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THERMALMODELINGANDANALYSISOF193nmPULSEDEXCIMER LASERCALORIMETERS By DONGHAICHEN ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2001 ACKNOWLEDGEMENTS ItakethisopportunitytoexpressmysincereappreciationtoDr.ZhuominZhang forhis constant guidance, encouragement and support. He is always helpful in the achievementofmygoalsandprovidesalotofhelpbeyondtheresearchwork. Iwould alsoliketothankDrs.JacobChung,DavidHahn,JillPeterson,andDavidTannerfor servingonmysupervisorycommittee. I also gratefully acknowledge Drs. Marla Dowell, Christopher Cromer, and ThomasScottoftheNationalInstituteofStandardsandTechnology(NIST)forproviding valuableinformationandgivingmeachancetoworkatNIST. Iamthankfultomy colleaguesintheMicroscaleThermalRadiationLabfortheirassistance. Ialsoextend mythankstoDr. RaviKumar, DavidPearson, FerdinandRosa, andJorgeGarciafor helpingmetoimprovemyEnglish. Iextendmywarmestthankstomyparentsanddearwifewhohavebeenasource ofgreatinspirationandsupportthroughouteverychallengeinmylife. The final thanks go to the financial supporters ofthis project: the National InstituteofStandardsandTechnology,andtheNationalScienceFoundation. n TABLEOFCONTENTS page ACKNOWLEDGEMENTS ii ABSTRACT v CHAPTERS 1 INTRODUCTION 1 2 DEVELOPMENTANDAPPLICATIONSOFLASERCALORIMETERS 5 BriefReviewofCalorimeters 5 CWLaserCalorimeters 9 Pulsed-LaserCalorimeters 11 BasicPrinciplesofLaserCalorimetryandtheCalibrationSystem 14 3 THERMALMODELANDNUMERICALSIMULATIONMETHOD 23 PreviousStudyofLaserHeating 23 ThermalModelDevelopment 25 NumericalSimulationMethod 30 4 ANALYSISOFTHERMALMECHANISMSINVOLUMEABSORBER 38 ThermalModelofthe193nmCalorimeter 38 Three-DimensionalModeling 42 AxisymmetricModeling 47 AnalysisoftheProposedDesign 50 5 MULTIPHOTONABSORPTIONINVOLUME-ABSORBINGGLASS 67 Introduction 67 LaserIntensityandPenetrationDepth 68 TheAxisymmetricHeatingModel 72 ResultsoftheNumericalModeling 75 6 PARAMETRICSTUDYOFEXCIMERLASERCALORIMETERS 86 m TheFiniteElementModel 86 ResultsandDiscussion 89 7 AXISYMMETRICMODELINGOFTHECALORIMETERCAVITY 99 AxisymmetricModeloftheCavity 99 ResultsandAnalysis 102 8 NONEQUIVALENCEANALYSISOFLASERCALORIMETERS 112 ThermalModeloftheCavity 112 NonequivalenceAnalysis 118 9 SUMMARYANDCONCLUSIONS 130 ThermalMechanismsoftheVolumeAbsorber 130 ParametricStudyoftheLaserCalorimeter 132 NonequivalenceoftheLaserCalorimeter 132 APPENDIX NOMENCLATURE 134 REFERENCES 138 BIOGRAPHICALSKETCH 143 iv AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy THERMALMODELINGANDANALYSISOF193nmPULSEDEXCIMER LASERCALORIMETERS By DonghaiChen May2001 Chairman:ZhuominZhang MajorDepartment:MechanicalEngineering Thisworkdescribesthethermalmodelingandanalysisofpulsedexcimerlaser calorimetersatawavelengthof193nm. Differentthermalmodelshavebeendeveloped and the finite element method is employed to perform the thermal modeling ofthe volumeabsorberandthecavityinthe193nmlasercalorimeter. Inthiswork,theheatgenerationratesinvolumeabsorberandtheheatfluxonthe coppersurfacehavebeenderivedandthefiniteelementmethodisemployedtosimulate thespace-andtime-dependenceoftemperatureintheabsorber. Athree-dimensional modelandanaxisymmetricmodelhavebeenbuiltandusedtostudytheheatingeffects ofsinglepulseandmultiplepulses,respectively. Theproposeddesign, inwhichthe volumeabsorberisnotopticallythick,wasanalyzedunderconsiderationofthereflection andabsorptionattheinterface.Thecomparisonofthepresentdesigntotheproposed designshowsthatthe accuracyanddynamic range canbe improved forthevolume v absorberwithlowabsorptioncoefficient. Thetwo-photonabsorptioninthevolume- absorbingglassisinvestigatedandtheresultsshowthatthetwo-photonabsorptioncan compressthevolume-absorbingeffecttosurfaceabsorptionwithhigh-power,short-pulse laserirradiation. Theparametricstudyofexcimerlasercalorimeterhasbeenperformedforpulsed- laserheating,average-powerlaserheating,andelectricalheatingusingtheaxisymmetric modelinwhichthevolumeabsorberwithsmallthicknessandhighabsorptioncoefficient wasconsidered. Themaximumtemperatureishigherforpulsed-laserheatingthanfor electrical heating when the amount of total deposited energy is the same. The equivalencebetweenpulsed-laserheatingandaverage-power laserheatingisverified throughtheaxisymmetricmodelingofthecavity. Athree-dimensionalmodelofthefull cavityisemployedtopredictthecalibrationfactorforlaserheating. Thenonequivalence ofthelasercalorimeterisevaluatedbasedontheresultsofthefullcavitymodeling. Detailedthermalmodelingandanalysisoflasercalorimeterareprovidedwhichhelp understand the thermal response ofthe volume absorber and the cavity under laser heatingandelectricalheating. Thisworkwillhelpimprovethefuturedesignofpulsed- lasercalorimeters. vi CHAPTER 1 INTRODUCTION Excimerlasershavebeencommerciallyavailablesince1975andarewidelyused in a number of applications demanding the highest resolution in addition to semiconductor manufacturing, such as micromachining, heat-sensitive materials processingandphotorefractivekeratectomy(PRK). Themostpopularwavelengthsare 157, 193, 248, 308, and 351 nm. Applications of248 nmpulsed excimer laser in semiconductor industry led to the construction ofcalibration system forpulsed-laser energy/powermetersatthiswavelength. Calibrationtechnologiesforenergy/powermetersofpulsedexcimerlaseratthe wavelengthof193nmaremotivatedbyitsscientific,industrialandmedicalapplications. Inmedicalapplications,suchasPRK, 193nmexcimerlaserisusedtoremovetissue precisely from cornea to correct the diopter with the minimum heat effects on surroundingtissue(Patzel,1999). TheSemiconductorIndustryAssociationroadmaplists 193nmexcimerlaserasoneimmediatecandidateforprintingfeatureof0.18pm,along with extensions of248 nmexcimerlaser(Rothschildetal., 1997). The wavelength change from 248 to 193nm in photolithographic techniques and other applications requiresparallelprogressinthecalibrationtechnologies. Lasercalorimeters,knownfor their long-term stability and overall accuracy, are widely used to calibrate laser energy/powermetersatdifferentwavelength. Hence,itisnecessarytobuildcalorimeter 1 2 forcalibratingenergy/powermetersofpulsedexcimerlasersat193nmbasedonDUV calorimetersatthewavelengthof248nm(LeonhardtandScott,1995). Anisoperibollasercalorimeterconsistsofanabsorbingcavitythatissurrounded byaconstant-temperatureheatsink(Westetal., 1972). Laserenergy(orpower)is absorbedbythecavityandconvertedintointernalenergyoftheabsorbingcavity. The temperaturedifferencebetweenthecavityandtheheatsinkisameasureoflaserenergy (orpower). Electrical-calibrationmethodsprovideadirectcomparisonbetweenoptical andelectricalheatingthuseliminatingtherequirementforprecisemeasurementsofa calorimeter’s thermal properties. Electrical-calibration methods also provide direct traceability to SI units and improve calibration accuracy (WestandChumey, 1970). Calorimetershavebeendesignedtooperateatspecificwavelengthsandpower/energy levelsbythecarefulselectionofabsorbingmaterialsforthecavity. Surfaceabsorbers, suchasblackpaint,havebeenwidelyusedincalorimetersforlowpower,continuous- wave (CW) measurements. However, surface absorbers arenotappropriate forhigh power pulsed-laser measurements because the high transient temperature gradients producedatthesurfacecanleadtosurfacedamage. Forthisreason,volume-absorbing materials, which disperse the absorbed energy over a larger volume, are used in calorimetersforpulsed-lasermeasurements. Itisimportanttoselectavolume-absorbingmaterialappropriateforthepulsed excimerlaserat193nmbecausethelong-termexposuretohighpeakpoweroutputfrom excimerlasers,aresultofhighphotonenergiescombinedwithshortpulsewidths,causes damagetomostconventionalopticalmaterials. Inaddition,thehighpeakpowerofthe 193nmpulsedexcimerlasercanresultinahightemperatureonthesurfaceofvolume 3 absorberandanonequivalencebetweenpulsed-laserheatingandelectricalcalibration, whichlimitthedynamicrangeandaccuracyofcalorimeter,respectively. Concernsfor theseissuesaremainlythethermalresponsesofthevolume-absorbingmaterialtopulsed- laserheatingandelectricalheating,andtheuncertaintyofthepulsed-lasercalorimeter. Therefore,thermalmodelingisperformedtopredictthethermalresponsesofthevolume absorberandthecavity. In the present study, the main objectives are to understand the heat transfer mechanisms in the volume-absorbing glass with different thickness and absorption coefficients,toevaluatethenonequivalenceofthepulsedlasercalorimeter. Different thermalmodelarebuiltusingthefiniteelementsoftwareANSYS5.4-5.6,basedonthe 193nmlasercalorimeterinwhichtheabsorbersarevolume-absorbingglass. Athree- dimensionalmodelofthevolumeabsorberisusedtostudythesingle-pulseheating. An axisymmetricmodelofthevolumeabsorberisemployedtomodelthemultiple-pulse heating,performtheparametricstudyofexcimerlasercalorimeters,andinvestigatethe multiphotonabsorption inthevolume-absorbingglass; anaxisymmetricmodelofthe cavity is built foranalyzing the difference between thepulsed-laserheatingandthe average-powerlaserheating;athree-dimensionalmodelofthefullcavityisdevelopedto predictthenonequivalenceofthe193nmpulsed-lasercalorimeter. Theorganizationofthisdissertationisasfollows. Chapter2presentsareviewof thedevelopmentandapplicationsoflasercalorimeters. Thethermalmodelofvolume- absorbingglassirradiatedbylaserpulseandabriefreviewoftheworkrelatedtolaser heatingaredescribedinChapter3. Thethermalmechanismsofthevolume-absorbing glassunder193nmpulsed-laserirradiationandtheinfluenceoftheabsorptioncoefficient 4 onthethermalresponseoftheglassareanalyzedinChapter4. Multiphotonabsorption in the volume-absorbing glass under 193 nm pulsed-laser irradiation is presented in Chapter5. TheparametricstudyofexcimerlasercalorimetersisdescribedinChapter6. Theequivalencebetweenthepulsed-laserheatingandtheaverage-powerlaserheatingis analyzedinChapter7. Thenonequivalenceofthe 193nmpulsed-lasercalorimeteris predictedinChapter8. Finally,summaryandconclusionsaregiveninChapter9.