Micromachined Inductors and Transformers for Miniaturized Power Converters

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Micromachined Inductors and Transformers for Miniaturized Power Converters
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1 online resource (174 p.)
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english
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Meyer, Christopher D
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University of Florida
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Degree:
Doctorate ( Ph.D.)
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University of Florida
Degree Disciplines:
Electrical and Computer Engineering
Committee Chair:
Arnold, David
Committee Members:
Yoon, Yong-Kyu
Bashirullah, Rizwan
Jiang, Peng

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Subjects / Keywords:
circuit -- converters -- electroplating -- inductors -- integrated -- metallization -- microfabrication -- power -- transformers
Electrical and Computer Engineering -- Dissertations, Academic -- UF
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Electrical and Computer Engineering thesis, Ph.D.
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
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Abstract:
Switched-mode dc-dc power converters are a ubiquitous part of modern, feature-rich portable electronic devices and are essential for efficiently transferring electrical energy out of battery sources and into various power-hungry loads, such as microprocessors, displays, sensors, and communications systems. These converters often comprise a significant portion of total system size/weight, and the largest offenders are often the associated power inductors and transformers. A significant reduction in the size the inductors and transformers would have a transformative effect in enabling new applications, such as mobile autonomous microsystems. Increasing the switching frequency of the power converters offers to reduce the values of the required passives. However, the expected switching frequencies of next generation power converters fall into a gap between magnetic film inductors and transformers operable at < 10 MHz and microwave air-core devices with high performance at > 1 GHz. In answer, a new class of air-core microinductors and microtransformers is presented in this document that leveraged microfabrication-enabled advancements to attain high performance in the desirable very high frequency (VHF) switching range and to enable fully integrated power management systems in the smallest possible packages. In order to design these devices, models were analyzed to uncover the ideal characteristics for operating in the VHF range. Compared to traditional air-core components, these new ones featured thicker windings and had more intricate windings for lower loss and higher density. A multilevel microfabrication process was developed for molding three-dimensional (3D) copper parts with the necessary characteristics of thickness, minimum feature size, and out-of-plane stacking. The 3D copper process enabled the microfabrication of inductors with measured inductance densities up to 170 nH/mm2 and quality factors as great as 33. Transformers were measured with even greater inductance densities: up to 325 nH/mm2 was obtained in a configuration for voltage gain of 3.5 with up to 78% efficiency. Performance figures for both inductors and transformers were shown to outstrip a number of other microfabricated examples found in the literature, particularly in the frequency range of 10 MHz–1 GHz. Microfabricated inductors were tested within the circuits of both a prototype 100 MHz switched-mode hybrid boost converter and a commercially-available surface-mount converter with up to 4 MHz switching frequency. With up to 37% efficiency at a conversion ratio of 6, the performance of the prototype 100 MHz converter when using a 14 nH microfabricated inductor largely matched that obtained when a larger 43 nH surface-mount inductor was used in the same converter at up to 1 mA load current. A packaging solution was devised for testing with the surface-mount converter. An embedded multilevel copper module consisting of both an inductor and interconnects was detached from its silicon fabrication substrate and served as a platform to which a surface-mount converter and capacitors were soldered.
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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Description based on online resource; title from PDF title page.
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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 Christopher D Meyer.
Thesis:
Thesis (Ph.D.)--University of Florida, 2012.
Local:
Adviser: Arnold, David.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2013-05-31

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MICROMACHINEDINDUCTORSANDTRANSFORMERSFORMINIATURIZE D POWERCONVERTERS By CHRISTOPHERD.MEYER ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2012

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c r 2012ChristopherD.Meyer 2

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Idedicatethistomylovingfamily. 3

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ACKNOWLEDGMENTS Iwouldliketothankeveryonewhohascontributedtothesucc essofthework presentedinmydissertation.Ithankmyadviser,Dr.DavidA rnold,whoprovidedme withtheopportunitytoworkonexcitingtopicsinpowermagn eticsandwhointroduced metomicrofabricationattheUniversityofFloridacleanro om.IthankDr.Rizwan Bashirullahwhoservedonmycommitteeandwhoisdeveloping theveryhighfrequency powerconvertercircuitsthatmotivatedmywork.IthankDrs .Yong-KyuYoonandPeng Jiangfortheirvaluableinsightswhilealsoservingonmyco mmittee.IthankXueLin fortestingmymicroinductorwithinhishybridboostconver ter.IthankChristopher Doughertyforenlighteningmeontheconsiderationsthataf fecthighfrequencyconverter designs.IthankJessicaMeloyforherhelpinwirebonding. IthanktheU.S.ArmyResearchLaboratory(ARL)forfundingt heprojectand mycolleaguesatARLfortheirsupport.IthankDr.BrianMorg annotonlyforleading thePowerforMicrosystemsprojectfromwhichmyresearchde rived,butalsoforthe clarityhebroughtandforhismentoringme.IthankDr.Sarah Bedairforcountless discussionsandforhersageadvicecontributingtomygrowt hbothtechnicallyand professionally.IthankManricoMirabelliforhismicrofab ricationassistanceandfor sharinghisphotolithographyexpertise.IthankJamesMulc ahyofthecleanroomstafffor maintainingandxingthetoolsthatwerevitaltothiswork. IthankWilliamBenardfor headingthecleanroomandkeepingitrunningsmoothly. Ithankmygrandfather,whoseprideinmeinspiredmetocompl etemydoctoral degree.Ithankmywife,Jennifer,forhersteadfastlove.Fi nally,Iwouldliketothankmy parentsfortheircontinuoussupportandlovingdevotion. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 13 CHAPTER 1INTRODUCTION ................................... 15 1.1TheCaseforSmall ............................... 17 1.1.1DistributedOn-ChipPowerforMicroprocessors ........... 17 1.1.2MobileAutonomousMicrosystems .................. 18 1.2Switched-ModePowerConverters ...................... 18 1.3Impedance ................................... 21 1.4HighFrequencyBenetsandChallenges .................. 22 1.5SurveyofExistingMicrofabricatedInductorsandTrans formers ...... 23 1.6Air-CorePassiveComponentsforMicroscalePowerConve rters ...... 24 2BACKGROUND ................................... 27 2.1HighFrequencyPowerConverters ...................... 27 2.2Inductors .................................... 28 2.3Transformers .................................. 30 3INDUCTORDESIGN ................................. 35 3.1QualityFactorDenition ............................ 35 3.1.1QualityFactorofNon-IdealReactiveComponents ......... 35 3.1.2QualityFactorofInductor ....................... 37 3.2PerformanceTrilemma ............................. 38 3.3StackedPlanarSpiralLayout ......................... 39 3.4LowFrequencyAnalyticalInductorModel .................. 40 3.5TrendsandOptimization ............................ 43 3.5.1Analytical ................................ 43 3.5.2FastHenry ................................ 44 3.6RadioFrequencyEffects ............................ 47 3.6.1CapacitiveCoupling .......................... 47 3.6.2EddyCurrents .............................. 53 3.7SummaryofInductorDesign ......................... 57 5

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4TRANSFORMERDESIGN ............................. 59 4.1OverviewandGoals .............................. 59 4.2MaximumEfciency .............................. 60 4.2.1FromScatteringParameters ...................... 60 4.2.2FromCoilQualityFactorsandCouplingCoefcient ......... 61 4.3Layout ...................................... 65 4.3.1TurnsRatio ............................... 65 4.4PerformanceUnderLoad ........................... 66 4.4.1DerivationofEfciencyandVoltageGainforArbitrar yLoad .... 66 4.4.2ConjugateImpedanceMatchedLoading ............... 69 4.5SummaryofTransformerDesign ....................... 70 5FABRICATION .................................... 72 5.1ProcessOverview ............................... 73 5.1.1SequentialLayerRemoval ....................... 73 5.1.2UltrasonicAgitationinSolvents .................... 74 5.2FeaturesandVariationsontheProcess ................... 76 5.2.1PlanarProcessing ........................... 76 5.2.2PhotoresistasaStructuralElement .................. 78 5.2.3SubstrateVersatility .......................... 79 5.3ProcessSteps ................................. 79 5.4SpecialProcessingConsiderations ...................... 82 5.4.1Sputtering ................................ 82 5.4.2Photolithography ............................ 85 5.4.3Electroplating .............................. 87 5.4.4ArgonSputterEtch ........................... 89 5.4.5PhotoresistSkinRemoval ....................... 90 5.4.6CopperSeedEtch ........................... 91 6INDUCTORCHARACTERIZATION ......................... 93 6.1EquipmentandSetup ............................. 93 6.2InductorCharacterizationMethods ...................... 94 6.2.1One-PortInductorMethods ...................... 94 6.2.2Two-PortInductorMethods ...................... 95 6.2.3InductorCharacteristicsObtainedfromImpedance ......... 97 6.3One-PortInductorCharacterization ...................... 98 6.3.1One-PortInductorsonPyrexSubstrates ............... 98 6.3.1.1Comparisontomodelpredictions .............. 101 6.3.1.2Currentrating ........................ 101 6.3.1.3Interwindingcapacitance .................. 102 6.3.2One-PortInductorsonSiliconSubstrates .............. 105 6.3.2.1Copperlayerthickness: 10 m vs. 30 m ......... 105 6.3.2.2Inductorshape:squarevs.circularspirals ........ 106 6

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6.4Two-PortInductorCharacterizationonSiliconSubstra tes ......... 110 6.4.1CapacitiveCouplingthroughtheSubstrate .............. 110 6.4.2WindingLosses ............................. 113 6.5SummaryofInductorCharacterization .................... 118 7TRANSFORMERCHARACTERIZATION ..................... 119 7.1EquipmentandSetup ............................. 119 7.2ImpedanceParameters ............................ 120 7.3Load-DependentEfciencyandVoltageGain ................ 122 7.4CharacterizationofTransformerswith 10 m ThickLayers ......... 124 7.4.1ExtractionofNominalInductancesandResistances ........ 125 7.4.2Load-DependentPerformanceof 1:1 Transformer ......... 127 7.4.3Load-DependentPerformanceof 1:3.5 Transformer ........ 131 7.5CharacterizationofTransformerwith 30 m ThickLayers .......... 135 7.6SummaryofTransformerCharacterization .................. 140 8PACKAGINGANDTESTINGWITHCIRCUITS .................. 142 8.1MicroinductorWireBondedtoVeryHighFrequencyBoostC onverter ... 142 8.1.1AbouttheMicroinductor ........................ 142 8.1.2AbouttheConverterandTestResults ................ 143 8.2TestingwithCommercialSurface-MountConverter ............. 145 8.2.1AbouttheTexasInstrumentsTPS61240Converter ......... 146 8.2.2ModuleDesignandProcessing .................... 146 8.2.3ConverterModuleTesting ....................... 149 8.3SummaryofInductorPackagingandTestingwithinConver terCircuits .. 154 9CONCLUSION .................................... 157 9.1SummaryofWork ............................... 157 9.2LessonsLearned ................................ 158 9.3FutureWork ................................... 160 REFERENCES ....................................... 166 BIOGRAPHICALSKETCH ................................ 174 7

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LISTOFTABLES Table page 2-1Literaturesurveyofmicroinductors ......................... 33 2-2Literaturesurveyofmicrotransformers ....................... 34 3-1CoefcientsformodiedWheelerandcurrentsheetexpre ssions ........ 41 5-1Processparametersforpassivesfabrication .................... 81 5-2Recipeforacidcoppersulfateelectroplatingbath ................. 88 6-1Comparisonofmeasuredinductorperformance .................. 99 6-2Comparisonofmodel-predictedtomeasuredinductorper formance ....... 100 6-3Performancecomparisonofinductorswithdifferentlay erthicknesses ...... 106 6-4Geometricparametersofsquareandcircularinductors ............. 107 6-5Performancecomparisonofsquareandcircularinductor s ............ 107 7-1Comparisonoftransformercircuitparameters ................... 126 8-1Componentsizesinfunctionalconvertermodule ................. 149 8

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LISTOFFIGURES Figure page 1-1Commonconvertercircuits ............................. 20 1-2Reviewofmicroinductors .............................. 23 1-3Reviewofmicrotransformers ............................ 25 3-1Circuitdiagramofsimpleinductormodel ...................... 39 3-2Diagramofspiraldimensions ............................ 42 3-3Trendsofinductancetoresistanceratiovs.packingden sity ........... 45 3-4Trendsofinductancetoresistanceratiovs.outerdiame ter ........... 46 3-5Trendofinductancevs.verticalgapbetweenstacksimul atedinFastHenry .. 46 3-6Diagramofcapacitivecouplingoftracesthroughsubstr ate ........... 49 3-7Circuitmodelofinductorwithsubstratecapacitance ............... 49 3-8Substrateresistanceeffectoninductorimpedance ................ 50 3-9Circuitmodelofinductorwithwindingandsubstratecap acitances ....... 51 3-10Substratevs.windingcapacitanceeffectoninductori mpedance ........ 52 3-11COMSOLsimulationsofskineffectinwindingcrosssect ions .......... 55 3-12Measuredeffectofeddycurrentsoninductorimpedance ............ 57 4-1Transformerenergyowdiagram .......................... 61 4-2Transformerefciencycalculatedbyqualityfactorsan dscatteringparameters 64 4-3Transformerlayoutwindingdiagram ........................ 65 4-4Circuitdiagramoftwo-portnetworkcascadedwithshunt load .......... 67 4-5Circuitdiagramoftwo-portnetworkcascadedwithserie sload .......... 68 4-6Circuitdiagramoftwo-portnetworkwithsourceandload impedances ..... 69 5-1Illustrationsofadditiveprocessstage ........................ 74 5-2Illustrationsofsubtractiveprocessstage ...................... 75 5-3Scanningelectronmicrograph(SEM)ofinductorwith 10 m thicklayers .... 75 5-4SEMofinductorwith 30 m thicklayers ...................... 76 9

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5-5Crosssectiondiagramsofprocessadditivestage ................. 83 5-6Crosssectiondiagramsofprocesssubtractivestage ............... 84 5-7Adhesionofcoppertophotoresist ......................... 85 5-8Electroplatingleakagebetweenfeatures ...................... 86 5-9Electroplatedcoppercantilever ........................... 89 5-10Comparisonimagesshowingargonsputteretcheffecton adhesion ....... 90 5-11Photoresistblockinglayerformedbyargonsputteretc h ............. 91 5-12Sidewallrougheningcausedbycopperetch .................... 92 6-1SEMimagesofone-portandtwo-portinductors .................. 94 6-2Two-portinductorimpedancenetwork ....................... 95 6-3Identicationofinductorspecicationsfromplots ................. 99 6-4Currentratingofinductors .............................. 100 6-5Comparisonimagesofinterlayerphotoresist ................... 103 6-6Comparisonofinterlayerdielectriceffectonimpedanc eofsmallinductor .... 104 6-7Comparisonofinterlayerdielectriceffectonimpedanc eoflargeinductor .... 104 6-8Comparisonoflayerthicknessesforsmallinductor ................ 108 6-9Comparisonoflayerthicknessesforlargeinductor ................ 108 6-10Comparisonofshapeofsmallinductor ....................... 109 6-11Comparisonofshapeoflargeinductor ....................... 109 6-12Padcapacitancediagram .............................. 111 6-13Shuntcapacitanceattwoportsofinductor ..................... 115 6-14Impedanceplotsfromtwo-portinductor ...................... 115 6-15SEMimagesofinductorswithsolidvs.lamentedtraces ............ 116 6-16SEMimagesofsolidvs.lamentedtraces ..................... 116 6-17Impedanceplotsoflamentedvs.solidtraces .................. 117 6-18Changeinresistanceduetolamentedvs.solidtraces ............. 117 7-1Circuitrepresentationoftwo-portimpedanceparamete rs ............ 121 10

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7-2Lowfrequencytransformermodel ......................... 122 7-3SEMimagesofmicrofabricatedtransformers ................... 125 7-4Impedanceplotsof 1:1 transformerwith 10 m thicklayers ........... 126 7-5Impedanceplotsof 1:3.5 transformerwith 10 m thicklayers .......... 127 7-6Efciencyof 1:1 transformer ............................ 128 7-7Voltagegainof 1:1 transformer .......................... 128 7-8Magnitudeandphaseofmatchedloadimpedancefor 1:1 transformer ..... 129 7-9Efciencyandvoltagegainvs.loadimpedancefor 1:1 transformer ...... 130 7-10Efciencyof 1:3.5 transformer ........................... 132 7-11Voltagegainof 1:3.5 transformer ......................... 132 7-12Magnitudeandphaseofmatchedloadimpedancefor 1:3.5 transformer ... 133 7-13Efciencyandvoltagegainvs.loadimpedancefor 1:3.5 transformer ..... 134 7-14SEMimageofmicrotransformerwith 30 m thicklayers ............. 136 7-15Impedanceplotsof 1:1 transformerwith 30 m thicklayers ........... 137 7-16Efciencyofthicker 1:1 transformer ........................ 138 7-17Voltagegainofthicker 1:1 transformer ...................... 138 7-18Magnitudeandphaseofmatchedloadimpedanceforthick er 1:1 transformer 139 7-19Efciencyandvoltagegainvs.loadimpedanceforthick er 1:1 transformer .. 141 8-1Microinductorwirebondedtocircuitfortesting .................. 143 8-2Impedanceofwirebondedinductor ........................ 144 8-3Measuredefcienciesofconverterwithwirebondedmicr oinductor ....... 145 8-4Copperlayoutofconvertermodule ......................... 147 8-5Photographofreleasedcopperframework ..................... 148 8-6Photographsoffunctionalconvertermodule .................... 149 8-7Impedanceofinductorusedinconvertermodule ................. 151 8-8Measuredefciencyvs.outputcurrentofconvertermodu le ........... 152 8-9Boostconvertercircuitdiagram ........................... 152 11

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8-10Inductorvoltagewaveformforseveralinputvoltages ............... 153 8-11Waveformsofinductorvoltagefordifferentloadcurre nts ............. 155 8-12Waveformsofoutputvoltagefordifferentloadcurrent s .............. 155 9-1Reviewofmicroinductorsincludingnewresults .................. 159 9-2Reviewofmicrotransformersincludingnewresults ................ 159 9-3Illustrationsofpackageassembly .......................... 161 9-4SEMimagesofcoppersockets ........................... 163 9-5SEMimagesofteethcontactingtosurface-mountcompone nt .......... 163 9-6Surface-mountresistorandcapacitoralongsidemicroi nductors ......... 164 9-7Measuredimpedancesofsocketedresistorandcapacitor ............ 165 12

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy MICROMACHINEDINDUCTORSANDTRANSFORMERSFORMINIATURIZE D POWERCONVERTERS By ChristopherD.Meyer May2012 Chair:DavidP.ArnoldMajor:ElectricalandComputerEngineering Switched-modedc-dcpowerconvertersareaubiquitouspart ofmodern,feature-rich portableelectronicdevicesandareessentialforefcient lytransferringelectricalenergy outofbatterysourcesandintovariouspower-hungryloads, suchasmicroprocessors, displays,sensors,andcommunicationssystems.Theseconv ertersoftencomprise asignicantportionoftotalsystemsize/weight,andthela rgestoffendersareoften theassociatedpowerinductorsandtransformers.Asignic antreductioninthesize theinductorsandtransformerswouldhaveatransformative effectinenablingnew applications,suchasmobileautonomousmicrosystems. Increasingtheswitchingfrequencyofthepowerconverters offerstoreducethe valuesoftherequiredpassives.However,theexpectedswit chingfrequenciesof nextgenerationpowerconvertersfallintoagapbetweenmag neticlminductors andtransformersoperableat < 10MHz andmicrowaveair-coredeviceswithhigh performanceat > 1GHz .Inanswer,anewclassofair-coremicroinductorsand microtransformersispresentedinthisdocumentthatlever agedmicrofabrication-enabled advancementstoattainhighperformanceinthedesirableve ryhighfrequency(VHF) switchingrangeandtoenablefullyintegratedpowermanage mentsystemsinthe smallestpossiblepackages. Inordertodesignthesedevices,modelswereanalyzedtounc overtheideal characteristicsforoperatingintheVHFrange.Comparedto traditionalair-core 13

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components,thesenewonesfeaturedthickerwindingsandha dmoreintricatewindings forlowerlossandhigherdensity.Amultilevelmicrofabric ationprocesswasdeveloped formoldingthree-dimensional(3D)copperpartswiththene cessarycharacteristicsof thickness,minimumfeaturesize,andout-of-planestackin g. The3Dcopperprocessenabledthemicrofabricationofinduc torswithmeasured inductancedensitiesupto 170nH = mm 2 andqualityfactorsasgreatas 33 .Transformers weremeasuredwithevengreaterinductancedensities:upto 325nH = mm 2 was obtainedinacongurationforvoltagegainof 3.5 withupto 78% efciency.Performance guresforbothinductorsandtransformerswereshowntoout stripanumberofother microfabricatedexamplesfoundintheliterature,particu larlyinthefrequencyrangeof 10MHz – 1GHz Microfabricatedinductorsweretestedwithinthecircuits ofbothaprototype 100MHz switched-modehybridboostconverterandacommercially-a vailablesurface-mount converterwithupto 4MHz switchingfrequency.Withupto 37% efciencyata conversionratioof 6 ,theperformanceoftheprototype 100MHz converterwhenusing a 14nH microfabricatedinductorlargelymatchedthatobtainedwh enalarger 43nH surface-mountinductorwasusedinthesameconverteratupt o 1mA loadcurrent. Apackagingsolutionwasdevisedfortestingwiththesurfac e-mountconverter.An embeddedmultilevelcoppermoduleconsistingofbothanind uctorandinterconnects wasdetachedfromitssiliconfabricationsubstrateandser vedasaplatformtowhicha surface-mountconverterandcapacitorsweresoldered. 14

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CHAPTER1 INTRODUCTION Switched-modedc-dcpowerconvertersareaubiquitouspart ofmodern,feature-rich portableelectronicdevices.Thesepowerconvertersarees sentialforefciently transferringelectricalenergyoutofbatterysourcesandi ntovariouspower-hungry loads,suchasmicroprocessors,displays,sensors,andcom municationssystems. Theneedforpowerconvertersarisesfromthefactthatelect ricityisutilizedin manydifferentformsevenwithinasinglesystem.Ofteneach subsystemhasadifferent expectationforelectricalcurrent(the“rate”),voltage( the“force”),anddutycycle(the on/offtimes).Loadsmayoperateerraticallyornotatallif thesourceisincapableof deliveringenoughelectricalcurrent,atagivenvoltagele vel,andforacertainamountof time.Batteriesaredesignedtoprovidecurrentataxedvol tage,whichmaynotmatch theneedsoftheloads.Thebatteryvoltagealsooftendecrea seswithhighercurrent drawsorwithtimeasitsenergystorageisdepleted.Powerco nvertersprovidethe handshakingthatisnecessaryforthesourcesandloadstoin teroperatewitheachother. Onebasicroleofthedc-dcswitched-modepowerconverteris toacceptelectrical powerthatisinputtoitatonevoltagelevelandoutputthatp oweratadifferentvoltage level.Intelligentcontrolmechanismswithintheconverte rcanrespondtouctuationsin sourceandloadconditionstohelpsmooththedeliveryofpow erandpreventlevelsfrom fallingoutofspecication. Althoughtheterm“dc”impliesthattheinputandoutputvolt agesofthedc-dc converterareideallyconstanttotheoutsideworld,inside theconverterareswitches thatdynamicallyreconguretheelectricalcurrentpathso ftheconvertercircuitmany thousandstomillionsoftimespersecond.Powerconversion utilizesthereactionsof inductorsandtransformerstotheswitch-inducedchangesi nelectricalcurrentwithin theconvertertoraiseorlowerthevoltagetodesiredlevels .Suchinductivecomponents possessthecharacteristicofinducingavoltagedifferenc etoresistchangesinthelevel 15

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ofcurrentpassingthroughthem.Thefundamentalequationd escribingthisbehavioris v L ( t )= L di dt (1–1) where v L ( t ) isthevoltageinducedacrosstheinductor, di = dt isthechangeincurrent throughit,andtheratio L isdenedastheinductance,measuredin henries ( H ).Foran electricalcurrentinitiallyat 0 andrisingtoalevel I ,theenergy E storedintheinductoris E = 1 2 LI 2 (1–2) Inductanceisgenerallyproportionaltotheareaenclosedb yacoiledconductor. Becausephysicalvolumeandmassareplacedatapremiuminpo rtableelectronics applications,smallinductorsaredesiredbuthavecorresp ondinglysmallinductances. Theinductorsandtransformersmust,forthesakeofefcien cyhowever,storeenough energyperswitchingcycletoovershadowthepowerlostduri ngconversion.Asaresult, theinductivecomponentscancompriseamajorportionofthe entireconvertersystem sizeandmass,especiallywhentherestoftheconvertercirc uitisintegratedontoa single,tinysemiconductorchipwith nm -scaletransistors. Thelargeinductivecomponentsare,duetotheirsize,gener allyaddedasdiscrete componentsconnectedoutsidetheconverterpackage.Exter nalconnectionsfurther addtothebulkofthesystemaseachcomponentrequiresitsow npackaging,pads, andsolderjoints.Asignicantsizeandweightsavingswoul dbeobtainedifthe inductorsandtransformerscouldbeintegratedwiththeres toftheconvertercircuit withinthesamepackage.Bulkyexternalconnectionscouldb ereplacedbymuchleaner wirebonds,embeddedinterconnects,orip-chipbumpsviaa System-in-Package (SiP)approach.Furthersizesavingswouldbeobtainedthro ughtheSystem-on-Chip (SoC)approachofmonolithicallyfabricatinginductorsan dtransformersdirectlyonthe integratedcircuitschip. 16

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TorealizetheseSiPorSoCconceptsforpowerconverters,in ductivecomponents mustrstdecreaseinsizetothepointwhereintegrationisn otcost-prohibitive.One routetodecreasingtheinductor/transformersizeistoinc reasetheswitchingfrequency oftheconverter,sothatthecurrentvariations, di = dt ,aregreaterandoccurmoreoften. Theothermeansofreducingsizeistoincreasetheinductanc edensityoftheinductors andtransformers. Theinductorsandtransformerspresentedinthisdocumentl everagemicrofabrication technologiesforincreaseddensityandaredesignedtooper ateatincreasedfrequencies thathavebeenemergedfrominnovativeintegrated-circuit converters.Thegoalofthis workistoenablefully-integratedhigh-frequencyswitche d-modedc-dcpowerconverters withultra-miniaturized,high-densityinductorsandtran sformers. 1.1TheCaseforSmall Fromtheadventoftheintegratedcircuitinthe1950suptoth epresentday, electronicsystemshavebeencontinuallypackedintorapid lyshrinkingdeviceswith ever-greaterprocessingpower.Contemporaryconsumerele ctronicsaremarked byexamplesofportablecomputers,mobilephones,andmedia playersinsvelte formswithincreasinglyconvergentfunctionality.Thenee dforfullyintegratedpower convertersisreachingacriticalpoint,however,asthesca lingofpowercomponents hasstruggledtokeeppacewiththatofdataprocessingandst orage.Butbeyondjust theconsumer-drivenaestheticofsmallforthesakeofsmall ,asignicantreductionin thesizeofpowersubsystemscouldalsohaveatransformativ eeffectinenablingnew applications,likemobileautonomousmicrosystems,andin improvingthedistributionof power,suchasformicroprocessors.1.1.1DistributedOn-ChipPowerforMicroprocessors Modernmicroprocessorsarehighlyparallelinoperation.F acingtheupperlimits ofusinghigherclockfrequenciestoprocessdataquicker,d esignershaveleveraged thebenetsofacontinually-shrinkingtransistorsizeand areintegratingmultiple 17

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microprocessorcopies,orcores,onasinglechip.Thecores areabletoprocess datainparallel,buthaveatendencytobeunder-utilizedin situationswheretasks requireserialprocessing.Althoughtodaysmicroprocesso rsreceivepowerthatis suppliedbyaconverterlocatedoutsidethemicroprocessor package,theabilityto integratemanypowerconvertersonthechipitselfcouldena bleindividualportionsof themicroprocessorcircuittoberapidlyturnedonandoffas needed,reducingpower consumptionandincreasingthethermalbudgetoftheactive portions.On-diepower converterswouldadditionallyreducethecomplexityofuti lizingindependentvoltage levelsforportionsofthemicroprocessoroperatingatdiff erentfrequenciesforfurther reductionsinpowerconsumption[ 1 2 ]. 1.1.2MobileAutonomousMicrosystems Anemergingresearcheffortisfocusedatdevelopingmobile autonomous microsystems,tinyroboticdevicesthatcannavigatethrou ghtheirenvironmentby ying,crawling,orhopping.Thenumberandcomplexityofsu bsystemsenvisionedfor thesemobilemicrosystemsisstaggering.Inadditiontothe actuatorsforlocomotion, thesemanmadebugsareexpectedtocontainsensorsforsitua tionalawareness,logic blocksfordataprocessing,communicationssystemsforrel ayinginformation,and possiblygeneratorsforharvestingenergyfromtheenviron ment.Interoperationofthese subsystemsislikelytobeachallengeaseachislikelytoreq uireoperationatunique voltages,currents,anddutycyclesforbestperformance,a ndwillrequireanadvanced powermanagementsystemthatmustfurthermorebevanishing lysmallandlightsoas tonotinterferewiththemobilityofthebug[ 3 ]. 1.2Switched-ModePowerConverters Amultitudeofcircuittopologiesexisttoachieveswitched -modepowerconversion. Someprovideastep-upfromlowerinputvoltagetoahigherou tputvoltage,andsome provideastep-down.Somearecapableofprovidingeitherst ep-uporstep-down on-the-y,whileothershaveinputandoutputvoltagesthat areequaltooneanotherbut 18

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provideisolationtoprotecttheoutputfromhighvoltagesp ikesthatmayoccuronthe inputsideofthecircuit.Commonswitched-modeconvertert opologiesincludetheboost, buck,buck-boost,andybackcircuits. ThebasicboostconverterisdrawninFigure 1-1A .Currentowsthroughthe inductor L whenswitch Q isclosed,andenergyisstoredinthemagneticeldofthe inductor.When Q isopened,avoltageisinducedacrosstheinductortooppose any suddenreductionincurrent,pushingcurrentthroughdiode D ,ontotheoutputcapacitor C ,andouttotheload R .Thevoltageinducedacrosstheinductorinthislaststepis negativewithrespecttothereferencefor v L ( t ) labelledonFigure 1-1A ,meaningthatthe voltageacrosstheloadisgreaterthantheinputvoltage V in .Theroleofthecapacitor C istostorechargebetweenswitchingcyclesandensurethatt heoutputvoltageremains atarelativelysteadyvalue.Theconversionratio M fortheboostconverteriscontrolled bythedutycycleoftheswitchinitsclosedposition,asplot tedinFigure 1-1B .Whenthe switchisclosedforalongerportionofthecyclethanitiscl osed,theconversionratioof theconverterislarger. Thebuck(Figure 1-1C )andbuck-boost(Figure 1-1E )circuitsoperatesimilarlyin thattransientcurrentthroughchargedinductorsinducevo ltagesacrosstheinductors thatareutilizedtocreatevoltagedifferenceswithrespec ttotheinput.Thedutycycleof theswitch-closedtimeagainprovidesmodulationoftheout putvoltage.AsperFigure 1-1D thebuckcircuitisabletoprovideanoutputvoltagethatisl essthantheinput,while thebuck-boostprovidesaninvertedvoltagethatcanrangei nmagnitudefromlevelsthat arebothgreaterandlesserthantheinput(Figure 1-1F ). TheybackconverterofFigure 1-1G derivesfromthebuck-boostconverter,except thattheinductorofthebuck-boostisreplacedbyanisolati ngtransformer.Theswitch inFigure 1-1G ispositionedfornon-invertingoutput,sotheconversionr atioplottedin Figure 1-1H fora 1:1 transformeristhesameasthatofthebuck-boostbutopposit ein polarity.Astep-uptransformerwithnon-unitygainmaybeu tilizedinthiscircuittorealize 19

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+ + v L ( t ) L Q D CR + V out V in ABoostconvertercircuit 0 0.25 0.5 0.75 1 0 1 2 3 4 5 Conversion Ratio M (V/V)Duty Cycle D BBoostconversionratio + L Q D CR + V out V in CBuckconvertercircuit 0 0.25 0.5 0.75 1 0 0.5 1 Conversion Ratio M (V/V)Duty Cycle D DBuckconversionratio + L QD CR + V out V in EBuck-boostconvertercircuit 0 0.25 0.5 0.75 1 -5 -4 -3 -2 -1 0 Conversion Ratio M (V/V)Duty Cycle D FBuck-boostconversionratio + Q D CR + V out V in 1: n GFlybackconvertercircuit 0 0.25 0.5 0.75 1 0 1 2 3 4 5 Conversion Ratio M (V/V)Duty Cycle D HFlybackconversionratio Figure1-1.Commonconvertercircuitsandtheiridealizedc onversionratios M as functionsofswitchingdutycycle D .FiguresadaptedfromEricksonand Maksimovic[ 4 ]. 20

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moredrasticconversionratiosthanwouldbehadfromthebuc k-boost.Thetransformer additionallyprovidesisolationprotectionbetweeninput andoutput. 1.3Impedance WhileEquation 1–1 describesthecharacteristictransientbehaviorofinduct ive componentsininducingvoltagesinoppositiontochangesin thecurrentpassingthrough it,animpedanceanalysisisusefulforcharacterizingtheb ehaviorofaninductorwhen thechangesaresinusoidalorperiodic.Theimpedance Z ofaninductorrelatesthe voltage V acrosstheinductortothecurrent I passingthroughit Z = V I (1–3) wherebothvoltageandcurrentaresinusoidallyvarying.Ot hernon-sinusoidalperiodic excitationscanbeconsideredusingFourieranalysistodec omposethesignalintoa summationofsinusoidalsignals. Whendeterminingimpedance,thevoltageandcurrentwavefo rmsarerepresented byphasors,eachbeingavectorwithmagnitudeequaltotheam plitudeofthewaveform andwithangleequaltothephasedifferencebetweenthewave formandsomecommon reference.Incomplexform,therealpartoftheimpedancere presentsthein-phase energy-dissipative(resistive)componentandtheimagina rypartrepresentsthe out-of-phaseenergy-storagecomponent.Theimpedanceofa nidealinductorwith inductance L atanangularfrequencyof is, Z L = j L (1–4) Whilethecurrentthroughanidealinductorlagsthevoltage acrossitby 90 (aquarter wavelength),resistiveandcapacitiveeffectscausefrequ ency-dependentmagnitudeand phaserelationships. 21

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1.4HighFrequencyBenetsandChallenges Becausetheimpedanceofanidealinductorscaleswithfrequ ency,power converterswithhigherswitchingfrequenciescanutilizel ower-valuedandphysically smallerinductors.However,increasingtoveryhighfreque ncy(VHF)switching ( > 10MHz )alsointroducesseveralchallengesthatcouldseverelyli mitperformanceof theseconvertersifnotaddressed. Manymagneticcorematerials,whichareusedtoincreasemag neticinductionin inductors/transformers,areunabletophysicallyswitcht heirmagnetizationfastenough inresponsetoaVHFappliedeld.Thetimelagbetweenchange sintheappliedeld andtherespondingchangeinmagneticinductioninthemater ialleadstopowerlosses inthecore.Designersoftenutilizemagneticmaterialanis otropy(orsometimesadcbias magneticeld)perpendiculartotheappliedmagneticeldi nordertoimprovethehigh frequencyresponsetimeofmagneticmaterialsattheexpens eoflowerpermeability[ 5 ]. Eddycurrentgenerationwithinelectricallyconductivema terialsresultsintheskin effect,theconnementofelectricandmagneticeldstothe materials'surfaceathigh frequencyexcitation.Theskineffectlimitstheeffective crosssectionalareaofboth theelectricwindingandthemagneticcore,leadingtogreat erresistanceandlesser inductance. IntheVHFswitchingrange,theconvertercircuitdesigndem andscomponentswith inductanceandcapacitancevaluesthatareontheorderofth eunintendedparasitic inductancesandcapacitancesthatinherentlyoccurbetwee ncomponentsandinthe interconnectionsbetweenthem[ 6 ].Thedesignoftheinductorsandtransformersmust considerthelargeparasiticcapacitanceexperiencedasen ergyisstoredintheelectric eldbetweenadjacentconductortraces.Thisparasiticcap acitancelimitsthemaximum operatingfrequencyandefciencyoftheinductor/transfo rmer. 22

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1.5SurveyofExistingMicrofabricatedInductorsandTrans formers Gardneretal.[ 7 ]publishedinlate2009acomprehensivereviewofcontempor ary on-chipinductorswithmagneticlmsandevaluatedtheirap plicationtointegrated powerconverters.Thereviewreachedsomeinterestingconc lusions.Amajorityof theworksfeaturedinductorswithinductancedensitiesofl essthan 100nH = mm 2 callingintoquestionwhetherthemagneticlmsareprovidi ngsufcientinductance improvementtowarranttheirinclusion.Additionally,few resultswereapplicabletohigh frequencyswitching( > 100MHz ).Thereviewidentiedqualityfactorasperformance parameterofinterestforefcientpowerconversion,withq ualityfactorof 1 asthe minimumbelowwhichinductorsactedmorelikeresistorstha nasintendedasenergy storingcomponents[ 7 ].Air-coremicroinductors,ontheotherhand,havemostlyb een designedfor GHz radiofrequency(RF)applications.Suchdevicescanattain highquality factorswhensuspendedaboveconductivesubstratesbuttyp icallyhavelowinductances ontheorderofonlyseveral nH Ahn, NiFe Yamaguchi, FeAlO Sato, FeCoBN Song, FeZrBAg Fukuda, NiZn Wang, NiFe Viala, FeHfN Flynn, NiFe Orlando, NiFe Lee, CoTaZr Park, Air Young, Air Choi, Air Weon, Air Yoon, Air 1 10 100 1 10 100 1000 10000 Peak Quality Factor Frequency for Peak Quality Factor (MHz) Figure1-2.Reviewofbothmagnetic-lm(shadedinblue)and air-core(shadedingreen) microinductorswitheachplottedintermsofpeakqualityfa ctorandthe frequencyatwhichthepeakqualityfactorwasobtained.Bub blesizeis proportionaltoinductancedensity.[ 8 – 22 ] 23

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Asurveyofexistingmicroinductors,includingbothmagnet iclmandaircores, revealedthattherewasasignicantgapwherefewmicrofabr icatedinductorswere designedforfrequenciesrangingfromtensof MHz upto 1GHz .Thegapwasevident inFigure 1-2 ,whereanumberofmicroinductorswereplottedagainstthei rpeakquality factorandthefrequencyatwhichthepeakqualityfactorwas attained.Atypical magneticlmmicroinductorhadaninductancedensityofabo ut 55nH = mm 2 ,almost twicethatofthetypicalaircorecounterpart,whichhadabo ut 30nH = mm 2 .Thesituation wasreversedforthepeakqualityfactorwherethemedianair coreinductorhadapeak qualityfactorof 50 ,fargreaterthanthemedianmagneticlminductorataquali tyfactor of 9 Asimilarfrequencygapwasfoundamongsttheresultsgather edfromworks reportingexistingmicrotransformersascanbeseenonthep lotinFigure 1-3 .Both magneticlmandaircoremicrofabricatedinductorswerepl ottedagainstmaximum efciencyofpowertransferthroughthetransformerandthe frequencyatwhich themaximumefciencyoccurred.Mostoftheworkswerefound tofocusonlyon transformerswith 1:1 turnsratioswithnear-unityvoltage/currentgain. 1.6Air-CorePassiveComponentsforMicroscalePowerConve rters Betweenmagnetic-lm-coredevicesoperableat < 10MHz andmicrowaveRF air-coredeviceswithhighperformanceat > 1GHz liesalargefrequencygapamongst thereportedmicroinductorsandmicrotransformers.Coinc identally,theexpected switchingfrequenciesofnextgenerationpowerconverters fallrightintothisgapfor whichnoinductor/transformertechnologycanyetclaimcha mpionship.However, thedevelopmentispresentedhereforanewclassofair-core microinductorsand microtransformersthatleveragemicrofabrication-enabl edadvancementstoattainhigh performanceinthisdesirableswitchingfrequencyrangean dtoenablefullyintegrated powermanagementsystemsinthesmallestpossiblepackages 24

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Yamaguchi, Air Laney, Air Zolfaghari, Air Ng, Air Aly, Air Mino, CoZrRe Kurata, CoFeSiB Yamaguchi, CoNbZr Mino, CoZrRe Xu, NiFe Sullivan, NiFe Sullivan, NiFe Brunet, NiFe Park, NiFe Rassel, NiFe Yun, NiFe Wang, NiFe 0% 20% 40% 60% 80% 100% 1 10 100 1000 10000 Efficiency Frequency for Maximum Efficiency Figure1-3.Reviewofbothmagnetic-lm(shadedinblue)and air-core(shadedingreen) microtransformerswitheachplottedintermsofmaximumef ciencyandthe frequencyatwhichthemaximumefciencywasobtained.Bubb lesizeis proportionaltovoltagegain.[ 23 – 40 ] Inordertodesignthesedevices,modelsareanalyzedtounco vertheideal characteristicsforoperatingintheVHFrange.Comparedto traditionalair-core components,thedevicesherefeaturethickermetaltracesa rrangedintointricate three-dimensionalwindingsforlowerlossandhigherdensi ty.Amultilevelmicrofabrication processisdevelopedformoldingcopperpartswiththeneces sarycharacteristicsof thickness,minimumfeaturesize,andout-of-planestackin g. Thisdissertationhasbeenorganizedasfollows.InChapter 2 informationgathered fromasurveyofexistingmicrofabricatedinductorsandtra nsformersispresented. Chapter 3 highlightsthegoalsandconsiderationsthatmotivatedthe designof themicroinductors.Similarly,thedesignofthemicrotran sformersisdiscussedin Chapter 4 alongsideanintroductiontothemathandmethodsusedtocha racterizethe microtransformerperformance.PresentedinChapter 5 isthefabricationprocessthat wasdevelopedtoresponsetotheaforementioneddesignneed sandtheshortcomings ofexistingprocessesinmeetingtheseneeds.Characteriza tionofthemicrofabricated 25

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inductorsandtransformersatradiofrequenciesiscovered separatelyinChapters 6 and 7 fortheinductorsandtransformers,respectively.Chapter 8 presentsthepackaging andtestingofmicrofabricatedinductorswithinaprototyp eVHFhybridboostconverter circuitandwithacommercialconverterchip.Chapter 9 concludesthedissertationwith asummaryoftheadvancementsledbythisworkinllingthega pformicroscalepower inductorsandtransformersatVHFandenablingfullyintegr atedpowerconverters. 26

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CHAPTER2 BACKGROUND Thischapterprovidesbackgroundinformationonexistingw orksthathave contributedtothestateoftheartofmicrofabricatedinduc torsandtransformers. Highlightedrstareseveralsignicantdemonstrationsof veryhighfrequencyswitched modepowerconvertersthathavecreatedthepossibilityfor fullintegrationofall convertercomponentsinasinglepackage.Powerinductorsa ndtransformersfromprior worksarethensurveyedwithattentionfocusedonthechalle ngesandaccomplishments metbyeach.Quantitativeresultsfromthesurveyedinducto rsandtransformersare outlinedintabularformattheendofthechapteralongwithr esultsfromselected GHz RFaircorecomponentsforcomparison.Theworkshavebeense lectedfortheir inclusionofdetailedperformancecharacteristicsreleva nttowardenablingintegrated switchedmodepowerconverters. 2.1HighFrequencyPowerConverters Examplesofveryhighfrequencyswitchingpowerconverters aresummarized heretodemonstratetheviabilityofthisnewbreedofconver tersinprovidinghigh performancewith nH -levelinductivecomponents.Theresultsfromtheseworksp rovided anideaofwhatswitchingfrequencieswouldbeusedinnext-g enerationconvertersand whatsizeinductorswouldberequired. Hazuchaetal.[ 2 ]reportedresultsfromafour-phasedc-dcbuckconverter implementedin 90nm CMOSanddesignedtooperateatswitchingfrequenciesrangi ng from 100 600MHz .Theoptimalswitchingfrequencywasdeterminedbythesize ofthe inductors.Four 6.8nH discreteinductorsweresolderedontothepackageforaswit ching frequencyof 233MHz .Theauthorsquotedqualityfactorsfortheinductorsof Q =20 at 100MHz and Q =30 at 300MHz .Thechipareaoftheconverterwas 1.26mm 2 .The converterdelivered 0.3A at 0.9V froma 1.2V inputwith 83% efciency. 27

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Lietal.[ 41 ]reportedtwodiscontinuousconductionmodedc-dcboostco nverters fabricatedinstandard 0.13 m CMOS,bothutilizingoff-chipdiscreteinductors.One wasa 100MHz 4-phaseboostconverterthatdelivered 240mW froma 1.2V supplywith outputrangingfrom 3 5V andpeakefciencyof 64% .Thisconverterusedfour 22nH inductors,oneperphase,andtheCMOSareaalonecomprised 0.55mm 2 .Theother reportedconverterwasa 45MHz hybridboostconverterdelivering 20mW at 6 10V alsofroma 1.2V supply,withpeakefciencyof 37% .Thehybridconverterusedasingle 43nH inductor,whiletheCMOSareawas 0.17mm 2 .Theauthorsstatedthatbothhigh switchingfrequencyanddiscontinuousconductionmodewer eutilizedtoreducethesize oftherequiredoff-chipcomponents. 2.2Inductors Ahnetal.[ 22 ]constructeda 4mm 1mm 130 m toroidalinductoronasilicon waferviaamultilevelmetallizationprocess.Theinductor consistedof 33 turnsof 40 m -thickcoppertraceswoundarounda 30 m -thickelectroplated Ni 81 Fe 19 magnetic core.Thiscompositionof NiFe wascitedasbeingchosenforachievingmaximum permeability,minimumcoercivity,minimumanisotropy,an dmaximummechanical hardness.Permeabilityofthemagneticcorewasdetermined atapproximately r =800 bothbyvibratingsamplemagnetometryandmagneticcircuit evaluationwithacore ofknowndimensions.Themeasuredinductancewas 400nH at 10kHz ,butthisvalue decreasedwithfrequencytoavalueofapproximately 50nH at 1MHz .Suchapplications fortheinductorwerelistedassensors,actuators,andpowe rconverters. Yamaguchietal.[ 42 ]demonstrateda 7.6nH thin-lminductorwithqualityfactor of 7.4 at 1GHz intendedforuseinimpedancematchingatthefront-endrece iver ofa 1GHz mobilecommunicationhandset.Thesquare-spiralinductor measured 370 m 370 m andwascomprisedof 4 turnsof 2.8 m -thicksputterdeposited AlSi windings.Afterencapsulatingthewindingswitha 3.5 m -thickinsulatinglayerof polyimide,a 0.1 m -thick Fe 61 Al 13 O 26 magneticlmwassputterdepositedoverthecoils 28

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andwaspatternedbyionmilling.Theauthorsacknowledgedt hatsimplycoveringthe inductorwiththemagneticlmcouldonlydoubletheinducta nceatbestbutpredicted theimprovementwouldprovesufcientforcommercialuse.A ninverserelationshipwas foundinthe FeAlO lmsbetweenthemagneticlmresistivityanditsresonantf requency, althoughhighvaluesofeachweredesiredtoavoidexcesslos sesatthe GHz range.Slits werecreatedinthemagneticlmtoinhibiteddycurrentgene ration,resultingina 31% reductionintheacresistanceat 1GHz comparedtothecaseofthelmwithoutslits. Satoetal.[ 11 ]developedarectangularspiralinductorfor 5MHz switching dc-dcconverters.Theinductorsmeasured 6310 m 3466 m inareaandfeatured 50 m -thickelectroplatedcopperwindingscappedwitha FeCoBN magneticthinlm. Themagneticlmwasdepositedbydcmagnetronsputteringwi thfouralternatinglayers of 1.5 mFeCoBN and 0.4 mAlNx tosuppresseddycurrents.Filmpermeabilitywas estimatedat 900 upto 300MHz .Themultilayerlmwasetchedinasinglewetstep withmixtureofphosphoric,acetic,andnitricacidsusedto dissolvebothconstitutive materialsatonce.Inductancewasmeasuredat 370nH withapeakqualityfactor of 15 at 7MHz .Theinductorwastestedin 5MHz switchedmodepowerconverters constructedofdiscretecomponentsinbothboostandbuckco ngurations.Thebuck converterproducedanoutputof 3V froma 5V inputwithapeakefciencyofabout 82% atanoutputcurrentupto 500mA .Theboostconverteroperatedwiththesame conversionratioinreverse;anoutputof 5V wasobtainedfroma 3V input.Asimilar peakefciencyofabout 82% wasachievedfromtheboostconverterat 150mA output current. Fukudaetal.[ 9 ]fabricateda 6mm 6mm planarsquarespiralinductorthat wasfullyencapsulatedbetweentwo NiZn ferritemagneticlayers.Ferritecomposition was NiO = CuO = ZnO = Fe 2 O 3 inratiosof 16 = 12 = 23 = 49 .Thelowerferritelayerwasrst screen-printedoverasiliconwaferandsinteredat 900 1000 C toanalthickness of 40 m .Relativepermeabilityofthelowerferritelayerwasmeasu redat 120 .Copper 29

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windingswerethenelectroplated 50 m -thickontopofthelowerferritelayer.The upperferritelayerwasscreenprintedontopofthewindings andwashardenedbutnot sintered.Duetothelowerrelativepermeability—measured at 25 —thenalupperferrite layerwasdepositedmorethantwiceasthickat 100 m .Characterizationoftheinductor revealedaninductanceof 1.4 H withapeakqualityfactorof 40 at 5MHz .Magnetic eldanalysisbytheniteelementmethodindicatedthatthe inclusionofmagneticferrite inthespacesbetweenadjacentturnsofthecoilwerebeneci alinconningmagnetic uxtothecore,minimizingeddycurrentlossinthecopperco il. Vialaetal.[ 14 ]reportedasquarespiralinductorwithadensityaround 90nH = mm 2 andpeakqualityfactorofabout 10 at 1.5GHz withsputtered FeHfN lmsoverspiral inductors,butonlynotedamodestincreaseininductanceof 35% overtheair-corecase. Themagneticlmswerelaminatedandconsistedoftenaltern ationsof 0.1 m -thick (Fe 97.6 Hf 2.4 ) 90 N 10 magneticand 500 A -thick SiO 2 insulatinglayers.Theauthorsnoted difcultyinusingmagneticlmswithspiralsduetotheirha vingbothin-planeand out-of-planemagneticeldcomponents. Characteristicsoftheabovementionedinductorsweresumm arizedinTable 2-1 alongsidethosefromothersignicantworks. 2.3Transformers Minoetal.[ 23 ]presenteda 3mm 4mm transformerfabricatedbyacompletely dryprocessonasiliconsubstrateandconsistingofcopperc oilswrappedarounda magneticlayerof CoZrRe .Themagneticlmwasdepositedbyionbeamsputteringand wasquotedashavingarelativepermeability > 3000 .Thecoppercoilswerewrapped aroundthecoreinaprimary:secondaryratioof 12:3 toobtainassociatedprimaryand secondaryinductancesof 350nH and 40nH ,respectively.Themicrotransformerwas mountedinaceramicpackageandtestedwithinaforwardconv ertercircuitoperatingat 32MHz .Outputfromtheconverterwas 0.6V toa 10n loadwith 10V sourceinput.The 30

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efciencyoftheconverterwasnotgivenbutwasreportedly“ low”duetothelowprimary inductanceofthetransformer. Yamaguchietal.[ 33 ]fabricateda 2.4 3.1mm 2 microtransformerwithstacked primaryandsecondaryspiralcoppercoilssandwichedbetwe enmultilayered CoNbZr = SiO 2 magneticlmsonaglasssubstrate.RFsputteringwasusedto depositboththecopper windingsandthemagneticlms,whichwereeachpatternedby aphotoresistlift-off method.Annealingofthemagneticcorewasperformedat 250 C for 1hour under vacuumwitharotatingmagneticeld.Thecoppertraceswere deposited 7.5 m thick andpatterned 100 m widewith 10 m spacing.Theturnsratioofprimary:secondary coilswas 8:7.3 .A 10n loadwasattachedtothesecondarywindingformeasurement ofthetransformerefciencywith 1V sinusoidalinputtotheprimaryinthefrequency rangeof 1 20MHz .Amaximumefciencyof 67% wasobtainedat 10MHz ,beyond whichpointefciencywassaidtodecreaseduetocoreloss. SullivanandSanders[ 27 ]measuredtheperformanceofmicrofabricatedpower conversiontransformerswithareasontheorderof 10mm 2 andprimary:secondary turnsratiosof 8:4 .Primaryandsecondarywindingswereinterleavedinanelon gated spiral(racetrack)andconsistedof 20 m -thickelectroplatedcopper.Amultilayer laminated NiFe = SiO 2 materialactedasthemagneticcorewitharelativepermeabi lityof 2000 .Twodesignswerefabricated:onehadasandwichcongurati onwiththecopper windingsembeddedbetweenseparatelayersofmagneticmate rial,whiletheother designfeaturedaclosedcorethatfullyenclosedthewindin gs.Thesandwichdesign wassaidtonotonlydecreaseinductancebyafactorof 5 comparedtotheclosedcore, butalsoproducedan“unfavorableelddistribution”thatf urtherincreasedlosses.A half-bridgeforwardconverterservedasatestbedforthesa ndwichtransformerand measured 43.4% efciencywith 3.74W inputat 30V and 1.625W outputat 4.21V .The sameconvertercircuitwastestedagainwithalitzwiretran sformerhavingthesame inductanceasthesandwichtransformerbutassumedtohaven oloss.Bycomparing 31

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thedifferenceinefciencywiththelitzwireversusthesan dwichtransformer,the sandwichtransformerefciencywasestimatedat 61% .Theclosedcoretransformerwas testedwithanetworkanalyzerandprojectedtohaveanefci encyof 70% .Higherthan expectedlosseswereattributedtohysteresislossesandsh ortingbetweenlayersinthe core. Brunetetal.[ 28 ]presenteda 30mm 2 microfabricatedtransformerconsistingof interleaved,racetrack-shapedprimaryandsecondarycoil sencapsulatedin 4 m -thick electroplated Ni 81 Fe 19 magneticcore.Thecoppercoilswereelectroplated 43 m thick andwerearrangedinaturnsratioof 4:2 .Electricalcharacteristicswereobtainedusing animpedanceanalyzer.Aprimaryinductanceof 0.9 H wasmeasuredtobeconstant upto 5MHz .Leakageinductancewasdeterminedat 0.4 H measuringtheprimary inductancewhileshortingthesecondarycoil.Thetransfor merwastestedinafull-bridge dc-dcconverterat 2MHz .Converterefciencywasmeasuredat 40% forinputvoltages > 2V .Thecorewasfoundtosaturateataninputvoltageof 4.5V foramaximumoutput powerof 0.4W Characteristicsoftheabovementionedinductorsweresumm arizedinTable 2-2 alongsidethosefromothersignicantworks. 32

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Table2-1.Literaturesurveyofmicroinductors. InductancePeak Q DC ReferenceLayoutCoreAreaInductancedensityPeakfrequen cyresistance material (mm 2 )(nH) ( nH = mm 2 ) Q ( MHz )( n ) Ahnetal.[ 22 ]Toroid Ni 81 Fe 19 44001001.510.3 Yamaguchietal.[ 42 ]Spiral Fe 61 Al 13 O 26 0.1377.6567.410006.5 Satoetal.[ 11 ]Racetrack FeCoBN21.937016.9157 Songetal.[ 13 ]Racetrack FeZrBAg14610006.8425103.95 Fukudaetal.[ 9 ]Spiral NiZn36140038.94050.67 Wangetal.[ 10 ]Racetrack NiFe5.6916028.1640.261 Vialaetal.[ 14 ]Spiral FeHfN0.0910111101500 Flynnetal.[ 20 ]Toroid NiFe10194019422 Orlandoetal.[ 21 ]Toroid NiFe31.450015.92020.095 Leeetal.[ 19 ]Solenoid CoTaZr0.8870.279.76.5250.67 ParkandAllen[ 8 ]SpiralAir 1.6937.822.44412002.76 Youngetal.[ 15 ]SolenoidAir 0.25145618820 Choietal.[ 16 ]SpiralAir 0.1444.631.8503500 Weonetal.[ 17 ]SolenoidAir 0.052.1427840000.342 Yoonetal.[ 18 ]SolenoidAir 0.061.1719.5842600 33

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Table2-2.Literaturesurveyofmicrotransformers. PrimarySecondary ReferenceAreainductanceinductanceCouplingVoltageEf ciencyFrequencyCore (mm 2 )( nH )( nH )coefcientgain( MHz )material Minoetal.[ 23 ] 12.0350400.50.3 3%32CoZrRe Yamaguchietal.[ 33 ] 7.445004500.767%10CoNbZr Kurataetal.[ 24 ] 1.3850500.921 54%100 250CoFeSiB Minoetal.[ 25 ] 258208200.931 58% 25CoZrRe Xuetal.[ 26 ] 48008000.90.6377% 10Ni 80 Fe 20 SullivanandSanders[ 27 ] 8.421380 3450.5 61%8NiFe SullivanandSanders[ 27 ] 11.853176 7940.5 70%10NiFe Brunetetal.[ 28 ] 29.92900225 0.58 40%2Ni 81 Fe 19 ParkandBu[ 29 ] 5.74404400.851 32%25Ni 80 Fe 20 Rasseletal.[ 30 ] 4.95100800.90.9 1%0.5NiFe Yunetal.[ 31 ] 78.4830830 0.910.984% 5Ni 81 Fe 19 Wangetal.[ 32 ] 23.74004000.930.8972%5NiFe Yamaguchietal.[ 33 ] 7.4470650.430%10 Air Cheungetal.[ 34 ] 0.168 8 0.75 1 1000 Air Cheungetal.[ 34 ] 0.250.5 12 0.75 5 1000 Air Laneyetal.[ 35 ] 0.16 1.651.650.551 56%2500 Air Long[ 36 ] 0.168.58.50.841 2000 Air Ribasetal.[ 37 ] 0.098.68.60.791 32% 10000 Air Zolfagharietal.[ 38 ] 0.06 11 180 329% 1500 Air Ngetal.[ 39 ] 0.09230.81.2 60%8000 Air AlyandElsharawy[ 40 ] 0.324.794.790.881 56% 2000 Air Asteriskedvalueswereestimatedbasedontheotherinforma tiongatheredfromtherespectivereferences.34

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CHAPTER3 INDUCTORDESIGN Thischapteroutlinesamethodologyfordesigningmicroind uctorsforusein high-frequencyswitched-modepowersupplies.Thequality factorisinvestigatedas ametricfortheefciencyoftheinductorinstoringenergy. Threeinductorattributes affectingpeakqualityfactor—inductance,resistance,an dmaximumoperating frequency—arediscussedintermsofthetrade-offsinattem ptingtomaximizeany oneofthesequantities.Thestackedplanarspirallayoutis chosenforthemicroinductors withthegoalofreachinghighqualityfactorbymaximizingi nductivecouplingwhile minimizingelectricalresistance.Amodelingstrategyisp resentedforoptimization ofthedesignofsuchinductorsandpredictionoftheirperfo rmance.Themodels provideamethodfordeterminingtheoptimalgeometricprop ortionsbasedoncertain combinationsofdesiredcriteria:inductance,size,opera tingfrequency,andmaximum qualityfactor. 3.1QualityFactorDenition Thequalityfactor, Q ,ofacircuitisadimensionlessquantitythatgenerallypro vides ametricofhowmuchenergyisstoredinacircuitversushowmu chenergyisdissipated byit.However,thegeneralityofthisconcepthasledtoconf usionofthedenitionof Q amongstresearcherssincetherearemanyapplication-spec icinterpretationsand methodsofextractionof Q [ 38 43 – 46 ].Forexample,onetraditionaluseof Q isin quantifyingtheselectivityofaresonantltercircuit[ 47 ].Insuchlteringapplications, Q isdenedastheratioofthecircuitresonantfrequencytoit shalf-powerbandwidth. 3.1.1QualityFactorofNon-IdealReactiveComponents Incontrasttothesingle-valuedqualityfactorofresonant circuits,thequalityfactor Q ofanenergystoringcircuitcomponent(e.g.inductororcap acitor)quantieshow muchenergyisstoredinthecomponentversushowmuchisdiss ipatedbyit ateach 35

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frequency .However,eventhisalternatedenitioncantakeondiffere ntmeaningsto differentcommunitieswhenthedeviceisoperatednearitsr esonantfrequency. Thediscrepancyindenitionarisesfromthefactthataltho ughtheimpedanceofa deviceunderalternatingcurrent(ac),sinusoidalexcitat ionatitsresonantfrequencyis purelyresistive,energyisbeingstoredandtransferredwi thintheelectricalandmagnetic eldswithinthedevice.Bydenition,thereactivepartoft heimpedancefallstozeroat resonance,andnoneoftheenergystoredinthedeviceisavai labletotheexternalcircuit attachedtoit.Passivecomponentsinpowerconversionappl ications,however,needto storeenergyfromthecircuitandthenprovidethatenergyba cktothecircuit.Forthis reason,aseparatedenitionof Q ismostappropriateforpowerconversionapplication withthepropertythat Q fallstozeroatresonance.Thesimplieddenitionof Q usedfor quanticationofpower-passiveperformanceistheratioof theimaginarytotherealpart ofthecompleximpedancelookingintothedevice, Q = =f Z g
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Applyingpropertiesofcomplexconjugates,therealandima ginarypartoperatorscanbe expandedintoequivalentalgebraicexpressionsas Q = V I VI = j 2 V I + VI = 2 (3–4) whichsimpliesthroughmanipulationto, Q = V I V I = j 2 V I + V I = 2 (3–5) ThevoltageandcurrenttermsinEquation 3–5 arearrangedsothattheimpedance equivalentisreadilyidentiedas, Q = Z Z = j 2 Z + Z = 2 (3–6) Bypropertiesofcomplexconjugates,Equation 3–6 isidenticaltotheoriginalformulation of Q inEquation 3–1 astheratiooftheimaginarytotherealpartofthecomplex impedanceofcomponent.3.1.2QualityFactorofInductor AsdiscussedinSection 3.1.1 ,thequalityfactor Q providesametricoftheac energystorageefciencyofactual,non-idealreactivecir cuitcomponents,suchas microinductors.Theformulationof Q astheratioofimaginarytotherealpartofthe inductorimpedance(asinEquation 3–1 )providesagureofmeritthatquantiesthe degreetowhichaninductoractslikeaninductortoanattach edcircuit. Forexample,whenusedwithdirectcurrent(dc)thereisnoel ectricalcharacteristic thatdifferentiatesaninductorfromatraceofwirewithsom eresistance.Although energyisstoredinthemagneticeldinducedbythecurrent owingthroughtheinductor evenatdc,intheabsenceofanyvariationincurrentovertim e,thatenergyisneverput backintothecircuit. Whenthereareacuctuationsinthecurrentowingthrought heinductor,energy isstoredasthecurrentincreasesinmagnitudetoitspeakle velandisthenretrieved 37

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fromthemagneticeldbackintothecircuitasthecurrentde creasesinmagnitude. Someenergyisdissipatedasheatduetotheresistanceofthe electricalpaththrough theinductor.Atlowfrequencies,therateofenergystorage /retrievalislessthanthe powerdissipatedbytheinductor,andtheinductorhasconse quentlylowquality.As thefrequencyofthecurrentoscillationincreases,howeve r,sotoodoesrateofenergy storage/retrievalwhilethepowerdissipatedremainsrela tivelyconstant,andtheinductor thereforeattainsahigher Q .Iftheinductorismodeledastheserialcombinationofan idealresistor R andanidealinductor L ,theexpressionforqualityfactoratanangular frequencyof ascalculatedfromEquation 3–1 is Q RL = L R (3–7) Thissimpliedexpressionignoresthechangesinresistanc ethatoccuratveryhigh frequenciesandalsoignorescapacitiveenergystorageint heelectriceldthatinvariably existsintheinductor. Becauseofparasiticcapacitance, Q diminishesneartheself-resonantfrequencyof theinductorasmoreenergyisstoredintheelectriceldbet weentraces.Bydenition, Q =0 atresonanceasequalamountsofenergyaretradedbetweenel ectricand magneticelds,andthespiralagainappearsasaresistorto thecircuit. 3.2PerformanceTrilemma FromEquation 3–7 thequalityfactorofaquasi-idealinductor(ignoringeffe cts ofcapacitance)isdependentonitsinductance,resistance ,andoperatingfrequency. Ideally,thequalityfactorwouldbemaximizediftheinduct anceandoperatingfrequency weremaximizedandtheresistanceminimized.Inpractice,h owever,allofthese quantitiesarelinked,sothatimprovementstoanyoneofthe sethreeattributesis oftendoneatthedetrimentoftheothertwo. ConsiderthesimplemodeloftheinductorshowninFigure 3-1 withinductance L ,seriesresistance R ,andshuntcapacitance C .Self-resonancelimitsthemaximum 38

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operatingfrequencyoftheinductorandforthecaseoflowre sistanceisapproximately equaltothenaturalfrequency, 0 = r 1 LC (3–8) Theaboveequationclearlyshowsthatincreasinginductanc edirectlyresultsin decreasingresonantfrequency.However,attaininghigher inductanceoftenentails increasingthetracelengthoftheinductorwinding,result inginhighercapacitance, whichinturnfurtherdecreasestheresonantfrequency.The increasedtracelength alsoincreasestheresistanceoftheinductor.Designingin ductorsmustbalancethese competinggoalstodeliveradevicethatistailoredtotheap plication. C R L Figure3-1.Circuitdiagramofsimpleinductormodelwithin ductance L ,seriesresistance R ,andshuntcapacitance C 3.3StackedPlanarSpiralLayout Inresponsetothepreviouslymentionedconcernsformaximi zinginductancewhile minimizingresistanceandcapacitance,thestackedplanar spirallayoutwasselected fortheinductorsofthiswork.Theplanarspirallayoutfeat uresconductivetracesthat areconcentricallywoundintoaatspiralasdepictedinFig ure 3-2 .Thislayoutisthe mostpopularamongstallintegratedinductorsbecauseitof fershighdensitythrough tightspiralpackinganditiseasytofabricateviaconventi onalplanarmicrofabrication steps.Whenalltracesareconstrainedtoonlyasingleplane ,however,performanceis limitedbypoormagneticcouplingbetweenouterandinnerwi ndings.Asthenumberof spiralturnsisincreased,theseparationbetweeninnerand outerwindingscanbecome sogreatthattheinnerturnscontributemoretowardsincrea singtheresistanceofthe inductorthantowardsitsinductance. 39

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Toovercometheplanarlimitation,verticalstackingofpla narspiralsisusedto increaseboththeinductancedensityandthequalityfactor softheinductors.Because theplanarspiralisbynaturewiderindiameterthanitisthi ck(giventypicalconductor thicknesses),stackingspiralsprovidesexcellentmagnet iceldcouplinginthevertical direction.Assumingperfectcoupling,theinductanceofat wo-layerstacked-spiral inductorcanreachuptofourtimesthatofasinglelayerwhil etheresistanceisonly doubled.Inthissimpliedexample,theinductancetoresis tanceratioofthetwo-layer deviceisimprovedtotwicethatofasingle-layerdevice. 3.4LowFrequencyAnalyticalInductorModel Thelow-frequencymodeloftheinductorincludesonlytheel ectricalresistance alongthelengthofthetracewindingandthemagneticeldge neratedwhenan electriccurrentpassesthroughthewinding.Thecurrentis assumedtoowuniformly throughthecrosssectionofeachtrace,ignoringcurrentcr owdingduetointeractions betweenmovingchargecarriers.Inductanceandresistance arerstcalculatedfora single-layerwindingofuniformtracewidthandthickness. Thevaluesarethenextended asappropriatewhentwolayersareverticallystacked. Bytheyear1928Wheeler[ 48 ]hadderivedbyempiricaldataanexpressionto predicttheinductanceofdiscreteradiocoils.Morethan70 yearslaterMohanetal.[ 49 ] modiedtheexistingexpressiononlyslightlytobevalidal soformicroinductors, L mw = K 1 0 n 2 d avg 1+ K 2 p (3–9) Intheaboveexpression, K 1 and K 2 areempiricallyderivedvaluesthatarespecicto theshapeofthespiral(i.e.square,hexagonal,octagonal) andarelistedinTable 3-1 AnadditionalexpressionwaspresentedinMohanetal.[ 49 ]forcalculatinginductance basedonacurrentsheetapproximation[ 50 ], L gmd = n 2 d avg c 1 2 ln c 2 + c 3 + c 4 2 (3–10) 40

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Table3-1.CoefcientsformodiedWheeler(Equation 3–9 )andcurrentsheet(Equation 3–10 )expressions[ 49 ]. Shape K 1 K 2 c 1 c 2 c 3 c 4 Square2.342.751.272.070.180.13Hexagonal2.333.821.092.230.000.17Octagonal2.253.551.072.290.000.19Circle--1.002.460.000.20 forwhichexpressiontheshaped-dependentcoefcients( c 1 c 2 c 3 ,and c 4 )areprovided notonlyforsquare,hexagonal,andoctagonalshapesbutals oforcircular.These coefcientsarealsolistedinTable 3-1 .Thechoicebetweenusingthetwopreviously listedexpressionsdependsonthesituation.Ifacircularl ayoutisdesired,thecurrent sheetexpressioninEquation 3–10 providesthebestaccuracy.Ifrearrangingthe expressiontosolveforadifferentvariable,themodiedWh eelerexpressioninEquation 3–9 issimplertosolve. Theauthorsoftheseexpressionsnotedthateachhadbeenval idatedonlyfor inductors < 100nH withouterdiametersrangingfrom 100 480 m [ 49 ].Aspartof thisdissertationwork,theinductancevaluescalculatedf romEquation 3–9 wereveried againstmagnetoquasistaticsimulationswithlessthan 5% errorforinductorsupto 1050nH andouterdiametersupto 2.5mm (seeSection 6.3.1.1 ). AlloftheothervariablesinbothEquation 3–9 andEquation 3–10 —i.e.thenumber ofturns n ,thepackingdensity p ,andtheaveragediameter d avg —areobtainedfromthe geometryofthespiral.Thegeometryofthespiralcanbeuniq uelyspeciedintermsof thewindingtracewidth w ,thespacingbetweenadjacentwindingtraces s ,thenumber ofwindingturns n ,andtheouterdiameter D .Thesedimensionsaremarkedonthe diagramofanexamplespiralinFigure 3-2 .Inner( d )andouter( D )diameterswere measuredfromthecenterlinesoftheinnermostandoutermos ttraces,respectively. Theinnerdiameter d representsthespacecontainedwithinthespiralthatiscle arof 41

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w s d D Figure3-2.Diagramofplanarspirallayoutwith n =3 turnsandallotherdimensions labelled. windingsandiscalculatedasafunctionoftheotherdimensi ons, d = D 2 [ wn + s ( n 1 )] (3–11) Theaveragediameteristhensimplycalculatedas d avg = D + d 2 (3–12) Thepackingdensity p representsthefractionoftheinductorareathatislledwi th windingsandisdenedas p = D d D + d (3–13) Extendingtheaforementionedinductanceandresistanceca lculationsforasingle layerspiral,thetotalinductanceforaninductorwithtwoi denticalspiralsstacked verticallyiscalculatedinproportionto L 0 ,theinductanceofasingle-layerspiralfrom eitherEquation 3–9 or 3–10 L dc =2 ( 1+ k ) L 0 (3–14) 42

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where k isthecouplingcoefcientrepresentingtheportionofshar edmagneticux linkingthetopandbottomspirals.Thevalueof k canvarybetween 1 and 1 .Ifthe spiralsarepositionedsothatnomagneticuxissharedbetw eenspirals, k =0 andthe totalinductanceistwicethatofthesingle-layercoil.Whe nalluxissharedbetween coils, k =1 andthetotalinductanceisfourtimesthatofthesingle-lay ercoil.Ifthe coilsarestackedsothatthemagneticuxesofeachcoilarei nopposition, k canhave anegativevalueastheopposingmagneticeldsnullifyandr educethetotalamountof uxlinkingthecoils. Thedcresistanceoftheinductorcanbecalculatedbythefam iliarexpressionfor resistance, R dc = l wt (3–15) where istheelectricalresistivityofthetracematerial, l isthetotalelectricalpathlength oftheinductor,and t isthethicknessofthetrace.Thetotaltracelengthofthest acked spiralwindingscanbecalculatedfromthegeometrydesignv ariables.Forthetwo-layer stackedsquarespiral,thetotalelectricaltracelengthis evaluatedas l =2 4 nD ( 2 n 1 ) 2 ( w + s ) (3–16) Thetracelengthforthetwo-layerstackedcircularspiralc aseiscalculatedas l =2 [ nD n ( n 1 )( w + s )] (3–17) 3.5TrendsandOptimization 3.5.1Analytical TheexpressionslistedinSection 3.4 forestimatingthelow-frequencyinductance andresistanceofspiralswereusedtoexploreperformancet rendsassociatedwith sweepingcertaindesignvariables.Asquarespiralshapewa sassumedforeasein rapidlyiteratinglayoutandmodeling.Perfectcoupling( k =1 )wasassumedforall cases.Thetargetmetricforthissimpliedanalysiswasthe inductancetoresistance 43

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ratio L = R ,whichisproportionaltothequalityfactoratlowfrequenc ies(seeEquation 3–7 ). Therstcasewastodeterminetheoptimalpackingdensity.T hespacingbetween turnswasxedat s =10 m ,whilethewidthofthetraceswasvaried.Thenumberof turnswassweptfromtheminimumnumberofturns( n =1 )turnuptothemaximum numberofturnsthatcouldphysicallybepackedwithintheal lottedarea.Separate runswerecompletedforeachdifferentouterdiameter D .Theresultswereplottedfor D =500 m (Figure 3-3A )and D =1000 m (Figure 3-3B ).Forallouterdiametersand widths,the L dc = R dc ratiosincreaseddrasticallyasthenumberofturnswasincr eased from1butthenreachedtheirmaximalvaluesatapackingdens ityofapproximately p =0.4 ,whichisequivalenttothepointsatwhichinnerdiametersw erebarelygreater than40%oftheouterdiameters.Alsofromtheseplots,thema ximum L dc = R dc ratio increasedwithincreasingtracewidthuptoabout w =50 m ,pastwhichnosignicant furtherincreaseswererecorded. TheplotsofFigures 3-3A and 3-3B alsosuggestedthatthe L dc = R dc mightalso increasewithouterdiameter.Totestthisidea,outerdiame tersfrom D =0.5mm up to D =2.5mm wereevaluatedusingtheoptimalwidthsandpackingdensiti esalready learned.Foreachtrialwithdifferentouterdiameter,thet racespacingwasxedat s =10 m ,thetracewidthwasxedat w =50 m ,andthenumberofturns n was calculatedsuchthatthepackingdensitywouldbeapproxima tely p =0.4 .Inthissetup, the L dc = R dc computedforeachouterdiametershouldrepresentapproxim atelythepeak valuesofthecurvesseeninFigure 3-3 .Theresultsfromsweepingtheouterdiameter areplottedinFigure 3-4 andindicatealinearrelationshipbetweenthe L dc = R dc ratioand theouterdiameteroftheinductor.3.5.2FastHenry FastHenryisasoftwareprogramthatcansolvethemagnetoqu asistaticinductance andresistanceofathree-dimensionalstructureusinginte gralequation-basedmesh 44

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0 0.2 0.4 0.6 0.8 1 6 8 10 12 14 16 18 20 22 24 26 Packing Density pL dc /R dc (nH/ W ) 20 m m 30 m m 40 m m 50 m m 60 m m 70 m m 80 m m Width w AOuterdiameter D =500 m 0 0.2 0.4 0.6 0.8 1 5 10 15 20 25 30 35 40 45 50 55 Packing Density pL dc /R dc (nH/ W ) 20 m m 30 m m 40 m m 50 m m 60 m m 70 m m 80 m m Width w BOuterdiameter D =1000 m Figure3-3.Trendsofinductancetoresistanceratiovs.pac kingdensityforvarioustrace widthsandouterdiameters. 45

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0.5 1 1.5 2 2.5 20 40 60 80 100 120 140 Outer Diameter D (mm)L dc /R dc (nH/ W ) Figure3-4.Trendsofinductancetoresistanceratiovs.out erdiameterusing w =50 m s =10 m ,and n suchthat p 0.4 10 -1 10 0 10 1 10 2 10 3 80 100 120 140 160 Interlayer spacing ( m m)Inductance (nH)4L 0 2L 0 FastHenry simulation results k=0 k=1 Figure3-5.Trendofinductancevs.verticalgapbetweensta ckin 1mm 1mm as simulatedinFastHenry. 46

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analysiscombinedwithamultipole-acceleratediterative solutionalgorithm[ 51 ].A varietyofstackedinductordesignsweresimulatedinFastH enry,rsttovalidatethe analyticalmodelresultsandthenalsotodeterminetheeffe ctofverticalseparation betweenthetwostackedlayersonthemutualinductancebetw eenthem.Thesame inductordesignwassimulatedseveraltimesinFastHenrybu twithincreasingvertical layerseparationineachsimulationtrial.PlottedinFigur e 3-5 isthelowfrequency inductanceobtainedfora 1mm 1mm withinterlayerseparationvariedfrom 0.1 1000 m .Drawnontheplotarelinesindicating 2 and 4 theinductance L 0 thatwould beobtainedforasinglewindinglayer.Forthesimulationwi thtwowindinglayersthe inductanceasymptoticallyapproaches 4 L 0 ( k =1 )and 2 L 0 attheextremesofshort andlongseparations,respectively.FastHenrysimulation sindicatedthattherewouldbe minimalimprovementtotheinductancewithseparationsles sthan 1% oftheinductor diameter.Averticalseparationof 10 m wasusedforthemicrofabricateddevicesas shorterseparationswouldserveonlytodetrimentallyincr easetheparasiticcapacitance betweenlayers. 3.6RadioFrequencyEffects Althoughdirectcurrent(dc)assumptions(e.g.uniformcur rentdistribution)enabled asimpliedoptimizationoftheinductorlayout(suchasdia meterandnumberof turns),inductorsdesignedformicroscalepowersystemsne edtooperateatsuch highfrequencies( > 10MHz )thatcomplexelectromagneticbehavioraltersthe apparentinductancesandresistancesfromtheexpecteddcv alues.Thedominant electromagneticeffectscanbeclassiedasduetocapaciti vecouplingorduetoeddy currentgeneration.3.6.1CapacitiveCoupling Capacitivecouplingresultsfromvariationsinvoltagepot entialthatexistwithin differentpartsoftheinductor.Itisespeciallyprominent betweentheterminalendsofthe inductorswherethedifferenceinpotentialisthegreatest .Becausetheterminalends 47

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arewheretheinductorisconnectedtotherestofacircuitor wherelargelandingpads provideelectricalconnectiontoprobetipsformeasuremen tandcharacterization,the effectofcapacitivecouplingcanbehighlydependentonfac torsthatareexternaltothe designoftheinductor. Intrinsictothedesignoftheinductor,however,isthecapa citivecouplingthat occursbetweenadjacentwindingsofaninductor.Microindu ctorsintendedfor GHz RF applicationstypicallyconsistofasinglewindinglayeran dametalunderpassproviding electricalconnectiontotheinnermostturn.Theinterwind ingcapacitanceofthese single-layerinductorshaslongbeenknowntobedominatedb ytheareaswherethe windingsandtheunderpassoverlap[ 52 53 ].Thestackingofwindingsforgreater inductancedensity,asintheinductorsofthiswork,wouldr esultinevengreaterlevelsof interwindingcapacitanceduetothesignicantlyincrease dareaofoverlap.Thegeneral expressionforcapacitancebetweenparallelplateelectro des, C = A g (3–18) showsthatinadditiontotheoverlapareabetweenplates A ,theotheraspectsaffecting capacitivecouplingarethepermittivity ofthematerialbetweentheplatesandthe distance g ofthegapbetweenthem.Themultilevelthick-lmfabricati ontechnology presentedinChapter 5 minimizesthecapacitivecouplingbetweenupperandlower windinglayersbyseparatingthelayersbyupto 30 m andremovingalldielectric materialfrombetweenlayers. Iftheinductorsarefabricatedonaconductivesubstratesu chassilicon,the substratecreatesanadditionalpathforcapacitivecoupli ng.Toelectricallyisolate theinductorfromthesubstrateathindielectriclayersuch assilicondioxideisoften depositedoverthesubstrate.Consideringascenariowhere twotracesofaninductorat differentvoltagepotentialssitatopthedielectriclayer incloseproximity,capacitorsare 48

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formedwiththedielectriclayerbetweeneachtraceandthes ubstratewiththesubstrate providinganelectricalconnectionbetweenthetwotracesa sillustratedinFigure 3-6 Copper TraceCopper Trace Conductive Substrate Dielectric Layer Figure3-6.Diagramillustratingcapacitivecouplingthro ughsubstratebetweencopper tracesofinductorwinding. Liketheinterwindingcapacitance,theshuntcapacitancet hroughthesubstrate contributestoresonantbehaviorasenergyoscillatesbetw eeninductiveandcapacitive storageelements.However,theniteresistanceofthecapa citivelinkthroughthe substratecanhaveaprofoundeffectontheperceivedinduct orbehaviornearthe resonance.Thesubstrateresistancecanbemodeledasaresi stor R c inserieswiththe capacitancetothesubstrate C s ,asdrawninthecircuitdiagraminFigure 3-7 C s R dc L dc R c Figure3-7.Circuitdiagramofinductormodelwithdcinduct ance L dc ,seriesresistance throughtheinductor R dc ,shuntcapacitancetothesubstrate C s ,and resistancealongthecapacitivepaththroughthesubstrate R c 49

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10 7 10 8 10 9 10 -9 10 -8 10 -7 10 -6 10 -5 Frequency (Hz)Inductance (nH) R c =0 W R c =10 W R c =100 W R c =1000 W AEffectiveInductance 10 7 10 8 10 9 10 -2 10 0 10 2 10 4 10 6 Frequency (Hz)Resistance ( W ) R c =0 W R c =10 W R c =100 W R c =1000 W BEffectiveResistance 10 7 10 8 10 9 0 20 40 60 80 100 120 Frequency (Hz)Quality Factor R c =0 W R c =10 W R c =100 W R c =1000 W CEffectiveQualityFactor Figure3-8.Modeledeffectofsubstrateresistanceonovera llinductorimpedance. Impedancecalculatedfromcircuitmodelforinductorwithd cinductance L dc =100nH anddcresistance R dc =1n .Substrateresistance R c variedin serieswithsubstratecapacitance C s =1pF incircuitmodel. 50

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Whenthecapacitancethroughthesubstrateisthedominantc apacitance contributingtoresonancewiththeinductor,thesubstrate resistancecausesadamping oftheresonantbehavior.Toillustratetheeffectofthisda mping,thecircuitmodelof Figure 3-7 wassimulatedwithvaluesofinductance,resistance,andca pacitancethat wouldbetypicalofmicroinductorsfabricatedaccordingto themethodsofthiswork. Theeffectiveinductance,resistance,andqualityfactorl ookingintothelumpedinductor circuitwereextractedfromthemodeleddataandplottedinF igure 3-8 fordifferent valuesofsubstrateresistance.Theplotsshowthat,compar edtothecaseofzero substrateresistance,increasingsubstrateresistancere sultsinalowerpeakinductance nearresonanceandalowerfrequencypointatwhichtheeffec tiveresistanceraises aboveitsdcvalueduetoresonance.Theoveralleffectisasm oothingoftheresonant peaksandadecreaseinthequalityfactoroftheinductorath igherfrequencies. C s R dc L dc R c C L Figure3-9.Circuitdiagramofinductormodelwithdcinduct ance L dc ,seriesresistance throughtheinductor R dc ,shuntcapacitancebetweenwindingsof C L ,shunt capacitancetothesubstrateof C s ,andresistancealongthecapacitivepath throughthesubstrateof R c Atevenhighervaluesofsubstrateresistance,thissimplem odel(includingonly capacitancewiththesubstrate)showsthattheresonantbeh aviorwouldbecomeever increasinglydamped.Withmoreandmoredamping,theinduct ancewouldremainever atterwithfrequency,andtheriseineffectiveresistance wouldbepushedouttogreater frequencies.Asthisresonanceisdampedoutwithveryhighs ubstrateresistance, thequalityfactorwouldimproveagainastheinductorwould behavemoreideally(i.e. withoutcapacitance).Inpractice,however,asthesubstra tecapacitanceisdamped 51

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10 7 10 8 10 9 10 -9 10 -8 10 -7 10 -6 10 -5 Frequency (Hz)Inductance (nH) C L =100 pF C L =10 pF C L =1 pF C L =0.1 pF AEffectiveInductance 10 7 10 8 10 9 10 -4 10 -2 10 0 10 2 10 4 Frequency (Hz)Resistance ( W ) C L =100 pF C L =10 pF C L =1 pF C L =0.1 pF BEffectiveResistance 10 7 10 8 10 9 0 20 40 60 80 100 120 Frequency (Hz)Quality Factor C L =100 pF C L =10 pF C L =1 pF C L =0.1 pF CEffectiveQualityFactor Figure3-10.Modeledeffectofcompetitionbetweenwinding capacitanceandsubstrate capacitanceonoverallinductorimpedance.Impedancecalc ulatedfrom circuitmodelforinductorwithdcinductance L dc =100nH anddc resistance R dc =1n .Windingcapacitance C L variedwithnoseries resistancewhilesubstratecapacitance C s =1pF hadseriesresistance R c =1000n incircuitmodel. 52

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out,theintrinsicinterwindingcapacitancebeginstodomi nate.Tomoreaccurately modelthebehaviorofthemicroinductorsthecircuitmustin cludetheinterwinding capacitanceasdrawninFigure 3-9 ,withtheinterwindingcapacitance C L placedin parallelwiththecapacitancethroughthesubstrate.Unlik ethecapacitancethrough thesubstrate,theinterwindingcapacitanceisrelatively lossless,assumingonlyairor alow-lossdielectricbetweenthetraces.Ifthevalueofthe interwindingcapacitance isofsimilarvalueorlargerthanthecapacitancetothesubs trate,theinterwinding capacitancewilldominatetheoverallresonantbehaviorof theinductor.Thecircuitof Figure 3-9 withbothinterwindingandsubstratecapacitancewassimul atedtoshowthe competitionofthetwocapacitances.Thesimulatedimpedan celookingintoaninductor withtypicalparameterswasplottedinFigure 3-10 forvariousvaluesofinterwinding capacitance.Asshownintheplots,theresonanceshowedsha rperpeaksineffective inductanceandresistancewhentheinterwindingcapacitan cewasgreaterthanthe substratecapacitance,duetotheabsenceofresistanceins erieswiththeinterwinding capacitance.Thequalityfactor,however,isloweredevenf urtherbyinterwinding capacitancecomparedtothecaseofassumingonlysubstrate capacitance.Thisis duetotheresonantfrequencyoftheinductorbeingloweredf romthecaseinwhich resonanceisgovernedbythesubstratecapacitance.3.6.2EddyCurrents Eddycurrentsdisrupttheowofcurrentthroughcurrentthr oughinductortraces andresultfromtheinteractionofaconductorwiththetimevaryingmagneticeldofhigh frequencyelectricalcurrents.Whenanelectriccurrentis passedthroughanyconductor, acorrespondingmagneticeldisgeneratedinthespacesurr oundingthecurrent. Whenthedirectionofcurrentowalternates(acexcitation ),sotoodoesthepolarityof theassociatedmagneticeld.AccordingtoLenz'slawelect ricalcurrentsareinduced innearbyconductorssoastoopposetheincidentalternatin gmagneticeld.These inducedcurrentsarecallededdycurrents,andtheseconne thecurrenttoowingonly 53

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throughareducedcross-sectionoftheinductortraces.The effectsofeddycurrents havecommonlybeenseparatedintotheeffectsofanaccurren ttoitsowndistribution (skineffect)andtheeffectstoothernearbycurrentpaths( proximityeffect). Theskineffectreferstothetendencyofahigh-frequencyac currenttoconneitself onlyalongthesurfaceofaconductorratherthanowingeven lythroughoutthecross sectionoftheconductor.Thiseffectistheresultofeddycu rrentsgeneratedwithinthe conductoroftheaccurrentitself.Anoft-citedparameterr elatedtothiseffectistheskin depth,whichreferstothedistancefromthesurfaceofacond uctoratwhichthecurrent densityisreducedto 1 = e 0.37 ofitsnominalvalueatthesurface.Forgoodconductors ( =! 1 )theskindepthisapproximatelygivenby s 2 (3–19) where istheconductivityand isthemagneticpermeabilityoftheconductormaterial and istheangularfrequencyoftheaccurrent. However,theapproximationaboveisonlyapplicableincert aincases,suchasthat ofanelectromagneticwaveincidentonaninniteslabofcon ductororofcurrentthrough aconductorwithcircularcrosssection.However,thetrace softhemicroinductorsinthis andmostcontemporaryworksareofrectangularcrosssectio n.Toillustratetheeffect ofshapeontheskineffect,COMSOLsimulationswereperform edtoplotthecurrent densityandmagneticeldsacrossthecrosssectionsoftwoc opperwindingswiththe sameareabutdifferentaspectratiosasinFigure 3-11 .Thetracewithcloserto 1:1 aspectratioexhibitedamoreuniformdistributionofcurre ntdensityarounditsperimeter, whiletheattertraceexhibitedgreatercurrentcrowdinga longitsshorteredges.Forthe samelevelvoltageexcitation,themaximumcurrentdensity inthe 50 m 10 m traceis 15% greaterthanthatofthe 25 m 20 m trace.Theminimumcurrentdensityisalso 15% lessinthethinnertracecomparedtothethickerone. 54

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ACoppertrace: 50 m 10 m BCoppertrace: 25 m 20 m Figure3-11.COMSOLsimulationsat 100MHz ofcurrentdensityandmagneticeldin crosssectionalviewofcopperwindingshavingthesamearea butdifferent aspectratios. 55

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Regardingthegeneralquestionastowhichsurfacesofacond uctorwouldcarry highfrequencycurrent,Wheeler[ 54 ]answeredwithasimplerule: “Theruleis,thatthecurrentfollowsthepathofleastimped ance.” Thissimpleruleaidsintheunderstandingofthesegregatio nofcurrentalongtheshort sidesofarectangularconductor.Atdc,impedanceispurely resistiveandcurrentows uniformlythroughastraightconductor.Withincreasingac frequency,aconductor's impedanceisincreasinglydominatedbyaninductivecompon ent.AsWheeler[ 54 ] observed,theanswerastodeterminingthedistributionofh ighfrequencycurrentthen becomesoneofndingthepathofleastinductance.Inaatre ctangularconductor,the regionsofgreatestcurrentdensityattheshortends(seeFi gure 3-11A )canbethought ofasseparateparallelwireswithcurrentowinginthesame direction.Inductance isthenminimizedwhentheparallelcurrentpathsarefarthe stseparatedandtheir magneticeldscancelintheinterioroftheconductor. Therelationshipbetweeninductanceandresistanceathigh frequenciesisevident inhowthesevalueschangeinaninductorasfunctionsoffreq uency.Wheeler[ 54 ] discussedan“incremental-inductancerule”bywhichtheef fectiveresistanceof conductorscouldbecalculatedasequaltothechangeinreac tanceresultingfromeddy currentsincertaincases.Althoughthepremiseofthisrule isinvalidforthetraceswith rectangularly-shapedcrosssections[ 55 ],asimilarresultwasfoundinthemeasurement ofthemicroinductors.Aftermeasuringthefrequency-depe ndentresistance R ( f ) andreactance L ( f ) ofanexampleinductor,thedeviationsinresistance( R )and reactance( X )fromtheirvaluesatlowerfrequencies( R dc and L dc ,respectively) wereplottedinFigure 3-12 .Whilethelargeincreasesinbothresistanceandreactance intheplotpast 200MHz areduetoself-resonance,thedeviationsinresistanceand reactancefromtheirlower-frequencyvaluesareroughlyeq ualandoppositefromabout 20 – 200MHz asindicatedbytheplotof R + X remainingrelativelyat. 56

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10 7 10 8 10 9 -10 -5 0 5 10 Frequency (Hz)Impedance ( W ) D X= w L(f)w L dc D R=R(f)-R dc D R+ D X Figure3-12.Measuredeffectofeddycurrentsoninductorim pedance.Plotshowsthe measureddeviationsinresistance( R )andreactance( X )fromtheir valuesatlowerfrequencies( R dc and L dc ,respectively). 3.7SummaryofInductorDesign Theprecedingchapteroutlinedamethodologyfordesigning air-coreinductorsfor switchedmodepowerconverters. Qualityfactorwasshowntobeametricofhowmuchenergyisst oredinan inductorpercyclecomparedtohowmuchisdissipatedbyit. Thethreecomplementaryeffectsofinductance,resistance ,andparasitic capacitancewerediscussedfortheirrolesinaffectingind uctorqualityfactor, whichmotivatedastackedplanarspiraldesignthatbalance dthethreeeffects. Ananalyticalmodelwaspresentedwiththegoalofpredictin ginductorperformance atlowfrequencies. Themodelwasanalyzedtouncovertrendsaffectingtheinduc tancetoresistance ratiowhenvaryinggeometricparameters.Anoptimalgeomet rywasfoundwitha tracewidthof 50 m andapackingdensityof 40% Acircuitmodelforcapacitivecouplingbetweentheinducto randsubstraterevealed thatincreasesinsubstrateresistancewouldresultinadam peningoftheresonant behavioroftheinductorandareductioninthepeakqualityf actor. 57

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Eddycurrentswerediscussedasleadingtoskinandproximit yeffectsthat wouldincreasetheresistanceofinductorwindingsathighe rfrequenciesasthe currentwouldseektoowthroughapathofminimumimpedance (i.e.minimum inductanceathighfrequencies). 58

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CHAPTER4 TRANSFORMERDESIGN Thischapterdiscussestheconsiderationsthatshapethede signoftransformers. Thesimilaritiesanddifferencesbetweenthedesignsofind uctorsandtransformers arerstestablished.Maximumtransducerefciencyisintr oducedasametricfor transformeroptimizingtransformerperformance.Inaneff orttoutilizelessonslearned fromtheinductordesign,ahigh-level,abstractedlookate nergyowingthrougha transformershowshowthequalityfactorsofindividualind uctorscanprovideinsights intothemaximumefciencyofatransformer.Fromtheseinsi ghts,awindinglayout schemeforthetransformersisselectedthatallowsbothhig hperformanceand step-up/downopportunities.Acircuitmodelforthetransf ormersisthenpresented toexplainthefrequencybehaviorofthedevices.Finally,n etworkanalysisisusedto deriveexpressionsfortheload-dependenceofthetransfor merefciencyandvoltage gain. 4.1OverviewandGoals Thetransformerspresentedinthisworkconsistessentiall yofapairofcoiled inductorssopositionedthattheirmagneticuxesarelinke dandenergycanbe transferredfromonetoanother.Whileitispossibletocrea tetransformersincorporating morethantwocoilsformorecomplexpowerdistribution,the analysesinthischapter arelimitedtotwo-coildevices.Thetwocoilsarereferredt oasprimaryandsecondary; thepowersourceisconnectedtotheprimarycoilandpoweris transferredtotheload connectedtothesecondarycoil. Justasthequalityfactorisimportantinestablishingthee fciencyofmagnetic energystorageinaninductor,sotoodoesthemagneticenerg ytransferinatransformer relyoncurrentsowingthroughitswindings,ideallywitha slittleresistivelossas possibleforhighefciency.However,duetoimperfectmagn eticuxcouplingbetween thecoilsinatransformer,someenergyisstoredintheindiv idualwindingsandnot 59

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transferred.Athighfrequenciesasignicantproportiono fenergyisalsocapacitively storedintheelectriceldbetweencoils.Theinteractions betweentheseeffectsis furthercomplicatedbytheloadimpedance,whichcanaltert hephaseatdifferent partsofthetransformertohelporharmefciency.Theprima rygoalofthedesignisto maximizetheefciencyofpowertransferthroughthetransf ormer. 4.2MaximumEfciency Astwoportdevices,thetransformersrequireadifferentme tricforefciency thanthequalityfactorusedforinductors.Further,theef ciencyofthetransformer willdependontheloadthatisattachedtoit.Forthefollowi nganalysesefciencyis denedastheratioofrealpoweroutputtotheloadversusthe realpowerinputtothe transformer.Oneusefulcaseisthatofthemaximumpossible efciencyassuming conjugate-impedancematchedloading.4.2.1FromScatteringParameters Intherealmofradiofrequency(RF)systems,efciencyisre ferredtoaspower gain,theratioofoutputtoinputpower.Characterizationo fRFdevicestypically entailsdeterminationofscatteringparameters,whichare obtainedbymeasurement ofsinusoidalsignalsincidenton,reectedfrom,andtrans mittedthroughthedeviceto betested[ 56 ].Themaximumpowergain(efciency)thatcanbeattainedfr omageneric two-porttransducer(e.g.atransformer)isobtainedforth ecaseofconjugate-impedance matchedloadingandcanbecalculatedfromthescatteringpa rameters[ 57 ], G max = j S 21 j j S 12 j K p K 2 1 (4–1) where K istheRolletStabilityCondition,whichisdenedas K = 1 j S 11 j 2 j S 22 j 2 + j S 11 S 22 S 12 S 21 j 2 2 j S 12 S 21 j (4–2) However,thiscomplicatedexpressionforefciencydoesno tlenditselftobeingeasily interpretedtoaidinthedesignoftransformers. 60

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4.2.2FromCoilQualityFactorsandCouplingCoefcient Asimpliedanalysismaybeperformedforthecaseofconjuga te-impedance matchedloading,whichenablesthederivationofmaximumtr ansformerefciencyin termsoftargetabledesignvariables,namelycoilqualityf actorandcouplingcoefcient betweenprimaryandsecondarycoils.Undermatchedconditi ons,nopowerisreected tothesource.Whenacertainenergy E in isinputtotheprimarytransformercoilsome ofthatenergyisstoredinthemagneticeldaroundtheprima rycoilandsome E d 1 is dissipatedbyit.Themagneticallystoredenergyiscompris edofboththatenergy E m whichismutuallysharedbetweentheprimaryandsecondarya ndthatenergy E s 1 which isnotcoupledwiththesecondary.Writtenalgebraically,t hesumofprimarycoilenergies is E in = E d 1 + E s 1 + E m (4–3) Oftheenergy E m thatiscoupledtothesecondarycoil,someenergysome E d 2 is dissipated,whilesome E s 2 isstoredsolelyinthemagneticeldofthesecondary.Final ly, theremainingenergy E out isoutputtotheload.Thesumofsecondarycoilenergiesis E m = E d 2 + E s 2 + E out (4–4) ThisenergyowisshownschematicallyinFigure 4-1 E d 1 E d 2 E s 1 E s 2 E in E out PrimarySecondary E m Figure4-1.Diagramofenergyowingintoprimarytransform ercoil.Someofthatenergy isstoredordissipated,andtherestistransferredtothese condarycoil. Someofthatenergyisstoredordissipated,andtherestisou tputtothe load. 61

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Thecouplingcoefcient k speciesthefractionofthetotalmagnetically-stored energythatistransferredbetweentheprimaryandsecondar ycoils.Intheprimarycoil, themagnetically-storedenergyisthatwhichisinputminus thatwhichisdissipatedby theprimary,sothatthecouplingcoefcientcanbewrittena s k = E m E in E d 1 = E m E s 1 + E m (4–5) Thesamecouplingcoefcientcanbeequivalentlywrittenin termsofthesecondary coilenergies.Inthesecondarycoil,thetotalmagneticall y-storedenergyisthatwhich istransferredfromtheprimaryplusthatwhichisstoredsol elyinthesecondary.The couplingcoefcientcanthereforebewrittenas k = E m E s 2 + E m (4–6) Thequalityfactorsofeachcoilaretheotherdesignvariabl esofinterestand representthetotalenergystoredinthemagneticeldofeac hcoil—bothcoupled( E m ) anduncoupled( E s )—tothatdissipatedbyit.Fortheprimarycoilthequalityf actoris Q 1 = E s 1 + E m E d 1 (4–7) andforthesecondarythequalityfactorissimilarly Q 2 = E s 2 + E m E d 2 (4–8) IfEquations 4–7 and 4–8 aremultipliedwithEquations 4–5 and 4–6 ,theresulting expressionsaresimply kQ 1 = E m E d 1 (4–9) and kQ 2 = E m E d 2 (4–10) Finally,theaboveEquations 4–9 and 4–10 canbecombinedtoderiveasimple expressionforthemaximumtransformerefciency.Interms oftheenergyvariables, 62

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theoverallefciency ofthetransformerisdenedastheratioofusefulenergyoft he secondary,thatis,theoutputenergyplusthesecondarysto redenergy,overtheuseful energyoftheprimary,thatis,theinputenergyminusthepri marystoredenergy, = E out + E s 2 E in E s 1 (4–11) Fromthesumsattheprimary(Equation 4–3 )andsecondary(Equation 4–4 )energy nodes,Equation 4–11 canberewrittenas = E m E d 2 E m + E d 1 = 1 E d 2 = E m 1+ E d 1 = E m (4–12) Substitutingtheratiosofdissipatedtotransferredenerg yintheaboveequationwith expressionsofcouplingcoefcientandqualityfactorofEq uations 4–9 and 4–10 Equation 4–12 becomes = 1 1 kQ 2 1+ 1 kQ 1 = k 1 = Q 2 k +1 = Q 1 (4–13) Thisnalexpressioncalculatesthemaximumtransformeref ciencygivenonly theindividualcoilqualityfactorsandthecouplingbetwee ncoils.Tovalidatethisresult, Equation 4–13 andtheclassicexpressionfor G max givenbyEquation 4–1 wereboth usedtocalculateefciencyusingthesamemeasureddata.Bo thcalculationswere plottedasinFigure 4-2 anddisplayedexcellentagreementatfrequencieswellbelo wthe rstresonantfrequencyofthetransformer.Neartheresona ntfrequency( > 200MHz inFigure 4-2 forexample),theefciencycalculatedas G max wasmuchgreaterdueto itsaccountingforthecapacitiveenergystorageandadjust ingtheloadaccordingly, whereasthesimpleexpressionofEquation 4–13 wasderivedassumingnocapacitive storage. Equation 4–13 revealsseveralinsightsthatareusefulfordesigningtran sformersfor optimalefciency.Therstinsightisthattheimportanceo fcouplingbetweenprimary andsecondarydiminisheswithincreasingqualityfactorof eachcoil. 63

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10 7 10 8 0 20 40 60 80 100 Frequency (Hz)Efficiency (%) G max (S 11 ,S 12 ,S 21 ,S 22 ) h (Q 1 ,Q 2 ,k) Figure4-2.Transformerefciencycalculatedbyboth Q factorsand S parametersand measureddatatakenfromanexampleinductor.Excellentagr eementwas obtainedupto 200MHz ,atwhichpointthetransformerapproached resonanceandcapacitivestoragedominated. Thesecondinsightisthat,becausethequalityfactorsofEq uation 4–13 are dependentonfrequency,theprimaryandsecondarycoilssho uldattaintheirhighest qualityfactorsatthesamefrequenciestoobtainthehighes toveralltransformer efciency.Isolationtransformerswith 1:1 turnsratiosusuallyhavenearlyidentical primaryandsecondarycoilsandthuseasilysatisfytherequ irementformatching frequencybehavior.Transformerswithnon-unityturnsrat ios,however,arecomprised bynecessityofmismatchingcoilswithunequalinductances .Thecoilwithlesser inductanceisoftenphysicallysmallerwithlessparasitic capacitanceandhigherself resonantfrequencythanthecoilwithgreaterinductance.T hesmallercoilistherefore likelytoattainhigherqualityfactorathigherfrequencyt hanthelargercoil.Thisissue limitstheefciencyofhighfrequencytransformerswithla rgeturnsratios. 64

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4.3Layout Thelayoutforthetransformersofthisworkemployedahybri dcombinationoftwo windingtechniques:interleavingandnesting.Utilizingt hesameanalyticalexpressions fromtheinductordesign(Section 3.4 ),theprimarycoilwasrstlaidoutaccordingto therequiredspecication,exceptwithextraspaceprovide dbetweenturns.Withinthis space,thesecondarycoilwasinterleavedasanexactcopyof theprimarybutrotated 180 .Theresultinglayoutwouldbethatofa 1:1 transformer.Inordertoachieve voltage/currentgain,additionalsecondaryturnswerethe nnestedwithinthespace clearedbytheprimarycoil.Anexamplelayoutofamicrotran sformerisdepictedin Figure 4-3 ALowerwindinglayer BUpperwindinglayer Primary Winding Secondary Winding Via CKey Figure4-3.Diagramsillustratingtransformerwindinglay outonlowerandupperwinding layers.Keyidentieswindingsbelongingtoprimaryandsec ondarycoilsand locationofvias. 4.3.1TurnsRatio Theturnsratioofatransformerisroughlyameasureofitsvo ltageorcurrentgain. Thisratiohasbeentraditionallyusefulfortransformersw ithsuchhighpermeability magneticcoresthatthemagneticuxinducedbywireswrappe daroundthecoreare essentiallyfullycontainedwithinthecore.Forsuchtrans formerswithnearlyperfect magneticcoupling,themagneticuxinducedbytheprimaryc oilisfullysensedbythe 65

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secondarycoil.Thegainisthenequaltotheprimarytosecon daryratioofthenumberof physicalturnsofwirearoundthecore,assuggestedbythete rm“turnsratio.” However,microscaletransformerswithnoorlowpermeabili tymagneticcoresdo notexhibitperfectcoupling.Furthermore,notallturnsof themicrotransformercoilshave equalcontributionstotheinductanceduetothedifference inareasenclosedbyinner andouterloops.Theturnsratioofa 1: n microtransformerisinsteadcalculatedby n = r L 2 L 1 (4–14) where L 1 istheprimaryinductancethatwouldbeobtainedifthesecon darywere open-circuitedand L 2 isthesecondaryinductancethatwouldbeobtainedifthepri mary wereopen-circuited. 4.4PerformanceUnderLoad TheVectorNetworkAnalyzer(VNA)wasusedforcharacterizi ngmicrotransformers. BecausetheVNAmeasurementistypicallyperformedwith 50n loading,theresults mustbere-interpretedtoderiveperformanceforotherload ingconditions. AlthoughEquation 4–1 canbeusedtoquicklycalculatethemaximumattainable transformerefciencyfrommeasuredscatteringparameter s,ithasseveralshortcomings: itassumesmatchedloadingateveryfrequencypointbutdoes notactuallyindicate thematchedloadimpedancerequired,itdoesnotprovideinf ormationabouthow bigaperformancehitissufferedifthefrequencyorloaddev iatesfromtheiroptimal intersections,anditdoesnotprovidetheassociatedvolta gegain.Forthisreason, asetofexpressionswasderivedthatcouldprovidemoredeta iledinformationabout load-dependentperformance.4.4.1DerivationofEfciencyandVoltageGainforArbitrar yLoad Modiedtransmissionparameters A 0 B 0 C 0 D 0 werefoundthatrepresentednottrue transmissionparametersbutinsteadprovidedrelationshi psbetweentheinputand outputvoltagesandcurrents.Thesemodiedparameterswer ecalculatedintermsof 66

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theoriginal ABCD transmissionparametersofthetransformerandtheloadimp edance Z L .The ABCD parameterscouldbederivedeitherfrommodelingorfrommea surement. Thevoltageacrosstheloadandthecurrentthroughitwerere presentedby V 0 2 and I 0 2 ,respectively.Thesequantitieswerefoundseparatelythr oughnetworkanalyses oftwocascadednetworksrepresentingthesamesituationof aloadattachedtothe transformer.Relationshipsofeachofthesequantitiestot heinputvoltage V 1 andinput current I 1 weredenedas 264 A 0 = V 1 V 0 2 B 0 = V 1 I 0 2 C 0 = I 1 V 0 2 D 0 = I 1 I 0 2 375 (4–15) Load-conditionedparameters A 0 and C 0 werefoundbycascadingthetransformer networkwithashuntloadandleavingtheoutputasanopencir cuit, A BC D Z L I 2 =0 V 0 2 I 1 V 1 Figure4-4.Circuitdiagramoftwo-porttransformertransm ission( ABCD )network cascadedwithshuntload. Theresultingnetworkwithshuntloadwas 264 A 0 B C 0 D 375 = 264 AB CD 375 264 10 1 = Z L 1 375 = 264 A + B = Z L B C + D = Z L D 375 (4–16) Load-conditionedparameters B 0 and D 0 werefoundbycascadingthetransformer withaseriesnetworkrepresentingtheloadandthenshortin gtheoutput,asshownin thegurebelow. Theresultingnetworkwithparallelloadnetworkwas 264 AB 0 CD 0 375 = 264 AB CD 375 264 1 Z L 01 375 = 264 AAZ L + B CCZ L + D 375 (4–17) 67

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A BC D Z L I 0 2 V 2 =0 I 1 V 1 Figure4-5.Circuitdiagramoftwo-porttransformertransm ission( ABCD )network cascadedwithseriesload. Themodiedparameterstakenfromeachofthetwocascadedne tworkstogether formedthefollowingsetofrelationships, A 0 = V 1 V 0 2 = A + B Z L B 0 = V 1 I 0 2 = AZ L + B C 0 = I 1 V 0 2 = C + D Z L D 0 = I 1 I 0 2 = CZ L + D (4–18) Efciencywasdenedastheratiooftherealpowerdelivered fromthetransformer toaloadversustherealpowerdeliveredfromasourcetothet ransformer,thatis, = P load P in = < V 0 2 I 0 2 < V 1 I 1 (4–19) Bypropertiesofcomplexnumbers,theexpressionwassimpli edas = V 0 2 I 0 2 V 0 2 I 0 2 = 2 V 1 I 1 + V 1 I 1 = 2 = 1+ V 0 2 I 0 2 I 0 2 V 0 2 V 1 V 0 2 I 1 I 0 2 V 1 I 0 2 I 1 V 0 2 = 1+ Z L = Z L A 0 D 0 + B 0 C 0 (4–20) Thisexpressioncouldalsobewrittenintermsoftheorigina ltransformer ABCD parametersandtheloadimpedance, = Z L + Z L ( AZ L + B ) ( CZ L + D ) + ( AZ L + B )( CZ L + D ) =
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Thevoltagegainprovidedtothetransformertovariedloads wasalsoderivedfrom thisanalysis,simplyastheinverseof A 0 A v = j V 0 2 j j V 1 j = 1 A 0 = Z L AZ L + B (4–22) 4.4.2ConjugateImpedanceMatchedLoading Themaximumefciencythroughthetransformeroccurswhent hesourceandload impedancesattachedtothetransformerareconjugatematch edtoitsinputandoutput impedances,respectively[ 57 ].Agenerictwo-port ABCD networkwasanalyzedto determinethe Z L thatwouldresultinconjugateimpedancematchingforagive n ABCD AslabelledinFigure 4-6 ,theimpedanceslookingintotheprimaryandsecondary coilsofthetransformerweredenoted Z 1 and Z 2 ,respectively,andthesourceandload impedancesweredenoted Z S and Z L A BC D Z L Z L Z 2 Z 1 Z S Figure4-6.Circuitdiagramoftwo-porttransformertransm ission( ABCD )networkwith sourceandloadimpedances Z S and Z L ,respectively. Conjugateimpedancematchingrequiresthat Z S and Z 1 arecomplexconjugate pairs,thatis, Z S = Z 1 (4–23) Thesameconditionisrequiredof Z L and Z 2 Z 2 = Z L (4–24) Fromnetworktheory,theimpedancelookingintothetransfo rmerinputportisgivenby Z 1 = AZ L + B CZ L + D (4–25) 69

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andtheimpedancelookingintotheoutputportis Z 2 = DZ S + B CZ S + A (4–26) FromEquation 4–23 andEquation 4–25 ,thematchedsourceimpedanceiswritten, Z S = AZ L + B CZ L + D (4–27) Theaboveexpressionformatchedsourceimpedanceisthenre placedintothe expressionforoutputportimpedanceofEquation 4–26 Z 2 = D AZ L + B CZ L + D + B C AZ L + B CZ L + D + A = Z L (4–28) whichisrelatedto Z L fromEquation 4–24 .Equation 4–28 canthenbealgebraically manipulatedintotheform, AC + A C Z L 2 + BC B C + A D AD Z L BD + B D =0, (4–29) whichisidentiedasaquadraticequation. Solvingthequadraticequationfor Z L yieldstheloadimpedancerequiredforthe conjugatematchedimpedanceconditionformaximumpowerga in.Thevalueof G max ,as calculatedfromEquation 4–1 ,isidenticallyequaltotheresultobtainedwhenthevalue of Z L (Equation 4–29 )isreplacedintoEquation 4–21 .However,thelattercalculation revealstherequiredmatchedloadimpedance,whichisnotot herwiseknown. 4.5SummaryofTransformerDesign Theprecedingchapteroutlinedconsiderationsaffectingt hedesignoftransformers intendedforswitchedmodepowerconverters. Efciencywasforwardedasametricformaximizingthepower deliveredtothe loadwhileminimizingthatdissipatedinthetransformer. 70

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Atwo-layerhybridcombinationofbothinterleavedandnest edprimaryand secondarycoilswaspresentedasalayoutthatwouldprovide bothstrongcoupling andopportunitiesfornon-unityvoltagegain. Threemethodsofdeterminingefciencywerediscussedbase dontheinformation requiredtocalculateeach:measuredscatteringparameter s,measuredor designedqualityfactorsandcouplingcoefcient,andmeas uredormodeled ABCD parameters. ABCD analysiswasfurtherusedtocalculateefciencyforanyarb itraryload impedanceandtodeterminethecorrespondingvoltagegain. 71

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CHAPTER5 FABRICATION Thischapterdescribesamultilevelwafer-levelmicrofabr icationprocessthatwas speciallydevelopedasameanstorealizingthree-dimensio nal(3D)electroformed coppercomponents.Theprocesswastailoredtodeliverthe nedimensionsand complexroutingneededformicroinductorsandtransformer swithhighperformancein integratedhighfrequencypowerconverters.Inthischapte r,anoverviewrstoutlines thefundamentalstepsattheheartofthismicrofabrication process.Severalvariations toenableextendedcapabilitiesofthecoreprocessarethen discussed.Detailsof themajorstepsintheprocessarethenprovidedforadeeperu nderstandingofthe considerationsmotivatingtheselectionvarioussequence sandparameters.Scanning electronmicroscope(SEM)imagesarefrequentlyusedinthi schaptertodepictfeatures ofthemicrofabricateddevices. The3Dcoppermicrofabricationprocesswasdevelopedinres ponsetodeciencies thathavesofarpreventedair-coremicroinductorsfrombei ngintegratedwithpower converters.Thisprocesswasrequiredtosimultaneouslyac hievethreegoals:thick copperwindings,multilayerstackingofwindings,andlowc apacitancebetween windings.Whilemagneticmaterialshavebeenusedinotherw orkstoincreasethe inductancethroughagivenlengthofconductor,theaircore spiralspresentedhere requiredalongerelectricalpathtoachievethesameinduct ance.Thelengthofthe coilscouldleadtoahighseriesresistance.Thickcopperwa snecessaryinorderto minimizetheelectricalresistancethroughtheinductors. Becausetheplanarspiral designoccupiedalargeareacomparedtoitsthickness,mult ilayerstackingprovided thebestmagneticcouplingtoincreaseinductancedensitie s.Multilayerstackingalso enabledthecomplexroutingschemesneededfortransformer swithstrongmagnetic couplingbetweenprimaryandsecondarycoils.Removalofdi electricfrombetween 72

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adjacenttracesreducedthecapacitancethatlimitedtheup peroperatingfrequency. Thesedesigndecisionshavebeencoveredingreaterdetaili nChapters 3 and 4 5.1ProcessOverview Themicrofabricationprocessconsistedprincipallyoftwo stages:anadditive stageinwhichcopperwaselectroplatedlayer-by-layerthr oughpatternedphotoresist moldsandafollowingsubtractivestageinwhichthemoldswe reremovedleavinga freestanding3Dcopperstructure. Duringtheadditivestage,thickcoppertraceswereformedv iaathrough-mold electroplatingtechnique.Athincopperseedlayerwasrst depositedacrosstheentire surfaceofthewafertoserveasaconductivebaseontowhicht hickercopperwould beelectroplated.Aphotoresistmoldwasthenpatternedont opoftheseed,andthe thicklayerofcopperwaselectroplatedthroughthemold.Th esemold-llingstepswere repeatedasillustratedinFigure 5-1 foreachlayerofthedevicesothatstructureswith three-dimensionalfeaturesmaybeobtained. Afteralldesiredlayerswereadded,thefabricationproces senteredthesubtractive stage,duringwhichthephotoresistmoldsandcopperseedsw ereremovedinoneoftwo ways.5.1.1SequentialLayerRemoval Thin( 10 m )suspendedfeatureswithgreaterwidthsthanthicknessesw ereprone tosnappingdownduringthewetremovalprocess,aproblemkn ownasstiction[ 58 ].For wafershavingsuchstructures,thephotoresistmoldsandco pperseedlayershadtobe sequentiallyremovedinphotoresistdeveloperandcoppere tchant,respectively.The sequentialremovalenabledthepatterningofselectivepor tionsofthephotoresistmold intoinsulatingstructuralelementstopreventstictionbe tweenoatingtraces.Figure 5-2 illustratestheprogressionofreleasingasuspendedinduc torbysequentiallayer removal. 73

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ALayer1moldovercopperseed BLayer1platedthroughmold. CLayer2platedthroughmold. DLayer3platedthroughmold. ELayer4platedthroughmold. Figure5-1.Illustrationsofadditiveprocessstage. Amicroinductorthatwasreleasedbysequentiallayerremov alwith 10 m thick tracesandanouterdiameterof 500 m isdepictedinthescanningelectronmicrograph (SEM)imageofFigure 5-3 .Bothupperandlowerwindinglayersarevisibleinthisimag e alongwiththescaffoldingandsupportpoststhataidinanch oringandproppingupthe windings.5.1.2UltrasonicAgitationinSolvents Iftheelectroplatedcoppersweresufcientlyrobust,remo valbothphotoresist andcopperseedwasaccomplishedthroughultrasonicagitat ioninaphotoresist 74

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ALayer4moldandseedremoved. BLayer3moldandseedremoved. CLayer2moldandseedremoved. DLayer1moldandseedremoved. Figure5-2.Illustrationsofsubtractiveprocessstage. Figure5-3.SEMimageofmicrofabricatedinductorwith 10 m thickcopperwinding layerswithphotoresistsupportpostsbetweenwindinglaye rs. 75

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Figure5-4.SEMimageofmicrofabricatedinductorwith 30 m thickcopperwinding layerswithupperwindinglayerheldinplaceonlybyvias. strippersuchasacetoneorasolutioncontaining n methyl 2 pyrrolidone (BAKER PRS-3000).Thissimpliedreleasemethodwasappropriatef ordeviceswhereany suspendedstructureswereatleast 30 m thickandnotconsiderablywiderthanthick. Figure 5-4 showsa 600 m microinductorwith 30 m thicklayers,themoldinglayers ofwhichwereremovedbyultrasonicagitationinBAKERPRS-3 000.Nophotoresist supportpostswererequiredforthisinductor,asthethicke rtracesprovidedample mechanicalsupporttoresiststiction. 5.2FeaturesandVariationsontheProcess 5.2.1PlanarProcessing Thesequenceofstepsinthisprocesswasdevisedsothataat ,planarsurface wouldbemaintainedthroughoutthefabricationofthedevic esforcompatibilitywith planarmicrofabricationtechniques.Aconsequenceofthet hrough-moldelectroplating techniquewasthattheconductivecopperseedinregionsbet weenelectroplated tracesofeachlayerwascoveredbythemold.Thecopperseede lectricallyshorted 76

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alltracestogetherandhadtoberemoved,whichinturnneces sitatedremovalofthe moldtogainaccess.Removingthemoldandseedimmediatelya fterelectroplating wouldhaveresultedinanon-atsurfacetopographywithrec essedregionswhere themoldonceexistedbetweenthickerelectroplatedregion s.Thistopographywould createproblemswhenbuildingmultilayerstructures:most photoresistsneedtobespun ontopofaatsurfacewithtopographicaldisturbancesmuch lessthanthedesired thicknessofthephotoresistlayerinordertoobtainaunifo rmphotoresistthickness. Anon-uniformphotoresistthicknesswouldnotdevelopprop erlysincethickerregions wouldunderdevelop,whilethinnerregionswilloverdevelo p.Also,thetopographyofthe surfacewouldnotallowtheregionsofphotoresisttobeinco ntactwiththemaskinthe caseofcontactmasklithographyorwouldleadtoregionstha tareexposedoutoffocus inthecaseofprojectionlithography.Ineithercasetheres ultwouldbepoorresolution withdiffractionoflightaroundtheareastobeexposed. Variousworkshavepresentedoptionsforcreatingaplanars urfaceabove electroplatedfeatures.Somehaveutilizedphotosensitiv ebenzocyclobutene(BCB) appliedovertheelectroplatedfeaturesafterremovalofth emold[ 59 60 ].BCBexhibits redistributionofmaterialtollgapsbetweenunderlyingf eaturestoformaplanarsurface whilecuring[ 61 ].Anotheroptionthathasbeenusedextensivelyinindustry forsurface planarizationwhileprocessingthecoppermetallayersofm icroprocessorsischemical mechanicalpolishing(CMP). Thefabricationmethoddescribedinthischapterontheothe rhandmaintained aplanarprocessingsurfacebyleavingthecopperseedlayer sinplacethroughout theadditivestageandnallyremovingeachoftheseedlayer sduringthesubtractive stage.Additionally,becausetheelectroplatingstepswer etimedsothatthedeposited copperlledtotheheightofthesurroundingmold,aplanars urfacewasmaintainedafter electroplatingeachlayerwithouttheneedforanyreoworC MPplanarizingsteps. 77

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5.2.2PhotoresistasaStructuralElement Onecapabilitythatdifferentiatedthisprocessfromother multilevelmetallization processeswasthatportionsofthephotoresistmoldcouldbe leftasstructural elementstoprovidemechanicalsupporttothemoldedcopper parts.Theability toformphotoresiststructuralelementswasdevisedinresp onsetondingthatthe wetprocessingstepsfortheremovalofthemoldingscausedb endingandbinding ofdeviceelementstoeachother,aproblemknownasstiction [ 58 ].Inthecaseof themicrofabricatedinductorsandtransformersthisstict ionledtoelectricalshorting ofwindingsthatdrasticallyloweredtheperformanceofthe devices.Becausethe photoresistthatformedtheplatingmoldswasadielectricm aterialwithnegligible conductivity,itwasusabletoprovidemechanicalandelect ricalisolationbetween windings. Thefabricationofthephotoresiststructuralelementsspe cicallyrequireda positive-tonephotoresist,oneinwhichexposuretoultrav ioletlightinitiatesachemical modicationinthephotoresistthatmakesitsoluble(i.e.e tchable)inabasicsolution (thedeveloper).Thecapabilityalsorequireduseoftheseq uentialremovalmethodfor thesubtractivestage.Inthisprocesseachlayerofphotore sistwasexposedtwice.The rstexposuredenedthemold.Regionsofthephotoresistwe reexposedandremoved indevelopersolutiontoformthedesiredmold.Thisphotore sistmoldwasthenexposed asecondtimeeverywhereexcepttheregionsthatwouldserve asstructuralelements. Howeverthephotoresistwasnotimmediatelydevelopedafte rthesecondexposure. Instead,theprocessproceededwiththeadditionofmorelay erstothestructureuntilall partsofthedevicehadbeenadded.Thenduringthesubtracti vestageeachmoldwas removedinphotoresistdeveloperexceptthoseunexposedre gionsofphotoresistthat becamestructuralelements. 78

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5.2.3SubstrateVersatility Themultilevelcoppermicrofabricationprocesswasrelati velyinsensitivetothe choiceofsubstrate.Structureswereformedontopofbothsi liconandPyrexwafers withminimalvariationoftheprocessstepsrequiredbetwee nthedifferentsubstrates. Theconductivesiliconwafersneededtobeelectricallyiso latedfromthecopper,which accomplishedbyplasma-enhancedchemicalvapordepositio n(PECVD)ofsilicon dioxideorsiliconnitridedielectriclayersoverthesurfa ceofthesilicon.Ininstances wheretheinductorsandtransformerswereintendedtothesi liconsubstratethroughout testing,reactiveionetching(RIE)wasusedtoselectively removeregionsofthe dielectriclayertoelectricallygroundthesiliconsubstr atewiththegroundcomponentsof thecopperlayers.Inallcases,athinlayeroftitaniumwass putter-depositedontopof thesilicondioxide,siliconnitride,orPyrextoimproveth eadhesionofthecopperpartsto thesesurfaces. Thedielectriclayerwasalsousedinotherinstancesasasac ricialmaterialthat alloweddetachmentofmultilevelcopperpartsfromthefabr icationwafer.Asdescribed ingreaterdetailinSection 8.2 ,integratedpowerconvertermoduleswereformedby encapsulatingmicrofabricatedinductorsandamultilevel routingandinterconnect frameworkinepoxy.Theencapsulatedcoppermoduleswereth enreleasedfroma siliconsubstratebyetchinginconcentrated 49% hydrouoricacidthelayerofsilicon dioxidethatinsulatedthetwofromeachother.Anetchingti meofseveralhourswas requiredforthehydrouoricacidtofullyundercutthesili condioxidefrombeneaththe 3mm 3mm modules. 5.3ProcessSteps Therststepsofthemicrofabricationprocessconcernedth eadhesionand insulationbetweenthesubstrateandthemultilevelcopper structurestobefabricated. Forsiliconsubstratesadielectriclayerofsilicondioxid eorsiliconnitridewasrst depositedovertheblankwaferbyplasma-enhancedchemical vapordeposition 79

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(PECVD).Thedielectriclayerprovidedelectricalinsulat ionbetweenthecopperand theconductivesiliconsubstrateorinsomecaseswasusedas asacriciallayerto physicallydetachcopperpartsfromthewaferafterfabrica tion.Thethicknessofthe dielectriclayerwasvariedfrom 200nm upto 2 m dependingontheintendedpurpose. Whenthedielectriclayerwasusedasasacricialmaterialt hethickestdepositionwas used.Whenusedonlyforelectricalinsulation,openingswe reformedinthedielectric layersothatthethegroundnodesofthecopperweredirectly incontactwithandwould groundthesiliconsubstrate.Toformtheopenings,resistw asphotolithographically patternedontopofthedielectricandtheexposeddielectri cwasremovedbyreactiveion etching(RIE).TheresistthatremainedaftertheRIEwasstr ippedinoxygenplasma. Thewafer—eitherfreshPyrexordielectriccoatedsilicon— thenenteredthesputter toolforcleaninganddepositionofthestartingseedlayer. Becausethesputtertoolhad multiplechambers,thesurfaceofthewaferwasabletobecle anedrstwithashort bombardmentetchofradio-frequency(RF)excitedargonion s.Whileremainingunder vacuumtopreventanycontaminationoroxidation,thewafer wastransferredtoanother chamberwherea 50nm thinlayeroftitaniumwassputterdepositedacrossthefull surfaceofthewafertoprovideimprovedadhesionbetweenth ePyrexordielectriclayer andthecopperstructures.Thewaferwastransferredtoathi rdchamberwherea 200nm thickcopperseedlayerwassputterdeposited.Onsubsequen tlayers,onlytheRFetch andcopperdepositionwereused,astitaniumwasonlyutiliz edfortheinitialdeposition onthewafer. Exceptfortherstlayerthatadditionallyrequiredtitani umdepositionbeforecopper, eachlayerofthemultilevelcopperstructurewasaddedbyre petitionofabasicsetof steps.Thestepswere: 1. In-situ argonsputteretch. 2. Sputterdepositionof 200nm copperseedlayer. 3. CoatingofAZ9245positivetonephotoresistandspinningto targetedthickness. 4. Heatingwaferonhotplatetodriveoutsolventfromphotores ist. 80

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Table5-1.ProcessparametersforpassivesfabricationatU .S.ArmyResearch Laboratory StepToolUsedDetails DepositdielectricLAM790 SiO 2 or SiN bytimeddeposition. ArgonsputteretchMetron3290 50W 40s SputterTiMetron3290 300W 30s SputterCuMetron3290 1.18kW 40s SpinphotoresistSUSSMicroTecACS200AZ9245photoresist.SoftbakeHotplate 95 C PhotoresistexposureSUSSMicroTecMA6 20mW = cm 2 PlasmadescumMetrolineM4L 200sccmO 2 400W 30s ElectroplateCuDynatronixDuPR10-3-6Timed,directcurre nt. DryingbakeHotplate 95 C 5min. SkinremovalMetrolineM4L 200 = 20sccmO 2 = CF 4 250W 5min. 5. Alignmentandcontactingofmasktowaferandultraviolet(U V)exposureof photoresist. 6. Developmentofphotoresist. 7. De-scumetchofresidueoutfromtrenchesinphotoresistmol d. 8. OptionalsecondUVexposureofphotoresist. 9. Electrodepositionofcopper. 10. Heatingwaferonhotplatetodry. ThesecondUVexposurewasonlyusedwhenasequentiallayerr emovalwas requiredasdescribedinSection 5.1 .Thetoolsandparametersusedforeachofthese stepsarelistedinTable 5-1 .MoreprocessingparametersarediscussedinSection 5.4 assomeweredependentonthechoiceoflayerthickness,whic hwastestedin thicknessesof 10 m and 30 m .Cross-sectiondiagramsinFigure 5-5 illustratehow eachstepoftheadditiveprocessstagecontributedtothebu ildingupofthemultilevel stack.Aftercompletionoftheadditivestage,theprocesse nteredthesubtractivestage, duringwhichthemoldingwasremovedbyeitherultrasonicag itationinasolventor bythesequentiallayerremovalprocess.Structureswithth incopperlayersrequired sequentialremovalofthemoldingtoenablepartsofthephot oresistmoldtobeused asstructuralelementstopreventpartsfromsnappingtoget her.Duringthesequential removal,thefollowingstepswererepeateduntiltheentire moldedcopperstructurewas releasedfromthemolding: 81

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1. Developphotoresist. 2. Copperetch. 3. Skinremoval. Cross-sectiondiagramsinFigure 5-6 illustratehoweachstepofthesequentialremoval contributedtoreleasingthecopperstructurefromitsmold 5.4SpecialProcessingConsiderations 5.4.1Sputtering Sputterdepositionofcopperwasrequiredintheprocesstof ormtheconductive seedlayersontowhichthethickcoppertracesofthedevicew ouldbeelectroplated.The onlyothermetalusedinthisprocesswasathinlayeroftitan iumdepositedatthestart oftheprocesstoaidinadhesionofthecopperdevicetothesu bstrate,whichwaseither Pyrexornitride-oroxide-coatedsilicon.Thetitaniumwas dcmagnetronsputteredat 300W for 30s forathicknessofroughly 50nm overthesurfaceofthewafer.Copper wasthensputteredontopofthetitaniumadhesionlayertopr ovidetheseedforcopper electroplating. Formingsubsequentlayersintheprocessrequireddepositi onofcopperonto asurfaceconsistingofbothphotoresistandelectroplated copper.Obtaininggood coverageofthissurfacebythecopperseedpresentedsevera lchallenges:thesputtered copperdidnotalwaysadherewelltoeitherthephotoresisto rtheelectroplatedcopper, andthelmoftenbrokealongtheboundariesbetweentheelec troplatedcopperandthe photoresist. Adhesionofthesputteredcopperlmontopofelectroplated copperwasimproved byargonsputteretchingoftheelectroplatedcoppersurfac eimmediatelypriorto sputterdeposition(seeSection 5.4.4 fordiscussion).Goodadhesionofthesputtered copperlmtophotoresistwasachievedwithhighpowerdcmag netronsputteringat 1.18kW .InFigure 5-7 ,acoppertracewaspeeledbackandippedover,revealing underlyingphotoresistpoststhatremainedattachedtothe trace.Thefactthateach photoresistpostremainedattachedtothetraceaboveit—ra therthantothetracebelow 82

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ASputterdepositTiandCu. BDeposit,pattern,anddescumphotoresist. CFloodexposephotoresist. DElectroplateCuanddrybake. ESputteretchsurfaceanddepositCu. FDeposit,pattern,anddescumphotoresist. GFloodexposephotoresist. HElectroplateCuanddrybake. ISputteretchsurfaceanddepositCu. JDeposit,pattern,anddescumphotoresist. KExposephotoresistwithpattern. LElectroplateCuanddrybake. MSputteretchsurfaceanddepositCu. NDeposit,pattern,anddescumphotoresist. OFloodexposephotoresist. PElectroplateCuanddrybake. Figure5-5.Crosssectiondiagramsoftheadditiveprocesss tage. 83

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ADevelopphotoresist. BCopperetchand O 2 / CF 4 plasmaetch. CDevelopphotoresist. DCopperetchand O 2 / CF 4 plasmaetch. EDevelopphotoresist. FCopperetchand O 2 / CF 4 plasmaetch. GDevelopphotoresist. HCopperetch. ITitaniumetch. Figure5-6.Crosssectiondiagramsofthesubtractiveproce ssstage. it—indicatedthatadhesionofthesputteredcopperontothe photoresistwasbetterthan thatofthephotoresistontothecopper. Sputteringcopperatlowerpowersresultedindelamination ofthelmfromthe photoresist.Thisproblemwasevidentwhenphotoresistwas curedontopofthe sputteredcopperlm.Duringsolventevaporation,tension fromtheresistwouldpullat thecopperlm,detachingitfromthephotoresistandbreaki ngthelmattheboundaries betweentheunderlyingphotoresistandelectroplatedcopp er.Accuratemaskalignment wasnotpossibleduetotheshiftinglmblockingtheunderly ingfeatures.During 84

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Figure5-7.SEMofcoppertracepeeledbackfrominductortor evealphotoresistspacer blocksattachedtocopper.Thisindicatedthatadhesionofc oppersputtered ontophotoresistwasbetterthanthatofphotoresistspunon tocopper. development,thebrokencopperlmwouldalsoallowphotore sistdevelopertoseep downaroundandetchintolowerphotoresistlayers,causing awideningofthemoldand electroplatingofcopperbetweentracesasshowninFigure 5-8A Atasputteringpowerof 1.18kW nobreakingorshiftingofthecopperlmwas observedandelectroplatingwaswell-connedtothemolds, yieldinggoodseparation offeaturessuchasthoseshownforcomparisoninFigure 5-8B .Atsputteringpowers greaterthan 1.18kW ,excessiveheatingofthewafercausedbubblingofthephoto resist. 5.4.2Photolithography AZ9245positivetonephotoresistwasusedforitsabilityto formthicklayersand compatibilitywiththecopperelectroplatingbath.Twosep aratesetsofphotolithography parametersenabledtheresisttobespuntoathicknessofeit her 10 m or 30 m per layer.Ineithercase,thephotolithographystepsconsiste dofthefollowing: 1. Photoresistwasdispensedontowaferandspuntoobtainanev encoatofuniform thickness.Thetime,acceleration,andspeedofthespinwer etailoredyieldthe 85

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ACopperdepositionbetweenfeaturesduetopoorseedlayeradhesion BGoodisolationoffeaturesachievedasaresultofimprovedadhesion Figure5-8.SEMimagesofcopperchannels.Pooradhesionofc opperseedlayerto photoresistresultedincracksbetweenfeaturesthroughwh ichcopperwas electroplatedwherenotdesired. targetthicknessof 10 m or 30 m .Insteadofapplyingthethickestlayersin multiplecoats,aslowspinspeedandshortdurationwereuse dtoobtainthe thickestcoatinasinglespin.Thesinglespinwasfoundtore sultinthemost uniformcoatofsurfacetopography. 2. Thewaferwithafreshcoatofphotoresistwasplacedonahotp lateforthe soft-bakesteptodrivethesolventoutfromandcurethephot oresist.Dueto themultilayernatureofthisprocess,whichcalledforfurt herphotolithography andprocessingontopofalready-patternedphotoresistlay ers,alowsoft-bake temperatureof 95 C wasusedtoavoiddeformationofthealready-patterned layersthatwouldoccurattemperaturesbeyond 100 C 3. Edge-beadremovalwasperformedbyspinningthewaferandap plyingasteady streamofacetonealongtheedge.Thepurposewastoremoveth ethickerbead ofphotoresistthatpooleduparoundtheedgeofthewaferdur ingcoatingtoallow ushcontactwithphotomaskandtopreventoutgassingthatw ouldoccurinthe excessivelythickbead.Thisstepalsoallowedcoppertobep latedaroundtherim ofthewaferforimproveddeposituniformity(Section 5.4.3 ). 4. Anadditionalbakeonthehotplatedrovesolventoutfromthe newlyformededge duringedge-beadremoval.Theacetoneusedforedge-beadre movaltendedto absorbintoandsoftenthephotoresistaroundtheedge.Thee dgeneededtobe curedagaintopreventthewaferfromstickingtothephotoma sk. 5. Rehydrationofthephotoresistwasnecessarytorestorethe watercontentthat hadbeenbakedoutofthephotoresistduringthecuringproce ss.Thewaterwas neededforthephoto-reactionthatoccurredduringultravi oletexposuretomakethe resistdevelopable.Toreducethetimerequiredforrehydra tionandthesensitivity 86

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toambienthumidityconditions,rehydrationwasaccomplis hedbysubmergingthe waferinadishofwater. 6. Thewaferwasalignedtothephotomaskandcontactedwithvac uumtopullthe waferushagainstthephotomask.Ultraviolet(UV)exposur ewasthentimedtothe appropriatedosedependingonphotoresistthickness. 7. DevelopmentofphotoresistwasdonebysubmersioninAZ400K potassium hydroxidebaseddeveloper.Afterdevelopmentthewaferwas rinsedindeionized waterandblowndrywithnitrogen. 8. Ade-scumetchinoxygenplasmawasrequiredtoremoveresidu eoutfrom trenchesinphotoresistmold.Thescumwasotherwisefoundt odisrupttheinitial electrodepositionofcopperinregions,leadingtoanonuni formcopperll.In particular,mostoftheresiduewasfoundtoaccumulateatth eendsofrecessed channelsinthephotoresistduetocapillarywickingofthel iquiddeveloperasthe waferwasdried[ 62 ]. 9. AnoptionalsecondexposureofthephotoresisttoUVenabled thelayerstobe sequentiallyremovedinphotoresistdeveloperduringthes ubtractivestageof theprocess.Thissecondexposurecouldoptionallybemaske dsothatsome regionsoftheresistmoldwouldremainaspartofthenaldev icestructure.Itwas importantthatthesecondexposurewasperformedfollowing theplasmadescum steptoavoidheatingjust-exposedresist.Duringexposure ,diazonaphtoquinone photo-active-compoundsinthepositivephotoresistdecom posedandreleased nitrogengas,whichslowlydiffusedthroughtheresist[ 63 ].Iftheresistwasheated toosoonafterexposure,theexcessnitrogengasthathadnot yetdiffusedout wouldexpandandcausebubblingandcrackingoftheresist. 5.4.3Electroplating Copperelectroplatingwascarriedoutinanacidcoppersulf atebath.While mostcommercially-availablecopperelectroplatingbathe lectrolyteshavecontained proprietaryconcoctionsofsurfactantsandotherorganica dditivestoimprovevarious depositcharacteristics,suchassurfacesmoothnessandha rdness,theadditionagents havealsobeenknowntoco-depositwiththeplatedcopperand causeembrittlement orresidualstress[ 64 ].Becausetheinductorsandtransformersofthisworkcalle dfor relativelylongstretchesofsuspendedcoppertraces,anel ectrolytechemistrywas usedwithoutanyadditiveagentsinordertominimizetheres idualstressinthecopper deposit. 87

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Table5-2.Recipeper 1L acidcoppersulfateelectroplatingbath.Adaptedfrom Rothschild[ 65 ]. StepIngredientQuantity StartDeionizedwater 500mL StirinCoppersulfatepentahydratecrystals 60g AddSulfuricacid 120mL FillDeionizedwaterUpto 1L totalsolution Inplaceoftheadditiveagents,otherelectroplatingparam eterswereoptimized toyieldauniformdeposit.Agitationofthebathelectrolyt eduringplatingyieldedthe greatestimprovementtouniformitywhencomparingtherate sofcopperplatinginareas ofhighversuslowfeaturedensity.Inastillbathwithoutag itation,regionsofawafer withlargeareasofexposedcopperplatedatasignicantlys lowerratethaninregions withlittlecopperarea(mostlymasked).Bathagitationwas accomplishedbypumping theuidandattachingthewafertoahorizontally-oscillat ingholder.Thebathelectrolyte itselfwasalsoformulatedwithalowconcentrationofdisso lvedcopperandahigh concentrationofsulfuricacidtoincreaseitsthrowingpow er,theabilityofthebathto provideauniformdepositthicknessoveranirregularshape s[ 64 ].Therecipeforthe copperplatingbathwasadaptedfromtheworkofRothschild[ 65 ]andislistedinTable 5-2 A 4mm ringofphotoresistwasremovedaroundtherimofthewaferto expose theunderlyingcopperseed.Thefunctionofthisexclusionz onewastwo-fold.First,it allowedforelectricalconnectionfromthefrontsideofthe wafertothenegativeterminal ofthepowersupplyforelectroplating.Thesecondfunction oftheexclusionrimwas asacurrentbafetoprovideuniformelectriceldstrength acrossthewafersurface. Becauseitwasalsoincontactwiththeelectroplatingbath, copperwaselectroplated ontotheseedlayerexposedaroundtheperimeter.Havingsuc halargeelectroplating areaaroundthewaferedgewasfoundtoaidintheuniformityo fthedepositionrate amongstfeaturesofdifferentdimensionsacrossthewafers urface. 88

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Theanodesconsistedof 0.5in nuggetsofcopperwith 0.04 0.06% phosphorus content.Thequantityofcopperanodematerialwasadjusted downwardtoprevent copperionconcentrationfromincreasinginthebathoverti me.Toohighofaconcentration ofcopperioninthebathpresentedtheformationofwart-lik enodulesonthecopper surface. CantileverstructuressuchastheonedepictedinFigure 5-9 wereco-fabricated alongsidetheinductorsandtransformers.Atupto 1 m longand 10 m thick,the cantileversdidnotexhibitanyperceptiblecurvatureafte rrelease,indicatingthatno stressgradientwaspresentthroughoutthethicknessofthe copper. AFull1mmcantilever BCantilevertip Figure5-9.SEMimagesof 1mm -longcoppercantilever.Minimalresidualstressis presentinelectroplatedcopperstructuresasevidencedby minimal curvatureoflongcoppercantilever. 5.4.4ArgonSputterEtch Aftereachthicklayerofcopperwaselectrodepositedtoll thephotoresistmolds, anargonsputteretchwasrequiredtocleanthecoppersurfac e.Thisetchwasrequired inordertoimprovetheadhesionbetweentheelectroplatedc opperandthecopperseed layersputterdepositedontoitssurface.Figure 5-10 comparesimagesofdevicesthat werefabricatedwith(left)andwithout(right)thisargons putteretchstep. Separationwasevidentbetweeneachofthelayersofthedevi cesfabricated withouttheargonsputteretchasshownforexampleinFigure 5-10A .Althoughsome 89

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AWithoutsputteretch BWithsputteretch Figure5-10.SEMimagesofdevicesfabricatedwithandwitho utargonsputteretching betweenlayerdepositions.Separationbetweenlayerswase videntwithout thesputteretchandwaseliminatedusingthesputteretch. layersremainedinplace(suchastheoneshowninthegure), manydevicesexhibited catastrophicdelaminationduringthenalwetprocessings tepsoffabrication,andthe yieldwasconsequentlylow.Incontrast,thedevicesthatre ceivedtheargonsputteretch stepsexhibitedstrongadhesionbetweencopperlayers.Ass howninFigure 5-10B ,the sputteretchwaseffectiveineliminatingtheseparationbe tweenlayers. Argonsputteretchingwasperformed insitu immediatelypriortosputterdeposition ofcopper.Inthismanner,theetchremovedtheoxidizedsurf aceoftheelectroplated copper,andthecleanedsurfaceremainedundervacuumuntil afterthecoatedwas completed.5.4.5PhotoresistSkinRemoval Anunintendedbyproductofthepreviouslydescribedargons putteretchwasthe alterationofthephotoresistsurface.Thesputteringresu ltedintheformationofathin, impermeableskinontheexposedsurfaceofthephotoresistt hatconsequentlyblocked theunderlyingphotoresistfrombeingremovedinthephotor esistdeveloperduring sequentiallayerremoval(Section 5.1.1 ).InFigure 5-11A ,aportionoftheblockingskin removedbyphysicallyscratchingitawayandtherestofthep hotoresistwasetchedin 90

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acetone.Theunbrokenskinscouldbeseenspanningtrenches betweencoppertraces attheinterfacesbetweenlayers. AWithout CF 4 plasmaetch BWith CF 4 plasmaetch Figure5-11.SEMimagesofcoppertrenches.Photoresisthas beenetchedby KOH -baseddeveloperineachcase,butthinsurfacelayersremai nbetween trencheswithout CF 4 plasmaetch Thesephotoresistskinscouldnotberemovedby O 2 plasmaashingalonebutwere successfullyremovedbyaplasmaetchconsistingofboth O 2 and CF 4 .Figure 5-11B by comparisonshowshowonesuchtrenchshouldappearwhenthep hotoresistskinswere removedateachlayerbythe CF 4 plasmaetch. 5.4.6CopperSeedEtch Afteralllayerswereaddedbyelectrodepositionthroughph otoresistmods,removal ofthecopperseedsateachlayerwasnecessarytoelectrical lyisolateelectroplated traces.Whenitwasusedtoremovethemolds,ultrasonicagit ation(Section 5.1.2 ) inacetoneorBAKERPRS-3000wasabletobreakupallofthesee dlayersthathad beendepositedontopofphotoresist.Thebottommostcopper seedlayer,however, andeachofthecopperseedlayerswhensequentiallayerremo valwasperformed, neededtobeetchedawaywithacopperetchant.Becausethese edandthethicker traceswerebothcomposedofcopper,theseedetchantalsoet chedthetraces.As shownbythecomparisonbetweenelectroplatedcopperfeatu resbeforeandafter seedlayerremovalinFigure 5-12 ,thisetchingproducednoticeablerougheningofthe 91

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coppersidewallprole,whichwassmoothlydenedbythepho toresistmold.Without etchselectivitybetweenseedandtrace,theseedremovalre liedontimingsincethe 200nm thickseedwouldbefullyetchedmuchquickerthanthe 10 m thicktraces. Ceric-ammonium-nitrate-basedCyantekCR9chromiumetcha ntwasusedtoetchthe copperseedsduetoitsslowetchrate,whichallowedeasytim ingoftheetchtominimize over-etchingtheelectroplatedfeatures.Fulletchingofa seedlayertookapproximately 1min withmoderateagitation. ABeforecopperetch BAftercopperetch Figure5-12.SEMimagesshowingsidewallofcopperfeatures beforeandaftercopper etch.Thesidewallisshowntobemuchsmootherbeforethecop peretch thanafterwards. 92

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CHAPTER6 INDUCTORCHARACTERIZATION Thischapterdiscussescharacterizationofthemicrofabri catedinductorsunder radio-frequencyexcitation.Anoverviewofthetestingset upprovidesrelevantbackground regardingmeasurementwiththevectornetworkanalyzer(VN A)tool.Thesectionon characterizationmethodsdetailshowscatteringdatameas uredfromtheVNAwere convertedtoimpedancecharacteristics.Measurementsare reportedrstforone-port inductorsfabricatedonPyrexsubstrates.Theseresultspr ovideabroadviewofthe designspaceintermsoftheelectricaleffectofvaryinggeo metryparameterssuch asdiameters,tracewidths,andspacings.Subsequentsecti onsexploretheeffectof modifyingtheinterlayerdielectric,switchingthesubstr atetosilicon,andchangingthe shapefromsquaretocircle. 6.1EquipmentandSetup Characterizationofthemicroinductorsatradiofrequenci es(RF)wasaccomplished usingaVectorNetworkAnalyzer(VNA).Themeasurementswer emadewitheither anAgilentE8361Awithuseablefrequencyrangeof 10MHz 30GHz oraRohde &SchwarzZVA/Bwithauseablefrequencyrangeof 300kHz 8GHz .Thegeneral workingprincipleoftheVNAwastoexcitethedeviceunderte stwithasinglefrequency signalandtosampletheamplitudeandphaseoftheincident, reected,andtransmitted waves.Fortheworkpresentedhere,theexcitationfrequenc ywassweptfrom 10MHz uptoatleast 8GHz toobtainthefullfrequency-dependentbehaviorofthedevi cesupto andbeyondtherstresonantfrequencyofeach.Thedatawere recordedascomplex scattering( S )parameters,denedasvariousratiosofthemeasuredwavev ectors[ 56 ]. Electricalconnectiontotheinductorsandtransformerswa smadebyradio-frequency (RF)probeswithground-signal-ground(GSG)tipfootprint congurationand 150 or 200 m tippitch.Fixturecompensationwasperformedwithacalibr ationsubstrate havingopen,short,through,and 50n loadstandards[ 66 ]. 93

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6.2InductorCharacterizationMethods Themicroinductorsweredesignedinbothone-portandtwo-p ortcongurationsas showninFigure 6-1 .Inallcasesthesignalpadwas 100 m 100 m inareaandwas ankedonbothsidesbygroundpadsofconsiderablylargerar eaandspaced 50 m apart. AOne-port BTwo-port Figure6-1.SEMimagesdepictinginductorswitheitheroneportortwo-port connections. 6.2.1One-PortInductorMethods Theendsofaninductorintheone-portcongurationwereter minatedatthesignal padandatoneoftheadjacentgroundpads.One-portcharacte rizationwasconvenient inthattheinductorimpedancewasdirectlyreportedonthes creenofthevectornetwork analyzer(VNA),butforinductorsfabricatedonsiliconthe capacitancethroughthe substratebetweensignalandgroundterminalswaslumpedin tothemeasurement.Also, becausethemicroinductorsofthisworkwereasymmetricint hatonehalfofthewinding wasphysicallyclosertothesubstratethanthetophalf,the one-portmeasurementwas furthermoresensitivetowhetherthetoporbottomhalfofth ewindingwasconnectedto thesignalpad.Becausethesubstratewasheldatagroundpot ential,thecapacitance wasgreaterifthehalfofthewindingclosesttothesignalpa dwaslocatedonthe bottom. 94

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Inductordataobtainedwithone-portmeasurementyieldedo necomplexscattering value S perfrequencypoint.Eachscatteringvaluewasconvertedto animpedance value, Z ,viatherelationship, Z = Z 0 1+ S 1 S (6–1) where Z 0 wasthecharacteristicimpedanceofthemeasurementline;i nthiscase Z 0 =50n 6.2.2Two-PortInductorMethods Thetwo-portcongurationwasspecicallyutilizedtoiden tifyandseparateout theeffectsofcapacitivecouplingthroughthesubstrate.I nductorsinthisconguration wereconnectedwiththeendsterminatingatthesignalpadof eachport.Groundpads stillankedthesignalpadsandwereconnectedbetweenthet woportsbutwerenot connectedbycoppertoeitherofthesignalpads.Thistwo-po rtcongurationprovided aricherdatasetthatenabledseparationoftheimpedanceth roughthesignalterminals (i.e.theinductorimpedance)fromtheshuntimpedancebetw eenthesignalandground terminalsateachport(i.e.thesubstratecapacitancebetw eentheconnectionpads). Z S 1 Z S 2 Z T Figure6-2.Two-portinductorimpedancenetwork. Thetwo-portinductorimpedancesweremodeledaccordingto thecircuitshownin Figure 6-2 ,where Z T wastheimpedancethroughtheinductorand Z S 1 and Z S 2 were theshuntimpedancestothesubstrateateachport.Conversi onofthemeasured S parametersto ABCD facilitatedcharacterizationofthetwo-portinductorsan dextraction ofthethroughandshuntimpedances.The ABCD parametersforthecircuitnetwork ofFigure 6-2 werefoundusingthepropertythatthe ABCD parametermatricesof 95

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cascadednetworksectionscouldbemultipliedtogethertoo btainthe ABCD parameters oftheoverallcircuit.Theoverall ABCD parametermatrixforthecircuitwithshunt impedance Z S 1 followedbyseriesimpedance Z T followedbyshuntimpedance Z S 2 was obtainedas 264 AB CD 375 = 264 10 1 Z S 1 0 375 264 1 Z T 10 375 264 10 1 Z S 2 0 375 = 264 1+ Z T Z S 2 Z T 1 Z S 1 + 1 Z S 2 + Z T Z S 1 Z S 2 1+ Z T Z S 1 375 (6–2) Fromthe ABCD parameters, Z T couldthereforebeextractedsimplyas Z T = B (6–3) Theshuntimpedances Z S 2 and Z S 1 werethenextractedbyrearrangingtheequivalencies forthe A and D parameters,respectively, A =1+ Z T Z S 2 ; Z S 2 = Z T A 1 = B A 1 (6–4) and D =1+ Z T Z S 1 ; Z S 1 = Z T D 1 = B D 1 (6–5) Thetwo-portmodelalsoenabledsimulationoftheimpedance thatwouldhavebeen measurediftheinductorwereexcitedinaone-portcongura tionwiththeotherport shortedtoground.Theinputimpedancelookingintoport1wi thport2shortedtoground wassolvedas Z 1 = 1 1 Z T + 1 Z S 1 = B D (6–6) Similarly,theinputimpedancelookingintoport2ifport1w ereshortedtogroundwas obtainedas Z 2 = 1 1 Z T + 1 Z S 2 = B A (6–7) 96

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6.2.3InductorCharacteristicsObtainedfromImpedance Inductorimpedancevaluesweresplitintofrequency-depen dentresistancesand inductances.Resistancesrepresentedtherealpartofthec ompleximpedances, R =
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6.3One-PortInductorCharacterization 6.3.1One-PortInductorsonPyrexSubstrates One-portinductorswerefabricatedonPyrexsubstrateswit hvariedgeometries. Althoughphotoresistwasusedtoseparatetheupperandlowe rwindinglayers,it waspatternedintosmallpoststominimizeitscontribution tothecapacitanceofthe inductors.Thesedeviceswereidealforvalidationofthemo delinganddesignconcepts thatwerepresentedinChapter 3 .Thecharacteristicsofseveralinductorsofvarious geometriesweremeasuredandsummarizedinTable 6-1 .Theareas,tracewidths, spacings,andnumbersofturnswerereportedinthetablebas edonthecomputer-aided drawings(CAD)ofthephotomasksusedinfabrication.There portedvaluesfor L dc R dc SRF Q max ,and f @ Q max wereaveragedoverthenumberofknown-goodinductors.The yieldwasreportedinthetableasthenumberofknown-goodin ductorsoutofthetotal numberofinductorsofagivendesignthatweretested.Thesm allerdevicesexhibited greateryield—100%ofthetestedinductorsupto 2.4mm 2 functionedproperly.Some largerinductorssufferedfromshortingbetweenwindings, andthecharacteristicsof thosemalfunctioninginductorswasnotrecorded.Thenames listedinthetablewere usedtorefertoallcopiesofinductorsofaspecicdesign. Severalinterestingperformancetrendswererevealedbyco mparingdataamongst differentdesigns.InductorsI1andI2wereidenticalineve rywayexceptfortracewidth andspacing—bothhadthesame 60 m tracepitch,butonehad 40 m tracewidthand 20 m spacing,whiletheotherhad 50 m widthand 10 m spacing.Althoughthedc resistancewassignicantlylesserforthewider-tracedin ductor,themaximumquality factorwassignicantlygreaterforthenarrow-tracedindu ctor.Thefrequencyvalues relatedtoresonance( SRF and f @ Q max )werealmostequalbetweenthetwoinductors, indicatingthatthecapacitanceinthedevicethatleadtose lf-resonancewasdominated bythetracelengthratherthanproximityofadjacenttraces 98

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10 7 10 8 10 9 -2 -1 0 1 2 x 10 -7 InductanceFrequency (Hz) SRF L dc AInductancewith L dc and SRF 10 7 10 8 10 9 10 0 10 2 10 4 ResistanceFrequency (Hz) SRF R dc BResistancewith R dc and SRF 10 7 10 8 10 9 -20 0 20 40 Quality FactorFrequency (Hz) f@Q max SRF Q max CQualityfactorwith Q max f @ Q max ,and SRF Figure6-3.Identicationofinductorspecicationsfromp lotsofinductance,resistance,andqualityfactordataobt ained fromVNA. Table6-1.Comparisonofmeasuredinductorperformance.Va lueswereaveragedoverthenumberofdevicestested. AreaWidthSpacing#turns#devices L dc R dc SRFf @ Q max Name( mm 2 )( m )( m )perlayertested( nH )( n )( MHz ) Q max ( MHz ) I1 0.284020316 / 1614.80.73429033.01740 I2 0.275010316 / 1614.40.55426027.51760 I3 1.02501054 / 490.21.8792220.0395 I4 0.9750564 / 41082.1386515.5376 I5 2.40501054 / 41983.4047921.2207 I6 2.40501083 / 43274.7733017.3148 I7 4.125010102 / 46768.2517615.881 I8 4.331001063 / 42262.8629315.8131 I9 6.656010103 / 48949.9311113.951 99

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Table6-2.Comparisonofmodel-predictedtomeasuredinduc torperformance. AnalyticalFastHenryMeasuredAnalyticalFastHenryMeasu red Name L dc ( nH ) L dc ( nH ) L dc ( nH ) R dc ( n ) R dc ( n ) R dc ( n ) I1 14.314.114.80.700.690.73 I2 13.113.814.40.560.550.55 I3 89.989.590.21.891.871.87 I4 1051081082.082.062.13 I5 2142051983.263.273.40 I6 3443433274.554.524.77 I7 7547476767.597.548.25 I8 2462512262.292.242.86 I9 105610468948.318.249.93 0 200 400 600 0.5 0.6 0.7 0.8 0.9 1 Current (mA)Resistnace ( W ) AInductorI2( 0.5mm 0.5mm ) 0 200 400 600 2 3 4 5 Current (mA)Resistnace ( W ) BInductorI3( 1.0mm 1.0mm ) 0 200 400 600 2.5 3 3.5 4 4.5 Current (mA)Resistnace ( W ) CInductorI5( 1.5mm 1.5mm ) Figure6-4.Measuredresistanceofdifferent-sizedinduct orsasafunctionofapplieddccurrent.Inductorstestedupt o onsetofthermalrunaway.100

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6.3.1.1Comparisontomodelpredictions Thelowfrequencyinductances L dc andresistances R dc measuredfromthe inductorswerecomparedtothosevaluescalculatedfromthe analyticalexpressions usedintheirdesign(Section 3.4 )andwerealsocomparedtoFastHenrysimulations (Section 3.5.2 ).DCresistancewascalculatedusingacopperresistivityo f 3.3 n cm avaluethatwasobtainedbymeasuringresistanceteststruc turesthatwereco-fabricated alongsidetheinductors.Themeasured,calculated,andsim ulatedvaluesarelisted inTable 6-2 .Theclosestagreementbetweenthevalueswasfoundforthes maller inductorsuptoabout 200nH .Thelargerinductorsconsistentlymeasuredlower inductancesandhigherresistancesthancalculatedorsimu lated. 6.3.1.2Currentrating Whilesaturationofaferromagneticcoreoftenlimitstheup percurrentcapabilityof aninductor,theair-coremicroinductorstestedherewerel imitedbyresistiveheating. Thecurrentratingofthemicroinductorswastestedbyrunni ngsuccessivelygreater currentsthroughthecoilsuntilthepointatwhichexcessiv eheatingledtothermal runaway. Thermalrunawayoccurredwhenastableoperatingcurrentco uldnotbemaintained. Becausetherateofheatgenerationinthedevicewasproport ionaltoitselectrical resistanceandtheresistanceofthecopperalsoincreasedw ithtemperature,this positivefeedbackresultedinanunstableconditionathigh currents.Atthispointheat generationandresistanceincreasedwithoutboundsuntilt hedeviceburntup. Threeinductordesignsofdifferentsizesweretestedforth ermalrunawayto estimatetheircurrentrating:I2,I3,andI5.Thedeviceswe refabricatedona 100mm diameter, 500 m -thickPyrexsubstrateandweretestedwhileremainingatta chedto thewholewafer.Thewaferwasplacedonalargestainlessste elchuckheldatroom temperature,whichwasapproximately 25 F .Theresistanceofeachinductoratdirect current(dc)wasplottedinFigure 6-4 asafunctionoftheappliedcurrent.Inductor 101

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I2experiencedthermalrunawayat 600mA ,I3at 470mA ,andI5at 450mA .Priorto runaway,thephotoresistbetweentraceswasseentomelt,an dthecopperwindingsof eachinductorcouldbeseentochangecolorasthecopperoxid ized.Thedccurrentat whichthecopperofeachinductornoticeablychangedcolorw as 550mA forI2, 350mA forI3,and 450mA forI5.Theprecedingdatahoweverwereparticulartothespe cic setupandtheactualmaximumcurrentwoulddependontheheat transfercharacteristics ofagivenapplication.6.3.1.3Interwindingcapacitance Totesttheeffectofaninterlayerdielectriconinterwindi ngcapacitance,abatchof inductorswerefabricatedwiththesamelayoutsasthoselis tedinTable 6-1 but,instead ofpatterningtheresistintosupportposts,thesewerefabr icatedwithacontinuous layerofphotoresistbetweentheupperandlowerwindinglay ers.TheimagesinFigure 6-5 illustratethephysicaldifferencebetweenaninductorwit hpatternedresistsupport postsandonewithaninterlayerofcontinuousphotoresist. Twodesigns,I1andI6,were selectedtohighlighttheeffectoftheinterlayerphotores istonthemeasuredimpedance ofasmallandalargeinductor,respectively.Comparingthe measuredimpedancesas plottedinFigure 6-6 fortwoinductorsofdesignI1,thepatterningofthephotore sistinto supportpostsincreasedtheselfresonantfrequency(SRF)f rom 3.77GHz to 4.20GHz animprovementof 11% .FortheimpedancesofthetwolargerinductorsofdesignI6a s plottedinFigure 6-7 ,patterningthephotoresistintosupportpostsincreasedt heSRF from 265MHz to 326MHz ,anincreaseof 23% .AsaresultoftheincreasedSRF,the measuredqualityfactoralsoincreasedfrom 16.0 to 17.3 .Comparingtheimpedancesof otherdesignsboresimilarresults,inwhichlargerinducto rswithmoreturnsexhibiteda greaterimprovementfromminimizingtheinterlayerdielec tricthroughpatterningofthe photoresistsupportposts. 102

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APatternedresistposts BContinuousresistlayer Figure6-5.Scanningelectronmicrograph(SEM)imagesofon einductorwithpatterned photoresistsupportpostsbetweenupperandlowerwindingl ayersandone withacontinuouslayerofphotoresistbetweenwindings. 103

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10 7 10 8 10 9 10 10 10 1 10 2 10 3 10 4 Inductance (nH)Frequency (Hz) Unpatterned layer Patterned posts AInductance 10 7 10 8 10 9 10 10 10 0 10 2 10 4 Resistance ( W )Frequency (Hz) Unpatterned layer Patterned posts BResistance 10 7 10 8 10 9 10 10 0 10 20 30 40 Quality FactorFrequency (Hz) Unpatterned layer Patterned posts CQualityFactor Figure6-6.Comparisonofinterlayerdielectriceffectoni mpedanceforasmallinductor(designI1,outerdiameter D =500 m ). 10 7 10 8 10 9 10 10 10 1 10 2 10 3 10 4 Inductance (nH)Frequency (Hz) Unpatterned layer Patterned posts AInductance 10 7 10 8 10 9 10 10 10 0 10 2 10 4 Resistance ( W )Frequency (Hz) Unpatterned layer Patterned posts BResistance 10 7 10 8 10 9 10 10 0 10 20 30 40 Quality FactorFrequency (Hz) Unpatterned layer Patterned posts CQualityFactor Figure6-7.Comparisonofinterlayerdielectriceffectoni mpedanceforalargeinductor(designI6,outerdiameter D =1.5mm ).104

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6.3.2One-PortInductorsonSiliconSubstrates Severaliterationsofinductordesignswerealsofabricate donsiliconsubstrates. AsdetailedinSection 3.6.1 themeasuredimpedancesoftheinductorswereheavily impactedbycapacitivecouplingoftheinductorthroughthe substrate.Compared tothoseonPyrexsubstrates,allinductorsfabricatedonsi liconexhibitedlower self-resonantfrequencies( SRF )andresonancesthatwerehighlydampedbythe resistanceofthesubstrate.Theeffectwasdependentonthe thicknessoftheinsulating dielectriclayerbetweensiliconandcopperandontheresis tivityofthesubstrate. Becausethecapacitancethroughthesubstratewaslumpedin tothemeasured impedanceoftheone-portinductors,theresultsthatlooke datsubstrateeffects weremeasuredwithtwo-portinductorsinSection 6.4 .Twosetsofexperimentswere conducted,however,withone-portinductorsfabricatedon siliconsubstratestohighlight theeffectofcopperlayerthicknessandinductorshapeonme asuredimpedance. 6.3.2.1Copperlayerthickness: 10 m vs. 30 m Twoinductordesigns(smallandlarge)wereeachimplemente dinaversionwith 10 m thicklayersofcopperandinanotherversionwith 30 m thicklayersofcopper. Thesmallerofthetwoinductordesignshadanouterdiameter D =500 m ,tracewidth w =30 m ,spacingbetweentraces s =10 m ,and n =3 turnsperlayeroneach ofthetwowindinglayers.Thelargerhadanouterdiameter D =1000 m ,tracewidth w =30 m ,spacingbetweentraces s =10 m ,and n =5 turnsperlayeroneachofthe twowindinglayers.Theverticalgapheightbetweentheuppe randlowerwindinglayers ofeachinductorwasequaltothethicknessofeachofthewind inglayersofthatinductor. Theimpedanceswereplottedforthesmallerandlargerdesig nsinboththicknesses inFigure 6-8 and 6-9 ,respectively.Themeasuredperformanceparametersobtai ned fromeachwerelistedinTable 6-3 forcomparison.Thethickerinductorsofbothdesigns wereshowntohavegreatlyreducedlowfrequencyresistance s,resultingingreater qualityfactorsupto 100MHz .Theresistancesofthethickertracesalsoshowed 105

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Table6-3.Measuredperformanceparametersoftwoinductor designs,each implementedinversionswith 10 m and 30 m thickcopperlayers. DesignLayerNominalNominalMaximumFrequencyfor sizethicknessinductanceresistancequalityfactormaxmi mumquality Small 10 m21nH2.0n3.9116MHz Small 30 m17nH0.25n8.760MHz Large 10 m125nH3.9n5.140MHz Large 30 m110nH0.85n1228MHz steeperincreaseswithfrequencyduetoincreasededdycurr entlosses.Asaresult, thefrequenciesatwhichthemaximumqualityfactorswereme asuredforthethicker inductorswaslowerthanforthethinnerversions.Thethick erinductorsyieldedslightly lowerinductancesaswellfromreducedmutualcouplingbetw eenlayersasaresultof theincreasedverticalgapheightcomparedtothethinnerve rsions.Thereductionwas greaterbetweenthoseofthesmallerdesignsincethediffer enceinverticalgapheight wasgreaterinproportiontoitsdiameter.6.3.2.2Inductorshape:squarevs.circularspirals Anothersetofinductordesignswasimplementedinsmalland largediameterswith squareandcircularspirallayouts.Alloftheinductorswer econstructedwith 30 m thick copperlayers,buttheouterdiameterswerevariedbetweent hesquareandcircular layoutssothatthelargerandsmallercopiesofeachhadroug hlymatchinginductances. ThegeometricparametersarelistedinTable 6-4 withthecircularlayoutshavinglarger outerdiameterstooffsettheirsmallerareas. Measurementoftheimpedancesofeachinductorrevealedonl yminordifferences resultingfromtheshapeofboththesmallerandthelargerde signsasplottedin Figures 6-8 and 6-9 .Theperformancecharacteristicswereextractedfromthis data andlistedTable 6-5 .Overall,theinductance-to-resistanceratiosofthecirc ular-shaped inductorsofbothsizeswereimprovedbyapproximately 10% .Theimprovementwas alsoassociatedwitha 6 – 8% improvementinthemaximumqualityfactorsmeasuredfor thecircular-shapedinductors. 106

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Table6-4.Geometricparametersoflargeandsmallinductor sinsquare-and circular-shapedspirallayouts.Allwereimplementedwith 30 m thickcopper layers. SizeShapeOuterdiameterTracewidthTracespacingTurnspe rlayer SmallSquare 540 m20 m12 m5 SmallCircular 585 m20 m12 m5 LargeSquare 960 m32 m16 m6 LargeCircular 1015 m32 m16 m6 Table6-5.Measuredperformanceparametersofsmall-andla rge-sizedinductorswith square-andcircular-shapedspirallayouts. DesignNominalNominalMaximumFrequencyfor sizeShapeinductanceresistancequalityfactormaxmimumq uality SmallSquare 42nH0.60n10.888MHz SmallCircular 45nH0.59n11.460MHz LargeSquare 117nH0.97n10.730MHz LargeCircular 117nH0.88n11.630MHz 107

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10 7 10 8 10 9 10 1 10 2 10 3 Inductance (nH)Frequency (Hz) 10 m m thick layers 30 m m thick layers AInductance 10 7 10 8 10 9 10 -1 10 0 10 1 10 2 10 3 Resistance ( W )Frequency (Hz) 10 m m thick layers 30 m m thick layers BResistance 10 7 10 8 10 9 0 5 10 15 Quality FactorFrequency (Hz) 10 m m thick layers 30 m m thick layers CQualityFactor Figure6-8.Comparisonoflayerthicknessesforsmall(oute rdiameter D =500 m )one-portinductoronsiliconsubstrate. 10 7 10 8 10 9 10 1 10 2 10 3 Inductance (nH)Frequency (Hz) 10 m m thick layers 30 m m thick layers AInductance 10 7 10 8 10 9 10 -1 10 0 10 1 10 2 10 3 Resistance ( W )Frequency (Hz) 10 m m thick layers 30 m m thick layers BResistance 10 7 10 8 10 9 0 5 10 15 Quality FactorFrequency (Hz) 10 m m thick layers 30 m m thick layers CQualityFactor Figure6-9.Comparisonoflayerthicknessesforlarge(oute rdiameter D =1000 m )one-portinductoronsiliconsubstrate.108

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10 7 10 8 10 9 10 1 10 2 10 3 Inductance (nH)Frequency (Hz) Square Circle AInductance 10 7 10 8 10 9 10 -1 10 0 10 1 10 2 10 3 Resistance ( W )Frequency (Hz) Square Circle BResistance 10 7 10 8 10 9 0 5 10 15 Quality FactorFrequency (Hz) Square Circle CQualityFactor Figure6-10.Comparisonofshapeofsmallinductor. 10 7 10 8 10 9 10 1 10 2 10 3 Inductance (nH)Frequency (Hz) Square Circle AInductance 10 7 10 8 10 9 10 -1 10 0 10 1 10 2 10 3 Resistance ( W )Frequency (Hz) Square Circle BResistance 10 7 10 8 10 9 0 5 10 15 Quality FactorFrequency (Hz) Square Circle CQualityFactor Figure6-11.Comparisonofshapeoflargeinductor.109

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6.4Two-PortInductorCharacterizationonSiliconSubstra tes 6.4.1CapacitiveCouplingthroughtheSubstrate Comparedtoinductorsfabricatedoninsulatingsubstrates suchasPyrex,the measurementofinductorsfabricatedonsiliconwasseverel yaffectedbycapacitive couplingofwindingsthroughthesubstrate.Asdiscussedin Section 3.6.1 theeffects ofthisincludedsignicantreductionsinself-resonancea ccompaniedbysignicant increasesintheeffectiveresistancesthroughtheinducto rs.Capacitivecoupling throughthesubstratewasstrongestwhenpointsofmaximump otentialdifferencewere positionedincloseproximitytoeachotherandtothesubstr ate.Becausethemaximum potentialdifferenceoccursbetweentheendterminalsofap roperlyfunctioninginductor, theobservedinductorcharacteristicswerehighlydepende ntonthemannerinwhichthe measuringprobeconnectionsweremadetotheendterminals. Forcharacterizationathighfrequencies( > 10MHz )theendsofthemicrofabricated inductorswereterminatedatpadsthatweredesignedspeci callytocorrespondto standardradio-frequency(RF)probetipsinground-signal -ground(GSG)congurations. Withathindielectriclayerofsilicondioxideprovidingel ectricalisolationbetween thepadsandtheconductivesiliconsubstrate,capacitorsw ereinadvertentlyformed betweenthepadsandtheconductivesubstrateasillustrate dinFigure 6-12 Theresistancethroughthesubstratebetweenthetightly-s pacedadjacentground andsignalpadsoftheoneportinductorscouldbeestimateda stheresistancebetween twopointsonthesurfaceofaninniteconductiveslab,calc ulatedas R s = 2 s p (6–11) with beingthebulkresistivityoftheslaband s thelateralseparationbetweenthe points.Fromtheaboveequationtheresistancebetweentwop adsseparatedby s p = 50 m wascalculatedatapproximately R s =300n ona =10n cm siliconwafer. InGSGconguration,thetwoparallelpathsbetweenthesign alpadandthetwo 110

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CuPadCuPad ConductiveSubstrate ProbeTipProbeTip DielectricLayer Figure6-12.Diagramillustratingcapacitivecouplingthr oughsubstratebetweeninductor measurementpads. groundpadstoeithersidewouldreducetheoverallsubstrat eresistanceinhalftoabout R s =150n Theinductorsinthissectionwerefabricatedwitha 2 m insulatinglayerof plasma-enhancedchemicalvapordeposited(PECVD)silicon dioxidebetweenthe electroplatedcopperandthesiliconwafer.Somehadopenin gsintheoxideforelectrical connectionofthegroundpadstothesiliconsubstratewhile othershadacontinuous oxidelayer.Ineithercase,becausetheareaofthegroundpa dwasmuchlarger, capacitancebetweenpadswaslargelydeterminedbythesize ofthesignalpad,which wasxedinlateralareaat 100 m 100 m .Thecapacitanceoftheoxidelayer betweenthesignalpadandthesubstratewasestimatedassum ingastandardparallel platecapacitance C s = r 0 A t (6–12) where r istherelativepermittivityoftheoxidelayer, A isthelateralareaofthepad, and t isthethicknessoftheoxidelayer.AssumingthePECVDsilic ondioxidetohavea 111

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relativepermittivityof r =3.5 ,thecapacitancebetweenthesignalpadandthesilicon wasestimatedat 0.15pF Atwo-portinductorwasfabricatedwith 30 m thickcopperlayersona = 10n cm siliconwafer.Theinductorconsistedoftwowindinglayers inacircular spiralcongurationwith n =6 turnsperlayer, D =940 m outerdiameter, w =36 m tracewidth,and s =15 m spacingbetweentraces.Thestructureoftheinductor wasdepictedinFigure 6-1B witheachofthetwoportslocatedonoppositesides oftheinductor.Oneoftheports,referredtoasPort1,wasco nnectedtotheupper windinglayer,whiletheother,Port2,wasconnectedtothel owerwindinglayer.The shuntimpedancesbetweeneachoftheportsandgroundwereex tractedfromthe measurementdataaccordingtoEquations 6–4 and 6–5 Plotsoftheequivalentseriesresistancesandcapacitance sasfunctionsof frequencyrevealedsignicantdifferencesbetweentheshu ntimpedancesateachport asshowninFigure 6-13 .TheequivalentseriescapacitanceatPort2, C s 2 wasgreater atavalueofabout 1.4pF duetothelargeareaofthelowerwindinglayertowhichit wasdirectlyconnected.Bycomparison,theequivalentseri escapacitanceatPort1, C s 1 ,wasroughly 0.7pF andmorecloselyrepresentedonlythecapacitancebetweent he signalpadandthesiliconsubstrate.Themeasuredvalueof C s 1 wasgreaterthanthe estimatedvalueof 0.15pF ,whichcouldhaveresultedfromdeviationsinthethickness ofthesilicondioxidelayerortherelativepermittivity.T heequivalentseriesresistance (ESR)oftheshuntimpedanceatPort2waslessthanthatatPor t1, R c 2 =50n vs. R c 1 =115n ,againduetothelargerareaofthelowerwindinglayerthatw asdirectly connectedtoPort2.WhilethemeasuredvalueofESRatPort1w asslightlylessthan theestimatedvalueof 150n ,thisresultshowedthatEquation 6–11 providedasimple methodofobtainingagoodroughestimate. Equations 6–6 and 6–7 werealsousedtocalculate(fromthetwo-portmeasured data)theimpedanceoftheinductorthatwouldbeseenateach portiftheoppositeport 112

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hadbeenshortedtoground.Thefrequency-dependentinduct ances,resistances,and qualityfactorswereplottedinFigure 6-17 forthetwocases.Inshortingthegreater shuntcapacitanceofPort2toground,theone-portimpedanc elookingintoPort1 exhibitedanincreasedself-resonantfrequency( SRF )of 875MHz comparedtoan SRF of 554MHz whenlookingintoPort2withPort1shorted.Themaximumqual ity factorwasalsogreateratavalueof 14.6 whenlookingintoPort1comparedto 13.3 whenlookingintoPort2.Theseresultshighlightedtheimpo rtanceofconsideringall connectionstotheinductorswhenmeasuringonaconductive substratesuchassilicon. 6.4.2WindingLosses AsshowninSection 6.3.2.1 bythecomparisonofidenticalinductordesigns implementedwitheither 10 m or 30 m thickcopperlayers,increasesinthethicknesses ofthecopperwindingsledtomorepronouncedincreasesinse riesresistanceatlower frequencies.Withtheincreasedvolumeofcoppercrossedwi thmagneticeldsinthe inductorswith 30 m thicktraces,anattemptwasmadetomitigatelossesduetoed dy currentgenerationbysplittingthewindingsintoseveralp arallellamentedtraces. TheconceptoflamentedtracesstemmedtheuseofLitzwires inhighfrequency transformers,whichfeaturemanysmallparallelwiresthat havebeenbunchedintoone. Filamentedtraceshavebeenproposedtobenetthehighfreq uencyresistanceofcoils bycreatinggapsacrosswhicheddycurrentsshouldnotbeabl eto“ow”[ 67 ].However, experimentsinthisworkprovidedevidencethatsimplepara llellamentsexhibitnearly identicalimpedanceathighfrequencies( 10MHz 10GHz ). Twoinductorswerefabricatedonahighresistivity( > 10000n cm )siliconwafer with 30 m thickcopperlayersandidenticalgeometries:twowindingl ayersincircular spiralcongurationswith n =6 turnsperlayer, D =940 m outerdiameter, w =36 m tracewidth,and s =15 m spacingbetweentraces.However,asshowninFigure 6-15 whileonehadsolidtraceslikethoseofallotherinductorsp resentedinthiswork,the otherinductorfeaturedtracesthatwerelamentedwithsli ts.Showningreaterdetailin 113

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Figure 6-16 ,thelamentedtracescontainedsetsoftwoparallel 3 m -wideslitsrunning alongthetracelength.Coppercrossbarsbridgedtheslitse very 10 toimprovethe structuralintegrityofthecoil. Themeasuredimpedanceswerefoundtobealmostindistingui shablebetweenthe inductorwithlamentedtracesthestandardonewithsolidt races.Figure 6-17 compares plotsofthefrequencydependentinductances,resistances ,andqualityfactorsofthe impedancesthrougheachinductor,whichwereextractedacc ordingtoEquation 6–3 to minimizeeffectsduetothesubstrate.Duetothelossofcros s-sectionalareathrough thetraces,thelow-frequencyresistanceoftheinductorwi thlamentedtraceswas about 10% greaterat 0.90n vs. 0.82n withsolidtraces.PlottedinFigure 6-18 isthe changetothemeasuredresistanceinimplementinglamente dtracesasapercentage oftheresistancewithsolidtraces.Atabout 200MHz theresistancesbetweenthetwo inductorscrossedover,beyondwhichpointthelamentedtr acesmeasuredupto 10% lowerresistancearound 1GHz 114

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10 7 10 8 10 9 10 10 10 -1 10 0 10 1 10 2 10 3 Capacitance (pF)Frequency (Hz) C s2 C s1 AShuntCapacitance 10 7 10 8 10 9 10 10 10 0 10 5 Resistance ( W )Frequency (Hz) R c2 R c1 BEquivalentSeriesResistanceofshuntcapacitances Figure6-13.Plotsofshuntcapacitances( C s 1 and C s 2 )andequivalentseriesresistances( R c 1 and R c 2 )ofshunt capacitancesvs.frequencyatPorts1and2ofinductor. 10 7 10 8 10 9 10 10 10 1 10 2 10 3 Inductance (nH)Frequency (Hz) L 2 L 1 AInductance 10 7 10 8 10 9 10 10 10 0 10 2 10 4 Resistance ( W )Frequency (Hz) R 2 R 1 BResistance 10 7 10 8 10 9 10 10 0 5 10 15 Quality FactorFrequency (Hz) Q 2 Q 1 CQualityFactor Figure6-14.Plotsofimpedancevs.frequencyfortwo-porti nductorlookingintoPort1( L 1 R 1 Q 1 ),andlookingintoPort 2( L 2 R 2 Q 2 ).Ineachcasetheoppositeportwasshortedtoground.115

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AInductorwithsolidtraces BInductorwithlamentedtraces Figure6-15.SEMimagesdepictinginductorswithsolidand lamentedtraces. ASolidtraces BFilamentedtraces Figure6-16.SEMimageszoomedcloserinonsolidandlament edtraces. 116

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10 7 10 8 10 9 10 10 10 1 10 2 10 3 Inductance (nH)Frequency (Hz) Solid Filamented AInductance 10 7 10 8 10 9 10 10 10 0 10 2 10 4 Resistance ( W )Frequency (Hz) Solid Filamented BResistance 10 7 10 8 10 9 10 10 0 5 10 15 20 25 Quality FactorFrequency (Hz) Solid Filamented CQualityFactor Figure6-17.Plotsofimpedancevs.frequencyfortwo-porti nductorswithlamentedandwithsolidtraces. 10 7 10 8 10 9 10 10 -20 -10 0 10 20 Change in resistance ( % )Frequency (Hz) Figure6-18.Differencebetweenresistancesthroughinduc torwithlamentedvs.solidtracesplottedasapercentofth e solidtraceresistance.117

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6.5SummaryofInductorCharacterization Theprecedingchapterpresentedandcomparedthemeasuredc haracteristicsofa varietyofinductorstohighlighttheelectricaleffectsre sultingfromdesigndecisions. Theinductancesandresistancesmeasuredfromtheinductor satlowfrequencies matchedwellwiththevaluescalculatedfromtheanalytical expressionsusedin theirdesign. Severalinductorswith 10 m thickcopperwindinglayersweresubjectedtohigh currentlevelsandwerefoundtosustainuptoabout 500mA beforethermal runawaycausedthewindingstoburnup. Thebulkremovalofphotoresistfrombetweentheupperandlo werwindinglayers wasfoundtoincreasetheself-resonantfrequenciesofindu ctorsbyabout 10 – 20% Increasingthethicknessofeachcopperwindinglayerfrom 10 m to 30 m yielded inductorsandtransformersthathadsignicantlyimproved directcurrent(dc) resistanceswithonlyslightlydecreasedinductances.How ever,thebenetof thethickerlayersatdcwaslostatfrequenciesgreaterthan about 100MHz as theresistancesofthethickerwindingsincreasedmorerapi dlywithincreasing frequencyduetoincreasededdycurrentlossesinthecopper Changingtheshapeoftheinductorsfromsquaretocircularp rovidedminor improvementsofabout 10% ininductance-to-resistanceratios. Thecharacterizationofinductorsfabricatedonsiliconsu bstratesshowed thatcapacitivecouplingtothesubstratehadastrongeffec tonthemeasured performance.Inparticular,higherself-resonantfrequen ciesandqualityfactors weremeasuredbygroundingtheterminalconnectedtothelow erwindinglayer andapplyingthesignalattheterminalconnectedtotheuppe rwindinglayer. Splittingtheinductorwindingsintoparallellamentedwi ndingshadalmostno effectonthemeasuredimpedanceoftheinductor. 118

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CHAPTER7 TRANSFORMERCHARACTERIZATION Thischapterdiscussesthemethodsandresultsofcharacter izingthemicrofabricated transformersunderradio-frequencyexcitation.Adescrip tionoftheequipmentandsetup outlinesthevectornetworkanalyzertoolasitwasusedtoch aracterizethetwo-port microtransformers.Conversionofthemeasuredscattering parameterstoimpedance parametersisthendiscussedasarouteforinterpretationo fthedataintermsthat wererelevanttopowerconverters.Theload-dependenceoft hetransformerefciency andvoltagegainisaddressedwithappropriatemathematica ltoolstoquantifythe dependence.Theresultsofcharacterizingthreemicrofabr icatedtransformersisthen presented.Thersttwotransformerswereimplementedwith 10 m thickcopperlayers withsquarespirallayoutsandturnsratiosof 1:1 and 1:3.5 .Thelasttransformer wasanupdated 1:1 transformerwithcircularspiralcoilsandanimproveddesi gn implementedin 30 m thickcopper.Theperformancecharacteristicsarecompare d amongstthemicrotransformerstohighlightthemeasurable electricaleffectsassociated withthevariousdesignoptions. 7.1EquipmentandSetup AnAgilentE8361AVectorNetworkAnalyzer(VNA)wasusedfor two-port measurementofthetransformers.TheVNAexcitedthetransf ormerundertestwith afrequencysignalononeportandsampledtheamplitudeandp haseoftheincident, reected,andtransmittedwavesonbothports.Bothportswe realternatelyexcited tofullycharacterizethetransformerinbothdirections.F ortheworkpresented here,theexcitationfrequencywassweptfrom 10MHz – 8GHz toobtainthefull frequency-dependentbehaviorofthedevicesuptoandbeyon dtherstresonant frequencyofeach.Thedatawererecordedascomplexscatter ing( S )parameters, denedasvariousratiosofthemeasuredwavevectors[ 56 ]. 119

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Electricalconnectiontotheinductorsandtransformerswa smadebyradio-frequency (RF)probeswithground-signal-ground(GSG)tipcongurat ionand 150 or 200 m tip pitch.Fixturecompensationwasperformedwithacalibrati onsubstratehavingopen, short,thru,and 50n loadstandards[ 66 ]. 7.2ImpedanceParameters Two-portmeasurementofthetransformerswiththeVectorNe tworkAnalyzer(VNA) yieldeda 2 2 matrixofcomplexscatteringparametersforeachfrequency point, 264 S 11 S 12 S 21 S 22 375 (7–1) Whilescatteringparametershaveproventobeusefulinawid evarietyofradio-frequency (RF)applicationssuchascommunicationssystems,impedan ceparameterswere moreappropriateforcomparisonwithotherpowertransform ersandforextracting performancecharacteristicssuchascouplingcoefcients andturns-ratiosthatwere affectedbydesigndecisions. Thescatteringvalueswereconvertedtoimpedancevaluesvi athefollowing relationships, Z 11 = Z 0 ( 1+ S 11 )( 1 S 22 ) + S 12 S 21 ( 1 S 11 )( 1 S 22 ) S 12 S 21 (7–2) Z 12 = Z 0 2 S 12 ( 1 S 11 )( 1 S 22 ) S 12 S 21 (7–3) Z 21 = Z 0 2 S 21 ( 1 S 11 )( 1 S 22 ) S 12 S 21 (7–4) Z 22 = Z 0 ( 1 S 11 )( 1+ S 22 ) + S 12 S 21 ( 1 S 11 )( 1 S 22 ) S 12 S 21 (7–5) Theimpedanceparameterscorrespondedtotheelementsofth ecircuitdiagram drawninFigure 7-1 .Forthetransformersmeasuredinthiswork, Z 11 representedthe 120

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+ + Z 21 I 1 Z 12 I 2 Z 22 Z 11 I 1 I 2 Figure7-1.Circuitrepresentationoftwo-portimpedancep arameters. impedanceoftheprimarycoil, Z 22 representedthatofthesecondarycoil,and Z 12 and Z 21 representedthecouplingbetweenprimaryandsecondarycoi ls. Thecompleximpedancevalueswerethensplitintorealandim aginaryparts,and thefrequency-dependentresistancesandinductanceswere extractedinthesame mannerasfortheinductors(Section 6.2.3 ).Frequency-dependentresistanceswere reportedastherealpartofthecompleximpedances, R xx =
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regardlessofwhetherthetransferwasfromprimarytosecon daryorinreverse.For thisreason,themutualinductances L 12, dc and L 21, dc werereportedasasinglevalue L m Thecouplingcoefcient k wascalculatedfromthenominalinductances, k = L m p L 11, dc L 22, dc (7–8) Theresistances, R 12, dc and R 21, dc ,ofthemutualimpedanceswereomittedfromthe modelasdepictedinFigure 7-2 asthesevalueswerenegligiblysmallsincethe transformershadnomagneticcores. L 11, dc R 11, dc L m R 22, dc L 22, dc Figure7-2.Lowfrequencytransformermodelconsistingofi mperfectlycoupledinductors withseriesresistance. 7.3Load-DependentEfciencyandVoltageGain Althoughthequalityfactorsoftheprimaryandsecondaryco ilcouldbecalculated fromthemeasuredimpedancesandwouldprovidesomeinsight intothemaximum transformerefciency(seeSection 4.2.2 ),theefciencyofpowertransferthroughthe transformerwashighlydependentontheloadimpedance.Sin cethevectornetwork analyzer(VNA)wascalibratedtoreportscatteringdatainr elationto 50n characteristic impedance,theefciencyandvoltagegainwerecalculatedd irectlyfromthescattering parameterdata.Theefciency,i.e.thepowerdeliveredtot heloadasapercentof thepowerdeliveredintothetransformer,wascalculatedfo rthe 50n characteristic impedanceoftheVNAby Z 0 = j S 21 j 2 1 j S 11 j 2 (7–9) 122

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andthevoltagegainwascalculatedas A Z 0 = S 21 1+ S 11 (7–10) Determinationofthetransformerefciencyandvoltagegai nunderotherloading conditionswasestimatedviathemethoddescribedinSectio n 4.4 ,inwhichconversion ofthescatteringparametersto ABCD parametersenabledsimulationofthetransformer performancegivenanarbitraryload.Thevaluesforefcien cyandvoltagegainwere calculatedfromthemeasureddataandarbitraryloadimpeda nces Z L usingEquations 4–21 and 4–22 ,respectively.Repeatingtheequationshereforconvenien ce,the efciencywascalculatedby =
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efciencyandcorrespondingvoltagegainundermatchedloa dconditions,whichwas identicallyequaltothemaximumefciencyascalculatedby Equation 4–1 7.4CharacterizationofTransformerswith 10 m ThickLayers Twotransformerswith 10 m thickcopperlayersweretestedonPyrexsubstrates:a 1:1 isolationtransformeranda 1:3.5 step-uptransformer,bothofwhichhadidentical 50nH primarycoils.Thesecondarycoilofthe 1:1 transformerwasdesignedasa mirrorimageoftheprimarycoilwiththegoalofprovidingdi rectcurrent(dc)isolation betweenprimaryandsecondarywithunitygain.Thesecondar ycoilofthe 1:3.5 transformerwascomposedofnineadditionalturnsonbothup perandlowerwinding layersthatwerenestedwithintheareaclearedbytheprimar ycoil.Thescanning electronmicrograph(SEM)imagesinFigure 7-3 comparethestructuresofthetwo transformers,showingsimilarlayoutbutwithmoreturnsin sidethe 1:3.5 transformer,all ofwhichbelongedtothesecondarycoil. Thelayoutofbothtransformersbeganwiththe 1:1 transformer,whichwas designedwithinterleavedprimaryandsecondarycoilswith 1.5mm outerdiameter, 30 m widetraces, 50 m spacebetweentracesofthesamecoil, 10 m spacebetween adjacentcoils, 10 m verticalspacebetweenupperandlowerwindinglayers,and 2 turnsofeachcoilperlayer.Thesecondarycoilofthe 1:3.5 transformerwasextended withanadditional 9 turnsperlayerintheinnerregionofthetransformerwith 10 m spacebetweenturns. Thefrequency-dependentinductancesandresistanceswere plottedinFigures 7-4 and 7-5 forthe 1:1 and 1:3.5 transformers,respectively.Forthe 1:1 transformer, theinductances( L 11 and L 22 )andresistances( R 11 and R 22 )wereessentiallyequal betweentheprimaryandsecondarybydesign.Themutualindu ctadisnces( L 12 and L 21 )wouldhavebeenequalto L 11 and L 22 ifcouplingwereperfectbetweenprimary andsecondarybutinpracticewerelessduetoimperfectcoup ling.Forthe 1:3.5 transformer,withitssecondarywindingcontainingmanymo returns,thesecondary 124

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A 1:1 transformer B 1:3.5 transformer Figure7-3.SEMimagesof 1:1 and 1:3.5 microtransformers.Thestructuresofeach aresimilarexceptthatthe 1:3.5 transformercontainsnineextraturns nestedwithinitsarea. inductance L 22 andresistance R 22 werebothmuchgreaterthantheprimaryinductance L 11 andresistance R 11 .Inbothcases,thecoupledresistances R 12 and R 21 weretrivially smallatlowfrequenciesandfellwithinthenoiseofthemeas urement,indicatingthat corelosswaspracticallynonexistentastherewasnomagnet iccore.Thecoupled resistancesappearedtorisewithfrequencyonlyduetocapa citivecouplingbetweenthe coilsaffectingthephaseofthecouplingimpedance.7.4.1ExtractionofNominalInductancesandResistances Thenominal,low-frequencyvaluesforinductancesandresi stanceswereextracted fromthemeasureddataandwerelistedinTable 7-1 forcomparison.Alsoincludedare datathatwereextractedfromanimproved 1:1 transformerwith 30 m layersthatis discussedinSection 7.5 .Theprimarycoilsofthe 1:1 andthe 1:3.5 transformers provedtobeidenticalbothphysicallyandelectrically.Th emeasurementsboreoutthis factastheprimaryinductances L 11, dc andresistances R 11, dc wereessentiallyequal acrossbothdesigns.Theinductancesandresistancesofthe secondarycoilofthe 1:1 transformeralsomatchedthatoftheprimarybydesign.The 1:3.5 transformer, withitsnestedsecondarywindings,exhibitedgreatlyincr easedsecondaryinductance 125

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10 7 10 8 10 9 10 10 10 1 10 2 10 3 Frequency (Hz)Inductance (nH) 10 7 10 8 10 9 10 10 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 Frequency (Hz)Resistance ( W ) L 11 L 22 L 12 L 21 R 11 R 22 R 12 R 21 Figure7-4.Plotsoffrequency-dependentinductanceandre sistanceof 1:1 transformer with 10 m thicklayers. Table7-1.Comparisonoftransformercircuitparameters. TurnsLayerPrimarySecondaryMutual ratiothicknessArea L 11, dc R 11, dc L 22, dc R 22, dc L m k 1:110 m2.4mm 2 47nH2.1n47nH2.1n41nH0.87 1:3.510 m2.4mm 2 47nH2.1n496nH9.0n96nH0.63 1:130 m1.08mm 2 45nH0.5n44nH0.5n41nH0.92 L 22, dc comparedtothatofthe 1:1 transformerattheexpenseofgreatersecondarydc resistance R 22, dc aswell.Additionally,thecouplingcoefcientwassignic antlybetter betweentheinterleavedwindingsofthe 1:1 transformercomparedtothatofthenested windingsofthe 1:3.5 126

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10 7 10 8 10 9 10 10 10 1 10 2 10 3 10 4 Frequency (Hz)Inductance (nH) 10 7 10 8 10 9 10 10 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 Frequency (Hz)Resistance ( W ) L 12 L 21 L 22 L 11 R 11 R 22 R 12 R 21 Figure7-5.Plotsoffrequency-dependentinductanceandre sistanceof 1:3.5 transformerwith 10 m thicklayers 7.4.2Load-DependentPerformanceof 1:1 Transformer Theefciencyofthe 1:1 transformerwasplottedinFigure 7-6 ,bothforthe as-measuredcasewith 50n loadingandforthecaseofmaximumefciencywith matchedloadsateachfrequencypoint.Thepeakefciencyme asuredwith 50n loading was 84% at 350MHz ,whilethemaximumestimatedefciencywithamatchedloadw as foundtopeakat 930MHz with 92% .Bydenition,themaximumefciencyasestimated withmatchedloadswasgreateroverallfrequencypointstha nasmeasuredwitha 50n load.However,theefcienciesofthetwocasesmostclosely matchedinvaluesaround 127

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thepeakvaluesofboth.Thissuggestedthatthevalueofthem atchedloadatthese frequenciesapproached 50n 10 7 10 8 10 9 10 10 0 20 40 60 80 100 Frequency (Hz)Efficiency % Matched Loads 50 W Load Figure7-6.Efciencyof 1:1 transformerforboth 50n andconjugatematchedloads. 10 7 10 8 10 9 10 10 0 0.2 0.4 0.6 0.8 1 Frequency (Hz)Voltage Gain (V/V) 50 W Load Matched Loads Figure7-7.Voltagegainof 1:1 transformerforboth 50n andconjugatematchedloads. Thevoltagegaincorrespondingtothesameloadingconditio nsateachfrequency wasplottedinFigure 7-7 .Asmeasuredwith 50n loading,thevoltagegainwas approximately 0.8V = V atfrequenciesupto 100MHz ,beyondwhichpointthevoltage 128

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gaindecreasedwithincreasingfrequency.Withmatchedloa ds,bycomparison,the voltagegainwasloweratfrequencies < 45MHz thanthe 50n casebutincreasedtoa peakvalueof 0.94V = V at 500MHz .Ineitherloadingcase,thepeakvoltagegainwas foundtooccuratfrequenciessimilartothoseatwhichthepe akefcienciesoccurred. 10 7 10 8 10 9 10 10 10 0 10 1 10 2 10 3 Frequency (Hz) Magnitude of Load Impedance |Z L | ( W ) 10 7 10 8 10 9 10 10 -90 -45 0 45 90 Angle of Load Impedance Z L (Degrees) Figure7-8.Magnitudeandphaseofmatchedloadimpedancefo r 1:1 transformer. Thecalculatedimpedanceofthematchedloadforeachfreque ncypointwasplotted inFigure 7-8 intermsofitsmagnitudeandphase.Asindicatedbythephase remaining atanegativelyvalueofabout 45 uptoalmost 1GHz ,thematchedloadimpedance hadequalcomponentsofcapacitanceandresistanceovermos toftheusablefrequency range.Thiscouldhavebeenimplementedasaloadresistance placedinseriesorin parallelwithacapacitor,withvaluesdependingonthefreq uencytoequatewiththe matchedloadimpedance. 129

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0 200 400 600 800 1000 -1000 -500 0 500 1000 0 20 40 60 80 100 X L ( W ) R L ( W ) Efficiency (%) AEfciency 0 200 400 600 800 1000 -1000 -500 0 500 1000 0.6 0.8 1 1.2 1.4 1.6 X L ( W ) R L ( W ) Voltage Gain (V/V) BVoltageGain Figure7-9.Efciencyandvoltagegainof 1:1 transformer( 10 m thickwindinglayers) plottedasfunctionsofacomplexloadat 100MHz xedfrequency. 130

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Bysweepingthecomplexloadimpedanceforagivenxedfrequ ency,surfaceswere obtainedfortheefciencyandvoltagegainofthe 1:1 transformersuchasplottedin Figure 7-9 for 100MHz .ThesurfaceplotinFigure 7-9A showedthatpeakefciencyof the 1:1 transformerat 100MHz wouldbeobtainedforimpedanceswithrealresistances lessthan 100n andaslightcapacitivecomponent.ThesurfaceplotinFigur e 7-9B showedthatthevoltagegainat 100MHz wasnearlyatat 0.88V = V overmostvalues ofimpedance,exceptintheregionofnearlyzeroresistance ,aroundwhichveryslightly inductiveloadimpedancesresultedindrasticallyreduced voltagegainandveryslight capacitiveloadimpedancesresultedinincreasedvoltageg ains. 7.4.3Load-DependentPerformanceof 1:3.5 Transformer Theefciencyofthe 1:3.5 transformerwasplottedinFigure 7-10 ,bothfor theas-measuredcasewith 50n loadingandforthecaseofmaximumefciency withmatchedloadsateachfrequencypoint.Thepeakefcien cyof 35% at 55MHz measuredwith 50n loadingwasmuchlowerthanforthe 1:1 transformer.However theestimatedmaximumefciencywithamatchedloadwasfoun dtopeakupto 78% at 150MHz .Incontrasttothe 1:1 transformer,themeasuredefciencyofthe 1:3.5 transformerwith 50n deviatedtogreaterextentsfromthemaximumefciencywith matchedloadsasthefrequencyincreasedawayfrom 10MHz .Thissuggestedthatthe valueofthematchedloadwascloseto 50n at 10MHz butprogressivelydeviatedfrom thisvalue. Thevoltagegaincorrespondingtothesameloadingconditio nsateachfrequency wasplottedinFigure 7-11 .Asimilarresultwasfoundforthevoltagegain,wherethe voltagegaincalculatedformatchedloadsdeviatedtoalarg erextentfromthatmeasured with 50n loadingincontrasttotheresultwiththe 1:1 transformer.Asmeasuredwith 50n loading,thevoltagegainwasapproximately 1.3V = V onlyupto 15MHz ,beyond whichpointthevoltagegainquicklydecreasedwithincreas ingfrequency.Withmatched loads,however,thevoltagegainstartedlowatlowfrequenc iesandincreasedto 3.1V = V 131

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10 7 10 8 10 9 10 10 0 20 40 60 80 100 Frequency (Hz)Efficiency % Matched Loads 50 W Load Figure7-10.Efciencyof 1:3.5 transformerforboth 50n andconjugatematchedloads. 10 7 10 8 10 9 10 10 0 1 2 3 4 Frequency (Hz)Voltage Gain (V/V) Matched Loads 50 W Load Figure7-11.Voltagegainof 1:3.5 transformerforboth 50n andconjugatematched loads. 132

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at 100MHz .Inthematchedloadcase,thepeakvoltagegainwasfoundtoo ccurat frequenciessimilartothoseatwhichthepeakefciencieso ccurred,whereasthepeak efciencyandvoltagegaindidnotoccuratthesamefrequenc iesforthe 50n load. 10 7 10 8 10 9 10 10 10 1 10 2 10 3 10 4 Frequency (Hz) Magnitude of Load Impedance |Z L | ( W ) 10 7 10 8 10 9 10 10 -90 -45 0 45 90 Angle of Load Impedance Z L (Degrees) Figure7-12.Magnitudeandphaseofmatchedloadimpedancef or 1:3.5 transformer with 10 m thicklayers. Thecalculatedimpedanceofthematchedloadforeachfreque ncypointwasplotted inFigure 7-12 intermsofitsmagnitudeandphase.Asindicatedbythephase remaining atanegativelyvalueofnearly 65 upto 100MHz ,thematchedloadimpedancewas morecapacitivethanforthe 1:1 transformer.Theresultsforthe 1:3.5 transformer showedinsummarythatastrongvaluecapacitanceintheload wouldbeanessential componentforreachinghighefcienciesandvoltagegains. Bysweepingthecomplexloadimpedanceforagivenxedfrequ ency,surfaceswere obtainedfortheefciencyandvoltagegainofthe 1:3.5 transformersuchasplottedin 133

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0 200 400 600 800 1000 -1000 -500 0 500 1000 0 20 40 60 80 100 X L ( W ) R L ( W ) Efficiency (%) AEfciency 0 200 400 600 800 1000 -1000 -500 0 500 1000 0 2 4 6 8 10 12 14 X L ( W ) R L ( W ) Voltage Gain (V/V) BVoltageGain Figure7-13.Efciencyandvoltagegainof 1:3.5 transformer( 10 m thickwinding layers)plottedasfunctionsofacomplexloadat 100MHz xedfrequency. 134

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Figure 7-13 for 100MHz .ThesurfaceplotinFigure 7-13A showedpeakefcienciesat 100MHz wouldbeobtainedfromthe 1:3.5 transformerforawiderangeofimpedances withrealresistancesof 100 – 400n andastrongcapacitivereactanceof 100 – 500n .The surfaceplotinFigure 7-13B showedthatavoltagegainof 2V = V couldbeobtainedfor awiderangeofimpedancesat 100MHz .Intheregionofnearlyzeroresistance,loads withcapacitanceofabout 7.5pF wereshowntoresultinvoltagegainsofalmost 14V = V 7.5CharacterizationofTransformerwith 30 m ThickLayers Inresponsetotherelativelyhighseriesresistancethroug hthecoilsofthe transformerspresentedintheprevioussection,animprove d 1:1 transformerwith 30 m thickcopperwindingswasfabricatedonaPyrexsubstrate.A sseeninthe scanningelectronmicrographimageofthetransformerinFi gure 7-14 ,thelayoutalso featuredinterleavedcircularshapedspiralcoilsforimpr ovedinductancetoresistance ratio.Becausethepurposeofthisdesignwastomaximizeper formanceofthe 1:1 transformerwithoutcomparisontoahigherturns-ratiodes ign,agreaterllfractionwas usedthanforthetransformerwith 10 m thickwindings,whichledtohigherinductance densityandbettercoupling.Bothprimaryandsecondarycoi lswerelaidoutwiththe samegeometry:circular-shapedspiralswith 1.1mm outerdiameter, 32 m tracewidth, 64 m spacingbetweentracesofthesamecoil, 16 m spacingbetweenadjacentcoils, 30 m verticalgapbetweentheupperandlowerwindinglayers,and 4 turnsofeachcoil perlayer. Thefrequency-dependentinductancesandresistanceswere plottedinFigure 7-15 Theagreementbetweentheinductances L 11 and L 22 andbetweentheresistances R 11 and R 22 veriedthedesignedgoaloftheprimaryandsecondarycoils tobeinallways equaltoeachother.Themutualinductances L 12 and L 21 droppedslightlybelow L 11 and L 22 duetoimperfectcoupling.Thecoupledresistances R 12 and R 21 wereverylow atlowfrequencies,indicatingtheabsenceofcorelossasth erewasnomagneticcore, 135

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Figure7-14.SEMimageof 1:1 microtransformerfeaturing 30 m thickcopperlayers andcircularspirallayout.Theprimaryandsecondarycoils areinterleaved. androsewithfrequencyonlyduetocapacitivecouplingbetw eenthecoilsaffectingthe phaseofthecouplingimpedance. Nominallow-frequencyparameterswereextractedfromthei mpedancedataand arereportedinTable 7-1 forcomparisonwiththetransformersofSection 7.4 ,which wereimplementedwith 10 m thicklayers.Theprimaryandsecondaryinductances ( L 11, dc and L 22, dc )wereverysimilartothoseoftheprevious 1:1 transformerwith 10 m thicklayers.Thisthicker 1:1 transformerwith 30 m layers,however,featureda 4 improvementinresistancesofthecoilsdownto 0.5n .Theredesignedtransformer alsoutilizedanareaof 1.08mm 2 ,lessthanhalfthatofthepreviousresultowingtothe increasedturncount( 4 vs. 2 ).Theincreasedutilizationoftheareaalsoresultedinan improvedcouplingcoefcientof k =0.92 ,upfromtheprevious k =0.87 Theefciencyofthethicker 1:1 transformerwasplottedinFigure 7-16 ,both fortheas-measuredcasewith 50n loadingandforthecaseofmaximumefciency withmatchedloadsateachfrequencypoint.Thepeakefcien cyof 90% at 333MHz 136

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10 7 10 8 10 9 10 10 10 1 10 2 Frequency (Hz)Inductance (nH) 10 7 10 8 10 9 10 10 10 -2 10 -1 10 0 10 1 10 2 10 3 Frequency (Hz)Resistance ( W ) L 12 L 21 R 11 R 22 R 12 R 21 L 11 L 22 Figure7-15.Plotsoffrequency-dependentinductanceandr esistanceof 1:1 transformerwith 30 m thicklayers. measuredwith 50n loadingwasveryclosetothepeakefciencyof 91% withmatched loads.ComparedtoFigure 7-6 fortheprevious 1:1 transformerwith 10 m thick layers,themeasuredefciencieswitha 50n loadofthethickertransformermore closelyapproachedthematchedloadefciencyatpeakvalue sbutdeviatedtoagreater extentatlowerfrequencies.Thematchedloadefciencyoft heredesignedtransformer wasmuchimprovedattheselowerfrequencies,reaching 70% efciencyat 10MHz as comparedto 20% inthepreviousgeneration. Thevoltagegaincorrespondingtothesameloadingconditio nsateachfrequency wasplottedinFigure 7-16 .Asshownintheplot,therewasahighdegreeofoverlap 137

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10 7 10 8 10 9 10 10 0 20 40 60 80 100 Frequency (Hz)Efficiency % Matched Loads 50 W Load Figure7-16.Efciencyof 1:1 transformer( 30 m thickwindinglayers)asafunctionof frequencyforboth 50n andconjugatematchedloads. 10 7 10 8 10 9 10 10 0 0.2 0.4 0.6 0.8 1 Frequency (Hz)Voltage Gain (V/V) Matched Loads 50 W Load Figure7-17.Voltagegainof 1:1 transformer( 30 m thickwindinglayers)asafunction offrequencyforboth 50n andconjugatematchedloads. 138

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betweenthevoltagegainsforthe 50n loadandforthematchedload.Asmeasured with 50n loading,thevoltagegainwasapproximately 0.90V = V upto 180MHz .With matchedloads,however,thevoltagegainincreaseduptoava lueof 0.94V = V at 160MHz .Bothforthe 50n loadandforthematchedloads,thevoltagegainand efciencywereeachmaintainedatvaluesneartheirpeaksth roughoutthefrequency rangefrom 100 – 400MHz 10 7 10 8 10 9 10 10 10 0 10 1 10 2 10 3 Frequency (Hz) Magnitude of Load Impedance |Z L | ( W ) 10 7 10 8 10 9 10 10 -90 -45 0 45 90 Angle of Load Impedance Z L (Degrees) Figure7-18.Magnitudeandphaseofmatchedloadimpedancef or 1:1 transformerwith 30 m thicklayers. Thecalculatedimpedanceofthematchedloadforeachfreque ncypointwasplotted inFigure 7-18 intermsofitsmagnitudeandphase.Likethe 1:1 transformerwith 10 m thicklayers,thephaseremainedatavalueof 45 upto 1GHz ,similarlyindicatingthat thematchedloadimpedancehadequalcomponentsofcapacita nceandresistanceover mostoftheusablefrequencyrange.Throughoutthefrequenc yrangeupto 450MHz the 139

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magnitudeofthematchedloadimpedanceforthethickerrede signedtransformerwas roughlyhalfthatofthetransformerwith 10 m thicklayers. Bysweepingthecomplexloadimpedanceforagivenxedfrequ ency,surfaces wereobtainedfortheefciencyandvoltagegainofthe 1:1 transformerwith 30 m thicklayerssuchasplottedinFigure 7-19 for 100MHz .ThesurfaceplotinFigure 7-19A showedthatat 100MHz peakefciencywouldbeobtainedforimpedanceswithreal resistanceslessthan 100n andaslightcapacitivecomponent.Thesurfaceplotin Figure 7-9B showedthatthevoltagegainat 100MHz wasnearlyatat 0.93V = V over mostvaluesofimpedance,exceptintheregionofnearlyzero resistance,aroundwhich veryslightlyinductiveloadimpedancesresultedindrasti callyreducedvoltagegainand veryslightcapacitiveloadimpedancesresultedinincreas edvoltagegains. 7.6SummaryofTransformerCharacterization Theprecedingchapterpresentedandcomparedthemeasuredc haracteristicsof twoinductorsfabricatedwith 10 m thickcopperlayerswithturnsratiosof 1:1 and 1:3.5 andoneinductorfabricatedwith 30 m thickcopperlayerswithaturnsratioof 1:1 Thetwotransformerswith 10 m bothhadtheidenticalprimarycoils,butthe transformerwith 1:3.5 turnsratiohadextraturnsofthesecondarycoilnested intotheinnerareaclearedbythetransformer.Mutualmagne ticcouplingwas consequentlylessforthe 1:3.5 transformerat k =0.63 comparedto k =0.87 for the 1:1 transformer. Theefcienciesandvoltagegainsofthetransformersweres howntobehighly dependentontheload.Greaterefcienciesandvoltagegain swerefoundtobe achievablewhentheloadshadcapacitivecomponents.Thede greeofdesired capacitancewasgreaterforthe 1:3.5 transformerthanforthe 1:1 transformers. Asaresult,the 1:1 transformersexhibitedbetterefcienciesandvoltagegai ns thanthe 1:3.5 transformerwith 50n loadingasmeasuredwiththevectornetwork analyzer. 140

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0 200 400 600 800 1000 -1000 -500 0 500 1000 0 20 40 60 80 100 X L ( W ) R L ( W ) Efficiency (%) AEfciency 0 200 400 600 800 1000 -1000 -500 0 500 1000 0.8 1 1.2 1.4 1.6 X L ( W ) R L ( W ) Voltage Gain (V/V) BVoltageGain Figure7-19.Efciencyandvoltagegainof 1:1 transformer( 30 m thickwindinglayers) plottedasfunctionsofacomplexloadat 100MHz xedfrequency. 141

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CHAPTER8 PACKAGINGANDTESTINGWITHCIRCUITS Thischapterdiscussesthepackagingofthemicrofabricate dcomponentsand theirtestingwithinpowerconvertercircuits.Twodistinc ttestsaredescribed.The rstutilizedwirebondstoconnectamicrofabricatedinduc torontoaprintedcircuit board(PCB)tobetestedwithaprototype 100MHz hybridboostconvertercircuit implementedinComplimentaryMetalOxideSemiconductor(C MOS).Thesecond testinvolvedmicrofabricationofaninductoralongsidear outingcircuitforconnection toacommercially-availableballgridarray(BGA)boostcon verterandsurface-mount capacitors.Inthissecondtest,thesubstrateonwhichthei nductorandcopper frameworkwerefabricatedwascompletelyremoved,resulti nginaconvertermodule withminimalpackagingoverhead. 8.1MicroinductorWireBondedtoVeryHighFrequencyBoostC onverter Forpreliminarytestingwithaveryhighfrequency(VHF)pow erconverter,a processedPyrexwaferwasdicedtoformaseparatechipconta iningamicrofabricated inductor.Thechipwasthenafxedtoaprintedcircuitboard (PCB)withtapeandthe terminalendsofthemicroinductorwereelectricallyconne ctedtothepadsonthePCB withgoldwirebonds.Theattachedchip,depictedinFigure 8-1 ,wasthenencapsulated inepoxyformechanicalprotection.8.1.1AbouttheMicroinductor Theinductorutilizedforthistesthadanouterdiameter D =520 m ,winding tracewidth w =40 m ,spacingbetweentraces s =20 m ,twowindinglayers,each withthickness t =10 m ,and n =3 windingturnsperlayer.Theimpedanceof thisinductorwasmeasuredwithavectornetworkanalyzer(V NA)initsas-fabricated statebeforewirebondingandwasthenmeasuredwithanimped anceanalyzerafter attachmenttothePCBandafterwirebonding.Themeasuremen tswiththeVNA weretakenbyprobingdirectlytothecopperpadsatthetermi nalsoftheinductorand 142

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representedtheimpedancethroughonlythemicrofabricate dcopperinductor.Anominal inductanceof 14nH andresistanceof 0.8n weresomeasuredwiththeVNA.The probesoftheimpedanceanalyzerhoweverwerelandedonthet inPCBpads,andso themeasurementincludedtheimpedancesthroughthewirebo ndsinserieswiththe inductor.AsplottedinFigure 8-2 ,thewirebondsaddedapproximately 7nH tothe inductancethroughthedeviceasmeasuredatthePCBpadsand alsocontributedan additional 0.2n totheresistance. Figure8-1.MicroinductorwirebondedtoaPCBfortestingwi th 100MHz CMOShybrid boostconverter. 8.1.2AbouttheConverterandTestResults Thehybridboostconverterconsistedofasingleswitched-i nductorbooststage followedbytwoswitchedcapacitorstages.Itwasfabricate dina 130nm1.2V CMOS processandoperatedat 100MHz .Detailsoftheconverterimplementationwere presentedbyXueetal.[ 68 ].Withthefabricatedmicroinductorconnectedinthe switched-inductorstage,theconverterachievedaconvers ionratioof 6 froma 1.2V sourcewithupto 37% efciency[ 69 ].Themeasuredconverterefciencywasplotted inFigure 8-3 asafunctionofloadcurrentforconversionratiosof 6 ( V out =7V )and 143

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10 4 10 6 10 8 10 0 10 1 10 2 Frequency (Hz)Inductance (nH) Impedance Analyzer Network Analyzer AInductance 10 4 10 6 10 8 10 -1 10 0 10 1 Frequency (Hz)Resistance ( W ) Impedance Analyzer Network Analyzer BResistance 10 4 10 6 10 8 10 -2 10 0 10 2 Frequency (Hz)Quality Factor Impedance Analyzer Network Analyzer CQualityFactor Figure8-2.Plotsofimpedancevs.frequencyformicrofabri catedinductorusedwith 100MHz hybridboostconverter.Datameasuredwithnetworkanalyze r beforewirebondingtoPCBandmeasuredwithimpedanceanaly zerafter wirebondingtoPCB. 144

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8 ( V out =10V )[ 69 ].Forcomparison,themeasuredefciencywasalsoplottedf or theconverterwhenusingacommercially-available 43nH surface-mountinductor. Althoughthevaluesofinductancebetweenthetwodidnotmat ch,theoverallefciency wasverysimilaratloadcurrentslessthan 1mA betweentheconverterusingthe microinductorandthatusingthesurface-mountinductor.A tloadcurrentsgreaterthan 1mA ,theefcienciesbetweenthetwobegantodiverge,withthem icrofabricated inductorresultingingreaterloss,duelikelytoitsgreate rseriesresistance. 0% 5% 10% 15% 20% 25% 30% 35% 40% 0 0.5 1 1.5 2 2.5 3 fsw=50MHz, Vout=7V fsw=50MHz, Vout=10V fsw=45MHz, Vout=7V fsw=45MHz, Vout=10V Microfabricated inductor L=25nH Surface-mount inductor L=43nH Load Current (mA) Efficiency Figure8-3.Measuredefcienciesofconverterasafunction ofloadcurrentwith 1.2V inputsourceand 7V and 10V outputvoltage.Plotscompareefcienciesof converterusingmicrofabricatedinductortothatusingasu rface-mount inductor.Adaptedfrom[ 69 ]. 8.2TestingwithCommercialSurface-MountConverter Duetotheexperimentalnatureoftheveryhighfrequency(VH F)converters, subsequenttestingofthemicroinductorswasdoneusingaco mmercially-available converter:theTexasInstrumentsTPS61240step-upconvert erwithxed 5V output.In additiontotheinductor,theconverterchipalsorequiredt wosurface-mountcapacitors, oneeachattheinputandoutputnodesforltering.Toconnec tthemicroinductor, converterchip,andcapacitorsapackagingmethodwasdevis edtoutilizethesame 145

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multilevelcopperprocesstoformaroutingandinterconnec tframeworksurroundingthe inductorsunderfabrication.Themultilevelcopper,inclu dingbothinductorsandrouting, wasthenencapsulatedanddetachedfromthesubstrate,resu ltinginaexiblelmwith intricate,embeddedcoppertraces.Theconverterandcapac itorswerethenattachedto thecoppertoformthecompletedtestmodule.8.2.1AbouttheTexasInstrumentsTPS61240Converter Featuringaswitchingfrequencyofupto 4.5MHz ,theTPS61240wasselected becauseitfeaturedthefastestswitchingfrequencyamongs tboostconvertersthatwere commercially-availableatthetimeofthispublication.As aresultofthehighswitching frequency,thedatasheetfortheconvertercalledforanext ernalinductorwithavalueof only 1 H ,which,whilehighformicroinductors,wasconsiderablyle ssthanthatrequired formanyotherconverters.TheswitchingfrequencyoftheTP S61240variedatruntime dependingontheloadcurrent.Atlightloads,theconverter operatedinPulseFrequency Modulation(PFM)mode.InPFMmode,theconverterswitchedt heinductorwithatrain ofseveralpulsesonlyasnecessarytomaintainanoutputgre aterthananinternally-set thresholdvoltage.Whentheoutputcurrentwastoogreattob esupportedbyPFM mode,theconverterautomaticallyswitchedtoPulseWidthM odulation(PWM)mode. Theconverterchipwasobtainedinadie-sizedballgridarra y(DSBGA)packagewithsix solderbumpsarrangedonitsundersidewith 0.4mm pitch. 8.2.2ModuleDesignandProcessing Thetestplatformfortheconverterconsistedofamicroindu ctorandroutingthat werefabricatedonasiliconwaferusingthemultilevelcopp erprocessdetailedin Chapter 5 withthreelayersofcopper,each 30 m thick.ThelayoutillustratedinFigure 8-4A showstheoutlineofthemoduleformedincopper.Padswereal soformedin thecopperforconnectiontothesixsolderbumpsoftheconve rterchipandtothe endsofthetwosurface-mountcapacitors.Themicroindutor consistedoftwostacked square-shapedspiralwindingswith 992 m outerdiameter, 32 m tracewidth, 20 m 146

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spacingbetweentraces,and 6 turnsperlayer.Thescanningelectronmicrograph(SEM) imageinFigure 8-4B depictsthecopperstructureofthemoduleafterthemolding process.Althoughthemanufacturer'sdatasheetfortheTPS 61240converteradvisedto useaninductorwithaminimuminductanceof 1 H [ 70 ]themicroinductorwasdesigned foravalueof 130nH outofconcernsoverthehighseriesresistancethroughgrea ter valuedmicroinductors. ACADdrawing BSEMoffabricatedcopper Figure8-4.CopperlayoutofconvertermoduleasdrawninCom puter-AidedDesign (CAD)softwareandasfabricatedonasiliconwafer. Theelectroplatedcopperstructuresonthewafersurfacewe rethencoatedwith BrewerScienceA2-22resist.Thisresistwasselectedforit schemicalresistanceto hydrouoricacid,whichwasusedtoseparatethecopperfram eworkfromthesilicon fabricationsubstrate.Priortoelectroplatingcopper,th esiliconwaferwasrstcoated byplasma-enhancedchemicalvapordeposition(PECVD)ofa 2 m thicklayerof silicondioxide.Thenalayeroftitanium,whichhadservedt hepurposeofimproving theadhesionofcoppertothesilicondioxide,wassputter-d epositedtoanincreased thicknessof 300nm .Thesilicondioxideandtitaniumconstitutedasacricial layerthat wasetchedawayin 49% hydrouoricacidtodetachtheencapsulatedcopperfromthe 147

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siliconsubstrate.Figure 8-5 depictsanexampleofanembeddedcopperframeworkthat wasdetachedfromawafer. Figure8-5.Photographofmicrofabricatedcopperframewor kencapsulatedinepoxyand releasedfromsubstratebysacriciallayeretch. Afterdetachment,thebottommostlayerofthemultilevelco pperwasdirectly accessibleontheundersideofthemodule,enablingelectri calconnectionoftheexternal componentstothecopper.Forstabilitywhileconnectingto componentsandwhile probing,theembeddedcopperlmwastemporarilyafxedbot tom-side-upwithadropof siliconetoanaluminumnitridechip.Attachmentofthecomp onentswasaccomplished bydepositingsolderpasteontothepadsofthecopperframew orkwheretheconverter chipandtwolteringcapacitorsweremanuallypositioned. Thesolderinthepastewas thenreowedonahotplatesetto 210 C toxthecomponentsinplace. Figure 8-6 depictsthenalconvertermoduleasitwastestedwiththeTP S61240 converterchipandtwo 4.7 F surfacemountcapacitorssolderedontopadsofthe embeddedcopperframework.AsseeninthephotographsinFig ure 8-6 ,thesurface 148

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ATopview BSideview Figure8-6.Photographsoffunctionalconvertermodulewit hcontrollerandcapacitors mountedontomultilayeredcopperframework. Table8-1.Componentsizesinfunctionalconvertermodule. ComponentLateralareaThicknessVolume TPS61240converter 1.26 0.86=1.08mm 2 625 m0.67mm 3 Filteringcapacitors(each) 1 0.5=0.5mm 2 500 m0.25mm 3 Microinductor 1.04 0.99=1.03mm 2 90 m0.09mm 3 Total 3 3=9mm 2 700 m1.98mm 3 mountcomponentswereseveraltimesthickerthanthecopper framework.Thefootprint ofthemoduledominatedbythethreepadsimplementedinthec opperframeworkthat wereconnectedtotheinput,output,andgroundnodesofthec onverter.Whilethe inductoralsohadarelativelylargefootprintatroughly 1mm 2 ,aninventoryofthesizes ofthevariouscomponents(listedinTable 8-1 )revealedthat,owingtoitsthinness,the inductorcomprisedonly 4.5% ofthetotalvolumeoftheconvertermodule. 8.2.3ConverterModuleTesting Beforetheconverterchipandcapacitorswereconnectedtot hemodule,the microinductor(embeddedinProTekA2-22resistanddetache dfromthesilicon substrate)wasrstcharacterizedusingaRohde&SchwarzZV A/Bvectornetwork analyzer(VNA)toextractitsimpedancewithfrequencyswep tfrom 1MHz – 1GHz .The 149

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inductance,resistance,andqualityfactoroftheinductor wereplottedasfunctionsof frequencyinFigure 8-7 .Themeasurementsshowedaninductanceof 124nH anda resistanceof 0.88n atlowfrequencies( < 2.5MHz ),andpeakqualityfactorof 12.4 at 177MHz .Aqualityfactorof 3.2 wasmeasuredat 4MHz WiththeTPS61240converterchipandthetwo 4.7 F capacitorssolderedontothe module,needleprobeswereusedtomakeelectricalconnecti ontotheinput,output,and groundpadsimplementedinthecopperframework.TwoKeithl ey2400SourceMeters wereusedinthetestsetup:oneattheinputactedasthesourc etoregulatetheinput voltage V in andtomeasuretheinputcurrents I in ,andoneattheoutputactedasthe loadtoregulatetheoutputcurrentatsetvalues I out andtomeasuretheresultingoutput voltages V out .Inputandoutputpowerswerecalculatedfromthesetandmea sured voltagesandcurrentsreportedbyeachoftheSourceMeters. Efciency conv was calculatedastheratiooftheoutputpower P out totheinputpower P in conv = P out P in = V out I out V in I in (8–1) AnadditionalhighimpedanceprobeconnectedtoaLeCroyosc illoscopewasusedto measurethevoltagewaveformsacrossvariousnodesintheci rcuit. Themeasuredconverterefciency conv wasplottedinFigure 8-8 asafunctionof outputcurrentforseveralvaluesofinputvoltage.Inevery casetheoutputvoltagewas consistentlyregulatedatavaluenear V out =5.05V .Thepeakmeasuredefciencyof 62.4% wasobtainedforaninputvoltage V in =4V andanoutputcurrent I out =5mA Themaximummeasuredpoweroutputwas 152mW at 58.2% efciencywithaninput voltage V in =4V andanoutputcurrent I out =30mA .AsseeninFigure 8-8 ,the overallconverterefciencydecreasedconsiderablywithd ecreasinginputvoltage(i.e. increasingconversionratio)butremainedcomparativelyc onsistentacrosstherangeof outputcurrents.Athigheroutputcurrentsthanthoseplott edinFigure 8-8 theconverter 150

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10 6 10 7 10 8 10 9 10 1 10 2 10 3 Inductance (nH)Frequency (Hz) AInductance 10 6 10 7 10 8 10 9 10 0 10 2 10 4 Resistance ( W )Frequency (Hz) BResistance 10 6 10 7 10 8 10 9 0 5 10 15 Quality FactorFrequency (Hz) CQualityFactor Figure8-7.Plotsofimpedancevs.frequencyformicrofabri catedinductorusedin convertermodulewithTPS61240converter.Datameasuredwi thVNAafter inductorwasembeddedinProTekA2-22resistanddetachedfr omsilicon substrate. 151

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0 10 20 30 30 40 50 60 70 Output current (mA)Efficiency (%)V in =3.5V V in =4.0V V in =3.0V Figure8-8.Measuredefciencyvs.outputcurrentofconver termodulewithoutput voltageregulatedat 5.05V exhibitedsevererippleintheoutputvoltage,whichindica tedcontrolloopinstabilityas theconvertertransitionedfromthePFMmodeofoperationto PWM. + V in L C out + V L C in +V out Figure8-9.Boostconvertercircuitdiagramwithmarkedvol tagescorrespondingto reportedmeasuredwaveforms. Measurementofthevoltagewaveformacrosstheinductor, V L asmarkedon thecircuitdiagraminFigure 8-9 ,providedinsightintothetrendsinefciencyacross operatingpoints.AsinFigure 8-10 ,acomparisonoftheinductorvoltagewaveforms fordifferentinputvoltagesrevealedasimilarseriesofpu lsesineachcase.Theduty cycle,thefractionofeachperiodduringwhichvoltagewasa ppliedacrosstheinductor, increasedwithincreasingconversionratio.Apulsewidtho f 67ns wasmeasuredwith 152

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0 0.5 1 1.5 -6 -4 -2 0 2 4 6 8 Time ( m s)Inductor Voltage (V) A V in =5V 0 0.5 1 1.5 -6 -4 -2 0 2 4 6 8 Time ( m s)Inductor Voltage (V) B V in =4V 0 0.5 1 1.5 -6 -4 -2 0 2 4 6 8 Time ( m s)Inductor Voltage (V) C V in =3V Figure8-10.Voltagewaveformsmeasuredacrosstheinducto rintheconvertermodule forseveraldifferentvaluesofinputvoltages. 153

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V in =4V ,whileawidthof 124ns wasmeasuredwith V in =3V .Thelongerduration ofappliedvoltageacrosstheinductorresultedinreducede fciencyastherewasmore timeforthecurrentthroughtheinductortoreachitspeakva lue,atwhichpointnofurther energywouldhavebeenstoredmagneticallybutratherwould havebeendissipated throughtheresistanceofthecoil.Thecurrent i L throughasemi-idealinductorwith inductance L andseriesresistance R inresponsetoastepvoltageinput v in canbe representedasafunctionoftime t bytheexpression, i L ( t ) = v in R 1 e R L t (8–2) Fromtheaboveexpression,thetimetakenforcurrentthroug haninductortoreachits peakvalueisdeterminedbytheratio R = L ,withgreater R andlower L contributingto ashortertimetakentoreachpeakcurrent.Thishelpstoexpl ainwhythedrop-offin efciencyathigherconversionratioswasmoredrasticwith thegreater R = L ratioofthe microinductorthanwasportrayedinthedatasheetwitha 1 H surface-mountinductor withseriesresistance 80mn [ 70 ]. Whereasincreasingtheconversionratioincreasedthepuls edutycycle,increasing theoutputcurrentincreasedonlythefrequencyatwhichthe seriesofpulseswere issued.AscanbeseenincomparingFigures 8-11A and 8-11C ,thepulseserieswere nearlyidenticalregardlessofoutputcurrent.However,sa mplingoveralongerperiodof timeasinFigures 8-11B and 8-11D showedthattheseriesofpulseswereissuedwith greaterfrequencyatgreateroutputcurrents.Thepulsefre quencywasalsoseeninthe rippleoftheoutputvoltageasinFigure 8-12 ,withtherippleremainingrelativelyequalin magnitudeacrossvariousloadcurrentsbutincreasinginfr equencywithincreasingload current. 8.3SummaryofInductorPackagingandTestingwithinConver terCircuits Thetwotestspresentedinthischapterdemonstratedthevia bilityofmicrofabricated inductorstobeusedinnext-generationvery-high-frequen cyswitched-modepower 154

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0 0.5 1 1.5 -4 -2 0 2 4 6 8 Time ( m s)Inductor Voltage V L (V) ALoadcurrent I out =10mA 0 5 10 15 20 -4 -2 0 2 4 6 8 Time ( m s)Inductor Voltage V L (V) BLoadcurrent I out =10mA 0 0.5 1 1.5 -4 -2 0 2 4 6 8 Time ( m s)Inductor Voltage V L (V) CLoadcurrent I out =30mA 0 5 10 15 20 -4 -2 0 2 4 6 8 Time ( m s)Inductor Voltage V L (V) DLoadcurrent I out =30mA Figure8-11.Measuredvoltagewaveformsacrosstheinducto rforaninputvoltage V in =4.0V andoutputcurrentsof I out =10mA and I out =30mA Waveformsatrightshowsingleseriesofpulsesforeachload current. Longertimesampledonplotsatrightshowmultipleseriesof pulses. 0 20 40 60 80 100 4.9 4.95 5 5.05 5.1 5.15 5.2 Time ( m s)Output Voltage (V) ALoadcurrent I out =1mA 0 20 40 60 80 100 4.9 4.95 5 5.05 5.1 5.15 5.2 Time ( m s)Output Voltage (V) BLoadcurrent I out =5mA Figure8-12.Measuredvoltagewaveformsatoutputfordiffe rentloadcurrentswithinput voltage V in =3.0V 155

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convertersandtoenablenewtechnologiesforintegratinga llcomponentswithminimal packagingoverhead: A 14nH microinductorwasattachedtoaprintedcircuitboard(PCB) using wirebondsandtestedwithina 100MHz boostconverterimplementedin ComplementaryMetalOxideSemiconductor(CMOS).Amaximum efciency of 37% wasobtainedwithaconversionratioof 6 Amicroinductorwasfabricatedwith 3 thickercopperlayerstodeliver 124nH with seriesresistancesimilartothatofthe 14nH inductorintheprevioustest—an 8 improvementintheinductance-to-resistanceratio.Theth ickercopperalsoenabled apackagingsolutionwherebythemicroinductorandacopper routingframework wereembeddedinresistandthefabricationsubstratewasre moved.Theinductor wastestedwithasurface-mountconverterandcapacitorsso lderedontothe embeddedcopper.Thesurface-mountcomponentstogetherac countedfor 13 greatervolumethanthatofthemicroinductor.Amaximumef ciencyof 62% was obtainedwithaconversionratioof 1.26 .Accountingforthetotalvolumeofall convertercomponents,amaximumpowerdensityof 76mW = mm 3 wasrecorded fortheoverallsystem. 156

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CHAPTER9 CONCLUSION Thisdissertationdocumentedtherealizationofmicroscal eair-coreinductorsand transformerswithhighinductancedensitiesandhighefci encyfornext-generation miniaturizedpowerconverterswithswitchingfrequencies ontheorderof 100MHz Fabricationofthecomponentswasenabledbyanadvancedmic rofabricationprocess thatwasdevisedspecicallytoaddresslimitationsthatha dsofarpreventedair-core microinductorsfrombeingintegratedwithpowerconverter s. Thischapterhighlightstheaccomplishmentoftheeffortto dateandthenoutlines severalwaysinwhichfutureworkcanbuildonthisfoundatio ntoenablenewcapabilities. 9.1SummaryofWork Theinductorsandtransformersofthisworklledthevoidin highqualitymicroscale inductivecomponentsforpowerconvertersintheveryhighf requency(VHF)range. Whilemicroscalecomponentsbasedonmagneticlmshadalre adyprovidedhigh qualityatfrequencies < 10MHz andair-coreinductivecomponentshavebeenused incommunicationsapplicationsatfrequencies > 1GHz ,themultilayeredthick-lm microfabricatedinductorsandtransformersdemonstrated excellentperformancein thefrequenciesspanningthegapbetweenthesepre-existin ggroups.Comparing resultsobtainedfromthenewinductorstothoseofpriormag neticlmandair-core examplesasinFigure 9-1 ,thenewlydevelopedcomponentshavebeenshowntoexhibit excellentinductancedensitiesandqualityfactorsintheV HFfrequencyrangethathad notpreviouslybeenaddressedbymicroscaleinductors.The resultsfromthemultilayer thick-lmmicrotransformershavebeensimilarlyoutstand ingwhencomparedtoprevious examplesasinFigure 9-2 Theresearchworkhasresultedinseveralmajoraccomplishm ents: Amethodologywasestablishedfordesigningmicroinductor sandmicrotransformers withanemphasisonhighdensityandhighefciencyinpowerc onversion applications. 157

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Thedesignmethodswereshowntoaccuratelypredictthevalu esofinductance andresistanceofavarietyofcomponentswithstackedwindi ngsinsizesfrom 0.25 – 2.5mm 2 andinductancesfrom 15 – 350nH Anewmicrofabricationprocesswasdevisedthatenabledthe multilayerconstruction ofthree-dimensional,high-density,freestandingcopper structureswithlayer thicknessesfrom 10 m upto 30 m Air-coreinductorswerefabricatedinthemultilayerproce sswithmeasured inductancedensitiesupto 170nH = mm 2 andqualityfactorsashighas 33 Air-coretransformerswerefabricatedwithinductanceden sitiesupto 325nH = mm 2 inacongurationforvoltagegainof 3.5 withupto 78% efciency. Microfabricatedinductorsweretestedwithinfunctionalp owerconvertercircuits: aprototypestep-upconverterwithaswitchingfrequencyof 100MHz yieldeda conversionratioof 6 atupto 37% efciencyusinga 14nH microinductor;anda commercialsurface-mountstep-upconverterwithamaximum switchingfrequency of 4MHz yieldedaconversionratioof 1.26 atupto 62% efciencyusinga 124nH microinductor. Asubstratedetachmentprocesswasdevisedtoformaminiatu rizedpower convertermodulewithanembededmicrofabricatedinductor andinterconnect structuretowhichacommercialsurface-mountconverteran dcapacitorswere attachedandtested.Thepowerconvertermoduleproducedam aximumoutput powerof 152mW fromapackageoccupyingintotallessthan < 2mm 3 9.2LessonsLearned Inadditiontothemajoraccomplishmentslistedabove,this researchalsoyielded importantndingsthatshouldshapeanyfutureeffortstoim provemicroscaleair-core powerinductorsandtransformers: Increasingthethicknessofeachcopperwindinglayerfrom 10 m to 30 m yielded inductorsandtransformersthathadsignicantlyimproved directcurrent(dc) resistanceswithonlyslightlydecreasedinductances.How ever,thebenetof thethickerlayersatdcwaslostatfrequenciesgreaterthan about 100MHz as theresistancesofthethickerwindingsincreasedmorerapi dlywithincreasing frequencyduetoincreasededdycurrentlossesinthecopper .Measurementswere comparedbetweeninductorsofdifferentthicknessesinSec tion 6.3.2.1 Thebulkremovalofdielectricmaterial(e.g.photoresist) frombetweenthe upperandlowerwindinglayersofstackedinductorsincreas edtheself-resonant frequenciesbyabout 10 – 20% 158

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Ahn, NiFe Yamaguchi, FeAlO Sato, FeCoBN Song, FeZrBAg Fukuda, NiZn Wang, NiFe Viala, FeHfN Flynn, NiFe Orlando, NiFe Lee, CoTaZr Park, Air Young, Air Choi, Air Weon, Air Yoon, Air I2 I1 I3 I4 I5 I6 I7 I9 1 10 100 1 10 100 1000 10000 Peak Quality Factor Frequency for Peak Quality Factor (MHz) Figure9-1.Measuredresultsofmicrofabricatedinductors presentedinthiswork (orange)plottedintermsofpeakqualityfactorandthefreq uencyatwhich thepeakqualityfactorwasobtained.Resultsarecomparedt oreviewed magnetic-lm(blue)andair-core(green)inductors.Bubbl esizeis proportionaltoinductancedensity.[ 8 – 22 ] Yamaguchi, Air Laney, Air Zolfaghari, Air Ng, Air Aly, Air Mino, CoZrRe Kurata, CoFeSiB Yamaguchi, CoNbZr Mino, CoZrRe Xu, NiFe Sullivan, NiFe Sullivan, NiFe Brunet, NiFe Park, NiFe Rassel, NiFe Yun, NiFe Wang, NiFe Meyer, 1:1 Meyer, 1:3.5 0% 20% 40% 60% 80% 100% 1 10 100 1000 10000 Efficiency Frequency for Maximum Efficiency Figure9-2.Measuredresultsofmicrofabricatedtransform erspresentedinthiswork (orange)plottedintermsofmaximumefciencyandthefrequ encyatwhich maximumefciencywasobtained.Resultsarecomparedtorev iewed magnetic-lm(blue)andair-core(green)transformers.Bu bblesizeis proportionaltovoltagegain.[ 23 – 40 ] 159

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Changingtheshapeofthemicroinductorsfromsquaretocirc ularresultedinonly minorimprovementsininductance-to-resistanceratioson theorderof 10% Segmentingthethicktracesofaninductorhorizontallyint oseveralparallel tracesofthinnerwidthswasfoundtoyieldanalmostimmeasu rablechangeto theimpedanceoftheinductor.Theconceptoflamentedtrac es,motivatedby thestrandedLitzwiresfoundinlargerscalehigh-frequenc ytransformers,was ineffectiveinreducingtheeddycurrentsinthewindings.I nordertoreducethe eddycurrentsinducedbytheproximityeffectbetweenadjac entconductors,the windingswouldhavetobecrossedinmannersthatincreaseth eorthogonalityof adjacentcurrentpaths,asisachievedinLitzwiresbytwist ingorbraidingindividual strandstoreducebundle-leveleffects. Thecharacterizationofinductorsfabricatedonsiliconsu bstratesdemonstrated thestronginuenceofcapacitivecouplingonthemeasuredp erformance characteristics.Increasedsubstrateresistancewasfoun dtodampentheresonant behavioroftheinductorsandtodecreasethepeakqualityfa ctor. 9.3FutureWork BuildingoffthesuccesspresentedinChapter 8.2 inembeddinganddetaching microfabricatedcopperinductorsandinterconnectsfroms iliconwafers,themultilevel copperprocesscouldenableanewplatformforembeddingthe three-dimensional(3D) inductorsandtransformersside-by-sidewithheterogeneo uscomponentsallwithina high-densitypackage. Theenvisionedpackagingprocesswouldconsistofthefollo wingsteps,whichare illustratedinFigure 9-3 : 1. Fabricationofthickcopperinductor,transformer,androu tingframeworkontopof anoxide-coatedsiliconsubstrate. 2. Populationoftheframeworkwithactivecircuitsandsurfac e-mountcomponents snappedintocoppersockets. 3. Fillingandcoatingoftheframeworkandcomponentswithane poxy-basedpotting compound. 4. Releaseofthelledpackagefromthesiliconsubstratebyet chingtheoxideout frombetweenthecompositeandthesubstrate. Inthiswaythethick3Dinductorsandtransformerswouldpla cedside-by-sidewith theactivecircuits,ratherthanontopashasbeenthecasewi thmonolithicintegrationor 160

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ACopperframeworkonsilicon. BComponentsplacedintosockets. CPackagelledwithpottingcompound. DPackagereleasedbysacricialetch. EUndersideshowinginput/outputpads. Figure9-3.Illustrationsofpackageassemblyprocess. 161

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chipstacking(3Dintegration).Thiscongurationisadvan tageousforavoidingcapacitive andinductivecouplingofthepassiveswiththeconductives ubstratesoftheactive circuits. Oneuniquefeatureofthispackagingtechnologywouldbethe abilitytoformthe copperintosocketsthatwouldallowtinycomponentstobesn ap-tintoplaceusing withdeformablecoppertoprovideelectricalconncection. Thisabilitywasmotivatedby thefactthatthestate-of-the-artsurface-mountcomponen tsizeasofthiswriting,metric 0402 (imperial 01005 ),withanominalfootprintof 0.4mm 0.2mm ,haddimensionsofa similarorderasthethicknessoftheelectroplatedcoppers tack.Thesetinycomponents havebeendifculttouseinindustryduetomisalignmentand thetomb-stoningthat canoccurfromimbalancesbetweenthewettingcharacterist icsattheterminalsofthe component[ 71 – 74 ].Whilethelm-typesurface-mountinductorsofthissizes tillhave toogreatofresistance(e.g.,upto 8n fora 68nH inductorwitha 0.6mm 0.3mm footprint[ 75 ]),themore-energy-densesurface-mountcapacitorswould bewell-suitedfor high-frequencypowerconverters. Asatestofthisconcept,apowerpackageframeworkwasfabri catedinthreelayers ofcopper,each 30 m thick,thatconsistedofthehigh-densitymultilayerinduc tors andtransformersthathavebeendiscussedthroughoutthisw orkalongwithsocketsto acceptmetric 0402 -sizedresistorsandcapacitors.Twosuchsocketsaredepic tedin thescanningelectronmicrograph(SEM)imageofFigure 9-4A .Inthetopmostcopper layer, 20 m -long 10 m -wideteethprotrudedintothesocketareaasdepictedinFig ure 9-4B .Theteethservedseveralpurposes.Therstwastoaccountf ordeviationsin theexactsizesofthecomponentsresultingfromimperfectm anufacturingtolerances. Thesecondpurposewastophysicallysecureandelectricall ycontactthecomponent afterplacement.Bysecuringthecomponentinplace,asolde rreowcouldthenbe performedtoensuredurablecontactwithoutthepossibilit yofthecomponentshiftingor tomb-stoningduringthereow. 162

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ATwo 0402 sockets BClose-upofteeth Figure9-4.Scanningelectronmicrograph(SEM)imagesofme tric 0402 -sizedcopper socketsandaclose-upofthecopperteeththatprotrudeinto thesocketarea tocontactthesurface-mountcomponent. Bysizingthesocketlargerthanthelargestsizeexpectedof acomponentandsizing theteethlongerthanthedeviationinexpectedcomponentsi zes,theteethcoulddeform tocontactacomponentovertheentirerangeofsizestolerat edinitsspecication. Figure 9-7 showshowthecopperteethdeformedandburiedintothetinco ntactofa surface-mountcomponentthatwaspressedtot.Theconcept ofdeformablecopper teethcouldbeextendedtoformcontactswithvertically-or ientedchips. AHorizontaldeformation BVerticaldeformation Figure9-5.Scanningelectronmicrograph(SEM)imagesofth edeformablecopperteeth contactingthetinpadofasurface-mountcomponent. 163

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Figure9-6.SEMimagedepictingasurface-mountresistoran dcapacitormountedinto socketsalongsidemicrofabricatedhigh-densityinductor s. Finally,Figure 9-6 showsasurface-mountresistorandcapacitorplacedintoso ckets alongsideabankoffourcoppermicroinductors.Todemonstr atethatelectricalcontact wasmadetothesecomponents,theimpedancewasmeasuredwit hanAgilentHP 4294aimpedanceanalyzerbylandingprobesonthecoppersoc ketstoeithersideofthe components.Theresistanceofa 47n resistorandthemeasuredcapacitanceofa 47pF capacitorweremeasuredaftereachhadbeensocketed.Theme asurements,plottedin Figure 9-7 matchedtheexpectedvaluesofthesecomponents.Thesharpd eviationsat thehigherfrequenciesweretheresultofresonanceintheme asurementcables. Formingsocketstoembedsurface-mountcomponentswithinh igh-densitypackages isonlyoneexampleofhowtheversatilityofthemultilayert hicklmcopperprocessin producingne-featured3Dconductivepartscouldenablene wcapabilitiesacrossawide rangeofapplications. 164

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10 4 10 6 45 46 47 48 49 50 Frequency (Hz)Resistance ( W ) AResistor 10 4 10 6 42 43 44 45 46 47 Frequency (Hz)Capacitance (pF) BCapacitor Figure9-7.Measuredresistanceof 47n resistorandcapacitanceof 47pF capacitor aftereachhadbeensocketed. 165

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BIOGRAPHICALSKETCH ChristopherDavidMeyerwasbornOctober23,1983inFt.Laud erdale,Florida toPatriciaandDonaldMeyer.HegrewupinCoralSprings,Flo rida,notfarfromhis birthplace,andgraduatedfromCoralSpringsHighSchoolin 2002.Heattendedthe UniversityofFlorida(UF),whereheearnedtheBachelorofS ciencedegree cumlaude inelectricalengineeringwithaminorinGermanin2006andt heMasterofScience degreeinelectricalengineeringwithaminorinmechanical engineeringin2009. InspiredbyagraduatecourseonMicro-ElectromechanicalS ystems(MEMS), Chrisbeganhisdoctoralresearchwithcontributionstothe developmentofthin-lm thermoelectricpowergenerators.Whilecontinuinghisres earchonpowercomponents, ChrisspentseveralyearsoninternshipattheU.S.ArmyRese archLaboratory(ARL) inAdelphi,MD.AtARLhedevelopedthemicrofabricationpro cessthatenabledthe powercomponentspresentedinthisdissertation.Upongrad uationwiththeDoctorof Philosophydegree,ChriswilljoinARLfull-timeasanelect ronicsengineer. InNovember2011ChrismarriedJennifer n ee Thompson,whomhehadmetasan undergraduatestudentatUF. 174