发布时间 : 星期二 文章Ultra-short pulse laser ablation of copper更新完毕开始阅读9a3bb4b3a5e9856a5612609c
Ultra-shortpulselaserablationofcopper,silverandtungsten:experimentaldataandtwo-temperature451
Fig.3(a)Thecalculatedthreshold?uenceforcopperversusthelaserpulseduration(bluecircles).(b)Thecalculatedmeltingdepthatthethreshold?uenceversusthelaserpulseduration(blacksquares).Threeregimesareseen:aconstantvaluebelow1ps,atransitionregion,andthenapowerlawatlongerpulsedurations.Thereddashedlineisa?ttothedatapointsbelow1ps,andthegreendash-dottedlinea?ttothedata≥40ps.Theblacksolidlinein(a)representsananalyticalexpressiongivenby(9)
3.2Pulse-durationdependenceofthemeltingdepthThemeltingdepthisde?nedasthemaximumdepthatwhichthecombinedenergyintheelectronandlatticesystemsex-ceedstheenergyneededforthematerialtoundergoheatingandmelting.Formally,itcanbewrittenas
??
Cl,maxlTl,max+
TC(T??)dT??
Te0
≥??Hm+Cl(Tm?T0),
(10)
where??Hmistheenthalpyofmelting,Tmisthemeltingtemperature.
AscanbeseenfromFig.3(b),themeltingdepthatthethreshold?uenceincreasesdramaticallyaslongerpulsesareapplied.Thesamethreeregionsasbeforeareseen.Weobserveameltingdepthindependentofpulsedurationforpulsesshorterthan1ps(reddashedlineinFig.3(b)),thenatransitionregionand?nallyanincreaseproportionaltoτ0.51forpulseslongerthan～40ps(greendash-dottedline
inFig.3(b)).Againa√
τdependencecanbederivedfromapproximatecalculations,see,e.g.,[3]and[20].Themelt-ingdepthisseentoincreasefrom32nmat100fstomorethan1μmat20nspulseduration.
Alasersystemforanapplicationrequiringaspeci?cpre-cisioncanthusbefoundfromFig.3(b).Ifitisdesiredtohavesmallheataffectedregions,e.g.,inordertomaintainthenativestrengthofagivenmaterial,itisseeminglynec-essarytoemployultra-shortlaserpulses.
4Comparisonwithdata
Theexperimentalapproachisdescribedindetailin[16].ThelaserisaTi:Sapphire-basedchirped-pulse-ampli?cation(CPA)system.Thepulsedurationisapproximately100fs,thecentralwavelengthis800nmandthepulseenergiesintherangefrom9to185μJ.Anf=45mmachromaticlensisusedtofocusthelaserontothesampleswhicharepo-sitioned500μmbehindthefocustogeta1/espotsizeofapproximately40μm.Withthisspotsizetheassumptionofa1Dmodelasdiscussedaboveisvalid.Thedesirednumberofpulsesisselectedbymeansofamechanicalshutter.Ahe-liumpurgeenclosesthefocalregiontominimizenonlineareffectsandavoidopticalbreakdown[4].
Thedepthsoftheholesarefoundusinganopticalmicro-scope,seedetailsin[16].Plottingtheablationdepthversustheappliednumberofpulses,theablationratecanbefoundfromtheslopeofthecurve.Whenmorethanapproximately100pulsesareapplied,theablationrateisobservedtode-crease,soonlyfew-shotablationisemployed.Thismethodof?ndingtheablationdepthmeans,however,thattheab-sorptanceofthesampleplaysacrucialrole.Inmulti-shotablation,theabsorptancerapidlyincreasesasmorepulsesareapplied,soweneedtointroduceanaverageabsorptancetomatchthemulti-shotexperimentaldatatothesingle-shottheoreticalsimulation.
ThevaluesappliedtomatchthedataareACumulti=0.32,AAg
multi=0.26andAWmulti=0.80.Notethattheabsorptanceistheonlyadjustableparameter,andusingthesevalues,goodagreementwiththedataisobtainedovertheentire?uencerange,seeFig.2.Theabsorptancevaluesmayincludepos-siblechangesinre?ectivityduringthelaserpulse,whichisclaimedtobesigni?cantin[21],whileotherinvestiga-tionsindicatethatattheintensitylevelsofthepresentstudy,changestotheopticalpropertiesarenegligible[11,22,23].
452Fig.4ThegreenlinerepresentstheTTMsimulationofsilverwiththeinclusionofballisticelectrons.Muchbetteragreementwiththedata,particularlyinthelow?uenceregime,isobserved.LegendasinFig.2
Theroleofballisticelectronsforheattransporthasbeendiscussedintheliterature,see,e.g.,[24–26].Thetreatmentofballisticelectronsrequiresinprincipleadescriptionofnon-equilibriumelectrondistributions.Thiscannotbedoneintheframeworkofthecurrentinvestigation.Instead,weusethesimpleapproximationthattheballisticelectronsmerelycontributetotheheat-penetrationlength.ThelasersourcetermthenbecomesQ=
AI(t)e?2r
2/ω2
e?z/(α1
+λball)
1α+λ,(11)
ball
whereλballisballisticelectronpenetrationdepth.Itisseenthatinthisdescriptiononlythedepositiondepthoftheen-ergyischanged.However,thiscanalsodrasticallychangethethreshold?uence.Figure4showstheeffectofincorpo-ratingballisticelectronsintothemodel.
Sinceenergyiscarriedintothedeeperpartsofthemate-rial,thethreshold?uenceissigni?cantlyhigherastheen-ergydensityatthesurfaceisdecreased.Itisseenthatthereisamuchbetteragreementwiththedata,particularlyinthelow?uenceregime,whenballisticelectronsareincluded.Itis,however,onlyofminorimportancefortransitionmetalsascanalsobeseeninthecaseoftungsteninFig.2.
Thevalueoftheballisticelectronpenetrationdepthisestimatedasfollows:Theeffectivepenetrationdepthcanbefoundfromtheexperimentaldatabymakinga?tofthelow-?uencedatapointstotheequationL??=??·lnF
istheeffectivepenetrationdepth.ThesimulatedFth
,where??penetrationdepthintheabsenceofballisticelectronsisfoundby?ttingthesimulateddepthstothesameequation.Theballisticelec-tronpenetrationdepthcanthenbefoundasthedifference,i.e.,λball=??exp???sim.
We?ndλCu=15±4nm,λAg
ball=53±7nm,andnosignatureofball
ballisticelectronsfortungsten.Thesevalues
J.Byskov-Nielsenetal.
shouldbecomparedtotheopticalpenetrationdepthsof13,12and23nmforcopper,silverandtungsten,respec-tively.Weemphasizethatthesevaluesoftheballisticelec-tronrangeinthenoblemetalsmustbeincorporatedinade-scriptionapplyingtheTTMbeforeanaccuratepredictionoftheablationratescanbemade.Notethatreproductionoftheexperimentaldatacannotbeachievedbysimplyadjust-ingtheabsorptance;thiswillonlyshiftthecalculatedcurvealongthe?uenceaxis,butnotchangeitsshape.
Therangeoftheballisticelectronsdependsonthespe-ci?cbandstructureofthematerials.Itsorderofmagnitudecanbefoundfromtheelectronmean-freepaths,??mfp=vF·τr,wherevFistheFermivelocityandτristheDruderelax-ationtime.Themean-freepathisestimatedfromtabulatedvaluesin[27],assumingthattheelectronstravelthroughasamplewhichisessentiallyatmatesare??Cunmand??Ag
roomtemperature.Theesti-mfp=42agreementwithmfp=56nm,whichisseentobeinreasonableourvalues.
Thesevaluesaresomewhatsmallerthantheelectronmean-freepathreportedin[25],wherevaluesof70nmand142nmforcopperandsilverarefound.However,thespe-ci?ccharacteristicsofthesamplemayin?uencethisrange.Forinstance,thethicknessandparticularlythecrystallinityofthesampleareimportant.Themean-freepathisex-pectedtobemuchlongerinsingle-crystallinesamplesthaninamorphousmaterial.
5Conclusions
Experimentallymeasuredablationratesasafunctionof?u-enceforthreedifferentmetalsarecomparedtocomputersimulationsbasedonthetwo-temperaturemodel.Whenin-corporatingballisticelectronsintothemodel,we?ndverygoodagreementbetweenexperimentandsimulation.Bothdataandsimulationsseemtobeconsistentwithalinearde-pendenceathigh?uence.
Fromthesimulations,wealsoshowthatthethreshold?u-enceandmeltingdepthareconstantforpulsesshorterthan1psandincreaseasτ0.47andτ0.51,respectively,forpulseslongerthanapproximately40ps.Thelong-pulsebehaviorisingoodagreementyieldinga√
withapproximateanalyticalcalculations
τdependence.
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