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Time-Resolved Infrared Spectroscopy of Magnetic Semiconductors and Superconductors

Permanent Link: http://ufdc.ufl.edu/UFE0021280/00001

Material Information

Title: Time-Resolved Infrared Spectroscopy of Magnetic Semiconductors and Superconductors
Physical Description: 1 online resource (180 p.)
Language: english
Creator: Zhang, Haidong
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: dms, dynamics, infrared, magnetic, probe, pump, quasiparticle, semiconductor, spectroscopy, superconductor, synchrotron, timeresolved
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The photo-induced non-equilibrium dynamics of certain condensed matter systems have been studied with the pump-probe, time-resolved infrared spectroscopy. The broadband synchrotron radiation was used as a probe light source at the National Synchrotron Light Source (NSLS), Brookhaven National Laboratory (BNL), which was synchronized with a near infrared pump laser. We have studied a NbTiN thin film to explore the quasiparticle (QP) relaxation process in the BCS superconductivity. The temperature dependent linear optical transmittance supported the Tinkham's thin film transmission equation and BCS Mattis-Bardeen theory. The time-resolved experiments showed excellent agreement with the Rothwarf-Taylor theory and Gray's model, thus proved the phonon-trap effect and that the effective relaxation followed a simple exponential decay shape. The experiments showed that the excess QP effective lifetime was in the range of 1 ns time scale. The temperature dependence measurements supported Kaplan's theoretical prediction in the middle to high temperature range. We did not observe the two-component relaxation processes as reported in other literature, and we believe it was due to the more efficiency of the heat transferring mechanics in our experiments. The pump fluence and magnetic field dependence of the photo-induced experiments were studied with the broad band probing at a best of 300 ps time resolution. We found that the effective relaxation at high fluence behaved much different with the low fluence regime which could be explained qualitatively. The magnetic field dependence experiments showed that the effective lifetime did not decrease as the field enhanced. The photo-induced gap shift effects were observed and directly measured by the time-resolved spectroscopy. The result supported the Owen-Scapapino model. We also studied the InGa(Mn)As/InGaAs thin film to explore the electron-hole recombination process in the Dilute Magnetic Semiconductor system. From the broadband time-resolved experiments, we found a two-component decay with the fast one in the ns and the slow one in the tens of ns time scales. We proposed a model to explain this phenomenon. The time-resolved spectroscopy experiments gave the carrier density by fitting with the Drude model. We first observed Franz-Keldysh effect from the DMS system through a photoinduced transmission measurements. This effect is due to the internal electric field introduced by Mn doping. The internal field is in the order of tens of kV/cm.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Haidong Zhang.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Tanner, David B.
Local: Co-adviser: Stanton, Christopher J.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021280:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021280/00001

Material Information

Title: Time-Resolved Infrared Spectroscopy of Magnetic Semiconductors and Superconductors
Physical Description: 1 online resource (180 p.)
Language: english
Creator: Zhang, Haidong
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: dms, dynamics, infrared, magnetic, probe, pump, quasiparticle, semiconductor, spectroscopy, superconductor, synchrotron, timeresolved
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The photo-induced non-equilibrium dynamics of certain condensed matter systems have been studied with the pump-probe, time-resolved infrared spectroscopy. The broadband synchrotron radiation was used as a probe light source at the National Synchrotron Light Source (NSLS), Brookhaven National Laboratory (BNL), which was synchronized with a near infrared pump laser. We have studied a NbTiN thin film to explore the quasiparticle (QP) relaxation process in the BCS superconductivity. The temperature dependent linear optical transmittance supported the Tinkham's thin film transmission equation and BCS Mattis-Bardeen theory. The time-resolved experiments showed excellent agreement with the Rothwarf-Taylor theory and Gray's model, thus proved the phonon-trap effect and that the effective relaxation followed a simple exponential decay shape. The experiments showed that the excess QP effective lifetime was in the range of 1 ns time scale. The temperature dependence measurements supported Kaplan's theoretical prediction in the middle to high temperature range. We did not observe the two-component relaxation processes as reported in other literature, and we believe it was due to the more efficiency of the heat transferring mechanics in our experiments. The pump fluence and magnetic field dependence of the photo-induced experiments were studied with the broad band probing at a best of 300 ps time resolution. We found that the effective relaxation at high fluence behaved much different with the low fluence regime which could be explained qualitatively. The magnetic field dependence experiments showed that the effective lifetime did not decrease as the field enhanced. The photo-induced gap shift effects were observed and directly measured by the time-resolved spectroscopy. The result supported the Owen-Scapapino model. We also studied the InGa(Mn)As/InGaAs thin film to explore the electron-hole recombination process in the Dilute Magnetic Semiconductor system. From the broadband time-resolved experiments, we found a two-component decay with the fast one in the ns and the slow one in the tens of ns time scales. We proposed a model to explain this phenomenon. The time-resolved spectroscopy experiments gave the carrier density by fitting with the Drude model. We first observed Franz-Keldysh effect from the DMS system through a photoinduced transmission measurements. This effect is due to the internal electric field introduced by Mn doping. The internal field is in the order of tens of kV/cm.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Haidong Zhang.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Tanner, David B.
Local: Co-adviser: Stanton, Christopher J.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021280:00001


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Iwishtoexpresssincereappreciationtoallthosewhomadeitpossibleformetocompletethisdissertation.Firstandforemost,IwouldliketoexpressgreatgratitudetoProfessorDavid.B.Tanner,myadvisorandsupervisorycommitteechair,forthevaluableopportunitytoworkonthischallengingandveryinterestingproject.Thisstudywouldneverhavebeenachievedwithouthisinvaluableguidanceandinspiration,extremepatience,andconstantsupportduringmygraduatecareer.Ithasbeenwithagreatpleasuretoworkwithhim,andwhatIhavelearnedfromhimwillbenetmeallmylife.IamverygratefultoProfessorChristopherJ.Stanton,theco-chairofmycommittee,forhissupportandvaluableadvice.Ihavelearnedtheoreticalcalculationmethodsonsemiconductorsfromhimandhisgroup.IwouldalsoliketothankProfessorDavidH.Reitze,amemberofmycommittee,forhishelpandadvicewiththetime-resolvedproject.Ilearnedthelaseroperationsfromhimandhisgroup.AppreciationisextendedtoProfessorPeterJ.HirshfeldandProfessorFanRenforservingonmycommitteeandreadingthisdissertation.DuringmyworkatBrookhavenNationalLaboratory(BNL),IreceivedgreathelpfromDr.G.LawrenceCarr.Withouthisvaluableadviceandassistance,thisworkcouldnotpossiblyhavebeencompleted,andIwishtoexpressspecialappreciationtohim.AlsoIwouldliketothankDr.RicardoP.S.M.Lobo,whosevaluabledataacquisitionandanalysisprogramsmadethetime-resolvedprojectmucheasier.IwouldalsoliketothankRandyJ.SmithfromNationalSynchrotronLightSource(NSLS)forhisassistanceandfriendship.MythanksgotoallmycolleaguesinProfessorTanner'sgroupfortheirfriendshipandcooperation.Iwouldalsoliketothank:Dr.ShengboXu,Dr.RongliangLiuandDr.YongkeSun. 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 9 LISTOFFIGURES .................................... 10 LISTOFSYMBOLS .................................... 14 ABSTRACT ........................................ 16 CHAPTER 1INTRODUCTIONANDOVERVIEW ....................... 18 1.1IntroductionandMotivation .......................... 18 1.2Organization .................................. 20 2EXPERIMENTANDINSTRUMENTS ....................... 21 2.1Introduction ................................... 21 2.2SynchrotronRadiation ............................. 21 2.3VUVRingandU12IRBeamline ........................ 23 2.4PumpLaserSystem ............................... 25 2.4.1Mode-lockedTi:SapphireLaser ..................... 25 2.4.2Laser-synchrotronSynchronization ................... 28 2.4.3LaserInsertion .............................. 31 2.5OtherApparatus ................................ 33 2.5.1SpectrometerandDetectors ...................... 33 2.5.2OxfordOptistatBathCryostat ..................... 34 2.5.3RatioBox ................................ 34 2.5.4Ox-BoxSampleChamber ........................ 35 2.5.5OxfordInstrumentVertical-boreSuperconductingMagnet ...... 36 2.6Pump-probeTechnique ............................. 38 2.7DierentialMeasurementMethod ....................... 39 2.8Summary .................................... 40 3NON-EQUILIBRIUMSUPERCONDUCTIVITYTHEORY ........... 41 3.1HistoryofSuperconductivity .......................... 41 3.2Non-equilibriumsuperconductivity ...................... 43 3.2.1ASimpleSurvey ............................. 43 3.2.2Owen-ScapapinoModel ......................... 44 3.2.3Non-equilibriumsuperconductivityDynamics ............. 45 3.2.3.1Introduction .......................... 45 6

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................... 47 3.2.3.3Gray'sapproximation .................... 50 3.2.3.4Kaplanmodel ......................... 55 3.3FittingModel .................................. 63 3.4Summary .................................... 68 4OPTICALSTUDIESOFNB0:5TI0:5NTHINFILMS ............... 70 4.1Introduction ................................... 70 4.2DeterminationofTc 71 4.2.1Synchrotron-choppinginMagneticField ............... 71 4.2.2Laser-choppingMeasurement ...................... 72 4.3TransmissionandConductivity ........................ 73 4.3.1Theory .................................. 74 4.3.2TemperatureDependentTransmission ................ 76 4.3.3MagneticFieldDependentTransmission ............... 78 4.3.4Discussion ................................ 79 4.4BroadbandTime-ResolvedMeasurements ................... 82 4.4.1TemperatureDependence ........................ 84 4.4.1.1Experimentaldetails ..................... 84 4.4.1.2Discussion ........................... 86 4.4.2FluenceDependence ........................... 93 4.4.2.1Experimentaldetails ..................... 95 4.4.2.2Discussion ........................... 101 4.4.3HeatTransferinLiquidandGaseousHeliumBath .......... 108 4.4.3.1Experimentaldetails ..................... 108 4.4.3.2Discussion ........................... 109 4.4.4MagneticFieldDependence ...................... 110 4.4.4.1Experimentdetails ...................... 111 4.4.4.2Discussion ........................... 112 4.5Time-ResolvedSpectroscopy .......................... 114 4.5.1Experimentdetails ........................... 117 4.5.2Discussion ................................ 120 4.6Summary .................................... 124 5OPTICALSTUDIESOFDMSINGAMNAS/INGAASTHINFILMS ...... 126 5.1Introduction ................................... 126 5.1.1AHistorySurvey ............................ 126 5.1.2OverviewofTheIII-VDMSBandStructureTheory ......... 129 5.2TransmissionData ............................... 135 5.3Time-ResolvedMeasurements ......................... 139 5.3.1ExperimentDetails ........................... 142 5.3.1.17-BunchStretchedBeam ................... 142 5.3.1.2One-BunchBeam ....................... 142 5.3.1.37-BunchDetunedBeam ................... 145 7

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................................ 149 5.4Time-ResolvedSpectroscopy .......................... 155 5.4.1Far-IRRegion .............................. 155 5.4.1.1Experimentalresults ..................... 155 5.4.1.2Discussion ........................... 156 5.4.2Mid-IRandNear-IRRegions ...................... 159 5.4.2.1Experimentalresults ..................... 159 5.4.2.2Discussion ........................... 160 5.5Summary .................................... 163 6CONCLUSION .................................... 165 APPENDIX APHOTOINDUCEDTRANSMISSIONCHANGE ................. 168 BSOURCES,BEAM-SPLITTERSANDDETECTORS ............... 170 REFERENCES ....................................... 173 BIOGRAPHICALSKETCH ................................ 180 8

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Table page 2-1OperatingparametersfortheVUVringatthenormaloperation. ........ 23 2-2OperationalModes. ................................. 23 4-1TcatmagneticeldforNb0:5Ti0:5N. ......................... 72 4-2Samplecharacterizationparameters. ........................ 77 4-3Fitparametersforthebroadbandtime-resolvedtransmittancemeasurements. 86 4-4Estimatetheboundaryofthehigh-uenceregime. ................. 94 4-5FluencedependenceforTransmittancewithtemperatures. ............ 95 4-6Fluencedependenceforreectancewithtemperatures. .............. 96 4-7Fitparametersforthegaseousandliquidheliumcontactingexperiments. .... 109 4-8Fitparametersforthemagneto-opticaltime-resolvedmeasurements. ...... 111 4-9Fitparametersforthemagneto-opticaltime-resolvedmeasurements. ....... 111 5-1TOandLOfrequenciesat300K. ......................... 136 5-2InPenergygap. .................................... 141 5-3Fitparametersforone-bunchsynchrotronprobeexperiment. .......... 144 5-4Fittingparametersforthe7-bunchdetunedsynchrtronprobeexperiments. .. 146 5-5Fittingparametersfortheuencedependenceexperiments. ............ 148 5-6Fitparameters. .................................... 157 5-7TheFranz-Keldyshoscillationextremaenergieswiththeoscillationnumbers. 162 9

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Figure page 2-1Thecomparisonofsynchrotronwiththeconventionallamps. ........... 22 2-2TheU12IRbeamlinewiththespectrometerattached.TheoriginalplotwasprovidedbyLoboetal. ..................................... 25 2-3OpticaldiagramoftheMiralasercavity. ...................... 26 2-4Diagramofthelasersystem. ............................. 27 2-5Eectsofthepulsepickeronthelaserpulsetrain. ................. 28 2-6Diagramofthetimingexperimentsetupatthebeamlineandlaserhutch. ... 29 2-7Time-resolvedexperimentsetup. .......................... 30 2-8Synchronizedlaserandsynchrotronpulses. ..................... 31 2-9DiagramoflaserinsertionsetupwiththeOxfordOptistatcryostat. ....... 32 2-10SchematicdiagramofBruker125/HR. ....................... 33 2-11OxfordOptistatBathCryostat. ........................... 35 2-12DiagramoftheOx-Boxsamplechamber. ...................... 36 2-13DiagramoftheOxfordInstrumentvertical-boresuperconductingmagnet. .... 37 2-14Diagramforthesampleinsertinthemagnet. ................... 37 2-15Schematicsetupforthelaser-synchrotronpump-probeexperiments.TheoriginalplotwasprovidedbyCarretal. ........................... 38 3-1Photoexcitationandrelaxationinsuperconductors. ................ 48 3-2LifetimesforPb. ................................... 60 3-3ExcessQPsDensitywitherrorbar. ......................... 61 3-4TemperaturedependenceoftheexcessQPswithdierentR0=B0ratio. ..... 63 3-5Typicalphotoinducedsignals. ............................ 66 3-6Photoinducedintegratedsignalwitht. ...................... 68 3-7Derivativesignalwitht. .............................. 69 4-1Temperaturesweptmeasurementinmagneticeldsbychoppingsynchrotronbeam. ......................................... 72 10

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........................ 73 4-3Superconductingtransitionrangeinthelaser-choppingexperiment. ....... 74 4-4PlotofthemeasuredTS=TNdatawiththet. ................... 78 4-5Thetemperatureandfrequencydependentconductivityratio. .......... 79 4-6MeasuredratioofTS=TNatmagneticelds. .................... 80 4-7Theratiooffar-infraredtransmissionatmagneticeld. .............. 81 4-8FittotheT(H)=T(10K)curvesthroughthetwo-componentmodel. ....... 82 4-9SuperconductingandNormalregionsfromthetwo-componentt. ........ 83 4-10DierentialphotoinducedsignalforNb0:5Ti0:5Nsuperconductinglm. ...... 86 4-11TheintegrateddatafortheNb0:5Ti0:5Nsample. ................. 87 4-12Thetforthedierentialdataat4K. ....................... 88 4-13Thetfortheintegrateddataat4K. ....................... 89 4-14Fitthetemperaturedependenceoftheeectivelifetime. ............. 90 4-15TheamplitudeAfromtheexperiment. ....................... 92 4-16high-uenceboundary. ................................ 94 4-17Temperature-anduence-dependenceoftheeectivelifetimeintransmission. 96 4-18Temperature-anduence-dependenceoftheamplitudeintransmission. ..... 97 4-19Temperature-anduence-dependenceoftheeectivelifetimeinreection. ... 98 4-20Temperature-anduence-dependenceoftheamplitudeinreection. ....... 99 4-21The\max"and\min"pointsinthedierentialcurve ............... 100 4-22Approximationoftheintegratedsignal. ...................... 100 4-23Sweptandtime-resolvedmeasurementsintransmittance. ............. 101 4-24Sweptmeasurementsforreectance. ........................ 102 4-25Comparisonofsweptandtime-resolvedmethodsforreectance. ......... 103 4-26Comparisonofsweptandtime-resolvedmethodsat25mW. ........... 104 4-27Comparisonofsweptandtime-resolvedmethodsatdierentlaserpowers. .... 105 4-28The"max"and"min"signalsat50mWforreectance. ............. 106 11

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................ 109 4-30EectivelifetimevsmagneticeldforNb0:5Ti0:5N ................. 112 4-31Photoinducedsignalintransmissionvstimedelayatseveralmagneticelds. .. 113 4-32Eectivelifetimeatmagneticeldfromtime-resolvedandsweptmeasurements. 114 4-33AmplitudevsmagneticeldforNb0:5Ti0:5Nat3K. ................ 115 4-34Fractionofthesuperconductingregionvsmagneticeld. ............. 116 4-35GapshifteectsweremeasuredbetweenpointAandB. ............. 117 4-36PhotoinducedspectrumforNb0:5Ti0:5N. ...................... 118 4-37PhotoinducedspectrumforNb0:5Ti0:5Nat20mW. ................ 119 4-38PhotoinducedspectrumforNb0:5Ti0:5Nat73mW. ................ 120 4-39Photoinducedspectrumatmagneticeldsat20mW. ............... 121 4-40Photoinducedspectrumatmagneticeldsat73mW. ............... 122 5-1CalculatedelectronbandstructureforInGaAsat20K. .............. 136 5-2CalculatedelectronbandstructureforInGa(Mn)Asat20K. ........... 137 5-3Temperaturedependenttransmissioninthefar-tomid-IRrange. ........ 138 5-4Temperaturedependenttransmissioninthefar-IRrange. ............. 139 5-5Photoinducedprocessesinthesemiconductorsatlowtemperatures. ....... 140 5-6TemeraturedependentInPenergygap. ....................... 141 5-7Samplewasexcitedandrelaxedinthreeconsecutivelaserpulses. ........ 143 5-8Time-resolvedmeasurementwiththesampledecayupto170nsat20K. .... 144 5-9Time-resolvedmeasurementwiththesampledecayupto170nsat80K. .... 145 5-10Thefastdecaylifetimesinthephotoinducedexperiments. ............ 146 5-11Theslowdecaylifetimesinthephotoinducedexperiments. ............ 147 5-12Normalizedphotoinducedtransmissionsignalswithtemperature. ........ 148 5-13DMSsampledecayattemperaturesfarbelowandaboveTcprobedby7-bunchdetunedsynchrotronbeam. ............................. 149 5-14Timeconstantsmeasuredat882nmlaserand7-bunchdetunesynchrotronprobe. 150 12

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151 5-16Signalamplitudewithuencedependenceinthe7-bunchdetunedmeasurements. ............................................. 152 5-17Modelforexplanationofthetwocomponentdecayprocesses. .......... 153 5-18Transmissionspectrachangeinthefar-IRregionatdierenttemperatures. ... 156 5-19TheDrudettothephotoinducedspectrachangedataatdierenttemperatures. 158 5-20Thephotoinducedtransmissionchangeinthemid-IRandnear-IRregionforabothsidepolishedsample. .............................. 160 5-21EnergystructuresoftheDMSsampleat20K. .................. 161 5-22TheFranz-Keldyshoscillationextremaenergieswiththeoscillationnumbers. .. 163 B-1Emissionspectrafornormalinternalsources. .................... 170 B-2Frequencyrangesofbeam-splitters. ......................... 171 B-3Frequencyrangesofdetectors. ............................ 172 13

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2 Energygapinsuperconductor Aphononwithenergy 14

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Thephoto-inducednon-equilibriumdynamicsofcertaincondensedmattersystemshavebeenstudiedwiththepump-probe,time-resolvedinfraredspectroscopy.ThebroadbandsynchrotronradiationwasusedasaprobelightsourceattheNationalSynchrotronLightSource(NSLS),BrookhavenNationalLaboratory(BNL),whichwassynchronizedwithanearinfraredpumplaser. WehavestudiedaNb0:5Ti0:5Nthinlmtoexplorethequasiparticle(QP)relaxationprocessintheBCSsuperconductivity.ThetemperaturedependentlinearopticaltransmittancesupportedtheTinkham'sthinlmtransmissionequationandBCSMattis-Bardeentheory.Thetime-resolvedexperimentsshowedexcellentagreementwiththeRothwarf-TaylortheoryandGray'smodel,thusprovedthephonon-trapeectandthattheeectiverelaxationfollowedasimpleexponentialdecayshape.TheexperimentsshowedthattheexcessQPeectivelifetimewasintherangeof1nstimescale. ThetemperaturedependencemeasurementssupportedKaplan'stheoreticalpredictioninthemiddletohightemperaturerange.Wedidnotobservethetwo-componentrelaxationprocessesasreportedinotherliterature,andwebelieveitwasduetothemoreeciencyoftheheattransferringmechanicsinourexperiments. Thepumpuenceandmagneticelddependenceofthephoto-inducedexperimentswerestudiedwiththebroadbandprobingatabestof300pstimeresolution.Wefound 16

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Thephoto-inducedgapshifteectswereobservedanddirectlymeasuredbythetime-resolvedspectroscopy.TheresultsupportedtheOwen-Scapapinomodel. WealsostudiedtheInGa(Mn)As/InGaAsthinlmtoexploretheelectron-holerecombinationprocessintheDiluteMagneticSemiconductorsystem.Fromthebroadbandtime-resolvedexperiments,wefoundatwo-componentdecaywiththefastoneinthensandtheslowoneinthetensofnstimescales.Weproposedamodeltoexplainthisphenomenon.Thetime-resolvedspectroscopyexperimentsgavethecarrierdensitybyttingwiththeDrudemodel.WerstobservedFranz-KeldysheectfromtheDMSsystemthroughaphotoinducedtransmissionmeasurements.ThiseectisduetotheinternalelectriceldintroducedbyMndoping.TheinternaleldisintheorderoftensofkV/cm. 17

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1 { 5 ]andisauniquetechniquetoexplorethesub-nsdynamicsoverabroadregionoftheelectrodynamicspectrum.Thesynchrotronisabright,broadband,andpulsedlightsource.Thehighbrightnessgivesahighersignal-noise-ratio(S/N),makingitveryusefulforsurfacescienceandmicroscopy[ 6 7 ];thebroadbandfeaturefromfarinfraredthroughx-ray,combinedwiththewelldevelopedinterferometertechniques,isonemajoradvantageofsynchrotron[ 8 ].Thepulsednaturemakesthepump-probepossible.MostworkinthisdissertationmadeuseofsynchrotronspectroscopytostudysolidstatesystemsatbeamlineU12IRoftheNationalSynchrotronLightSource(NSLS),BrookhavenNationalLaboratory(BNL).TherestoftheworkwasdoneintheDepartmentofPhysics,UniversityofFlorida. Onesystemstudiedistheexcessquasiparticle(QP)recombinationprocessesinsuperconductors.Inthesuperconductingstate,twoelectronsformapaircalledCooperpairthroughtheinteractionwithphonons.Whenthesuperconductorisexcitedbyanexternalsource,someCooperpairswillbreak,producingunpairedelectrons(calledquasiparticles)inexcitedstatesandthesystemisdrivenintoanon-equilibriumstate.Aftertheexternalsourceisstopped,thoseextraQPswillrecombineintoCooper 18

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ItiswellknownthatnormalcorescalledvorticesareproducedinthetypeIIsuperconductorinamagneticeld.TherelaxationcurvesinthemagneticeldareessentialtounderstandtheinteractionsofvorticeswiththeQPs. Theothersystemwestudiedistheelectron-holerecombinationdynamicsinsemiconductors.Whenasemiconductorispumpedwithphotonenergygreaterthanthebandgap,theelectronsinthevalencebandwilljumpintotheconductionbandandleavebehindholes.Inreturningtoequilibrium,thehighenergyelectronswillundergoelectron-electronandelectron-phononcollisionstowardstheedgeoftheconductionband.Throughtheradiativetransitionprocesstheelectronswillrecombinewiththeholes.Thisprocessleadstonstimescale.OurinterestistostudythisrecombinationinaMn-dopeddilutemagneticsemiconductors(DMS)system.Theworkinthisdissertationstudiedtherecombinationrateandthenon-equilibriumbroadbandspectrum,whichmadeasolidfoundationtofurtherstudythetransportphenomenaandthepropertiesofDMSsemiconductorsinamagneticeld. 9 10 ]. 19

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InChapter2,theexperimentalinstruments,setupsandtechniquesaredescribed.Thesynchrotronradiationandpump-probetechniquearepresentedindetail. InChapter3,westartwithabriefreviewofthegeneraltheoryofsuperconductivity,andthenintroducenon-equilibriumQPrelaxationtheory.Someoftheresultsareusedtodiscussthenextchapter'sexperiments. InChapter4,wediscusstheexperimentsonsuperconductorNb0:5Ti0:5Nthinlms.Wedescribethesamplepreparation,thelineartransmittancemeasurementswhichdeducedsomeimportantsampleparameters,thenthetime-resolvedstudies. InChapter5,similarly,wediscussthelinearandtime-resolvedexperimentalresultsforaDMSsemiconductorInGa(Mn)Aslm. Finally,Chapter6hastheconclusions. 20

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11 ]rstpublishedequationstodescribesynchrotronradiationincludingtheangleandspectraldistributions.Sincethen,synchrotronradiationhasbeenusedasalightsourceformanydecades.Initially,peopleuseditforvisible,ultravioletandx-raysources.Inthelate1970sand1980s,pioneeringworkwasdoneusingsynchrotronradiationasaninfraredlightsource[ 12 ].Since1987,anumberofbeamlinesdedicatedtoinfraredspectroscopyhavebeenconstructedaroundtheworld[ 13 { 16 ]. Synchrotronradiationisthelightemittedbyhighlyrelativisticelectrons(orotherchargedparticles)astheytransitinthemagneticeldswhichguidethemalongaclosedorbit.Theemittedradiationextendsfrommicrowavetohardx-rayregionthereforeincludestheentirespectralrangeconventionallyusedforstudiesoftheopticalpropertiesofsolids. Thesynchrotronsourceoershigherbrightnessthannormalsources.Becauseofthesmallsourcesize,theintrinsicbrightnessofsynchrotronradiationismuchlargerthanthatofathermalsource. 21

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Thecomparisonofsynchrotronwiththeconventionallamps.Uptoafrequencyof450cm1,anHgarclampisused.Abovethat,aGlobarlampisusedasthesource.TheoriginalplotwasprovidedbyLoboetal. Figure 2-1 showstheratiosofintensityforasynchrotronsourcetoconventionalthermalsources(Hg-arclampandGlobar)asmeasuredthroughaperturesofdierentsizes.Theinsetshowsaplotofintegratedintensityofthefar-infraredregionforthetwosourcesasafunctionofaperture.Thesynchrotronprovidesmoreintensityatlongwavelengths,andbecomescomparabletothethermalsourcesnear400cm1withthe10mmdiameteraperturewhichessentiallypassesallthelightfrombothsources.Thesynchrotronwinsmoreoverthethermalsourcesastheaperturebecomessmaller. Thebrightnessisoneofthegreatadvantagesofsynchrotronradiation.Measurementtimesaregovernedbysignal-to-noise(S/N)ratio,notabsolutepower,sothehighbrightnessofsynchrotronallowsthestudyofsmallsamplesorsurfacesciencewithoutrequiringlongsamplingtimes. 22

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OperatingparametersfortheVUVringatthenormaloperation. ParameterValue StoredElectrionBeamEnergy0.808GeVInjectedCurrent1.0ALifetimeat200mAunstretched(Streched)6(9.8)hrCircumference51.0mRFFrequency52.887MHzElectronOrbitalPeriod170.2nsHorizontalSize536-568mVerticalSize170-200mHorizontalSourceDivergence686-373radVerticalSourceDivergence55-20radHorizontalDampedEmittance160nm-radVerticalDampedEmittance4nm-rad Table2-2. OperationalModes. ModeFillPatternImax(mA)PRF(MHz)TPRF(ns)pw(ns) 7b-stretched111111100100052.918.91.2-2.47b-detuned11111110085052.918.90.6-1.07b-compressed11111110025052.918.90.3-0.53b-symmetric10010010060017.656.70.7-1.41b-stretched1000000004005.9170.21.0-2.0 Synchrotronradiationispulsed,withtypicallysub-nanosecondduration.Alotofstudieswithinfraredsynchrotronradiationutilizedthehighbrightnessofthesource,forexample,grazingincidencemethodsforsurfacesciencestudies[ 17 ],infraredmicroscopy[ 18 19 ]andellipsometry[ 20 ].Thepulsednatureofthesourceislessused.Wetakeadvantageofthischaracterofsynchrotronradiationtoperformtime-resolvedinfraredspectroscopyinasub-nanosecondtimescale,whichtechniquewasdevelopedinrecentyears. 23

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vTrf(2{1) whereDistheorbitcircumference,visthevelocityofelectron,whichisclosetothespeedoflightc,TrfistheRFperiod.FortheNSLSVUVring,themaxbucketnumberis9.AnarbitrarynumberofbucketslessthanNmaxcanbelled.Thesynchrotronbeamcanbeoperatedatafewmodesdependingontherequirements.Thenormaloperationisintheformof7-bunchstretchedmodeforthereasonsofitshigherinjectingcurrentsandlongerlifetime.Table 2-1 showstheoperationparametersfornormaloperations.ThecommonoperationalmodesaresummarizedinTable 2-2 .Themostoftenusedbeammodesforthetime-resolvedexperimentsare7b-compressed,7b-detuned,and1b-stretchedmodedependingonthedesiredproperties.7b-compressedbeamprovidesthenarrowestpulsewidthof300psthusthehighesttimeresolution,whileitslowcurrentresultsinlowS/N;the7b-detunedbeamprovidesahighS/Nwiththepriceoftherelativelylowpulsewidthof800ps;the1b-stretchedbeamprovidesthelongestdelaytime,butsacricestimeresolutionandtheS/N. TheU12IRBeamlineoftheVUVringisintendedprimarilyforfar-infrared(far-IR)spectroscopy,spanningthespectralrangefromabout6cm1upto600cm1.Thebeamlineandspectrometersystemareactuallycapableofprovidingspectratoover4000cm1. AsshowninFigure 2-2 ,thelongwavelengthsynchrotronbeamiscollectedbyagoldcoated,water-cooledsiliconcarbidemirror(M1)withalargeextractionsolidangle(90mrad90mrad).Thebeamlineconsistsofahighvacuum(109torr)ringsideanda 24

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TheU12IRbeamlinewiththespectrometerattached.TheoriginalplotwasprovidedbyLoboetal. roughvacuum(20mtorr)ofthecollimatingopticsandspectrometerside,whichareseparatedbyan11mmdiameter,about0.35mmthickwedgedchemicalvapordeposited(CVD)diamondwindow.Thebeamissteeredandfocusedbyacombinationofellipsoidal(M3)andplanarmirrors(M1andM2)tothediamondwindowthroughalargelightcone.Afterthediamondwindow,thebeamisfocusedbyasetofsphericalmirrorando-axisparaboloidreectorstotheendstationwhichcanbeaspectrometeroracustommadesamplechamber. 25

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OpticaldiagramoftheMiralasercavity. 2-3 showstheopticsetupintheMiralasercavity.TheMiraispumpedbycoherentVerdi(Nd:Vanadate)pumplaserwhichisadiode-pumpedfrequency-doubledsolid-statelaserwithsinglefrequencyat532nm(green).TheVerdiprovidesamaximumpowerof10W,andapowertrackingsoftwareensuresitsstability.WiththemaximumpumppowerofVerdi,theMiralaserdeliversoutputpowerabout1W. TheMiralasermaybeoperatedinthreemodes:continuous(CW),mode-locked(ML)andbeta-locked(L).TheCWmodelasercanbeusedforsteady-statephotoinducedexperiments.TheMLandLmodesmaybeusedfortime-resolvedexperiments.Themode-lockingmakesuseoftheKerreectwhichselffocusesintheTi:sapphirecrystal,andthistechniqueiscalledKerrlensmode-locking[ 21 22 ].Themode-lockedstateisachievedbyadjustingeitherthelaserwavelengththroughthemicrometeradjustmentofthebirefringentlterorthecavitylengththroughtheadjustmentofhighfrequencypiezo-electrictransducer(PZT)mirror,sothecavitylengthisintegernumbertimesofthehalfwavelength.TheLmodemakesuseoftheGires-Tournoisinterferometer(GTI)mirrortolockthelaserautomaticly.Ifalossoflockhappens,theGTIdithersuntilthelasergetslockedthenstopsataconstantvoltage. 26

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Diagramofthelasersystem.(1)Verdi,(2)Mira,(3)Photodiode,(4)SafetyShutter,(5)Faradayisolator,(6)Cylindricallens,(7)EOM/2pulsepicker,(8)EOM/Npulsepicker,(9)Photodiode(10)1/2waveplate TheMiralaserisoperatedatthepulserepetitionrate(PRF)of105.8MHzwhichistwiceofthe52.9MHzPRFofNSLSVUVstorageringsinthe7-bunchoperationmode.Tomatchthesynchrotronfrequency,onlyoneofthetwoconsecutivelaserpulsesisselectedandtheotherisrejected.Thisisachievedbyusingacommercialelectro-opticaldivide-by-twopulsepickercalledEOM/2(ConOptics,model360-40).Thedevicerotatesthepolarizationofeveryotherpulseby90degreethroughaPockelscell,andthefollowingpolarizingbeamsplitterallowsonlycertainpolarizedpulsestotransmitandreectstheorthogonalones.Therejectedpulsesarenotwasted,butrecycledaftera9.45nsopticaldelayandtheirpolarizationsarerotatedbacktotheiroriginalstatebyahalf-waveplate.Thecoincidenceoftherecycledandthefollowingpulsesisachievedwhentheyareindistinguishableatafastphotodiode.Ashighas80%rejectedpowercanberecycledinthisway.Incaseofthree-bunchmode(17.6MHz)orone-bunchmode(5.9MHz),thedivide-by-NpulsepickercalledEOM/NisusedtomatchtheVUVRFsystemfrequency. 27

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Eectsofthepulsepickeronthelaserpulsetrain.(A)Nopulsepicker,laserPRFof105.8MHz.(B)WithEOM/2pulsepicker.(C)and(D)withEOM/Npulsepickertomatchthethree-bunchandone-bunchmodes.Variationsinpeakheightdonotreectthepoweructuations,andtheyareduetotheundersamplingbythedigitaloscilloscope.TheoriginalplotwasprovidedbyLoboetal. Therejectedpulsesaresenttoabeamdumpandnotrecycledinthesecases.Figure 2-5 showstheconsequencesofusingdivide-by-2anddivide-by-Npulsepickers. 28

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Diagramofthetimingexperimentsetupatthebeamlineandlaserhutch. AsshowninFigure 2-6 ,anarbitrarybutxedphaserelation(timedelay)betweenthelaserandsynchrotronisestablished.Thetimedelaycanbechangedinopticalorelectronicways,forexample,thecoaxialcablelength(4.2ns/mforthestandard50coaxialcable)andthevoltagecontrolledphaseshifterbetweenthepulsegeneratorandtheSynchro-Lockcontrolboxcanbeusedasdelayelements.Theaccurate,variabletimedelayisachievedthroughapulsegenerator(HP81101A).ThepulsegeneratorisfedwiththeVUVringRFsignalandtriggeredtogeneratevoltagepulsesofthesamefrequencywithvariabledelayof5psminimumsteps.BesidestheRFsignal,approximately100HzlowfrequencysquarewavesignalgeneratedbythefunctiongeneratorisalsofedtothepulsegeneratorthroughaDCbiasTee(Mini-circuits,ZFBT-6GW).TheInternalOscillatorofthelock-inamplier(StanfordResearchSystems,ModelSR830DSP)servesasthefunctiongenerator.Thislowfrequencysignalisusedforthelaserditherinthederivativemeasurements.ThereasonsforderivativemeasurementsareintroducedatSection 2.7 .ThedelayedRFsignalandthesquarewavesignalaremixedandtransmittedtotheSynchro-Lockcontrolboxthroughcoaxialcablesasreference,thusthetimedelaybetween 29

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Time-resolvedexperimentsetup.Thespectrometerinfrontofthesampleortheratioboxafterthedetectorisnotshownforsimplicity.TheoriginalplotwasprovidedbyLoboetal. laserandsynchrotronaswellaslaserditherareachieved.Figure 2-7 showsavisualizeddiagramwiththeowofopticalandelectricalsignals. WhentheringRFisoperatedat52.9MHzat7-bunchmode,thelaserpulsetrainisdividedintotwogroupsbytheEOM/2pulsepicker:passingorbeingrejected.EithergroupmaybeselectedbyEOM/2andthereisa9.45nsdelaydierencebetweenthem.TheConOpticsModel10electronicsprovidesabiasadjustknobfortheEOM/2pulsepickersothateitherlaserpulsetraincanbeeasilyselectedinthree-bunchorone-bunchmode,theEOM/NpulsepickerisusedandthelaserissynchronizedtoaparticularbucketintheringcalledRF/9;Atimedelayupto170nscanbegenerated.Figure 2-8 showsthexed4nsdelaytimebetweenthelaserandsynchrotronpulses. 30

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Synchronizedlaserandsynchrotronpulses.TheoriginalplotwasprovidedbyLoboetal. 2-9 showstheoptimizedsetupdiagram.LensAandBarebothconversinglenseswithfocallengthsof40mmand160mm,respectively.Thelensesarescrewedintoalenstubeandtheirpositionsareadjustablealongthetube.Togettheminimumspotsizeatthesample,thedistancefromlaserhead(pointO)totherstlens(pointA)issettobe40mmsothatthelaserafterlensAiscollimated.ThetotaldistancefromlensBthroughthenear-IRreectorCtothesampleDis160mm.Theminimumspotsizeis 40=4dfiber(2{2) 31

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DiagramoflaserinsertionsetupwiththeOxfordOptistatcryostat. wheredspotisthediameteroflaserspotsizeatthesamplesurface,dfiberisthediameteroftheopticalbercorewhichis62.5m.Thustheminimumspotsizeis0.25mminthissetup.AlargerspotsizecanbegotbyscrewinglensAinorouttodefocusthelaser. Thephotoinducedexperimentmustguaranteethelasertoilluminateatthesamplesurface.Asmallcamera(CreativeLabsWebcamLiveUltraforNotebookComputer,VF0070)isusedtomonitorthelaserspotatthesample.TheUSBcontrolledunitcantoleratethevacuumconditioninthesamplechamberandiscapabletoobservethenear-IRpumplaserlight.Whenfocusingthelaseratsamplesurface,onethingtheuserneedstobeawareofisthatthesamplepositionmovesnotonlyvertically,butalsohorizontallyduringpumpingdown.Becauseofthis,itisnecessarytorecheckthelaserandsynchrotronfocusingatvacuum.Thiscanbedonebyputtingthecamerainthebacksidetowardsthelightandobservingthelightchangefortransmission.Aremotelasersteeringsystemisdesirableforcorrectthelaseralignmentwithoutbreakingthevacuum. 32

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SchematicdiagramofBruker125/HR. 2.5.1SpectrometerandDetectors 2-10 )whichoerstheworld'shighestresolutionFT-IRspectracommerciallyavailablewithresolvedlinewidthsof0.001cm1(0.124eV)intheidealconditionandcancoverafrequencyrangefrom5cm1(620.5eV)inthefar-infraredto50000cm1(6.205eV)intheUV. Thefar-IRdetectorsarea1.5Klarge-aperturebolometerwithrangeof5to100cm1anda4.2Kstandardbolometerwitharangeof20to600cm1.The1.5Kbolometerismoresensitivesoisdesirablefortherangeitcovers.Therearetwomid-IRdetectors.Oneisa77KliquidnitrogencooledMCTmid-IRdetectorinstalledinsidethedetectorchamberoftheBrukerIFS125/HRspectrometerandcoveringfrom400to7000cm1;theotherisa4.2KCu/Gedetectorcoveringfrom350to4000cm1.Forthenear-IRregion, 33

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Far-IRbeamsplittersare125mthickmylarforthe5to22cm1range,andaGecoated6mthickmylarforthe20to600cm1range.AGecoatedKBrbeamsplitterservestherangeofmid-IRandnear-IRfrom400to10000cm1.Thusforapropercombinationofdetectorswithbeamsplitters,basicallythewholeinfraredrangefrom5to10000cm1canbecovered. 2-11 )whichallowsthesampletemperaturetochangecontinuouslyfrom1.5Kto300K.Thecryostatcontainsa2.5literliquidheliumreservoir,aliquidnitrogenreservoiranda20mmdiametersamplespace.Aprogramable,automaticneedlevalvecontrolstheliquidheliumowintothesampleareathroughtheOxfordITC502temperaturecontroller,allowingtheowratetobeoptimizedtosuittheoperatingrequirement.AheatexchangeratthebottomofthesampleareaisttedwithaheaterandRhFetemperaturesensor.Thesampleholderhasthreeverticallyarrangedopenapertures,thusthreesamplescanbemountedatthesametime.Thereisanothersetoftemperaturecontroller(ScienticInstruments9650)attachedtothesamplerod,withthetemperaturesensormountedclosetothetopsampleposition.Usuallythereisasmalltemperaturedierencefromthethetwosensors:thetemperaturerecordedfromthebottomatITC502isclosertothebottomsampleandfromSI9650isclosertothetopsample.TheinsidewindowsarecoldsapphireandZnSe.Theouterwindowsareexchangeable,andcurrentlytheyare0.1mmthickmylarforfar-IRandKBrformid-IRandnear-IRregions. 34

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OxfordOptistatBathCryostat. alltheexperimentsrelatedtothesynchrotronbeamstrength.Aratioboxisdesignedtomakeupforthiseect.TheringcurrentamplitudesignalisfedintotheratioboxasadenominatorandthedetectorsignalasnumeratorthroughBNCcables.Assumingthatthesample'sopticalresponseislinearwiththebeamintensity,theoutputsignalisthenormalizeddetectorsignalthrough: 35

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DiagramoftheOx-Boxsamplechamberwithtopview(A)andsideview(B). ofmirrorM8.AsshowninFigure 2-12 ,whenM8ispulledout,itunblocksthemirrorM4andthecurrentpositionisfortransmission;whenM8ispushedin,itblocksthetransmissionlightfromM4,anddeliversthereectionlightfromM7.TheOx-BoxisespeciallydesignedfortheOxfordOptistatbathcryostatshowninFigure 2-12 (B),butalsoaccepttheHelitrancryostat.ThesourceinputportcanbeconnectedtothesideportoftheBruker125/HRinFigure 2-10 ,ortothebeamlineoutputdirectlytoavoidthebeamsplitterlossinthebroadbandtime-resolvedexperiments. 2-13 .Thelightfromthespectrometerpassesaseriesofreectorsandfocusesatthebottomparaboloidandentersthemagnetthroughseveralquartzwindows.Thereectorsandtheparaboloidprovidetheabilitiesoffocusingandsteeringofthesynchrotronbeam.Thesampleisclampedbyasetoflight-conesatthetipofthevariabletemperatureinsert(VTI)whichprovidesthetemperaturerangefrom2to300K,andplacedatthecenterofthemagnet.ThedetaileddiagramisshowninFigure 2-14 36

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DiagramoftheOxfordInstrumentvertical-boresuperconductingmagnetconnectedtotheBruker125/HRwithlaserinsertionatU12IR.TheoriginalplotwasfromG.L.CarratNSLS. Figure2-14. Diagramforthesampleinsertinthemagnet. 37

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Schematicsetupforthelaser-synchrotronpump-probeexperiments.TheoriginalplotwasprovidedbyCarretal. 23 24 ].Forexample,acommondetectorforthefar-infraredisabolometer.Abolometerisathermaldetectorandthemostsensitivebolometersforfar-infraredhaveresponsetimeofabout1ms.Consequently,wecannotachievehightemporalresolutionbygatingthedetector.Evenwhenfastdetectorsareavailable,itisstillunworkable[ 2 ].ThereasonisthatthedetectornoiseincreasesasB1=2whereBisthedetector'sresponsebandwidth.Toachieve1nstimeresolution,thedetectorwillhaveabandwidthofatleast1GHz.Thusthesignal-to-noiseratiowillbe100timesworsethanatypicalinfrareddetectorwithBof100KHz.However,thepump-probetechniquecanovercometheselimitations.Inthisexperiment,weuseamode-lockedTi:sapphirelaserasthepumpsourcetogeneratephoto-excitations.Thelaser 38

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Iftheopticalresponseofthesampleissensitivetothetemperature,itwouldbehardtodistinguishtheheatingandthephotoexcitationeects.Soweemployedhigh-sensitivitydierentialmethodstoperformthetime-resolvedmeasurementsduetoitsadvantageoflesssensitivitytoheatingeectsandmoresensitivitytosmallsignals. Thismethodistoditherthelaserdelayanduselock-intechniquestomeasurethederivativesignal,sodierentialspectraaretakenbetweentwotimedelays.Inprinciple,onemaydithereitherthelaser(pump)pulseorthesynchrotron(probe)pulse,butinpractice,ditheringthelaseristheonlychoice.Thelaserdelaycanbeadjustedbythe 39

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40

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25 ].Thiswasthediscoveryofsuperconductivityandthedisappearanceofelectricresistanceisoneofthetwobasicpropertiesofsuperconductivity.Theotherone,calledtheMeissnereect,wasdiscoveredin1933byMeissnerandOchsenfeld[ 26 ]:asuperconductorisaperfectdiamagnet. In1934,GorterandCasimir[ 27 28 ]proposedthe\two-uid"modelinwhichafractionoftheelectronswereregardedassuperconducting,whiletherestremained\normal"electrons.Thismodelwassuccessfulinexplainingthehighdegreeofinterrelationshipbetweenthemagneticandthermalpropertiesofsuperconductors. In1935,F.LondonandH.London[ 29 ]developedsocalledLondonequationsthroughamodicationofanessentialelectrodynamicsequation,toexplaintheMeissnereect.Thismodelprovidedaphenomenologicaldescriptionoftheanomalousdiamagnetismofsuperconductorsinaweakexternaleld. In1950,GinzburgandLandau[ 30 ]deducedanotherphenomenologicaltheory,whichfurtherextendedthecasetostrongelds.Thistheoryplayedanimportantroleinunderstandingthephysicsofsuperconductivityandthevaliditywasprovenlateronthebasisofthemicroscopictheory. Thosephenomenologicaltheoriesplayedimportantrolesandprovidedvaluableconcepts,butthenatureofsuperconductivityremainedunsolved.Asystematic,microscopictheoryofsuperconductivitywasformulatedin1957byBardeen,CooperandSchrieer(BCStheory)[ 31 ].Thistheorypointsoutthattheinteractionbetweenelectronsandlatticevibrationsresultsinanattractiveforcebetweentheelectrons.Theelectron-lattice-electronattractionthusleadstoagroundstatebelowthetransition 41

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Atabsolutezerotemperature,theenergygap20isderivedbythesolutionto: 1 whereN(0)isthedensityofBlochstatesofonespinperunitenergyattheFermisurface,~!DistheDebyeenergy.Intheweakcouplinglimit,i.e.,N(0)V1,itreducesto 02~!Dexp1 AtnitetemperaturesbelowTc,theenergygap2(T)isgivenbythesolutionto: 1 wheref(E)istheFermifunction: 1+exp(E kT)(3{4) AtnitetemperaturesnearTc,thevalueofthegapcanbeapproximatedby: (T) 0'1:741T Tc1=2(3{5) Andfor~!DkBTc,therelationbetweenthegap20andTcintheweakcouplinglimitN(0)V1is 42

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whichisnotdependentontheparametersVand!D. 3.2.1ASimpleSurvey 9 ],assumingaphotonemissionprocess,andtheyestimatedtherecombinationtimetobearound0.4s.Ginsberg'stunnelingexperiments[ 32 ]determinedtherecombinationtimesthatweremanyorderssmallerthanthisindicatingaphononemissionprocess.SchrieerandGinsberg[ 10 ],RothwarfandCohen[ 33 ],andGray[ 34 ]allconsideredtheelectron-phononinteractionandcalculatedtherecombinationtimesonan100pstimescaleattemperatureTTc=2.RothwarfandTaylor[ 35 ]pointedoutthattheactualeectivelifetimeshouldbelongerthantheintrinsiclifetimeduetophonontrappingeects.Kaplanetal.[ 36 ]calculatedseveralscatteringratesofQPsandphononsformetallicsuperconductors. Inlate1960sandearly1970s,manyexperimentswereperformedattemptingtostudythenon-equilibriumsuperconductivity[ 34 37 { 40 ].Testardi[ 41 ]showedthatthenon-equilibriumstatecouldbegeneratedbylightofsucientintensitywithphotonenergygreaterthanthegap,thenParkerandWilliams[ 42 ]measuredtherecombinationratesinilluminatedtunneljunctions.OwenandScalapino[ 43 ]proposedtheenergygapshifteectsduetotheexcessQPs,andthismodelwassupportedbytheexperimentsofSai-Halaszetal.[ 44 ]forthelowuenceregime.Themajorshortcomingsofmostpreviousworkisthattheymeasuredtherelaxationtimeindirectly. Huetal.[ 45 ]performeddirecttime-resolvedstudieswithatime-resolutionintensofnanosecondsscaleintunneljunctionexperiments.Intheearly1990s,Johnson[ 46 ]rstachieveddirecttime-dependentstudywithtimeresolutionsof100psinthetransientelectricalphotoresponsemeasurements,withtheobservedsignalslimitednear 43

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47 ]usedcoherentterahertzlaserspectroscopyandobservedtheCooperpairbreakinginlessthan1ps.However,theQPrecombinationprocesswasnotinvestigatedforordinarysuperconductors.Theopticalultrafastpump-probetechniqueshavebeenappliedtotheHigh-Tcsuperconductorswithpicosecondorevenfemtosecondrelaxationtimedetected[ 48 { 56 ].PeoplehavereportedcontradictoryresultsfortheQPrecombinationtimefromthethesemeasurements,withvaluesrangingfrompicoseconds[ 51 ]tomilliseconds[ 50 ].Therecently-developedbroadband,time-resolvedsynchrotronspectroscopymightresolvethesedierences. Synchrotronradiationwasusedfortime-resolvedexperimentsstartingat1990sbyEdereretal.[ 4 ]andCarretal.[ 5 ].Sincethelate1990sthebeamlineU12IRattheNSLS,BNL,hasbeendesignedspeciallyforoptimalfarinfraredperformance,especiallyfortime-resolvedpump-probespectroscopy[ 1 { 3 57 { 59 ]. 10 33 42 43 60 61 ].Whenasampleinthesuperconductingstateisexposedtolightwithphotonenergygreaterthantheenergygap,someCooperpairsarebrokentoelectronsinexcitedstatesorquasiparticles.Thisprocessweakensthesuperconductingstate.Testardi[ 41 ]didexperimentsin1971andrstshowedthatthesuperconductingstatecanbetotallydestroyedbyasucientintensityoflight.InhisexperimentsthesuperconductivityofPblmwasconvertedtonormalbylaserlight,eventhoughthelmremainedunderthecriticaltemperature.OwenandScalapino[ 43 ]developedamodeltoexplainthisphenomenon,thatanexcessquasiparticle(QP)populationreducedthesuperconductor'sorderparameter(theenergygap).Theydescribedtheexcitedstatebyaneectivechemicalpotentialandcalculatedtheenergygap2asafunctionofexcess 44

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03=8<:" 02+n2#1=2n9=;2(3{7) wherenisthedimensionlessvariablewhichistakentobetheexcessQPnumberinunitsof4N(0)0,N(0)isthesinglespindensityofstatesinunitsofstates/(eVcm3),and0istheunperturbedenergygapatT=0.Theaboveequationreducesforn0:1andTTcis: 012n(3{8) Soon,ParkerandWilliams[ 42 ]quantitativelyconrmedtheOwen-Scalapinomodelthroughsuperconductingtunneljunctionsilluminatedwithopticalradiationexperiments.Twoyearslater,in1974,microwavereectivitymeasurementsbySai-Halaszetal.[ 44 ]conrmedtheOwen-ScalapinomodelinweakpairbreakinglimitthattheQPscreatedbythephotoexcitationismuchsmallerthanthosethermallyproduced.Alsoin1974,Hu,DynesandNarayanamurti[ 45 ]reportedrstdirectmeasurementoftherelaxationprocesswithatimeresolutionof30nsanddetectedthegapshiftinthephotoexitedstatebytunneljunctionsexperiments. 3.2.3.1Introduction 45

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TheworkdescribedinthisdissertationcoversthecasewherethereisnosteadyQPinjectionmechanism;thesystemisexcitedalmostinstantlyandrelaxestotheoriginalstatemoregradually.Therelaxationprocessesinthiscasearequitecomplex.Whenthesuperconductingspecimenisexcitedbyaphotonuxwithenergyconsiderablylargerthantheenergygap,therstgeneratedQPshaveenergyashighastheincidentphotons,i.e.thoseQPsmayhaveenergiesabove1eVwithanear-infraredexcitationlaserwhichisabouttwoordersinmagnitudehigherthantheusualsuperconductingenergygaps,whichareafewmeV.Atthismoment,thesystemhasmanyexcitedQPsbutfewphonons.Infemtosecondtimescale,thehighenergyQPsinteractwithotherelectronsmainlythroughtheelectron-electron(e-e)scattering.Thisprocessdistributesenergywithinelectronsystem,henceitproducedadditionalQPexcitations.Inthefollowingpicosecondtimescale,thoseQPshaveenergystillgreaterthantheenergygapandwillfurtherrelaxtothegapedge(T)throughthedominatingelectron-phonon(e-ph)scattering.ThisprocesscalledmultiplicationproducedexcesspopulationofQPswithenergiesaroundthegapedge.Thee-phscatteringtimeincreaseswhenthetemperatureisdecreasedandthephononsarefrozenout.Theseprocessescanbeimaginedasahigh-speedping-pongballhittingabasketofballsatrest,resultinginabunchoflow-speedballs.Typicallye-eande-phscatteringaremuchfasterthanthenalexcessQPrecombinationprocess.Inprinciple,theQPrecombinationcanbeaccompaniedbyeitherphononorphotonemission,however,thephotonemissionisslowandphononsdominate[ 9 33 62 ].SointheprocessofexcessQPrecombination,mainlyexcessphononsarecreated.Intheearly1960s,SchrieerandGinsberg[ 10 ]andRothwarfandCohen[ 33 ]separatelydidinitialtheoreticalcalculationsoftheQPrecombinationtimeR.Thecalculationswerebased 46

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35 ]pointedoutthattherstassumptionmightnotbesatiseddependingonthetemperatureandtheinjectioncurrent;andthesecondonewasneversatised.TheextraphononsmayagainbreakCooperpairsandproduceQPs.TheextraenergyistrappedinthephononandQPsystemuntilthe2phononsescapetotheenvironment(thesubstrate,heliumbath,orsampleholder)orlosttheirenergytobelowthegapthroughinelasticscatteringotherthanQPcreation.Thisphonon-trappingeect[ 63 ]greatlyenhancesthesystem'stotalrelaxationtimeoreectivelifetime.Weuseerepresentingthesystemeectivelifetime,andtheQPrecombinationtimeR,pairbreakingtimeBandthephononescapetimearealldenotetheintrinsicprocesses. Figure 3-1 showsthemainprocessesinthephotoinducedexperimentinasuperconductor.NotethatifthephononescapetimeisnotsignicantlysmallerthantheintrinsicQPrecombinationtimeRorpairbreakingtimeB,willformabottlenecktothewholesystemeectivelifetime. 35 ]in1967developedasetofdierentialequationstodescribethedynamicsoftheQPandphonondensitiesinthinlmsattemperaturesmuchlowerthanTc: whereNqpisthetotalnumberofQPs,Ristheintrinsicrecombinationcoecient,I0isthelocalQPsinjectionrate(cm3s1),Nisthetotalnumberofphononswithenergygreaterthan2,istheQPcreationrateduetoprocessesinwhichthephononswithenergy 47

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PhotoexcitationandRelaxationinSuperconductors.TheoriginalplotwasfromG.L.Carr. 64 ]: ThetermsRN2qp=2andN=2representtheintrinsicrecombinationandpair-breakingprocesses.Thefactorof1=2comesfromthefactthatitrequirestwoQPstocreateonephonon.Intheseequations,RothwarfandTaylorassumedthattheN(T)RN2qp(T)becomessimplyNRN2qp,andneglectedthediusionofQPs.Theyalsoassumedthat 3{10 comesfromthefactthatonephononbreaksoneCooperpairwhilecreatestwoQPs.ThustherelationbetweenandBis1 2=1B. 48

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Settingequations 3{9 and 3{10 equalto0,thesteadystatesolutionsareobtained: 2I0(3{13) Withoutinjectioncurrent: RothwarfandTaylorfurtherassumedthatRandareindependentoftheinjectedQPsdensity,obtainingfromequation 3{9 : ConsideringthatboththetotalQPsandphonondensitiesconsistofathermalpartandanextrapartfromexternalexcitation: RothwarfandTaylorobtainedtheexpressionsfortheextraQPsandphononsinthenewsteadystate: 2RNqp(T)+Nqp(T) 4N(T))1 2Nqp(T) 49

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2I0(3{19) RothwarfandTaylorrstpointedoutfromtheaboveequationstheexistenceofadditionalphononescapetermfortheextraQPsandphonondensities.ThismeansthattheextraphononsmaybreakuptheCooperpairsbeforetheyescapetothesubstrate,whichwillenhanceandmaybecomeabottleneckforthetotaleectivelifetime. InthelimitofI0=0,theaboveequationsreduceto: Thoseequationsmeanthatifthereisnosteadyexternalenergysupply,thenewequilibriumstatewouldbeidenticaltotheoriginalone. 64 ]: whereN=NN(T),N=NN(T)and1=,RN(T)=1R. Thesteadystatesolutionsforthelinearizedequationsare: 2I0R(1+1 2)(3{24) 50

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2I0(3{25) Graypointedoutthatboth1 2andareroughlyindependentoftemperature. Thetime-dependentequationsare: RNqp=I0(1+ RN=I0 where =+1 2+2 ThesolutionfortheexcessdensityofQPsis: 2I0R(1+1 2)+Aexp(p+t)+Bexp(pt)(3{29) whereAandBareconstantsand 2n281R1=2o(3{30) NotethatGrayusedincorrectsolutionsforNqpinequation 3{29 withthepdenedinequation 3{30 Theequation 3{29 givesusanimportantresult.ItshowsthatthetimedependenceoftheextraQPdensityfollowsexponentialshapeswithtwotimescalesp+andp.The 64 ]Nqp=1 2I0R(1+1 2)+Aexp(p+t)+Bexp(Pt)hastoassociatewithp=1 2n281R1=2otobeequivalenttoequation 3{29 and 3{30 51

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Hence,thesuperconductingspecimen'sresponsetoexternalexcitationfollowsasimpleexponentialtypedecay.Becausetheopticalresponse,i.e.thetransmittanceorreectance,isdirectlyrelatedtotheQPdensityinthespecimen,thechangeofopticalresponseisdirectlyrelatedtotheextraQPdensity,thustheopticalprobeshouldalsofollowasimpleexponentialdecayshape. Notethissolutionisidenticaltotheonein[ 57 ]: 1 whereBistheintrinsicCooperpairbreakinglifetimeduetoabsorptionofa~!2phonon,andBcanalsorepresentsthelifetimeofthephononduetoabsorptionwithpairbreaking.,initiallydenedbyRothwarfandTaylorequations 3{9 and 3{10 ,andthenadoptedbyGray,denesarateofQPs'creationduetoCooperpairbreakingby2phonons.OnephononbreaksoneCooperpairandcreatestwoQPs,thustherelationbetweenandBis 1 2=1B(3{33) With=1and1 2=1B,onendsthat =2 2+=21R+1B+1(3{34) and 52

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Considerthelimitof!1, 1 or 1 1 With!1,thephononswillneverescapethespecimen,sothesystemwillmovetoanewdynamicbalancebetweentheQPsandphonons,andwillneverreturntotheoriginalequilibriumstate.Thus+representsthelifetimefortheexcessQPandphononpopulationstoreachthenewsteadydynamicbalance,and,whichisinnityinthiscase,meaningthattheprocessitrepresentsneverhappens,istheeectivelifetimeforthesystemtorelaxfullytotheoriginalfundamentalstate.Inconclusion,ifthereissteadyexternalenergysupply,thesystemwillmovetoanewequilibriumstatedierentwiththeoriginalone,andthetimeconstantisrepresentedby+;iftheexternalenergysupplystops,thesystemwillreturntotheoriginalequilibriumstate,andthetimeconstantisrepresentedby.Theexperimentsperformedinthisdissertationexploredthefullyrelaxationdynamicsofthesystemwhichiscasewithoutsteadyenergysupply,sorepresentstheexperimentalmeasuredeectiverelaxationtime.Thusthenewequilibriumcorrespondingtothecasewithsteadyenergysupplywillneverbeachieved,whichmeans+!1,andp+=1 e(3{39) 53

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Thedenitionof1=RistherateforQPrecombination,andeachrecombinationeventproducesoneCooperpair,onephonon,andremovestwoQPs.BecausetherecombinationcanhappenonlywhentwoQPs\meet"eachother,forasmalldensityofQPs'populationatlowtemperatures(TTc),therearelesspossibilitiesforQPstomeetthusitleadstoaslowerrecombination,thatisRislarge.Astemperaturerises,thedensityofQPsincreasesandRdecreases.AttemperatureclosetoTc,thelargeQPpopulationmakestherecombinationeasytoachieve,soRbecomessmall.Ontheotherhand,1=Bistheintrinsictransitionprobabilityforthe2phononstobreakCooperpairs,andthisrateisdecidedbyhowdicultitisfora2phonontondtheCooperpairs.Atlowtemperatures(TTc),thelargepopulationofCooperpairsleadstoafasterpair-breakingtime,whichmeansBissmall.Astemperatureincreases,thedecreaseofCooperpairavailabilityincreasesthetimeforaphonontondpairsthusresultinginalongertimeorlargeB.,thephononescapetime,dependsonthelmgeometry,theacousticmatchingbetweenthelmandthesubstrate,andwhetherthelmisvacuumortheliquidbath[ 57 64 65 ].Foraroughapproximation,itisexpectedtobetemperatureindependent[ 57 64 ]. SofarwehaveestablishedapictureofR,Band: 54

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21R+1B+12811R1(3{41) Asdiscussedabove,atallthetemperaturerangesotherthanthecriticaltemperatureTc,thefollowingstatementisalwaysvalid: so 21R+1B+12811R21R+1B+1411R Thustheeectivelifetimecanbededucedtobe: 2R(1+ Further,basedonthediscussionofrelationsbetweenBandabove,wehave 36 ]in1976derivedthetemperature-andenergy-dependentintrinsicrecombinationtimeRandthephononpairbreakingtimeBfromthematerialparametersforadirtylimitsuperconductoratorverynearthermalequilibrium.Theypointedout 55

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1 (3{48) 1 (3{49) whereRistheintrinsicQPrecombinationtimeandBisthelifetimeofaphononofenergyduetoCooperpairbreaking;!istheenergyofQPsjustbeforerecombination,istheusualtemperaturedependentenergygap(T),Z1(0)istheQPrenormalizationfactor,Nisthedensityofions,N(0)isthesingle-spinelectronicdensityofstatesattheFermisurface(notincludingelectron-phononrenormalizationeects),andf(!)andn(!)areFermi-DiracdistributionandBose-Einsteindistribution,respectively. InordertocalculateRandB,2()andF()needtobedeterminedeitherexperimentallyortheoretically.Inprinciple,2()canbeobtainedfromtunnelingexperimentsandF()canbefoundfromneutronscatteringexperiments.Atlow 56

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66 { 68 ].Asimplemodeltotreattheproblemistoapproximate2()F()byitslowfrequencyform wherebisaconstantparameterdecidedbymaterialsandcanbedeterminedfromelectrontunnelingexperiments. Usingthisapproximation,Kaplanetal.[ 36 ]deducedthat whereR0istheintrinsicpairrecombinationtimeclosetoTc=2andKR(;T)isaninniteseriesinvolvingthemodiedBesselfunctionsK0andK1: n+2kT n2#K1n nK0n 57

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Kaplanetal.neglectedthefrequencyandtemperaturedependencyofZ1(w)atfrequenciessmallcomparedwithtypicalphononfrequencies,Z1(0)=Z1(w).Theseriesrapidlyconvergesatlowtemperatures.Theleadingtermis: Tc1=2e0 If2()F()cannotbeapproximatedbyb2attheenergygap20,amoregenerallowtemperatureapproximationforRis TherecombinationprocessinducestwoQPscombiningtoformapair;thus,theexponentialincreaseoftheintrinsicrecombinationlifetimeRreectstheexponentialdeceaseinthepopulationofQPsatlowtemperatures. Kaplanetal.alsodeducedtheresultforBintermsofacharacteristictimeB0atthephononenergy2: 58

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0[12f((T))](3{58) with 32FavZ102()F()d(3{60) whereB0representsthelifetimeofaphononwithenergy20duetopair-breakingprocessat0K,andh2Fiavistheelectron-phononcoupling2()F()functionaveragedoverthewholephononspectrum.AsdiscussedinSection 3.2.3.3 ,veryroughlythephononpair-breakingtimeisinverselyproportionaltotheCooperpairdensity,soitdecreaseswithtemperature. Thepair-breakingtimeBofaphononwithenergyatTccanbeexpressedas: 1+exp Figure 3-2 showsthelifetimese,B,RandforPbusingtheequations 3{32 3{48 and 3{49 withtheapproximation2()F()=b2.TheplotisvalidforaweakcouplingBCStemperaturedependencefortheenergygap,withQPsenergyandphononsenergy2.Also,thephononescapetime,=280ps,istakentobetemperatureindependentaswediscussedinSection 3.2.3.3 .Theparametersarefromreference[ 36 ],withR0=196psandB0=34pscalculatedfromequations 3{52 and 3{59 Inthermodynamicequilibrium,theCooperpairbreakingrateisequaltothepaircreationrate: 1 2Nqp Figure 3-2 showsthatatRdivergesat0KandBissmall.Thus,fromequation 3{62 ,onegetsN!0atlowtemperatures,whichmeansthatalltheabsorbedenergy 59

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LifetimesforPb. isintheformofexcessQPsatlowtemperatures;incontrast,thesimilarargumentsshowthatnearTc,alltheabsorbedenergyisintheformofexcessphonons.Atnitetemperatures,theenergydistributesamongthe2phononsandtheQPs.HenceonebuildsapicturethattheextraenergyfromtheabsorbedphotonschangesfromanexcessofphononstoanexcessofQPstheastemperaturedecreases. Consideringthesameamountofenergyabsorbedat0KandatanitetemperatureT,onegets: 60

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ExcessQPsDensitywitherrorbar.R0=B0=5:8. Usingequation 3{62 ,theaboveequationbecomes 1+B Notethatequation 3{64 describestheexcessQPdensityasafunctionofthetemperatureintheconditionofequilibrium.ForPb,thecorrespondingplotoftherelativeexcessQPdensityisshowninFigure 3-3 3 57 ],incorrectexpressionswereused:Nqp 1+2B=R 61

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where!isenergy,C(!)isnotdecidedbytheparticularmaterialparameters,andcanbeshownfromequations 3{48 and 3{49 tobe: 1f(!)0 (22)1=2(!)+2 (3{66) where2()F()=b2isused. Thus,thedensityofexcessQPsdependsonlyontheratioofR0=B0whiletheeectivelifetimedependsonR0=B0aswellas,R.TheR0=B0ratiodependenceofexcessQPsmightbeusedtodeterminethisratio.Inourexperiments,wecandeterminetheenergygap20withaccuracyof1cm1,soinFigure 3-3 thedottedlinesaboveandbelowthesolidlineshowtheerrorbarsduetotheenergygap.Figure 3-4 showshowthetemperaturedependentexcessQPsdensityvariesastheratioofR0=B0ischanged. Notethatequation 3{64 isobtainedundertheconditionthatthephononandQPpopulationsareinequilibrium.Itisworthnoticingthatinourexperiments,thisconditionisinvalidatthemomentoflaserincidence. 8 62

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TemperaturedependenceoftheexcessQPswithdierentR0=B0ratio. 2 ],whenthesample'sresponseislinear: whereIpump(t)andIprobe(t)are,respectively,thetemporalintensityprolesofthepumpandprobepulses.G(t)isthesample'simpulseresponsefunctionwhichisthequantityofinterest. Weuseanabout30mlengthofmulti-mode,graded-indexopticalbertotransportthelaserlightfromthelaserhutchtothesampleatthebeam-line.The800nm 63

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andrewriteequation 3{67 as Itshowsthatthemeasuredresponseisaconvolutionofthesynchrotronpulseshapewiththesample'sintrinsicresponse. ThusS(t),thechangeinresponseS(t)duetomodulationtwhichisaroundaparticulardelaytimet,isgivenbythetimederivativeofequation 3{69 @t+1Zdt1Iprobe(t1+t)G(t1)(t)(3{70) whentheamplitudeofthetemporalmodulationtissmall,themeasurementessentiallygivesthederivativeofthephotoinducedsignalwithrespecttotime,andthedetectedsignalisthedierenceinthesystem'sresponsebetweendelaytimesttandt+t. AsdiscussedinSection 3.2.3.3 ,thespecimen'sphotoinducedfar-IRresponsecanbemodeledasasingleexponentialdecay,then 64

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ThesynchrotronpulsemaybemodeledasaGaussianpulsewithfullwidthathalfmaximum(FWHM)recordedattheNSLS: FWHM=1:67p whereisthestandarddeviation Themeasuredresponseatthedetectorisaconvolutionoftheprobepulsewiththeinstantaneousphotoresponse, thus p Withoutlossofgeneralitythelaserandthesynchrotroncoincidencemaybetakenast0=0, 69 ],thepulsewidthwasdenedas!=p 70 ].11 65

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Typicalphotoinducedsignals,themeasuredderivativesignald dtT T,andthecomputedintegratedsignalT T,usingthedierentialmethod. p Equation 3{76 isconsistentwith[ 69 ].Hencethemeasuredsignalisaderivativeoftheconvolutionoftheexponentialdecayofthephoto-carriersandrelativelybroadsynchrotronpulse,andthederivativesignalisintegratedtoobtainthephotoinducedchange.Figure 3-5 showsthetypicaldierentialandintegratedsignalsinthephotoinducedexperiments. Thesolutionofequation 3{75 is: whereerf(x)=Rx0exp(t2)dtistheerrorfunction. 66

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3{77 canbeusedtottheintegrateddata.Aandecanbededucedastparameters.Figure 3-6 showsthetusingequation 3{77 totheintegratedsignal.Thetisexcellentandthusprovedtheeectivenessifourmethod.Figure 3-6 alsoshowstheresponseofthesamplewithouttheGaussianshapesynchrotronpulseinthephotoinducedexperiments.Notethatthepeakoftheexponentialisgreaterthanthesignalamplitudeandalsothatthepeakpositionsshiftedtosometimegreaterthanzero.Thoseeectscanbeexplainedbytheconvolutionofthesynchrotronpulse:thebroaderthesynchrotronpulse,thesmallerthesignalpeak.Whentheeectivelifetimeismuchsmallerthanthesynchrotronpulsewidth,themeasuredsignalapproachesthesynchrotronpulseshape,andthesample'sresponsetrendstobeunresolvable.Hencethesynchrotronpulsewidthisthelimitingfactorforthetime-resolution.Theshortestsynchrotronpulsewidthavailableisabout300psatthetimeofwritingthisdissertation,sogenerallyspeakingthebesttimeresolutionforourexperimentsisgreaterthan300pswithoutanyknowledgeoftherelaxationshape.Ifweknowthesample'sresponsefunctioninadvance,forexampleansimpleexponential,thetimeresolutioncanbeimprovedtoabout100ps Intheactualexperiments,aDCosetmaybemixedinthesignal.Theintegratedtfunctiondoesnotincludethiseect.Inthiscase,aderivativettingfunctioncanbeused, 67

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Photoinducedintegratedsignalwitht.ThetparametersareA=32.1(arb.),ande=270ps.Thedashedlineshowsthespecimen'sresponsewithoutthefactorofsynchrotronpulse. whereS0representstheDCosetandisusedasanotherttingparameter.Figure 3-7 showsthetwithequation 3{78 forthederivativesignal. 43 ]developedamodeldescribingtheenergygapshiftduetotheexcessQPpopulation,whichwasconrmedbyaseriesofexperiments[ 44 45 ].RothwarfandTaylor[ 35 ]developedasetofdierentialequationstodescribetheeectivelifetimeinthenon-equilibriumsuperconductivity.Thekeypointoftheirmodelwastoincludethephonontrappingeecttoexplainthediscrepancybetweenearliertheoreticalcalculations[ 10 33 62 ]andexperiments[ 32 37 71 ].Gray[ 64 ]linearizedtheRothwarf-Taylor 68

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Derivativesignalwitht. equationsintheweakperturbationlimitanddeducedasimpleexponentialrelaxationprocess.UsingGray'smodel,weexplicitlydeducedthetemperaturedependentrelationsbetweentheQPeectivelifetimeeandotherscatteringrates:R,Band.Kaplanetal.[ 36 ]calculatedseveralscatteringratesformetallicsuperconductorsincludingRandB.Hence,assumingatemperatureindependentphononescapetime,weareabletoexplicitlydescribethetimedependenteetivelifetimee,intrinsicQPrecombinationtimeRandpairbreakingtimeB. 69

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72 73 ].Infraredspectroscopyhasbeensuccessfullyusedtostudysuperconductivityproperties,includingthegap[ 74 { 78 ].MattisandBardeen[ 79 ]rstappliedtheBCStheorytotheopticalpropertiesofsuperconductingthinlms,obtainingthecomplexopticalconductivityforweak-coupling,dirty-limitsuperconductors.Fromtheircalculations,theimaginarypartoftheopticalconductivity2(!)isproportionalto1=!andtherealpart1(!)iszeroatabsolutezerotemperatureforphotonenergiessmallerthanthesuperconductinggap.Henceonecanshowthatthetransmissionofsuperconductingthinlmhasadominant/!2behaviorforfrequencieswellbelowtheenergygapinEquation 4{5 Non-equilibriumsuperconductivityhasbeenattractingpeople'sattentionsinceearly1960sjustafterthedevelopmentofBCStheory.Thisnon-equilibriumstatecorrespondstotheCooperpairbreakingandthegenerationofunpairedelectronsappearinginexcitedstatesknownasquasiparticles.IfasignicantnumbersofCooperpairsarebroken,theenergygapgetssmaller,orevendisappearsshowingasaweakenedordestroyedsuperconductivity.Inreturningtoequilibriumstate,theexcessQPseventuallyrelax 70

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InthischapterwearegoingtoshowtheexperimentaldetailsforasuperconductingNb0:5Ti0:5Nthinlmusingthelaser-pumpsynchrotron-probetime-resolvedexperimentsattheBeamlineU12IR. 4-1 .ThetransitiontemperaturesareshowninFigure 4-2 .TheTcinthemagneticeldcanbedecidedshowninTable 4-1 .ThetemperaturesweptexperimentshowedthattheHc2was 71

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Temperaturesweptmeasurementinseveralmagneticeldsbychoppingsynchrotronbeam.Theunitiny-axishasvoltagedimensionwhoseabsolutevalueislessimportantsincethesignalgainischangeable. Table4-1. H(T)0123456789 greaterthan9TandtheTcwasabout10.4Katzerothemagneticeld.Anotherresultisthattheoveralltransmissioninfar-infraredincreasedastemperaturedecreasedinthesuperconductingstate. 72

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4-1 anditshowsalinearrelationbetweenTcandH. TheexperimentswereperformedwiththeOxfordOptistatbathcryostatattheOx-Boxwhichconnectedtothebeamlinedirectlybypassingtheinterferometer.The1.5Kbolometerwasusedtodetectthe7-bunchstretchedsynchrotronbeamsignal.Thelaserwasoperatedat920nmandchoppedatthelaserhutch.Theoutputpowershownherewasmeasuredatlaserhutchbeforechopping;andaboutonly75%wassuccessfullydeliveredtothesample.TheresultsareshowninFigure 4-3 .Thedatashowthatthetransitionhappenedfrom10.3Kto10.8KwhichisingoodagreementwiththeTc=10:4Kdecidedinthemagneticeldexperiments.Thelittlediscrepancycamefromthedierenttemperaturesensorpositions. 4.2 wehavealreadyseenthatthespectrallyaveragedtransmissionincreasesasthetemperaturedecreasesinasuperconductingstateinthefar-infrared 73

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Superconductingtransitionrangeinthelaser-choppingexperiment. region.Afrequencyresolvedstudyoftransmissioninsuchasystemcanrevealtheinformationoftheconductivityandenergygap. 72 80 ].Theresultis: whereTistheratioofthepowertransmissionwithlmtothatwithnolm;Z0istheimpedanceoffreespace(4=c,cgs;377ohms,mks);disthelmthickness. Forametalinthenormalstate,theeectiveconductivitymaybetakentoanexcellentapproximationtohaveonlyarealpart,~'N,with 74

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whereRNisthedcresitancepersquareofthelm.WiththeknowledgeofRN,thelmthicknesscanthusbeestimated.Thenormalstatetransmittanceofthethinlmisaconstant,dependingonlyonNdandexpressedas: Inthesuperconductingstate, ~(!)=1(!)+i2(!)(4{4) thus Thustheratioofthetransmissionofthesuperconductingstatetothatofthenormalstateis: 2N+1T1 2N1 2N2 MattisandBardeen[ 79 ]deducedtheexpressionof1(!)=Nand2(!)=NbasedontheBCStheory[ 31 ].Theirresultsare: (20E2)1 2(E+~!)2201 2(4{8) 75

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where1and2aretheBlochenergiescorrespondingtoEandE+~!,respectively: 2(4{10) 2(4{11) NotethatthesecondtermofEquation 4{7 requires~!>20,inwhichcasethelowerlimitoftheintegralinEquation 4{8 is0insteadof0~!.Alsog(E)isalwayspostitiveinEquation 4{7 FurtherforT=0,theintegralsinEquations 4{7 and 4{8 canbecarriedoutanalytically: 220 whereE(k)andK(k)areellipticintegralswith j20+~!j(4{14) 2(4{15) ForT>0,Equations 4{7 and 4{8 havetobesolvednumerically. 76

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SamplecharacterizationparametersfromtheMattis-BardeentstotheTS=TNcurves.Adirtylimitapproximation(1 Materiald(nm)RN()Tc(K)20(cm1=meV)20=kBTc bolometerand7-bunchstretchedbeamwereemployed.ThenormalstateofNb0:5Ti0:5Nwasmeasuredat12Kandthesuperconductingstatewasmeasuredfrom3K(0:3Tc)to9K(0:9Tc).Figure 4-4 showsTS=TN,theratioofthetransmissionatsuperconductingstate(T
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PlotofthemeasuredTS=TNdatawiththet.TNwasat12K.Symbolsaredatapoints,linesarethetsusingtheMattis-Bardeencalculationswithacorrectionforstrongcoupling[ 82 { 84 ]. Themagnetotransmissionexperimentswereperformedusingthe1.5KbolometerattheBrukerIFS125/HRspectrometer.Thespectrawererecordedfromabout5cm1to100cm1inthefar-infraredregion.Thesamplewasclampedwiththecoldngercryostatinthesuperconductingmagnet.wemeasuredthesuperconductingtransmissionTS(H)atsampletemperature3K(0:3Tc)andmagneticeldupto10T.TheTNbackgroundwas 78

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ThetemperatureandfrequencydependentconductivityratiobasedonthetsfromFigure 4-4 measuredat12Kwithouttheeld.ThetransmissionratioofthesuperconductingstatetothenormalstateisshowninFigure 4-6 ThedatainFigure 4-6 showsthatthetransmissionat10Twasstilldierentfromthatofthenormalstate,thusthesampleat3Kwasnotcompletelyconvertedtonormal,soHc2forthisNb0:5Ti0:5Nlmisgreaterthan10Tat3K. 4-4 and 4-6 isthatthepeakpositionredshiftedinthetemperature-dependentexperimentsandstayedalmostatthesameposition(28cm1)inthemagneticelddependentcaseasthesuperconductingstategotweaker.Becausethepeakpositionisanindicationoftheenergygap,thismeansthattheenergygapwasnotaectedbymagneticeld.Tomakethisclear,Figure 4-7 showstheratioofa 79

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MeasuredratioofTS=TNforNb0:5Ti0:5Nlmatmagneticeldsbetween0and10T. seriesofloweldtransmissiontothatinahigheld(10T)ataxedtemperature(3K).Itisobviousthatthepeakpositionisalmostunchangedbuttheamplitudeconsistentlydecreasesasthemagneticeldincreases.Thismeansthattheenergygapdidnotchangeasthemagneticeldwaschanged.Instead,theeectofthemagneticeldistodevelopthevorticeswithnormalcoresinthattypeIIsuperconductor.Theeldbarelyaectedthesuperconductingregion.Thedecreaseoftheamplitudemeansthatthepopulationofvortices,andthusthenormal-regionarea,growwiththeeld. IfwecanapproximatelydividethetypeIIsuperconductorintotworegions:superconductingandnormal,attothedatainFigure 4-7 maybeabletodecidethe 80

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Theratiooffar-infraredtransmissionofNb0:5Ti0:5Natlowermagneticeldtothatat10Tataxedtemperature3K. fractionofthosetworegions.Figure 4-8 showstheresultofusingthisverysimpletwo-componentmodel: whereAisthearea.Thetsshowsthetrendofthedata:thepeakpositionsstaynearlyunchangedandtheamplitudesdecreaseastheeldstrengthgrows.Therearesomedeviationsfromthetsanddata,probablybecauseoftheoversimplemodel.Thus,thismodelcangiveussomeideaofthesuperconductingareafactorsasafunctionofmagnetic 81

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FittotheT(H)=T(10K)curvesthroughthesimpletwocomponentmodel.Thesymbolsaretheexperimentaldata,andthelinesarethets.ThetparametersareshowninFigure 4-9 elds.TheresultsareshowninFigure 4-9 .Notethatthesuperconductingareaisnotlinearlydecreasedastheeldisincreased.Thetlinesareempiricalwithaformof: whereSisthesuperconductingregionfraction. 82

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SuperconductingandNormalregionsfromthetwo-componentt.Thesymbolsaretheratiosandthelinesareanempiricaltforthesupercondctingregionfraction.ThetisshowninFigure 4-8 thespectrometercanbebypassed.Becausethebeamsplitterweakensthesignal,incaseofdetectingsmallsignalorthenoiselevelishigh,weconnectedtheOx-Boxtothebeamlineoutputdirectly. TheexperimentscanbesetatthesamplecompartmentoftheBrukerIFS125/HRspectrometerorwiththeOx-Box.Itwasrelativelyeasiertosetupatthespectrometer'sowncompartment,however,onlytransmittanceexperimentscanbeconducted;thealignmentoftheOx-Boxwasmoredicultbecausethetransmittanceandreectancehavetobealignedinthesametime,however,onceitwasopticallyaligned,itwasveryeasytochangemeasurementsbetweentransmittanceandreectance.Ourexperimentshaveusedbothsetups. 83

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4.4.1.1Experimentaldetails Themode-lockedTi:sapphirepumplaserwasoperatedat52.88MHzatawavelengthof930nm.Thetimeintervalbetweentwolaserpulsesis18.9ns,longenoughforthesampletoyrelaxfully.Thelaser-ostatecorrespondstotheunperturbatedsuperconductingstateatgiventemperaturesandthelaser-onstateistheperturbatedsuperconductingstate 84

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4.2 .)Therelativesignalwemeasuredwastheratiooftransmissiondierencewiththelaseronandthelaserotothebackground(laserostate).Thephotoinducedchangeinthetransmissionisduetothephotoinducedabsorptionchangeinexcitedstates.Itcanbeshownthat: wheredisthelmthickness,istheabsorptioncoecient.Thus NotethattheyaxisofFigure 4-11 isdenedas TTonToff Thelaseroutputpowerwasabout10mWatthesampleandwecarefullychosethissmallpowerofpumplasertobesureinthelow-uenceregime.Thespotsizeatthesamplewasabout2.3mmindiameter.Theshortest7-bunchcompressedsynchrotronbeamwasusedwithFWHMofabout340pstogetthebesttimeresolution. Figure 4-10 showsthemeasureddierentialsignalfortheNb0:5Ti0:5NsampleattemperaturesbelowTcinthephotoinducedtransmittancemeasurement.AsdiscussedinChapter3,thedierentialdatacanbeintegratedtogeneratethetime-resolvedchangeintransmission,asshowninFigure 4-11 Similartothetransmissionmeasurements,thedenitionofreectancechangeinthereectancemeasurementsis RRonRoff 85

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DierentialphotoinducedsignalforNb0:5Ti0:5Nsuperconductinglm. Table4-3. Fitparametersforthephotoinducedbroadbandtime-resolvedtransmittancemeasurementattemperatureT.eistheeectivelifetime,Aisthemagnitude,andwistheprobepulsewidth. T(K)e(ns)A(arb.)w(ns) 40:6350:0271:7940:0330:3320:00550:4530:0151:7410:0310:3340:00470:2540:0111:4770:0430:3330:00590:2120:0151:0030:0510:3370:008 WettedthedatausingthemodelofsimpleexponentialdecayproposedinSection 3.3 .TheillustrationtforbothdierentialandintegrateddatausingEquation 3{77 and 3{78 wereshowninFigure 4-12 and 4-13 .ThetresultisshownatTable 4-3 4-12 and 4-13 showexamplesofthetstothespectrallyaveragedfar-infraredtransmissionusingthetmodelinSection 3.3 .Generallythetsareverygood.Thisfact 86

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TheintegrateddatafortheNb0:5Ti0:5Nsample. ensuredusthatthetmodelthatthespecimen'srelaxationfollowsasingleexponentialisappropriateforthistypeofnon-equilibriumsuperconductingdecay.Thustheexperimentsprovedthenon-equilibriumsuperconductivitydynamicstheoryinitiallyproposedbyRothwarf-Taylor(Section 3.2.3.2 )andlaterlinearizedbyGray(Section 3.2.3.3 ).Theexperimentsalsoprovidestheeectivelifetimeintheorderof1ns UsingKaplan'smodel(Section 3.2.3.4 )forBandR,wetthetemperature-dependenteectivelifetimeasshowninFigure 4-14 .Thetsagreesthepredictionofe,RandBdiscussedinSection 3.2.3.3 .ThetsisgoodfortemperaturesaboveTc=2,butdeparts 4.4.3 87

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Thetforthetime-resolvedexperimentat4K.Theblackdotsarethedierentialdatapointsandtheredlineisthetcurve. fromthedatapointbelowTc=2withthetvaluesgreater.ThereasonisthatinthetheoreticalcalcultionsweconsideredtheQPswithenergytorecombineintoCooperpairsandhigherenergyQPsrecombinationpartwasnotincluded.IfweincreasetheQPenergy!inEquation 3{48 (Section 3.2.3.4 ),Rdecreasesthusedecreasestobeabletotthelowtemperaturedata.However,discrepancybetweenthecalculationandtheexperimentaldataaroseatthehightemperaturepart.ThisthusindicatesthatthehighenergyQPdensityandtheircontributionstothewholerecombinationprocessesaredierentwithtemperatures.AtemperaturedependentQPdistributionwithenergypriortorecombinationmaygiveamorecompletedescriptionofthealltemperatureeectivelifetime.Anotherpossibilityisthatthesystementeredastrongperturbationregionatlowtemperatures.ThepopulationofthermallygeneratedQPsdropedsharplyasthe 88

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Thetforthetime-resolvedexperimentat4K.TheblackdotsaretheintegratedsignalfromFigure 4-12 andtheredlineisthetcurve. temperaturedecreased.ThestrongperturbationincreasedtheQPpopulationwhichcouldrecombineintopairsthendecreasedtherecombinationtimeRthusdecreasedtheeectivelifetime.Asimplequantitivecalculationcanmakethisclear. Thepumplaserwasoperatedatthewavelengthof930nmwhichcorrespondingtothephotonenergyofabout2:11019J.Thusthephotonsprovidedbyonelaserpulseonthesamplewas: 0:01W18:9ns/pulse 2:11019J0:23cm NotethatonephotonmaybreakmultipleCooperpairs,inacrudeapproximationwesuppose5%photonseventuallywereabsorbedbythelmforbreakingpairsforallthe 89

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Fitthetemperaturedependenceoftheeectivelifetimeinthetime-resolvedexperiments.Theblackdotsaretheexperimentallydecidedeectivelifetime.ThecurvesareseveralscatteringlifetimescalculatedwithtvalueofR0=B0'2:3.=200psisassumedtobetemperatureindependent(Section 3.2.3.3 ). temperatures (27:50:12411:61022)J0:23cm (4{23) Ontheotherhand,thethermallygeneratedQPdensityforalowreducedtemperaturecanbeexpressedas[ 42 ]: 90

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withN(0)31:71021states/(eVcm3)[ 36 ],20=27:5cm1(Section 4.3.2 ),onendsthat Theestimationshowsthatatabout0:5Tctheweakperturbationstillheldandat0:4Tc,theexcessQPsdensitywasclosetothethermalQPdensityanditenteredthehigh-uenceregime.Andat0:3Tc,itwasclearlyinthehigh-uenceregime.Thispictureisconsistentwiththetwhichagreedwiththedataabove0:5Tc,anddiscrepancyhappenedbetweenthedataandthecalculationsat0:4Tcandat0:3Tctherewasabigdiscrepancy.TheestimationaboveisconsistentwithmoreaccurategapshiftexperimentsandthecalculationsinSection 4.5 Figure 4-15 showstheexperimentallydecidedamplitudeAwhichisameasureoftheexcessQPdensityatthemomentoflaserincidence.Figure 4-15 alsoshowsacalculationoftheexcessQPfromEquation 3{64 inSection 3.2.3.4 .Apparentlytheexperimentaldatashapeisdierentfromthecalculatedlinewiththeexperimentaldatagreater.Thisisreasonablebecausethetwokindofdatawerenotobtainedinthesameconditions.AswementionedinSection 3.2.3.4 ,thecalculationwasbasedonanequilibriumrelationsEquation 3{62 : ThisrelationisvalidattheconditionwhenthephononandQPpopulationsareinequilibrium.Thusthecalculation 91

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TheamplitudeAfromtheexperiment(dotswithdashedline)atthemomentoflaserincidenceandthecalculatedexcessQPpopulations(solidline)atequilibriumstate.TheexperimentaldataaregiveninarbitraryunitsNqp.Thelaseruenceis10mW. 1+B isapplicabletothesteadystateexperiments,forexample,continuousexternalenergysupplymovedthesystemtoanewbalanceorapproximatevalidifthephononescapetimeisveryslowcomparingwiththeotherscatteringlifetimes.Theexperimentsweperformedwereobviouslynotinthosecases.TheamplitudeAwasobtainedatverymomentoflaserincidence,apopulationofexcessQPswerejustcreatedandthiswasattheoppositelimitoftheequilibriumofexcessQPsandphonon.Henceitisnotdiculttounderstand 92

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Inourexperimentswedidnotobservealong-livedtailwiththesampledirectlycontactingwithliquidorgasphaseHelium.Johnson[ 46 ]andCarretal.[ 3 ]reportedthelongtailusingcoldngercryostats.Loboetal.[ 57 ]reportedlong-livedtailsobservationwithcoldngersandnotailswithdirectlyHeliumcontacttypecryostat.Allthereportsareconsistentinthatthelongtailrelatedtotheinecienceofcoldngertypecoldingmechanics.Thusthelongrelaxationtimeisnottheintrinsicsuperconductingproperties,andcomesfromthethermaleects. 4.4.1.2 .Alternativelyandmorepracticallywecandecidethehigh-uenceregimebyexperiments.Anaccuratemethodistodoagap-shiftexperimentwhichrequirestheinterferometerandtakesalongtime.Asimplecrudeestimationcanbedonebylookatthechangeofthecoincidencesignalfromthelock-inwhilechangingthepumplaserpower.Assumingthatthecoincidencesignalvaluechangeslinearlywiththelaserpowerinthelow-uenceregime,whenthissignalunlinearlyincreases,weknowthatithasenteredthehigh-uenceregime.TheresultofthissimplemethodisshownatTable 4-4 andFigure 4-16 .Notethattheratioshouldbeapproximatelyunchangedinthelow-uenceregime,andbecomessmalleratthehigh-uenceregime.Thedatashowthatbelow66mWtheratiosdonot 93

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Estimatetheboundaryofthehigh-uenceregime.Thelaseroutputpowerisshownontheleft;middlecolomnisthelock-inreadingvalue.Notetherandomorderofthelaserpowerwasonpurposetominimizetheaccumulatefactor. Power(mW)V(mV)V/P(mV/mW) 17.5472.6920512.5533852.58451082.40661592.411322742.082643931.49 Figure4-16. high-uenceboundary.They-axisistheratioofpeaksignalvaluetothelaserpower. changemuchwhileclearlydropat132mWandthe264mWvaluedropsfurthertoabout55%ofthevalueat17.5mW.Soat132mWthesystemhasalreadyenteredthehigh-uenceregime. 94

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FluencedependenceforTransmittancewithtemperatures. Power(mW)244896192360 T(K)e(ps) 2.510503072020470103401032010396020630204501031010290105490104101030010240102301072601025010230102201029010921010210102301055040110240 A(Arb.) 2.535:920:3470:860:98141:980:99272:250:24384:970:24336:450:2968:870:76144:340:23267:050:88385:650:52535:850:2570:660:72137:680:38248:870:55271:360:39732:270:2763:450:16124:870:18187:010:16109:830:08924:850:3244:640:4369:760:5512:580:361:460:43 4-5 andFigure 4-17 and 4-18 ThereectanceresultsareshowninTable 4-6 andFigures 4-19 and 4-20 Thereisanothermethodtomeasuretheeectivelifetimevs.temperature.ConsidertheintegratedsignalinFigure 4-21 ,itcanbeapproximateatriangleasshowninFigure 4-22 Therelationsbetweenthedistancel,m,nare: upslope=l m(4{30) 95

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Temperaturedependenceoftheeectivelifetimefrombroadbandtransmittanceatuencebetween24and360mW. Table4-6. Fluencedependenceforreectancewithtemperatures. Power(mW)2550100200360 T(K)e(ps) 2.59608059020360102201018010387070590203201021010200105450203801025010190102001072501023010220102001030010921010190102301035020210201025010---A(Arb.) 2.50:0460:0010:1040:0020:3180:0061:2210:0312:4950:14030:0480:0010:1030:0020:3440:0061:2640:0292:5090:05850:0750:0010:1570:0030:4740:0081:5590:0272:3310:04470:1410:0020:2740:0060:6730:0121:6250:0201:1400:02090:2130:0050:4240:0070:7850:0130:0810:0020:0140:001100:1990:003---96

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Temperaturedependenceoftheamplitudeatuencesbetween24and360mW,measuredintransmittance.Theerrorbarsarestatisticfromhundredsofdatapoints,andsomeofthemaresmallandcoveredbythedatapoints. downslope=l n(4{31) andthus downslope(4{32) Theapproximationisthatmisdirectlyproportionaltothesynchrotronpulsewidthtpwandnisdirectlyproportionaltotheeectivelifetimeeforanexponentialtypedecay,thatis 97

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Temperaturedependenceoftheeectivelifetimefrombroadbandreectanceatuencebetween25and360mW. thus downslope(4{35) Whileinourderivativemeasurements,thepositivemaximumsignal\max"inthedierentialdatacurveisjusttheupslopeoftheintegrateddatacurveandthenegative 98

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Temperaturedependenceoftheamplitudeatuencesbetween25and360mW,measuredinReectance.Theerrorbarsarestatisticfromhundredsofdatapoints,andsomeofthemaresmallandcoveredbythedatapoints. maximumsignal\min"inthedierentialdatacurvecorrespondstothedownslopeinFigure 4-21 .Putalltheabovetogether,onegets downslope=tpwmax min(4{36) Wethenxedthetimedelayatthemaxandminsignal,sweptthetemperature,andcollectedthedataatthosetwopositions.ThetemperaturedependenceoftheeectivelifetimeisthusobtainedfromEquation 4{36 .Theresultsofthesweptmeasurementscomparingwiththeusualtime-resolvedmeasurementsareshowninFigures 4-23 and 4-25 .MoreclearcomparisonsareinFigures 4-26 and 4-27 99

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The\max"and\min"pointsinthedierentialcurvecorrespondtotheupslopeanddownslopeintheintegratedcurve. Figure4-22. Approximationoftheintegratedsignal. 100

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Sweptmeasurementsandthetime-resolvedmeasurementsintransmittance.Thesoliddotsarethesweptmeasurementswitha350psosettakenaway.Theopendotsarethedatapointsfromthetime-resolvedmeasurements. 4-28 ,showingthatitisnotreliableveryclosetoTc. Thesweptmethodisanapproximationfortheabsolutevalueoftheeectivelifetime.However,goodconsistencywiththeaccuratetime-resolveddataprovesthatitisaccuratethatitshowsthechangingtrendofewhenavariableischangingcontinuously,like 101

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Sweptmeasurementsforreectance.A250psosetweretakenaway. temperatureormagneticeld(Section 4.4.4 ).Theconsistencybetweenthesweptandusualtime-resolvedmethodsintransmittanceandreectancemeasurementsassuresthevalidationofthedatashowninFigures 4-17 and 4-19 Thedatashowthatthebasictrendisthattheeectivelifetimedecreasesasthelaseruenceincreases.ThistrendisvalidfortemperaturesnotveryclosetoTcinthelowandmiddleuenceregimes,andalsoforlowandmiddletemperatures(below5K0.5Tc)inthehigh-uenceregime.Thehigh-uencedataat200mWdeviatesfromthistrendatabout7K0.7Tcandthehighestuencedataat360mWdeviatesfromthistrendearlieratabout5K.Althoughwelacktheoryinthehigh-uenceregimebecauseKaplan'sexpressionsforRandBarevalidinorverynearthermalequilibrium,notsuitableforourcase,itisnotdiculttounderstandthistrendqualitatively.AtagiventemperaturebelowTc,moreexcessQPsarecreatedasthelaseruenceincreases.ThusthetotalQP 102

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Comparisonofthesweptandusualtime-resolvedmethodsforreectance.Theopendotsaresweptmeasurementdataandthesoliddotsarethetime-resolveddata. population,whichincludesboththethermalpartandthephotoexcitedpart,increasesinmostcases.BecausetheQPrecombinationtimeRisinverselyproportionaltothetotalQPdensity,Rdecreaseswithincreasinglaseruence.NotethattheeectivelifetimeeisalwayspositivelyrelatedtoR.Tounderstandthis,itisusefultoconsiderthelimitingsituationwhentheothertwotimeconstantsBandareverysmallcomparedwithR.Thismeanspair-breakingandphononescapingprocessesareveryfastandtheQPrecombinationisthebottleneckthuseR.Ontheotherlimit,considerB!1,thismeansthepairbreakingprocessaretoolongtoactuallyhappen,thusthereisnophonontrappingeecttoo,sotheonlyprocessistheQPrecombinationandhenceagaineR.AlsorefertoEquation 3{44 forlow-uencecase.HenceedecreaseswithR. 103

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Comparisonofthesweptandusualtime-resolvedmethodsforreectanceat25mW. Thedatashowthattheeectivelifetimesatthetwohighestuences(200mWand360mW)arealmostthesameatlowtemperature.Notethatthisisnotduetosaturationofthephotonabsorption,becauseFigures 4-18 and 4-20 showbigdierencesintheamplitudeA,whichisanindicationoftheexcessQPdensity.Rather,itisanindicationthat,startingfrom200mW,aconsiderableexcessofQPsareproduced,makingRverysmallcomparedto.WehavejustdiscussedthatealwaysgoeswithR(andtau)nomatterBislargeorsmall.So,theeectivelifetimee!. Thehigh-uencedataalsoshowsapeakoftheeectivelifetimeathightemperatures.Sowhataboutthisfeature?Thehigh-uencesystemdiersfromthelow-uenceoneinthatthehigh-uencelaserbreaksmoreCooperpairsandcreatesmoreexcessQPs.Astemperatureincreasesinasuperconductor,theenergygap2shrinks.Inthelow-uencecase,thephoto-brokepairs'populationaresosmallthatithardlydependsonthetotal 104

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Comparisonofthesweptandusualtime-resolvedmethodsforreectanceat50mW,100mW,200mWand360mW. CooperpairdensitythustheexcessQPsdensityapproximatelykeepsconstant.Moreaccuratelytosay,thepopulationofexcessQPduetothephotoexcitationshouldincreasealittlebitastheenergygapshrinksandtheenergyrequiredforbreakingpairsdecreasesastemperaturegoesup.Also,inthelow-uenceregime,theexcessQPdensitylinearlychangeswiththelaserpower.BothofthetwofeaturesareshowninFigure 4-18 and 4-20 .Ontheotherhand,high-uenceisdierentinthattheexcessQPpopulationdependsonthetotalCooperpairsavailableathightemperatures.Thewholepicturewouldbeasfollows:atthebeginningthetemperatureislowandtheCooperpairdensityislarge.Themaximumthelaseruenceavailabletous,360mW,isnotstrongenoughtoaectthetotalCooperpairdensity,thustheexcessQPspopulationbehavesjustlikethelow-uencecase|slightlyincreasingwithtemperature.Forthe360mWuencethistemperature 105

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The"max"and"min"signalsofthesweptmeasurementsat50mWforreectance.Thesoliddotsarethe"max"signalandtheopendotsarethe"min"signal. isbetween3Kand5K,andforthe200mWthistemperatureisabout7KasshowninFigure 4-18 and 4-20 .WeknowatlowtemperaturestheexcessQPdensitydoesnotchangemuchbecausethetotalCooperpairdensityonlyslightlyaectedbythelaser.Asthetemperatureincreases,thetotalCooperpairdensitygraduallydecreases.Itisnotthecaseathightemperatures.Oncethetemperaturegoesbeyondsomepoint,thetotalCooperpairdensityisaectedbythelaser.SincetheexcessQPdensityisrestrictedtothedensityoftotalCooperpairsatthepresenttemperature,theexcessQPdensitydecreasestogetherwiththeCooperpairs.ThesefeaturesareclearlyshowninFigure 4-18 and 4-19 after5Kforthe360mWand7Kforthe200mWcurves. 106

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4-17 4-19 and 4-24 :theincreaseof100mWcurvefromabout9Kto9.7K,the200mWcurvefrom8Kto8.9Kandthe360mWcurvefrom6.6Kto7.6K.Asthetemperaturecontinuestoincrease,theCooperpairdensitybecomessmallathightemperatures.SoalthoughtheCooperpairdensitykeepsdecreasing,thenumberofthedecreasedCooperpairsbecomessmaller,whilethethermalQPdensitybecomeslarge.ThustheeectofincreasingthethermalQPswilldominatebeyondacertaintemperatureTb.For100mW,Tb=9:7K;for200mW,Tb=8:9Kandfor360mW,Tb=7:6K.AttemperaturesgreaterthanTb,therapidlyincreaseofthetotalQPdensitydecreasestherecombinationtimeR,thuse.ThisisalsoshowninFigure 4-17 4-19 and 4-24 .Notethisfeatureisuniversalandexistseveninlow-uenceregimeattemperaturescloseenoughtoTc.Forexample,the24mWdatashowadecreaseofAandaincreaseofeatthe10KinFigure 4-20 and 4-19 107

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4-17 and 4-19 alsoshowthatstartingfromabout7K,theeectivelifetimesgotoasimilarvalueandtheslopesoftheloweruencecurvesbecomeatthusindicatesthatestartsapproachingwhichisabout200ps,Rissmallanddoesnotaecte. 108

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Nb0:5Ti0:5Nsampleincontactingwiththegasousandliquidhelium. Table4-7. Fitparametersforthegaseousandliquidheliumcontactingexperiments. Phasee(ns)A(arb.) Gaseous0:6030:02956:450:092Liquid0:7390:03355:450:063 liquidhelium,andthusthesample,at4.2K 4-29 .ThetparametersareshowninTable 4-7 4-29 areverysimilartoeachother,sotheabilityforthegaseousandliquidtoconductingheatissimilar.AlsothetwoamplitudesAinTable 4-7 areveryclose.AistheindicationoftheexcessQPdensitywhichshould 109

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3{45 3{46 and 3{47 ,thereisalwaysarelationthate/, 4-7 )bychangingthegasowanddensity. 4-18 and 4-20 theamplitudeAwerestilllinearwiththelaserpower.Eveninthehigh-uenceregime,Figures 4-17 and 4-19 for200mWand360mWstillshoweforthereasonswediscussedinSection 4.4.2.2 ,henceweconcludee/. 110

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Fitparametersforthemagneto-opticaltime-resolvedmeasurements. T(K)H(T)e(ns)A(arb.) 300:880:030:1140:003311:100:020:0690:001321:000:020:0630:001331:050:020:0510:001341:040:020:0550:001351:540:040:0480:001 Table4-9. Fitparametersforthemagneto-opticaltime-resolvedmeasurementsateldupto9T. T(K)H(T)e(ps)A(arb.) 4.40762311:3600:0304.4370777:5040:0474.47.591265:3950:0224.49898471:1300:021 experimentshadbeenreportedonthisquestionyetwhenwestartedourexperimentstryingtoanswerit. 4-8 ,Figures 4-30 and 4-33 .Withthesimilarsetting,anotherrunextendedtheeldto9Tat4.4K.TheresultisshowninFigure 4-31 andTable 4-9 Wealsodidthesweptmeasurementsdiscussedatsection 4.4.2.1 withlaserpowerabout50mWatsampleand7-bunchcompressedsynchrotronbeam.Wexedthetemperatureat4.5Kandsweptthemagneticeldfrom0Tto8Tatthe\max"and\min"positions.TheresultisshowninFigure 4-32 withthetime-resulteddata.Withintheerrorbars,theyagreedasthetrend. 111

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EectivelifetimevsmagneticeldforNb0:5Ti0:5Nat3K. Figure 4-33 showsthattheamplitudeAdecreasesasthemagneticeldstrengthens.Thisagreeswithourexpectations.TheamplitudeAisasignalindicatingthetotal 58 ],wehadnothaveanexplanationyet. 112

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PhotoinducedsignalintransmissionvstimedelayatseveralmagneticeldvaluesforNb0:5Ti0:5N. excessQPscreatedinthephotoinducedexperiments.Usuallythesuperconductingregiondoesnotchange,andwhatchangesisthecouplingstrengthorthegapparameterinatemperaturedependentexperiments,soAalsorepresentstheexcessQPdensity.Thesituationisdierentinthemagneto-opticalexperimentsbecausevorticeswithnormalcoresgrowinthesuperconductorwiththemagneticeldandthegapparameterbarelychanges.AisstillanmeasureoftheexcessQP,butnowAisrathertheindicationofthesuperconductingareathanthedensity.IfthetypeIIsuperconductorinamagneticeldcanbedividedintotwoparts:superconductingandnormalregion,theareaofsuperconductingregiondecreasesasthemagneticeldsisraised.UsingtheempiricalEquation 4{17 ,Figure 4-34 showsthecomparisons. ThediscrepancyofthetwodatasetsinFigure 4-34 showsthattheapproximateEquation 4{17 whichfromcrudetsinFigure 4-8 isnotveryaccurateduetothe 113

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EectivelifetimeforNb0:5Ti0:5Natmagneticeldfromtime-resolvedandsweptmeasurements.Thesoliddotsarefromtime-resolvedmeasurementsat4.4Kandtheopendotsarefromthesweptmeasurementsat4.5K.Theerrorbarsforthesweptdataarestatistical,fromthevariationsoftwotrials. simplicityofthetwo-componentmodel.Buttheyagreeswiththebasictrend:thedecreaseofthesuperconductingregionisnotlinearwiththedecreaseofthemagneticeld. 3.2.2 ,theenergygapwillshrinkaccordingtoEquation 3{8 ,hencethespectrumwillrstshowaredshiftinthegapatthemomentofcoincidence;thiswillgraduallycomebackasthesystem 114

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AmplitudevsmagneticeldforNb0:5Ti0:5Nat3K. relaxes.Inprinciple,thespectrumcanbemeasuredateverypointinthedecaycurvebetweenpointBandCinFigure 4-35 ,sothatthespectrumforeverystepinthesystemrelaxationdynamicsmayberevealed;butthespectralchangesaresmalleectsandthesignal-noise-ratioislow,sowemeasuredthedierencebetweenthebackgroundpointAorCandthepeakpointBtogetthebestS/N.PointArepresentsthecasewhenthesynchrotronprobebeamarrivedatthesamplebeforethepumplaser,thusitcorrespondstothelaserostateinthechopperexperiment;pointBapproximatelyrepresentsthecoincidencewhenthesynchrotronandthelaserarriveatthesamtime,correspondingtothelaseronstate;pointCrepresentsthecasewhenthesynchrotronarriveslongafterthelaserwhichissimilartopointAinacycle.Ateachpointthetimedelaybetweenthelaserandthesynchrotronisxedforaperiodoftimeduringwhichtheinterferometerscansforafewhundredtimestogetaspectrumatthisperticulardecaytime.Then,thetimedelay 115

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FractionofthesuperconductingregionvsmagneticeldforNb0:5Ti0:5N.Thesoliddotsaretheamplitudesfromthetime-resolvedexperimentswhichhavebeennormalizedto1withouteld.TheopendotsarethepredictionfromtheEquation 4{17 movestoanotherpointandisxedthereforthesameperiodoftimeforthespectrometertoscanatthatsecondpointtogetanotherspectrum.Thetimedelaythenshiftsbackandforthseveralhundredtimestogetseveralhundredspectraforeach.FinallyanaverageistakentoreducetheS/Nandthephotoinducedspectrumiscalculatedas: T=TonToff Inthismeasurementnolaserditherisneeded.Thisisamultiplespectraaveragedexperimentsothehighestscannervelocitywasdesirabletosavetime. 116

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GapshifteectsweremeasuredbetweenpointAandB. 4-36 showsthegapshifteectfortransmittanceoftheNb0:5Ti0:5Nsample. ThetransmittanceoflightthroughathinlmonsubstratewasexpressedinEquation 4{6 anddiscussedatsection 4.3.1 .Equation 4{6 showsthatthetransmittancedepends 117

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PhotoinducedspectrumforNb0:5Ti0:5N.Thelaserpowerwas10mWandthetemperaturewas5K.Thetparameteris(2)=0:21cm1. onopticalconductivitywhichsubsequentlydependsontheenergygapcanbediscribedusingtheMattis-Bardeenequationsinequilibrium.Thesituationcanbeexpressedas: T=T(+)T() where(2)isthegapchangeduetothephotoexcitation.ThetinFigure 4-36 wasthusbasedonTinkham'stransmissionequationcombinedwiththeBCSMattis-Bardeenexpressionsfortheopticalconductivity.Thegapshift(2)wastheonlyadjustableparameterinthetandotherparameterswerexedusingthesamevalueinthetofTS

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PhotoinducedspectrumforNb0:5Ti0:5Nat3Kwitht.Thelaserpowerwas20mW.Fitparameter(2)=0:11cm1. inFigure 4-4 .Theresultwas(2)=0:21cm1whichmeansthegapwasredshiftedabout0.21cm1or0.026meV. Thegapshifteectswerealsomeasuredinamagneticeld.Theexperiments'setupweredierentfromtheaboveinthatthesamplewasplacedintheverticalboredmagnetcoldngercryostat.Thepumplaserwasoperatedat860nm,about20mWand73mWatthesamplerespectively.Thesynchrotronwasoperatedin7-bunchdetunedmodetogetbetterS/Nduetoalargerbeamcurrentoverthecompressedmode.Thetemperaturewasxedat3K.TheresultswithoutmagneticeldsareshowninFigure 4-37 and 4-38 .Themagneticeldweresetat5Tand10T.TheresultsareshowninFigure 4-39 and 4-40 119

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PhotoinducedspectrumforNb0:5Ti0:5Nat3Kwitht.Thelaserpowerwas73mW.Fitparameter(2)=0:28cm1. 4-36 4-39 and 4-40 .Thetsweregenerallygoodathighenergiesandpooratlowenergieswiththetheoreticalpredictionsmoresharpthanthemeasurements.ThediscrepancymightcomefromthepoortinthelowfrequencyregionofTs=TncurvesinFigure 4-4 .ButthetanddatareectedtheexpectationsthattheexcessQPdensityaectedthesuperconductinggapandtheenergygapwasredshifted.InSection 3.2.2 ,therelationsbetweentheexcessQPdensity,Nqp,andthegapshift,(2),werediscuss[ 43 ]: 120

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PhotoinducedspectrumforNb0:5Ti0:5Nat3K.Thelaserpowerwas20mW.Magneticeldswere0,5and10T. 012n=12Nqp while 0=20(2) 20=1(2) 20(4{41) thus 20=2Nqp Equation 4{42 canbeusedtoestimatetheexcessQPdensityduetothephotoexcitations.ForFigure 4-36 4-37 and 4-40 thegapshiftwere0.21cm1,0.11cm1and0.28cm1,respectively.HencetheratioofexcessQPdensitytotheCooperpairsis: 121

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PhotoinducedspectrumforNb0:5Ti0:5Nat3K.Thelaserpowerwas73mW.Magneticeldswere0,5and10T. InSection 4.4.1.2 ,wehavediscussedthedensityofthermallygeneratedQPs[ 42 ]inEquation 4{24 : 122

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andthephotoexcitedexcessQPsandthethermallycreatedQPscanbecomparedas: 2 thusat5Kwith10mWlaseroutputatsamplewith20=27:5cm1, at3Kwith20mW: at3Kwith73mW: ThoseresultsareconsistentwiththeestimationinSection 4.4.1.2 consideringthefactthattheabsorptionchangesatdierenttemperatures.ThusoneoftheapplicationofthegapshiftexperimentsistoaccuratelydecidethephotoexcitedexcessQPpopulationandalsotodividethelow-andhigh-uenceregimes. 123

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4-39 and 4-40 showthegapshifteectsinamagneticeld.Bothguresshowthesametrendinthatthecurvesbecomeatterandnoisierasmagneticeldisincreased,whichmeansasmallersignal,onaccountofasmallersignal.Thisisunderstandablebecauseasvorticesnumbergrowswithmagneticeld,thesuperconductingregiongotsmaller.Althoughinthesuperconductingregionthegapshiftedthesimilaramountasiftherewasnomagneticeld,thedeductionoftotalareasdecreasedthesignalthustheS/N. ThecriticaltemperatureTcinamagneticeldwasdeterminedthroughspectrally-averagedtransmissionmeasurements.Thetemperatureandmagneticelddependencyofthefrequency-dependenttransmissionratioofthesuperconductingstatetothenormalstatewasstudied.ThetemperaturedependenceagreedwiththeTinkham'sthinlmtransmissionequationcombinedwithBCSMattis-Bardeentheory;Thetwo-componentmodelwasgoodtodescribethebasictrendofthemagneticelddependence,butmaynotbeveryaccurateduetoitsoversimplicity. Photoinducednon-equilibriumdynamicswasthoroughlyexploredinpump-probetime-resolvedexperimentswithtimeresolutionsupto100ps(supposingweknowthespecimen'sdecayshape).Weemployedbroadbandsynchrotronradiationastheprobesourcesynchronizedtothepumplaser.ThetsandtemperaturedependentdatashowedexcellentagreementwithatfunctioncomingfromtheRothwarf-TaylarequationsandGray'smodel.Theeectivelifetimewasinagreementwiththereportedvalues.ThetemperaturedependenceagreedwithKaplan'spredictioninmiddletohightemperaturesverywell;thediscrepancyinlowtemperaturesmightbeduetothelossofthehigherenergyQP'srecombinationorhigh-uenceeects.Notwo-componentrelaxationwasobserved. 124

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ThemagneticelddependenceresultsshowedthattheQPeectiverelaxationdidnotshowadecreaseastheeldincreased.Wegiveanexplanationtothisphenomenon. Thesuperconductivitygapshifteectsweredirectlymeasuredinafrequencydependentspectrum.PhotoexcitedexcessQPdensitywasthusestimatedfromthegapshiftvalues,andthisvaluewasinreasonableagreementwiththeexpectationbasedonthephotonenergyabsorbedbythesample.AcomparisonofthephotobrokenQPtothethermallygeneratedQPpopulationdenitivelydecidedthelevelofpumpuence. 125

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5.1.1AHistorySurvey 87 ].Inthelate1980sandearly1990sferromagneticDMSinIII-Vbasedsemiconductors(III-VDMS),alsoreferedtoasIII-Vmagneticalloysemiconductors,haveattractedmuchattentionaspossiblematerialsforspin-relatedapplications[ 88 89 ]. Generallyspeaking,asemiconductorwithafractionofitsconstituentionsreplacedbysomespeciesofmagneticions(i.e.ionsbearinganetmagneticmoment)isadilutemagneticsemiconductor.ThesubstitutionalmagneticionscanbetransitionelementssuchasMn,Fe,orCr,etc.Thecommonpropertiesofthetransitionelementsarethattheyallhavedelectronswhichdon'tformafullshell.Forexample,Mnionsaremostlyusedasmagneticdopants,andMn2+hasahalflleddshell(1s22s22p63s23p63d5)withspin5/2.ItcansubstituteforthegroupIIIelementsinzincblendIII-Vsemiconductors,e.g.(Ga,Mn)As. DMShaveexhibiteduniqueproperties,suchaslargeLandeg-factors,hugeZeemansplitting,giantFaradayrotationandgiantnegativemagnetoresistance,whichnotonlyattractfundamentalresearchinterestbutalsohavedemonstratedpotentialintheelectronicindustry.Someinterestingpropertiesarelistedbelow: 126

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89 { 92 ]inIII-VDMSwasdiscovered,whichhadopenedupnewpossibilitiesofthecombinationofferromagnetismandsemiconductors.TheCurietemperaturesaretunablebyvaryingtheMnfraction.Therefore,astudyofthemagneticpropertiesofDMSmakesitpossibleforustocomparethemagneticbehaviorofspinsindierenthosts. TheuniquepropertiesofDMScomefromthespinexchangeinteractionbetweenthelocalizedmagneticionsandbandelectrons.Spintronics,orspin-basedelectronics,alsoknownasmagnetoelectronics,referstothestudyandapplicationwhichexploitthequantumspinstatesofelectronsinsteadof,orinadditionto,makinguseoftheirchargestates.Thediscoveryofgiantmagnetoresistance(GMR)in1988byBaibichetal.isconsideredasthebirthofspintronics[ 93 ].TheGMRmaterialwasappliedasanewstoragetechnologydevelopedbyIBMin1997,andGMRhadpotentialsinthemagneticrandomaccessmemory(MRAM)devicewhichwouldhavesomeexcellentcharacteristicsuchasbeingsmall,fast,cheap,needinglesspowerandbeingrobustinextremeconditionslikehightemperaturesorhighlevelradiationenvironments.DMSspintronicshasalso 127

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94 ]. Beforethe1990smanystudieswerefocusedontheII-VIcompoundDMSsuchasCdMnTe,ZnMnSe,CdMnSe,HgMnTeetc.However,therearefundamentalproblemslimitingtheusageofspintronics.Forexample,thelargeg-factor,whichactuallyindicatesalargespinsplitting,isonekeypointintheapplicationofDMS.ThefactthatmostII-VIDMSareparamagneticandthespinsplitting(thustheg-factor)issmallathightemperaturespreventedroomtemperatureapplications.OnepossiblesolutionistheferromagneticIII-VDMSinwhichhightemperaturespinsplittingisexpected.However,theproductionofIII-VDMSisnoteasybecausetheMnionisnotverysolubleintheIII-Vsemiconductors.ItisknownthattheDMSferromagnetismdependsnotonlyontheholeconcentrationandtheMncontent,butalsoonthelessunderstoodstructuralstatesdeterminedbythesample'sgrowthcondition.Itwasnotuntil1989therstIII-VDMSofIn1xMnxAs(x<0:18)wasgrownwithnon-equilibriumgrowthprocedures[ 89 91 ]bymolecular-beam-epitaxy(MBE)technique.Alotofstudieshavebeenmadetothe(In,Ga,Mn)AsDMS[ 88 89 96 { 98 100 ].Usually(In,Mn)AsiseasiertoaccommodatealargerdensityofMninthehostcrystallatticewhile(Ga,Mn)AsexhibitsahigherCurietemperaturethan(In,Mn)As[ 88 89 95 101 102 ].ACurietemperatureof35Kwasachievedatap-typeInMnAs/GaSbheterostructure[ 95 ],andtherecentreportofthehighestCurietemperatureofGa1xMnxAsreachesthehighestvalueof173Kwith8%nominalMndopingafterannealing[ 99 ].Besides(In,Ga,Mn)As,therewerealsoreportsforotherIII-VDMSorII-IVDMSwithhighCurietemperatures.Somegroupsreported 128

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103 ],andothergroupsreportedaferromagnetictransitiontemperatureabove900K[ 104 ].GaMnPwasreportedwitharoomtemperatureferromagnetic[ 105 106 ].GaCrN[ 107 ]andGaGdN[ 108 ]werebothreportedwith>400Kferromegnetism,Zn1xCrxTewasreportedCurietemperatureof30010Kwithx=0:20[ 109 ],andGeMn[ 110 111 ],SiMn[ 112 ]werealsoreportedferromagnetism. AnotherproblemlimitingspintronicsapplicationisthedicultyofmanipulationandcontrolofthespinsintheDMS.Theusualmethodadoptednowistogenerateandtransferthespinfromaferromagneticmetalinametal/semiconductorheterostructure.Butthetransportandcontrolofspinsarestilldicultandfarfromunderstood. 96 ].Therearemainlyfourmodelstodescribethecarrierinducedferromagnetism:RKKYmechanism[ 113 { 115 ],Zener'sModel[ 116 ],BoundPolaronModel[ 117 { 119 ]andDoubleExchangeTheory[ 120 121 ].Therstthreearebasedonmeaneldtheoryandthelastoneisbasedonthed-electrons.Eachofthemodelscanexplainsomespecicaspectsofferromagnetism,buteveryonehasdrawbacksandcannotbeapplieduniversally. AlthoughtherearemanyvaluablepropertiesofDMS,thisdissertationfocusesontheopticalandtransportpropertieswhichdependontheelectronicbandstructureandwavefunctions.Wearegoingtobrieyintroduceacalculationmethodbasedonkptheory. Thekpmethod,ortheeectivemasstheory,isaperturbationtheoryintroducedbyBardeen[ 122 ]andSeitz[ 123 ].Manystandardtextbooks[ 125 { 127 ]havedetailed 129

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where m0!p+~ where~p=i~risthemomentumoperator,m0isthefreeelectronmass,andV(~r)istheeectivelatticeperiodicpotential: where~Risanarbitraryvector.Notethespin-orbitinteractionHamiltonianisincluded: wherearethePaulispinmatrices: TheeigenvaluesEinthenthbandwithawavevector~ksatisfy: 130

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whereun!kisthenthbandunperturbedperiodicfunction.Thesolutionisgivenbysecondorderperturbationtheory: where 1 and;=x;y;z. Tosimplifytheproblem,onlyenergeticallyadjacentbandswereconsideredwhenstudyingthe!kexpansionofonespecicband.TheKanemodel[ 128 ]whichwasbasedonkptheoryconsideredonlythestronglycoupledbands.Consideringtheelectronspin,thestrong-coupledbandsaretwoconductionbandswhichares-likeattheconductionbandedge,andsixvalencebandswhicharep-likeatthevalencebandtop.TheeightbandedgefunctionsjS"i,jS#i,jX"i,jX#i,jY"i,jY#i,jZ"i,andjZ#iformasetofbasisstateswhichcanbeequivalentlytransformedtotheconvenientbasisformedbytheeigenstatesofangularmomentumJandmJ.ThenewbasisstatesaretwoconductionbandsjS"i,jS#iwhichareunchangedfromoldbasis,twoheavy-holebandsjHH"i,jHH#i,twolight-holebandsjLH"i,jLH#i,andtwosplit-oholebandsjSO"i,jSO#i,whicharealsoeigenfunctionofH0inequation 5{2 2;1 2=jS"i; 2;1 2=jS#i;

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2;3 2=1 2;3 2=1 2;1 2=1 2;1 2=1 2;1 2=i 2;1 2=i IncludingtheW(!k)inequation 5{3 ,theeigenenergiescanbesolvedforthetotalHamiltonianH0+W(!k).Theresultsfortheconductionband, 1 light-holeband, 1 heavy-holeband, 132

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andsplit-oband, 1 whereEgisthebandgap,andisthesplit-oenergy: =3i~ @xpy@V @ypxY(5{20) NotethatbecausethedistantbandcouplinghasnotbeenincludedintheHamiltonian,theeectivemassintheheavy-holebandisstillthebareelectronmass.TheeectsoftheenergeticallydistantbandscanbetreatedasaperturbationtothesecondorderusingLowdin'smethod[ 129 ].TheHamiltonianmatrixcanbeexpressedas[ 124 ]: 3Vkzi 3VkzL0iq 2L+1 2L+000iq 3Vkz1 3VkzL+0iq 2L1 2L0i where 133

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andthe1,2,3,4aretherenormalizedLuttingerparameters: 134

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WedenotebyWtheenergetically-distantstateslabeledwithsubscript.Then Usingtheeight-bandKanemodelplusthecontributionsfromtheremoteband,theDMSbandstructurecanbecalculated.Figures 5-1 and 5-2 5-2 isduetothespinsplittinginducedbyMnions. 1 135

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Calculatedelectronbandstructurefor(In0:53Ga0:47)1xMnxAswithx=0%withoutmagneticeldat20K. Table5-1. TOandLOfrequenciesat300K. TO(cm-1/meV)LO(cm-1/meV) InAs218.9/27.2243.3/42.6GaAs273.3/33.9297.3/36.9InP307.0/38.1343.3/42.6 and17cm2/Vsatroomtemperature,respectively.Figure 5-3 showsthetemperaturedependenttransmissionforthe(In0:53Ga0:47)0:925Mn0:075As/In0:53Ga0:47As/InPsampleinthefar-infrared(Far-IR)andmid-infrared(mid-IR)regionfromabout14cm1to3900cm1.Aboveabout520cm1,thetransmissiondatagraduallydecreases,whichprobablycomesfromacombinationoftheintrabandfree-carrierabsorptionwiththestrongscatteringduetotheunpolishedbackside. 136

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Calculatedelectronbandstructurefor(In0:53Ga0:47)1xMnxAswithx=7:5%withoutmagneticeldat20K.Thesolid(dashed)linesrepresentthespin-down(up)splittingstates. Figure 5-4 showsthefar-IRtransmissionfrom14cm1to650cm1withsomeimpurityabsorptionandmulti-phononabsorptionfeatures.Theveryfar-IRtransmissionfrom14cm1to100cm1isabout50%,andincreasesasthetemperatureisdecreased.Thisisoneofthereasonsmanyofourphotoinducedexperimentswereprobedatthisregion.CombinedwiththethickestMylarbeamsplitter125m,thesensitive1.5Kbolometeriscapableofdetectingsignalintherangeof5cm1to100cm1withgoodS/Nratio.Figure 5-4 alsoshowssomebasicnaturalvibrationalfrequenciesofthetransverseoptic(TO)andlongitudinaloptic(LO)phononmodesatk=0intheabsenceoftheexternallighteldforGaAs,InAs,InPat300K.TheirvaluesareshowninTable 5-1 .BetweentheTOandLOfrequencies,itshowsstrongabsorptionfeature,representingthe 137

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Temperaturedependenttransmissionforthe(In0:53Ga0:47)0:925Mn0:075As/In0:53Ga0:47As/InPsampleinthefar-tomid-infraredspectrumrange. reststrahlenband.TheTOandLOfrequenciessatisfytheLyddane-Sachs-Tellers(LST)relationship: whereLOandTOarethestaticandhighfrequencydielectricconstants,respectively: 138

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Temperaturedependenttransmissionforthe(In0:53Ga0:47)0:925Mn0:075As/In0:53Ga0:47As/InPsampleinthefar-infraredspectrumrange. ForInPat300K,TO=307.0cm1,andLO=343.3cm1,thus 139

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Photoinducedprocessesinthesemiconductorsatlowtemperatures.TheoriginalplotwasfromG.L.Carr. andmuchfasterthanwecandetectit.Thenextprocessisthatthosecarriersfurtherrelaxtothebandedgesthroughcollisionswithacousticphononsinabout100ps.Theywilleventuallyrecombinethroughradiativetransitionandthesystemcomesbacktotheoriginalequilibriumstate.Thisprocessismuchlongerandleadstoananosecondorevenlongertimescale.Theexperimentsdescribedherearetostudythedynamicsintheradiativeprocess.ThetypicalphotoinducedproceduresareshowninFigure 5-5 TostudytherecombinationofelectronsandholesintheInGa(Mn)AslayersinsteadofthethickInPsubstrate,thepumplaserwavelengthmustbegreaterthanthebandgapofInGa(Mn)AswhilelessthanthebandgapofInP.Figure 5-1 showsthatthedirectbandgapEg'0:8eVcorrespondingtophotonswithwavelengthof1550nmforIn0:53Ga0:47Asat20K,andthisvalueagreestherecommendedvaluefromtheliterature[ 130 { 136 ].FortheMn-dopedlm(In0:53Ga0:47)0:925Mn0:075As,Figure 5-2 showsthegapEg'0:77eVcorrespondingto1610nmphotonat20K. ForthesubstrateInP,theenergygaphasbeenstudiedextensively.OnerecentresultisshowninFigure 5-6 [ 137 ].Theenergygapbelow50Kcorrespondsto875nmphotonenergy,at100K,to879nm,asshowninTable 5-2 .Thismeansthatifthepumplaser 140

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TemeraturedependentInPenergygap.Leftaxisisthegapenergywithtemperatureandtherightsideisthecorrespondingphotonwavelength. Table5-2. InPenergygap. T(K)Eg(eV)(nm) wavelengthissetlongerthan879nm,theelectronscannotbeexciteddirectlyfromthevalencebandtotheconductionbandinthesubstrate. Thetime-resolvedexperimentsdiscussedbelowweremeasuredinthefar-IRrange(5cm1-100cm1)wherethebestS/Nratioisavailablewiththe1.5KsensitivebolometerandMylar125mthickbeamsplitter. 141

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2.7 ).Figure 5-7 illustrateshowtheDMSsamplewasexcitedandrelaxedinthreeconsecutivelaserpulsewithaPRFof18.9nsat10Kwithboththederivativeandintegratedsignals.The7-bunchstretchedsynchrotronbeamprovidesthebestS/Nratiobutlimitedtotheworsttimeresolutionof1.5to2ns.ThegureprovesthatthetotalrelaxationtimeoftheDMSsystemislongerthanthelaserperiodof18.9ns,whichcanbeeasilyidentiedfromthedecaypattern.Thefactthatthenonzerotransmissionchangelastsalmostallthetimeshowsthattherelaxationissolongthatthesystemdoesnotfullyrelaxfollowingonelaserpulsebeforethearrivalofthenext.Onemayaskthepossibilitythatthesample'srelaxationtimejustataboutthelaserPRF.Thiscanalsobeeliminatedbythenegativevaluesofderivativedataat18.9nsdelaytimeinbothgures. 142

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Thesamplewasexcitedandrelaxedinthreeconsecutivelaserpumpingperiodsat10K. conductionbandinthesubstrateInPbelow100K(seeTable 5-2 ).Wealsoappliedthislaserataround100Kascomparison. Figures 5-8 and 5-9 illustratethedecaydynamicsattemperature20Kand80KprobedbythePRF170.2nssynchrotronbeam.Theguresclearlyshowthattherearemorethanonedecayprocessesinbothtemperatures.ThetisbasedonthediscussioninSection 3.3 withtwodecayprocesses.Thefastandslowdecaytimeconstantsvarywithtemperaturefrom10Kto100K,whichareshowninFigures 5-10 and 5-11 .Theseplotsshowthatthedecaytimeconstantshavebigchangesatabout40K:thefastdecaytimeconstantsbelow40Karelongerthanthoseabove40K,whiletheslowdecaytimeconstantsbelow40Kareshorterthanthoseabove40K. 143

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Time-resolvedmeasurementwithtinthephotoinducedexperimentswiththesampledecayupto170ns.At20Kandpumplaserwavelengthof882nm. Table5-3. Fitparametersforone-bunchsynchrotronprobeexperiment. T(K)f(ns)Af(arb.)s(ns)As(arb.) 102:230:772:130:3730:613:623:570:22203:090:372:910:1537:942:014:200:13302:380:472:860:2936:932:404:540:15401:560:242:690:36103:628:73:610:05501:710:353:700:5591:4513:124:010:10601:630:204:170:38154:8647:684:000:07701:270:193:710:4975:083:844:470:05801:100:303:020:8276:225:044:580:06901:440:362:180:49111:859:005:430:061000:910:452:011:2274:992:906:770:05 144

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Time-resolvedmeasurementwithtinthephotoinducedexperimentswiththesampledecayupto170ns.At80Kandpumplaserwavelengthof882nm. 5-12 .Thisgureshowsthenormalizeddecaysignalsmeasuredwith882nmpumplaserand7-bunchdetunedsynchrotronbeamfrom5Kto100K.ItisclearthatbelowTc'40K,thereareonlysmallchangeswithtemperatures;OnceaboveTc,thedecaycurvechangesdramatically. SomeoriginaldatawithoutnormalizationareillustratedinFigure 5-13 whichalsoshowsthetsattemperaturesfarbelowandaboveTc.For5Kand75K,thedataarettedwithonesimpleexponentialdecaywhileat100Ktwoexponentialdecaysare 145

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Thefastdecaylifetimesinthephotoinducedexperimentswiththe882nmpumplaserandone-bunchmodeforthesynchrotron-probebeam. Table5-4. Fittingparametersforthe7-bunchdetunedsynchrtronprobeexperiments. T(K)(ns)A(arb.) 517:603:0611:220:142017:162:1513:390:123020:714:2412:460:15507:130:1014:980:05753:330:079:280:09 necessarytotthedata.Thisisnotsurprisingbecauseatabout100K,the882nmpumplaserstartedtoexciteelectronsattheInPsubstrate.Amoredetailedanalysisisinthediscussionsection. Figure 5-14 andTable 5-4 showthetimeconstantchangewithtemperatureusing7-bunchdetunedsynchrotronprobe.Becausethefulldecaytimeismuchlargerthan18.9ns,electronsandholesaccumulateintheconductionbandandvalenceband, 146

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Theslowdecaylifetimesinthephotoinducedexperimentswiththe882nmpumplaserandone-bunchmodeforthesynchrotron-probebeam. respectively.Thisaccumulationthusformsa"stack"eectwhichgathersmorecarriersbeforerelaxation.ThestrengthofthisstackeectdependsonthesystemrelaxationtimeandthestrengthoftheelectronstransitingfromtheundopedlayertotheMn-dopedlayer.ItisunderstandablethatthesystemdecaybehavesdierentwithdierentpumplaserPRFduetothestackeect.Thelifetimemeasuredinthe7-bunchdetunedmodeisacombinationofthelifetimesinfastandslowdecaysmeasuredatone-bunchmode.AsuddenlifetimechangeisobservedatTcinFigure 5-14 .MorediscussiononthisisinSection 5.3.2 Figure 5-15 andTable 5-5 showtheuencedependenceofthemeasuredtimeconstant.Itshowsthattherelaxationtimechangeswiththelaserpower.Figure 5-16 showsthattheamplitudeislinearlyproportionaltothelaserpower,andprovesthatupto192mWlaseroutputpower('462nJ/(pulsecm2)),itisstillinlowuenceregime. 147

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Normalizedphotoinducedtransmissionsignalswithtemperature.Samplewasexcitedby882nm,PRFof18.9nslaserandprobedby7-bunchdetunedmodesynchrotronbeam. Table5-5. Fittingparametersfortheuencedependenceexperiments. Power(mW)(ns)A(arb.) 2413:420:691:780:014812:540:773:450:029613:820:906:740:0419217:172:1513:390:12 148

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DMSsampledecayattemperaturesfarbelowandaboveTcprobedby7-bunchdetunedsynchrotronbeam.TheopendotsareExperimentaldataandlinesarets.5Kand75Karettedbyonecomponentdecay;100Kisttedbytwocomponentdecay. 149

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Timeconstantsmeasuredat882nmpumplaserand7-bunchdetunemodesynchrotronprobe. scatteringrateislowatthepureInGaAsbuerlayer,butmuchhigherintheheavilydopedInGaMnAslayer. Weproposeapossiblemodeltoexplainthetwocomponentrecombinationdynamics 150

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Eectivelifetimewithuencedependenceinthe7-bunchdetunedmeasurements. counteractthecontinueddiusionofchargecarriers.FortheptypeMn-dopedlayer,theFermienergylevelisclosertothevalencebandcomparingwiththeundopedlayer.ThebandsmustthereforeadjustattheboundarysothattheFermienergy(electrochemicalpotential)isaconstant;hence,theenergygapofInGaAslayerwillgraduallybendtottheFermienergy.Whenapumplaserexcitesthesample,morecarriersareproducedinbothlayers.VeryquicklytheextraelectronsattheMn-dopedlayerdiusetotheundopedlayerandtheholesgototheotherdirection.Theseprocessesareexpectedtobelessthan1pstimerangeandwecannotdetectthem.Eventually,theunbalancedsystemwillcomebacktotheoriginalequilibriumstate.Therearetwoprocessesinvolved.Oneisthattheelectron-holemayrecombinelocallyinthesamelayerwhichisthefastprocesswedetectedinafewnstimescale.Theotheristhatiftheelectron-holerecombinationhappensindierentlayers,itwouldbeveryslowbecauseelectronwillghtwiththebackward 151

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Signalamplitudewithuencedependenceinthe7-bunchdetunedmeasurements. electriceld(junctionbarrier).ApossibleprocessforthelongdecaymightbethattheelectronsfromundopedlayerrstdiusebacktotheconductionbandofMn-dopedlayer,thenrecombinewithholeslocally.Theprocesscanbefurtherslowdownbecausetheelectronshavetotransfertoahigherenergylevelbesidesthejunctionbarrier.ThismodelisschematicallyshowedinFigure 5-17 Thispictureexplainswhythe7-bunchdecaybehavesdierentlythanone-bunchdecay.AswediscussedinSection 5.3.1.3 ,thestackeectaccumulateelectronsintheconductionbandofMndopedlayerandholesintheundopedlayer.ThisisequivalenttousingahighpowerlasertooodtheMnlayerwithholesandtheundopedlayerwithelectrons,tendingtoattenoutthebarrier.ThatiswhyweonlyobservedonecomponentdecayinsteadoftwointhehighPRFpumplaserexperiments.InTable 5-3 ,thedataat100Kwastwithtwo-componentdecayinsteadofoneinthe7-bunchmeasurements. 152

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Modelforexplanationofthetwocomponentdecayprocesses. Thisisbecauseatabout100Kthe882nmlaserstartstoexcitetheelectron-holepairsinthesubstrateInP,andasimilarpicturetoFigure 5-17 canbeestablishedexceptnowsomeelectronsgatherattheconductionbandofInP. Thestackeectdependsonthesystem'srelaxationinterval,soatestwouldbetokeepthepumplaseruence,butchangethePRF,thentheelectronaccumulationstatewouldchangeandtherelaxationcurvewouldchangetoo.Forexample,simplyremovethedivide-by-2ordivide-by-Npulsepicker,thelaserPRFwillbeat105.8MHzor9.44ns/pulse,theelectronaccumulationwillbeenhancedandthebarrierwillbefurtherattedout,soweexpecttoseeafasteronecomponentexponentialdecay. IflowPRFas170.2nsintheone-bunchcasebutveryhighuencelaserisusedtoatoutthebarrier,oranexternalreverseelectronvoltageisappliedtoeliminatetheinternaleld,weexpecttoobservethesimilaronecomponentdecayasinthehighPRFcase. Figures 5-10 and 5-14 bothshowthatthelifetimedecreasedwhenthetemperaturesisincreasedaboveTc.Theremaybetwopossiblereasons. 153

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1 wherehCjrepresentstheconductionband,jVirepresentstheheavyholeorlight-holeband,andQfisthedensityofnalstates. Forasmalldensity,i.e.,1015cm3,theholesmainlystayaroundthepointatthevalencebandedge.BelowTc,theinternalmagnizationduetothespinalignmentchangestheenergybandstructureoftheMn-dopedlayerasshowninFigure 5-1 and 5-2 .Theheavyholeandlight-holebandssplitintospin-upandspin-downbandswithapproximatelyhalfdensityofstatesateachsplitband.Thustherstmechanismisthatthedecreaseofthenaldensityofstatesdecreasesthetransitionrate,andincreasesthelifetime. Thereisanotherpossibility.Theheavyholeeectivemassisabout9timesthelightholeeectivemassin(In0:53Ga0:47)As,sothedensityofstatesintheheavy-holebandisabout27timesthatinthelight-holeband.Alsoequation 5{11 showsthattheheavyholecoecientis1=p Aroundthepoint,thespin-upband(dashedlineinFigure 5-2 )ofthelightholesriseswhiletheheavy-holebanddrops,sothatthelight-holebandishigherthantheheavy-holeband.Althoughthespin-downheavy-holebandalsorises,itmaynotbeabletocounteracttheeectofthedropofthespin-upband.Thetotaleectthusmayhavemoreholesgatheringatthelight-holebandattemperaturesbelowTcthanaboveTc.Sincethetransitionrateismuchloweratthelight-holeband,aslightlyriseoflight-holeband 154

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5-10 and 5-14 Thesecondmechanismmightonlyhaveaweakeectbecausewedidnotobserveabigchange,i.e.greaterthan10times,inthelifetimechange.Sowetendtobelievethedecreaseofthedensityofstatesisthemainreasonfortheincreaseofthelifetime. 4.5 wemeasuredthegapshifteectbytime-resolvedspectroscopy.Twotypesofexperimentswereperformed.Onewastousethepulsedlaserandsetaxeddelaytimebetweenthelaserandtheprobesynchrotronbeam,thenthetransmissionspectrachangecanbemeasuredatcertainpointatthesystemrelaxationcurve.Inthefar-IRregionwherethesynchrotronradiationwinsovertheconventionalthermalsources,i.e.mercurylamp,orwhentheS/Nratioislarge,thismethodisdesirablesinceitcanprovideacompletehistoryoftherelaxationdynamics,andsincethelaserilluminatesthesampleallthetime,itavoidsthelargetemperatureuctuations.Thistechniqueisquiteuniqueandatthetimewhenthisdissertationiswritten,wearetheonlygroupintheworldtobeabletoperformsuchkindofexperiments. AnothermethodistouseCWmodelasercombinedwitheitherthesynchrotronorconventionallamps.Thismethodsimplyperformslaseron/oforacertainoftimewhilethespectrometertakesthespectra.WhenthephotoinducedsignalissmallortheS/Nratioistoolow,wehavetoincreasethelaserpowertostrengthenthesignal.Inthiscase,aCWlaserisusedsinceitprovidesastableoutputpowergreaterthanthepulsedlaserbyremovingEOM/2,EOM/Npulsepickersandtherecyclingparts. 5.4.1.1Experimentalresults 155

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Themeasuredtransmissionspectrachangeinthefar-IRregionatdierenttemperatures. T=TcoincidenceTbackground atthemomentwhenalaserpulseisincident.TbackgroundreferspointAorC,andTcoincidencereferstopointBinFigure 4-35 Figure 5-18 showsthespectraoftransmissionchangeatdierenttemperaturesatthemomentwhenthelaserpulsehitsthesample.Itiseasytoseethatatallthreetemperaturesthedatacurvesarepositive,whichmeansthatthetransmissionoftheDMSsystemdecreaseswhenelectron-holepairsaregeneratedbyphoto-excitation. 4{1 ,asimplerelationcanbededucedas(thedetailsofdeductionisintheAppendix)fortherefractiveindexn=3:53ofInPinfar-IR: 156

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Fitparameters. T(K)Slope(cm2)InterceptionDC(1m1)(cm1)n(cm3) 200.33518.368.439.67:81014400.23805.944.059.27:51014750.17994.335.676.57:91014 T=1661d(5{34) where1istherealpartofthecomplexopticalconductivity,anddisthetotalthicknessofthemagneticlayerandbuerlayer.Inourcase,theMn-dopedlayerisabout50nm,andtheundopedlayerisabout120nm,thusd=170nm.ApplytheDrudemodel, whereDCistheordinarydcconductivity,!isthefrequency,isthemomentumscatteringtimeandistheDrudewidth.Combineequations 5{34 and 5{35 ,onegets: T1=1 166DCd+1 166DCd2!2(5{36) Equation 5{36 meansthatthetermT T1linearlychangeswith!2.Thus,bylinearlyttingEquation 5{36 ,theDrudewidthandtheDCconductivitycanbededuced.Further, m=ne2 wherenisthecarrierdensity,mistheeectivemassofelectrons.Hencethecarrierdensityncanbecalculated.ThetsandresultsareshowninFigure 5-19 andTable 5-6 Atallthreetemperaturesthephoto-generatedcarrierdensitiesareapproximatelyequal,whichisreasonablebecausethepumplaseroutputpowerandwavelengthwerekeptconstant. 157

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TheDrudettothephotoinducedspectrachangedataatdierenttemperatures.Thedotsarethedatapointsandthestraightlinesarethelinearts. Infact,wecanestimatetheproducedcarrierdensitydirectly.Thelasertraveledthroughabout30mber,acollimatingandafocallens,anear-IRreectingmirror,aMylarwindowandasapphirewindowtoarriveatthesample.Thepowersuccessfullydeliveredtothesurfaceofthesampleisestimatedabout200mWontoadiameterof2.7mmsize.ThelaserRPFis52.88MHz,correspondingto18.9ns/pulse.Thustheenergydeliveredperpulseis3.78nJ/pulse.Thelaserwavelengthis930nm,correspondingto1.33eVor2:11019J,thusthephotonnumbersineachlaserpulseare1:81010,andthephotondensityis3:11011photons/(pulsecm2).Assuming30%reectanceand20%absorption,andif1/3oftheenergywaseventuallyusedtogeneratetheelectron-holepairs,thedensityofcreatedcarriersare8:61014/(pulsecm3).ThisestimateisingoodagreementwiththeresultsfromtheDrudet. 158

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5.4.2.1Experimentalresults Figure 5-20 showsthefrequency-resolvedphotoinducedtransmissionchangeinthemid-IRandnear-IRregionattemperaturesbelowandabovetheCurietemperature.Theyaxisisdenedsimilartoequation 5{33 as: T=TonToff Figure 5-20 showsseveralinterestingfeatures.Atfrequenciesfromabout500cm1to2113cm1(pointAinFigure 5-20 ),itshowsthattherearenophotoinducedeectsonthetransmissionaboveTcat42Kand60K,butstrongeectsattemperaturesbelowTcat5Kand20Kwiththephotoinducedtransmissionincreasingincurve.From2113cm1to9500cm1,thebasicfeatureisthatthephotoinducedtransmissionissmallerthanthecasewhenthereisnolaserpumping.At2113cm1allfourcurvesmeeteachother.From2113cm1toabout4000cm1,thephotoinducedtransmissiondecreaseslinearlywithfrequencies.From6495cm1to7945cm1,astrongoscillationswereobserved 159

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Thephotoinducedtransmissionchangeinthemid-IRandnear-IRregionforaInGaMnAs/InGaAs/InPsamplewithbothsidespolished. withthecentralextremeat6881cm1(pointC).Fromabout5970cm1(pointD)to9326cm1(pointB),theslopesofthetemperaturesbelowTcarenegative,andaboveTcarepositive,whichmeansthatthephotoinducedtransmissionincreasesbelowTcanddecreasesaboveTc.StartingfromaboutthepointB,hightemperaturecurves(42Kand60K)changetoanegativeslopeandthelowtemperaturecurveschangetoalargernegativeslope,whichmeansthatthephotoinducedtransmissionstartstoincreasewithfrequenciesforallthetemperatures. 5-20 correspondtotheenergystructuresoftheDMSsystem.Figure 5-21 showssomebandparametersofthesampleat20K.ThebandgapsofInGaMnAsandInGaAslayersarecalculatedwiththemethodintroducedinSection 5.1.2 .AndthebandosetvaluebetweentheInGaAsandInPheterojunctionarefrom[ 136 ].It 160

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EnergystructuresoftheDMSsampleat20K. showthatconductionbandoset(CBO)oftheheterojunctionbetweenInGaAsandInPis2095cm1,whichagreeswithpointAwiththeexperimentalerrors.Atfrequencieshighthan2095cm1,theelectronsfromtheconductionbandstarttotransittotheconductionbandofInP.ThustheCBOexplainsthefactthatthephotoinducedtransmissionstartstochangeforallthetemperaturesatpointA.Similarly,electronsstarttotransitfromtheInPvalencebandtotheInGaAsconductionbandatfrequencyofabout9347cm1,whichisthereasonthatthecurveschangesslopesforallthetemperaturesinFigure 5-20 TheoscillationfeaturearoundpointCisveryinteresting.ItrepresentstheFranz-Keldysheect[ 138 { 140 ],whichisduetotheinternalelectriceldattheheterojunctionbetweentheInGaMnAsandInGaAslayers.TheFranz-Keldysheectisinfactaphoton-assistedtunnelingphenomenon.Thebasiceectsare: 161

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TheFranz-Keldyshoscillationextremaenergieswiththeoscillationnumbers. nWavenumber(cm1)En(eV) 165110.808266490.825367570.839468960.856570500.875671430.886772660.902874210.921 TheinternalelectriceldEisinverseproportionaltotheoscillationfrequency[ 141 { 143 ].Therelationsare: 3EnEg whereEistheelectriceld,~istheelectro-opticenergy,Egistheenergybandgap,nistheindexofthenthextremum,Enisphotonenergyattheextremum,andisthereducedelectron-holemass: 1 wheremh=mhhormlhfortheheavyorlightholetransition,respectively. At20K,theenergygapfortheInGaMnAslayeris0.69eV;It's0.815eVfortheInGaAslayer,soweestimatethebandgapattheheterojunctiontobeatthemiddleabout0.75eV.ThiscrudeestimationisduetolackofdetailedknowledgeoftheheterojunctionintroducedbytheMnion.Table 5-7 andFigure 5-22 thusshowtheexperimentaldatawithalineart.Theslopeis(~)3=2=0:00335eV3=2fromEquation 5{40 AssumingthetransitionismainlyheavyholetypeduetothereasonsinSection 5.3.2 ,thereducedmassis=0.0393m0.ThustheinternalelectriceldFis32.76kV/cm. 162

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TheFranz-Keldyshoscillationextremaenergieswiththeoscillationnumbers.Thetislinear. Theeight-bandkptheorywasintroducedincalculatingthebandstructure,whichisbasedonKanemodelandLowdin'smethod.TheenergybandsfortheMn-dopedlayerandundopedlayerwerecalculatedattemperaturesbelowTc,andtheresultsshowboththeconductionandvalencebandsplitduetotheinternalmagnization. Time-resolvedphotoinducedexperimentswereperformedinthefar-IRregion,withdierentprobingsynchrotronbeams.Weobservedtwocomponentdecayswiththeone-bunchprobesynchrotron,andonecomponentdecaywith7-bunchbeamwhichisexplainedbytheelectronstackeect.Itistherstreportonthetwo-componentdecayforaDMSsysteminthenstimescale.Weproposedamodeltoexplainthisphenomenon. 163

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WealsoobservedtherecombinationtimeisshorteroncethetemperatureisincreasedbeyondTc.Thisisexplainedmainlybythedecreaseofthedensityofstates.TheDrudetgivesthecarrierdensitywhichisingoodagreementwiththevalueestimatedfromthelaseruence. Inmid-IRandnear-IRregions,weperformedphotoinducedtransmissionchangewithlaseron/oexperiments.TheFranz-Keldysheectwasobserved.ThisistherstobservationandreportoftheFranz-KeldysheectinaDMSsystemduetotheinternaleldintroducedbyMndopinginsteadofanexternalelectriceld.TheinternaleldisthuscalculatedwithttingtheoscillationdataanditisintheorderoftensofkV/cm.Wealsoobservedthecurveslopechangesatabout2113cm1and9326cm1whichareexplainedwiththebandosetsofInGaAs/InPhetertostucture.CombinedwiththeFranz-Keldysheectandthebandosetconrmation,ourexperimentssupportthemodel 5-17 andbandstructure 5-21 164

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Thisdissertationhaspresentedasystemicopticalstudyofthenonlineardynamicsofcertaincondensedmattersystemsusingthetime-resolvedtechniqueatNSLS,BNL.Thelaser-synchrotronpump-probetechniquehasbeenappliedandprovedtobepowerfulinexploringquasiparticlerelaxationprocessesinaBCSsuperconductor,andelectron-holerecombinationprocessesinaDMSsemiconductor. Adetaileddescriptionoftheexperimentapparatuswaspresented,includingthesynchrotronradiation,thebeamlineU12IRatNSLS,thespectrometer,thedetectors,thecryostatandthelasersystem.Thepump-probetechniqueandexperimentalmethodsweredescribed. ThelinearopticalpropertiesoftheNb0:5Ti0:5NsuperconductingthinlmwereextractedfromthetemperaturedependentFar-IRtransmissionmeasurementswhicharewellttedwiththeTinkhamthinlmtransmissionequationandtheBCSMattis-Bardeentheorywitharstorderstrongcouplingcorrection.Aseriesofbroadbandtime-resolvedexperimentswereperformed:temperaturedependence,laserwavelengthdependence,uencedependenceandmagneticelddependence.Thebasicresultsexhibitonesimpleexponentialshapedecay,andagreewiththepredictionfromRothwarf-TaylortheoryandGray'smodel.ThetemperaturedependencedatawerettedaccordingtoKaplan'smodel,andthepairbreakingtimeandQPrecombinationtimewereextracted.Nolaserwavelengthdependencewasobserved.Thetemperaturedependenteectivelifetimeinhighuenceregimeshowsdierentbehaviorthaninlowuenceregime,whichcanbeexplainedbythetotalQPdensitychangeincludingthephotoexcitedandthermallycreatedQPs.Themagneticelddependenceshowsthattheeectivelifetimedoesnotdecreasewhentheeldisincreased.ThisisbecausethenormalcoresofthevorticeshavenoenergygapthustheQPstherecannotrelaxtothegroundstateCooperpairs,andeventuallythoseQPsrelaxaftertheydiuseoutofthevortices.Through 165

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Theinvestigationoftheelectron-holerecombinationtimeintheDMSsemiconductor(In0:53Ga0:47)0:925Mn0:075As/In0:53Ga0:47As/InPshowsdecayoftwoexponentialcomponents.AmodelwasproposedthattheIn0:53Ga0:47AsbuerlayerenergygapbendingtotthefermienergywhichresultsinaninternalelectriceldbetweentheMndopedlayerandtheundopedlayer.Thefastdecayisthusexplainedwiththeelectron-hole'slocalrecombination,andtheslowdecayisfromtherecombinationprocesswiththespatiallyseparatedelectronsandholesindierentlayerswheretheelectronshavetoghtwiththebackwardinternalelectriceld.ThismodelissupportedbythephotoinducedspectroscopymeasurementsthattheFranz-KeldysheectwasobservedintheNear-IRregion.Thevalueofinternalelectriceldwasestimatedtobeabout33kV/cm.Anotherimportanteectobservedfromthetime-resolvedexperimentswasthatthefastprocesslifetimesharplyincreasesbelowTc.ThisisduetothedecreaseofthedensityofstatesinthesplittedtopvalencebandsbelowTc.TheDrudettotheFar-IRtime-resolvedspectroscopygivesthecarrierdensity. Thelaser-synchrotronpump-probeisapowerfulnewtechniquedevelopedforabout10years.Thetime-resolvedspectroscopyisveryuniquethatthefrequencyresolvedspectrumcanbeinvestigatedatanydelaytimeduringthesystem'srelaxationhistory.Therearemanyphenomenathatneedtobeinvestigatedwithtime-resolvedinfraredspectroscopyinthenanosecondrange.Thisdissertationhaveshownthisnewlydevelopedtechniquehelpustounderstandtwocondensedmattersystems:BCSsuperconductorsandDMSsemiconductors.Someexperimentsandobservedeectsinthisdissertationarereportedforthersttime,forexample,theuencedependenceoftheeectivelifetimeinthesuperconductor,thetwocomponentdecayprocessesandtheFranz-Keldysheect 166

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167

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FromGlover-Tinkhamequation: n+1(A{1) wheredisthelmthickness,nistherefractiveindexofthesubstrate,andz0=4 cincgs;377inmks. Forourthinlmsample,d107m1,thus (3772d)2(3771d+n+1)2(A{4) so n+12(A{5) also so n+1(A{7) T=TT0 T0(A{8) T'23771d n+1(A{9) ForInPsubstrate,n=3:53forthefar-IRfrom10to100cm1,so 168

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T'1661d(A{10) 169

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FigureB-1. Emissionspectrafornormalinternalsources. 170

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Frequencyrangesofbeam-splitters. 171

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Frequencyrangesofdetectors. 172

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HaidongZhangwasborninShandongProvinceofP.R.China.HeenteredtheBeijingInstituteofTechnologyin1992andreceivedtheBachelorofSciencedegreein1996,thenenteredtheInstituteofHighEnergyPhysics,ChineseAcademyofSciences,andstudiedtheoreticalparticlephysicswithProfessorTaoHuangandreceivedaMasterofSciencedegreein1999.HeattendedtheUniversityofMiami(FL)asagraduatestudentforoneyearandenteredtheUniversityofFloridainAugustof2001.Later,hejoinedProfessorDavidB.Tanner'sgroupandstudiedthecondensedmatterphysicsinGainesville,FL.HereceivedthePh.D.in2007. 180