Table Of ContentTHERMALMODELINGANDANALYSISOF193nmPULSEDEXCIMER
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.
