurposes,suchastheoceanographicmonitoringofEarth,orforlearningaboutoursolarsystem.Muchcare,andthereforeexpense,istakentoassurereliabilityandsuccessofeachmission,sincelaunchingsuchcraftisexpensiveintherstplace,andbecausespacecraftarenoteasilyserviceableifanonboardcomponentfails.Radiationexistsineveryenvironment,includingonEarth,butsomeenvironmentsareespeciallyharsh.Spacecraftdesignersneedtoknowtheenvironmentsandcomponentexposuretimetoplanforeachmission.Additionally,theyalsomustknowhowdifferenttypesofradiationinteractwiththematterintheirspacecraft,andwithmorecomplexsystemsintheirspacecraft,suchascircuits.Sincethelaunchofeventherstsatellites,TIDradiationeffectshavebeenobservedtocausereallifeon-boardanomalies[ 2 ].Atbest,thisresultsinadditionalandunplannedworkloadongroundcontrollers.Atworst,TIDeffectscancausemissionoutages.Groundcontrollersworkcontinuouslyduringspacemissions,monitoringtheon-boardconditionsandoutsideradiationenvironmentssothattheycandeterminefaultsasquicklyaspossible.Whenafaultisdetected,thesecontrollersmustthenidentifythecauseormechanismofeachfault,anddeviserecongurationstrategies 15

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[ 2 ].Ascienticunderstandingoftheeffectofradiationindevicesmakesthesetaskspossible.TotalfailuresfromTIDarerare,butthisisbecauseofextremeoverdesign,andhistoricallyfromextremeinaccuracyofprimitiveshieldingcalculations.However,theseeffectsarestillamajorconcernduringthedesignphase,anddegradationofcomponentsduetoTIDiswell-documented[ 2 ].TID-induceddegradationhasbeenespeciallyobservedinmissionsinwhichtheenvironmentwasextremelyharsh,suchastheNASAJupiterprobes,orinsatellitesoperatingformuchlongerthattheirintendedlifetimes.Togiveabackgroundofwhatdesignersofspacecraftelectronicshavetoconsider,thenextsectiondiscusseshowradiationistypicallycharacterizedintestinglaboratories,andinthevariousspaceenvironmentsinwhichspacecraftoperate.Then,severalreallifeexamplesofTID-inducedanomaliesandsystemfailuresarediscussed. 1.1.1CharacterizingRadiationforSpacecraftDesignandTIDStudiesInthelaboratory,radiationsourcesareorganizedaccordingtoatomicnumber,charge,andenergy(E)forparticleswithmass,andbywavelengthorenergyforphotons.HighenergyparticlesthatinducechargeincommonICmaterialsarethemostrelevant.Specically,threegroupsareoftenconsidered:electronswithE>100keV;protonsandneutronswithE>1MeV,andheavyionswithE>1MeV/nucleon;and-raysorphotonswithwavelengthsshorterthan0.01nm,orfrequenciesabove1020Hz[ 3 ].Organizingradiationsourcesinthiswayisusefulfortheory,andwhenconductingcontrolledexperiments.Thepresentworkismainlyconcernedwith-raysandenergeticelectrons.Whenconsideringspace,however,radiationisoftenorganizedbyenvironment,orbyphysicalsource.Forexample,theon-EarthenvironmentcontainsparticleswithenergiesgreatlyreducedbyinteractionwiththeEarth'satmosphere[ 3 ];thenear-earthenvironmentcontainsbeltsofhighlyenergeticelectronsandprotonstrapped 16

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bytheEarth'smagneticeld;protonaresandphotonscomingfromourSunareabigconcern;andradiationalsocomesfromextra-galacticsources.Categorizingradiationinthiswayisusefulwhenplanningamission.Designersmustknow,basedontheuncontrollablesourceoftheradiation,whatradiationtypesthespacecraftwillencounterduringthemission.Knowingabouteachspaceenvironmentallowsdesignerstocalculatetheestimatedtotaldosethecraftandcomponentswillreceive,basedonthetimethecraftwillspendineachenvironment.Inthepresentwork,wearemainlyconcernedwithelectronstrappednearplanets,andgammaraysfromthesunandfromman-madesources. 1.1.1.1Neartheearth:trappedradiationItwastheveryrstUSarticialsatellite,launchedonJanuary31,1958,thatrstandunexpectedlydiscoveredtheexistenceofradiationintheEarth'supperatmosphere[ 4 ].AGeigercounteronboardthesatellitesaturatedearlyonduringthemission.FurtherstudyrevealedthatenergeticelectronsandprotonsaretrappedintoroidalbeltsaroundtheEarth.ThisradiationwasnamedtheVanAllenbelt(s),afterJ.A.VanAllen,whohadoriginallyproposedincludingtheGeigercounteronboardthesatellite[ 2 ].Theoriginsoftheelectronsarenotknown,butmeasuredabundanceratiossuggestbothterrestrialandinterplanetarysources[ 3 ].Theelectrons,whicharecharged,aretrappedbytheLorentzforcecausedbytheEarth'smagneticeld[ 3 ].Thiseldiscomposedmainlyofthecoreeld,whichisinducedbytheconvectivemotionofthemoltenuidintheEarth'score;andthecrustaleld,whichisinducedbyferromagneticmaterialsintheEarth'scrust[ 5 ].Anexamplecalculationofthetrappedelectrondistributionthatresultsfromthiseld,usingNASA'sJetPropulsionLaboratory's(JPL's)AE8code,isshowinFig. 1-2 [ 6 ].Thesecalculationsincorporatedatafromseveralsatellites,includingtheCRRESsatellite(Fig. 1-3 )[ 7 ]. 17

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Figure1-2. AnexamplecalculationusingJPL'sAE8modelshowingtheSouthAtlanticAnomaly(SAA)andthedistributionofenergeticelectronsaroundEarth[ 6 ]. Figure1-3. AnexampleofdatafromtheCRRESsatellite,whichmeasuredtotaldoseatdifferentdistancesfromtheEarth.TheEarthistheblueball.[ 6 ]. Thetrappedprotonsand1eVto10MeVelectronsarewhatmostlycontributetoTIDinLowEarthOrbit(LEO)[ 2 ],especiallywhenpassingthroughtheSouthAtlanticAnomaly(SAA),aconcentrationofsuchparticlesduetoanoffsetoftheEarth'smagneticaxiscomparedtoitsrotationaxis[ 2 ].ThisregionisclearlyseeninFig. 1-2 ,nearBrazil.Similarbeltshavebeenobservednearotherplanetsinthesolarsystem[ 3 ].Forexample,Jupiterwasdiscoveredtohaveamagnetospherewithtrappedelectronsin1959throughanalysisofJovianUHFradioemissions[ 8 ].TIDwasthemaincauseofcomponenterrororfailureonNASA'sGalileomissiontoJupiterfortworeasons.First,thespecially-designed,rad-hardchipstheyusedforthemissionwereeffectively 18

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insensitivetosingleeventeffects.Second,Jupiterhasamagneticeld20timeslargerthanEarth,andthemaximumenergyanduxlevelsoftrappedparticlesareproportionaltomagneticeldstrength[ 3 ]. 1.1.1.2OtherradiationsourcesThoughforthepurposesofthisworkwearemainlyconcernedwiththeenergeticelectronstrappedinplanetarymagnetospheres,othersourcesofradiationarebrieydiscussedbelowforcompleteness.Outsideofplanetarymagnetospheres,interplanetaryradiationsourcesconsistofsolarprotonsandphotons,galacticcosmicrays(GCRs),andinterplanetaryelectronsandprotons. Figure1-4. Thesolarirradiancespectrumshowingtheintensityof-raysfromtheSun.After[ 9 ]. Theintensityof-raysfromthesunrelativetootherwavelengthsintheelectromagneticspectrumareshowninFig. 1-4 .OriginallydetectedbysensorsonEarth,GCRsare 19

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madeupofinterplanetaryprotons,electrons,andionizedheavynucleiwithenergiesbetween1MeV/nucleonand1010eV/nucleon.Theyarebelievedtobegalacticorextragalacticinoriginbecauseobserveduxesoftheseparticlesareisotropic[ 3 ].However,becauseoftheirsmallintensitylevels,interplanetaryelectronsandprotonsdonothavealargeimpactontheradiationenvironment[ 3 ].Radiationalsocomesfrommanmadesources.Nuclearexplosionsdetonatedintheatmosphere,suchastheStarshPrimetestbytheUnitedStatesin1962,contributedsignicantradiationtotheVanAllenbeltswhichlastedwellintothe1970s[ 2 ].Anotherexampleofman-madesourcesarethethermalheatersusedonboardspacecraft,eitherforheatdirectly,ortoconvertheattoelectricity,sincesolarpanelsarenotefcientifspacecraftmusttravelfarawayfromthesun[ 3 ]. 1.1.2On-OrbitAnomaliesduetoTIDEventakingintoaccounttheprobabilitythatasignicantamountofinformationregardingsatellitefailuresmaybeclassiedorkeptsecretformilitaryorcommercialreasons,itisneverthelesssurprisinghowseldomTIDfailureisreported.TheTIDfailuresonpublicrecords[ 10 12 ]areforspacecraftthatwereexposedtoextremeradiation,orareend-of-lifereportsofsystemsthatsurvivedwellbeyondthelifetimesforwhichtheyhadbeendesigned[ 2 ].Thisisbecauseoftheexcessivedesignmarginsthatareadoptedbythespaceindustry.Thereisalotofuncertaintyinspacemissionplanning,fromunknownsabouttheactualradiationenvironmentthatthespacecraftwillencounter,uncertaintyinthetemporalvariationoftheradiationenvironment,suchassolaractivity,uncertaintiesintheinteractionofradiationwithspacecraftandcomponentshielding,anduncertaintiesintheaccuracyofcomponenttestprocedures,includingtestsonindividualelectronicsparts.Poormodelingorunderstandingofallthesephysicalprocessescontributestotheuncertainty.Inthislight,itisnotsurprisingthatextremeoverdesignofspacesystemsisoftenchosenasawaytoensurethattheoverallmissiondoesnotfail. 20

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1.1.2.1TelstarexampleTherstreallifeexampleofspacecraftfailureduetoTIDoccurredwithTelstar,therstactivetelecommunicationsatellite,whichwasdesignedandbuiltbyBellLabs,AT&T,andNASA,andlaunchedonJuly10,1962.TheUShadconductedahighaltitudenucleartestonlythedaybeforetheTelstarlaunch,injectingextremelyhighlevelsofelectronsintotheEarth'sradiationbelts.ThisradiationincreasedaftermoretestsbytheSovietUnion,causingdegradationofelectroniccomponentsinthesatelliteatafasterratethanexpected,untiltotallossoccurredonFebruary21,1963,attributedtoTIDdegradationofdiodesinthecommanddecoder[ 2 ]. 1.1.2.2HIPPARCOSexampleAnotherexampleofTIDfailureistheEuropeanSpaceAgency(ESA)starmappingmissionHIPPARCOS,whichwaslaunchedonAugust8,1989.Oneoftheonboardmotorsfailed,andthesatellitecouldnotmoveoutofitsinitialGTOorbit.Thesatelliteremainedinthisorbitfortheentiredurationofitsmission,resultinginamuchlargerdoseexposurethanitwasdesignedfor.Afterthreeyearsofexposure,allthegyroscopesfailedovera6-monthperiod.Noiseanderraticdatawereaproblembeforeeventuallyallcommunicationwaslost.ThoughHIPPARCOSisanexampleofreallifefailureduetoTID,thecraftactuallyoperatedforlongerthanitsintendedlife,andsuccessfullycarriedoutitsscienticgoals,duetotheextremeoverdesignthatiscommoninthespacecommunity[ 2 ]. 1.1.2.3GalileoprobeexampleTheGalileoprobeisalsoagoodexampleofacasewhereTIDwasthemainchallengefacinggroundcontrollersduringthemission.Atonepointduringthemission,theonboardcomputererroneouslydeterminedthatGalileo'santennawasnotpointedatEarthandredthrusterstocorrectthesupposederror,causingsixunexpectedmaneuversbeforetheJPLteamcouldregaincontrol.IfthecomputerhadredthethrustersinsuchawayastocausetheantennatonotbepointingtowardsEarth,then 21

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theywouldhavenotbeenabletogivetheprobeanycommands.UsingtheresultsofearlierJupiterprobesPIONEERandVOYAGERwhendesigningGalileo,JPLwasabletocompletethemission,eventhoughtheprobewassubjectedtobetween10and50krad(Si)duringeachorbit,mainlyattheperiapsis[ 13 ].Theyusedtherestofthetimeinorbittoannealdamagedparts,extendingthelifetimeofcriticalsystems[ 13 14 ].TheexamplesofTIDfailuresinthissectionshowthatTIDhasbeenaproblemsincetheveryrstspacemission.Theyalsogiveanindicationoftheextremeoverdesign,andthusextratimeandcost,commonlyadoptedorevenrequiredbythespaceindustry.Overtime,asunderstandingofradiationeffectsinmaterialsandelectroniccomponentshasincreased,andasmodelingeffortshavebecomemoreaccurateandquantitative,manyoftheseexcessivemarginshavebeensignicantlyeased.Forexample,ontheESAINTEGRAL-rayspacetelescope,theexpecteddosefortheprojectwaseasedfromof120krad(Si)to6krad(Si)becauseofbettershieldingcalculationsutilizingmoderncomputingpower[ 15 ]. 1.2Motivation:UnderstandingTIDRadiationEffectsinDevicesThissectionrstgivesabriefoverviewoftheeffectsofradiationinSiO2ingeneral.Then,theeffectofionizingradiationonthedevicecharacteristicsofsiliconCMOSandbipolarstructuresarediscussed.ThegatedlateralPNPteststructure,whichisacombinationCMOSandbipolardevice,isintroduced.Finally,examplesfromtheliteratureofthecomplicatednatureoftheobserveddegradationofthesestructuresisreviewed,includingexperimentsthataredesignedtoshowtheeffectofhydrogenanddoserateonthedegradation. 1.2.1IonizingRadiationinSiO2Theeffectofionizingradiationinanymaterialisacomplexprocess.Eventakingintoconsiderationtheeffectofonlyoneincidentparticleiscomplicated,becausethissingleparticlemayproducemanysecondaryparticlesthroughthecascadeprocesswhichmaybeverydifferentinenergyandcompositionthantheoriginalparticle. 22

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Thenewparticlesmayalsocreatetheirownsecondaries.Becauseofthiscomplexreality,thecascadeprocesscannotbemodeledanalytically,andisatbesttreatedasprobabilisticprocessusinghighpowercomputingcodes[ 3 ].Inthiswork,wearemainlyconcernedwithaccuratelymodelingwell-controlledexperimentswhichwereperformedusingthe-rays,orenergeticphotons,ofdecaying60Coasaradiationsource.A60Co-raysourceisoftenusedinthelaboratorytotestcomponentsbecausetheycontain1.17and1.33MeVphotons[ 16 ],whichinducesecondaryelectronsinSiO2whichmimictheelectronenvironmentoftheVanAllenbelts.Thissectionwilldiscusstheinitialphoton-matterinteractionprocess(Comptonscattering)thatproducessecondaryelectrons(Comptonelectrons);reviewexperimentsshowingthattheeffectofComptonelectronsinSiO2areequivalenttothehighenergyelectronsinthevanAllenbelts;discusshowhighenergyelectrons,includingComptonelectrons,createEHPsinSiO2;andnallydiscusshowcreationandinitialrecombinationoftheseEHPsisquantitativelymodeled. Figure1-5. Photon-matterinteractiontypeasafunctionofatomicnumber(Z)andphotonenergy.From[ 17 ].60Co-rays(photons)of1.17and1.13MeVarermlyintheComptonregime.CourtesyofNorthropGrummanCorporation. 23

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1.2.1.160Co-raysinduceComptonscatteringinSiO2-on-SistructuresPhotons,whichareunchargedandmassless,interactwithmatterprimarilythroughoneofthreeprocesses,dependingontheenergyoftheincidentphotonandtheatomicnumberZofthetargetmaterial.Atlowenergies,aslongasincidentphotonsareofanenergygreaterthantheworkfunctionofthetargetmaterial,i.e.theelectronbindingenergy,theyarecompletelyabsorbedbyK-shellelectronsinthetarget,whicharethenemittedasphotoelectrons.Thisiscalledthephotoelectriceffect.Athigherenergies,whenthephotonenergyismuchgreaterthanthebindingenergyoftheelectrons,thephotonsscatterelasticallywithelectronsinaprocesscalledComptonscattering,whichdominatesoverthephotoelectriceffect.InComptonscattering,thehighenergyincidentphotonimpartsmostofitsenergytoanatomicelectronwhichisnotemittedbutinsteadcontinuestotravelinthetargetmaterial,creatingahighlyenergeticsecondaryorComptonelectron,whichinturngenerateselectron-holepairsintheSiO2conductionband.Atevenhigherenergies,photonsthatstrikesahigh-Ztargetmayproducepositron-electronpairs,inaphenomenoncalledpairproduction[ 17 18 ].Fig. 1-5 from[ 17 ]summarizesinanillustrationhowphoton-matterinteractiontypedependsonZandphotonenergy.Theequalitylinescorrespondtoequalinteractioncrosssectionsfortheneighboringprocesses.Forsilicon(Z=14),Comptonscatteringdominatesbetween50eVand20MeV.Oxygenissimilar,withZ=8.Thus,Comptonscatteringisthedominantphoton-matterinteractionprocessinSiO2-on-Sistructuresexposedto60Co-rays,whicharephotonsof1.17and1.33MeV. 1.2.1.2Equivalencyof60Co-raysandhighenergyelectronsourcesDirectlyexposingSiO2toenergeticelectronshasbeenshowntoproducethesameeffectasexposureto60Co-rays.BoeschandMcGarrity[ 19 ]exposedMOScapacitorsto12-MeVelectronpulses,whileOldhamandMcGarrity[ 20 ]exposedthesamestructuresto60Co-radiation.Theholeyieldinducedbytheradiationsourceswas 24

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Figure1-6. HoleyieldsextractedfrommeasurementsonSiO2exposedto12-MeVelectronpulsesand60Co-raysmatcheachother,aswellascalculatedholeyieldusingthegeminaterecombinationmodel.After[ 16 ]. extractedineachcase.Thetwoexperiments,replottedinFig. 1-6 ,agreewellwitheachother.ThesecondaryorComptonelectroncanhavearangeofenergiesbetween0.5and1.0MeV,andisusuallytreatedasafreeelectron.Thedosetotheoxideisdeliveredmostlybythesesecondaryelectrons,whichgenerateEHPsintheSiO2[ 16 ].BasedonexperimentalresultsofCurtis,etal.[ 21 ],AusmanandMcLean[ 21 ]calculatedthat,onaverage,oneEHPiscreatedforevery183eVofenergydepositedinSiO2.Amorerecentsetofmeasurementshasdeterminedthisnumbermoreaccuratelytobe171eV[ 22 ]. 1.2.1.3ConductionbandEHPgenerationandrecombinationTheEHPsgeneratedbytheComptonelectronsundergoaninitial,directelectron-holerecombinationstepduringtherstfewpicosecondsaftergeneration[ 16 ].TheEHPsinitiallygeneratedinSiO2bytheenergeticelectrons,includingthesecondaryelectronsinducedby60Co-rays,aresignicantlyfarapartinSiO2thattherecombinationofeachpaircanbetreatedseparately.Thisapproximationistermedgeminaterecombination. 25

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TheEHPsinducedinSiO2bythehigh-energysecondaryelectronsfrom60Co-raysaregeneratedquitesparselyandthegeminatemodeltsexperimentalresultsverywell[ 16 ],[ 23 ].ThisisshowninFig 1-6 ,wheretheholeyielddatafrom60CoandenergeticelectronsourcesalsomatchcalculationsbasedonthegeminaterecombinationmodelbyAusman[ 24 ].Thepercentofelectronsorholessurvivingthisinitialrecombinationisgenerallyreferredtoastheyield,andisafunctionoflocalelectriceld,whichactstoseparatetheEHPs,andaverageseparationdistancebetweenEHPsatthetimeoftheircreation.Theaverageseparationdistanceisdeterminedbytheincidentparticletypeandenergy,andthetargetmaterial[ 16 ],[ 23 ].TIDrepresentsthetotalamountofenergydepositedbyaparticlethatresultsinEHPproductioninagivenmaterial[ 25 ].Thus,theunitsofdose,heretherad(SiO2),standsforradiationabsorbeddoseinSiO2,where1rad(Si)=100ergs/g(Si),torelatetoSIunits[ 3 ]. 1.2.2TIDEffectsinCMOSUsually,irradiationcausesanetpositivechargebuildupindeviceoxides[ 23 ],referredtoasoxidetrappedcharge(Not),andisduetotheenergeticallyfavorablecaptureofaholeinaneutraloxygenvacancy.Thisresultsintheformationofthewell-knownoxygenvacancydefects,theE0centers.Someoftheseholetrapsareverydeep,withenergylevelswellintotheSiO2bandgap.Positivechargebuildupinoxidesresultsinnegativethresholdvoltageshiftsforbothn-channelandp-channelMOSFETs[ 25 ].Fig. 1-7 showsanillustrationofthiseffectforthen-channelcase.IftheVtshiftbecomeslargeenoughduetocontinualchargedepositionbyradiation,theneventuallyitwillbecomeimpossibletoturnthen-channeldeviceoff,orthep-channeldeviceon,andthecircuitwillfail.AnotherkindofSiO2-relateddefectthatnegativelyaffectsdeviceoperationresidesontheSi/SiO2interface,andisassociatedwiththeobserveddanglingbondsorPbcentersthere[ 26 ].Fig. 1-8 showstheeffectofpositiveinterfacechargeontheIV 26

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Figure1-7. IllustrationshowingtheeffectofxedoxidetrappedchargeontheVtofn-channelMOSFETs. Figure1-8. IllustrationshowingtheeffectofinterfacetrapchargeontheVtofn-MOSFETs. characteristicsofann-channeldevice.Theinterfacechargecausesanincreaseinsubthresholdswing,causingstretch-out(Vit)intheId-Vgsresponse,aswellasashiftinthresholdvoltage.Experimentshaveshownthat,atandaboveroomtemperature,interfacetrapsarenotformedbydirectholeinteraction[ 25 ],[ 27 ],anddensityfunctionaltheorycalculationsconrmthatthisisnotanenergeticallyfavorablereaction[ 28 ].Instead,theformationofdanglingbondsattheSi/SiO2interfacereliesonseveralreactionsthatmustoccurbeforehandtoreleaseprotons,eitherfromhydrogen-containingdefects 27

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(suchasahydrogenatedvacancyordopant-Hcomplexes[ 29 ]),orfrommolecularhydrogenresidinginterstitially[ 30 ].Then,protonstravelingbydriftordiffusioncaninteractwithhydrogen-passivateddanglingbondsattheSi/SiO2interface,leavingapositively-chargeddanglingbondattheinterface(DB+int),andahydrogenmoleculetodiffuseaway[ 23 ].Thedensityofdanglingbondsattheinterfacearereferredtoastheinterfacetrapdensity,(Nit). 1.2.3TIDEffectsinBipolarDevicesTIDeffectsinbipolardevicesbecameaprevalentconcernfortheradiationcommunitywhenthesemiconductorindustrybeganusingoxideisolationstructures[ 31 ].In1983,Pease,etal.explainedwhybipolarpartsthatwereexpectedtosurvivemorethan1Mradfailedataonlyafewkrad,byshowingthatradiation-inducedoxidechargehadbuiltupintheisolationoxidesoverthebaseregionsofthesestructures[ 32 ].Thischargehadtheeffectofturningonparasiticleakagepaths.Whenchargeistrappedabovethebase,thebasebecomespartiallyinverted,causingahighercollectorcurrent,ordecreasedgain.In1991,Enlow,etal.[ 33 ]observedacomplicatingTIDeffectinstructurescontainingbipolarisolationoxideswhichhasproveddifculttounderstandandmodel.Theauthorsreportedincreaseddegradationofbipolardevicecharacteristicsforpartsirradiatedatlowdoseratescomparedtothoseirradiatedatthestandardhighdoseratesusedinhardnessassurancetesting[ 33 ],andthephenomenacametobereferredtoasEnhancedLowDoseRateSensitivity,orELDRS.RecentexplanationsandmodelsforthebasicmechanismsbehindELDRSattributethisobservedeffecttoreduceddegradationathighdoseratesduetooneormoreofseveralpossiblereasonsincludingmorerecombinationathigherdoserates,spacechargeeffects,ortheextremelyslowmotionofprotons[ 31 ].TheoriginaldatawereforverticalNPNdevices,buttheworstcaseisforlateralPNPdevices[ 34 ],wheremoreofthebaseregiondirectlysharesaninterfacewithSiO2,and 28

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Figure1-9. Illustrationshowinghowanincreaseinpositively-chargedinterfacetrapsontheSi/SiO2interfaceoftheisolationoxideandn-typesiliconbaseofPNPlateralbipolardevicesinducessurfaceSRH(SSRH)recombination,drawingmoreelectronsfromthebasecontactandincreasebaseleakagecurrent. becausethebasedopingislowerthantheNPNcase.Fig. 1-9 illustrateshowtheholestrappedoninterfacedanglingbondsofthePNP'sbaseisolationoxidecanrecombinewithelectronsfromthen-typebaseregioninsurfaceShockley-Read-Hall(SSRH)recombination.Thispullsmoreelectronsfromthebasecontact,increasingbasecurrent,anddegradingthegainofthesedevices.In1994,Johnston,etal.publishedlow-dose-rateirradiationresultsnormalizedtodamageatahighdoserate(50rad(SiO2/s)[ 35 ].ThismethodofcharacterizingtheseverityoftheELDRSeffectwasadoptedbytheradiationcommunity,andcametobeknownastheLowDoseRateEnhancementFactor(LDREF)[ 31 ]or,moresimply,theEnhancementFactor(EF).TheresultsofsomeearlyELDRSstudiesappearedtoconict[ 31 ],butthereasonforthiswasidentiedbyKruckmeyer[ 36 ]asduetothefactthatseveralofthepartsbeingusedintheearlystudieshadthesamename(forexample,theNationalSemiconductorLM139),butweremanufacturedinatleasteightdifferentfabricationfacilitiesatdifferenttimes,usingdifferentmanufacturingprocesses,anddifferentlayouts.Toaddresstheseissues,severalspecializedteststructuresweredevelopedalongsidetheNationalSemiconductorLM124quadopamp[ 31 ],anELDRS-sensitivepartcommonlyusedinsatellitedesign.Theseteststructuresincludedagatedlateral 29

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Figure1-10. 2DrepresentationoftheGLPNPteststructure,after[ 37 ].[Reprinted,withpermission,fromX.J.Chen,etal.,Behaviorofradiation-induceddefectsinbipolaroxidesduringirradiationandannealinginhydrogen-richand-depletedambients,IEEEIRPS2008,pp.115,Figure1,May2008.] PNP(GLPNP)structurewhichwasusedtoextractaccurateNotandNitmeasurements.A2DrepresentationoftheGLPNPisshowninFig. 1-10 .Inthisstructure,ametalgateisdepositedabovethebaseisolationoxide.Thestructureisirradiatedwith0-biasonthegate,tomatchspaceconditionswheremetallinesoftencrossabovebipolarisolationoxides.Afterirradiation,experimenterscanperformagatesweep,bringingthebaseregionoftheMOSstructurethroughaccumulation,intodepletionandinversion.ThisextraMOS-likecontrolofthebaseregionisimportantbecausemaximumSSRHrecombinationoccurswhenelectronandholeconcentrationsarebalanced(n=p),whichoccursindepletion.AnalyzingbasecurrentduringthegatesweepallowsforextractionofNotandNit.AnexamplegatesweepmeasurementonthisGLPNPfromBall,etal.[ 38 ]isshowninFig. 1-11 .Indepletion,electronsaredepletedfromthesurface,untileventuallyn=p.Aspikeinthebasecurrentisseenatthisvoltage.Thedensityofinterfacetrapscanbe 30

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Figure1-11. ResponseofGLPNPbasecurrentduringgatesweepsbeforeandafterirradiation.Apeakisobservedinthebasecurrentwhenthegateisbiasedsuchthatthechannelregionisindepletion,i.e.whenn=pandmaximumSSRHoccurs.Thispeakshiftsduetooxidechargebuildup,allowingforanextractionofNot,andincreaseinpeakheightallowsforextractionofinterfacetrapcharge,Nit.After[ 38 ].[Reprinted,withpermission,fromD.R.Ball,etal.,Separationofionizationanddisplacementdamageusinggate-controlledlateralPNPbipolartransistors,IEEETrans.Nucl.Sci.,vol.49,no.6,pp.3187,Figure4,Dec.2002.] extractedfromtheheightofpeakcurrentviasrv=2IB qSpeakniexp(qVEB 2kBT) (1)Nit=srv vth (1)wheresrvissurfacerecombinationvelocity,IBisthemaximumincreaseinbasecurrent,qisthechargeonanelectron,Speakisthespreadofthebasecurrentpeak,niistheintrinsiccarrierconcentrationofsilicon,VEBistheemitter-basevoltage,kBisBoltzmann'sconstant,Tistemperature,iscarriercapturecrosssection,andvthisthermalvelocity[ 38 ].Theoxidechargedensity,denedasthechargeintheoxidethatdoesnotinteractwiththeinterface,canbeextractedfromtheshiftintheIB-VGcurve,via Not=CoxVmg q(1) 31

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whereCoxisoxidecapacitance,andVmgisthemidgapvoltageshift,inthiscasetheshiftinVGatwhichthepeakbasecurrentoccurs[ 38 ].Anotherfactorthataffectedtrendsinexperimentalresultswasdifferencesinpackagingmethods,someofwhichintroducedtraceamountsofhydrogenintothedeviceenvironment.Forexample,astudybyPeaseetal.comparedirradiationsoftheAD590temperaturetransducerintwodifferentpackages.Theyobservedadifferenceindegradationbyasmuchastwoordersofmagnitude,forcertaindoses,wherethehigherdegradationwasforthedevicesinhydrogen-containingat-packs,comparedtotheonespackagedinmetalcans,whichdonotcontainhydrogen[ 39 ]Thoughitistheinteractionofinterfacetraps(Nit)withthesiliconbaseregionthatisattributedtoTIDbipolardevicedegradation,thebuildupofoxidetrappedcharge(Not)isarelatedandessentialmechanismwhichmustbeaccountedforconcurrently,forseveralreasons.Thischargecontributestothelocalelectriceldinthedeviceandthusthedriftofchargedparticles,suchasradiation-inducedelectronsandholes,andalsotheprotonsthatcreateNituponreachingtheinterface.Inaddition,holetrappingintheoxideisanessentialrststepforthesubsequentreleaseofprotons.Becauseofthisclose-couplingofeffects,itisessentialtounderstandandmodeltheseeventssimultaneously,which,asdiscussedinChapter 2 ,hasnotbeenavailableinpreviouswork.AnalvariableconsideredinthisworkthatcomplicatesobservedTID-induceddegradation,especiallyinELDRS-sensitiveparts,istime.Thebuildupofoxideandinterfacetrapsoccursthroughseveraltimedependentprocesses,includingthegenerationandtransportofEHPsonveryshorttimescales,toholetrappinginmediumtimescales,andtoprotontransportandholereleaseonlongtimescales.Trapannealingalsotakesplaceconcurrentlywithtrapformation,andhasaneffectonmeasureddegradation.Ifthetimescalesofthedifferentmechanismsarenottakeninto 32

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accountinthedesignofexperiments,apparentdoserateeffectsmaybeobserved,asopposedtotruedoserateeffects,suchasELDRS[ 31 ]. Figure1-12. Datafrom[ 40 ]showingthedifferencebetweentime-dependentandtruedoserateeffectsatmultipletotaldoses.[Reprinted,withpermission,fromM.R.Shaneyfelt,etal.,Thermal-stresseffectsandenhancedlowdoseratesensitivityinlinearbipolarICs,IEEETrans.Nucl.Sci.,vol.47,no.6,pp.2543,Figure9,Dec.2000.] Forexample,Fig. 1-12 ,after[ 40 ],illustratesthedifferencebetweenatime-dependenteffect(TDE)andatruedoserateeffect(TDE).Thetotaldoseforallthreecurvesis50krad(SiO2).Irradiatingatahighdoseratetakesashortertimetoreachthisdosethanirradiatingatalowdoserate.Thetopcurveshowsdatafordevicesirradiatedatadoserateof0.01rad/s,andthebottomcurveforadoserateof50rad/s,butthemiddlecurveshowswhathappenstothehighdoseratedevicesafteranannealforthesametimerequiredtoperformthelowdoseratetests.Thisallowsabettercomparisonbetweenthehighandlowdoseratetests,becausethenbothsetsofsamplesexperienceannealingforthesameamountoftime.Itisonlytheincreaseddegradationbetweenthemiddleandtopcurvesthatisconsideredatruedoserate,orELDRSeffect.Chapter 2 ofthisworkwillpresentamodelforthetime-dependentformation,destruction,andinterrelationofNit,Not,andhydrogenthatcanexplainthecomplicatedELDRSeffectoveralargerangeofdoserates,andwhichencompasseseventswhich 33

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takeplaceontimescalesrangingfrompicosecondstotensofyears.Thenalsectionofthischapter,below,presentstheexperimentalworkintheliteraturethatwillbeusedtotesttheaccuracyanduniversalityofourmodel. 1.2.4ELDRSinTesting,Prediction,andHardnessAssuranceWehavechosenseveralsetsofpublisheddatatakenfromtheGLPNPteststructuredescribedabovefromwhichNitandNothavebeenextractedoveralargerangeofdoseratesandambienthydrogenconcentrations.Allstepsofeachexperimentwereperformedatroomtemperature,includingthehydrogensoaking,irradiation,andelectricalmeasurementsteps.TheradiationsourceforthesedatasetsisaCo60-raysource,andthetotaldosescomprisearangefrom10to30krad(SiO2).Becausethechipmanufacturinglot,radiationsource,radiationdose,andtrapdensityextractionmethodsallmatch,weassumethatagoodphysics-basedmodel,suchastheoneweoutlineinChapter 2 ,shouldbeabletomatchallthedataquantitativelywithoutvaryingparametersfromdata-settodata-set.TherstsetofdataweconsiderisfromChen,etal.[ 41 ].Intheirwork,NitandNotwasextractedfromGLPNPmeasurementsoverawiderangeofambienthydrogenconcentrations(Fig. 1-13 ).Neitherdosenordoseratewasvaried,andthedoseratewashigh.Beforeirradiation,thechipsweresoakedinthevariousH2concentrationsatconstantpartialpressureuntiltheconcentrationofH2intheSiO2saturated.ThedatainFig. 1-13 showthat,atthishighdoserate,bothinterfaceandoxidechargedensitiesincreasewithambienthydrogenconcentration.DensitiesplateauatlowandhighconcentrationsofH2,withatransitionregionatintermediaryH2concentrations.WewilldiscussmodelingtheeffectofH2concentrationoninterfacetrapbuildupinChapter 4 ,andmodelingtheeffectofH2concentrationonoxidetrapbuildupinChapter 5 .ThesecondsetofdataweconsiderisfromPease,etal.[ 42 ],whoextractedinterfacetrapdensityversusdoserate,orELDRScurves,fromGLPNPtestsamplesatthreeambientH2concentrations(Fig. 1-14 ).Thebottom-mostcurveshowsdatataken 34

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Figure1-13. ExtractedNitandNotmeasurementsfromChen,etal.takenoverawiderangeofambientH2concentrationsatahighdoserate[ 41 ].[Reprinted,withpermission,fromX.J.Chen,etal.,Mechanismsofenhancedradiation-induceddegradationduetoexcessmolecularhydrogeninbipolaroxides,IEEETrans.Nucl.Sci.,vol.54,no.6,pp.1915,Figure6,Dec.2007.] ataverylowH2concentration(i.e.itshowsdatatakeninair).TheELDRStrendforthiscurveshowsanenhancementfactorof5,withhigh-dose-rateNitvaluesplateauingat4x1010cm)]TJ /F2 7.97 Tf 6.59 0 Td[(2,andlow-dose-ratevaluesincreasingto2x1011cm)]TJ /F2 7.97 Tf 6.59 0 Td[(2orperhapshigher.ThemiddlecurveshowsanELDRSresponseforanintermediatevalueofhydrogen,oneinthemiddleofthetransitionregionofthehydrogencurveofChen,etal.inFig. 1-13 .ThisELDRSresponseissimilartothelow-H2response,butwithhigherNitdensitiesatalldoserates.Theenhancementfactorissimilartothelow-H2case,buttheoveralldegradationishigherduetotheincreasedH2. 35

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Figure1-14. DatashowingtheELDRSresponseoftheteststructuresatdifferentH2ambientconcentrations[ 42 ].[Reprinted,withpermission,fromR.L.Pease,etal.,Theeffectsofhydrogenontheenhancedlowdoseratesensitivity(ELDRS)ofbipolarlinearcircuits,IEEETrans.Nucl.Sci.,vol.55,no.6,pp.3170,Figure3,Dec.2008.] ThetopcurveinFig. 1-14 showsanELDRSresponsefordevicesinwhichtheH2concentrationhassaturatedatthemaximumvaluepossibleintheSiO2.Despitethelinesdrawnbytheauthorstoguidetheeye,thishigh-H2curveismuchatterthantheothers,andthedegradationatalldoseratesissimilartothelowdoseratedegradation,i.e.itissimilartothemaximumdegradationobservedatthelowestdoserateusedinthestudy,whichismostsimilartotheactualspaceenvironment.Theseresultsledtheauthorsofthisstudy[ 42 ]tosuggestthatsaturatingdevicesinhydrogenduringhighdoseratetestingmaybeagoodwaytoemulatethedegradationthatwouldbeobservedinthelowdoseratespaceenvironment,butyetaccomplishpartsqualicationandtestinginreasonabletime.WewilldiscussthemodelingofthedifferentELDRSresponsesindifferentH2environmentsinChapter 4 .Oxidechargeextractionswerenotreportedinthiswork,butwouldbeaninformativeandusefuladditiontoouroxidechargemodelingworkpresentedinChapter 5 36

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Thetimedifferencebetweenlowdoserateandhighdoseratetestingisnottrivial.AsimplecalculationwillrevealthatthedatapointinFig. 1-14 takenatthelowestdoserateof0.02rad/srequiredonemonthofcontinuousirradiationtoproduce.Thespaceenvironmentoftenintroducesradiationatevenlowerdoserates.YetevenatPease'slowestdoserateandlongestmeasurementtimes,itisnotclearwhetherthesecurveswillplateau. Figure1-15. Datashowinginterfacetrapmeasurementsatdifferenttotaldoses,doserates,andmeasurementtimes[ 43 ].[Reprinted,withpermission,fromI.S.Esqueda,etal.,Modelingtheeffectsofhydrogenonthemechanismsofdoseratesensitivity,RADECS11Proceedings,Figure2,Sep.2011.] ThethirdsetofdataconsideredisfromEsqueda,etal.[ 43 ],whoextractedinterfacetrapdensityversustotaldose,fordifferentambientH2concentrationsanddifferentdoserates(Fig. 1-15 ).Thisthirddatasetallowsustotestourmodelatadditionaltotaldoses,andalsoatanadditionalmeasurementtimes.Thiswork,discussedinChapter 6 ,providedinsightsintothedifferentmechanismsresponsiblefortimedependentandtruedoserateeffects. 1.3ChapterSummaryThemaingoalofthisworkistogaininsightintothebasicmechanismsbehindtheobservedELDRSeffectinbipolardeviceswhichcandirectlyinformthemandatory 37

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ELDRStestingofpartsforsatelliteandspacevehicledesign.TheGLPNPteststructureisdirectlyrelatedtomanylegacypartsstillusedbythespaceindustry,suchastheLM139comparatorandtheLM124opampdiscussedearlier.Inaddition,anincreaseintheunderstandingofchargetrappingandtransportintheGLPNPbaseandisolationoxideisgenerallyapplicabletootherSiO2-on-Sisystems.Finally,themethodsdescribedindetailinthisworkandintheresultingpublicationsareapplicableforstudyingchargetrappingandtransportinothersystemsandinterfaces.AnexampleofthepossibleapplicationofthisworktothemodelingandcharacterizationofTIDdegradationinshallowtrenchisolation(STI)oxidesinamodernCMOSprocessisincludedinChapter 7 38

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CHAPTER2UNDERSTANDINGANDMODELINGA-SIO2PHYSICSThischapterwillrstreviewthediscoveryandsubsequentinvestigationofseveralvacancydefectcomplexesinSiO2viaelectronparamagneticresonance(EPR)orelectronspinresonance(ESR)spectroscopy.Thesetoolscanprobespeciesthathaveoneormoreunpairedelectron.ThismethodhasbeenusedoncrystallineandamorphoussamplesofirradiatedSiO2tostudythechemicalreactionsandradicalsformedasaresultoftheradiation.Severaldefectcentershavebeenidentied,characterizedbytheirenergy,andlabeled.Secondly,importantinsightsgainedfromatomistic,theoreticalmodelingofthesecomplexesusingdensityfunctiontheory(DFT)orrstprinciplescalculationswillbereviewed.ThesequantummechanicalcalculationsprovideinsightintothestructureofdefectsanddefectreactionsfoundbyEPRmeasurements.Usingtheseinsights,DFTcalculationscansuggestwhichpossiblereactionsaremostlikelytooccuratgiventemperatures.Usually,DFTresultsareanalyzedalongwithexperimentalobservationstonarrowdownthepossiblechoicesofreactionsintheSiO2.InSection 2.2 ofthischapterwediscussmorerecentDFTresults,anddevelopfromtheseasetofreactionstostudyinFLOODS.Chapter 3 discusseshowthesereactionsareimplementedinFLOODStobuildaphysics-basedmodelforradiationdamageinSiO2. 2.1OxygenVacancyComplexesinSiO2AnexcellentreviewofE0centersinamorphousSiO2wasdonebyPantelides,etal.[ 44 ].Inthispaper,theauthorsgiveabriefoverviewofthehistoryofE0centersina-SiO2,highlightingspeciccontributionsofEPRmeasurementsandDFTcalculations. c[2011]IEEE.Section 2.1 includescontent,withpermission,from[N.L.Rowsey,M.E.Law,R.D.Schrimpf,D.M.Fleetwood,B.R.Tuttle,S.T.Pantelides,AQuantitativeModelforELDRSandH2DegradationEffectsinIrradiatedOxidesBasedonFirstPrinciplesCalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2937-2944,Dec.2011]. 39

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TheirresultingconsensusisthattwobasictypesofoxygenvacancycentersexistinamorphousSiO2:therstisashallowtrapwiththedimercongurationthatcorrespondstotheEPRE0signal;thesecondtypeofoxygenvacancycomplexisadeeptrapthatcorrespondstotheEPRE0signal.However,theyalsoacknowledgecontinuingdebateaboutthenatureoftheE0centers,andcallforfurthertheoreticalworktoshedlightontheissues.TherstreportofEPRmeasurementsofradiation-induceddefectsoncrystallineandamorphousSiO2waspublishedin1956byRobertA.Weeks[ 45 ].Later,theseresonanceswerecorrelatedwithopticalspectradata[ 44 ],andtheserieswaslabeledE0n,wherenisaserialnumberandtheprimeindicatesthenumberofelectrons.TherewassomedebateastowhetherthesignalswereduetooxygenvacanciesorSidanglingbonds[ 44 ],[ 46 ],[ 47 ].Thisdebatewaspartiallyresolvedin1974byFeigl,etal.[ 48 ]withpreliminarycalculationsonsmallclusters.In1987,semiempiricalcalculationsonlargerclustersconrmedthattheE01centerwasadimer[ 49 ].Inthe1980's,focusshiftedfromtheE0centersincrystallinequartztotheE0centersinthermaloxidesinelectronicdevices.TwodistinctcentersnowknownasE0,adeepholetrap,andE0,ashallowholetrap,wereidentied[ 50 ].Fig. 2-1 givesarepresentationofthesetraplevelswithinthebanddiagramofSiO2,andindicateshowholesbehaveinthevicinityofthesetraps.E0correlatesinamorphousSiO2totheE01incrystallineSiO2.Oxygenvacancies(Vo)arethedominantdefectinSiO2[ 51 ],[ 30 ],[ 52 ],[ 53 ],[ 54 ],andbothE0centersoriginatefromthisdefect.AmodernDFTrepresentationoftheandvacancyprecursorstructuresareshowninFigs. 2-3 and 2-2 .TheneutraloxygenvacancyincludesoneSi-SibondinsteadoftwoSi-Obonds.Inamajorityofcases,thepositivelychargedoxygenvacancyhasmainlythesamebondstructure,withslightenhancementoftheSi-Sibondlength(Fig. 2-2 ).Thisdefectisobservedinthepositivechargestatewithelectronparamagneticresonance(EPR),whereitislabeledE0[ 52 ], 40

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Figure2-1. Banddiagramindicatinghowholesgeneratedbyradiationinteractwithshallowtraps(E)anddeeptraps(E).Itiseasyforholestohopinandoutofshallowtraps,migratingtowardstheSiO2interfacebecauseofthebuilt-inelectriceldoftheMOSstructure.However,holesstayforlongtimesindeeptrapsneartheinterface,andaresometimesreferredtoasxedoxidecharge. Figure2-2. DFTrepresentationofVo. [ 55 ],[ 56 ],[ 57 ].Inthiswork,werefertothisdefectanditsneutralprecursorasV+oandVo,respectively.Thisdefectisashallowholetrap,anditsassociatedenergiesreectthis.PositivelychargedvacanciescanundergoadramaticrelaxationwheretheSi-Sibondexpandsandbreaks,withoneSiatommovingtotheanti-bondingposition, 41

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Figure2-3. DFTrepresentationofVo. takingthepositivechargealongtoformabondwithanetworkoxygenatom(Fig. 2-2 ).Thisso-calledpuckeredstateisalsoobservedwithEPR,whereitislabeledE0.Thepuckeredstateonlyoccursincasesofpositivechargeandthenonlyforaminorityofthevacancies[ 30 ],[ 52 ],[ 54 ],[ 55 ].However,theorysuggests[ 56 ]thattheneutralprecursorstoE0aredistinctfromthoseofE0.Also,Voisamuchdeeperholetrap.InFLOODS,VoandVoareimplementedasdistinctspecieswithdistincttrappingenergies.Defectscanalsobehydrogenated[ 58 ],ordoublyhydrogenated.Lu,etal.[ 59 ]reviewedthelocalgeometriesthatleadtotheE0congurationsandextractedrulesregardingthepositionofatoms.Then,amillionatommodelofSiO2wasexaminedusingacomputeralgorithmbasedontheserules,withtheconclusionthatapproximately90%ofoxygenvacanciesfavorE0(thedimerconguration),andonly5%favoreachoftheE0congurations.WenotethatDFTarebulkcalculationsonly.Theexistenceoftheoxygen-poortransitionregionattheSiO2/SiinterfacecomplicatestheconclusionsaboutconcentrationofE0speciesattheinterface.TheexistenceandmodelingofthisregionwillbediscussedmoreinChapter 3 ,Section 3.4.2 ,andtheeffectofthisregionontheresultsofourmodelingarediscussedinChapter 4 ,Sections 4.3.2 and 4.3.3 .TheclaimsabovearesupportedbynewerEPRdata[ 60 ]whichreportsthat,immediatelyafterradiation,thereisalargeconcentrationofE0centers,butthat 42

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20hourslaterthisconcentrationisreducedwhiletheconcentrationofE0centershasgrown.ThereasoningisthattheshallowE0wouldcaptureholesatearlytimes(immediatelyafterradiation),butthengivethemuplater,intothedeepE0trapswhichwouldnotgivethemup. 2.2ChargeTrappingandHydrogenReactionsinThermalSiO2Thissectiondiscusseshowprotonsareliberatedasaresultoftheradiation-inducedelectronsandholesinteractingwithH2anddefectsintheoxide.Abriefsummaryisasfollows:Electron-holepairs(EHPs)areinducedbyradiation.Thebuilt-inelectriceldoftheMOSstructureinthetestdevice,whichincludesthelateralPNPbaseoftheteststructure,anisolationoxideaboveit,andametalgate,drivesholes(h+)thatescapeinitialrecombinationtowardstheSiO2/Siinterface,andelectrons(e)]TJ /F1 11.955 Tf 7.08 -4.34 Td[()towardsthegate.Holesarecapturedbyneutraloxygenvacancycomplexes.Electronsmayrecombinewithtrappedholes.Molecularhydrogen(H2),presentintentionallyorunintentionally,canoccupyopeninterstitialregions,andmayreactwithpositivelychargeddefectstocreateprotonsandhydrogenateddefects[ 61 ].Positively-chargedhydrogenateddefectsmaydirectlyreleaseprotons.Theequationsbelowdescribethesereactionsandthecalculatedforwardandreverseenergybarriersincludedinthepresentmodel.Atableofthesereactions,foreasyreference,isincludedinAppendix 7.3 .Interfacequantitieshaveunitsofcm)]TJ /F2 7.97 Tf 6.58 0 Td[(2.Allotherconcentrationsarecm)]TJ /F2 7.97 Tf 6.58 0 Td[(3.Theinterfacereaction,H++Si-H,Nit+H2 (2) c[2011]IEEE.Section 2.2 isreprinted,withpermission,from[N.L.Rowsey,M.E.Law,R.D.Schrimpf,D.M.Fleetwood,B.R.Tuttle,S.T.Pantelides,AQuantitativeModelforELDRSandH2DegradationEffectsinIrradiatedOxidesBasedonFirstPrinciplesCalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2937-2944,Dec.2011]. 43

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whereSi-Harehydrogen-passivateddanglingbondsontheinterface,andNitisthedensityofinterfacetraps,describeshowprotonsthatreachtheSiO2/SiinterfacereacttherewithSi-Hcomplexestoforminterfacetraps[ 62 ],releasingH2.NeutralprecursorstotheE0defect(Vo)aredeep,semi-permanentholetrapslocatedmainlyneartheSiO2/Siinterface.Whenneutral,thisdefectcancaptureahole( 2 ).Whenpositivelycharged,thisdefectcancrackmolecularhydrogentoreleaseaproton( 2 ),orserveasarecombinationcenter( 2 ).Vo+h+,V+oEf0=0.0Er0=4.5 (2)V+o+H2,VoH+H+Ef1=0.5Er1=0.8 (2)V+o+e)]TJ /F3 11.955 Tf 10.41 -4.94 Td[(,VoEf2=0.4Er2=9.0 (2)NeutralprecursorstotheE0defect(Vo)areshallowtrapslocatedthroughouttheSiO2bulk.Thesetrapsacttomodulateholetransport,accountingfortheobservedhoppingbehaviorofholes[ 63 ].Whenneutral,thisdefectcancaptureahole( 2 ).Whenpositivelycharged,thisdefectcanalsocrackmolecularhydrogentoreleaseaproton( 2 ),buttheenergybarrierforittodosoishigh,sothisdoesnotoccuratroomtemperature.Therefore,whenthisdefectispositivelycharged,itservesasarecombinationcenter( 2 ).Vo+h+,V+oEf3=0.0Er3=0.6 (2)V+o+H2,VoH+H+Ef4=1.4Er4=0.8 (2)V+o+e)]TJ /F3 11.955 Tf 10.4 -4.93 Td[(,VoEf5=0.0Er5=9.0 (2)FirstprinciplescalculationspredictthattheVoprecursorexistsintheoxidepriortoirradiationinhighconcentrations,forexample1018cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3.Voprecursorconcentrationsarebelievedtobemuchlower,lessthan1015cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3.Singly-hydrogenatedoxygenvacancydefects,VoHandVoH,whichhaveformedeitherduringhigh-temperatureprocessingsteps[ 30 ],orvia( 2 )and( 2 ),can 44

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captureahole( 2 ),( 2 )anddirectlyreleaseaproton( 2 ),( 2 ),orserveasrecombinationcenters( 2 ),( 2 ).VoH+h+,VoH+Ef6=0.0Er6=4.5 (2)VoH+,Vo+H+Ef7=2.0Er7=1.8 (2)VoH++e)]TJ /F3 11.955 Tf 10.41 -4.94 Td[(,VoHEf8=0.0Er8=7.5 (2)VoH+h+,VoH+Ef9=0.0Er9=0.6 (2)VoH+,Vo+H+Ef10=0.5Er10=0.6 (2)VoH++e)]TJ /F3 11.955 Tf 10.4 -4.94 Td[(,VoHEf11=0.0Er11=3.0 (2)DirectprotondissociationfromVoHhasahighbarrier( 2 ),sothismechanismdoesnotoccuratroomtemperature,butthebarrierfordirectprotondissociationfromaVoHislow( 2 ),comparabletotheH2crackingbarrier( 2 ).WhenasufcientconcentrationofVoHpreexistsintheoxide,thisdirectreleasemechanism( 2 )-( 2 )canaccountforsignicantprotonproduction.However,rstprinciplescalculationsindicatethatsingly-hydrogenatedvacanciesofeithertypepreexistintheoxideonlyatverylowconcentrations,lessthan1015cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3.Itisnotknownhowsignicantlythisconcentrationincreasesduetoprocesseslike( 2 ),( 2 ),( 2 )and( 2 ),tobediscussed.Eventhough( 2 )-( 2 )arenotlikelycandidatesforprotonreleasebasedoninterpretationofrstprinciplesresults,theyareincludedintheFLOODSsimulationsforthreereasons.First,weareabletotestatwhichinitialVoHconcentrationsthesemechanismsbecomesignicant.Second,wewanttoconsiderthemincaseVoHandVoHincreasesignicantlybyothermechanisms.Finally,itisnotpossibletopredictbeforeconductingthesimulationswhethertheVoHdefectscompetesignicantlywiththeotherdefectsforholecapture. 45

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Doubly-hydrogenatedvacancydefects,VoH2andVoH2,haveholecapture( 2 2 ),directprotonrelease( 2 2 ),andrecombinationmechanisms( 2 2 ),similartothesingly-hydrogenateddefects.H2dissociationisalsopossible( 2 2 ).VoH2+h+,VoH+2Ef12=0.0Er12=0.6 (2)VoH+2,VoH+H+Ef13=0.4Er13=0.8 (2)VoH+2,V+o+H2Ef14=0.4Er14=0.6 (2)VoH+2+e)]TJ /F3 11.955 Tf 10.4 -4.93 Td[(,VoH2Ef15=0.0Er15=9.0 (2)VoH2+h+,VoH+2Ef16=0.0Er16=0.6 (2)VoH+2,VoH+H+Ef17=0.4Er17=0.8 (2)VoH+2,V+o+H2Ef18=0.5Er18=1.2 (2)VoH+2+e)]TJ /F3 11.955 Tf 10.41 -4.94 Td[(,VoH2Ef19=0.0Er19=9.0 (2)FirstprinciplesresultsindicatethattheinitialconcentrationofVoH2defectsisapproximately1016cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3.Underthisassumption,reactions( 2 )-( 2 )describethedominantmechanismsofprotonproductionatlowH2concentrations.UnderdifferentassumptionsVoHcanplaythisroleinadditiontoorinsteadofVoH2andVoH2,thoughthedoserateresponsediffersduetotheextraH2mechanism( 2 ). 2.3ExistingDeviceDegradationModelsSeveraldevicedegradationmodelsexistintheliterature,withqualitativeresultsshowinghowcertainkeymechanismscanproducecorrecttrends.WewilldiscusshereonlytheattemptsthataremostsimilartotheFLOODSTCADapproach.Compactmodelsandnon-physics-basedttingmodelswillnotbediscussedhere.Theexampleshighlightedbelowshowtheimportanceofincludingarecombinationmechanisminthemodel,thesuccessofthecrackingreaction,andtheimportanceof 46

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theconcentrationofpre-existingdefects.ThesestudiesalsoshowthedifcultyofttingthecoupledTIDeffectssimultaneously.Chapters4,5,and6willdiscusshowtakingintoaccountDFTinsightsmorefully,suchasthosediscussedintheSection 2.2 ,provideanimproved,quantitativedescriptionoftheTIDphenomenaofinterestinthiswork,namelyinterfacetrapbuildup,oxidechargebuildup,theELDRSeffect,andthedependenceoftheseonhydrogen. Figure2-4. Simulateddegradationvs.doseratecurvefromBoch[ 64 ]usingonlyoneunspeciedrecombinationmechanism.[Reprinted,withpermission,fromJ.Boch,etal.,Physicalmodelforthelow-dose-rateeffectinbipolardevices,IEEETrans.Nucl.Sci.,vol.53,no.6,pp.3658,Figure3,Dec.2006.] 2.3.1RecombinationMechanismsFig. 2-4 showsaninformativeattemptbyBochthatqualitativelymodelstheELDRS,ordoserateeffect,withoneunnamedsimplerecombinationmechanism[ 64 ].ThequalitativesuccessofthismodelshowstheimportanceofrecombinationmechanismsincapturingELDRS. 47

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Figure2-5. DatashowingtheELDRSresponseoftheteststructuresatdifferentH2ambientconcentrations[ 42 ].[Reprinted,withpermission,fromR.L.Pease,etal.,Theeffectsofhydrogenontheenhancedlowdoseratesensitivity(ELDRS)ofbipolarlinearcircuits,IEEETrans.Nucl.Sci.,vol.55,no.6,pp.3170,Figure3,Dec.2008.] 2.3.2TheImportanceoftheCrackingReactionWecanseefromtheELDRSdatabyPease,etal.[ 42 ],reproducedinFig. 2-5 ,thatthedataroughlyfollows,ingeneral,thetrendoutlinedbyHjalmarson'shandcalculation,evenifwelookonlyattheactualdatapoints,andnotthelinesdrawntoguidetheeye.HandapproximationsbyHjalmarson[ 65 ],reproducedinFig. 2-6 neatlyshowthisqualitativetrend,andhighlighttheimportanceofrecombinationinanyphysicalmodellingattempt.Hjalmarsonhasbeenpursuingasimilareffortaspresentedheresince2000[ 66 ].FLOODSalreadyhasmanyofthemathematicaltoolsthatHjalmarsonhadtoimplementhimself,suchastheabilitytodealwithtransienteventsthathappenonvastlydifferenttimescales(suchaspicosecondstotensofyears).Hjalmarson'squalitativematch,reproducedinFig. 2-7 ,showsthepromiseofthephysicalmodelwehaveimplemented.Oursisanimprovementbecauseweareestimatingourreactionenergiesmoreaccurately,usingDFTcalculations.Furthermore,ourMOSsystemandstructure 48

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Figure2-6. ReproducestheresultsofahandcalculationbyHjalmarson[ 65 ],showingthegeneralexpectedtrendoftheELDRScurve.[Reprinted,withpermission,fromH.P.Hjalmarson,etal.,Mechanismsforradiationdose-ratesensitivityofbipolartransistors,IEEETrans.Nucl.Sci.,vol.50,no.6,pp.1904,Figure2,Dec.2003.] (forexample,thedopinginthesilicon)ismuchmoreaccuratelycomparedtotherealdevicesmeasuredforTIDdata.ThesuccessoftheHjalmarson2008modelreiteratestheimportanceofhavingarecombinationmechanismtocapturetheELDRSeffect,andalsoshowstheimportanceofincludingboththeH2crackingreactionandtheH-source(VoHprecursor)reactiontocapturethedifferentELDRSeffectsindifferentH2ambients.Also,HjalmarsonandPeaseinthesepapersaboveconsideredonlyonetypeofoxygenvacancyprecursor.Ourmodelimprovesthisbytakingintoaccountthedifferentenergiesofboththedimerandpuckereddefect. 49

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Figure2-7. CalculationsshowingqualitativematchtoELDRStrend[ 66 ].DFTresultswerenotusedinthismodel.[Reprinted,withpermission,fromH.P.Hjalmarson,etal.,Calculationsofradiationdose-ratesensitivityofbipolartransistors,IEEETrans.Nucl.Sci.,vol.55,no.6,pp.3013,Figure3,Dec.2008.] 2.3.3Pre-ExistingDefectDensityandLocationChen,etal.presentedasimpliedmodelin2009[ 67 ].Theyperformedelectrostaticsteady-statecalculationsona2DrectangleofSiO2,usingwhattheyhypothesizetobethefewkeymechanismsgoverningradiationresponse,addedtotheelectron,hole,andprotoncontinuityequations.Theytreatdirectelectron-holerecombinationasthecoremechanismfortheELDRSeffect,insteadofrecombinationondefectsites.Equation 2 showsthetermtheyusedtoaccountforthisdirectrecombinationintheelectronandholecontinuityequations,RGn,p=recombnp (2) 50

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Figure2-8. Showscalculationsperformedby[ 67 ]atdifferentvaluesofambientH2thatqualitativelymatchELDRSdata.[Reprinted,withpermission,fromX.J.Chen,etal.,Modelingthedoserateresponseandtheeffectsofhydrogeninbipolartechnologies,IEEETrans.Nucl.Sci.,vol.56,no.6,pp.3200,Figure8,Dec.2009.] whererecombistheelectron-holerecombinationreactioncoefcient.Theyalsoincludetheforwardreactionofoneofourequationsabove( 2 )asaprotonproductionmechanism,usingRGH)]TJ /F6 7.97 Tf 6.58 0 Td[(source=rDHp+NDH (2)torepresentthehole-hydrogendefectreactionintheirholeandprotoncontinuityequations,whererDHisthehole-hydrogendefectreactionrateconstant,andNDHistheconcentrationofhydrogen-containingdefects(VoH).Finally,theymodelthepresenceofmolecularhydrogenasareductioninrecombinationefciency,suchthatrecombq(n+p) ox(H2) (2) 51

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wherethefunction(H2)isnotgivenexplicitly.ThistreatmentbasedonlyongeneralionicrecombinationtheorywasabletocapturequalitativelytheELDRSeffect.Chenalsoperformedasensitivityanalysisonhismodelparameters,fromtheresultsofwhichheconcludedthatthesensitivityoftheELDRSresponsetoVoHdefectconcentrationwasveryhigh,comparedtothesensitivitytorecombinationcoefcientsusedinhismodel.OurresultsinChapters 4 5 ,and 6 ,agreewithandexpanduponthisconclusion. 2.4ChapterSummaryIntherstpartofthischapterwepresentedaphysicalmodelfordefect-carrierinteractioninSiO2basedonalonghistoryofexperimentalandtheoreticalinvestigationsintotheatomicnatureofthismaterial.Wethendiscussedpreviousdrift-diffusionmodelingattemptswhichachievedqualitativesuccessindescribingtheELDRSeffectbasedonsimpliedcontinuityequations.Chapter 3 willshowhowwebuildoffthesesimplemodelsinFLOODS,implementinganimproveddescriptionoftheGLPNPtestdeviceandthefullsetofSiO2reactionsdescribedabovewiththeenergeticsfromDFT,withparameterswhichrealisticallymatchexperimentalconditions. 52

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CHAPTER3FLOODSIMPLEMENTATIONInthischapter,wedescribethedevelopmentofaphysics-basedTCADmodelforchargetransportandtrappinginSiO2-on-Sistructuresthatcanquantitativelydescribetheenhancedlow-dose-ratesensitivity(ELDRS)effectobservedinlinearbipolardevices.WedescribetheimplementationofthismodelinFLOODS,theFLoridaObjectOrientedDeviceSimulator[ 68 ],chosenforthisapplicationbecausethecodeiscomputationallyefcientandreadilycustomizable.First,thephysicalstructure,whichwasderivedfromdescriptionsofthestructurein[ 41 ],[ 42 ],and[ 43 ],isdescribedasimplementedinFLOODS.TheexperimentsthemselvesaredescribedindetailinSection 1.2.3 ofChapter 1 .Thebulkandinterfaceequationsthatareusedtocapturetheradiation-inducedbuildupofoxidechargeandinterfacetrapsaredescribedindetail.Next,wediscussthenecessityofpreliminarysolutionstoaidinitialguesses.Finally,weexplainthesensitivityanalysismethodweusedtoexplorethesimulationspace,whichmakesuseofthescriptingandthereforeautomationcapabilitiesofFLOODS.Chapters 4 and 5 willdiscusshowthesensitivityanalysismethodenabledustondthemostdominant,i.e.controllingmechanismsinthemodel,andtoobtainabestmatchtodata. 3.1PhysicalStructureA2Drepresentationofthephysicalteststructureusedby[ 41 ],[ 42 ],and[ 43 ]isshowninFig. 3-1 .Theactual3Dlayoutiscircular[ 69 ].InFLOODS,weimplementedthesensitiveELDRSregionconsistingofthealuminumgate(workfunction=4.1V),the1.2m-thickisolationoxide,andthesiliconn-typebase(Nd=1.1x1015cm)]TJ /F2 7.97 Tf 6.59 0 Td[(1).Thepurposeofthegateistwo-fold:itallowsseparationandextractionofoxidecharge(Not)andinterfacetrapcharge(Nit)viagatebiasingmethodsdescribedinChapter 1 Section 1.2.3 ,anditmimicsactualbipolardevicesinusewhichhavemetallinesrunningacrossisolationoxides. 53

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Figure3-1. 2DrepresentationoftheGLPNPteststructure[ 37 ].InFLOODS,wesimulatetheMOSregioncomprisedofthemetalgate,theisolationoxideabovethebase,wherethedeleteriouschargetrappingtakesplace,andthesiliconbaseregion.[Reprinted,withpermission,fromX.J.Chen,etal.,Behaviorofradiation-induceddefectsinbipolaroxidesduringirradiationandannealinginhydrogen-richand-depletedambients,IEEEIRPS2008,pp.115,Figure1,May2008.] ThisMOScapacitorstructureproducedthesameNotandNitresultsinFLOODSforboth1Dand2D,sothesimulationspresentedinChapters 4 6 willshowall1DMOSsimulationsoftime-dependentchargebuildup.Infuturework,2Dstructureswithsourceanddrainregions(whichwoulddoubleasemitterandcollectorregionsinthishybriddevice)shouldalsobeinvestigatedincasetherateofchargecollectionoftheradiation-inducedEHPsinthesiliconaffectchargetrappingandtransportintheSiO2.Here,wehavefocusedontheSiO2region,sinceelectronandholetransportismuchfasterinsilicon,andsincechargetrapsaremuchdeeperinSiO2. 3.2BulkPhysicsIntypicaldevicemodeling,nitevolumeandniteelementmethodsareusedtodiscretizeandsolvethecoupled,nonlineardrift-diffusioncontinuityequationswithPoisson'sequationona1-to3-Dmeshofarealisticdevice,calculatingelectrostatic 54

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potentialdistributionsandelectronandholeconcentrationsthroughoutthestructurebothinsteadystateoratvarioustimesteps[ 70 71 ].SiO2,oranyoxide,isusuallytreatedasanidealinsulator.Inotherwords,itistypicallyassumedthatneithermobilenorxedchargesexistintheoxide,andthatthereforetheelectriceldorelectrostaticpotentialdropacrosstheoxide,asdeterminedbyPoisson'sequationwithcharge=0,isconstant.Inthiscase,theelectrostaticpotentialoneithersideoftheinsulator,i.e.inthegateandsemiconductor,aretheboundaryconditionsforfullsolutionoftheproblem.However,inreality,chargecanbegeneratedinorinjectedintotheoxide,orontotheoxide/semiconductorinterface[ 16 ].Ionizingradiationisonesuchenvironmentalphenomenonthatisenergeticenoughtocreatecharge,intheformofelectron-holepairs,acrosseventhe9eVbandgapofSiO2.Theseelectronsandholesareknowntointeractwithoxygenvacancycomplexesandhydrogenousspeciespresentintheoxide,eventuallyleadingtoxedchargecenters(deepholetraps)[ 72 ],[ 54 ],andinterfacetrapbuildup[ 73 ],[ 74 ].Tonumericallyaccountforchargetransportanddefectinteractions,SiO2cannolongerbetreatedasahomogeneousinsulator.Here,SiO2istreatedasawideband-gapsemiconductor;drift-diffusioncontinuityequationsarespeciedintheoxideforeachspecies,usingappropriatevaluesofdiffusivityandmobilityforeachmobileparticlebeingsimulatedintheoxide.ThissectiondescribeshowthemaindeviceequationsarespeciedinFLOODS,includingrecombination/generation(RG)termswhichaccountforradiation-inducedEHPgeneration,andRGtermsderivedfromthechargetrappingreactionsdescribedindetailinChapter 2 3.2.1Drift-DiffusionModeling 3.2.1.1BulksiliconInsilicon,thesolutionvariablesareelectrostaticpotential,electrons,andholes.Poisson'sequationrelatestheelectrostaticpotential,,tothechargedensity,Q,viar2=)]TJ /F5 11.955 Tf 9.3 0 Td[(Q, (3) 55

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whereisthematerial-dependentpermittivity.Theionizeddopantatomsinsiliconarexedpointcharges,andassuchmustbeincludedinPoisson'sequation:QSi=q(n)]TJ /F5 11.955 Tf 11.96 0 Td[(p+N+d)]TJ /F5 11.955 Tf 11.96 0 Td[(N)]TJ /F6 7.97 Tf -.94 -7.89 Td[(a) (3)whereqisthechargeonanelectron,andN+dandN)]TJ /F6 7.97 Tf -.94 -7.29 Td[(aaretheionizeddopantsinthesilicon.TheFLOODSimplementationis setstr"eps*grad(DevPsi)-Hole+Elec+Ndplus-Naminus"pdbSetStringSiliconDevPsiEquation$strTheionizeddopantconcentrationsareknown,anddonotchangeinconcentration,andsothesepointdefectswillnothaveacontinuity,orddt(),equation.Electronsandholesarechargedandmobile,andsobothdriftanddiffusionmustbothbeaccountedfor.Inaddition,RGterms,whichwillbediscussedspecicallyinSections 3.2.2 and 3.2.3 ,mustalsobeincludedinthecontinuityequations.Inthissection,anetrecominationterm,U,foreachspeciesisusedforsimplicity.The1Delectronandholecontinuityequationsforsiliconaredn dt=1 qr(qnnF+qDndn dx))]TJ /F5 11.955 Tf 11.95 0 Td[(Un (3)dp dt=)]TJ /F9 11.955 Tf 10.73 8.08 Td[(1 qr(qppF)]TJ /F5 11.955 Tf 11.96 0 Td[(qDpdp dx))]TJ /F5 11.955 Tf 11.96 0 Td[(Up, (3)wheren,paretheelectronandholemobilities,Fiselectriceld,Dn,paretheelectronandholediffusioncoefcients,andUn,pisthenetrecombinationandgeneration(RG)ofelectronsandholes.InFLOODS,thesgrad()operatoraccountsforbothdriftanddiffusiontogether.ThisoperatorisdenedusingtheScharfetter-Gummelmethod[ 70 ],whichisnite-volumetechniquethathasbeenverysuccessfulinefcientlydiscretizingthecontinuityequationsforcarriertransportinsemiconductors.TheFLOODSimplementationforelectronandholetransportinsiliconisasfollows: setstrE"ddt(Elec)-MOB*sgrad(Elec,+DevPsi/Vt)+Un" 56

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setstrH"ddt(Hole)+MOB*sgrad(Hole,-DevPsi/Vt)+Up"pdbSetStringSiliconElecEquation$strEpdbSetStringSiliconHoleEquation$strH 3.2.1.2BulkSiO2SurveyingthechargetrappingreactionsfromChapter 2 ,wendthatthelistofsolutionvariablesinSiO2comprisesofelectrostaticpotential,electrons,holes,protons(H+),molecularhydrogen(H2),theunchargedoxygenvacancies(Vo,,Vo,H,andVo,H2),whichareunchargedpointdefects,andthechargedoxygenvacancies(V+o,,Vo,H+,andVo,H+2),whicharechargedpointdefects.AllthechargedspeciesmustbeincludedinPoisson'sequation:QSiO2=q(n)]TJ /F5 11.955 Tf 11.96 0 Td[(p+H++V+o+V+o+VoH++VoH++VoH+2+VoH+2), (3)andtheFLOODSimplementationis setstr"eps*grad(DevPsi)-Hole+Elec-Hplus-VoGplus-VoDplus"appendstr"-VoGHplus-VoDHplus-VoGH2plus-VoDH2plus"pdbSetStringOxideDevPsiEquation$strInaddition,positivelychargedinterfacetraps,Nit,contributeaspositivechargeontheSiO2/Siinterfacenode.ThisimplementationwillbediscussedinSection 3.3 .ContinuityequationsareconstructedinFLOODSforeachspeciesmodeledintheSiO2.Staticspeciesthatdonotchangeinconcentration,suchasN+dinsilicon,donotrequireacontinuityequation.Butstaticspeciesthatdochangeinconcentration,suchastheoxygenvacancycomplexes,requireacontinuityequationwithRGterms.Mobilespeciesthatarenotcharged,suchasH2,requirediffusionandRGterms.Finally,specieswhicharechargedandmobilerequiredrift-diffusionandRGterms. 57

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Forexample,electrons,holes,andprotonsarechargedandmobile:dn dt=1 qr(qnnF+qDndn dx))]TJ /F5 11.955 Tf 11.96 0 Td[(Un (3)dp dt=)]TJ /F9 11.955 Tf 10.73 8.09 Td[(1 qr(qppF)]TJ /F5 11.955 Tf 11.96 0 Td[(qDpdp dx))]TJ /F5 11.955 Tf 11.96 0 Td[(Up (3)dH+ dt=1 qr(qH+H+F+qDH+dH+ dx))]TJ /F5 11.955 Tf 11.96 0 Td[(UH+, (3)withdrift-diffusionspeciedinFLOODSwiththesgrad()operator setstrE"ddt(Elec)-MOB*sgrad(Elec,+DevPsi/Vt)+UnetElec"setstrH"ddt(Hole)+MOB*sgrad(Hole,-DevPsi/Vt)+UnetHole"setstrHp"ddt(Hplus)+MOB*sgrad(Hplus,-DevPsi/Vt)+UnetHplus"pdbSetStringOxideElecEquation$strEpdbSetStringOxideHoleEquation$strHpdbSetStringOxideHplusEquation$strHpMolecularhydrogenismobile,butnotcharged: setstr"ddt(H2)-MOB*grad(H2)+UnetH2"pdbSetStringOxideH2Equation$strwhichisaccountedforinFLOODSbythegrad()operator: setstr"ddt(H2)+D*grad(H2)+UnetH2"pdbSetStringOxideH2Equation$strPointdefectsarenotmobile,sohaveneitherdriftnordiffusion,butstillhavenetRGduetochargetrapping: pdbSetStringOxideVoGEquation"ddt(VoG)-UnetVo"pdbSetStringOxideVoDHEquation"ddt(VoDH)-UnetVoDH"pdbSetStringOxideVoGplusEquation"ddt(VoGplus)-UnetVoGplus"... 58

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3.2.1.3FLOODSscriptingandautomationInputingequationsbyhandformorethanthreespeciesgetsverycumbersome,andcanleadtocarelesserrors.Instead,aTclprocedureisusedthatwilltakethenameofeachvariable,andsomeinformationaboutthevariable,suchaswhetheritischargedandmobile,orxedanduncharged,tobuildacontinuityequationautomatically.Forexample,theprocedureAddSpecies procAddSpecies{NameMatConstValCharge}{seteqn"ddt(\$Name)"if{$Const=="D"}{appendeqn"-$Val*grad($Name)"pdbSetBoolean$Mat$Namemobile_yn1}if{$Const=="MOB"}{if{$Charge=="-"}{appendeqn"-$Val*Vt*sgrad(($Name),+DevPsi/Vt)"}if{$Charge=="+"}{appendeqn"-$Val*Vt*sgrad(($Name),-DevPsi/Vt)"}pdbSetBoolean$Mat$Namemobile_yn1}#AddchargedtermstoPoissonEquationif{$Charge!="0"}{if={[pdbIsAvailable$MatDevPsiEquation]}{seteqnP[pdbGetString$MatDevPsiEquation]seteqnP[appendeqnP"$Charge$Name"]pdbSetString$MatDevPsiEquation$eqnPputs"AmendingPoissonEqnin$Matto:$eqnP"} 59

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}#Storethetransportequationinthepdbputs"Adding$NameEquationin$Mat:$eqn"pdbSetString$Mat$NameEquation$eqn#forunderstandingthetypeofspeciesforthek-calcpdbSetString$Mat$NameConst$ConstpdbSetString$Mat$NameCharge$Charge}takesthespeciesname,itstransporttype(MOBfordrift-diffusion,Dfordiffusion,or0forxed),thevalueofthatconstant(mobilityincm2V)]TJ /F2 7.97 Tf 6.59 0 Td[(1s)]TJ /F2 7.97 Tf 6.58 0 Td[(1,diffusionincm2s)]TJ /F2 7.97 Tf 6.59 0 Td[(1,or0forxed)anditschargetype(+/-/0),andbuildstheappropriatecontinuityequationbasedonthisinformation,andalsoaddsanychargedspeciestoPoisson'sequation.Inthisway,manyspeciescanbeadded,withtheirequationsandparameterseasilyorganized: #Example:ProcedureNameMatConstValCharge#------------------------------------------------AddSpeciesH2OxideD1.7e-150Diffusivity(D)andmobility(orMOBinFLOODS)aredenedviatheArrheniusrelationship:D=D0exp()]TJ /F5 11.955 Tf 9.3 0 Td[(Ed kT) (3)andtheEinsteinrelation:=Dq kT (3)ThevaluesforEdareinformedbyDFTcalculationsasdiscussedinChapter 2 ,andaresummarizedinTable 3-1 .Thevaluesformobilityanddiffusivityaretakenfrom[ 16 ],andaresummarizedinTable 3-2 60

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Table3-1. Diffusivity ParameterValue(eV) Ed(n)0.0Ed(p)0.0Ed(H2)0.38Ed(H+)0.80 Table3-2. Mobility ParameterValue(cm2/s) n20.0p1.0e-5H21.0e-9H+1.0e-11 3.2.2RadiationModelRadiation-inducedEHPionizationandrecombinationininsulatorshasbeenactivelystudiedalmostsincethediscoveryofthedifferentformsofionizingradiationbyRoentgenandBecquerelin1895and1896[ 16 ].Here,weaccountfortheeffectofthe60CoirradiationofourMOScapacitorstructureviaanEHPgenerationterm[ 23 ],p.13-17 Uradiation=Yfg0Rd.(3)Rdisthedoserateoftheradiationinrad(SiO2/s).g0istheinitialEHPdensityperunitdoseofradiation.ThisiscalculatedfromtheEHPcreationenergy,Ep,inSiO2,whichwasdeterminedbyAusmanandMcLean[ 21 ]tobe183eV,basedonexperimentalresultsofCurtis,etal.[ 21 ].Amorerecentsetofmeasurementsdeterminedthisnumbermoreaccuratelytobe171eV[ 22 ].FromEp,theinitialEHPdensityperunitdoseofradiation,g0,isdeterminedtobetobe8.1e12cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3rad)]TJ /F2 7.97 Tf 6.59 0 Td[(1(SiO2),usingthedenitionoftherad:1rad=100erg/g=6.24e13eV/g,andthedensityofSiO2:2.3g/cm3.Thestraightforwardderivationofg0iscomplicatedbywhatisoftencalledinitialrecombination,andwhichreferstothedirectrecombinationofEHPswiththeirexactpartnersveryquicklyaftercreation.ThefractionofelectronsandholessurvivinginitialrecombinationisafunctionoftheaveragethermalseparationdistanceofEHPs, 61

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determinedbytheincidentparticletypeandenergy,andthetargetmaterial[ 16 ],[ 23 ].Theinitialrecombinationproblemhasbeentreatedanalyticallyfortwolimitingcases.Thersttreatmentisapplicablewhentheaverageseparationdistancebetweeneachelectronandholeinagivenpairissmall.Inthiscase,electronsandholescanbeconsideredtoexistinacylindricaldistributionaroundthetrackoftheincidentparticle,andisthustermedcolumnarrecombination[ 16 ].ThesecondtreatmentisapplicablewhenEHPsarecreatedrelativelyfarapart.TheEHPsinducedinSiO2bythehigh-energysecondaryelectronsfromCo-60-raysaregeneratedquitesparselyand,asdiscussedinSection 1.2.1 ofChapter 1 ,thegeminatemodeltsexperimentalresultswell,forbothenergeticelectronsand-rayirradiation[ 16 ],[ 23 ].ItmaybepossibletoincludeafullsolutionofgeminaterecombinationofinitialEHPsinFLOODS.Thistreatmentwouldbeideal,butisbeyondthescopeofthisworkandwouldrequireovercomingsignicantsimulationchallenges.Onesignicantchallengeisincludinginthedependenceoftheelectriceld,whichactstoseparateEHPs,andwhichisnotasolutionvariableinFLOODS,butinsteadarstderivativeofasolutionvariable.Anotherchallengeisthatcomputationaldifcultiesmayariseifextremelysmallgridspacingisrequiredtoresolvethedistancebetweentheelectronsandholesineachpair.ThegeminatemodelandpossibleFLOODSimplementationsarediscussedmoreinthefutureworksectionofChapter 7 .Here,weuseY,oryield,asasimpliednumericalparameterthatcanbevariedbetween0.0and1.0,toquantifythepercentofelectronsandholessurvivinginitialrecombination.BasedontheexperimentalresultsofShaneyfelt,etal.[ 75 ]ofMOSdevicesunderdifferentbiases,theyieldinourcase(0Vonthegate)is0.01.Followingtheexperimentalconditionsof[ 41 ],[ 42 ],and[ 43 ],transientFLOODSsimulationsarecarriedoutwhichincludetheradiationgenerationterm( 3 )forthetimeittakestoreachtotaldose(whichisdifferentforeachdose-rate).Forexample,theFLOODSimplementationofthisterminsiliconis 62

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setstrDP"eps*grad(DevPsi)+Ndminus-Naplus-Elec+Hole"setstrE"ddt(Elec)-MOB*sgrad(Elec,Vt)+Uradiation_Si"setstrH"ddt(Hole)+MOB*sgrad(Hole,Vt)+Uradiation_Si"pdbSetStringSiliconDevPsiEquation"$strDP"pdbSetStringSiliconElecEquation"$strE"pdbSetStringSiliconHoleEquation"$strH"Subsequently,theradiationgenerationtermisremovedfromtheelectronandholecontinuityequations,andanothertransientsimulationiscarriedoutfor10minutes.This10-minrelaxingorannealingtimesimulatesthetimeittookfortheexperimentaliststowalkbetweenirradiationandmeasurementlabs.Insomeexperiments,irradiateddeviceswereintentiallyallowedtorestforlongertimes.Inthesecases,wehavematchedtheannealingtimeinoursimulationstothetimeindicatedbytheauthorsoftheexperimentalwork.ThegeneralparametersfortheradiationmodelimplementedinFLOODSaresumarizedinTable 3-3 Table3-3. Radiationparameters ParameterSymbolValue generationg08.1e12EHP/rad/cm3totaldoseRADtot3.0e4raddoserateRd10)]TJ /F2 7.97 Tf 6.58 0 Td[(4-104timeirradiatedtrad(RADtot/Rd)sreadtimetreadtrad+10minyieldY0.01(varied) 3.2.3RecombinationandGenerationDuetoChargeTrappingRecombinationandgenerationofspeciesalsoarisesfromthechemicalreactionsusedtodescribethechargetrappinganddetrappingthatweconsiderinourmodel(Chapter 2 ).Eachtermisbuiltbasedonenergybalanceequations[ 76 ],withreactionratesformulatedfromtheenergeticscalculatedbyDFT. 63

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3.2.3.1RGtermsConsiderthersttwobulkreactionsfromChapter 2 ,Vo+h+,V+oEf0=0.0Er0=4.5 (3)V+o+H2,VoH+H+Ef1=0.5Er1=0.8, (3)underequilibrium.Fromthelawofmassaction,theconcentrationsofallthespeciesarerelatedinequilibriumviakf0[Vo][h+]=kr0[V+o] (3)kf1[V+o][H2]=kr1[VoH][H+] (3)wherethebracketindicatesconcentrationofthespeciesincm)]TJ /F2 7.97 Tf 6.59 0 Td[(3,andkfandkrarereactionrates,relatedtotheequilibriumconstantforthereactionvia Ceq=kf kr(3)Equations( 3 )and( 3 )abovearetrueinequilibrium.Fornon-equilibriumconditions,therewillbeeithernetrecombinationorgenerationofeachspeciesinvolvedinareaction.IntheFLOODSmodel,anRGtermisassembledforeachreaction,andthenthistermisthenaddedtoeachcontinuityequationinwhichspeciesarebeinggenerated,andsubtractedfromeachcontinuityequationforwhichspeciesarerecombining.Forexample,in( 3 ),orReaction0(R0),V+oisbeinggeneratedaccordingtoGV+o,R0=kf0[Vo][h+])]TJ /F5 11.955 Tf 11.95 0 Td[(kr0[V+o] (3)andVoandh+arerecombiningaccordingtoGh+,R0=kr0[V+o])]TJ /F5 11.955 Tf 11.96 0 Td[(kf0[Vo][h+] (3) 64

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Sincethesetermsaretheoppositeofeachother,wecansimplycreateonerecombination/generationtermforeachreaction:RG0=kf0[Vo][h+])]TJ /F5 11.955 Tf 11.95 0 Td[(kr0[V+o] (3)whichmustthenbesubtractedfromthecontinuityequationforeachspeciesonthelefthandsideofthereaction,andaddedtothethecontinuityequationforeachspeciesontherighthandsideoftheequation.Inotherwords,RG0mustbesubtractedfromthecontinuityequationsforVoandh+,andaddedtothecontinuityequationforV+o.WecanfollowthesameprocedureforReaction1(R1)in( 3 ):RG1=kf1[V+o][H2])]TJ /F5 11.955 Tf 11.95 0 Td[(kr1[VoH][H+]. (3)RG1mustbesubtractedfromthecontinuityequationsforV+oandH2,andaddedtothecontinuityequationsforVoHandH+.Thisproceduremayseemsimplewithonlytworeactionstoconsider,buttheprocesscangetconfusingandpronetoerrorasmorereactionsareadded.However,theprocessofaddingtheRGtermsduetoreactionsforeachappropriatecontinuityequationcanbeautomatedusingTclscriptinginFLOODS.ForthesimulationsinChapters 4 6 ,wecreatedanautomatedscriptthatparsedreactionsinputtedassimpletext,builttheRGterms,thenaddedorsubtractedthemfromtheappropriatecontinuityequations,allowingeasychangingofreactionsorreactionenergeticsforall20reactions. 3.2.3.2FormulationofthereactionratesFollowing[ 77 ],thereactionsrateskfandkrareformulatedbasedontheenergetics,EfandErofeachrespectivereaction,ascalculatedbyrstprinciplescalculations.Therearethreecasesofinterest:1)amobilespeciescombineswithastaticspecies,overcomingareactionbarrierthatislargerthanthediffusionbarrier,2)amobilespeciescombineswithastaticspecies,butthereactionbarrierislowerthanthediffusionbarrier, 65

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Figure3-2. Energydiagramshowingdiffusionandreactionenergiesintheforwardandreversedirections. and3)amobilespeciesescapesfromastaticspecies.ThepotentialenergydiagramsforthethreecasesareshowninFig. 3-2 .Theequationsforeachcaseareasfollows:(case1)kint=LcDexp)]TJ /F9 11.955 Tf 9.3 0 Td[((Ebar)]TJ /F5 11.955 Tf 11.95 0 Td[(Ed) kBT (3)(case2)kint=2LcD (3)(case3)kint=fexp)]TJ /F9 11.955 Tf 9.3 0 Td[((Et) kBT, (3)Lcisanestimatedcriticallengthorcriticaldistancebeyondwhichthemobileparticlecannotseethetrap,butlessthanwhichthemobileparticlewilldenitelybecapturedbythetrap.Thisdistanceisontheorderofafewatomicspacingsforunchargedinteractions.Ifoneormoreoftheparticlesischarged,thenthisdistancecanbeestimatedtobelarger.Disthediffusivityofthemobilespecies.TheEinsteinrelationisusedtoconvertbetweenmobilityanddiffusivity.Ebaristhereactionbarrierobtained 66

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fromrstprinciplescalculations.Edisthediffusionenergyofthemobilespecies.ItissubtractedfromEbarinordertoavoiddoublecountingdiffusionthroughbothDandthereactionkinetics.Etisthetrapenergy,ortrapdepth.fistheattempttoescapefrequencyofthetrappedparticle.kBisBoltzmann'sconstant,andTistemperature.Inalloursimulations,temperaturewasspeciedas300K,orroomtemperature,matchingtheconditionsoftheexperimentsof[ 41 ],[ 42 ],and[ 43 ].Thechemicalreactions,theircorrespondingenergybarriers(informedbyDFTcalculationsasdiscussedinChapter 2 ),andtheresultingvaluesofkaresummarizedinTable 3-4 .ThevaluesusedforLcandfaresummarizedinTables 3-6 and 3-7 .Table 3-5 showstheeffectvariousenergyvalueshaveonthereactionrate.Becauseoftheexponential,raisingtheenergybarrieronly0.1eVdecreasesthereactionratebyapproximatelytwoordersofmagnitude.Thiswouldbeequivalenttodecreasingadefectorcarrierdensitybytwoordersofmagnitude.ItisforthisreasonthatLccanbeestimated,becauseitonlyaffectskonalinearscale.Inaddition,itisimportanttokeepinmindthatthediffusionenergymustbesubtractedfromthereactionenergybarrierin 3 ,meaningthatsomeenergieslistedwiththereactionequationsinChapter 2 thatmaylookhighonrstglancemayactuallybelowerdependingonifoneofthereactingspecieshasahighdiffusionenergy. 3.3BoundaryConditionsForallotherboundariesthanthosespeciedinthissection,areectiveboundaryconditionisused.Electrostaticpotentialisspeciedtobecontinuousacrossallboundaries.Thesubstratecontacttothesiliconisdenedasohmic,andthealuminumgatecontactisdenedbyaworkfunctiondifferenceof4.1V. 3.3.1ElectronandHoleTransportfromSiO2toSiandAlElectronsandholesleavefreelythroughthegatecontact: SRVn)]TJ /F6 7.97 Tf 6.58 0 Td[(gate(nSiO2)]TJ /F4 11.955 Tf 11.96 0 Td[(small)(3) 67

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Table3-4. Reactionenergiesandresultantkvalues Reaction(eV)Ef(eV)Er(eV)kf(cm3/s)kr(cm3/s) R0Vo+h+,V+o0.04.51.03e-131.26e-62R1V+o+H2,VoH+H+0.50.81.92e-191.03e-19R2V+o+e)]TJ /F3 11.955 Tf 10.4 -4.34 Td[(,Vo0.49.01.97e-143.21e-138R3Vo+h+,V+o0.00.61.03e-134.16e+3R4V+o+H2,VoH+H+1.40.81.46e-341.03e-19R5V+o+e)]TJ /F3 11.955 Tf 10.41 -4.34 Td[(,Vo0.09.02.06e-073.21e-138R6VoH+h+,VoH+0.04.51.03e-131.26e-62R7VoH+,Vo+H+2.01.85.04e-228.21e-37R8VoH++e)]TJ /F3 11.955 Tf 10.4 -4.34 Td[(,VoH0.07.52.06e-075.07e-113R9VoH+h+,VoH+0.00.61.03e-134.16e+3R10VoH+,Vo+H+0.40.63.81e+51.03e-19R11VoH++e)]TJ /F3 11.955 Tf 10.41 -4.34 Td[(,VoH0.03.02.06e-072.00e-37R12VoH2+h+,VoH+20.00.61.03e-134.16e+3R13VoH+2,VoH+H+0.40.83.81e+51.03e-19R14VoH+2,V+o+H20.40.61.90e+54.02e-21R15VoH+2+e)]TJ /F3 11.955 Tf 10.4 -4.34 Td[(,VoH0.09.02.06e-073.21e-138R16VoH2+h+,VoH+20.00.61.03e-134.16e+3R17VoH+2,VoH+H+0.40.83.81e+51.03e-19R18VoH+2,V+o+H20.51.23.98e+33.35e-31R19VoH+2+e)]TJ /F3 11.955 Tf 10.41 -4.34 Td[(,VoH0.09.02.06e-073.21e-138 Table3-5. Numericaleffectofasampleofenergies E(eV)exp)]TJ /F6 7.97 Tf 6.59 0 Td[(E kBT 0.01.00.11.83e-020.23.35e-040.36.14e-060.41.13e-070.52.06e-091.04.25e-182.01.80e-35 Table3-6. Criticallength ParameterValue(nm) L+=)]TJ /F6 7.97 Tf -10.82 -7.67 Td[(c2.0L0c0.2 68

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Table3-7. Attempttoescapefrequency ParameterValue(s)]TJ /F2 7.97 Tf 6.59 0 Td[(1) fn5.0e13fp5.0e13fH+2.0e12fH21.0e12 SRVp)]TJ /F6 7.97 Tf 6.58 0 Td[(gate(pSiO2)]TJ /F4 11.955 Tf 11.96 0 Td[(small)(3)andholesexitfreelyfromtheSiO2intoSi,butnottheotherwayaround: SRVp)]TJ /F6 7.97 Tf 6.58 0 Td[(Si(pSiO2)]TJ /F4 11.955 Tf 11.95 0 Td[(small)(3)Intheseequations,SRVissurfacerecombinationvelocity,whichissetnominallyto106cm/s,whichmodelsanohmiccontact(thecarriersleaveassoonastheygetthere);smallisasmallnumber(1e-300),closetozero,representingtheequilibriumconcentrationofthecarrierinquestionattheboundaryontheSiO2side.Alsoimplementedistheoptiontoaccountforattheinterface,andinthiscase,theequilibriumconcentrationofholesandelectronsbasedonaMaxwell-Boltzmanndistributionisusedinstead,thoughthisisstillaverysmallnumber. 3.3.2InterfaceTrapReactionTheprotonscreatedthroughthevariousreactionsinChapter 2 canmigratetotheSi/SiO2interfaceviadriftanddiffusionandcreatepositivelychargeddanglingbonds(DB+)there[ 62 ],increasingtheinterfacetrapconcentration(Nit)asdescribedby: H++SiHint,DB+int+H2(3)suchthatthecontinuityequationforinterfacetrapdensityinonedimensionis: dNit dt=kint[H+int][SiHint](3)where[H+int]istheconcentrationofprotonsneartheinterface,[SiHint]isthearealconcentrationofhydrogen-passivateddanglingbondsattheinterface,andkintisthe 69

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effectiverateofthisinterfacereaction.Thereversereactionisassumedtobenegligibleatroomtemperature.TheFLOODSimplementationis #Hplusgetstrappedoninterface,replaceSiH=1e13-NitbyhandsetSiH_int_IC1e13;#initialSiHconconintsetRG_int"$kf_int*(Hplus_Oxide)*($SiH_int_IC-Nit)"appendRG_int"-$kr_int*(Nit)*(H2_Oxide)";#RGtermpdbSetStringOxide_SiliconNitEquation"ddt(Nit)-($RG_int)"pdbSetStringOxide_SiliconHplusEquation_Oxide"-($RG_int)";#lossfromOxidepdbSetStringOxide_SiliconDevPsiEquation"-Nit";#addNittoPoissonInthisimplementation,H+lossfromtheSiO2isaccountedfor,andNitisaddedtoPoisson'sEquation,sinceitispositivelycharged. 3.4InitialConditions 3.4.1GeneralAssumedQuantitiesTheinitialconcentrationofsomeofthespeciesinourmodelarerelativelywell-knownquantities.ThesevaluesaresumarizedinTable 3-8 .However,asdiscussedinChapter 2 ,thepre-existingconcentrationofdefectsinSiO2arearelativelyunknownquantity.DFTcalculationssuggestrelativeconcentrationsofdifferentpre-existingtrapspecies,andorderofmagnitudeestimatesoftheactualconcentrationofVoandVodefectshavebeensuggestedbyetch-backexperimentsofirradiatedoxides,wheretheauthorsattemptedtollallholetraps,andthenmeasuredV+oandV+odensities[ 78 79 ].Table 3-9 summarizetheseestimates. 3.4.2Oxygen-PoorInterfaceTransitionRegionFLOODSmodelsstructureswithahardanddenitiveboundarybetweenmaterialregions.Butinreality,thereexistsanoxygen-poorandthereforedefect-intensiveinterfacetransitionregionbetweentheSisubstrateandtheSiO2,approximately3-5nminthickness[ 16 23 ].TheconcentrationproleofdefectsintheSiO2most 70

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Table3-8. Initialconditions:well-knownICs ParameterValue H21011-1018cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3H+1.0e-300cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3V+o1.0e-300cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3V+o1.0e-300cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3VoH+1.0e-300cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3VoH+1.0e-300cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3VoH+21.0e-300cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3VoH+21.0e-300cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3Nit1.0e7cm)]TJ /F2 7.97 Tf 6.58 0 Td[(2SiHinterface1.0e13cm)]TJ /F2 7.97 Tf 6.59 0 Td[(2 Table3-9. Initialconditions:bulkpre-existingdefectconcentrations DefectPrecursorbulkconcentration(cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3) Vo1.0e15Vo1.0e18VoH1.0e14VoH1.0e14VoH21.0e16VoH21.0e16 probablylookslikeacomplementaryerror-functionneartheSiO2/Siinterface,duetothedependenceofdefectformationondiffusionofoxygenspecies[ 79 ],withsomebackgrounddefectconcentrationinthebulkoftheSiO2.AearlymeasurementoftheoxygentosiliconratioversusoxidethicknessinthisdisorderedsurfacelayerisreproducedinFig. 3-3 [ 80 ].Agridspacingoflessthan1Aisrequiredtoresolvetheshapeofanerrorfunctionina4-nmregion.Thiswouldprohibitedtransientorhigherdimensionalsolutionsbecauseoftimeandmemoryconstraints.Becauseofthis,inFLOODS,weimplementedasimpliedinitialconcentrationproleforpre-existingdefectstoapproximatethistransitionregion.Weusedaconstantbulkconcentrationcm)]TJ /F2 7.97 Tf 6.58 0 Td[(3,addedtoa4-or5-nmthickregionofhigherconcentrationneartheinterface,arectangularfunction.Inaddition,thishigh-concentrationtransitionareahadtobeshiftedoffthelastSiO2node 71

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Figure3-3. Measuredratioofoxygentosiliconvs.oxidedepth.TheratiofallsoffquicklyneartheSiinterface.From[ 80 ].[ReprintedwithpermissionfromT.W.Sigmon,etal.,Stoichiometryofthinsiliconoxidelayersonsilicon,AppliedPhysicsLetters,vol.24,no.3,pp.106,Figure2,Feb.1974.Copyright1974,AmericanInstituteofPhysics.] neartheinterfaceinordertonotinterferewiththeholeboundaryconditionthere,whichtransportsmostholesintothesilicon. 3.5SolvingAtransientcalculationisrequiredtosimulatetheexperimentsof[ 41 ],[ 42 ],and[ 43 ].However,beforeatransientcalculationcanbecarrierout,thesystemmustrstbesolvedinequilibrium(DC).Obtainingconvergenceofelectronsandholesintheoxidecanbeachallengeduetotheverysmallconcentrationsthere.SolvingPoisson'sequationalonerst,thenusingthissolutionasaninitialguessforthefullDCsolvewasrequired. 72

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3.5.1PreliminaryPoisson-OnlySolutionToachieveconvergenceforthenumericalsolutionofthecoupled,non-linearPoissonandcontinuityequations,itwasnecessarytorstperformaPoisson-onlysolution.Inotherwords,werstsolvedonlyelectrostaticpotentialasanindependentvariableinPoisson'sequation,andthenpluggedthissolutionintotheBoltzmannrelationsforelectronsandholestosimplycalculateelectronsandholes.Inthissimplecalculation,theFermilevelswereassumedconstant,denedbyappliedbiases.TheFLOODSimplementationforthisstepat0-biasis solutionaddname=DevPsipdedampcontinuous#usingthePoissonequationasdefinedaboveforDevPsisolutionaddSiliconname=Elecconstval=(Nc*exp(-Ec-0.0/kT))solutionaddSiliconname=Holeconstval=(Nv*exp(-0.0-Ev/kT))solutionaddOxidename=Elecconstval=(Nc*exp(-Ec-0.0/kT))solutionaddOxidename=Holeconstval=(Nv*exp(-0.0-Ev/kT))whereNc,Nv,Ec,andEvareappropriatelydenedforeachmaterial.The0.0representsthevalueoftheFermilevelwhenthesiliconisbiasedat0V.Ifthe0ofpotentialisdeneddifferently,orifthesiliconisbiasedatadifferentvalue,thenthisvaluewillhavetobechanged.AsimpleinitialguesswillsufceforaPoisson-onlysolution: selz=-4.1name=DevPsideviceThesolutionsinthissimpliedcaseissavedbyFLOODS,andcannowserveasaninitialguessforthefullDCsolution: solutionaddname=DevPsipdedampcontinuoussolutionaddname=Elecpde!negativesolutionaddname=Holepde!negative#usingthePoissonandcontinuityequations 73

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#asdefinedaboveforDevPsi,Elec,andHoledeviceinitModelingtheoxideasawidebandgapsemiconductorrequiresthisinitialPoisson-onlysolvebecauseequilibriumelectronandholeconcentrationsaresosmallthatconvergenceisdifcultotherwise. 3.5.2DCandTransientCalculationsBeforecarryingoutanytransientsimulation,werstsolvethesysteminDC,orequilibrium,toensurewearestartingwithasteady-statesystembeforeweperturbitwithradiation.FortheDCsolution,norecombination/generationtermsareincludedinthecontinuityequations.Finally,thetime-dependentcalculationisperformed.Justaseachdatapointontheexperimentalcurvesof[ 41 ],[ 42 ],and[ 43 ]representsadifferentexperimentalresultindifferentenvironmentalconditions,aseparatetransientsimulationisrequiredtomatcheachpoint.Thismeansthatatleast10transientsimulationsarerequiredforeachgureshowninChapters 4 6 .PreliminaryPoisson-onlyandDCsolveswerecarriedoutbeforealltransientsimulations.Scriptingwasusedtoautomatethecalculationswhenexploringthesimulationspace.Matchingtheexperiments,biasonthegatewas0V,resultinginlowelectriceldsacrosstherelevantoxide.Allparametersweresettomatchexperimentalconditions,includingtotaldose,doserate,ambienthydrogenconcentration,radiationexposuretime,Nitmeasurementtime,gateandsubstratebias,oxidethickness,andsubstratedoping.Thiswasnotthecaseforpreviousmodelingattempts.Wechosetolookatdatasetswhichcomprisedmanymeasurementsoverarangeofenvironmentalandexperimentalconditions.Thethreedatasetstakenfrom[ 41 ],[ 42 ],and[ 43 ]weredesignedtomeasuretheincreaseininterfacetrapsoverawiderangeofH2concentrations,doserates,totaldoses,andmeasurementtimes.Thiswasdonebecauseithasnotbeenstraightforwardtoquantifydegradationtrendsduein 74

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bipolardevicesduetotheseparameters.Wechosetoexaminehowtheparametersandmechanismsinourmodelaffectedeachdatasetonthewhole,insteadoflookingindividuallyatoneeffect.Inotherwords,wedecidedtolookattheH2,ELDRS,andTIDcurvesinsteadofindividualcalculatedvaluesofNitorNot.OnereasontheH2,ELDRS,andtime-dependenteffectshavebeendifculttopindownexperimentallyisthatthephenomenagoverningtheseeffectsarecoupled.Onewaysimulationcanbeveryusefulisintheoreticallydecouplingkeymechanisms.Understandingtheindividualcontributionsofproposedmechanisms,andhowresultschangeduetotheircoupling,canleadtoinsightsintothecauseofexperimentallyobservedeffectssuchasoxidedegradation.Theoreticaldecouplingwasonesimulationmethodweusedtoidentifywhichmechanismsweredominantunderdifferentexperimentalconditions.Thenextsectionexplainshowweusedtheuniquecapabilitiesofscriptednumericalsimulationtoexplorethelargesimulationspaceofsuchamodelwhich,duetothesheernumberofphysicaleffectstakingplaceandrequiringmodeling,hasmanyparameters. 3.6SensitivityAnalysisMethodThemodelweinvestigatedinthiswork,outlinedinthischapterandinChapter 2 ,includes16mobileandtrapspeciesinvolvedin21chargetrappingreactions.Whenexploringthislargesimulationspacewegenerallyusedthreemethods.First,westudiedeachproposedchargetrappingmechanismindividually,whichreducedthenumberofreactionstoonlythreeorfouratatime.Second,weranfullsplitsofdifferentcombinationsofassumedpre-existingneutraldefectconcentrationsandcomparedtheresults.Bothatorconstantvolumetricdefect-precursorprolesandrectangularstepproleswithmoredefectsneartheSi/SiO2interfacewereinvestigated.Theconcentrationsofpre-existingneutraldefects,suchasoxygenvacancies,andhydrogenatedoxygenvacancies,arenottypicallyknownso,whenpossible,theseweretheonlyadjustableparametersusedtoprovideamatchtothedata.However,these 75

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investigationsalonedidnotprovideenoughinsighttobeabletoquantitativelymatchthedatafrom[ 41 ],[ 42 ],and[ 43 ].Firstprinciplescalculations,suchasthoseusedtoobtaintheforwardandreversereactionenergiesdiscussedabove,containinherentstatisticalerror,andalsodependonassumptionsmadeaboutthephysicalsystem.WeusedFLOODStonarrowdownthiserror,andtotestthephysicalassumptionsmadebyperformingasensitivityanalysis.Afterexploringindividualmechanismsseparately,andafterperformingsplitsoninitialdefectconcentrationsandprole,wethenusedthescriptingcapabilitiesofFLOODStoperformasensitivityanalysis,varyingeachparametersuppliedbyDFTwithinthestatisticalerrorbarsoftherstprinciplescalculation,typically0.2eV.TheeffectofthisvariationontheFLOODSsimulationresults,inotherwordsoxideandinterfacetrapbuildup,wasobserved.Inthisway,wedeterminedwhichparametersaffecttheresultsverystrongly,andwhichdonothaveanyeffectontheresults,inotherwords,whichparametersaresensitive,andwhicharenot.SinceaseparateFLOODSsimulationisrequiredforeachpointontheH2,ELDRSandTIDcurves,thismeansover7000simulationswerecarriedouttoperformthisanalysis.Investigatingthismanysimulationresultswasnottrivial,sincechangingoneparameteroftenaffectedresultsinmultipledatasets,andnotalwaysinawaywhichcouldprovideamatchtoeachsimultaneously.However,thetaskwasnotimpossiblesincemanyparametersandevenmechanisms,previouslytheorizedtobeimportant,werefoundtoproducenoeffectonanyresults.Theinsightsfromthisexplorationwereusedtone-tuneourmodel,andwesuccessfullyidentiedaparametersetthatcanprovideaquantitativedescriptionofinterfaceandoxidetrapbuildupregardlessofdose-rate,hydrogen,totaldose,ormeasurementtime.ResultsarediscussedinChapters 4 6 76

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CHAPTER4INTERFACETRAPGENERATION:H2ANDELDRSEFFECTSInthischapter,resultsfromthephysics-basedTCADmodeldescribedinchapters 2 and 3 arepresentedthatcanexplaininterfacetrapbuildupinbipolarisolationoxides.QuantitativeagreementisfoundwithmeasureddataoverawiderangeofdoseratesandH2concentrations.Analysisofthedegradationeffectsofindividualdefecttypes,theimplementationofwhichhasbeeninformedbyrstprinciplescalculations,providesinsightsintothemechanismsbehindenhancedlow-dose-rateeffectsindifferenthydrogenenvironments.Theeffectsofinitialdefectconcentrationandlocationandtheenergeticsofthedefect-relatedreactionsareexplored.Conclusionsaredrawnabouttherolesofmolecularhydrogenandhydrogenateddefectsintheradiationresponseofthesedevices. 4.1BackgroundInformationThephenomenonofenhancedlow-dose-ratesensitivity(ELDRS),observedaschangesindevicecharacteristicsandinterpretedasradiation-inducedchargebuildupindeviceinsulators,hasbeendifculttointerpretandmodel.Thisisprimarilyaresultofthestrongroleofhydrogen,andthetypicalvariationsinhydrogenconcentrationsandreactionsthatoccurasafunctionofdeviceprocessing.Specializedteststructureshavebeendevelopedtoextracttrapconcentrations[ 82 ],andexperimentshavebeendesignedtocontroltheenvironmentalconditionsduringirradiation.However,chargetransportandtrappingdependonmanyfactors,includingthetotaldose,doserate,andamountofhydrogenavailabletothedeviceduringandafterirradiation.Thishasmadeitdifculttoidentifythebasicphysicalprocessesthatunderlietheobservedphenomena. c[2011]IEEE.Chapter 4 containscontent,withpermission,from[N.L.Rowsey,M.E.Law,R.D.Schrimpf,D.M.Fleetwood,B.R.Tuttle,S.T.Pantelides,AQuantitativeModelforELDRSandH2DegradationEffectsinIrradiatedOxidesBasedonFirstPrinciplesCalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2937-2944,Dec.2011][ 81 ]. 77

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Hence,previousanalyticapproachestoELDRSmodelinghavetypicallyreliedonsetsofequationsthatincludeseveraluncontrolledttingparameters[ 41 ],orhaveonlyprovidedqualitativedescriptionsoftheobservedphenomenaowingtoasimpliedsetofreactions[ 67 ]ormodelparametersthataredenedsemi-empirically[ 66 ].Inthischapter,weshowsimulationresultsfromaphysics-basedmodelthathasbeenimplementedintheFLOODSTCADsolver[ 68 ].Thepresentmodelincludesbothatwo-stageprotonproductionmechanism[ 63 ],aswellasmolecularhydrogencrackingmechanisms,eachofwhichisbasedonrstprinciplescalculationsusingdensityfunctionaltheory[ 30 51 ].Theresultsarefoundtoprovideanimproveddescriptionofthemeasurementsofradiation-inducedinterfacetrapdensitybyChen,etal.[ 41 ]andPease,etal.[ 42 ]overalargerangeofdoseratesandambienthydrogenconcentrations(Figs.1and2).Thesedatawereobtainedfrommeasurementsongated,low-qualityisolationoxidesoverthebaseregionoflateralbipolartestdevices.Irradiationwasperformedwithnobiasonthegate,resultinginlowelectriceldsacrosstherelevantoxide.ThepresentworkprovidesnewinsightintothecriticaldefectreactionsthatleadtoELDRSintheisolationoxidesprevalentinmanybipolardevices,aswellasnewinformationabouttheinitialconcentrationofhydrogenanddefectsinthematerials,andtheresultingeffectsonthedeviceradiationresponse. 4.2ModelingSummaryAdetaileddescriptionofthemodelingandthespecicFLOODSimplementationisgiveninChapter 3 .Thissectionprovidesanoverviewofthemodels,devicestructure,andsimulationmethodologiesimplementedtoproducetheresultsthatarethemainfocusofthischapter. 4.2.1Drift-DiffusionModelingThepresentmodelincludesaccuratedescriptionsofelectriceldandspeciestransport,electron-holepair(EHP)generationduringirradiation,generation/recombinationderivedfromenergy-balanceequationsforthechemical 78

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reactionsthatoccurduringandafteroxideirradiation,andboundaryconditionsatthegateandSiO2/Siinterface.Thecouplednonlinearequationsthatmodeltheseprocessesarediscretizedonagridandsolvedusingnite-elementandnite-volumetechniques[ 70 71 ].FLOODS,theFLoridaObjectOrientedDeviceSimulator,istheTCADtoolusedforthiswork,asthecodeiscomputationallyefcientandreadilycustomizable[ 68 ].Poisson'sequationisusedtocomputetheelectriceldandincludesallchargedspecies.Aseparatecontinuityequationaccountsforthechangeinconcentrationandtransportofeachspeciesineachmaterial,whereSiO2istreatedasawide-bandgapsemiconductor,insteadofaperfectinsulator.Transportintheoxideisdescribedbystandarddrift-diffusionequations,withappropriatevaluesofeffectivemobilityanddiffusivity.Transportbetweenbulkandinterfacenodes,ortransportbetweentheSiandSiO2bulkregions,isspeciedwhenappropriate.Thecontinuityequationsincludediffusiontermsifthespeciesaremobile,aswellasdrifttermsifthespeciesarechargedandmobile.Thenetcarrierrecombinationratesforthecontinuityequationforeachspeciesareformulated[ 76 ]fromtheequilibriumcoefcientsoftheradiationreactionsincludedinthepresentmodel.Reactionratecoefcientsareformulatedbasedondefect-mediateddiffusionmodelsthatdescribethecaptureofdiffusingspeciesbypointdefects[ 77 ].TheH2andH+diffusivitiesarebasedonexperimentalandtheoreticalstudies[ 30 83 84 ].Theforwardandreversereactionenergies,EfandEr,discussedindetailinChapter 2 andsummarizedbelow,areobtainedfromrstprinciplescalculationsemployingdensityfunctionaltheorywithinthegeneralizedgradientapproximation[ 30 51 ].WesubsequentlyevaluatedthesensitivityoftherstprinciplesresultsvianumericalexperimentsinFLOODS.Table A-1 inAppendix 7.3 providesasummaryoftherangesoverwhicheachenergywasvaried,aswellastheenergyvalueswhichbestmatchedthedata.Inthischapter,andinChapter 2 ,theenergiesgiveninthereactionequationsarethosewhichbestmatchthedata.Adjustmentswerewithinthestatisticalerrorof 79

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Figure4-1. DFTrepresentationofVo. Figure4-2. DFTrepresentationofVo. rstprinciplescalculations,approximately0.2eV.OnlyfourvaluesneededtobeadjustedfromtheoriginalDFTcalculations,asdiscussedbelow.Ef 1 wasoriginally0.4eV,andEf 13 ,Er 14 ,andEf 17 werealloriginally0.5eV.Thesewerethemostsensitiveparameters.However,theextensivevariationsallowednotonlyvericationoftheDFTresults,butalsoidenticationofthoseparameterswhichwerenotsensitive,andallowedidenticationofwhichparametersandthereforephysicalmechanismscontrolledtheELDRSandotherresponses.Boundaryconditionsallowholestopassfreelyfromtheoxideintothesiliconsubstrate,andforelectronsandholestobefreelyabsorbedintothealuminumgate.Theelectrostaticpotentialiscontinuousacrossallboundaries,andH2isallowedtoowintothedeviceaccordingtoexperimentalconditions.Biasesmatchexperimentalconditions,andinitialconditionsareassumedaccordingtothediscussioninChapter 3 80

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4.2.2TrappingSpeciesandReactionsThetrappingspeciesandreactionsweredenedinChapter 2 .Hereweprovideabriefsummary.OxygenvacanciesarethedominantdefectinSiO2[ 51 ],[ 30 ],[ 52 ],[ 53 ],[ 54 ],andcomein2maincongurations.ThegammacongurationisshowninFig. 4-1 ,andthedeltacongurationisshowninFig. 4-2 .EachdefectcongurationVoorVocanalsobesinglyhydrogenated,ordoublyhydrogenated.Eachofthesixdefects(Vo,Vo,VoH,VoH,VoH2,VoH2)cancaptureahole,andreleaseprotonsthroughinteractionwithvarioushydrogenousspecies.TheprotonsinteractwithdanglingbondsattheSiO2/Siinterfacetoforminterfacetraps.Thechargetrappingandprotonreleasereactionsaresummarizedbelow,andarealsotabulatedinAppendix 7.3 foreasyreference.Somereactionsaremorelikelyatroomtemperature,becauseofthedifferentforwardandreverseenergybarriers(EfandEr)whichmustbeovercomeinthedifferentcases.Section 3.2.3.2 ofChapter 3 discussestheformulationofthereactionrateskfandkrfromtheenergybarriers,howtheratesdependalsoondiffusionenergyofthemobileparticleandotherparameters,andwhyevenasmallchangeinenergycanresultinabigchangeinreactionrate.However,alsodiscussedinChapter 3 ,therateandlikelinessofeachreactionalsodependsontheconcentrationofreactantsavailable.Interfacereaction:H++Si-H,Nit+H2 (4)Voreactions(H2crackingmechanism):Vo+h+,V+oEf0=0.0Er0=4.5 (4)V+o+H2,VoH+H+Ef1=0.5Er1=0.8 (4)V+o+e)]TJ /F3 11.955 Tf 10.41 -4.93 Td[(,VoEf2=0.4Er2=9.0 (4) 81

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Voreactions:Vo+h+,V+oEf3=0.0Er3=0.6 (4)V+o+H2,VoH+H+Ef4=1.4Er4=0.8 (4)V+o+e)]TJ /F3 11.955 Tf 10.4 -4.93 Td[(,VoEf5=0.0Er5=9.0 (4)VoHreactions:VoH+h+,VoH+Ef6=0.0Er6=4.5 (4)VoH+,Vo+H+Ef7=2.0Er7=1.8 (4)VoH++e)]TJ /F3 11.955 Tf 10.41 -4.94 Td[(,VoHEf8=0.0Er8=7.5 (4)VoHreactions:VoH+h+,VoH+Ef9=0.0Er9=0.6 (4)VoH+,Vo+H+Ef10=0.5Er10=0.6 (4)VoH++e)]TJ /F3 11.955 Tf 10.4 -4.94 Td[(,VoHEf11=0.0Er11=3.0 (4)VoH2reactions(directreleasemechanism):VoH2+h+,VoH+2Ef12=0.0Er12=0.6 (4)VoH+2,VoH+H+Ef13=0.4Er13=0.8 (4)VoH+2,V+o+H2Ef14=0.4Er14=0.6 (4)VoH+2+e)]TJ /F3 11.955 Tf 10.4 -4.94 Td[(,VoH2Ef15=0.0Er15=9.0 (4) 82

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Figure4-3. FLOODSresultsshowingaquantitativematchtoNitdatatakenbyChen,etal.[ 41 ].[Reprinted,withpermission,fromN.L.Rowsey,etal.,AquantitativemodelforELDRSandH2degradationeffectsinirradiatedoxidesbasedonrstprinciplescalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2938,Figure1,Dec.2011.] VoH2reactions:VoH2+h+,VoH+2Ef16=0.0Er16=0.6 (4)VoH+2,VoH+H+Ef17=0.4Er17=0.8 (4)VoH+2,V+o+H2Ef18=0.5Er18=1.2 (4)VoH+2+e)]TJ /F3 11.955 Tf 10.41 -4.93 Td[(,VoH2Ef19=0.0Er19=9.0 (4) 4.3SimulationResultsWeimplemented1Dand2DnMOScapacitorsinFLOODSthatmatchthestructureanddopingoftheMOSregionoftheexperimentalteststructures.Theequationsabovewereimplemented,andaDCsimulationwascarriedoutunderpre-irradiationconditions. 83

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Figure4-4. FLOODSresultsshowingaquantitativematchtoELDRSdatatakenbyPease,etal.[ 42 ]indifferentH2ambientswithatotaldoseof30krad(SiO2).%and%refertotheH2concentrationusedby[ 42 ].AirreferstoaverylowH2concentration.[Reprinted,withpermission,fromN.L.Rowsey,etal.,AquantitativemodelforELDRSandH2degradationeffectsinirradiatedoxidesbasedonrstprinciplescalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2938,Figure2,Dec.2011.] TransientsimulationswerethenperformedusinganEHPgenerationterm, Uradiation=Yfg0Rd(4)whereYisfractionalyield,g0isinitialEHPdensityperunitdose,andRdisdoserate[ 23 ].Chen,etal.[ 41 ]measuredinterfacetrapgenerationatonehighdoseratebutmanyvaluesofambientH2(Fig. 4-3 ).Pease,etal.[ 42 ]measuredinterfacetrapgenerationoveralargerangeofdoserates,fortwolowvaluesandonehighvalueofambientH2(Fig. 4-4 ).Thetotaldosewas30krad(SiO2)inbothstudies.AllexperimentalconditionswerematchedintheFLOODSsimulation,includingdevicestructureanddoping,biason 84

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Figure4-5. ResultsshowhowtheseparatecontributionsofthecoupledH2crackingmechanismandthedirectprotonreleasemechanismcombinetoprovideaquantitativematchto[ 41 ].ThecrackingmechanismisdominantatmediumandhighconcentrationsofH2,whilethedirectreleasemechanismisdominantatlowH2concentrations.[Reprinted,withpermission,fromN.L.Rowsey,etal.,AquantitativemodelforELDRSandH2degradationeffectsinirradiatedoxidesbasedonrstprinciplescalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2940,Figure3,Dec.2011.] thegateandsubstrate,initialandambientH2concentration,totaldose,doserate,andmeasurementtime.TheFLOODSresultsagreewellwithbothsetsofexperiments(Figs. 4-3 and 4-4 ).Theunknowninitialconcentrationsoftheneutraltrapprecursorsweretheonlyadjustableparametersusedtotthedata.Fullsplitsofdifferentcombinationsofdefect-precursorconcentrationsweresimulatedandtheresultswerecompared.Bothatorconstantvolumetricdefect-precursorprolesandrectangularstepproleswithmoredefectsneartheSi/SiO2interfacewereinvestigated.Asensitivityanalysiswasalsoperformedforallforwardandreverseenergybarriersandthediffusionenergies,varyingeachenergy0.1eVandseeinghowthischangedtheH2and 85

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ELDRSresponses.AsaseparateFLOODSsimulationisrequiredforeachpointontheH2curve,andeachpointonthethreeELDRScurves,thismeansover7000simulationswerecarriedouttoperformthisanalysis.Themostinterestingresultsarediscussedbelow. 4.3.1IndividualContributionsofEachTrapSpeciesInvestigatingeachreactiongroupseparatelyshowedtherelativecontributionsofeachdefectinthedifferentH2anddoserateregimes.Figs. 4-5 and 4-6 showtheinterface-trapconcentrationvs.H2concentrationasafunctionofambientanddoserate,respectively.TheresultsofsimulationsoftheVocrackingmechanismandtheVoH2directprotonreleasegroupsconsideredindividuallyarecomparedtotheexperimentalresults.TheanalysisbelowsuggestwhythesetwodefectsaresignicantmechanismsinvolvedinthedifferentELDRSeffectsseenatdifferentH2concentrations.TheVodefect,whichreleasesprotonsviaH2cracking( 4 4 ),isthedominantdefectandreactiongroupformediumandhighconcentrationsofH2.Thisisexpected,since( 4 )isoneofonlytworeactionsinvolvingH2directly.InFig. 4-5 itisthedominantmechanismfortheentirerighthalfoftheH2curve.TheVodefectisalsothedominantdefectatallH2concentrationsatlowdoserates.InFig. 4-6 ,itdominatestheentirehigh-H2ELDRSresponse,andalsothesteeply-slopedlow-tomid-dose-rateresponse.Fig. 4-7 showstheELDRSresponsesoftheVoreactionsaloneatmanymoreH2concentrations.InboththisexampleoftheVoreactionsalone,andinsimulationsincludingallthereactions,anH2concentrationof1013cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3attheoxide/gasboundarytstheexperimentaldatatakeninairaccurately.TheconcentrationofH2inaircalculatedbyChenandPeasewas1011cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3.However,asboththeselowvaluesarewellbelowmeasurementtolerance,thevaluecanreasonablybeassumedtobewithintheerrorbarsoftheairmeasurements.ThisadjustmentisnecessarytoobtainattotheELDRSdatainthelow-H2,low-dose-rateregionforEf 1 =0.5eV. 86

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Figure4-6. Resultsshowhowtheseparatecontributionsofthetwoprotonproductionmechanismscombinetoproducethedoserateeffectseenin[ 42 ].TheH2crackingmechanismisdominantatalldoseratesforhighH2concentrations,butonlyatlowtomediumdoseratesforverylowH2concentrations(air).Thedirectprotonreleasemechanismcompetesatlowdoseratesforholeswiththecrackingmechanism,bringingthehigh-H2ELDRSresponsedownatlowdoserates(comparetoFig. 4-4 ).ThedirectprotonreleasemechanismisalsothemainproviderofprotonsathighdoseratesforverylowconcentrationsofH2.[Reprinted,withpermission,fromN.L.Rowsey,etal.,AquantitativemodelforELDRSandH2degradationeffectsinirradiatedoxidesbasedonrstprinciplescalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2940,Figure4,Dec.2011.] TheVodefectis,asexpectedfromthediscussionabove,tooshallowaholetrap,andV+ohastoohighabarrierforH2cracking,forthisdefecttobeasignicantsourceofprotonsandthusNitproduction.Theseenergies(Er 3 andEf 4 )werevariedinsplitsfrom0.0eVto2.0eV.Itwasdeterminedthat,forH2crackingtoproduceasignicantconcentrationofNit,theholetraphadtobedeep,Er 3 >1.2eV,andthecrackingbarrierhadtobelow,Ef 4 0.5,whichisapproximatelythecasefortheVodefect.Bothoftheseconditionshadtobemet. 87

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Figure4-7. ResultsshowthecontributionoftheH2crackingmechanismatalargerangeofH2concentrationscm)]TJ /F2 7.97 Tf 6.59 0 Td[(3,illustratinghowthelowdoserateresponseatverylowH2concentrationsdependsstronglyonH2concentration.WithEf 1 adjustedtosimultaneouslymatch[ 41 ],nootherparameterwasfoundtoshifttheH2=1011cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3resultsinagreementwith[ 42 ].However,theresultsat1013cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3werefoundtobeinagreementwiththedatatakeninair.ThesetwoverylowH2concentrationsarewithinmeasurementtoleranceofeachother.[Reprinted,withpermission,fromN.L.Rowsey,etal.,AquantitativemodelforELDRSandH2degradationeffectsinirradiatedoxidesbasedonrstprinciplescalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2940,Figure5,Dec.2011.] Atmediumandhighdoserates,anothersourceofhydrogenisrequiredtoproduceresultsthatmatchthedata.AnyorallofVoH,VoH2,orVoH2canservethispurpose,dependingontheinitialconcentrationofdefectsassumedtobeintheoxidepriortoirradiation.ThedirectprotonreleasebarrierforVoH+istoolargetobesignicantatroomtemperature.Thisisthecaseevenatveryhighinitialdefectconcentrationsintheoxide(1018cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3).However,thismeansthatVoH+wasamuchmoresignicantsourceofoxidechargethananyotherdefectbesidestheVodeeptrap.Forexample,comparing 88

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tomeasurementsofoxidecharge[ 41 ],whichisprojectedtotheinterfaceforextraction,thedeepV+otrapconcentrationapproximatelymatchedmeasurements,1012cm)]TJ /F2 7.97 Tf 6.59 0 Td[(2.Holescapturedonotherdefectsaccountedforlessthan104cm)]TJ /F2 7.97 Tf 6.58 0 Td[(2ofcharge,butVoH+accountedfor109cm)]TJ /F2 7.97 Tf 6.58 0 Td[(2or1010cm)]TJ /F2 7.97 Tf 6.58 0 Td[(2,dependingondoserateandH2concentration.WhilethisisstillmuchlessthanthecontributionfromV+o,itisworthnotingbecauseitissomuchgreaterthantheotherholetraps.TheVoHreactions( 4 )-( 4 )canproduceasignicantconcentrationofprotonsthroughthedirectprotonreleasemechanism,butnotatthelowinitialconcentrationsofVoHpredictedbyrstprinciplescalculations.Atconcentrationslessthan1015cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3,thisgroupproducedonlyenoughprotonstoinduceaninterfacetrapconcentrationof109cm)]TJ /F2 7.97 Tf 6.59 -.01 Td[(3,evenatthelowestdoserates,whichisanorderofmagnitudelowerthananypost-irradiationmeasurementtakenbyPeaseorChen.Thedoublyhydrogenatedvacancieshavesimilarlow-barrierdirectprotonreleasemechanisms,andeithercaninduceasignicantamountofinterfacetrapsatanydoserate.However,theVoH2reactionset( 4 )-( 4 )wasaslightlybettermatchtothelow-H2ELDRSdata,duetothemuchlowerH2absorptionbarrierofEr 14 thanVoH2(Er 18 ). 4.3.2DefectConcentrationManycombinationsofdefectconcentrationsweresimulatedandcompared.ThecombinationthatbesttallthreeELDRScurvesandtheH2curvesimultaneouslywaschosenforFigs. 4-3 and 4-4 .Theconcentrationsdiscussedbelowareforthesetofenergeticsandotherparametersdenedabove.Changingsensitivemodelparametersallowsdifferentsetsofdefectconcentrationstobechosentotthedata.Forexample,loweringtheyieldfractionrequiresahigherinitialconcentrationofdefects.ThissectiondiscusseshowthetotalarealconcentrationofdefectsaffectstheH2andELDRSresponses.Thenexttwosectionsaddresswhywechoseanon-constantdistributionofdefects,andwhywechosetheparametervaluesreportedabove. 89

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Figure4-8. ResultsshowhowtheinitialconcentrationofdefectsinthedevicebeforeirradiationaffectstheELDRSresponseathighandlowH2concentrations.Thelow-H2ELDRSresponseisaffectedbyincreasing(ordecreasing)theinitialconcentrationofVoH2,andtheeffectislargerathigherdoserates,indicatingmoreelectronrecombinationoccursathigherVoH2concentrations,causingadistortioninthelow-H2ELDRScurve.Thehigh-H2ELDRSresponseisaffectedbymodulatingtheconcentrationofVo,thoughtheshapeofthecurvedoesnotchangeinthiscase.[Reprinted,withpermission,fromN.L.Rowsey,etal.,AquantitativemodelforELDRSandH2degradationeffectsinirradiatedoxidesbasedonrstprinciplescalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2941,Figure6,Dec.2011.] TheVoconcentrationthattstheresultsisastepproleconsistingof1014cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3inthebulk,witha4-nmwiderectangularpeakof9x1018cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3neartheinterface,approximatingthedefect-intensivetransitionregionthere.Sigmon,etal.[ 80 ]measuredtheratioofoxygentosiliconinSiO2lmsthermallygrownonsilicon,andobservedthatthisratioexponentiallydecreasesneartheinterface.TheVoH2concentrationthattstheresultsisastepproleconsistingof1014cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3inthebulk,witha4-nmwiderectangularpeakof2x1018cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3neartheinterface.ThevalueoftheVoconcentrationdidnothavemucheffectontheresults,unlessitwasgreaterthan1019cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3.Theinitial 90

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concentrationsoftheotherdefectsthatwerenotinvolvedindominantprotonproductionmechanismswereleftatthenominalvaluesestimatedbyrstprinciplescalculationsasdiscussedpreviously.Fig. 4-8 showshowthetotalamountorintegrateddosecm)]TJ /F2 7.97 Tf 6.58 0 Td[(2ofdefectscontrolsroughlytheverticalpositionoftheELDRSresponse.Inthehigh-H2case,theshapeofthedoseratecurveisnotchangedatall.Takenseparately,theshapesofthelefthalfofthelow-H2ELDRScurve,whichisdominatedbytheVoreactions,andtherighthalfofthelow-H2ELDRScurve,whichisdominatedbytheVoH2reactions,donotchangeeither.Thisshowsthat,fortherectangularstepprolesofdefectsthattthedatawell,increasingthetotalconcentrationofdefectssimplyincreasestheamountofprotonsgeneratedbythesameamountatalldoserates. 4.3.3DefectLocationFlatorconstantvolumeconcentrationsofthekeydefects,VoandVoH2,werenotused.Instead,arectangularstepfunctionprolewasused,withmoredefectslocatedneartheSiO2/Siinterface,asdescribedabove.Thisdistributionwasusedtoapproximatethedefect-intensiveregionthere.AmorerealisticGaussiandistributionwasnotpracticalsincetherequiredgridspacingtorepresenttheGaussianaccuratelyintheless-than-7-nmregiontherewouldnotallowacalculationinacceptableCPUtime.Figs. 4-9 and 4-10 showthatthisspatiallynonuniformdistributionwasnecessarytoprovideamatchtotheELDRSdata.Thestepfunctiondistributionwasusedtocontrolboththeamountofelectronrecombinationintheoxidebulk,andeffectively,thetransittimeofreleasedprotons.ThesetwophenomenaaffecttheamountofcharacteristicfalloffintheELDRSresponses.Electronsgeneratedbyirradiationareswepttowardsthegatebythebuilt-ineldoftheMOSstructure.HolescapturednearerthegatethushaveamuchlargerchanceofrecombiningwithanelectronthanthoseneartheSi/SiO2interface.Thelengthoftheslopingregionofeachcurve,oramountofelectronrecombination,inFigs. 4-9 and 4-10 iscontrolledbythefractionofdefectslocatedinthe 91

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Figure4-9. Resultsshowhowthelocationofdefects,andnotonlytheconcentration,affectsthehigh-H2ELDRSresponse.Theresultsshownabovewerecalculatedwiththesametotalarealdefectconcentration.However,defectprolesthatareatterallowformoreelectronrecombinationatpositively-chargeddefectsites,resultinginamoreseverely-slopedELDRSresponseathighdoseratesthatdoesnotmatch[ 42 ].Conversely,assumingthedefectconcentrationishigherneartheinterface,commensuratewithobservation,producesanappropriatehigh-H2ELDRSresponse.[Reprinted,withpermission,fromN.L.Rowsey,etal.,AquantitativemodelforELDRSandH2degradationeffectsinirradiatedoxidesbasedonrstprinciplescalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2942,Figure7,Dec.2011.] oxidebulk.Theeffectismostpronouncedforthehigh-H2ELDRSresponse,dominatedbytheVoreactions.Thissupportstheidea[ 65 ],[ 85 ]thatthecharacteristicfalloffintheELDRScurveiscausedbyincreasedelectron-holerecombinationathigherdoserates.However,asshownmostclearlybyFig. 4-9 ,thefalloffduetoelectronrecombinationbeginsatahighdoserate,greaterthan102rad(SiO2)/s.ThefalloffatlowerdoseratesisduetotheslowtransportofprotonsfromtheSiO2bulktotheinterface.Asdiscussedmorebelow,protonsaresoslowthattheyareconnedtotheoxideforlongtimes,evenwhenmostdefectsareassumedtobeneartheinterfaceandtheprotonsproducedthere 92

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Figure4-10. Resultsshowhowtheinitialconcentrationofdefectsinthedevicebeforeirradiationaffectsthelow-H2ELDRSresponse.[Reprinted,withpermission,fromN.L.Rowsey,etal.,AquantitativemodelforELDRSandH2degradationeffectsinirradiatedoxidesbasedonrstprinciplescalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2942,Figure8,Dec.2011.] donothavefartotravel.Assumingmoredefectsinthebulkincreasestheamountoffalloffinthedoserateresponse,asahigherproportionofprotonsdonotmakeittotheinterfacebymeasurementtimewhendoseratesarehighandirradiationtimesareshort. 4.3.4SensitivityAnalysisTheenergieslistedinreactions( 4 )-( 4 )wereallobtainedfromrstprinciplescalculations,orfromestimationsbasedonrstprinciplescalculationsandthephysicalstructuresofeachindividualdefect.Firstprinciplescalculationsmustbebasedoncertainassumptionsandalwayscontainsomestatisticalerror,andthereforedonotpredictexactenergyorconcentrationvalues.Toaccountforthis,andtosearchforasetofparametersthatbesttstheentiresetofH2andELDRSdata,westartedwiththepredictionsfromrstprinciplescalculations,butvariedeachenergy,aswell 93

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asothermodelparameters,todeterminewhicharethemostsensitive,i.e.,whichparameters,whenvaried,causethelargestchangeininterfacetrapcreation.Sinceseveralparameterscanshiftthecurvesupordown,itispossiblethatusingdifferentenergieswouldallowcharacterizationofthesystemwithdifferentassumedinitialdefectconcentrations.Whenthettothedatawasreasonable,weusedtheenergiesobtainedfromrstprinciplescalculationsandadjustedthedefectconcentrations,tomaintaintheconnectiontothequantummechanicalcalculations.Incaseswheretheobtainedenergeticscouldnottthedata,weadjustedthemwithinthestatisticalerrorbarsoftherstprinciplescalculation.Weevaluatedhoweachparameteraffectedthesetofresultsthatmakeupeachcurve,ratherthanonevalueofNitatatime,sothatwecouldbetterunderstandthedoserateandhydrogentrendsasawhole,withthegoalofttingalltheresultssimultaneously,withouthavingtochangeparameterstotdifferentdatapoints.Varyingtheparametersoriginallyobtainedfromrstprinciplescalculationsenabledustondwhichparametersgovernedwhichpartofeachcurve.TheH2trend,whichwasobtainedatonedoserate,wasfoundtohaveonlythreegoverningparameters:theinitialconcentrationofVo,theinitialconcentrationofthedefectparticipatinginoneofthedirectprotonreleasemechanisms,andtheenergybarrierforH2cracking,Ef 1 .DefectlocationwasnotimportantfortheH2effectonitsown.TheELDRScurvesweremorecomplicated,andthusmoredifculttocharacterize.ThreekeyfeaturesoftheELDRSresponsewereidentied:theapparentlowdoserateorigin,wherealltheELDRScurvescometogether;theslopingtransitionregionthatcharacterizeselectronrecombination;andthehighdoserateplateau.Theresultsofthesensitivityanalysisweretabulatedaccordingtoeachparameter'seffectonthesefeatures. 94

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Figure4-11. Resultsofasensitivityanalysisonthehydrogencrackingenergybarrier.Thenominalbarrier,whichmatches[ 41 ],is0.5eV.Theresultsofalowerandhigherbarrier,0.4and0.6eV,respectively,showhowsensitivetheH2responseistothisenergy.Toputthisintoperspective,thebarrierobtainedfromrstprinciplescalculationswas0.4eV,withanerrorboundof0.1eV.Therefore,forthisenergy,evenasmallchangewithintheerrorboundsoftherstprinciplescalculationproducesachangeintheH2responseoveranorderofmagnitudeormore.[Reprinted,withpermission,fromN.L.Rowsey,etal.,AquantitativemodelforELDRSandH2degradationeffectsinirradiatedoxidesbasedonrstprinciplescalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2943,Figure9,Dec.2011.] 4.3.4.1H2trendIntheH2curve,interfacetrapbuildupinambientswithhighH2concentrationsisdominatedbytheH2crackingreactionsondeepVocomplexes,i.e.,( 4 )-( 4 )inthepresentmodel.Ontheotherhand,interfacetrapbuildupinambientenvironmentswithverylowH2concentrationsisdominatedbynon-molecularsourcesofhydrogen,i.e.,( 4 4 )inthepresentmodel.ThiswasshowninFig. 4-5 .Fig. 4-11 showshowtransitionbetweenthesetwoextremesisgovernedbytheheightoftheenergybarrierforH2cracking( 4 ).Thevalueobtainedforthisenergybarrierfromrstprinciples 95

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calculationsis0.4eV,whichproducesasimulatedH2curvesignicantlytotheleftofthedataofChen,etal..Betteragreementisobtainedforabarrierof0.5eV,whichiswithintheerrorboundsoftherstprinciplescalculation.IncreasingtheenergybarrierfurthershiftstheH2curve.SimilareffectswereobservedfortheotherenergiesdirectlyinvolvedwithH2.VaryingtheH2diffusionenergy,orthebarrierforH2capturebyVoH2(Er 14 ),producedsimilareffectstothetransitionregionoftheH2curveasinFig. 4-11 .Ef 1 waschosenforthegurebecauseitshowsthemostclearanddramaticchange,andprovidesafeelingfortherelativesensitivityandplausibilityofthevalueschosenforthemostcriticalmodelparameters. 4.3.4.2ELDRStrendBoththedirectreleaseandthecrackingmechanismsasmodeledproduceafalloffinthedoserateresponseatthelow10)]TJ /F2 7.97 Tf 6.59 0 Td[(2rad(SiO2)/sdoserateforallH2concentrations,inaccordancewithdata.Infact,whenVodefectsareassumedtobemostlyneartheinterface,holecaptureandprotonreleasealone,withoutanyelectronrecombination,canquantitativelymatchallthreeELDRScurves.ThisisexplainedbynotingtheverylowmobilityofprotonsinSiO2,(10)]TJ /F2 7.97 Tf 6.59 0 Td[(11-10)]TJ /F2 7.97 Tf 6.58 0 Td[(12cm2/V/s).Weplottedelectrostaticpotentialandnoticedamaximumvariationofapproximately0.6Voverhalftheoxide,0.6m.Crudelyestimatingtheelectriceld(104V/cm)andprotonvelocity(10)]TJ /F2 7.97 Tf 6.59 0 Td[(7cm/s)givesamaximumprotontransittimeof5to50min.Thus,theslowtransitofprotonscanexplaintheELDRSeffectonitsown.ForELDRSdatatakenatlowdoserates,theirradiationlastedlongenoughtoallowforalltheprotonsgeneratedtotraversetheoxideandreacttoforminterfacetraps.Forexample,10)]TJ /F2 7.97 Tf 6.59 0 Td[(4rad/s,thelowestdoseratesimulated,requires13yearsofirradiation,and10)]TJ /F2 7.97 Tf 6.59 0 Td[(2rad/s,thelowestdoseratemeasured,required34daysofirradiationtoreachtheconstanttotaldoseof30krad(SiO2).Attheselowdoserates,thetimeassumedbetweentheendofirradiationandmeasurementisinsignicant. 96

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Asthedoseratewasincreased,however,theirradiationtimedecreased.Adoserateof10rad/srequiresonly50minutesofirradiation.Forthesehigherdoserates,thetimebetweentheendofirradiationandmeasurementbecomesthedominantfactorinhowmuchNitisproducedandrecorded.Simulationconrmsthis;ChangingthemeasurementtimebyseveralhourstoyearslaterallowsalltheprotonstotraversetheoxideandformNit,resultinginaninterfacetrapdensityequaltothelow-dose-ratemaximumatalldoseratesandhydrogenconcentrations. 4.3.4.3HolecaptureandreleaseSeveraloftheenergiesgoverningholecaptureonadefectandtheescapeofthatholeaffecttheH2andELDRSresponses.Sincealloftheholecapturebarriersare0.0eV,andeachdefectiscompetingforthesameholes,relativedefectconcentrationandreversebarriersbecomeimportantindecidingwhichonewins.ThecompetitioneffectcanbeseenbycomparingFigs. 4-4 and 4-6 .Thehigh-H2ELDRSresultinFig. 4-6 ,whichtakesintoaccountonlytheH2crackingmechanism,showsamuchhigherconcentrationofNitatlowandmediumdoseratesthanitscounterpartinFig. 4-4 ,whichtakesintoaccountallthemechanisms.InFig. 4-6 ,theVodefectdoesnothavetocompetewithanyotherdefectforholes,whereasinFig. 4-4 ithassignicantcompetitionfromtheVoH2defect,which,inordertotboththelow-H2andhigh-H2data,isassumedtobepresentinlowerbutcomparableconcentrationsinthepresentmodel.Thiseffectisseeninthesensitivityanalysisaswell.RaisingorloweringtheholecapturebarriersforVo(Ef 0 ),andboththedoubly-hydrogenatedvacancies(Ef 12 andEf 16 ),shifteddownandupthepartsofthecurvesgovernedbytherelateddefect.Thereverseholecaptureenergy,ordepthoftheholetrap,wasanimportantparameterforshallowdefectssuchasVo(Er 3 ),VoH(Er 9 ),andthedoubly-hydrogenatedvacancies(Er 12 andEr 16 ).Thisenergydeterminestheaveragetimethattheholeistrapped,with 97

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Figure4-12. Sensitivityanalysisofshallowtrapdepth,forthelowH2oraircase.TrapenergyforVoH2wasvariedaroundthenominalresultproducedbyDFT,0.60.2eV.Loweringthetrapenergysignicantlyreducestheamountoftimetheholespendsinthetrap,reducingtheVoH+2concentrationsuchthatfewerprotonsarereleasedinthedirect-releasemechanism.HighertrapenergieswithintheDFTerrorboundshadnoeffectonsimulationresults. highertrapenergiesresultinginmoreofachanceforthesubsequentstepofdirectprotondissociation,andhenceNitcreation.Figs. 4-12 and 4-13 showresultsofasensitivityanalysisofoneoftheshallowholetrapenergiesforthe100%H2andaircases.ThevalueobtainedfromDFTcalculationsfortheVoH2trapenergyis0.6eV.WhentheVoH2trapistooshallow(0.5and0.4eV),theholedoesnotstayinthetrapforverylong,meaningthatatanygiventimetheVoH+2concentrationislow,leadingtolessprotonreleasefromthisparticulartrapspecies.AtlowH2(Fig. 4-12 ),thisaffectsmainlytheHDRregion,wheredirectreleasefromVoH+2isdominant.IntheLDRregions,whereH2crackingonV+oisdominant,thereislessofaneffect,thoughtheeffectisstillvisible. 98

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Figure4-13. Sensitivityanalysisofshallowtrapdepth,forthe100%H2case.TrapenergyforVoH2wasvariedaroundthenominalresultproducedbyDFT,0.60.2eV.Loweringtheshallowtrapenergysignicantlyreducestheprotonscreatedthroughthedirect-releasemechanism,whichisadditivetothecrackingmechanism. AthighH2(Fig. 4-13 ),ashallowVoH+2trap(0.5and0.4eV)stillmeansthatthedirectreleasemechanismdoesnotproduceasmanyprotons.ThoughprotonreleaseviaH2crackingonV+oisdominantathighH2,theprotonsproducedviaeachmechanismisadditive.InFig. 4-13 therearefewerdirect-releaseprotonstoaddtotheonesfromcracking,resultinginalowertotalNitdensity,butnochangeintheshapeofthecurve.RaisingtheshallowtrapenergywithintheboundsoftheerroroftheDFTcalculation,upto0.8eV,hasnoeffect,producingresultsidenticaltothe0.6eVcases. 4.3.4.4DirectprotonreleaseThebarrierstodirectprotonreleaseforVo(Ef 10 )andthedoubly-hydrogenatedvacancies(Ef 13 andEf 13 )mustbeapproximately0.5eVorlower,toreleaseprotonsinsignicantnumbers.Higherenergiesdonotresultinasignicantdensityofinterfacetraps. 99

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4.3.4.5ElectronrecombinationIngeneral,electronsintheconductionbanddonotexperienceenergybarrierswhenrecombiningwithpositivelychargeddefects.However,inthecaseofV+o,whentheelectronistrapped,causinganeutralSidanglingbondtobecomenegativelycharged,anearbySi+mustovercomeabarrierofapproximately0.4eVinordertorebondtoformaneutralVo.Ifrebondingdoesnotoccur,thentheelectronislikelytobere-emittedtotheconductionband.Toincorporatethiseffect,weinvokea0.4eVforwardbarrierforelectronrecombinationatV+o.IfdefectsareassumedtobelocatedmostlyneartheSi/SiO2interface,theelectronrecombinationbarriersarenotsensitiveparametersovertherangeofdoseratesmeasuredexperimentally.TheheightofthesebarrierscontroltheatnessoftheELDRScurvesatveryhighdoserates,greaterthan104rad(SiO2)/s;however,thesameeffectcanbeachievedbyassumingaslightlylongertime(5minmore)betweenirradiationandmeasurement.Ifmostdefectsareassumedtobeinthebulk,thenevenincreasingEr 2 toabove0.6eVresultsintoomuchELDRSfalloffathighH2concentrations. 4.3.4.6ParameterfortheELDRStransitionregionAparametergoverningtheleft-to-rightlocationoftheELDRScurveswasnotfound.OnlytheH2concentrationdeterminedoverwhichdoseratestheELDRStransitionregionoccurs,asshowninFig. 4-7 .H2concentrationisnotavariableparameter,sincethismustmatchexperiment. 4.4ChapterSummaryThischapterpresentedtheresultsobtainedfromourdevelopmentoftherstmodelforradiation-inducedinterfacetrapbuildupinlinearbipolardevicesthatcanquantitativelyexplaintheELDRSeffect,i.e.thedose-ratedependenceofinterfacetrapbuildup,overawiderangeofdoseratesandoveracomprehensiverangeofH2environments.ThenewFLOODSmodelprovidesanimproveddescriptionoftwokeyprotonproductionmechanismsbyincorporatingtheresultsofDFTcalculationsof 100

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theenergeticsofchargetransportandtrapping.Thedirect-releasemechanism,inwhichprotonsareliberatedfromshallow,hydrogen-containingdefectsafterthecaptureofaradiation-inducedhole,isfoundtobedominantinthelow-H2,high-dose-rateregime.Thesecondmechanism,H2crackingondeeplytrappedholes,isfoundtobedominantathighH2concentrations,andalsoatalllowdoserates,regardlessofH2concentration.Thekeydefectsintheoxidethatinteractwithradiation-inducedchargetocreatetheprotonsthatcauseabuildupofinterfacetrapdensityhavebeenexploredandanextensivesensitivityanalysishasyieldedtheirindividualcontributionstotheELDRSeffects.Theeffectofdefectconcentrationandlocationhasalsobeenexplored.Thecompletenessoftheapproachhasprovidedamoreaccuratedescriptionoftheobservedphenomenathanwaspossibleinpreviouswork.Thischapterhasfocusedoninterfacetrapbuildup(Nit)anddoserateeffectsindifferentH2environments.Chapter 5 willusethemodeldevelopedandrenedheretoinvestigateoxidechargebuildup(Not)indifferentH2environments,aphenomenonwhichisstronglycoupledtointerfacetrapbuildup,sinceitisthetrappedholes(oroxidecharge)whichinteractwithhydrogenousspeciestoreleaseprotons(whicharealsooxidecharge)whichovertimeslowlydrifttotheinterfacetocreateinterfacetraps.Chapter 6 willfocusonthetime-dependentnatureofalltheseprocesses,andwillusetheinsightsgainedhereandinChapter 5 toidentifythemechanismswhichseparatetime-dependentandtruedoserateeffects.TheimplicationsofthisworkforhardnessassurancetestingofbipolardevicesusedinthespaceindustryisdiscussedinChapter 7 101

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CHAPTER5RADIATIONINDUCEDOXIDECHARGEBUILDUPInChapter 4 ,resultsfromthephysics-basedTCADmodeldescribedinchapters 2 and 3 werepresentedthatcanquantitativelyexplaininterfacetrapbuildup(Nit)inbipolarisolationoxidesoverawiderangeofdoseratesandH2concentrations.Inthischapter,themodelisinvestigatedfurthertoobtaininsightintooxidetrappedcharge(Not)mechanismsinvaryinghydrogenambients,whicharestronglycoupledtotheinterfacetrapbuildupmechanismsinvestigatedinChapter 4 .HoletrappingisfoundtodominatesoxidechargebuildupfortypicalH2densities,butprotonscandominateathighH2densities.InadditiontotheprotonreleasemechanismsdiscussedinChapter 4 ,therateoftheinterfacetrapreaction,inwhichprotonsreactwithH-passivatedbondsattheSiO2/Siinterfacetoformdanglingbonds,isfoundtoplayakeyroleindeterminingthebuildupofprotonsintheoxidebulk,andthustherelativeconcentrationofoxideandinterface-trapcharge.ThroughasystematicinvestigationinFLOODSoftheholetrappingandinterfacereactionenergeticssuggestedbyDFT,quantitativeagreementbetweenmeasuredandsimulatedoxideandinterface-trapchargedensitiesisobtainedoverawiderangeofH2concentrations. 5.1BackgroundInformationThenatureofradiation-inducedoxidechargebuildupandannealinginsilicondevicesisnoteasilycharacterizedviaelectricalmeasurements.Withoutdetailedspectroscopicandtheoreticalinvestigationstocomplementtheelectricaltests,itistypicallynotpossibletoidentifythetypeorlocationofchargetrappedintheoxide.Furthermore,thepresenceofhydrogenaffectsdevicecharacteristicsovermany c[2011]IEEE.Chapter 5 containscontent,withpermission,from[N.L.Rowsey,M.E.Law,R.D.Schrimpf,D.M.Fleetwood,B.R.Tuttle,S.T.Pantelides,Radiation-InducedOxideChargeinLow-andHigh-H2Environments,AcceptedforpublicationinIEEETrans.Nucl.Sci.,2012][ 86 ]. 102

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decadesofirradiationandannealingtime.Interface-trapformationisalsoinextricablylinkedwithholetransportandhydrogenreleaseinthebulkoftheoxide.Thischapterexplorestheinterrelationsoftheseeffects.IntegratedcircuitsusedinradiationenvironmentsarehermeticallysealedinceramicpackagesthatsometimesunintentionallycontainhighconcentrationsofH2.Hydrogenalsocanbereleasedbyoutgassingfrommaterialsusedinpackaging.Thepresenceofthishydrogencanenhanceradiation-induceddegradation,reducingtheoperationallifetimesofMOSandbipolarICs[ 87 ].Radiation-induceddegradationincludesthebuildupofbulkoxidecharge(Not),whichcausesmidgapvoltageshifts,aswellasinterfacetraps(Nit)attheSi/SiO2interface,whichinteractwithchargeinthesiliconchannelcausingstretchout[ 16 ].MeasurementsbyChen,etal.showedthattheconcentrationofradiation-inducedoxidechargeatagiventotaldoseincreaseswithH2concentration[ 41 ].Inthischapter,wepresentaphysics-basedmodelthatprovidesinsightintothenatureoftheobservedincreaseofNitandNotin[ 41 ],overacomprehensiverangeofH2concentrations,fromH2-depletedtoH2-saturated.ResultsshowthatholetrappingatoxygenvacanciesdominatestheradiationinducedoxidechargefortypicalH2densities,butthatprotonscandominateathighH2densities.OxidechargebuildupisaccountedforbyvariousholetrappingandprotonproductionmechanismsknowntooccurinSiO2[ 66 ],asdiscussedinSection 5.3 .Electronrecombinationwithpositivelychargeddefectsisalsoincludedinthemodel[ 81 ]toaccountforthedose-ratedependenceofinterfacetrappedchargeformation.Thedose-rateandhydrogendependenceofinterfacetrapbuildupisdiscussedinmoredetailinChapter 4 .Wendthattheconcentrationofradiation-inducedtrappedholesatthedosesandratesusedintheexperimentsofChen,etal.[ 41 ]islargelydeterminedbyinitialoxygenvacancydefectconcentration.However,theconcentrationofradiation-inducedprotonsthataredetectedasNotisdeterminedbothbytheconcentrationofinitialdefectsand 103

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bythereactionrateofprotonswithpassivateddanglingbondsattheSi/SiO2interface.Thisrelationshipisexplored,andaquantitativematchtodataisdevelopedusingdevicesimulationsbasedonrstprinciplescalculationsoftheenergeticsanddynamicsofchargetrappingandtransportinirradiatedSiO2onSistructures. 5.2ModelingSummaryFLOODSmodelingisdiscussedinmoredetailinChapter 3 ,butabriefsummaryisgivenhere.Radiation-inducedoxidechargeformationismodeledusingaccuratedescriptionsofelectriceldandspeciestransportviaPoisson'sequationandseparatecontinuityequationsforeachspecies.Thecontinuityequationsincludediffusiontermsifthespeciesaremobile,aswellasdrifttermsifthespeciesarechargedandmobile.Thegeneration/recombinationduetotheoxidetrappingandprotonreleasemechanismsthatoccurduringandafteroxideirradiationisaccountedforviaanetcarrierrecombinationrateforeachspecies,derivedfromenergy-balanceequations[ 76 ].Theforwardandreversereactionenergybarriers,EfandEr,areobtainedfromrstprinciplescalculationsemployingdensityfunctionaltheory(DFT)withinthegeneralizedgradientapproximation[ 51 ],[ 30 ],andthereactionratesareformulated[ 77 ]fromtheequilibriumcoefcientsofthereactions.SiO2istreatedasawide-bandgapsemiconductor,withstandarddrift-diffusionequationsaccountingfortransport.Boundaryconditionsincludeelectrons(e)]TJ /F1 11.955 Tf 7.08 -4.34 Td[()andholes(h+)leavingthroughthemetalgate,holesleavingintothesilicon,andreactionofprotonstomakeinterfacetrapsattheSi/SiO2interface.Chen,etal.[ 41 ]measuredinterfacetrapgenerationforalargerangeofambientH2concentrations(Fig. 5-1 ),toatotaldoseof30krad(SiO2),atadoserateof26rad/s.Here,1DnMOScapacitorswereimplementedinFLOODS,matchingthestructureanddopingoftheMOSregionoftheexperimentalteststructuresin[ 41 ].ThisincludesthesiliconbaseregionofthelateralPNPteststructure,anisolationoxideaboveit,andametalgate.Allknownexperimentalconditions,includingbiasonthegateandsubstrate, 104

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Figure5-1. FLOODSresultsshowingasimultaneous,quantitativematchtoNitandNotdatatakenbyChen,etal.[ 41 ]overalargerangeofambientH2concentrations.Bothexperimentandsimulationwereperformedtoatotaldoseof30krad(SiO2)withadoserateof26rad/s.Simulatedandmeasuredoxidechargedensitiesareprojectedtotheinterfaceandplottedagainsttheambientmolecularhydrogenconcentrationinwhichtheteststructuredeviceshavebeensoaked.[Reprinted,withpermission,fromN.L.Rowsey,etal.,Radiation-InducedOxideChargeinLow-andHigh-H2Environments,IEEETrans.Nucl.Sci.,Figure1,2012] initialandambientH2concentration,totaldose,doserate,andmeasurementtimewerematchedintheFLOODSsimulations.Theunknowninitialdefectdensitiesoftheoxidewereusedasasimulationparameter,informedbyrstprinciplescalculations,asdescribedindetailinChapters 3 and 4 .Here,theVoconcentrationusedwasastepproleconsistingof1014cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3inthebulk,witha5-nmwiderectangularpeakof1.6x1020cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3neartheinterface,approximatingthedefect-intensivetransitionregionthere.Thedoubly-hydrogenatedvacancyconcentrationsusedwerestepprolesconsistingof1015cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3inthebulk,with5-nmwiderectangularpeaksof1.8x1018cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3neartheinterface.Avalueof1017cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3 105

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wasusedfortheVoconcentrationthroughouttheoxide,andavalueof1014cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3wasusedforthesingly-hydrogenatedvacanciesthroughouttheoxide.TheequationsimplementedinFLOODS,andaDCsimulationwascarriedoutunderpre-irradiationconditions.Subsequently,transientsimulationswerecarriedoutusinganelectron-holepair(EHP)generationtermtorepresentradiation-inducedcharge, Uradiation=Yfg0Rd(5)whereYfisthefractionalyield[ 75 ],g0istheinitialEHPdensityperunitdose,andRdisthedoserate[ 23 ].OxidechargeconcentrationswereextractedfromthesimulationatthetimecorrespondingtotheexperimentsperformedbyChen,etal.in[ 41 ].Theresultsofcalculatedoxidechargeconcentrationinour1Dstructure(cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3)wereprojectedtotheinterfacebymeansofaweighteddepthdistributioninFigs. 5-1 and 5-2 toallowforcomparisontotheNotvaluesextractedfrommeasurementin[ 41 ],whichapproximatedtheoxidechargedistributionasasheetchargeattheinterface.InterfacetrapdensityresultsarealsoshowninFig. 5-1 incomparisontomeasurements.Althoughinterfaceandoxidechargearemeasureddistinctlyandinteractwiththesiliconchannelindifferentways,thecreationmechanismsofthesetwotypesofchargearestronglycoupled,suchthatarobustmodelmustaccountforbothsimultaneously. 5.3OxideChargeBuildupThissectiondescribesthereactionsthataresuggestedbyDFTresultsforoxidechargebuildupandneutralization,andtherangeofenergybarriersassociatedwiththereactions[ 51 ],[ 30 ].TheH2andH+diffusionenergiesarebasedonexperimentalandtheoreticalstudies[ 30 83 84 ].Theunknowninitialconcentrationsofneutraltrapprecursorsweretheonlyadjustableparametersusedtoprovideamatchtothedata,usingthemethoddescribedinChapters 2 and 3 .Subsequently,FLOODScalculationswerecarriedouttodeterminetheeffectsofvaryingtheenergieswithintherangessuggestedbyDFT,asdiscussedbelow.Trapneutralizationmechanismsincludeboth 106

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Figure5-2. Simulatedandmeasuredtotaloxidechargedensity,andsimulatedoxidechargedensitybrokendownbytype,projectedtotheinterfaceandplottedagainsttheambientmolecularhydrogenconcentrationinwhichtheteststructuredeviceshavebeensoaked.Thedataarereproducedfrom[ 41 ].Trappedholesdominateatlow-andmid-H2concentrations,butprotonsdominateatveryhighH2concentrations.[Reprinted,withpermission,fromN.L.Rowsey,etal.,Radiation-InducedOxideChargeinLow-andHigh-H2Environments,IEEETrans.Nucl.Sci.,Figure2,2012] holereleaseandprotonreleasemechanisms;trappedholescontributeonlytobulkoxidecharge,butprotonscancontributetooxidechargeiftheyhavenotyetlefttheoxide,ortothegenerationofinterfacetrapsiftheyreactwithpassivateddanglingbondsthere. 5.3.1FixedOxideChargeTypesHolestrappedatoxygenvacanciesarethedominantradiation-inducedchargeundermostconditions.Oxygenvacanciesoccurintwocongurations,Vo,whichisashallowholetrapassociatedwiththeE0defectobservedinEPRmeasurements,andVo,whichisadeepholetrapassociatedwiththeobservedE0defects[ 54 72 ].Bothcongurationscanbehydrogenated,ordoublyhydrogenated.WhenVoissingly 107

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hydrogenated,thenaldefect(VoH)involvesahydrogenbetweentwosiliconatoms.SinceVoandVodefectsareoxygenvacancieswheretwoSiatomsformabond,introducingonehydrogenallowsforoneSi-Hbondtoform,leavinganotherSiwithadanglingbond.ThesituationleadstoadefectwithalevelwithintheSiO2bandgap.Becauseofthis,VoHandVoHaredeepholetraps.Voanddoublyhydrogenatedvacancydefectsareshallowholetraps.DFTresultsindicatethatthereisnoenergybarriertoholecaptureforeachofthesedefectsbeyondthebarriersforholediffusion,sinceeachhasadefectlevelinthebandgapofSiO2.Acapturedholemayescapeitstrap.Thereverseenergybarriersoftheholecapturereactionsdescribethedepthofeachholetrap,whichdeterminestheaverageamountoftimethattheholespendsinthetrap.ThiscanbeunderstoodfromtheformulaforreactionrateinChapter 3 ( 3 ).Incase3,(case3)kint=fexp)]TJ /F9 11.955 Tf 9.29 0 Td[((Et) kBT, (5)therateatwhichaholeescapesatrapischaracterizedbyanattempttoescapefrequency,f.ThephysicalpictureisaholesittinginsideatrapwithenergyEt,vibratingwiththermalenergykBT.Theattempttoescapefrequencycanbethoughtofasthenumberoftimespersecondtheholeattemptstojumpoutofthetrapduringoneofitsvibrations.Sincefhasunitsofs)]TJ /F2 7.97 Tf 6.59 0 Td[(1,case3canalsobecharacterizedbyatimeconstantof=1=f,whereistheaverageamountoftimeinsecondsthatholesspendinthetrap.Theexponentialcontainingthetrapenergydividedbythethermalenergyisunitless,suchthatincreasingthetrapenergyeffectivelydecreasestheattempttoescapefrequency(increasing),whereasraisingthetemperatureincreasestheattempttoescapefrequency(decreasing).TheholereleasebarriersofthedefectsdiscussedabovehavebeencalculatedforselectivecasesusingDFT.Inthesecalculations,bothatomicandelectronicrelaxationsareallowedasthesystemtransformsfromapositivelychargeddefecttoaneutral 108

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defectplusafreehole.OneshouldkeepinmindthatthebarriertoreleaseaholefromadefectisnotdirectlyrelatedtotheenergylevelofthedefectwithintheSiO2bandgap.AdirectreleaseofaholefromaV+oorV+ovacancybandgapdefectleveltoavalencebandstatewouldberoughly1.5or4.5eV,respectively.However,thebarrierisreduceddramaticallyifthesiliconatomsofthepositivelychargedvacancyrstmovetotheirneutralvacancypositions.Withatomicrepositioning,thetotalbarrierforholereleaseisbetween0.6and0.8eVfortheshallowtraps,includingtheenergyrequiredforrepositioning.Vo+h+,V+oEf3=0.0Er3=0.6-0.8 (5)Vo,H2+h+,Vo,H+2Ef12=0.0Er12=0.6-0.8 (5)Anadditionalbarrierexistsforthegammavacancytoassumethedeltaconguration,ifitisnotdoubly-hydrogenated.Overall,thebarrierforholereleasefromV+oandthesingly-hydrogenatedvacanciesisestimatedtobe0.8to1.0eV.Thesedeepholetrapsaremorelikelytocontributetoxedoxidetrappedcharge.Vo+h+,V+oEf0=0.0Er0=0.8-1.0 (5)Vo,H+h+,Vo,H+Ef9=0.0Er9=0.8-1.0 (5)Severalofthexedoxidechargetrapsabovecanalsobecomeneutralbyreleasingaproton.Thesemechanismsrequireasourceofhydrogen,andalsogoverninterfacetrapcreation.Thedepthoftheholetrapisanimportantparametergoverningprotonrelease,sinceadefectthattrapsaholeforlongerhasmorechancetoreleaseaproton. 109

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Singlyanddoubly-hydrogenatedvacanciescandirectlyreleaseaprotonwhencharged,neutralizingthedefect,andtransferringthechargetomobileprotons.VoH+,Vo+H+Ef7=2.0Er7=1.8 (5)VoH+,Vo+H+Ef10=0.5Er10=0.6 (5)Vo,H+2,Vo,H+H+Ef13=0.4Er13=0.8 (5)Non-hydrogenatedoxygenvacanciescancrackmolecularhydrogen(H2)[ 73 74 ],leavinganeutralsingly-hydrogenatedoxygenvacancyandamobileproton.V+o+H2,VoH+H+Ef1=0.5Er1=0.8 (5)V+o+H2,VoH+H+Ef4=1.4Er4=0.8 (5)TheenergeticsofholeandprotonreleasewereexaminedtogetherusingFLOODS.SinceVoH2andVoH2areshallowholetrapsthatdirectlyreleaseprotonswithoutanymolecularhydrogenrequired,theinitialconcentrationofthesespeciesgoverntheconcentrationofinterfacetrapsatlowH2concentrations[ 81 ],butdonotcontributesignicantlytooxidechargeatanyH2concentration.TheholereleaseenergyfortheshallowtrapsisnotasensitiveparameterintherangeindicatedbyDFT(0.6-0.8eV),butifthisenergyisdecreasedto<0.6eV,veryfewprotonsarereleasedandnotenoughNitiscreatedatlowH2concentrationstomatchthedatain[ 41 ].0.6eVisusedintheresultsinFigs. 5-1 and 5-2 .Voisfoundtobetooshallowasaholetraptocontributetooxidechargebuildup.Inaddition,theH2crackingbarrierforthisdefectistoohightocontributetoprotonrelease.SinceVo,VoH,andVoHaredeeptraps,theinitialconcentrationsofthesespeciesgoverntheconcentrationofoxidechargeatlowH2concentration.However,rstprinciplescalculationsindicatethattheinitialconcentration,priortoirradiation,ofsingly-hydrogenatedvacanciesisrelativelylowinSiO2,lessthan1015cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3.Assumingthislowinitialconcentrationofdefects,neitherVoHnorVoHcapturesenoughholesto 110

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Figure5-3. FLOODSsimulationsfollowingtheexperimentalconditionsof[ 41 ]in100%H2showtheprotonconcentrationneartheSiO2/Siinterfaceatseveraltimesfortheinterfacetrapreactionratethatbestmatchesthedatain[ 41 ].Irradiationwasperformedfrom0-25min,andtrapdensitieswereextracted10minuteslater,at35min.Inthiscase,theinterfacereactionrateislowenoughthatprotonspileupattheinterface,contributingtooxidecharge,buthighenoughthatenoughinterfacetrapsalsoform.[Reprinted,withpermission,fromN.L.Rowsey,etal.,Radiation-InducedOxideChargeinLow-andHigh-H2Environments,IEEETrans.Nucl.Sci.,Figure3,2012] signicantlycontributetooxidecharge.ThenalconcentrationofVoH+isatleastanorderofmagnitudebelowmoredominantoxidechargespecies,asshowninFig. 5-2 .ThenalconcentrationofVoH+islowerstill,between104and105cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3,dependingonH2concentration.ThisisbecauseVoH+hasalowbarrierforprotonrelease( 5 ),leavingmanyofthesevacanciesneutralwhenprotonsleavethesite,whereasVoH+hasahighbarrierforprotonrelease( 5 ).ThedepthoftheVoH+trapmayalsoplayanimportantroleintheprotontrappingin[ 88 ]and[ 89 ].Weconcludefromourcalculationsthatneitherofthesingly-hydrogenatedvacanciescontributestoNotorNitformation.Themaincontributionsarefrom 111

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thedoubly-hydrogenatedvacancies,asdiscussedaboveforthecaseoflowH2concentrations,andtheVodefectforthecaseofhighH2concentrations.AthighH2concentrations,V+ocracksH2andstronglyaffectstheconcentrationofinterfacetraps.TheholereleaseenergyforthedeepVotrapisaverysensitiveparameterintherangeobtainedfromDFT(0.8-1.0eV).Thebarrierismostsensitivebetween0.9and1.0eV,with0.9eVlargelypreventingthecrackingreactionfromproducingenoughprotonsathighH2concentrations,and1.0eVproducingtoomuchlow-H2oxidecharge.0.98eVproducesthebestmatchtothedatain[ 41 ],andwasusedintheresultsinFigs. 5-1 and 5-2 .ThisconrmstheimportanceofhydrogenreactionswithVodefectsindeterminingboththeoxideandinterface-trapchargedensitiesinirradiatedSiO2onSistructures[ 73 74 ]. 5.3.2InterfaceTrapRateandProtonConcentrationHolestrappedatthedeepV+odefectarethedominantformofradiation-inducedoxidechargeformostH2concentrations(Fig. 5-2 ).However,athighH2concentrations,theconcentrationofV+odecreasesduetotheH2crackingreaction( 5 ).ProtonsareanothersourceofoxidechargethathasbeensuggestedasacandidatefortheincreasedoxidechargeseenathighH2concentrations[ 88 89 ].Inoxidesassociatedwithbipolartransistors,protonsmaysurviveinSiO2layerswithhighoxygenvacancydensitiesandhydrogenconcentrationsforlongtimes[ 90 91 ].Theprotonscreatedthrough( 5 )andthroughthedirectreleasemechanisms( 5 )-( 5 )canmigratetotheSi/SiO2interfaceandcreatepositivelychargeddanglingbonds(DB+)there[ 62 ],increasingtheinterfacetrapconcentration(Nit)asdescribedby: H++SiHint,DB+int+H2(5)suchthatthecontinuityequationforinterfacetrapdensityinonedimensionis: dNit dt=kint[H+int][SiHint](5) 112

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Figure5-4. FLOODSsimulationsfollowingtheexperimentalconditionsof[ 41 ]in100%H2showthelowprotonconcentrationsneartheSiO2/Siinterfacewhentheinterfacereactionrateishigh.Inthiscase,amatchtotheNitdatacanbeobtained,butnottotheNotdata. where[H+int]istheconcentrationofprotonsneartheinterface,[SiHint]isthearealconcentrationofhydrogen-passivateddanglingbondsattheinterface,andkintistheeffectiverateofthisinterfacereaction.Thereversereactionisassumedtobenegligibleatroomtemperature.Following[ 77 ],thereactionratecoefcientcanberelatedtotheenergybarrierofthereactionvia kint=LcDexp)]TJ /F9 11.955 Tf 9.3 0 Td[((Ebar)]TJ /F5 11.955 Tf 11.96 0 Td[(Ed) kBT,(5)whereLcisanestimatedcriticallengthincm,similartotheconceptofcapturecrosssection,Disdiffusivityofthemobileparticleincm2/s,Ebaristhereactionenergybarrier,Edisthediffusionenergybarrierofthemobilespecies,kBisBoltzmann'sconstant,andTistemperature.TheEinsteinrelationwasusedtoconvertbetweenmobilityanddiffusivity.Edissubtractedfromthereactionenergybarriertoavoidcountingittwice. 113

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Tsetseris,etal.calculatedtheforwardenergybarrierfortheinterfacereaction( 5 )tobeapproximately0.95eV[ 92 ],whichincludedtheprotondiffusionenergyof0.8eV.Thisresultsinakintofapproximately5x10)]TJ /F2 7.97 Tf 6.59 0 Td[(21cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3/s.TestsinFLOODSwereperformed,varyingthisenergy.Forvaluesofkintbelow10)]TJ /F2 7.97 Tf 6.59 0 Td[(24cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3/s,theinterfacereactionwassoslowthatprotonswereentirelyconnedtotheoxidebeyondthemeasurementtimesofChen,etal.,andnointerfacetrapbuildupisobservedinthesimulations.Inthiscase,( 5 )isreaction-ratelimited.Forvaluesofkintabove10)]TJ /F2 7.97 Tf 6.58 0 Td[(20cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3/s,theinterfacereactionproceedsquickly,andanyprotonthatarrivesattheinterfacereactsandcreatesaninterfacetrapimmediately.TheFLOODSresultsinFig. 5-4 showsthelowprotonconcentrationsintheSiO2neartheSiO2/Siinterfacethatresultsfromahighkintatvarioustimesduring(0to25min)andafterirradiation(25to35min).Inthisentirelydiffusion-ratelimitedcase,asufcientmatchtointerfacetrapmeasurementscanbeobtained,butnottooxidechargemeasurements.Forvaluesofkintbetweenthesetwoextremes,protonspileupattheinterfaceinadditiontoformingNit,allowingamatchtobothinterfaceandoxidechargemeasurements.Inthiscase,( 5 )isbothdiffusion-limitedandreaction-limited,andthebarrierheightcontrolshowmanyprotonspassthroughversushowmanypileup.Thekintcalculatedfrom[ 92 ]fallswithinthisintermediaterange.ThebestsimultaneousmatchtotheNitandNotdataofChen,etal.,shownin( 5-1 ),isforkint=10)]TJ /F2 7.97 Tf 6.58 0 Td[(23cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3/s.Fig. 5-3 showsthehighprotonconcentration(>1018cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3)intheSiO2neartheSiO2/Siinterfaceforthisvalueofkint.SincethemeasurementsbyChen,etal.showthatoxidechargeincreaseswithH2concentration,thecrackingreaction( 5 )excludesV+ofrombeingthedominanthigh-H2oxidecharge.Thereverseenergybarriersofseveraloftheprotonreleasereactions,including( 5 ),arebetween0.6and0.8eV.Ithasbeensuggestedthatthesemoderatelyhighbarrierscanbeovercomeandthereactionsbedriveninreversewhenprotonconcentrationsarehigh,suchaswhentheH2concentrationishighand 114

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( 5 )isproducingmanyprotons.FLOODSsimulationsindicatethattheexcessprotonscreatedby( 5 )athighH2concentrationsindeedcausethesereactionstoproceedinreverse,butonlywhenkintissufcientlysmallthatprotonspileupathighconcentrationsattheinterface,andonlyenoughtoretardprotonproductionatmoderateH2concentrations.Forexample,atamediumH2concentrationof1016cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3,( 5 )proceedsinbothdirections.However,astheH2concentrationincreasesevenfurther,( 5 )proceedsonlyintheforwarddirection.EvenloweringthereverseenergybarriersfortheprotonreleasereactionscannotcausetheprotonproductionreactionstoreversestronglyenoughtoincreasetheconcentrationofxedoxidechargespeciesathighH2concentrationstothoseseenbyChen,etal.Thisisbecausethebarriertoprotondiffusionisitself0.8eV,andprotonsmustovercomethisminimumbarrierbeforeinteractingwithadefect.Overtheintermediaterangeofkintvalues,protontransportandreactionattheSi/SiO2interfaceaffecttheconcentrationofprotonsintheoxideovermanydecadesoftime.OursimulationsshowthatlargeconcentrationsofprotonscanbuildupneartheSi/SiO2interfacewhentheprotonconcentrationishigh,whilestillallowingasignicantnumberofinterfacetrapstoform.AthighH2concentrations,excessprotonsarecreateddueto( 5 ).TheseresultssuggestthatanelevatedconcentrationofprotonsintheSiO2accountsfortheexcessoxidechargeseenby[ 41 ]athighH2concentrations(Fig. 5-2 ).InthisChapter,wehavefocusedonexploringthemechanismsthatleadtotheH2concentrationdependenceonradiation-inducedoxideandinterfacetrapsasmeasuredbyChen,etal.,atroomtemperature,andwithnobiasacrosstheisolationoxide.Valuesofkintmayhavetoberecalibratedforotherdevicetechnologies,and/orsignicantchangesindoserate,bias,and/orprocessingtechnology.Similarly,defectdensitieswillalsochangewithprocesstechnology,andhydrogenconcentrationwillchangewithambientconditions,devicepassivation,etc..However,themodelingapproachandthe 115

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rstprinciplescalculationsoftheenergeticsanddynamicsofthechargetransportandtrappingaregenerallyapplicabletoirradiatedSiO2onSistructures. 5.4ChapterSummaryInthischapter,wehaveexpandedthemodeldevelopedinChapter 4 forinterfacetrapbuilduptoquantitativelyexplainoxidechargebuildupinbipolarisolationoxidesoveracomprehensiverangeofH2concentrations.Thefullyparameterized,physics-basedapproachinthischapterprovidesanimproveddescriptionoftheunderlyingphenomena.TheresultsfortypicalH2concentrationsareconsistentwithpreviousanalysisofoxidetrappedcharge:thedominantsourceofchargeisholestrappedatoxygenvacancies.However,theresultsofthischapterindicatethat,forhighH2concentrations,mostofthepositivechargeintheoxideisduetoprotons.Therateoftheinterfacetrapreactionisfoundtobeakeyphysicalparametergoverningtherelativeconcentrationsofoxidechargeandinterfacetraps. 116

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CHAPTER6SEPARATINGTIMEDEPENDENTANDTRUEDOSERATEEFFECTSInthischapter,ourquantitativemodelforradiation-inducedinterfacetrapbuildupidentiesprotonabsorptionandinterfacereactionrateascontrollingmechanismsseparatingtimedependentandtruedoserateeffects,supportinghydrogensoakingasanELDRStestmethod. 6.1BackgroundInformationEnhancedLowDoseRateSensitivity(ELDRS),oranobservedincreaseinradiation-induceddevicedegradationatlowdoserates(LDRs)[ 33 ],typicallyinbipolardevices,presentsachallengefortotalionizingdose(TID)hardnessassurancetesting.Fast,highdoserate(HDR)testsaredesirable,butcharacterizing,andthuspredicting,enhancementfactors(EFs),ordifferencesbetweenHDRandLDRdegradationmeasurements,probablyduetodifferencesinhydrogenconcentration,isdifcult[ 94 ].Inaddition,becauseLDRexposuresrequirelongerirradiationtimesthanHDRirradiationstothesametotaldose,distinguishingbetweentime-dependenteffects(TDEs),suchasslowprotontransport,andtruedoserateeffects(TDREs),suchasELDRS,canalsobedifcult[ 40 43 ].RecentmeasurementsonaspecializedteststructuredesignedtocharacterizeELDRSinsusceptiblebipolardevices,reproducedinFig. 6-1 ,observeddifferentdoseratetrendsdependingontheambientmolecularhydrogenenvironmentofthedevices[ 42 ].Irradiationswereallperformedtothesametotaldoseof30krad.DevicessaturatedwithH2,viasoakingofthedevicesina100%H2ambient,exhibitedanegligibleELDRSeffect,withHDRirradiationsresultinginapproximatelythesame c[2011]IEEE.Chapter 6 containscontent,withpermission,from[N.L.Rowsey,M.E.Law,R.D.Schrimpf,D.M.Fleetwood,B.R.Tuttle,S.T.Pantelides,ControllingMechanismsSeparatingTimeDependentandTrueDoseRateEffectsinIrradiatedBipolarOxides,AcceptedforpresentationinIEEENSREC'12,Jul.2012][ 93 ]. 117

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highlevelofdegradationasLDRirradiations.Devicessoakedin1%H2exhibitedsomeELDRS,whiledevicesirradiatedinair,whichhasaverylowH2concentration,exhibitedanorderofmagnitudelessdegradationduetoHDRirradiationcomparedtoLDRirradiations,oranEFof10.Basedontheresults,theauthorssuggestedthataTIDhardnessassurancetestthatinvolvedhydrogensoakingandHDRirradiationmaybeabletocharacterizedevicesfortheLDR,low-H2spaceenvironment[ 42 ].Chapter 4 presentedaphysics-basedmodelthatcanquantitativelyexplainthedifferentdoseratetrendsobservedby[ 42 ]indifferenthydrogenenvironments.Thischapterusesthemodeltoquantitativelyexplainadditionalandmorerecently-presentedTDEandTDREdata[ 43 ]onthesametestdevices,butatadditionaltotaldosesandforadditionalmeasurementtimes.Thenewsimulationsillustratehowslowprotontransport,hydrogencrackinganddimerization,thehydrogenambientenvironmentcontributedifferentlytoELDRSandtimedependenttrends.Theresultssupportthesuggestionby[ 42 ]thatHDR,high-H2irradiationscouldmoreaccuratelypredictmaximumLDR,low-H2radiation-induceddevicedegradation. 6.2ModelingSummaryChapter 4 showedthatourmodelcanquantitativelyexplainradiation-inducedinterfacetrapbuildupmeasurementsinbipolarisolationoxidesoveralargerangeofambientH2concentrationsanddoserates(Fig. 6-1 ).Athigherandlowerdoserates,themodelpredictsdoseratetrendssimilartothoseexpectedbyqualitativetheoreticalcalculations[ 65 ]oftheELDRSeffect.Themodelusesthreekeymechanisms,summarizedinthissectionforeasierreferral.Thesimulatedstructureisa1DMOScapacitorthatmatchesthethicknessoftheisolationoxideandthedopingofthesiliconbaseregionofthetestdevicesusedin[ 42 ].Theresultspresentedinthischapterare1DFLOODSsimulationsoftime-dependentdegradationoftheMOSregionmatchingtheisolationoxideandbaseregionoftheexperimentalteststructuresissimulatedin 118

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Figure6-1. FLOODSsimulationresultsshowthatthemodelusedherecanquantitativelyexplainthedifferentELDRStrendsmeasuredby[ 42 ]indifferentH2environments.ThetrendathighH2(100%H2saturatedorapproximately1018cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3)isfairlyat,showingverylittleenhancementfactor.ThetrendatlowH2(orinair,approximately1013cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3)showsafactorof10differencebetweeninterfacetrapdensityatlow(0.01rad(SiO2)/s)andhigh(100rad(SiO2)/s)doserates.Thegureandresultsarereproducedfrom[ 81 ].Thedataarereproducedfrom[ 42 ].[Reprinted,withpermission,fromN.L.Rowsey,etal.,AquantitativemodelforELDRSandH2degradationeffectsinirradiatedoxidesbasedonrstprinciplescalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2938,Figure2,Dec.2011.] 1Daccordingtoconditionsthatmatchtheexperiments,includingoxidethickness,basedoping,totaldose,doserate,measurementtime,H2concentration,andappliedbiases.Therstkeymechanismincludesholecaptureonshallow,H-containingdefects( 6 ),andsubsequentdirectprotonrelease( 6 ),VoH2+h+,VoH+2Ef12=0.0Er12=0.6 (6)VoH+2,VoH+H+Ef13=0.4Er13=0.8. (6) 119

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Figure6-2. FLOODSresultsshowthetwodominantprotonproductionmechanismssimulatedindependently.TheH2crackingmechanismisresponsibleforNitbuildupatalllowdoserates.[Reprinted,withpermission,fromN.L.Rowsey,etal.,AquantitativemodelforELDRSandH2degradationeffectsinirradiatedoxidesbasedonrstprinciplescalculations,IEEETrans.Nucl.Sci.,vol.58,no.6,pp.2940,Figure4,Dec.2011.] whereEfandEraretheforwardandreverseenergybarriersofthereaction,takenorestimatedfromtheresultsofrstprinciplescalculations.ThecontributionofthismechanismsimulatedaloneisplottedinFig. 6-2 .ItisdominantonlyindevicesnotsoakedinH2,andonlyathighdoserates(Rd<0.1rad(SiO2)/s).Weassume[ 30 51 ]thesehydrogen-containingdefectstobedoubly-hydrogenatedoxygenvacanciesintheconguration(VoH2),butsimilarH-containingdefectscouldplaythesamerole[ 81 ].Thesecondmechanismincludesholecaptureondeeptraps( 6 ),thenprotonreleaseviaH2cracking( 6 ).Vo+h+,V+oEf0=0.0Er0=4.5 (6)V+o+H2,VoH+H+Ef1=0.5Er1=0.8 (6) 120

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FLOODScalculationsofthismechanismsimulatedalone(Fig. 6-2 )suggeststhatthismechanismisdominantatalllowdoserates(Rd<0.1rad(SiO2)/s)regardlessofH2concentration,butalsodominantathighdoserateswhentheH2concentrationis>0.1%.Thedeepholetrapsareassumedtobenon-hydrogenatedoxygenvacanciesintheconguration(Vo),whichisthedefectassociatedwiththeE0defectobservedinEPRstudies.Themolecularhydrogenisassumedtobepresentinterstitially[ 30 ],leftoverintraceamountsfromprocessingorpackaging,orintroducedintheH2soakingstepsperformedbyPease,etal..Thethirdmechanismisincreaseininterfacetrapdensity(Nit),accountedforviatheinterfacereaction H++SiHint,DB+int+H2,(6)inwhichtheprotonscreatedthroughthedirectreleaseandhydrogencrackingmechanisms( 6 )-( 6 )canmigratetotheSi/SiO2interfaceandinteractwithhydrogenpassivateddanglingbondsthere(SiHint),creatingpositivelychargeddanglingbonds(DB+)[ 62 ].ThisinteractionincreasesNitasdescribedbythecontinuityequation(inonedimension): dNit dt=kint[H+int][SiHint](6)where[H+int]istheconcentrationofprotonsneartheinterface,[SiHint]isthearealconcentrationofhydrogen-passivateddanglingbondsattheinterface,andkintistheeffectiverateofthisinterfacereaction.Thereversereactionisassumedtobenegligibleatroomtemperature. 6.3HydrogenDimerizationandElectronRecombinationTheinterfacereactionratein( 6 )isderivedusingenergybalanceequations[ 76 ]and,following[ 77 ],isrelatedtotheenergybarrieroftheinterfacereactionvia kint=LcDexp)]TJ /F9 11.955 Tf 9.3 0 Td[((Ebar)]TJ /F5 11.955 Tf 11.96 0 Td[(Ed) kBT,(6) 121

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whereLcisanestimatedcriticallengthincm,similartotheconceptofcapturecrosssection,Disdiffusivityofprotonsincm2/s,Ebaristhereactionenergybarrier,takenfromrstprinciplescalculations[ 92 ],Edisthediffusionenergybarrierofprotons[ 30 83 84 ],kBisBoltzmann'sconstant,andTistemperature.TheEinsteinrelationisusedtoconvertbetweenmobilityanddiffusivity.Edissubtractedfromthereactionenergybarriertoavoidcountingittwice.Tsetseris,etal.calculatedaforwardenergybarrierfortheinterfacereaction( 6 )ofEf,int=0.950.2eV[ 92 ],includingthe0.8eVprotondiffusionenergy.Thisresultsinarangeofkintvaluesfromapproximately10)]TJ /F2 7.97 Tf 6.59 0 Td[(24to10)]TJ /F2 7.97 Tf 6.59 0 Td[(20cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3/s.Chapter 5 showedthatthisreactionrateisimportanttotheradiation-inducedoxidechargebuildup(Notinthesetypesofstructuresathighdoserates.Here,simulationresultsshowthattheinterfacereactionrateisalsoanimportantparametergoverningELDRStrendsfordevicesin>0.1%H2.Fig. 6-3 showsthesimulatedELDRStrendat1%H2(1016cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3)fortwodifferentvaluesofkint.Atlowenergyvalues(forexample,kint=10)]TJ /F2 7.97 Tf 6.59 0 Td[(21),protonsreachingtheinterfacereactquicklyandproduceresultsthatexceedmeasureddata.Athigherenergyvalues(forexample,kint=10)]TJ /F2 7.97 Tf 6.58 0 Td[(22),whentheinstantaneousconcentrationofprotonsishigh,suchasatHDR,protonsreachtheinterfacefasterthantheinterfacereactioncanproceed.Fig. 6-4 showsthat,inthesecases,protonspileupattheinterfacebeforereacting,waitingtheirturn,sufcientlyincreasinginconcentration(>1018cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3neartheinterface)suchthattheH2crackingreaction( 6 )isdriveninreverse,accordingtothegeneration/recombinationtermRG1=kf1[V+o][H2])]TJ /F5 11.955 Tf 11.95 0 Td[(kr1[VoH][H+], (6)wherekf1andkr1aretheforwardthereversereactionratesfor( 6 ),derivedfromEf1andEr1analogouslyto( 6 ).Inotherwords,forthisspecialcase,protonsareabsorbed 122

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Figure6-3. FLOODScalculationsoftheELDRStrendat1%H2(approximately1016cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3)fortwodifferentinterfacereactionrates.Atthehigherreactionrate,protonsreactattheinterfacetooquickly,producingahigherdensityofinterfacetrapsthanmeasuredbyPease,etal.indevicessoakedina1%H2ambient. andthehydrogenisdimerizedinsignicantquantities,lesseningtheNitbuildupatHDRforthe1%H2case.Thisobservationisnecessaryforobtainingamatchtothe1%H2ELDRStrendmeasuredby[ 42 ]atHDR.However,aslongaskintisintherangepredictedbytheenergycalculationsofTsetseris,etal.,higherH2concentrationspushthecrackingreactionagainintheforwarddirection.ThisiseasybecauseEf1forthecrackingreactionis0.4eV,whileEr1is0.8eV.Also,atLDR,regardlessofH2concentration,fewerprotonsarereleasedatanysingletime,andtheconcentrationisnotsufcienttodrivethecrackingreactioninreverse.Thisinterpretationofinterfacetrapbuildupat1%H2concentrationsuggeststhattheHDRELDRStrendinthisrangeofH2iscausedbyanincreaseintherateofreversereaction( 6 ),or,inotherwords,protonabsorptionbyH-vacanciesandhydrogen 123

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Figure6-4. CalculatedH+concentrationvs.oxidedepthatvarioustimesfollowingirradiation,atthevalueofkintthatbestmatchesELDRSdata[ 42 ]forallH2concentrations.Atthiskintvalue(10)]TJ /F2 7.97 Tf 6.59 0 Td[(21),theinterfacereactionissufcientlyslowsuchthatprotonspileupneartheinterfacetoaveryhighconcentration,approximately1018cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3,drivingthecrackingreaction( 6 )inreverse.[Reprinted,withpermission,fromN.L.Rowsey,etal.,Radiation-InducedOxideChargeinLow-andHigh-H2Environments,IEEETrans.Nucl.Sci.,Figure3,2012] dimerization.Thisisincontrasttoexplanationsinwhichdirectelectronrecombination[ 65 66 ]ortrap-assistedelectronrecombinationinaShockley-Read-Hall-likemodel[ 64 ]areusedtodescribeELDRStrendsqualitatively.Directelectron-holerecombinationisunlikelyacrossthe9eVbandgapofSi2,butinourmodelwehaveinvestigatedtrap-assistedelectronrecombinationinwhichelectronsrecombinewithholestrappedondefects.ThisisimplementedinourmodelviaVoH+2+e)]TJ /F3 11.955 Tf 10.41 -4.94 Td[(,VoH2Ef15=0.0Er15=9.0 (6)V+o+e)]TJ /F3 11.955 Tf 10.41 -4.93 Td[(,VoEf2=0.4Er2=9.0. (6) 124

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Figure6-5. FLOODScalculationsoftheELDRStrendsassumingthatinitialdefectdensitiesareuniformthroughouttheSiO2,formultipleenergybarriersforelectronrecombination.Resultsdonotmatchtheobservedtrendswell,predictingamuchhigherEFthanobservedby[ 42 ],especiallyforhighH2,whichshouldhavealmostnoEF.ThemechanismresponsibleforthelargecalculatedEFsiselectronrecombinationonV+o. Ingeneral,thereisnobarrierfortrap-assistedelectronrecombinationinSiO2,butinthecaseof( 6 ),abarrierof0.4eVisusedtoaccountfortheenergyrequiredforthetheV+otorstrebondintotheneutralcongurationsince,ifthisrebondingdoesnotoccur,thentheelectronislikelytobere-emittedtotheconductionband.Chapter 4 discussedhowweinvestigateddifferentinitialassumeddefectconcentrations.Whenweinvestigateduniformdefectdensities,simulationresultsshowedthattrap-assistedelectronrecombinationonV+ositessignicantlyaffectedtheamountofcalculatedELDRS(Fig. 6-5 ).SimilarcalculationsvaryingEf15(andallotherelectronrecombinationsitesdiscussedinChapter 2 )hadnegligibleeffectontheresults,indicatingthatelectronrecombinationonVoH+2ormechanism( 6 )isnotacriticalmechanismevenwhendefectconcentrationisassumedtobeuniform.Neitherenergy 125

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hadaneffectonresultswhentheV+odefectswereassumedtobewithin5nmoftheinterface.TheseresultsstronglysuggeststhatanothermechanismisresponsiblefortheELDRSeffect.Wereiteratethat,eventhoughwehaveusedimprovedmodelparametersandenergiesinformedbyDFT,simulatedELDRSresultsareconsistentwithpreviousstudies,showingtoomuchelectronrecombination,evenwhenraisingthebarriertothisrecombinationtoarticiallyhighvalues.Thisresultsintoolargeanenhancementfactor,especiallyformedium-andhigh-H2concentrations.Notetheincreasedrangeonthey-axis.Toobtainamatchtodata,wemustassumethatthedefectsarelocatedmostlywithin10nmorlessoftheinterface.Inthiscase,electronrecombinationandtheeffectofEf 2 arenegligible.Evenmodelswhichassumedeepholetrapdefectstobelocatedwithin25nmoftheinterfaceshowanEFof10,evenatextremelyhighH2concentrations[ 43 ],whichisnotconsistentwithdata[ 42 ].AsdiscussedinChapter 4 ,itisnecessarytoassumethattheoxygenvacancydefectsarelocatedmainlyneartheSiO2/SiinterfacetoprovideaquantitativematchtotheELDRSdata[ 42 ].Inthiscase,( 6 )and( 6 ),inotherwords,electronrecombination,hasnoaffectonsimulationresultsatanydoserateorH2concentration.ThereasonforthisisillustratedinFig. 6-6 ,whichshowselectronandV+oconcentrationversusoxidedepth.Theelectronconcentrationislowingeneral,and,becauseofthebuilt-inelectriceldofthe0-biasedMOSstructure,areswepttowardthegate,farawayfromtheinterfaceregioncontainingtheV+oonwhichtheymayrecombinevia( 6 ).Theseresultsunderscoretheimportanceofusingmodelparametersbasedonphysicalmechanism,andofquantitativelycomparingresultstodatainordertoevaluatetheaccuracyofmodels.Manymechanismscanshowgeneraltrends,butmaynotbeabletoachievequantitativeresultsoveralargerangeofexperimentalandenvironmentalconditions. 126

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Figure6-6. FLOODScalculationoftheelectron,V+o,andVoH+2defectconcentrationsversusoxidedepthatseveraltimesforanHDRirradiationin100%H2.Theelectronconcentrationisverylowingeneral,andisatitsmaximuminthebulkoftheoxide,farawayfromtheSiO2/Siinterface.Becauseofthis,andtheassumedlocationofdefectsmostlyneartheinterface,negligibleelectronrecombinationoccurs. 6.4TDEandTDREEffectsPease,etal.performedallmeasurementswithin10minfollowingirradiation.Thus,[ 42 ]doesnotdistinguishbetweentime-dependenteffects(TDEs)andtruedoserateeffects(TDREs),becausesamplesirradiatedathighdoserate(HDR)werenotannealedtothetimerequiredbylowdoserate(LDR).Forexample,thelowestdoseratein[ 42 ]is0.02rad(Si)/s.Irradiatingtoatotaldoseof30kradthusrequires1.5x106sofirradiation,approximately17days.However,thehighestdoseratein[ 42 ]was100rad(Si)/s,whichonlyrequires300sor5minofirradiation.ATDREmeasurement 127

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Figure6-7. FLOODSsimulationsatdifferenttotaldoses,doserates,ambientH2concentrations,andmeasurementtimesshowaquantitativematchtodatafrom[ 43 ].Modelparameterssuchasthereactionenergeticsarenotchangedbetweenthesecalculationsandthosematchingearliermeasurements[ 81 ]onthesamedevices[ 42 ],howeverinitialdefectconcentrationshavebeenincreasedslightlytotakeintoaccounttheincreaseddegradationobservedby[ 43 ].AnadjustmenttotheassumedH2concentrationofairduringmeasurementsinairisnecessarytoobtainamatchtotheHDR+annealmeasurement. wouldincludeacomparisonbetweenmeasureddegradationatLDRandmeasureddegradationatHDRplusa17-dayanneal.Inalaterstudyonthesamedevices,Esqueda,etal.performedsimilardoserateandH2measurements,butalsoreportedtotaldoseandaTDREmeasurement[ 43 ].ThesedataarereproducedinFig. 6-7 ,alongwithFLOODSsimulationscarriedouttothesametotaldose,doserates,andmeasurementtimesastheexperiment,andwhichquantitativelymatchthisnewerdata.Physicalmodelparameterssuchasthereactionsandenergeticswerenotchangedbetweenthesimulations.However,forFig. 6-7 theconcentrationofinitialdefectsassumedwasslightlyincreasedtoaccountfortheincreaseddegradationmeasuredby[ 43 ]onthesamedevicesandforthesame 128

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Figure6-8. CalculationsofthechangeinELDRStrendovertime,followingirradiationofdevicessaturatedin100%H2.Inthiscase,theTDREisveryslight,untilextremelyhighdoserates.(Rd>104rad(SiO2/s)).Thedataarereproducedfrom[ 42 ]. experimentalconditionsas[ 42 ].Inaddition,theassumedconcentrationofH2inairwasasensitiveparameterdeterminingthetimedependentresponse,andaffectedthebuildupofNitoverthe17-dayanneal.ItwasnecessarytoassumethattheconcentrationofH2inairwas1013cm)]TJ /F2 7.97 Tf 6.59 0 Td[(3tomatchtheELDRSmeasurements[ 42 ],but1013cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3tomatchtheHDR+anneal(orTDRE)measurementtakenby[ 43 ].TheseextremelylowH2concentrationsarewithinmeasurementtoleranceofeachother,butoursimulationspredictthatdifferencesineventraceamountsofH2canmakeabigdifferenceinthebuildupofNitover17days.Figs. 6-8 and 6-9 showFLOODScalculationsofhowELDRStrendschangeduringa17-dayanneal.Resultssuggestthatdevicessoakedin100%H2reachtheLDRmaximumquickly,withtheELDRSresponseremainingatattheLDRmaximumatalllatertimes.Fortheaircase,however,resultssuggestthattheHDRirradiateddevicesmaydegrademuchmoreseverelyoverthe 129

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Figure6-9. CalculationsofthechangeintheELDRStrendovertime,followingirradiationofdevicesirradiatedinair,whichcontainsonlytraceamountsofH2.TherearesignicantTDEandTDREcomponentstothedegradation,eventoRd=0.02rad(SiO2)/s. 17-dayannealperiodthanmeasuredimmediatelyfollowingirradiation,andthatinthiscaseofverylowH2concentration,atruedoserateeffectwouldbeobserved.Thecurvesbelowthefulltimecalculation(17days)showtimedependenteffects,andthecurvesabovethistimeshowadditionaldoserateeffects.Forthesoakeddevices,negligibleTDREeffectsarepredictedbelowdoseratesof104rad(SiO2/s),whereasdevicesirradiatedinairshowaTDREevenat10)]TJ /F2 7.97 Tf 6.59 0 Td[(2rad(SiO2/s).TheTDREsaboveRd=104rad(SiO2/s)wereaffectedbythehydrogendimerizationmechanismdiscussedearlier,buttherateofthetimedependentchangeintheairELDRSresponse,andthusthelevelofdegradationreachedattheendofthe17days,wasafunctionofinitialH2concentration,availabilityofH2intheambient,H2diffusivity,andforwardandreverseenergybarriersfortheH2crackingreaction. 130

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6.5ChapterSummaryInthischapter,wefurtherdemonstratedtherobustnessofourmodelfortheradiation-induceddegradationofbipolarisolationoxidesbyshowingthatthemodelcanquantitativelyexplainthedose-rateandhydrogeneffectsondegradationatadditionaltotaldosesandmeasurementtimes.Thenewsimulationswereusedtoexploretimedependentandtruedoserateeffects.Hydrogendimerization,inadditiontoH2cracking,wasshowntoplayanimportantrole.InChapter 5 ,weidentiedtheinterfacereactionrateasanimportantparameterthatgovernsthebuildupofprotonsneartheinterfaceinthepresenceofmolecularhydrogen,affectingoxidechargebuildup.Inthischapter,weshowedhowthisreactionratealsogovernsinterfacetrapbuildupindifferentwaysdependingonbothdoserateandH2concentration.SimulatedELDRScurves,orinterfacetrapdensitycalculationsversusdoserate,atdifferentmeasurementtimes,suggesthowH2crackingandprotontransportgovernthebuildupofinterfacetrapsoverlongtimes,suchasduringaspacemission.Resultssuggestthattruedoserateeffectsarenotduetoexcesselectronrecombinationathighdoserates,butinsteadexcesshydrogendimerization(i.e.protonrecombination)viathereversecrackingreactioninthepresenceofhighprotonconcentrationneartheinterface,asgovernedbytheinterfacereactionrate. 131

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CHAPTER7CONCLUSIONSANDFUTUREWORK 7.1ConclusionsThemaingoalofthisworkwastogaininsightintothebasicmechanismsbehindtheobservedELDRSeffectinbipolardevices,inotherwords,tounderstandwhatcausesthedependenceofradiation-inducedinterfacetrapbuildupondoserate.Inordertodothis,wealsohadtoinvestigateoxidechargespeciesandhydrogeninteractions,implementingmodelsofchargegeneration,transport,andtrappingwhichtakeplaceovervastlylargetimescales,frompicosecondstoyears.Previousresearchoverthecourseof20yearssincethediscoveryofELDRSin1991investigatedmanyaspectsofELDRSfromanexperimentalstandpoint,andtheoreticalstudieslaidthegroundworkforadetailedunderstandingofthemolecularstructureofprobablekeydefectsandcharge-defectinteractionsinthermalSiO2.WithFLOODS,wewereabletocomprehensivelystudythesesuggestedmechanismsandtheirsimultaneouseffectsoneachotherindetail,inaquantitativemanner,andatthedevicelevel,inacomprehensiverangeofdoseratesandhydrogenenvironments.Throughextensiveandwell-organizedscripting,wewereabletosystematicallyinvestigatealargesimulationspaceefcientlyandeffectively.Intheend,weidentiedtwoprotonproductionmechanismsthatcanquantitativelyexplainthehydrogen,doserate,andtimedependenciesofoxideandinterfacetrapbuildupinbipolarisolationoxides,characterizingELDRSoveralargerangeofexperimentalandenvironmentalconditions.AlthoughbothH2crackinganddirectprotonreleasefromH-vacancieshadpreviouslybeensuggestedasmechanismsbytheresultsofrstprinciplescalculations,quantitativemodelinginFLOODSwasabletodistinguishtheseaskeymechanismsamongmanyotherswhichhadalsobeensuggested.Weshowedhowthetwomechanismscontributedifferentlyunderdifferentconditions,andhowtheyinteractandcompete,togetherexplainingtheoverallELDRS 132

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effectsobservedindifferentH2ambients.WiththedevicesimulationcapabilitiesofFLOODS,wewerealsoabletoshowtheimportanceofthelocationofinitialoxidedefects,andofthecontributionofprotonconnementtobothoxidechargeandinterfacetrapbuildup,especiallythroughthemechanismofhydrogendimerizationincaseswhereahighconcentrationofprotonsformsneartheSiO2/Siinterface.Basedonexperimentalwork,ithasbeensuggested[ 42 ]thatH2soakingcouldbeusedasacharacterizationtechniquethatwouldallowHDRirradiationstomoreaccuratelypredicttheTIDdegradationofbipolardevicesintheLDR,low-H2spaceenvironment.Theresultsinthisworksupportthatidea,suggestingthat,becausethesamemechanismisresponsibleforthedegradationunderbothconditions,thattheadditionofH2duringHDRtestingmerelyspeedsupthedegradationthatwouldbeseenoverlongtimesinactualLDRspaceenvironments;thatanoverwhelmingH2concentrationpreventsthedoserateeffectcausedbyexcessiveprotonbuildupandH2dimerizationduringHDRirradiations;andthatin100%H2thesameLDRmaximumdegradationisachievedregardlessofdoserate.Timedependentsimulationscanhelpdesignerspredicttherateofdegradationwhenplanningforshortermissionsduringwhichdegradationwouldnotreachthemaximum.Onespecicimprovementtothemodelherewouldenablefurtherstudyofdose-rateeffects.Morecompleximplementationsoflocalelectriceldeffectscouldprovidethebasisforamoreaccuratecharacterizationofchargetransportandinteractionintheseandothersystems.Finally,sincetheinvestigativeapproachinthisstudyisbroadlyapplicabletotheinvestigationofchargetransportandtrappinginothermaterialsystemsanddevices,thenalsectionsofthischaptersuggestfurtherimprovementstothemodel,andpotentialapplicationsofthemethod. 7.2FutureWorkFutureworkshouldincludeexpansionofthemodeltoincludethedependenceofyieldandtrapenergiesonlocalelectriceld.Thisshouldincludealsoanexpansionof 133

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thesimulatedstructureto2D,includingsource-drainregionssothatchargedissipationinthesiliconismorerealisticallytreated.Additionalapplicationsofthismodelarealsosuggested. 7.2.1LocalElectricFieldDependencies 7.2.1.1InitialrecombinationandyieldItmaybepossibletoincludeafullsolutionofgeminaterecombinationofinitialEHPsinFLOODS,improvingtheaccuracyoftheyieldmodel.Thistreatmentwouldrequireovercomingsignicantsimulationchallenges,includingthefactthatelectriceldisnotadirectsolutionvariableinFLOODS,butinsteadarstderivativeofasolutionvariable,andassuchisnoteasilytreatedmathematically.Anotherchallengeisthecomputationaldifcultiesthatmayariseifextremelysmallgridspacingisrequiredtoresolvethedistancebetweenelectronsandholesineachgeneratedpair.Afullgeminatesolutionoftheinitialelectronandholeyieldisbeyondthescopeofthiswork.However,abriefoutlineofapossibleimplementationisincludedbelow,fromthediscussionin[ 16 ].TheSmoluchowskiequation[ 95 97 ]givestheprobabilitydensityofasingleelectronnearasingleholeinthepresenceofanappliedelectriceld:@P(r,t) @t=Dfr2P(r,t))]TJ /F5 11.955 Tf 18.01 8.08 Td[(e kTr[P(r,t)]g (7)Thisequationconsidersonlyonechargepair,specicallyincludingCoulombattraction,whichisnottypicalinTCADdevicesimulation.However,wenotethatthisequationhasadiffusion,drift,andrecombinationterm.Becauseofthis,itispossiblethattheprobabilitydensity,P(r,t),in 7 maybetreatedwithinbuiltFLOODSoperatorsinasimilarwaytoelectronsandholeshavebeentreated.Otherwise,itmaybepossibletouseananalyticalsolutiontothisequation,givenbyOnsagerinthecasethattheinitial 134

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distributionofelectronsaroundtheholesisisotropic: P(r,F)=1 Z0dP(r,F,) (7) =1 Z0dexp[)]TJ /F4 11.955 Tf 9.3 0 Td[(r(1+cos)]Zinfrc=rdsexp()]TJ /F9 11.955 Tf 9.3 0 Td[(2)I0f2[r(1+cos)s]1=2gwhereI0isthemodiedBesselfunctionoforderzero.Itispossibletosolve( 7 )numerically[ 98 105 ],sothismaybeanoptioninFLOODS,ifsolving( 7 )istoodifcult.Themainlimitationofthisapproachisthatthechargepairsarenotreallyisolated.Underthisidealization,theseparationdistancebetweenelectronsandholesineachpairbecomesaneffectiveaverage,losingsomeofitsphysicalmeaning,butallowingthecalculation[ 16 ]. 7.2.1.2Simulationsundernon-zerobiasingconditionsExperimentshavebeencarriedoutonirradatedMOSstructureswhichattempttostudyspacechargeeffectsandcarriermotionbyobservingtime-dependentoxideandinterfacetrapbuildupofthestructurewiththegatebiased.Insimulation,itisdifculttobiassuchawideband-gapmaterialsuchasSiO2andstillachieveconvergence.Inaddition,inducingadepletionregioninthesilicondecouplesthechannelregionfromtheboundaryconditioninthebulksilicon,alsomakingconvergenceachallenge.TheproblemisthattheequilibriumcarrierdensityofelectronsandholesinboththeSiO2andthedepletionregionisverysmall,andthenaturallogofthissmallnumber(i.e.theelectrostaticpotential)isapproximatelyinnity.However,itwouldbeusefultohavethiscapability,tostudyprotonmotionandtrapannealing.Inaddition,amodelwhichtakeselectriceldintoaccountfortraplevelswouldalsobeuseful.Rightnow,theenergiesEfandErinourmodelarefornegligiblebandbendingintheSiO2,whichisafairapproximationunderzerobias,butisnotentirelyaccurate. 135

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7.2.2Application:STIOxidesinModernCMOSOneadditionalapplicationofthemodelingworkpresentedhereisradiation-induceddegradationofshallowtrenchisolation(STI)oxides,whichareofsimilarpoorqualitytobipolarisolationoxides,andwhosedegradationcancauseparasiticleakagepathstoturnoninmodernCMOSdevices.Traditionally,TIDstudieswereconcernedaboutthedegradationofgateoxides,butthismaynotbemuchofaprobleminmoderndevices.References[ 25 ]and[ 16 ]includeexpressionsforthechangeinthresholdvoltageduetotrappedoxidecharge(Vot).ItcanbeshownthatVotisproportionaltothesquareofoxidethickness(t2ox).Also,itisknownthatE0centersnear(within3nm)theSi/SiO2interfaceexchangechargewiththeSi,resultinginpassivationofdefectsneartheinterfacebytunnelingelectronsfromtheSi[ 25 ],[ 23 ].Therefore,moderndevices,withthin(<1nm)gateoxides,arenotassusceptibletothiskindofdegradation. Figure7-1. Arepresentativecross-sectionofamodernCMOStechnology[ 25 ].[Reprinted,withpermission,fromH.J.Barnaby,Total-ionizing-doseeffectsinmodernCMOStechnologies,IEEETrans.Nucl.Sci.,vol.53,no.6,pp.3112,Figure16,Dec.2006.] However,modernCMOSprocessesdomakeuseofrelativelythickandpooroxidesintheshallowtrenchisolation(STI)regions,andtheseregionshavebeenshownto 136

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Figure7-2. Theworst-casecapacitor-voltageresponseofonesuchrepresentativestructureasFig. 7-1 ,irradiatedandthenbiasedasaFOXFET[ 25 ].[Reprinted,withpermission,fromH.J.Barnaby,Total-ionizing-doseeffectsinmodernCMOStechnologies,IEEETrans.Nucl.Sci.,vol.53,no.6,pp.3112,Figure17,Dec.2006.] bequitesusceptibletoradiationdamage,asdiscussedbelow.Figs. 7-1 and 7-2 showarepresentativecross-sectionofann-channelMOSFET,includingtheSTIregions,andthecapacitor-voltageresponseofanSTIeldoxideMOScapacitor(FOXCAP)fabricatedinacommercial130nmprocess,reproducedfrom[ 25 ].Inasimplehandcalculation[ 25 ],Barnabyshowsthattheamountofoxideandinterfacetraps(NotandNit)theoreticallyinducedbythevoltageshiftinFigs. 7-1 and 7-1 aremuchworsethanthatofbaseoxides,thermaloxides,andasilicon-on-insulatorburied(SIMOX)oxide.ItispossibletomodelthiseffectinFLOODS,bysimulatingradiation-inducedoxidechargeandinterfacetrapbuildupinanSTIregion,andcalculatingtheinversionlayerchargeinduced.ItisalsopossibletobiastheCMOSdevicesuchthattheSTIregionactsasagateoxide,calledaFieldOxideFET,orFOXFET.Asurface-Shockley-Read-HallrecombinationmodelwillaccountfortheeffectofNitonthechannelcharge.ItisalsopossibletoimplementanewgriddingschemeinFLOODSthat 137

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wouldallowforefcientlygriddingtheslopingwallsoftheSTIregion,butthisisbeyondthescopeofthiswork. 7.3FinalSummaryWehavepresentedhereaphysics-basedmodelimplementedintheFLOODSTCADdevicesimulatorthataccuratelyandsimultaneouslydescribestotalionizingdoseeffectsoverarangeoftotaldoses,doserates,ambientH2concentrations,andmeasurementtimes.TheELDRSeffecthasbeenexplainedasacombinationofhydrogencrackingonE0centersandprotonreleasefromhydrogenatedoxygenvacanciesinSiO2.Thecontributionofdifferentoxidechargespecieshasbeencharacterized,andhydrogendimerizationhasbeenidentiedasthemechanismdistinguishingbetweentimedependentandtruedoserateeffects.Basedontheinsightsgainedfromtheseinvestigations,wesupportH2soakingasanHDRtestmethodtocharacterizebipolardevicesforuseintheLDRspaceenvironment. 138

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APPENDIX:SENSITIVITYANALYSISRESULTSSUMMARY AsdescribedinChapters 3 and 4 ,asensitivityanalysiswasperformedinFLOODS,varyingthereactionenergybarrierswithinthestatisticalerroroftheDFTcalculationsandnotingthechangeinresults.Table A-1 providesaconvenientorganizationofthechargetrappingreactionsandenergeticsconsideredinthiswork,showingthespecicrangeoverwhicheachenergywasvaried,andtheenergieswhichprovidedthebestmatchtoNitandNotmeasurementsdiscussedthroughoutthiswork.They/noryes/noboxgivesacrudesummaryofwhetherornottheenergywassensitiveaccordingtothesensitivityanalysisresultsdiscussedthroughoutChapters 4 6 ,andassumes,asdiscussedinChapters 2 and 4 ,thatVoisthedominantdefectneartheinterface,andthattheconcentrationsofVo,Harelow,approximately1014-1015cm)]TJ /F2 7.97 Tf 6.58 0 Td[(3,asindicatedbyDFTresults. 139

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TableA-1. ResultsofSensitivityAnalysis ReactionEf(eV)y/nEr(eV)y/nbestrangebestrange R0Vo+h+,V+o0.00.0-0.2y4.50.6-4.5yR1V+o+H2,VoH+H+0.50.2-0.6y0.80.6-1.0nR2V+o+e)]TJ /F3 11.955 Tf 10.4 -4.34 Td[(,Vo0.40.0-1.0n9.0-nR3Vo+h+,V+o0.00.0-0.2y0.60.0-1.5nR4V+o+H2,VoH+H+1.40.0-1.4n0.80.6-1.0yR5V+o+e)]TJ /F3 11.955 Tf 10.41 -4.34 Td[(,Vo0.00.0-1.0n9.0-nR6VoH+h+,VoH+0.00.0-0.2y4.50.6-4.5nR7VoH+,Vo+H+2.01.0-3.0n1.81.0-3.0nR8VoH++e)]TJ /F3 11.955 Tf 10.4 -4.34 Td[(,VoH0.00.0-1.0n7.5-nR9VoH+h+,VoH+0.00.0-0.2y0.60.0-1.5nR10VoH+,Vo+H+0.40.3-0.7n0.60.4-0.8nR11VoH++e)]TJ /F3 11.955 Tf 10.41 -4.34 Td[(,VoH0.00.0-1.0n3.0-nR12VoH2+h+,VoH+20.00.0-0.2y0.60.0-1.5nR13VoH+2,VoH+H+0.40.4-0.8y0.80.6-1.0nR14VoH+2,V+o+H20.40.2-0.6n0.60.0-0.6yR15VoH+2+e)]TJ /F3 11.955 Tf 10.4 -4.34 Td[(,VoH0.00.0-1.0n9.0-nR16VoH2+h+,VoH+20.00.0-0.2y0.60.0-1.5nR17VoH+2,VoH+H+0.40.4-0.8y0.80.6-1.0nR18VoH+2,V+o+H20.50.3-0.7y1.21.2-1.8nR19VoH+2+e)]TJ /F3 11.955 Tf 10.41 -4.34 Td[(,VoH0.00.0-1.0n9.0-n 140

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BIOGRAPHICALSKETCH NicoleRowseyreceivedherB.S.E.degreeinelectricalengineeringfromPrincetonUniversityin2006.ShereceivedherPh.D.inelectricalengineeringfromtheUniversityofFloridain2012,supportedbyaUFAlumniFellowship,andanIntelFoundation/SRCEAscholarship.Herresearchinterestsincluderadiationeffectsmodeling,multi-gatedevicesimulation,andsemiconductorquantumdotstructures.Aftergraduation,shewilljoinIntelCorporationinChandler,AZ. 150